For the set of probability measures ${\sf I}(X)$, where $X$ is a compact Hausdorff space, we propose a new way to introduce the topology by using open subsets of the space $X$. Then, among other things, we give a new proof that for a compact Hausdorff space $X$ the space ${\sf I}(X)$ is also a compact Hausdorff space. For a Tychonoff space $X$, we consider the topological space ${\sf I_{\tau}}(X)$ of $\tau$-smooth idempotent probability measures on $X$,and show that the space ${\sf I_{\tau}}(X)$ is \v{C}ech-complete if and only if the given space $X$ is \v{C}ech-complete.

This article presents the results of the consideration of the Bertrand paradox in terms of geometric probability theory. Although the method and conclusions of this article are straightforward, no equivalent studies were found when reviewing the relevant literature. This could be conditioned by the fact that the hypotheses presented in this research have low intuitive obviousness and, in contrast, could be due to the historically established agreement regarding the issue. This article shows that out of three classical solutions to the problem described by Bertrand, two methods are inconsistent with the claimed relative objectivity. Although the remaining solution (1/4) seems to be the most correct, we cannot claim that we have exhaustively ruled out all aspects that could reduce its adequacy to solve the problem.

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails less than 50%. Theoretical models for a static case and for five dynamic cases, without and with rebounds, show that there is a small probability that the coin does not fall on its head or tail, depending on initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. For the dynamic model with rebounds, it is found that the probability that a 50 Eurocent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand.

The question does P = NP has confounded mathematicians and computer scientists alike for over 50 years and although there is an almost unanimous agreement that it in fact does not, there still is no absolute proof. In this paper, I attempt to prove to that P does not equal NP.

In this study, we investigate the performance of the saddlepoint approximation of the probability mass function and the cumulative distribution function for the weighted sum of independent Poisson random variables. The goal is to approximate the hazard rate function for this complicated model. The better performance of this method is shown by numerical simulations and comparison with a performance of other approximation methods.

We show the tensor properties of joint probabilities on a Riemannian parametric manifold. Initially we develop a binary data matrix for parameter measurements of a large number of particles confining in a closed system in order to retrieve the joint probability densities of related parameters. By introducing a new generalized inner product as a multilinear operation on dual basis of parametric space, we extract the set of joint probabilities and prove them to meet contravariant tensor properties in a general Riemannian parametric space. We show these contravariant tensors reduce to classical ordinary partial derivatives definition in ordinary Euclidean parametric space. Finally we prove by a theorem that symmetrized iterative contravariant derivative of cumulative probability function on Riemannian manifold gives the set of joint probabilities in those manifold. We bring some examples for compatibility with physical tensors.

Monitoring is an essential component in ecosystem management and leveraging existing data sources for multiple species of interest can be one effective way to enhance information when making management decisions. Here we analyzed juvenile Chinook Salmon (Oncorhynchus tshawytscha) bycatch data that has been collected by the recently established Enhanced Delta Smelt Monitoring program (EDSM), a survey designed to estimate the abundance and distribution of the San Francisco Estuary’s (estuary) endangered Delta Smelt (Hypomesus transpacificus). Two key aspects of the EDSM program distinguish it from other fish surveys in the estuary: a stratified random sampling design and the spatial scale of its sampling effort. We integrated the EDSM dataset with other existing surveys in the estuary and used an occupancy model to assess detection probability differences across gear types. We saw no large-scale differences in size selectivity, and while detection probability varied among gear types, cumulative detection probability for EDSM was comparable to other surveys due to the program’s use of replicate tows. Based on our occupancy model and sampling effort in the estuary during spring of 2017 and 2018, we highlighted under-sampled regions that saw improvements in monitoring coverage due to EDSM. Our analysis also revealed that each sampling method has its own benefits and constraints. Although the use of random sites with replicates as conducted by EDSM can provide more statistically robust abundance estimates relative to traditional methods, the use of fixed stations and simple methods such as beach seine may provide a more cost-effective way of monitoring salmon occurrence in certain regions of the estuary. Stronger inference on salmon abundance and distribution can be made by leveraging the strengths of each survey’s method. Careful consideration of these trade-offs is crucial as the management agencies of the estuary continue to adapt and improve their monitoring programs.

The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory, in terms of states as linear functional defined on category algebras. We clarify that category algebras can be considered as generalized matrix algebras and that the notions of state on category as linear functional defined on category algebra turns out to be a conceptual generalization of probability measures on sets as discrete categories. Moreover, by establishing a generalization of famous GNS (Gelfand-Naimark-Segal) construction, we obtain a representation of category algebras of †-categories on certain generalized Hilbert spaces which we call semi-Hilbert modules over rigs.

In this paper we establish some weighted integral inequalities of Ostrowski, Čebyšev and Lupaş type. Applications for continuous probability density functions supported on infinite intervals with two examples are also given.

Probability is initially defined on a Boolean algebra or a lattice of projectors. We propose here to start from a Heyting algebra.

In recent years, with the rapid development of technology, artificial intelligence(AI) security issues represented by adversarial sample attack have aroused widespread concern in society. Adversarial samples are often generated by surrogate models and then transfer to attack the target model, and most AI models in real-world scenarios belong to black boxes, thus transferability becomes a key factor to measure the quality of adversarial samples. The traditional method relies on the decision boundary of the classifier and takes the boundary crossing as the only judgment metric without considering the probability distribution of the sample itself, which results in an irregular way of adding perturbations to the adversarial sample, an unclear path of generation, and a lack of transferability and interpretability. In the probabilistic generative model, after learning the probability distribution of the samples, a random term can be added to the sampling to gradually transform the noise into a new independent and identically distributed sample. Inspired by this idea, we believe that by removing the random term, the adversarial sample generation process can be regarded as static sampling of the probabilistic generative model, which guides the adversarial samples out of the original probability distribution and into the target probability distribution, and helps to improve transferability and interpretability. Therefore, we propose a Score Matching-Based Attack(SMBA) method to perform the adversarial sample attacks by manipulating the probability distribution of the samples, which can show good transferability in the face of different datasets and models, and give reasonable explanations from the perspective of mathematical theory and feature space. In conclusion, our research establishes a bridge between probabilistic generative models and adversarial samples, provides a new entry angle for the study of adversarial samples, and brings new thinking to AI security.

Developing new ways to estimate probabilities can be valuable for science, statistics, and engineering. By considering the information content of different output patterns, recent work invoking algorithmic information theory has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam's razor, machine learning, and password guessing.

This paper provides a framework for the assessment of household-level risk, incorporating both a individual social risk perspective and a location-based perspective. We use this framework as a heuristic to explore the effect of social reintegration choices individuals face, which are not be addressed by current policies. For example, we explore how integrating extended family households during COVID-19 without social distancing may affect household and community risk. The goal is to aid individual decision makers, who are seeking to maintain quality-of-life while navigating local policy, with nuance relating to location-specific behavior and disease prevalence.

This paper proposes a solution for the problem of mobile robot navigation and trajectory interpolation in dynamic environments with large scenes. The solution combines a semantic laser SLAM system that utilizes deep learning and a trajectory interpolation algorithm. The paper first introduces some open-source laser SLAM algorithms and then elaborates in detail on the general framework of the SLAM system used in this paper. Secondly, the concept of voxel is introduced into the occupation probability map to enhance the ability of local voxel maps to represent dynamic objects. Then, in this paper, we propose a PointNet++ point cloud semantic segmentation network combined with deep learning algorithms to extract deep features of dynamic point clouds in large scenes and output semantic information of points on static objects. A descriptor of the global environment is generated based on its semantic information. Closed-loop completion of global map optimization is performed to reduce cumulative error. Finally, T-trajectory interpolation is utilized to ensure the motion performance of the robot and improve the smooth stability of the robot trajectory. The experimental results indicate that the combination of the semantic laser SLAM system with deep learning and the trajectory interpolation algorithm proposed in this paper yields better graph building and loop closure effects in large scenes at SIASUN large scene campus. The use of T-trajectory interpolation ensures vibration-free and stable transitions between target points.

For the parentage testing in canine microsatellite length polymorphism markers were used to check the efficacy of the markers. In the current study 5’ fluorescently labeled 12 SSR markers were used to check the use of the markers in popular owned-dog breeds (Labrador, German Shepherd, Pug, Mudhol Hound, Tibetan Mastiff, Gaddi dog, Beagle, Belgian Malinois, Pointer, and Cane Corso) maintained of India (not necessarily indigenous breeds). The number of alleles, heterozygosity, polymorphism information content, and probability of exclusion were determined for all the markers to check the effectiveness of the markers. The mean number of alleles per locus ranged from 5 to 29 and the effective number of alleles ranged from 3.6 to 15.2. The expected heterozygosity was greater than 0.73. The population inbreeding coefficient (FIS) demonstrated that there was no inbreeding in the breeds studied, as the samples were collected from owners and dog breeders belonging to various states, including Punjab, Haryana, Himachal Pradesh, and Karnataka. The polymorphism information content and the probability of the exclusion values were greater than 0.65. the combined probability of exclusion for all the breeds was (2.82E-12) 0.99999995. The results indicated that the selected 12 markers are effective enough to determine the parentage of the dogs.

