In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.

KLEPTOSE® CRYSMEB is a methylated cyclodextrin derivative displaying less methylated group substitution than randomly methylated cyclodextrin. It has demonstrated an impact on atherosclerosis and neurological diseases. linked in part to cholesterol complexation and immune response, but the impact on inflammatory cascade pathways was not clear. Thus, the impact of KLEPTOSE® CRYSMEB on various pharmacological targets was assessed using human umbilical vein endothelial cells in physiological and inflammatory conditions, followed by screening against twelve human primary cell-based systems designed to model complex human tissue and disease biology of the vasculature, skin, lung, and inflammatory tissues using the BioMAP® Diversity PLUS® Panel. Finally, the anti-inflammatory mechanism was investigated on peripheral blood mononuclear cells to evaluate anti-inflammatory or pro-resolving properties. The results showed that KLEPTOSE® CRYSMEB can modulate the immune system in vitro and potentially manage vascular issues by stimulating the expression of molecules involved in the crosstalk between immune cells and other cell types. It showed anti-inflammatory effects driven by pro-inflammatory cytokine secretion inhibition and could have different impacts on different tissue types. Moreover, this cyclodextrin showed no clear impact on pro-resolving lipid mediators. Finally, it appeared that the mechanism of action of KLEPTOSE® CRYSMEB seems to not be shared by well-known anti-inflammatory molecules.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses the relationship between stability and the Gaussian curvature, as well as the connections between queueing theory, information geometry, , Riemannian geometry, and the Theory of Relativity.

Overhydration (OH) is a common medical problem found in patients with kidney or heart failure, but still a specific marker has not been found. Clinicians today use bioimpedance spectroscopy (BIS), ultrasound (US) markers of fluid overload or markers of heart and kidney function like NT-pro-BNP, GFR or creatinine levels. New serum markers such as Ca-125, Galectin-3 (Gal-3), Adrenomedullin (AMD) and Urocortin-2 (UCN-2), are being researched with promising results. The need to discover a more precise marker of overhydration is dire mainly because physical examination is extremely imprecise. Signs and symptoms of fluid overload like edema or gradual increase of body mass are not always present, especially in patients with chronic kidney disease. This review paper summarizes actual knowledge of a patient's hydration status estimation focusing especially on kidney diseases.

The reported study was devoted to the investigation of viscoelastic behavior for solid and porous ultra-high-molecular-weight polyethylene (UHMWPE) under compression. The obtained experimental stress curves were interpreted using a two-term Prony series to represent the superposition of two coexisting activation processes corresponding to long molecular (~160 s) and short structural (~20 s) time scales, respectively, leading to good statistical correlation with the observations. In the case of porous polymer, the internal strain redistribution during relaxation was quantified using Digital Image Correlation (DIC) analysis. The strongly inhomogeneous deformation of the porous polymer was found not to affect the relaxation times. In order to generalize the results to three dimensions, X-ray tomography was used to examine the porous structure at the macro- and micro-scale levels. DIC analysis revealed positive correlation between the applied force and relative density. The apparent stiffness variation for UHMWPE foams with mixed open and closed cells was described using a newly proposed three-term expression. Furthermore, the in situ tensile loading and X-ray scattering study was applied for isotropic solid UHMWPE specimens to investigate their parameters of internal structure during orientation and stress relaxation process at another mode.

HLA class-I (HLA-I) polyreactive monoclonal antibodies (mAbs) reacting to all HLA-I alleles were developed by immunizing HLA-E monomeric heavy chain (HC) (Open Conformers, OCs). Two of the mAbs (TFL-006 and TFL-007) bound to the HC’s coated on a solid matrix. The binding was inhibited by a peptide 117AYDGKDY123, present in all alleles of the six HLA-I isoforms but masked by 2-microglobulin -m) in intact HLA-I trimers (Closed Conformers, CCs). Identical HLA-I polyreactivity is observed in IVIg administered to lower anti-HLA antibodies (Abs) in HLA-sensitized patients, but the mechanism is unknown. We hypothesized that the mAbs that mimic IVIg HLA-I polyreactivity might mimic the immunomodulatory functions of IVIg. We tested the relative binding affinity of the mAbs and IVIg for both OCs- and CCs and compared their effects on (a) the phytohemagglutinin (PHA)-activation T-cells, (b) the production of anti-HLA-II antibody (Ab) by B-memory cells, and anti-HLA-I Ab by immortalized B-cells, and (c) the upregulation of CD4+, CD25+, and Fox P3+ T-regs. The mAbs bound only to OCs, whereas IVIg is bound to both CCs and OCs. The mAbs suppressed blastogenesis and proliferation of PHA-activated T-cells, anti-HLA Ab production by B-cells and expanded the T-regs, better than IVIg. We conclude that a humanized version of the TFL-mAbs could be an ideal therapeutic IVIg-mimetic.

