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.     

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.     

A Statistical Journey through the Topological Determinants of the β2 Adrenergic Receptor Dynamics

Activation of G-protein-coupled receptors (GPCRs) is mediated by molecular switches throughout the transmembrane region of the receptor. In this work, we continued along the path of a previous computational study wherein energy transport in the β2 Adrenergic Receptor (β2-AR) was examined and allosteric switches were identified in the molecular structure through the reorganization of energy transport networks during activation. In this work, we further investigated the allosteric properties of β2-AR, using Protein Contact Networks (PCNs). In this paper, we report an extensive statistical analysis of the topological and structural properties of β2-AR along its molecular dynamics trajectory to identify the activation pattern of this molecular system. The results show a distinct character to the activation that both helps to understand the allosteric switching previously identified and confirms the relevance of the network formalism to uncover relevant functional features of protein molecules.     

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.     

New Parameterized Inequalities for η-Quasiconvex Functions via (p,q)-Calculus

In this work, first, we consider novel parameterized identities for the left and right part of the (p,q)-analogue of Hermite–Hadamard inequality. Second, using these new parameterized identities, we give new parameterized (p,q)-trapezoid and parameterized (p,q)-midpoint type integral inequalities via η-quasiconvex function. By changing values of parameter μ∈[0,1], some new special cases from the main results are obtained and some known results are recaptured as well. Finally, at the end, an application to special means is given as well. This new research has the potential to establish new boundaries in comparative literature and some well-known implications. From an application perspective, the proposed research on the η-quasiconvex function has interesting results that illustrate the applicability and superiority of the results obtained.     

Molecular structure,experimental and theoretical 1H and 13C NMR chemical shift assignment of cyclic and acyclic α,β‐unsaturated esters

The experimental ¹H and ¹³C NMR spectra of 13 phenyl cinnamates and four 4‐methylcoumarins were investigated and their chemical shifts assigned on the basis of the two‐dimensional spectra. For the unsubstituted cinnamic acid phenyl ester, optimized molecular structures were calculated at a B3LYP/6‐311++G(d,p) level of theory. ¹H and ¹³C NMR chemical shifts were also calculated with the GIAO method at the B3LYP/6‐311 + G(2d,p) level of theory. The comparison between experimental and calculated NMR chemical shift suggests that the experimental spectra are formed from the superposition spectra of the two lowest energy conformers of the compound in solution. The most stable s‐cis configuration found in our studies is also the conformation adopted for a related phenyl cinnamate in solid state. The experimental results were analyzed in terms of the substituent effects. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust Aggregation for Federated Learning by Minimum γ-Divergence Estimation

Federated learning is a framework for multiple devices or institutions, called local clients, to collaboratively train a global model without sharing their data. For federated learning with a central server, an aggregation algorithm integrates model information sent from local clients to update the parameters for a global model. Sample mean is the simplest and most commonly used aggregation method. However, it is not robust for data with outliers or under the Byzantine problem, where Byzantine clients send malicious messages to interfere with the learning process. Some robust aggregation methods were introduced in literature including marginal median, geometric median and trimmed-mean. In this article, we propose an alternative robust aggregation method, named γ-mean, which is the minimum divergence estimation based on a robust density power divergence. This γ-mean aggregation mitigates the influence of Byzantine clients by assigning fewer weights. This weighting scheme is data-driven and controlled by the γ value. Robustness from the viewpoint of the influence function is discussed and some numerical results are presented.     

Superheating Control of ORC Systems via Minimum (h,φ)-Entropy Control

The Organic Rankine Cycle (ORC) is one kind of appropriate energy recovery techniques for low grade heat sources. Since the mass flow rate and the inlet temperature of heat sources usually experience non-Gaussian fluctuations, a conventional linear quadratic performance criterion cannot characterize the system uncertainties adequately. This paper proposes a new model free control strategy which applies the (h,φ)-entropy criterion to decrease the randomness of controlled ORC systems. In order to calculate the (h,φ)-entropy, the kernel density estimation (KDE) algorithm is used to estimate the probability density function (PDF) of the tracking error. By minimizing the performance criterion mainly consisting of (h,φ)-entropy, a new control algorithm for ORC systems is obtained. The stability of the proposed control system is analyzed. The simulation results show that the ORC system under the proposed control method has smaller standard deviation (STD) and mean squared error (MSE), and reveals less randomness than those of the traditional PID control algorithm.     

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.     

The astrophysical S-factor of the reaction 7Be (p, γ)8B in the direct capture model

The astrophysical S-factor for the reaction ⁷Be(p, γ)⁸B up to an energy of 2 MeV (c.m.) and the capture cross section of ⁷Li(n,γ)⁸Li up to 1 MeV (c.m.) are calculated using the Direct Capture model (DC). Both calculations are in good agreement with experimental data.     