This paper considers the theoretical framework of the consumption-based asset-pricing model and derives successive approximations of the modified basic pricing equation using Taylor series expansions of the investor’s utility function during the averaging time interval Δ. For linear and quadratic Taylor approximations we derive new expressions for the mean asset price, mean payoff, their volatilities, skewness and amount of asset that delivers max to investor’s utility. We introduce new market-based price probability determined by statistical moments of the market trade values and volumes. We show that the market-based price probability results zero correla-tions between time-series of n-th power of price pn and trade volume Un, but doesn’t cause statis-tical independence and we derive correlation between time-series of price p and squares of trade volume U2. The market-based treatment of the random trade price describes impact of the size of market trade values and volumes on price probability. Predictions of the market-based price probability at horizon T should match forecasts of statistical moments of the trade values and volumes at the same horizon T. The market-based price probability emphasizes direct dependence on random properties of market trades.

The VUCA world is the epitome of the challenges linked with some of the undercurrents currently shaping businesses in the projectified society. The terms volatility, uncertainty, complexity and ambiguity (VUCA) are used as descriptive for the continuous flux project managers and project planners are forced to keep at bay. In this article, the authors present an idea to connect the VUCA concept as a risk identification platform to access, identify and isolate low-probability but high-impact events often called black swans or fat tail events. It is argued that the assumptions of conventional risk assessment in the domain of project management can lead to skewed general outcomes due to limitations of the intellect to assess probability. The outline of the VUCA meter is drafted and argued that the meter can augment the conventional risk assessment

Sword-duels are interesting, from a game-theoretical perspective, as they correspond to sudden-death interactions between players (i.e., defeat means removal from the game), and where victory/defeat depend on not just skill, but also luck. Analyzing probabilities of victory streaks, given a certain level of self and others' skill, is thus relevant for any application domain that can be modeled in the same way. This paper takes inspiration from Miyamoto Musashi, famously undefeated for 61 duels, and implements a Markov-chain Monte-Carlo simulation approach to evaluate this scenario. Results suggest that a 61 victory streak can be probabilistically observed when skill level is roughly 6.5 times that of the average duelist, and with 95\% confidence when skill level is roughly 1000 times that of the average duelist. More generally, this paper provides a method for determining chances of victory streaks in game-theoretical sudden-death encounters, when both "skill" and "luck" contribute to the outcome of the encounter. Specific scenarios can be modeled by modifying the utilized Markov chain and adjusting sampled distributions as required.

There is an increasing need for quantitative rockfall hazard and risk assessment that requires a precise definition of the terms and concepts used for this particular type of landslide. This paper suggests to use terms that appear to be the more logic and explicit as possible, and describes methods to derive some of the main hazard and risk descriptors. The terms and concepts presented concern the rockfall process (failure, propagation, fragmentation, modelling) and the hazard and risk descriptors, distinguishing the cases of localized hazards and diffused hazards. For a localized hazard, the failure probability of the considered rock compartment in a given period of time has to be assessed and the probability for a given element at risk to be impacted with a given energy must be derived combining the failure probability, the propagation probability and the exposure of the element. For a diffuse hazard that is characterized by a failure frequency, the number of rockfalls reaching the element at risk per unit of time and with a given energy (reach frequency) can be derived. However, when the element at risk is not replaced or repaired, the probability that it is impacted by at least one rockfall must be considered.

The use of large-scale antenna arrays grants considerable benefits in energy and spectral efficiency to wireless systems due to spatial resolution and array gain techniques. By assuming a dominant line-of-sight environment in a massive MIMO scenario with favorable propagation, we derive analytical expressions for the sum-capacity. % Then, we show that convenient simplifications on the sum-capacity expressions are possible when working at low and high SNR regimes. % Furthermore, in the case of a high SNR regime, it is demonstrated that the Gamma PDF can approximate the PDF of the instantaneous channel sum-capacity as the number of BS antennas grows. A second important demonstration presented in this work is that a Gamma PDF can also be used to approximate the PDF of the summation of the channel's singular values as the number of devices increases. Finally, it is important to highlight that the presented framework is useful for LPWAN's as we show that the transmit power of each device can be made inversely proportional to the number of BS antennas.

Steganography is the branch of cryptology that deals with concealing information inside another information. it’s prefer over cryptography as it hides a message inside another innocent looking message, while cryptography shows scrambled message that might arouse attention of an attacker, however the challenges in steganography is the modification of carrier that causes some abnormalities which is detectable and often the methods are not optimize. This paper presents a novel approach in cryptography and steganography, which utilizes mathematical concept of bits combination to optimize time of transmission using sets of multiple transmitter, and receiver’s addresses where each abstractly represents a bits combination without itself modified. In addition, the paper introduces a concept of dynamical clockwise and anti-clockwise rotation of bits combination over addresses after every transmission to reinforce resistivity against steganalysis.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy.” Upper and lower error bars on the accuracy are provided by the arithmetic mean and the -2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the -2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and -2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the -2/3 mean decreases/increases, respectively.

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit experiment is treatment of conditional probabilities corresponding to different experimental contexts as unconditional ones. Then we move to the Bell type inequalities. Bell applied classical probability theory in the same manner as Feynman and, as can be expected, he also obtained the impossibility statement. In contrast to Feynman, he formulated his no-go statement not in the probabilistic terms, but by appealing to nonlocality. This note can be considered as a part of the author's attempts for getting rid off nonlocality from quantum physics.

This paper introduces an approach that chooses the fault detection by calculating probabilities using probability mass function (pmf) and cumulative distribution function (CDF). This work used a method for multiple stuck-at faults by producing a new test pattern in combinational circuits. We assumed that existence of all multiple faults is only because of one single component that is faulty. A complete test set can be created by all possible single stuck-at faults in a combinational circuit using some combination of gates. The test set generation fault detection method is applied on two different 3-bit input variable and 4-bit input variable circuits. The probability of error occurrence is calculated at both 3-bit and 4-bit input variable circuits. The resulting feature is used to obtain maximum error occurrence probability to detect faults by the logic used that the complexity of the circuit is inversely proportional to the fault occurrence probability. Then again, undetectability is directly proportional to the complexity of the circuit. Therefore, finest feasible circuit should have large input variable components with less complexity to reduce the fault occurrence probability.

Critical thinking skills are important assets for scientific development. Therefore, there are many ways to enhance the critical thinking skills of students, researchers, etc., both in the field of education and scientific enterprise. In this article, we propose the practice of solving probability paradoxes and puzzles for the purpose since these problems are often complex, subtle and tricky; therefore, their solutions require many aspects of critical thinking. In the following, the Introduction outlines some of the current research on the topic without going into more details. We provide background descriptions of the paradoxes and probability paradoxes in Section 2. Section 3 provides a short description of critical thinking. We present several definitions since there is no clear consensus on one single definition, both in the literature and in the general literature. And in Section 4 current research on using puzzles for enhancing critical thinking is given. We then discuss several probability paradoxes, namely, the Monte Hall paradox, the two-envelope (exchange) paradox and the St. Petersberg paradox, in Sections 5, 6 and 7, respectively. In Section 8, a brief discussion of the statistical hypothesis testing is given emphasizing its controversial nature. We analyse these problems and concepts in such a way that critical thinking is evoked while keeping the technical details to a minimum.

The Covid19 pandemic and the current wars in some countries have put incredible pressures on the global economy. Challenges for the U.S. include not only economic factors, major disruptions and reorganizations of the supply chains, but also those of national security and global geopolitics. This unprecedented situation makes predicting economic crisis for the coming years crucial yet challenging. In this paper, we propose a method based on various machine-learning models to predict the probability of a recession for the US economy in the next year. We collect the U.S’ monthly macroeconomics indicators and recession data from January of 1983 to December of 2023 to predict the probability of an economic recession in 2024. The performance of the individual economics indicator for the coming year was predicted separately, and then all of the the predicted indicators were used to forecast a possible economic recession. Our results showed that the U.S. will face a high probability of being in a recession period in the last quarter of 2024.

This paper investigates the performance of dual hop UAV-assisted communication channels, employing a decode and forward relay architecture. The system utilizes Terahertz (THz) communication in the primary hop and Visible Light Communication (VLC) in the secondary hop. We conduct a thorough analysis by deriving closed-form expressions for end to end bit error rate (BER). Furthermore, we employ a Monte Carlo approach to generate best fitting curves and validate our numerical expressions with simulation results. Evaluation via BER and outage probability demonstrates the proposed system’s effectiveness. The outcomes of this research offer valuable insights into the feasibility and limitations of UAV-assisted THz- VLC systems.