Depletion of ore deposits, increasing demand for raw materials, the need to process low-grade, complex and finely disseminated ores and the reprocessing of tailings are challenges, especially for froth flotation separation technologies. Even though capable of handling relatively fine grain sizes the flotation separation of very fine and ultrafine particles faces many problems still. Further, the flotation of low-contrast semi-soluble salt-type minerals with very similar surface properties, many complex interactions between minerals, reagents and dissolved species often result in poor selectivity. This study investigates the flotation beneficiation of ultrafine magnesite rich in dolomite from de-sliming, currently reported to the tailings. The paper especially focuses on the impact of the depressant sodium hexametaphosphate (SHMP) on: (i) the froth properties using dynamic froth analysis (DFA), (ii) the separation between magnesite and dolomite/calcite and (iii) its effect on the entrainment. Furthermore, the application of 1-hydroxyethylene-1,1-diphosphonic acid (HEDP) is a more environmentally friendly and low-cost alternative to SHMP is presented and discussed. The paper contributes to understanding on the complexity of depressant responses in froth flotation.

Although congenital sensorineural hearing loss (SHL) in the bilateral cochleae mainly results from genetic abnormalities, chronic SHL progressing in later life is often influenced by systemic immune disturbances, including autoimmunity, chronic inflammation, and immunosenescence. We have investigated the relationship between the inner ear and systemic immunity and reviewed the possibilities to prevent SHL, including autoimmune SHL and age-related SHL. We also demonstrated two lymphocyte populations, interleukin 1 receptor type II (IL-1R2)-positive T cells (T1R2) and naturally occurring regulatory T cells (nTregs) in CD4⁺ T cells, which increase with aging, suppress host immune function and promote organ degeneration. Alterations in systemic immunity by fewer microbial antigen challenges in the living environment, elimination of immune suppressive lymphocytes, or immune rejuvenation with a reconstituted thymus may contribute not only to renew the cochlear function in SHL, but also to extend the healthy life of functional organs in a vigorous and youthful body, one of humanity’s greatest dreams.

It is known that knockdown of the mitochondrial 18 kDa translocator protein (TSPO) as well as TSPO ligands modulate various functions, including functions related to cancer. To study the ability of TSPO to regulate gene expression regarding such functions, we applied microarray analysis of gene expression to U118MG glioblastoma cells. Within 15 minutes, the classical TSPO ligand PK 11195 induced changes in expression of immediate early genes and transcription factors. These changes also included gene products that are part of the canonical pathway serving to modulate general gene expression. These changes are in accord with reverse transcriptase (RT) real-time -PCR. At the time points of 15, 30, 45, and 60 minutes, as well as 3 and 24 hours of PK 11195 exposure, the functions associated with the changes in gene expression in these glioblastoma cells covered well known TSPO functions. These functions included cell viability, proliferation, differentiation, adhesion, migration, tumorigenesis, and angiogenesis. This was corroborated microscopically for cell migration, cell accumulation, adhesion, and neuronal differentiation. Changes in gene expression at 24 hours of PK 11195 exposure were related to downregulation of tumorigenesis and upregulation of programmed cell death. In the vehicle treated as well as PK 11195 exposed cell cultures, our triple labeling showed intense TSPO labeling in the mitochondria but no TSPO signal in the cell nuclei. Thus, mitochondrial TSPO appears to be part of the mitochondria-to-nucleus signaling pathway for modulation of nuclear gene expression. The novel TSPO ligand 2-Cl-MGV-1 appeared to be very specific regarding modulation of gene expression of immediate early genes and transcription factors.

