Current theories of autoimmunity are diverse, sometimes contradictory, and suffer from incompleteness. Although substantial evidence exists that adaptive and innate immunity, sex, genetic predisposition, and the microbiome all play essential roles in autoimmune disease etiologies and pathogenesis, and that antigen processing is altered during disease induction, no existing theory integrates all of these factors through a single, coherent mechanism. In an attempt to focus the field on the need to elucidate such an integrative mechanism, I propose one possibility here that, if nothing else, helps to identify the nature of the problems that need to be addressed. My theory is that autoimmune diseases are induced by normal immunological responses to unique pairs of complementary antigens, at least one of which is a molecular mimic of a host target. Each antigen in the complementary pair induces a complementary immune response (T or B cell); although each immune response is idiotypic in origin, the antigenic complementarity results in what appears to be an idiotype-anti-idiotype relationship between the responses. Additionally, because of the antigenic complementarity, each immune response mimics one of antigens, abrogating the distinction between self and non-self. If at least one of the antigens mimics a host antigen, then the resulting immunological civil war spreads to a host tissue. Complementary antigens also alter antigen processing so that antigens that would normally be proteolytically digested are presented by the major histocompatibility complex (MHC) to T and B cell receptors inducing a cross-reactive immune response. The resulting civil war is supported by the innate immune system due to the complementarity of the initiating antigens.. Complementary antigens stimulate synergistic toll-like receptors (TLR) and/or nucleotide-binding oligomerization receptors (NOD) resulting in up-regulation of cytokine production and further stimulation of the adaptive immune response. Because the immune responses (e.g., antibodies) mimic the initiating antigens, this synergistic activation of innate immunity becomes chronic. Additionally, TLR and NOD function are highly sensitive to sex hormones, some becoming up-regulated and some down-regulated in the presence of either testosterone or estrogens. This sensitivity explains how sex modifies susceptibility to autoimmune diseases. Genetic mutations in TLR, NOD and MHC further alter antigen presentation and the degree to which antigens stimulate an immune response explaining how genetics also modifies susceptibility. Finally, sex hormones also alter the host microbiome, which in turn modulates autoimmune disease risk by shaping the immunological nature of self and by mediating susceptibility to microbial infection. Moreover, it appears that the microbiome camouflages itself from the immune system by mimicking the host antigenic repertoire; the mimicry between the antigens of the microbiome and the host results in selective attacks on microbiome constituents concomitant with any autoimmune attack on host tissues. This antigenic complementarity theory thereby integrates all major elements known to affect, or be affected by, autoimmune diseases and provides a set of testable implications.

The aim of the present work is to explore a different non-traditional approach to higher dimensional spacetime which differs from the usual approaches such as large extra space dimensions, warped extra space dimensions and multiple extra time dimensions. This approach will be referred to as "Dynamic" higher dimensional spacetime. By this term will be introduced a new kind of higher dimensional spacetime (more than the usual 3+1 dimensions), which behaves dynamically in the sense that time is not a fixed dimension but is the extra plus one dimension to the spatial dimensions of the phenomenon we are studying. For a higher dimensional phenomenon, the lower dimensional time will behave as space and the new time will be a plus one dimension, meaning if we study a 3-dimensional phenomenon then time is the usual 4th dimension but if we are studying a 4-dimensional phenomenon then its time will be an extra 5th dimension and for this phenomenon the 4th dimension will behave as space. All spatial dimensions are indistinguishable from each other and behave in the exact same way, which means that the important parameter is not the dimension we are studying (for example the 4th or the 5th) but the number of dimensions in which a phenomenon can interact and how higher dimensional phenomena interact with lower ones. This non-traditional approach to higher dimensional spacetime may appear confusing at first but will become clearer in the rest of the paper. For this reason, we will first associate the time dimension with propagation relative to space dimensions and change orthogonal to them in order to give the reader a better intuition. Following that, we will describe how higher - dimensional phenomena would appear to us, the 3 - dimensional observer and try to set some guidelines on how we should mathematically model higher - dimensional phenomena in order for us to make accurate predictions of their behaviour. Then we will express the general framework of a "Dynamic" higher - dimensional spacetime and turn our gaze to 4+1 – dimensional phenomena. We will explore how a mass term arises for 4 – dimensional waves by generalizing the frequency – speed – wavelength relation of 3D waves and give a basic description on a possible way to describe a 4+1 – dimensional disturbance in a scalar Energy Field in order to make accurate predictions on our 3+1 dimensional plane. In this framework we will derive the Klein – Gordon equation by generalizing the wave equation and ignoring all lower than 4+1 - dimensional disturbances and compere our mass term findings with the Klein – Gordon equation mass term and with results from gravity – induced quantum interference experiments. Lastly, we will describe how a "Dynamic" 5 - dimensional spacetime would appear in a 3D observer and examine whether our findings are compatible with quantum mechanics and the special theory of relativity.

Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number i, then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector i of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector i match the rules of multiplication and division of imaginary number i. Therefore, basis vector i is nothing but imaginary number i. Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms i, j and k. In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.

This work is a physical review, with elements of additions and thinning, on the methods of theoretical studies of nonlinear electrophysical phenomena in crystals with ion-molecular chemical bonds (CIMB). Crystals of this class include ionic dielectrics (characterized by high ionic conductivity), layered crystals, a special case of which are hydrogen-bonded crystals (HBC), defined as proton semiconductors and dielectrics (PSD).A scientific review (comparative analysis and justification of various approximations) was carried out on the methods of constructing and solving a generalized quasi-classical kinetic equation describing the mechanism of nonlinear relaxation polarization and conductivity processes in dielectric materials with ion-molecular chemical bonds (a special case is hydrogen-bonded crystals (HBC)) in a wide temperature range (1-1550 K) and polarizing field strengths (0.1-1000 V/m) at alternating field frequencies of the order of 1 kHz - 1000 MHz. The most important variant of the equations of the kinetic theory of dielectric relaxation in this work is the generalized non-linear by polarizing field quasi-classical kinetic equation of ionic (in HBC, proton) relaxation, based on the particle number balance equation (conductivity ions) in potential wells and having (in these models) the meaning of the ion current continuity equation (in HBC, protons), solved by the method of successive approximations by decomposition into infinite power series by degrees of a small dimensionless comparison parameter. It was found that in the area of ​ ​ weak fields (0.1-1 MW/m) at temperatures T = 50 - 550 K, for a number of ionic dielectrics (including HBC and similar dielectric properties and lattice structure) the generalized quasi-classical kinetic equation transforms to the linearized Fokker – Planck equation and, in the region of low (50-100K) and higher temperatures (250-550 K) begin to manifest non-linear polarization effects due to respectively proton tunneling (in the case of HBC) and volume charge relaxation (in the case of the HBC and for a wider class of ionic dielectrics). At ultra-low (1-10 K) temperatures in the region of weak fields (0.1-1 MW/m) and ultra-high temperatures (550-1550 K) in the region of strong fields (10-1000 MW/m), the contribution of this kind of effects to polarization is significantly enhanced. The effect of nonlinearities on relaxation times for microscopic acts of proton transitions across a potential barrier (assumed to be parabolic) is investigated. Nonlinear effects at volume-charge polarization in the hydrogen-bonded crystals (HBC) in alternating electric field, in radio frequency range are investigated. From the solution of the system of nonlinear Fokker-Planck equations (macroscopic kinetic equation) and Poisson, with blocking electrodes, using Fourier series, a recurrent (convenient for use in any approximation of perturbation theory) expression is constructed for complex amplitudes of relaxation modes of volumetric charge. Complex dielectric permittivity (CDP) is calculated as a series decomposition over even frequency harmonics of a variable field. The effect of quantum proton transitions and polarizing field parameters (strength, frequency) on the nonlinear properties of proton semiconductors and dielectrics has been established.

Two-Dimensional Nuclear Magnetic Resonance (2D NMR) spectroscopy has become a cornerstone in pharmaceutical research, offering enhanced structural elucidation capabilities for complex molecules. This technique overcomes the limitations of one-dimensional (1D) NMR by providing detailed insights into molecular interactions through the use of advanced spectroscopic methods like COSY, HSQC, and HMBC. In pharmaceutical applications, 2D NMR plays a crucial role in drug characterization, quality control, formulation development, and the structural analysis of natural products. Recent technological advancements such as high-field spectrometers and cryogenic probes have further improved the sensitivity and resolution of 2D NMR, making it indispensable for ensuring drug quality and intellectual property protection. This article delves into the principles and applications of 2D NMR in the pharmaceutical industry, highlighting its critical contributions to drug discovery, development, and quality assurance. Additionally, it addresses the future prospects of 2D NMR in areas like metabolomics, structural biology, and the development of new analytical tools. Despite its numerous advantages, 2D NMR presents challenges such as high operational costs, complexity in data analysis, and sensitivity issues when dealing with low-concentration samples. The article concludes by discussing the ongoing advancements in 2D NMR technology and its evolving role in pharmaceutical innovation.