On the α-q-Mutual Information and the α-q-Capacities

The measures of information transfer which correspond to non-additive entropies have intensively been studied in previous decades. The majority of the work includes the ones belonging to the Sharma–Mittal entropy class, such as the Rényi, the Tsallis, the Landsberg–Vedral and the Gaussian entropies. All of the considerations follow the same approach, mimicking some of the various and mutually equivalent definitions of Shannon information measures, and the information transfer is quantified by an appropriately defined measure of mutual information, while the maximal information transfer is considered as a generalized channel capacity. However, all of the previous approaches fail to satisfy at least one of the ineluctable properties which a measure of (maximal) information transfer should satisfy, leading to counterintuitive conclusions and predicting nonphysical behavior even in the case of very simple communication channels. This paper fills the gap by proposing two parameter measures named the α-q-mutual information and the α-q-capacity. In addition to standard Shannon approaches, special cases of these measures include the α-mutual information and the α-capacity, which are well established in the information theory literature as measures of additive Rényi information transfer, while the cases of the Tsallis, the Landsberg–Vedral and the Gaussian entropies can also be accessed by special choices of the parameters α and q. It is shown that, unlike the previous definition, the α-q-mutual information and the α-q-capacity satisfy the set of properties, which are stated as axioms, by which they reduce to zero in the case of totally destructive channels and to the (maximal) input Sharma–Mittal entropy in the case of perfect transmission, which is consistent with the maximum likelihood detection error. In addition, they are non-negative and less than or equal to the input and the output Sharma–Mittal entropies, in general. Thus, unlike the previous approaches, the proposed (maximal) information transfer measures do not manifest nonphysical behaviors such as sub-capacitance or super-capacitance, which could qualify them as appropriate measures of the Sharma–Mittal information transfer.     

A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups

A complex fuzzy set is a vigorous framework to characterize novel machine learning algorithms. This set is more suitable and flexible compared to fuzzy sets, intuitionistic fuzzy sets, and bipolar fuzzy sets. On the aspects of complex fuzzy sets, we initiate the abstraction of (α,β)-complex fuzzy sets and then define -complex fuzzy subgroups. Furthermore, we prove that every complex fuzzy subgroup is an (α,β)-complex fuzzy subgroup and define (α,β)-complex fuzzy normal subgroups of given group. We extend this ideology to define (α,β)-complex fuzzy cosets and analyze some of their algebraic characteristics. Furthermore, we prove that (α,β)-complex fuzzy normal subgroup is constant in the conjugate classes of group. We present an alternative conceptualization of (α,β)-complex fuzzy normal subgroup in the sense of the commutator of groups. We establish the (α,β)-complex fuzzy subgroup of the classical quotient group and show that the set of all (α,β)-complex fuzzy cosets of this specific complex fuzzy normal subgroup form a group. Additionally, we expound the index of -complex fuzzy subgroups and investigate the (α,β)-complex fuzzification of Lagrange’s theorem analog to Lagrange’ theorem of classical group theory.     

Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,…,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.     

Changing the Geometry of Representations: α-Embeddings for NLP Tasks

Word embeddings based on a conditional model are commonly used in Natural Language Processing (NLP) tasks to embed the words of a dictionary in a low dimensional linear space. Their computation is based on the maximization of the likelihood of a conditional probability distribution for each word of the dictionary. These distributions form a Riemannian statistical manifold, where word embeddings can be interpreted as vectors in the tangent space of a specific reference measure on the manifold. A novel family of word embeddings, called α-embeddings have been recently introduced as deriving from the geometrical deformation of the simplex of probabilities through a parameter α, using notions from Information Geometry. After introducing the α-embeddings, we show how the deformation of the simplex, controlled by α, provides an extra handle to increase the performances of several intrinsic and extrinsic tasks in NLP. We test the α-embeddings on different tasks with models of increasing complexity, showing that the advantages associated with the use of α-embeddings are present also for models with a large number of parameters. Finally, we show that tuning α allows for higher performances compared to the use of larger models in which additionally a transformation of the embeddings is learned during training, as experimentally verified in attention models.     