The abundant mechanical vibration energy in bridge road environment can be converted into electric energy by using the piezoelectric energy harvest technology, which could be an efficient way to provide energy required by the wireless sensor network in the bridge condition monitoring system. An autonomous energy harvesting system has been designed based on cantilever beams for sensing and acquiring the bridge vibration energy. After the analysis of the dynamic properties of the piezoelectric cantilever beam in the energy conversion, three kinds of interface circuits were compared through simulation and experimental results. It was shown that the VD interface circuit has less power loss. Furthermore, the proposed closed loop control method based on the VD circuit was simple, adaptive, and self-powered, which is suitable for the road energy harvesting application. Finally, the energy harvesting system based on VD circuit was realized with harvested power of around 0.8mW.

Heart failure (HF) management in type 1 diabetes (T1D) is particularly challenging due to its increased prevalence and the associated risks of hospitalization and mortality, driven by diabetic cardiomyopathy. Sodium-glucose cotransporter-2 inhibitors (SGLT2-i) offer a promising avenue for treating HF, specifically the preserved ejection fraction variant most common in T1D, but their utility is hampered by the risk of euglycemic diabetic ketoacidosis (DKA). This review investigates the potential of SGLT2-i in T1D HF management, alongside the emergent Continuous Ketone Monitoring (CKM) technology as a means to mitigate DKA risk, through a comprehensive analysis of clinical trials, observational studies, and reviews. The evidence suggests SGLT2-i significantly reduce HF hospitalization and enhance cardiovascular outcomes. However, their application in T1D patients remains limited due to DKA concerns. CKM technology emerges as a crucial tool in this context, offering real-time monitoring of ketone levels, which enables the safe incorporation of SGLT2-i into treatment regimes by allowing for early detection and intervention in the development of ketosis. The synergy between SGLT2-i and CKM has the potential to revolutionize HF treatment in T1D, promising improved patient safety, quality of life, and reduced HF-related morbidity and mortality. Future research should aim at clinical trials directly assessing this integrated approach, potentially guiding new management protocols for HF in T1D.

A plenty of theories on the origin of genetic codes have been proposed so far, yet all ignored the energetic driving force, its relation to the biochemical system, and most importantly, the missing “matchmaker” between proteins and nucleic acids. Here, a new hypothesis is proposed, according to which ATP is at the origin of the primordial genetic code by driving the coevolution of the genetic code with the pristine biochemical system. This hypothesis aims to show how the genetic code was produced e.g. by photochemical reactions in a protocell that derived from a lipid vesicle enclosing various life’s building blocks (e.g. nucleotides and peptides). At extant cell, ATP is the only energetic product of photosynthesis, and is at the energetic heart of the biochemical systems. ATP could energetically form and elongate chains of both polynucleotides and polypeptides, thus acting a “matchmaker” between these two bio-polymers and eventually mediating precellular biochemical innovation from energy transformation to informatization. ATP was not the only one that could drive the formation of polynucleotides and polypeptides, but favored by precellular selection. The protocell innovated a photosynthesis system to produce ATP efficiently and regularly with the aids of proteins and RNA/DNA. The completion of permanently recording the genetic information by DNA marked the dawn of cellular life operated by Darwinian evolution. The ATP hypothesis assumes or supports the photochemical origin of life, shedding light on the origins of both photosynthetic and biochemical systems, which remains largely unknown thus far. Based on ATP hypothesis, virus (like the new coronavirus) could not be the earliest life on Earth, as it has neither biochemical systems nor lipid bilayer membrane that provided relatively isolated environment for the development of protobiochemical reactions, although it owns the genetic code of a cellular life. Virus could not be a bridge between life and non-life, but is an anti-life substance, as it depletes cellular material for its own replication, and then spreads by destroying the host cells. It can be imagined that if cellular life are completely wiped out by the virus, the complete destruction of life on Earth would be inevitable.