This article presents multiple novel and compelling arguments to systematically disprove two widely accepted notions: one is that entropy is a measure of disorder, and the other is Schrödinger's notion of negative entropy (negentropy). These two notions have been cited hundreds of times annually in scientific literature for decades. To mathematically describe the second law of thermodynamics, the concept of entropy was created and defined in the 1860s as heat energy divided by thermodynamic temperature, and the entropy of an object increases when it absorbs heat. This is the uncontroversial and fundamental nature of entropy, which is pivotal to current thermodynamics and from which multiple facts are deduced. These facts consistently disprove the above two notions. Some biological facts, such as the one that life orderliness is encoded and provided by inherited genes rather than entropy decline, can also disprove Schrödinger's negentropy notion. Moreover, this article further clarifies the reasoning errors of the two notions. It also shows that the tendency of many natural or social systems to become more disordered over time does not result from the second law of thermodynamics.

Lightning is responsible for most annually burned area by wildfires in the extratropical region of the Northern Hemisphere. Hence, predicting the occurrence of wildfires requires reliable forecasting of the chance of cloud-to-ground lightning strikes during storms. Here, we describe the development and verification of a probabilistic lightning-strike algorithm designed to run on a uniform 20-km grid over the Continental USA and Alaska. The algorithm consists of a large set of logistic equations parameterized via logistic regression using long-term data records of observed lightning strikes and meteorological reanalysis fields from NOAA. Principal Component Analysis was employed to extract 13 Principal Components (strong predictors) from a list of 611 potential predictors. Our statistical analysis revealed that the occurrence of cloud-to-ground lightning strikes primarily depends on three factors: horizontal temperature distribution by pressure levels, amount of low-level atmospheric moisture, and wind vectors. These physical variables impact the vertical separation of electric charges in the lower troposphere during storms causing the voltage potential between ground and the cloud deck to increase to a level that triggers electrical discharges. Results from a forecast verification using independent data showed excellent model skill, thus making this algorithm suitable for inclusion into software systems forecasting the chance of wildfire ignitions.

Bell’s correlation formula is based on a classical Kolmogorov probability theory. It is tested in experiment with an estimate correlation. The latter is the raw product moment (rpm) correlation that is classical Kolmogorov based as well. We note that the famous Bell inequalities are derived from Bell’s correlation formula. The problem is that the hypothesis: “is it possible that in experiment Bell’s correlation is equal to quantum”, can only found to be false. This is not because the data generating process does not produce the required data. Or that the inequalities sufficiently show that the data cannot violate the inequalities. It is because the statistics of the Bell experiment is flawed. The rpm correlation in experiment cannot be equal to the quantum value in principle. This is because it requires the classical Kolmogorov rpm correlation to be not Kolmogorov.

Cooperative non-orthogonal multiple access (CNOMA) has been recently adapted with energy harvesting (EH) to increase energy efficiency and extend the lifetime of energy-constrained wireless networks. In EH, two protocols are usually used for CNOMA, namely, power splitting (PS) and time switching (TS). In order to improve the existing EH protocols, this paper investigates a hybrid EH protocol-assisted CNOMA, which is a combination of the two aforementioned main existing EH protocols. The end-to-end bit error rate (BER) and outage probability (OP) expressions of users in our scheme are derived over Nakagami-m fading channels. For the sake of comparison and to highlight the achievable gains, the performance of the hybrid EH (HEH) protocol is compared with the benchmark schemes (i.e., existing EH protocols and no-EH). Based on extensive simulations, it is shown that the analytical results match perfectly with simulations which demonstrates the correctness of the derivations. Numerical results clearly indicate the superiority of the proposed scheme over all the considered benchmarks. In addition, we discuss the optimum value of EH factors to minimize the error and outage in the proposed scheme and show that an optimum value can be obtained according to channel parameters.

Congestion pricing has received lots of attention in the scientific discussion. Congestion pricing means that the operator increases prices at the time of congestion and the traffic demand is expected to decrease. In a certain sense, shadow prices are an optimal way of congestion pricing: users are charged shadow prices, i.e., the expectations of future losses because of blocked connections. The shadow prices can be calculated exactly from Howard’s equation, but this method is difficult. The paper presents simple approximations to the solution of Howard’s equation and a way to derive more exact approximations. If users do not react by lowering their demand, they will receive higher bills to pay. Many users do not react to increased prices but would want to know how the congestion pricing mechanism affects the bills. The distribution of the price of a connection follows from knowing the shadow prices and the probability of a congestion state. There is another interesting distribution. The network produces profit to the operator, or equivalently, blocked connections produce a cost to the operator. The average cost rate can be calculated from Howard’s equation, but the costs have some distribution. The distribution gives the risk that the actual costs exceed the average costs, and the operator should include this risk to the prices. The main result of this paper shows how to calculate the distribution of the costs in the future for congestion pricing by shadow prices and for congestion pricing with a more simple pricing scheme that produces the same average costs.

In public health literature the risk of death or disease associated with a dietary, environmental of behavioral factor is most commonly denoted by odds ratio (OR), hazard ratio (HR) or risk ratio (RR). The ratio indices have several desirable statistical properties. However, the most important question is whether there are some evolved innate norms of perception of risk that people use and what they are. We conducted a simple one question survey of 98 individuals with different age, sex, educational and professional backgrounds. The respondents were asked to judge the relative perceived risk of four different hypothetical habits for which data on the percentage of people affected by the disease with and without the habit was given. They were asked to rank the risks for the four habits. Results showed that the habits that had the highest difference between probability of acquiring the disease were ranked high on risk perception. The probability ratios did not affect risk perception significantly. Further age, sex, profession or formal training in statistics did not affect the response significantly. Even individuals that were formally trained to use OR and HR as risk indicators, preferred using probability differences over ratios for judging their own risk in the perceived context. This preliminary inquiry into intuitive statistical perception suggests that designing statistical indices based on people’s innate perception may be a better strategy than trying to train people to understand the indices designed by expert statisticians.

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

A method for measuring the real part of the weak value of spin for non-zero rest mass atoms is presented using a variant on the original Stern-Gerlach apparatus. The experiment utilises helium in the metastable 2³S₁ state. A full simulation for observing the real part of the weak value using the impulsive approximation has been carried out and it predicts a displacement of the beam, Δ_w, that is within the resolution of our detector. It also indicates how this shift might be increased. The full analysis also indicated that there is a limit, L, to the applicability of the weak value approximation and has been evaluated for our apparatus. This experiment has the possibility to be expanded to utilise other nobal gas species such as neon and argon in the ³P₂ metastable state, but we shall restrict this paper to metastable helium only.

This paper aims to describe the geometrical structure and explicit expressions of family of finitely parametrized probability densities over smooth manifold $M$. The geometry of family of probability densities on $M$ are inherited from probability densities on Euclidean spaces $\left\{U_\alpha \right\}$ via bundle morphisms, induced by an orientation-preserving diffeomorphisms $\rho_\alpha:U_\alpha \rightarrow M$. Current literature inherits densities on $M$ from tangent spaces via Riemannian exponential map $\exp: T_x M \rightarrow M$; densities on $M$ are defined locally on region where the exponential map is a diffeomorphism. We generalize this approach with an arbitrary orientation-preserving bundle morphism; we show that the dualistic geometry of family of densities on $U_\alpha$ can be inherited to family of densities on $M$. Furthermore, we provide explicit expressions for parametrized probability densities on $\rho_\alpha(U_\alpha) \subset M$. Finally, using the component densities on $\rho_\alpha(U_\alpha)$, we construct parametrized mixture densities on totally bounded subsets of $M$. We provide a description of inherited mixture product dualistic geometry of the family of mixture densities.

Philippines as an archipelago and tropical country, which is situated near the Pacific ocean, faces uncertain rainfall intensities. This makes environmental, agricultural and economic systems affected by precipitation difficult to manage. Time series analysis of Philippine rainfall pattern has been previously done, but there is no study investigating its probability distribution. Modeling the Philippine rainfall using probability distributions is essential, especially in managing risks and designing insurance products. Here, daily and cumulative rainfall data (January 1961 - August 2016) from 28 PAGASA weather stations are fitted to probability distributions. Moreover, the fitted distributions are examined for invariance under subsets of the rainfall data set. We observe that the Gamma distribution is a suitable fit for the daily up to the ten-day cumulative rainfall data. Our results can be used in agriculture, especially in forecasting claims in weather index-based insurance.

Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp C., 2003). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).