Adaptive Diagnosis for Fault Tolerant Data Fusion Based on α-Rényi Divergence Strategy for Vehicle Localization

When applying a diagnostic technique to complex systems, whose dynamics, constraints, and environment evolve over time, being able to re-evaluate the residuals that are capable of detecting defaults and proposing the most appropriate ones can quickly prove to make sense. For this purpose, the concept of adaptive diagnosis is introduced. In this work, the contributions of information theory are investigated in order to propose a Fault-Tolerant multi-sensor data fusion framework. This work is part of studies proposing an architecture combining a stochastic filter for state estimation with a diagnostic layer with the aim of proposing a safe and accurate state estimation from potentially inconsistent or erroneous sensors measurements. From the design of the residuals, using α-Rényi Divergence (α-RD), to the optimization of the decision threshold, through the establishment of a function that is dedicated to the choice of α at each moment, we detail each step of the proposed automated decision-support framework. We also dwell on: (1) the consequences of the degree of freedom provided by this α parameter and on (2) the application-dictated policy to design the α tuning function playing on the overall performance of the system (detection rate, false alarms, and missed detection rates). Finally, we present a real application case on which this framework has been tested. The problem of multi-sensor localization, integrating sensors whose operating range is variable according to the environment crossed, is a case study to illustrate the contributions of such an approach and show the performance.     

λ-Deformation: A Canonical Framework for Statistical Manifolds of Constant Curvature

This paper systematically presents the λ-deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry. We show that, based on deforming the Legendre duality, all objects in the Hessian case have their correspondence in the λ-deformed case: λ-convexity, λ-conjugation, λ-biorthogonality, λ-logarithmic divergence, λ-exponential and λ-mixture families, etc. In particular, λ-deformation unifies Tsallis and Rényi deformations by relating them to two manifestations of an identical λ-exponential family, under subtractive or divisive probability normalization, respectively. Unlike the different Hessian geometries of the exponential and mixture families, the λ-exponential family, in turn, coincides with the λ-mixture family after a change of random variables. The resulting statistical manifolds, while still carrying a dualistic structure, replace the Hessian metric and a pair of dually flat conjugate affine connections with a conformal Hessian metric and a pair of projectively flat connections carrying constant (nonzero) curvature. Thus, λ-deformation is a canonical framework in generalizing the well-known dually flat Hessian structure of information geometry.     

Volatile metal β-diketonates — new precursors for the sonochemical synthesis of nanosized materials — sonolysis of thorium(IV) β-diketonates

Ultrasonic irradiation (22 kHz, Ar atmosphere) of Th(IV) β-diketonates Th(HFAA)₄ and Th(DBM)₄, where HFAA and DBM are hexafluoroacetylacetone and dibenzoylmethane respectively, causes them to decompose in hexadecane solutions, forming solid thorium compounds. The first-order rate constants for Th(IV) β-diketonate degradation were found to be (9.3±0.8)×10⁻³ for Th(HFAA)₄ and (3.8±0.4)×10⁻³ min⁻¹ for Th(DBM)₄, (T=92°C, I=3 W cm⁻²). The rate of the sonochemical reaction increased with the rising β-diketonate volatility and decreased with the rising hydrocarbon solvent vapor pressure. Solid sonication products consisted of a mixture of thorium carbide ThC₂ and Th(IV) β-diketonate partial degradation products. The average ThC₂ particle size was estimated to be about 2 nm. ThC₂ formation was attributed to the high-temperature reaction occurring within the cavitating bubble. The thorium β-diketonate partial degradation products formed in the liquid reaction zones surrounding the cavitating bubbles.     

Mechanistic study on Mo(CO)6‐catalyzed intramolecular [2 + 2] or [2 + 2 + 1] cycloaddition reaction of 5‐allenyl‐1‐ynes

By means of density functional theory, the Mo(CO)₆‐catalyzed intramolecular [2 + 2] or [2 + 2 + 1] cycloaddition reaction of 5‐allenyl‐1‐ynes was investigated. All the intermediates and transition states were optimized completely at B3LYP/6‐311++G(d,p) level (LANL2DZ(f) for Mo). Calculations indicate that the complexation of 5‐allenyl‐1‐ynes with Mo(CO)₆ occurred preferentially at the triple bond to give the complex M1 and then the complexation with the distal double bond of the allenes generates the complex M5 . In this reaction, Mo(CO)₆‐catalyzed intramolecular [2 + 2] cycloaddition is more favorable than [2 + 2 + 1] cycloaddition. The reaction pathway Mo(CO)₆ + R → M5 → T7 → M12 → M13 → T11 → M18 → P4 is the most favorable one, and the most dominant product predicted theoretically is P4 . The solvation effect is remarkable, and it decreases the reaction energy barriers. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

DFT study the interaction of β‐cyclodextrin with benzyl azide and phenyl acetylene in synthesis of 1,2,3‐triazoles