Leukemia, contributing to 3% of all cancer cases in the United States, presents a significant challenge in treatment due to its diverse subtypes, each dis-playing unique genetic and molecular abnormalities. The aggressive growth of ab-normal blood cells compromises immune function and poses challenges in developing effective therapeutic approaches. Unlike solid tumors, surgical resection is not an option, limiting treatment strategies to chemotherapy, immunotherapy, and radiation therapy, which may be nonspecific and lead to organ damage and toxicity. Anthracyclines, widely used in hematological tumors, face limitations due to severe cardiotoxicity, causing progressive cardiomyopathy and, in severe cases, congestive heart failure. Heart failure incidence is significantly higher in cancer patients treated with anthracyclines over 5, 10, and 15 years. Early detection of left ventricular dysfunction and cardiotoxicity is crucial to mitigate progression to congestive heart failure (CHF) in this population. Recent research by Bayrón-Marrero et al. reveals that lower levels of plasma soluble TREM-Like Transcript-1 (s-TLT-1), a platelet-specific receptor, correlate with left ven-tricular dysfunction in cardiovascular disease patients. Those with s-TLT-1 levels ex-ceeding 544 pg/mL exhibit a significant association with congestive heart failure. These findings suggest the potential use of s-TLT-1 as a diagnostic screening tool for early detection and treatment of anthracycline-induced CHF in leukemia patients.

O26 enteropathogenic Escherichia coli (EPEC), possesses a unique pseudocapsule composed of polysaccharides identical to the O antigen in their lipopolysaccharide (LPS) membrane. Therefore, the impact of O26 polysaccharides on the immune evasion mechanisms of capsulated O26 EPEC was investigated. Our findings reveal that the concentration of GlcNAc, an immunodominant unit of O26 polysaccharides capable of activating the MBL (Mannose Biding Lecting) pathway of the complement system, was found to be lower in capsulated EPEC O26 compared to naked shiga toxin-producing E. coli (STEC) O26 strain. It was noted that, unlike the naked STEC strain, the capsulated EPEC O26 strain was protected against lysis by the alternative pathway of the com-plement system by inhibiting C3b adhesion to its bacterial surface. Capsulated EPEC O26 strains were also able to avoid phagocytosis by macrophages. However, the immune evasion provided by the capsule was overcome in the presence of anti-O26 polysaccharide antibodies. Additionally, these antibodies were able to recognize O26 EPEC in the presence of biofilm and inhibit their adhesion to human epithelial cells. Overall, the results indicate that the O26 polysaccharides can generate an effective humoral immune response, making them promising antigens for the de-velopment of a vaccine against capsulated O26 E. coli

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses some info-geometric applications to Machine Learning are highlighted. Closing remarks with some challenging open problems combined with the next phase of research are given.

E-commerce businesses employ recommender models to assist in identifying a personalized set of products for each visitor. To accurately assess the recommendations’ influence on customer clicks and buys, three target areas—customer behavior, data collection, user-interface —will be explored for possible sources of erroneous data. Varied customer behavior misrepresents the recommendations’ true influence on a customer due to the presence of B2B interactions and outlier customers. Non-parametric statistical procedures for outlier removal are delineated and other strategies are investigated to account for the effect of a large percentage of new customers or high bounce rates. Subsequently, in data collection we identify probable misleading interactions in the raw data, propose a robust method of tracking unique visitors, and accurately attributing the buy influence for combo products. Lastly, user-interface issues discuss the possible problems caused due to the recommendation widget’s positioning on the e-commerce website and the stringent conditions that should be imposed when utilizing data from the product listing page. This collective methodology results in an exact and valid estimation of the customer’s interactions influenced by the recommendation model in the context of standard industry metrics such as Click-through rates, Buy-through rates, and Conversion revenue.

This article aims to analyze household energy data to predict electricity self-sufficiency and identify the key features that impact it. For this purpose, we use SHAP (Shapley Additive Explanations), LightGBM (Light Gradient Boosting Machine), and a correlation heatmap-based framework to analyze 12 months of energy and questionnaire survey data collected from over 200 smart houses in Kitakyushu, Japan. We use the SHAP summary plot to identify the impact-wise order of key features influencing the electricity self-sufficiency rate (ESSR). Using SHAP, we demonstrated that key features are; housing types, average monthly electricity bill, floor heating, electric capacity, number of washing and drying machines, fee plans, occupation of household head, total floor area, average monthly gas bill, cooking equipment, etc. Furthermore, we adopted the LightGBM classifier with $\ell^1$ regularization to extract the most significant features and predict the electricity self-sufficiency rate of households. This LightGBM-based model can also predict the electricity self-sufficiency rate of households that did not participate in the questionnaire survey. A heat map is also used to analyze the correlation among household variables. The findings discussed in this article offer valuable insights for energy policymakers to achieve the targets of energy self-sufficient houses.