Categorical variables are common in spatial data analysis. Traditional analytical methods for deriving probabilities of class occurrence, such as kriging-family algorithms, have been hindered by the discrete characteristics of categorical fields. This study introduces the theoretical backgrounds of linear Bayesian updating (LBU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to present the solid theoretical foundations of LBU and provide a categorical random field prediction method which yields relatively higher classification accuracy compared with conventional Markov chain random field (MCRF) approach. A real-world case study has also been carried out to demonstrate the superiority of our method. Since the LBU idea is originated from aggregating expert opinions and not restricted to conditional independent assumption (CIA), it may prove to be reasonably adequate for analyzing complex geospatial data sets, like remote sensing images or area-class maps.

When separation to the parameters of interest appears below resolution limit of the estimator, the ambiguity arises whether two parameter estimates relate to one source emitted twice or two close sources emitted once. In the paper, novel Bayes technique aimed to identify one/two sources below resolution limit by the pair of Gaussian estimates of a source(s) planar location as parameter is developed. Prior probabilities of the hypotheses on one/two sources are available from the analysis of physical characteristics of the emissions, assuming that they can be equally probable. The identifier recalculates a posteriori these probabilities subject to a distance between sources. It is applied to distinguish two location estimates obtained in the planar time difference of arrival mobile communication network. The work of the identifier is studied in the domain of closely spaced network users where covariance matrices of estimates are sufficiently approximated by the constant. The application gives an example of how the identifier revises the prior probabilities and can change thereby the initial preference of a hypothesis with a distance between users in some cases.

Probabilistic inference problems have very broad practical applications. To solve this kind of problems under conditions of certainty, an effective mathematical apparatus has been developed. In real situations, obtaining deterministic estimates of relevant probabilities is often difficult; therefore, problems with handling uncertain estimates of probabilities appear. This paper examines the problem of probabilistic inference with probability trees provided that the initial probabilities are given in the form of intervals of their possible values.

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc. A link is available for downloading an Excel program which calculates the degree of dependence of two events in a sample space with equally likely outcomes.

In this paper, we derive the distribution of eigenvalues for a 2×2 random confusion matrix stemming from a machine learning (ML) evaluation problem. Additionally, we present the distributions of both the matrix’s trace and the difference between the two traces of random confusion matrices. We also illustrate the application of these derived distributions in calculating the superiority probability of four baseline ML models.

This paper concentrates on the general birth-death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth-death processes with two-type catastrophes are is successfully expressed with the Laplace transform of transition probability function of the birth-death processes without catastrophe. The first effective catastrophe occurrence time is considered. The Laplace transform of its probability density function, expectation and variance are obtained.

The objective of this research is to propose a utility function that calculates the possible level of satisfaction that a music consumer would achieve after listening to a song according to the emotional response obtained from a song. Assuming that the consumer's musical preferences are satisfied if the predominant emotions of his current emotional state increase; the probabilistic emotional-musical model (Lugos Abarca, 2023) is used to construct such a utility function. By posing a hypothetical scenario, realistic results were obtained, which guarantee, in principle, its use in theoretical practice. The originality of this research lies in proposing a mathematical tool to study, quantitatively, the decision making of a musical consumer influenced by his emotions. The main conclusion being its importance in the music industry, since the function could predict, theoretically, whether a song will be accepted or rejected by the consumer in comparison with the competition.

This study investigates the stochastic dynamics of hepatitis B virus (HBV) infection using a newly proposed stochastic model. Contrary to deterministic models that fail to encapsulate the inherent randomness and fluctuations in biological processes, our stochastic model provides a more realistic representation of HBV infection dynamics. It incorporates random variability, thereby acknowledging the changes in viral and cellular populations and uncertainties in parameters such as infection rates and immune responses. We examine the solution's existence, uniqueness, and positivity for the proposed model, followed by a comprehensive stability analysis. We provide the necessary and sufficient conditions for local and global stability, offering deep insight into the infection dynamics. Furthermore, we utilize numerical simulations to corroborate our theoretical results. This research provides a robust tool for understanding the complex behavior of HBV dynamics, contributing significantly to the ongoing quest for more effective HBV control and prevention strategies.

Detection of virus in sample is an actual problem in biotechnology, virology, medicine using biosensor. History of problem dates back to middle of last century and is associated with development of an ion-sensitive solid-state device for neurophysiological measurements. Aim of work is theoretical investigation process of detection antibody+antigen (AB+AG) complexes using SOI-FET biosensor. On example of crystal with ten biosensors, estimates of probability detection AB+AG complexes influenza virus are made. In detection process, following four results are possible: – target complex is present in test sample, and it was correctly detected; – target complex is present in sample, but it was not detected; – target complex is absent in sample, but background particles are mistakenly detected as target complex; – target complex is absent in sample, background particles present in sample and are correctly detected as noise.

Understanding swash zone dynamics is of crucial importance for coastal management as the swash motion, consisting of the uprush of the wave on the beach face and the subsequent downrush, is responsible for driving changes the beach morphology trough sediment exchanges between the sub-aerial and sub-aqueous beach. Improved understanding of the probabilistic characteristics of these motions has the potential to allow coastal engineers to develop improved sediment transport models which, in turn, can be further developed into coastal management tools. In this paper, novel descriptors of swash motions are obtained by combining field data and statistical modelling. Our results indicate that the probability distribution function (PDF) of shoreline height (p(ζ)) and trough-to-peak swash heights (p(ρ)) measured at a high energy, sandy beach were both inherently multimodal. Based on the observed multimodality of these PDFs, Gaussian Mixtures are shown to be the best method to statistically model them. Further, our results show that both offshore and surf zone dynamics are responsible for driving swash zone dynamics, which indicates unsaturated swash. The novel methods and results developed in this paper, both data collection and analysis, could aid coastal managers to develop improved swash zone models in the future.

Developments of new probability models for data analysis are keen interest of importance for all fields. The log-Dagum distribution has a prominent role in the theory and practice of statistics. In this article, a new family of continuous distributions generated from a log Dagum random variable called the log-Dagum Weibull distribution is proposed. The key properties of the proposed distribution are derived. Its density function can be symmetrical, left-skewed, right-skewed and reversed-J shaped and can have increasing, decreasing, bathtub hazard rates shaped. The model parameters are estimated by the method of maximum likelihood and illustrate its importance by means of applications to real data sets.

One of creators of quantum mechanics P. Jordan in his work on quantum biology claimed that life's missing laws were the rules of chance and probability of the quantum world. The article presents author’s results of studying probabilities of nucleotides on so-called epi-chains of long DNA sequences of various eukaryotic and prokaryotic genomes. DNA epi-chains are algorithmically constructed subsequencies of DNA nucleotide sequences. According to the algorithm of construction of any epi-chain of the order n, the epi-chain is such nucleotide subsequence, in which the numerations of adjacent nucleotides differ by n (n = 2, 3, 4,…). Correspondingly each epi-chain of order n contains n times less nucleotides than the original DNA sequence. The presented results unexpectedly show that nucleotide probabilities on such DNA epi-chains of different orders are practically identical to nucleotide probabilities in the original long DNA sequence. These data allow considering DNA as a regular rich set of epi-chains, which can play a certain role in genetic and epigenetic phenomena as the author belives. Appropriate rules of nucleotide probabilities on epi-chains of long DNA sequences are formulated for further their tests on a wider set of biological genomes. These phenomenological data and their possible biological meaning are discussed.

Government support plays an important role in Chinese economy. New energy industries, concerning innovation-driven source and environmental protection, are also supported by government. This paper aims to study the effects of the traditional government support at supply side on firms’ innovation and development. In this paper, we propose enterprise behavior model including characteristics of new energy industries, and study the innovation reaction of firms to government support in different situation. We further use propensity score matching to verify the results in theoretical model, and conduct robustness analysis. Our main conclusions include: (1) In the normal years government support can only promote the innovation output of firms which have innovated, however, can not promote the innovation probability of firms which have not innovated. That is to say, government support can only enhance the intensive margin of innovation, but can not enhance the extensive margin of innovation with less competition. (2) In the situation of bad economic environment and intense competition, firms’ innovation probability rises as the government support increase. Therefore, government should provide more R&D special subsidies and implement strict financial supervision to make the effectiveness of support policies especially in the normal years.