Novel plasma biomarker surrogating cerebral amyloid deposition

Alzheimer’s disease (AD) is the most common and devastating dementia. Simple and practical biomarkers for AD are urgently required for accurate diagnosis and to facilitate the development of disease-modifying interventions. The subjects for the study were selected on the basis of PiB amyloid imaging by PET. Forty PiB-positive (PiB+) individuals, including cognitively healthy controls (HC), and mild cognitive impairment and AD individuals, and 22 PiB-negative (PiB−) HC participated. Employing our novel highly sensitive immunoprecipitation-mass spectrometry, we measured plasma amyloid β-proteins (Aβs; Aβ1-40 and Aβ1-42) and Aβ-approximate peptides (AβAPs), which were cleaved from amyloid precursor protein (APP). Among the AβAPs, APP669-711 appeared to be a good reference for deciphering pathological change of Aβ1-42. We evaluated the performance of the ratio of APP669-711 to Aβ1-42 (APP669-711/Aβ1-42) as a biomarker. APP669-711/Aβ1-42 significantly increased in the PiB+ groups. The sensitivity and specificity to discriminate PiB+ individuals from PiB− individuals were 0.925 and 0.955, respectively. Our plasma biomarker precisely surrogates cerebral amyloid deposition.     

Challenge to the suppression of tumor growth by the β4-galactosyltransferase genes

It has been well established that structural changes in glycans attached to proteins and lipids are associated with malignant transformation of cells. We focused on galactose residues among the sugars since they are involved in the galectin-mediated biology, and many carbohydrate antigens are frequently expressed on this sugar. We found changes in the expression of the β4-galactosyltransferase (β4GalT) 2 and 5 genes in cancer cells: decreased expression of the β4GalT2 gene and increased expression of the β4GalT5 gene. The growth of mouse melanoma cells showing enhanced expression of the β4GalT2 gene or reduced expression of the β4GalT5 gene is inhibited remarkably in syngeneic mice. Tumor growth inhibition is probably caused by the induction of apoptosis, inhibition of angiogenesis, and/or reduced MAPK signals. Direct transduction of human β4GalT2 cDNA together with the adenovirus vector into human hepatocellular carcinoma cells grown in SCID mice results in marked growth retardation of the tumors. β4GalT gene-transfer appears to be a potential tool for cancer therapy.     

The biological significance of ω-oxidation of fatty acids

The author focuses on the biological significance of ω-oxidation of fatty acids. Early studies revealed that there is a subsidiary pathway for β-oxidation of fatty acids when β-oxidation is blocked. Many studies demonstrated that the ω-oxidation serves to provide succinyl-CoA for the citric acid cycle and for gluconeogenesis under conditions of starvation and diabetes. Acylglucosylceramides which are composed of linoleic acid, long chain ω-hydroxy fatty acids, eicosasphingenine (or trihydroxyeicosasphingenine) and glucose, are responsible for normal epidermal permeability function in the skin. It is observed that ω- and (ω-1)-oxidation of fatty acids are related to energy metabolism in some laboratory animals such as musk shrews and Mongolian gerbils. Studies confirmed that ω- and (ω-1)-oxidation of fatty acids play crucial roles in the production of insect pheromones of honeybees and in the formation of biopolyesters of higher plants. In addition, the biological significance of ω-oxidation of prostaglandins and leukotrienes is described.     

Error Exponents and α-Mutual Information

Over the last six decades, the representation of error exponent functions for data transmission through noisy channels at rates below capacity has seen three distinct approaches: (1) Through Gallager’s E0 functions (with and without cost constraints); (2) large deviations form, in terms of conditional relative entropy and mutual information; (3) through the α-mutual information and the Augustin–Csiszár mutual information of order α derived from the Rényi divergence. While a fairly complete picture has emerged in the absence of cost constraints, there have remained gaps in the interrelationships between the three approaches in the general case of cost-constrained encoding. Furthermore, no systematic approach has been proposed to solve the attendant optimization problems by exploiting the specific structure of the information functions. This paper closes those gaps and proposes a simple method to maximize Augustin–Csiszár mutual information of order α under cost constraints by means of the maximization of the α-mutual information subject to an exponential average constraint.     