To investigate factors associated with the success of switching to faricimab for type 1 macular neovascularization (MNV) refractory to intravitreal aflibercept (IVA). This retrospective cohort study included patients with type 1 MNV who were switched to faricimab because they were refractory to IVA at two centers. The main outcome was an extension of the treatment interval after 6 months, and factors related to the success or failure of the extension and visual and anatomical outcomes were assessed. The analysis included 43 eyes of 43 patients. Extended dosing intervals of more than 2 weeks were identified in 14 eyes (32.6%). A short dosing interval before the switch, the absence of polypoidal lesions, and a thin central choroidal thickness before the switch were identified as factors involved in successful extension. For patients with refractory type 1 MNV, switching to faricimab is a safe and potential option to extend from existing dosing intervals.

The Bacillus Calmette-Guérin (BCG) vaccine has been used for over one hundred years to protect against the most lethal infectious agent in human history, tuberculosis. Over four billion BCG doses have been given and, worldwide, most newborns receive BCG. A few countries, including the United States, did not adopt the WHO recommendation for routine use of BCG. Moreover, within the past several decades, most of Western Europe and Australia, having originally employed routine BCG, have discontinued its use. This review article articulates the impacts of those decisions. The associated consequences include increased tuberculosis, increased infections caused by non-tuberculous mycobacteria (NTM), increased autoimmune disease (autoimmune diabetes and multiple sclerosis) and increased neurodegenerative disease (Parkinson’s disease and Alzheimer’s disease). This review also offers an emerged zoonotic pathogen, Mycobacterium avium ss. paratuberculosis (MAP) as a mostly unrecognized NTM that may have a causal role in some, if not all, of these diseases. Current clinical trials with BCG for varied infectious, autoimmune and neurodegenerative diseases have brought this century-old vaccine to the fore due to its presumed immuno-modulating capacity. With its historic success and strong safety profile, the new and novel applications for BCG may lead to its universal use –putting the Western World back onto the road not taken.

We wanted to investigate the current knowledge on the impact of diet on anti-TNF response in inflammatory bowel diseases (IBD), to identify dietary factors that warrant further investigations in relation to anti-TNF treatment response, and, finally, to discuss potential strategies for such investigations. PubMed was searched using specified search terms. One small prospective study on diet and anti-TNF treatment in 56 patients with CD found similar remission rates after 56 weeks among 32 patients with good compliance that received concomitant enteral nutrition and 24 with poor compliance that had no dietary restrictions (78% versus 67%, p = 0.51). A meta-analysis of 295 patients found higher odds of achieving clinical remission and remaining in clinical remission among patients on combination therapy with specialised enteral nutrition and Infliximab (IFX) compared with IFX monotherapy (OR 2.73; 95% CI: 1.73–4.31, p < 0.01, OR 2.93; 95% CI: 1.66–5.17, p < 0.01, respectively). In conclusion, evidence-based knowledge on impact of diet on anti-TNF treatment response for clinical use is scarce. Here we propose a mechanism by which Western style diet high in meat and low in fibre may promote colonic inflammation and potentially impact treatment response to anti-TNF drugs. Further studies using hypothesis-driven and data-driven strategies in observational, animal and interventional studies are warranted.

Due to its application as an anti-cancer drug, pazopanib (1) has attracted the interest of many researchers and several studies on pazopanib synthesis have been reported over the years. This paper provides a novel route for synthesizing N,2,3-trimethyl-2H-indazol-6-amine (5) which is a crucial building block in the synthesis of pazopanib from 3-methyl-6-nitro-1H-indazole (6). By alternating between the reduction and two methylation steps compound 5 was obtained in comparable yield (55.0%) to what has been reported (54%). Noteworthy, the last step of N2-methylation also yielded N,N,2,3-tetramethyl-2H-indazol-6-amine (5’) as a new compound ever reported. Furthermore, the data presented in this paper can serve as instrumental for future research aimed at further refining the synthesis process of pazopanib.