The evolution and acceleration of the effects of climate change on the water cycle demand adaptation and mitigation plans. Consequently, the implementation of public policies (management, governance, and strategy) regarding flood risk management or prevention (such as levee heights and spillway dimensions of dams) is based on the characterization of flood hazards. This requires understanding extreme climate phenomena and conducting a rigorous probabilistic analysis of hydrometric data. This study aims to estimate the flood quantiles for lake Nokoue. To achieve this, the adopted methodology involved fitting the Generalized Extreme Value (GEV) distribution, the Gumbel distribution, and the Generalized Pareto (GPA) distribution to the annual maximum water levels of lake Nokoue from 2015 to 2022. We estimated experimental probabilities using the Weibull formula. The assessment of the fit quality of the theoretical probability distributions to our data sample indicated that the Gumbel distribution was the most suitable, with a root mean square error (RMSE) of 0.0724, compared to 0.0754 and 0.0761 for the GEV and GPA distributions, respectively. The position and scale parameters (φ; α) of the Gumbel distribution were estimated to be 3.802 and 0.249, respectively. This allows for the calculation of the probability of an extreme water level occurring within a return period in a single day. Thus, the extreme water levels (flood quantiles) associated with return periods of 10, 50, and 100 years, as determined by the Gumbel distribution, are 4.36m, 4.77m, and 4.95m, respectively. These values are of crucial importance for the design of flood prevention structures (infrastructure) intended to mitigate flood risk.

The evolution and acceleration of the effects of climate change on the water cycle demand adaptation and mitigation plans. Consequently, the implementation of public policies (management, governance, and strategy) regarding flood risk management or prevention (such as levee heights and spillway dimensions of dams) is based on the characterization of flood hazards. This requires understanding extreme climate phenomena and conducting a rigorous probabilistic analysis of hydrometric data. This study aims to estimate the flood quantiles for lake Nokoue. To achieve this, the adopted methodology involved fitting the Generalized Extreme Value (GEV) distribution, the Gumbel distribution, and the Generalized Pareto (GPA) distribution to the annual maximum water levels of lake Nokoue from 2015 to 2022. We estimated experimental probabilities using the Weibull formula. The assessment of the fit quality of the theoretical probability distributions to our data sample indicated that the Gumbel distribution was the most suitable, with a root mean square error (RMSE) of 0.0724, compared to 0.0754 and 0.0761 for the GEV and GPA distributions, respectively. The position and scale parameters (φ; α) of the Gumbel distribution were estimated to be 3.802 and 0.249, respectively. This allows for the calculation of the probability of an extreme water level occurring within a return period in a single day. Thus, the extreme water levels (flood quantiles) associated with return periods of 10, 50, and 100 years, as determined by the Gumbel distribution, are 4.36m, 4.77m, and 4.95m, respectively. These values are of crucial importance for the design of flood prevention structures (infrastructure) intended to mitigate flood risk.

With the global warming and the frequent occurrences of harsh environments, mooring line failures are frequent. Response analysis of the platform structure and its residual mooring system under multiple mooring line failures is needed. Therefore, it is necessary to investigate the change law of platform motion response after mooring line failure to find out the reasons for the change. Studies for different failure combinations of mooring lines show that the variation of the steady-state equilibrium position of the platform is closely related to the stiffness, with a clear functional. The duration and amplitude of the transient response are mainly influenced by the Morison drag force. And it was found that the suspended mooring line reduced the motion responses. It is also found that the mooring line failure increased the effective tension and suspension length of the riser. Based on the improved Dezert-Smarandache theory (DSmT), it is calculated that mooring line failure has little effect on the failure probability in different zones of the riser.

: The radar multi target tracking (MTT) technique requires prior knowledge of a number of parameters about the sensor, the target and backgrounds. The Integrated Track Splitting (ITS) is a fully automatic track-while-scan (TWS) target tracking algorithm capable of extracting and tracking a target in a dense clutter environment using quality false track discrimination (FTD) methodology. The computational complexity in ITS algorithm is limited, compared to other algorithms they use statistical methods to discriminate between false and true tracks, such as multiple hypothesis tracking (MHT), mainly due to the FTD performed. The paper provides an analysis of tracking parameters that allows determining the limit of the possibility of successful target tracking. Extensive experiments have confirmed that the recursive determination of the probability of the existence of a track during tracking can confirm a true track and reject a false track. The clutter density, number of random occurred targets, targets load during the maneuver and the target detection probability were varied. The results of experiments, carried out via Monte Carlo simulations, shown over representative confirmed true tracks (CTT) diagrams, root mean square error position and normalized tracking efficiency parametric diagrams allow the user to select optimal multi-target tracking parameters for different scenarios and clutter densities.

This paper discusses about the quantum energy levels of muonic hydrogen considering only Coulomb interaction. The computational analysis in this paper will help the reader get a good understanding of how different a muonic hydrogen is from its electronic counterparts. Energy eigenvalues are calculated by numerical method and the probability density distribution of muon around the nucleus is plotted for different quantum states using special functions. The code is written in python. A comparative study of emission spectra between the muonic hydrogen and hydrogen has also been discussed.

Several articles have reported that the low number of COVID-19 cases in Japan is attributed to the small number of diagnostic RT-PCR tests performed. The criticism is based on the low number of the tests performed, and they suspected there would be more potential cases in Japan. The use of pre-test probability among tested subjects is proposed in order to evaluate of the sufficiency of test availability instead of the number of the tests. The pre-test probability means the average probability, i.e., ‘suspicion level’, of having coronavirus among the tested subject in a country. The higher pre-test probability is regarded as less sufficient opportunity of the tests, and the test availability could be evaluated by the pre-test probability. Thus, potential problems of underestimation of COVID-19 cases by insufficient amount of the test would be clear by using pre-test probability. The comparison of the pre-test probability could be replaced with that of the positive rate of the test because of the linear relationship between them under the assumption of common sensitivity and specificity. Japan shows the third lowest rate (8.6%), and is considered that the considerably sufficient number of the tests have been performed. In conclusion, the positive rate of the test as a surrogate index of the pre-test probability is useful to evaluate the sufficiency of test amount instead of the number of the tests performed. In present, the potential problem of underestimation by insufficient test availability would be less serious in Japan.

In the case that ship operators may not be aware of the potential risks of environmental factors in situation of high causation probability during the initial stage of the geometric probability analysis process, it is likely that higher-grade collision accident measures will not be taken. However, if any risks is told to the ship operators, more effective and intentional measures can be taken in time. Moreover, if the causation probability corresponding to environmental factors is no less than the risk early warning critical value calculated based on historical collision accident data, there would be a high-risk level that a collision may occur. A new method is put forward based on quantitative analysis of environmental factors and previous collision statistics to provide early warning of any accident risk, and a risk early-warning critical value (REWCV) can be obtained based on this simple but highly operational and practical method. A case study of Three Gorges Reservoir in China indicates that the range of environmental factors where the probability of collision accident grows rapidly is consistent with environmental limits defined by Chinese maritime standards. In addition, the relationship between the risk early-warning critical value and the number of previous collision accident is also clarified.

In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f. and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-differential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms,where one of the initial capitals is fixed at zero.

Pieron's and Chocholle’s seminal psychophysical work predicts that human response time to information relative to visual contrast and/or sound frequency decreases when contrast intensity or sound frequency increases. The goal of this study is to bring to the fore the ability of individuals to use visual contrast intensity and sound frequency in combination for faster perceptual decisions of relative depth (“nearer”) in planar (2D) object configurations on the basis of physical variations in luminance contrast. Computer controlled images with two abstract patterns of varying contrast intensity, one on the left and one on the right, preceded or not by a pure tone of varying frequency, were shown to healthy young humans in controlled experimental sequences. Their task (two-alternative forced-choice) was to decide as quickly as possible which of two patterns, the left or the right one, in a given image appeared to “stand out as if it were nearer” in terms of apparent (subjective) visual depth. The results show that the combinations of varying relative visual contrast with sounds of varying frequency exploited here produced an additive effect on choice response times in terms of facilitation, where a stronger visual contrast combined with a higher sound frequency produced shorter forced-choice response times. This new effect is predicted by cross-modal audio-visual probability summation.

This paper introduces innovative sensitivity indices based on Cliff's Delta for global sensitivity analysis of structural reliability. These indices build on Sobol's method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff's Delta, originally for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff's Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff's Delta​, exhibit properties analogous to those in Sobol's sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a comprehensive framework for evaluating the contributions of input variables and their interactions on structural reliability. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff's Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff's Delta is a disadvantage. Future research should optimize computational demands, especially for small Pf​, where the inner loop may often be unnecessary.

Abstract: Dispersal strategies of a species can affect its invasion success. Investigation into the dispersal strategies of invasive species in relation to different factors helps our understanding of the invasion mechanisms and provides knowledge for population management and invasion evaluation. Tetranychus ludeni Zacher (Acari: Tetranychidae) is an invasive species, which is native to Europe but now cosmopolitan. Here, we examined the effects of age and density on dispersal in mated females. Our results show that older females with more eggs were more likely to disperse and moved longer distances than younger ones with fewer eggs. Older females spread most of their eggs out of the natal habitats and over longer distances, which reduced competition and increased offspring fitness. Females significantly increased dispersal probability and distance with the increase of population density to avoid crowding. The synchronization of dispersal and reproduction, along with the positive density-dependent dispersal strategy, may facilitate habitat colonization and invasion speed of T. ludeni.