Identification and quantification of amyloid beta-related peptides in human plasma using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Proteolytic processing of the amyloid precursor protein (APP) by β-secretase and γ-secretase leads to the generation and deposition of amyloid β (Aβ) in Alzheimer’s disease (AD). N-terminally or C-terminally truncated Aβ variants have been found in human cerebrospinal fluid and cultured cell media using immunoprecipitation and mass spectrometry. Unfortunately, the profile of plasma Aβ variants has not been revealed due to the difficulty of isolating Aβ from plasma. We present here for the first time studies of Aβ and related peptides in human plasma. Twenty-two Aβ-related peptides including novel peptides truncated before the β-secretase site were detected in human plasma and 20 of the peptides were identified by tandem mass spectrometry. Using an internal standard, we developed a quantitative assay for the Aβ-related peptides and demonstrated plasma dilution linearity and the precision required for their quantitation. The present method should enhance the understanding of APP processing and clearance in AD progression.     

ϕ-Informational Measures: Some Results and Interrelations

In this paper, we focus on extended informational measures based on a convex function ϕ: entropies, extended Fisher information, and generalized moments. Both the generalization of the Fisher information and the moments rely on the definition of an escort distribution linked to the (entropic) functional ϕ. We revisit the usual maximum entropy principle—more precisely its inverse problem, starting from the distribution and constraints, which leads to the introduction of state-dependent ϕ-entropies. Then, we examine interrelations between the extended informational measures and generalize relationships such the Cramér–Rao inequality and the de Bruijn identity in this broader context. In this particular framework, the maximum entropy distributions play a central role. Of course, all the results derived in the paper include the usual ones as special cases.     

Metabolism of amyloid β peptide and pathogenesis of Alzheimer’s disease

The conversion of what has been interpreted as “normal brain aging” to Alzheimer’s disease (AD) via transition states, i.e., preclinical AD and mild cognitive impairment, appears to be a continuous process caused primarily by aging-dependent accumulation of amyloid β peptide (Aβ) in the brain. This notion however gives us a hope that, by manipulating the Aβ levels in the brain, we may be able not only to prevent and cure the disease but also to partially control some very significant aspects of brain aging. Aβ is constantly produced from its precursor and immediately catabolized under normal conditions, whereas dysmetabolism of Aβ seems to lead to pathological deposition upon aging. We have focused our attention on elucidation of the unresolved mechanism of Aβ catabolism in the brain. In this review, I describe a new approach to prevent AD development by reducing Aβ burdens in aging brains through up-regulation of the catabolic mechanism involving neprilysin that can degrade both monomeric and oligomeric forms of Aβ. The strategy of combining presymptomatic diagnosis with preventive medicine seems to be the most pragmatic in both medical and socioeconomical terms.     

Kullback–Leibler Divergence of a Freely Cooling Granular Gas

Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original H-theorem hypotheses do not fit here and the H-functional presents some additional measure problems that are solved by the Kullback–Leibler divergence (KLD) of a reference velocity distribution function from the actual distribution. The right choice of the reference distribution in the KLD is crucial for the latter to qualify or not as a Lyapunov functional, the asymptotic “homogeneous cooling state” (HCS) distribution being a potential candidate. Due to the lack of a formal proof far from the quasielastic limit, the aim of this work is to support this conjecture aided by molecular dynamics simulations of inelastic hard disks and spheres in a wide range of values for the coefficient of restitution (α) and for different initial conditions. Our results reject the Maxwellian distribution as a possible reference, whereas they reinforce the HCS one. Moreover, the KLD is used to measure the amount of information lost on using the former rather than the latter, revealing a non-monotonic dependence with α.     

Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C∗-Algebras

A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.     

From Rényi Entropy Power to Information Scan of Quantum States

In this paper, we generalize the notion of Shannon’s entropy power to the Rényi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the Rényi entropy power obtained, we show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called “cat states”, which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.     