Human endogenous retroviruses (HERV) are remnants of ancient retroviral infections that, over millions of years, became integrated into the human genome. While normally inactive, environmental stimuli such as infections have contributed to the transcriptional reactivation of HERV promoting pathological conditions including the development of autoimmunity, neurodegenerative disease and cancer. What infections then trigger HERV activation? Mycobacterium avium subspecies paratuberculosis (MAP) is a pluripotent driver of human disease. Aside from granulomatous diseases Crohn’s, sarcoidosis and Blau syndrome, MAP is associated with autoimmune disease: type one diabetes (T1D), multiple sclerosis (MS), rheumatoid arthritis and autoimmune thyroiditis. MAP is also associated with Parkinson’s disease. Autoimmune diabetes, multiple sclerosis and rheumatoid arthritis are the diseases with the strongest MAP/HERV association. There are several other diseases associated with HERV activation including diseases whose epidemiology and/or pathology would prompt speculation for a causal role of MAP. These include non-solar uveal melanoma, colon cancer, glioblastoma and amyotrophic lateral sclerosis (ALS). This article further points to MAP infection as a contributor to autoimmunity, neurodegenerative disease and cancer via unsilencing of HERV. We examine the link between the ever-increasing number of MAP- associated diseases, the MAP/HERV intersection with these diverse medical conditions and propose treatment opportunities based upon this association.

Breast Cancer Associated Susceptibility Proteins Type 1/2 (BRCA1/2) promote cellular functioning by modulating NRF2-mediated antioxidant signaling. Redox failure in women with BRCA1/2 insufficiency increases the risk for breast/ovarian/uterine cancers. Risk‐reducing salpingo‐oophorectomy (RRSO) is a prophylactic surgery of the reproductive organs, which is frequently conducted by the age of 40 to lower the occurrence of cancer in women with BRCA1/2 mutations. However, abrupt estrogen decline following RRSO causes ovarian failure, which implicates various cellular physiological processes, resulting in increased release of free radicals and subsequent severe onset of menopausal symptoms. Comfort measures (e.g., hormonal replacement therapy (HRT) and mindfulness-based stress reduction (MBSR)) may improve chronological menopause-related quality of life, but their specific effects are not clear in women with gene mutations. Aiming to fill the gap, this study used path analysis to examine the effects of HRT and MBSR on menopausal symptoms among RRSO patients (N = 199, mean age = 50.5 ± 6.7 years). HRT alleviated menopausal symptoms in BRCA2 carriers and women who were physically active, premenopausal at the time of RRSO, had a high BMI, and had no history of breast cancer. It increased the severity of urogenital symptoms in those with a history of cancer. MBSR, on the other hand, was associated with increased intensity of most menopausal symptoms. The results suggest that young women undergoing recent RRSO may benefit from HRT at an individual level while their need for extensive measures to optimize their psychological wellbeing is ongoing. Adverse effects of MBSR, which are captured in the present study imply that MBSR may interfere with redox sensitivity associated with estradiol fluctuations in BRCA1/2 carriers. Investigations are needed to test this hypothesis and elaborate on the underlying mechanisms in those women.

Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, dierential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.

There are unsolved problems related to inflation, gravity, dark matter, dark energy, missing antimatter, and the birth of the universe. Some of them can be better answered by assuming the existence of aether and hypoatoms. Both were created during the inflation in the very early universe. While aether forms vacuum, hypoatoms, composed of both matter and antimatter and believed to be neutrinos, form all observable matter. In vacuum, aether exists between the particle-antiparticle dark matter form and the dark energy form in a dynamic equilibrium: A + A-bar = gamma + gamma. The same reaction stabilizes hypoatoms and generates a 3-dimensional sink flow of aether that causes gravity. Based on the hypoatom structure, the singularity does not exist inside a black hole; the core of the black hole is a hypoatom star or neutrino star. By gaining enough mass, ca. 3 X 10²² M_sun, to exceed neutrino degeneracy pressure, the black hole collapses or annihilates into the singularity, thus turning itself into a white hole or a Big Bang. The universe is anisotropic. Its center, or where the Big Bang happened, is at 0.66^+0.03_-0.01 times the radius of the observable universe at Galactic coordinates (l, b) = (286⁺¹⁰_-10, -43⁺⁷_-6). If we look from the Local Group to the center of the universe, the universe is rotating clockwise.