In this paper, four probability functions are compared with the purpose of establishing a methodology to improve the accuracy of the estimated wind energy in a desert city in northwestern Mexico. For the statistical modeling, 3 time series of wind speed data were used, corresponding to the years 2017, 2018, and 2019, recorded with a sonic anemometer at a sampling frequency of 10 Hz. From these, the analysis is performed with different stationarity periods (5, 30, 60, and 600 seconds). The estimation of the parameters characterizing the probability density functions was performed using different methods; the statistical models were evaluated by the coefficient of determination and the Nash-Sutcliffe efficiency coefficient, while their accuracy by the measured quadratic error, the mean square error, the mean absolute error, and the mean absolute percentage error. It was found that Weibull with the energy pattern factor method and Gamma using the method of moments were the probability density functions that best describe the statistical behavior of the wind speed and, therefore, better estimate the energy generated, so it is concluded that the proposed methodology will allow having greater confidence, both in the estimation of the wind speed and in the small wind energy available for its use.

In this study, we define screening maps for Italy that classify sites based on their potential for triggering landslides. To this end, we analyze seismic hazard maps and hazard disaggregation results on a national scale considering four spectral periods (0.01s, 0.2s, 0.5s, and 1.0s) and three return periods (475, 975, and 2475 years). First, joint distributions of magnitude (M) and distance (R) from hazard disaggregation are analyzed by means of an innovative approach based on image processing techniques to find all modal scenarios contributing to the hazard. In order to obtain the M-R scenarios controlling the triggering of earthquake-induced landslides at any computation node, mean and modal M-R pairs are compared to empirical curves defining the M-R bounds associated with landslide triggering. Three types of landslides are considered (i.e., disrupted slides and falls, coherent slides, and lateral spreads and flows). As a result, screening maps for all of Italy showing the potential for triggering landslides based on the level of seismic hazard are obtained. The maps and the related data are freely accessible at the following web address: https://distav.unige.it/rsni/slideq.php.

A method for studying properties of the earth's surface tremor, measured by means of GPS, is proposed. Four characteristics of tremor are considered: the entropy of the distribution of wavelet coefficients, the Donoho-Johnston wavelet index, and two estimates of the spectral slope. The anomalous areas of tremor are determined by estimating the probability densities of extreme values of the studied properties. The criteria for abnormal tremor behavior are based on the proximity to, or the difference between, tremor properties and white noise. The greatest deviation from the properties of white noise is characterized by entropy minima and spectral slope and DJ index maxima. This behavior of the tremor is called "active". The "passive" tremor behavior is characterized by the maximum proximity to the properties of white noise. The principal components approach provides weighted averaged density maps of these 2 variants of extreme distributions of parameters in a sliding time window of 3 years are considered. Singular points are the points of maximum average densities. The method is applied to the analysis of daily time series from a GPS network in the West USA in 2009-2022. It turned out that singular points of tremor form well-defined clusters.

A method for studying properties of the earth's surface tremor, measured by means of GPS, is proposed. Four characteristics of tremor are considered: the entropy of the distribution of wavelet coefficients, the Donoho-Johnston wavelet index, and two estimates of the spectral slope. The anomalous areas of tremor are determined by estimating the probability densities of extreme values of the studied properties. The criteria for abnormal tremor behavior are based on the proximity to, or the difference between, tremor properties and white noise. The greatest deviation from the properties of white noise is characterized by entropy minima and spectral slope and DJ index maxima. This behavior of the tremor is called "active". The "passive" tremor behavior is characterized by the maximum proximity to the properties of white noise. The principal components approach provides weighted averaged density maps of these 2 variants of extreme distributions of parameters in a sliding time window of 3 years are considered. Singular points are the points of maximum average densities. The method is applied to the analysis of daily time series from a GPS network in the West USA in 2009-2022. It turned out that singular points of tremor form well-defined clusters.

As intercity buses are a mode that moves large scaled occupancy between regions, it accounts for the mode share-means for mid to long-distance movement in South Korea. However, the study on intercity bus safety needs to be more extensive, and safety policies are carried out based on traditional probability models without considering the data characteristics of bus accidents. Therefore, in this study, the Random Parameter Ordered Logit model was applied to derive fixed parameter factors that have the same effect on the severity of intercity bus accidents and random parameters that consider the heterogeneity of unique attributes by accident. It also analyzed the marginal effect of intercity bus accident severity. As a result of the study discovered that the influencing factors that reflect heterogeneity with Random Parameters were driver’s condition: drowsiness, vehicle size: medium, crash type: vehicle-pedestrian accident, road condition: wet pavement, and log form of AADT. The random parameter ordered logit model was traditionally found to be more suitable than the ordinal logit model, which only reflects fixed factors and more reliable predictions considering the heterogeneity of accident characteristics for each observation.

Silver iodide (AgI) is a system prototype allowing the flow of ions through its structure and has a phase transition at 420 K, characterized by an abrupt change in conductivity and a high ionic conductivity. Introducing low concentrations of graphite (C) into the AgI structure produces a new material with a mixed conductivity (ionic and electronic) which increases with increasing temperature. The experimental results of the logarithm of the ionic conductivity as a function of the inverse of temperature for the (AgI)x–C(1−x) system for low carbon concentrations 0.97 ≤ x ≤ 0.99 were well fitted using a phenomenological model with a probability distribution for the charge carriers based on the carrier density

In this paper, the definition of information entropy of Smoluchowski coagulation equation for Brownian motion is introduced based on coagulation probability. The expression of entropy is the function of geometric average particle volume and standard deviation with lognormal distribution assumption. The asymptotic solution with moment method shows that the entropy is a monotone increasing function of time, which is equivalence to the entropy based on particle size distribution. the result reveals that the present definition of entropy of Smoluchowski coagulation equation are inadequate because the particle average volume at equilibrium cannot be determined from the principle of maximum entropy. This provides a basis for further exploring the global properties of Smoluchowski coagulation equation.

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the lat- ter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the gen- eral definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg's and others' un- certainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

This paper investigates the problem of the optimal arrangement for both UAVs’ caching contents and service locations in UAV-assisted networks based on the context awareness, which considers the influence between users and environment. In the existing work, users within the coverage of UAVs are considered to be served perfectly, which ignores the communication probability caused by line-of-sight (LOS) and non- line-of-sight (NLOS) links. However, the links are related to UAV deployment. Moreover, the transmission overhead should be taken into account. To balance the tradeoff between these two factors, we design the ratio of users’ probability and transmission overhead as the performance measure mechanism to evaluate the performance of UAV-assisted networks. Then, we formulate the objective for maximizing the performance of UAV-assisted networks as a UAV-assisted caching game. It is proved that the game is an exact potential game with the performance of UAV-assisted networks serving as the potential function. Next, we propose the log-linear caching algorithm (LCA) to achieve the Nash equilibrium (NE). Finally, related simulation results reflect the great performance of the proposed algorithm.

Technology development changes society and society demands new and innovative technology development. We analyze technology to understand society and technology itself. Many researches have been introduced in various fields. Most of them were about patent analysis. This is because detailed and accurate results of research and development are patented. In this paper, we study on new patent analysis method based on count data model and Bayesian regression analysis. Using count data model, we analyze the technological keywords extracted from the collected patent documents. We use the posterior distribution of Bayesian statistics to reflect the experience and knowledge of the relevant technological experts in the analysis model. Moreover, we apply the proposed model to finding sustainable technologies. Finding and developing sustainable technologies is an important activity for companies and research institutes to maintain their technological competitiveness. To illustrate how our modeling could be applied to real domain, we carry out a case study using the patent documents related to artificial intelligence.

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.

AI is often looked at as a logical rational way to develop a games agent that methodically looks at options and delivers rational solutions. This paper is based on developing an AI agent that plays a game with a similar emotive content like a human. The purpose of the study was to see if the incorporation of this emotive content would influence the outcomes within the game Love Letter. In order to do this an AI agent with an emotive layer was developed to paly the game over a million times. A lower win/loss ratio demonstrates that to some extent this methodology was vindicated and a 100 per cent win for the AI agent did not happen. Machine learning techniques were modelled purposely so as to match extreme models of behavioural change. The results demonstrated a win/loss ration of 0.67 for the AI agent and in many ways reflectd the frustration that a normal player would exhibit during game play. As was hypothesised the final agent investment value was, on average, lower after matchplay than its initial value.