A group of glycosphingolipids found in an invertebrate: Their structures and biological significance

A novel group of glycosphingolipids was identified in the nervous tissue and skin of the mollusc, Aplysia kurodai, which lacks gangliosides. More than 30 glycolipids were detected on HPTLC plates and the structures of 9 major glycolipids were determined. They were pentaosylglycosphingolipids and their common core structure was GalNAcα1→3Galβ1→4Glcβ1→1ceramide, except for one glycolipid in which Galβ of the core structure was replaced by Galα. 3-O-MeGalβ or 4-O-MeGlcNAcα or 3,4-O-carboxyethylideneGalβ was at their non-reducing ends. Galα or Fucα binds to Gal of the core structure at 2C as a side chain sugar. One to three 2-aminoethylphosphonic acids and/or phosphoethanolamine link to the glycolipids. Immunohistochemically, glycolipids having carboxyethylideneGal at their non-reducing ends were localized exclusively in nerve bundles. Glycolipids activated cAMP-dependent protein kinase in the rat brain and may directly activate cAMP-dependent protein kinase in a manner similar, but not identical, to that of cAMP. The biological functions of glycolipids may share neurobiological functions proposed for gangliosides in vertebrates.     

Vitamin D and bone: — How does vitamin D regulate bone formation and resorption? —

Vitamin D was discovered as an anti-rachitic agent, but even at present, there is no direct evidence to support the concept that vitamin D directly stimulates osteoblastic bone formation and mineralization. It appears to be paradoxical, but vitamin D functions in the process of osteoclastic bone resorption. Osteoclasts, the only cells responsible for bone resorption, develop from hematopoietic cells of the monocyte-macrophage lineage. In 1992, we hypothesized that a membrane-bound factor, designated as “osteoclast differentiation factor (ODF)”, is expressed on the plasma membrane of osteoblasts/stromal cells in response to osteotropic factors including the active form of vitamin D₃, 1α,25-dihydroxyvitamin D₃ [1α,25(OH)₂D₃]. Recently, four research groups including ours independently identified three key molecules (RANKL, RANK, and OPG) responsible for osteoclastogenesis. A long-sought-after ligand, ODF, was identical to RANKL. RANKL was a member of the membrane-associated TNF ligand family, which induced differentiation of spleen cells (osteoclast progenitors) into osteoclasts in the presence of M-CSF. RANK, a member of the TNF receptor family, was a signaling receptor essential for the RANKL-mediated osteoclastogenesis. OPG, a secreted member of the TNF receptor family, was a decoy receptor for RANKL. The discovery of RANKL, RANK and OPG opens a new era in the study of bone biology and the therapy of several metabolic bone diseases such as osteoporosis, rheumatoid arthritis, and periodontal diseases.     

Optimal management of waste loading into a river system with nonpoint source pollutants

An optimization model, fit for practical use, to allocate COD (Chemical Oxygen Demand)-based wasteload into a river system among outfalls is developed within the framework of robust optimization (RO). Nonpoint source COD loading, estimated based on the unit loading factor to be assumed known, is treated as uncontrollable one. The total amount of expected allowable COD load from point sources is then, under all possible scenarios of uncertain input information, maximized while satisfying the constraints on in-stream COD and DO (Dissolved Oxygen) transport, effluent standards and river water quality standards. Advantage of the ε-RO model using the ε-constraint method for optimization practice is brought to light from theoretical and practical aspects, in comparison with the conventional RO model resorting to the Lagrangian method. Solving a simple hypothetical example problem, it is demonstrated that the model developed is competent for successfully generating noninferior and robust solutions on optimal COD load allocation.     

Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity

A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width δr between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as δr∼M3; (b) for supermassive black holes δr is typically orders of magnitude larger than the Planck length lP. Instead, for typical stellar-mass black holes, δr may drop well below lP. The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons.     

Contribution to ε′/ε from anomalous gauge couplings

Recently the KTev Collaboration has measured Re (ε′/ε)=(28±4.1)×10⁻⁴ which is in agreement with early measurements from NA31. The Standard Model prediction for ε′/ε is on the lower end of the experimentally allowed range depending on models for hadronic matrix elements. In this paper we study the contributions from anomalous gauge couplings. We find that the contributions from anomalous couplings can be significant and can enhance ε′/ε to have a value closer to data.     

On Default Priors for Robust Bayesian Estimation with Divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.