The phenyl acetylene and benzyl azide cycloaddition reaction in water in the presence of β‐cyclodextrin (β‐CD) as a phase transfer catalyst (PTC) can get a better yield in a shorter time. The interaction between β‐CD and phenyl acetylene or benzyl azide plays an important role in this reaction. This paper studies the complexes of β‐CD with phenyl acetylene and benzyl azide using density functional theory (DFT) method. In order to find out the orientations of guests in the cavity of β‐CD, binding energy and deformation energy are investigated, and the calculated results are confirmed by ¹H nuclear magnetic resonance (¹HNMR). The data from single point energy indicate that the inclusion complexes can improve the solubilities of phenyl acetylene and benzyl azide in water. The ¹³C and ¹⁵N spectra show that the most obvious variation concentrates on C₆ and C₈ of phenyl acetylene and N₁₅ of benzyl azide in complexes. Mulliken charge and frontier orbital are employed for revealing the charge distribution. The effect of β‐CD is discussed in terms of the calculated parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

β‐Elimination of an aziridine to an allylic amine: a mechanistic study

The base‐induced rearrangement of aziridines has been examined using a combination of calculations and experiment. The calculations show that the substituent on nitrogen is a critical feature that greatly affects the favorability of both α‐deprotonation, and β‐elimination to form an allylic amine. Experiments were carried out to determine whether E2‐like rearrangement to the allylic amine with lithium diisopropyl amide (LDA) is possible. N‐tosyl aziridines were found to deprotonate on the tosyl group, preventing further reaction. A variety of N‐benzenesulfonyl aziridines having both α‐ and β‐protons decomposed when treated with LDA in either tetrahydrofuran or hexamethylphosphoramide. However, when α‐protons were not present, allylic amine was formed, presumably via β‐elimination. Copyright © 2011 John Wiley & Sons, Ltd.     

Solid phase synthesis of novel α/β‐tetrapeptides,electrospray ionization mass spectrometric evaluation of their metal cation complexation behavior,and conformational analysis using density functional theory (DFT)

Thirty‐four novel α/β‐tetrapeptides ( 1–34 ) have been prepared employing solid‐phase and in‐parallel synthetic protocols. α/β ‐Tetrapeptides 1 – 34 were prepared by a combination of three α‐amino acid residues (alanine (Ala), phenylalanine (Phe), and isoleucine (Ile)) with one β‐amino acid residue (β³‐homophenylglycine). The corresponding complexes of several selected α/β‐tetrapeptides with alkali, alkaline earth, and transition metals, [tP + M⁺], were evaluated using ion electrospray‐ionization mass spectrometry (ESI‐MS). According to the results from analysis of mixtures, we can conclude that the position of the β‐amino acid is determinant in the affinity toward different metal cations. Computational modeling (DFT, B3LYP 6‐311++G) provided useful information regarding the most likely coordination sites of the metal ions on the receptor α/β‐tetrapeptide 12 , HO₂C‐α‐Phe‐α‐Phe‐α‐Ile‐β³‐hPhg‐NH₂, as well as the conformational changes induced by the metal upon [tP + M⁺] complex formation. Copyright © 2008 John Wiley & Sons, Ltd.     

Decay Dynamics of 3‐methyl‐3‐pentene‐2‐one from the light absorbing S2(ππ*) state ‐ Resonance Raman Spectroscopy and CASSCF Study

The photophysics of 3‐methyl‐3‐pentene‐2‐one (3M3P2O) after excitation to the S₂(ππ*) electronic state were studied using the resonance Raman spectroscopy and complete active space self‐consistent field (CASSCF) method calculations. The A‐band resonance Raman spectra were obtained in cyclohexane, acetonitrile, and methanol with excitation wavelengths in resonance with the first intense absorption band to probe the structural dynamics of 3M3P2O. The B3LYP‐TD/6‐31++G(d, p) computation was carried out to determine the relative A‐band resonance Raman intensities of the fundamental modes, and the result was used to reproduce the corresponding fundamental band intensities of the 223.1 nm resonance Raman spectrum and thus to examine whether the vibronic‐coupling existed in Franck‐Condon region or not. CASSCF calculations were carried out to determine the minimal singlet excitation energies of S_{1, FC}, S_1,min (nπ*), S_{2, FC}, S_2,min (ππ*), the transition energies of the conical intersection points S_n/S_π, S_n/S₀, and the optimized excited state geometries as well as the geometry structures of the conical intersection points. The A‐band short‐time structural dynamics and the corresponding decay dynamics of 3M3P2O were obtained by the analysis of the resonance Raman intensity pattern and CASSCF computations. It was revealed that the initial structural dynamics of 3M3P2O was towards the simultaneous C₃=C₄ and C₂=O₇ bond elongation, with the C₃=C₄ bond length lengthening greater at the very beginning, whereas the C₂=O₇ bond length changing greater at the later evolution time before reaching the CI(S₂/S₁) conical intersection point. The decay dynamics from S₂(ππ*) to S₁(nπ*) via S₂(ππ*)/S₁(nπ*) in singlet realm and from S₁(nπ*) to T₁(nπ*) via ISC[S₁(nπ*)/T₂(ππ*)/T₁(nπ*)] in triplet realm are proposed. Copyright © 2014 John Wiley & Sons, Ltd.