Background: wildfire modelers rely on Monte-Carlo simulations of wildland fire to produce burn-probability maps. These simulations are computationally expensive. Methods: we study the application of Importance Sampling to accelerating the estimation of burn probability maps, using L2 distance as the metric of deviation. Results: assuming a large area of interest, we prove that the optimal proposal distribution re-weights the probability of ignitions by the square root of expected burned area divided by expected computational cost, then generalize these results to assets-weighted L2 distance. We also propose a practical approach to searching for a good proposal distribution. Conclusion: these findings contribute quantitative methods for optimizing the precision/computation ratio of wildfire Monte Carlo simulations without biasing results, offer a principled conceptual framework for justifying and reasoning about other computational shortcuts, and can be readily generalized to a broader spectrum of simulation-based risk modeling.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

Living systems must solve the problem of realizing their environment to act appropriately to maintain external relationships and internal order for survival and reproduction. This problem is a biological version of the philosophical enigma of how the self can escape solipsism. This study develops a comprehensive model to solve this adaptation problem. LSs must be composed of material entities that have the property of detecting their external states. The detection of the outside is conceptualized as “cognition,” a related state change that occurs at three levels of nested hierarchy: physical, chemical, and semiotic cognitions. Any entity that cognizes the surroundings is a “cognizer.” The hierarchical extension of cognition to all levels of the world provides a monistic view that only cognizers exist. Semiotic cognition is essential for the emergence and evolution of life. Living systems invented semiotic cognitions based on physical and chemical cognitions to manage the probability distribution of events that occur to them. This study proposes a theoretical model in which semiotic cognition is an adaptive process in which inverse causality operations produce particular internal states as symbols that signify hidden external states. This operation makes the living systems aware of the external world.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

We give two examples of the appearance of heavy-tailed distributions in applications to social sciences. Among these distributions are the laws of Pareto, Lotka, and some new ones. The examples are illustrated by constructing suitable toy models.

According to the World Meteorological Organization, since 2000, there has been an increase in global flood-related disasters by 134 percent as compared to the two previous decades. Efficient flood risk management strategies necessitate a holistic approach to evaluating flood vulnerabilities and risks. Catastrophic losses can occur when the peak flow values in the rivers in a basin coincide. Therefore, estimating the joint flood risks in a region is vital, especially when frequent occurrences of extreme events are experienced. This study focuses on estimating the joint flood risks due to river flow extremes in the Grand River watershed in Canada. Determining the interdependence of floods at multiple locations using state-of-the-art tools, the associated damage probabilities, and their costs will be beneficial to various stakeholders, such as the insurance industry, the disaster management sector, and most importantly, the public.

Introduction: Weighting is widely used in applied statistics especially while dealing with survey data. In recent years, multilevel modeling under complex survey designs has increased, resulting into demand for level weights. However, survey data that are accessible to the public for use usually do not contain level weights that are useful in multilevel modeling, but final survey weights that are only appropriate for single level analyses. In this paper, we demonstrate how the final survey weights can be used to estimate level weights for multilevel data analysis, and compare a model that applied level weights with one that applied the final survey weights. Methods: A framework for approximating level weights proposed by the Demographic Health Survey (DHS) program was used to estimate the level weights. Models were fitted using a multilevel mixed effects logistic regression method. Estimates from a model that applied survey weights was compared to those from a model that applied level weights. Results: Application of final survey weights instead of level weights underestimated standard errors and led to loss of precision of model estimates. Conclusions: Use of level weights produces estimates with high precision and yields correct values of standard errors hence appropriately informing inference.

The conceptual and theoretical backbones of symmetry/asymmetry detections or similarity/dissimilarity, and identity/unidentity study are automorphism or isomorphism respectively. However, the development of equations and methods for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures deviates from these backbones. In this article, an equation was proposed for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures, and proved that its isoreflective pairs-points are functionally bijective and inverse. The proposal, called Kabirian-based optinalysis, is based on the conceptual and theoretical frameworks of automorphism and isomorphism. The Kabirian-based optinalysis is also proven and characterized as invariant (robust) under translation (i.e., scaling and location shift), and rotation or reflection. Computing codes were written in python language for Kabirian-based optinalysis to serve as working codes for application and verification.

In Los Angeles, at one point, the Covid-19 testing positivity rate was 6.25%, or one in sixteen. This translates to, on average, one in sixteen specimens testing positive and the vast majority testing negative. Usually, we run sixteen tests on sixteen specimens to identify the positive one(s). This process can be time consuming and expensive. Since a group of negative specimens pooled together for testing will produce a negative result, one single test could potentially eliminate many specimens. Only when the pooled specimen tests positive do we need further testing to identify the positive one(s). Based on this concept, we designed a strategy that will identify the positive specimen(s) efficiently. Assuming one in sixteen specimens is positive, we find that only four tests are needed. Furthermore, we can run them simultaneously, saving both resources and time. Although, in the real world, we cannot make the assumption of only one positive specimen, the same strategy works with slight modification and proves to be much more efficient than the conventional testing. Our strategy returns an answer 48% of the time in four tests and one time cycle. Overall, the average number of tests is seven or eight depending on the follow-up testing, and the average time cycle is about one and a half.

The relative operating characteristic (ROC) curve is a popular diagnostic tool in forecast verification, with the area under the ROC curve (AUC) used as a verification metric measuring the discrimination ability of a forecast. Along with calibration, discrimination is deemed as a fundamental probabilistic forecast attribute. In particular, in ensemble forecast verification, AUC provides a basis for the comparison of potential predictive skill of competing forecasts. While this approach is straightforward when dealing with forecasts of common events (e.g. probability of precipitation), the AUC interpretation can turn out to be oversimplistic or misleading when focusing on rare events (e.g. precipitation exceeding some warning criterion). How should we interpret AUC of ensemble forecasts when focusing on rare events? How can changes in the way probability forecasts are derived from the ensemble forecast affect AUC results? How can we detect a genuine improvement in terms of predictive skill? Based on verification experiments, a critical eye is cast on the AUC interpretation to answer these questions. As well as the traditional trapezoidal approximation and the well-known bi-normal fitting model, we discuss a new approach which embraces the concept of imprecise probabilities and relies on the subdivision of the lowest ensemble probability category.

In this work, we derive the spectral efficiency, secrecy outage probability, and bit error rate of a communication system assisted by a large intelligent surface (LIS). We consider a single-antenna user and an array of antennas at the transmitter side and the possibility of a direct link between transmitter and receiver. Additionally, there is a single-antenna eavesdropper with a direct link to the transmitter, which is modeled as a Nakagami-m distributed fading coefficient. The channels from transmitter to the LIS and from the LIS to the user may or may not have the line-of-sight (LoS) and are modeled by the Nakagami- m distribution. Moreover, we assume that the LIS elements perform non-ideal phase cancellation leading to a residual phase error that assumes a Von Mises distribution. We show that the resulting channel can be accurately approximated by a Gamma distribution whose parameters are analytically estimated using the moments of the equivalent signal-to-noise ratio. We also provide an upper bound for the error probability for M-QAM modulations. With the derived formulas, we analyze the effect of the strength of the LoS link by varying the Nakagami parameter, m.

The closed forms of the non-resonant thermonuclear function in the Maxwell-Boltzmann and Tsallis case with depleted tail are obtained in generalized special functions. The results are written in terms of H-function of two variables. The importance of the results in this paper lies in the fact that the reaction rate probability integrals in Maxwell-Boltzmann and Tsallis cases are not obtained by the conventional method of approximation or by means of a single variable transform technique but by means of a two variable transform method. The Behaviour of the depleted non-resonant thermonuclear functions are examined using graphs. The results in the paper are of much interest to astrophysicists and statisticians in their further work in this area.

In this paper we will show that standard physics to a large degree consists of derivatives of a deeper reality. This means standard physics is both overly complex and also incomplete. Modern physics has typically started from working with first understanding the surface of the world, that is typically the macroscopic world, and then forming theories about the atomic and subatomic world. And we did not have much of a choice, as the subatomic world is very hard to observe directly, if not impossible to observe directly at the deepest level. Despite the enormous success of modern physics, it is therefore no big surprise that we at some point have possibly taken a step in the wrong direction. We will claim that one such step came when one thought that the de Broglie wavelength represented a real matter wavelength. We will claim that the Compton wavelength is the real matter wavelength. Based on such a view we will see that many equations in modern physics are only derivatives of much simpler relations. Second, we will claim that in today’s physics one uses two different mass definitions, one mass definition that is complete or at least more complete, embedded in gravity equations without being aware of it, as it is concealed in GM, and the standard, but incomplete, kg mass definition in non-gravitational physics. First, when this is understood, and one uses the more complete mass definition that is embedded in gravity physics, not only in gravity physics, but in all of physics, then one has a chance to unify gravity and quantum mechanics. Our new theory shows that most physical phenomena when observed over a very short timescale are probabilistic for masses smaller than a Planck mass and dominated by determinism at or above Planck mass size. Our findings have many implications. For example, we show that the Heisenberg uncertainty principle is rooted in a foundation not valid for rest-mass particles, so the Heisenberg uncertainty principle can say nothing about rest-masses. When re-formulated based on a foundation compatible with a new momentum that is also compatible with rest-masses, we obtain a re-defined Heisenberg principle that seems to become a certainty principle in the special case of a Planck mass particle. Furthermore, we show that the Planck mass particle is linked to gravity and that we can easily detect the Planck scale from gravity observations. The Planck mass particle is unique as it only lasts the Planck time, and in that very short time period it can only be observed directly from itself, and it therefore closely linked to absolute rest.

Impressing discoveries in the field of the genetic code have been described by its researchers by means of the terminology borrowed from linguistics and the theory of communications. Leading experts on structural linguistics believe for a long time already that languages of human dialogue were formed not from an empty place, but they are continuation of genetic language or, anyhow, are closely connected with it, confirming the idea of information commonality of organisms. The aticle continues the theme about a connection of linquistic languages with the genetic language. It describes results of comparative study of long Russian literary texts (novels by L.Tolstoy, F.Dostoevsky, A.Pushkin, etc.) and long sequences of hydrogen bonds in double helixes of DNA of different organisms. Formalisms of quantum informatics are used in modeling some of these results taking into account thoughts of many researches about possible using principles of quantum informatics in organisation of living bodies.

The rapid development of the Industrial Internet of Things (IIoT) has brought enormous opportunities to the industrial environment but has also posed significant challenges to network security, especially the physical layer security challenges,which is crucial for the reliable transmission of messages interconnected devices and sensors. Focus on the enhancing the physical layer security in the IIoT communication, this paper proposed a mechanism of Spatial Secrecy Outage Probability (SSOP) to ensure the secure transmission of data. The SSOP algorithm assumes that the location of legitimate device is known, while eavesdropper on the random distribution of device locations, forming the SSOP model related to device locations from the perspective of insecure regions (ISR) and secure regions (SR), and deduce the closed-form expression for its upper bound. Subsequently under the constraint of SSOP conditions, establish an optimization model with the objective of system throughput maximization based on Spatial Secrecy Outage Probability(SRM-SSOP). By optimizing the transmission rate of legitimate channels or controlling the transmission power, the maximization of system throughput can be achieved, thus reducing the consumption of communication resources. Through sophisticated modeling and simulation in the MATLAB, we verified the accuracy of the definition and derived upper bound of SSOP. The experimental results also show that SSOP algorithm gradually converges to a specific value as the number of antenna elements increases. In addition, we observed that when the receiver device is aligned with the normal direction of the transmit antenna array, the SSOP reaches a minimum value. These performance are crucial for understanding and optimizing the security performance of IIoT communication systems.

Our paper deals with an advanced statistical tool for the volatility prediction problem in financial (crypto) markets. Firstly, we consider the conventional GARCH involved volatility models. We next extend the corresponding GARCH based forecasting and calculate a specific probability associated with the predicted volatility levels. Since the probability evaluation is based on a stochastic model, we next develop an additional data-driven estimation of this probability. The proposed advanced statistical estimation uses real (historical) market data. The obtained theoretic results for the statistical probability of levels are also discussed in the framework of the integrated volatility concept. A possible application of the established probability estimation to the volatility clustering problem is also mentioned. Our paper includes a concrete practical implementation of the resulting (combined) volatility prediction tool and considers a novel module for trading and volatility estimation in crypto markets recently developed by 1ex Trading Board group in collaboration with the GoldenGate Venture. Moreover, we discuss shortly a possible using of the proposed model based and data-driven volatility prediction methodology in the financial risk management.

The assessment of concrete structures' durability in chlorine environments is significantly impacted by the uncertainty inherent in existing durability models. It introduce an integrated approach for updating these models, based on detection information of existing structures. This approach narrows the gap between theoretical predictions and observed structural durability. Specifically, we refine the probability model of critical chloride content by analyzing steel bar corrosion sample proportions, using Bayesian theory for greater accuracy. The enhanced model enables more reliable life expectancy prediction, forming a solid foundation for maintaining and strengthening existing structures.This method was demonstrated through a case study of a reinforced concrete industrial building with a service life of 12 years.

The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.

This article is devoted to methods of processing random processes. Of particular relevance is the task of processing broadband non-stationary random processes. The processing of random processes is usually related to the assessment of their probabilistic characteristics. Very often, a non-stationary broadband random process is represented by a single implementation in a priori uncertainty about the type of distribution function. Such random processes occur in information and measuring communication systems in which information is transmitted at a real time pace (for example, radio telemetry systems of spacecraft). The use of methods of traditional mathematical statistics, for example, maximum likelihood methods to determine probability characteristics, in this case is not possible. The article discusses a method of processing non-stationary broadband random processes based on the use of non-parametric methods of decision theory. An algorithm for dividing the observation interval into stationary intervals using non-parametric Kendall statistics is considered, as well as methods for estimating probabilistic characteristics on the stationary interval using ordinal statistics. The article presents the results of statistical modeling using the Mathcad program.

Tidal stream energy is a renewable energy resource that might be developed to offset carbon emissions. A tidal energy demonstration (TED) area has been designated in Minas Passage, Bay of Fundy, for testing and installing marine hydrokinetic (MHK) turbines. Regulations require quantification of the potential for MHK turbine installations to harm local populations of marine animals. Here we use acoustic telemetry to quantify probability that post smolt Inner Bay of Fundy salmon encounter a turbine installation at the TED area. Previous work has quantified detection efficiency of Innovasea HR acoustic tags as a function of current speed and range from a moored HR2 receiver and also demonstrated that drifters carrying HR tags will be effectively detected when the drifter track crosses the array of HR2 receivers in Minas Passage. Salmon smolts were tagged and released in Gaspereau and Stewiacke Rivers, Nova Scotia, in order that the HR2 receiver array could monitor seaward migration of the post smolts through Minas Passage and particularly through the TED area. Presently we demonstrate methods by which tag signals detected by the HR2 array can be used to estimate the expected number of times that a post smolt would encounter a single near-surface MHK turbine installation during its seaward migration.

In this study, the application of the main algorithms used for SDM, namely Boosted Regression Tree (BRT), Generalized Linear Model (GLM), Multivariate Adaptive Regression Splines (MARS), Maximum Entropy (MAXENT) and Random Forest (RF), were considered in order to simulate the citrus probability of distribution in a Mediterranean area, based on presence data and a random background sample, and in relation to several predictors. The predictors were grouped under 19 bioclimatic variables, elevation described through a Digital terrain model, soil physical properties, and irrigation. Sensitivity analysis was carried out by: modifying the values of the main models’ parameters; and reducing the input presence points.

South Italy is characterised by a semi-arid climate with scarce rain and high evaporative demand, therefore the need to optimise water resources in this area is crucial, and climate change could worsen this condition. In citrus cultivation, which is one of the most important crops bred in Southern Italy, and more generally in Mediterranean regions, deficit irrigation strategies are im-plemented in order to cope with limited resource availability. On this basis, knowledge on how the territorial distribution of citrus would change in relation to these strategies constitutes valuable information for the stakeholders. Therefore, the objective of this study was to determine the prob-ability of presence of citrus in Sicily at changing of the percentage of water deficit application, in order to analyse change in the surface area and localisation of the crop. The methodology was based on the application of Species Distribution Models and Geographic Information Systems to the case study of the Province of Syracuse in Sicily. Different geostatistical and machine learning models were applied, based on 3-decades bioclimatic variables, DTM and irrigation; assessment of the outcomes was carried by using classification evaluation metrics. The analysis of the outcomes showed that uncorrelated predictor layers mainly included water input that affected most the probability of presence. Moreover, GIS analyses showed that deficit irrigation strategies would generate an overall reduction of cultivation surfaces in the territory and a decrease of citrus pres-ence in southern areas of the considered territory, where climate conditions are less favourable in terms of temperature and precipitations, thus providing useful information for decision support tools in agriculture and land use policy.

Maxwell's electric equation and Schrödinger quantum equation are used to find useful expressions for the probability of electrons existence and the electrons transport. The first expression which uses special relatively also shows that the probability of the electrons existence is higher for lower energy states compared to higher energy states where the probability is low. This means that electrons transport takes place from higher energy states to lower states. This conforms to the laws of chemistry where the atom tends to be stable by forcing electrons to occupy lower energy states. The second expression used the momentum velocity relation instead of special relatively. This expression shows also electrons transport from higher to lower states. It also shows that the probability of the electrons existence is higher for lower electrons density regions and lower for higher electrons density regions. This means that the electrons transport is from higher density regions to lower density regions. This conforms to the diffusion law.

In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, , Beckenstein bound and Bremermann limit.

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.