An equation proposed by Levy, Perdew and Sahni (Phys. Rev. A 30:2745, 1984) is an orbital-free formulation of density functional theory. However, this equation describes a bosonic system. Here, we analyze on a very fundamental level, how this equation could be extended to yield a formulation for a general fermionic distribution of charge and spin. This analysis starts at the level of single electrons and with the question, how spin actually comes into a charge distribution (...) in a non-relativistic model. To this end we present a space-time model of extended electrons, which is formulated in terms of geometric algebra. Wave properties of the electron are referred to mass density oscillations. We provide a comprehensive and non-statistical interpretation of wavefunctions, referring them to mass density components and internal field components. It is shown that these wavefunctions comply with the Schrödinger equation, for the free electron as well as for the electron in electrostatic and vector potentials. Spin-properties of the electron are referred to intrinsic field components and it is established that a measurement of spin in an external field yields exactly two possible results. However, it is also established that the spin of free electrons is isotropic, and that spin-dynamics of single electrons can be described by a modified Landau-Lifshitz equation. The model agrees with the results of standard theory concerning the hydrogen atom. Finally, we analyze many-electron systems and derive a set of coupled equations suitable to characterize the system without any reference to single electron states. The model is expected to have the greatest impact in condensed matter theory, where it allows to describe an N-electron system by a many-electron wavefunction Ψ of four, instead of 3N variables. The many-body aspect of a system is in this case encoded in a bivector potential. (shrink)

We review the early works which were precursors of the Conceptual Density Functional Theory. Starting from Thomas–Fermi approximation and from the exact formulation of Density Functional Theory by Hohenberg and Kohn’s theorem, we will introduce electronegativity and the theory of hard and soft acids and bases. We will also present a general introduction to the Fukui functions, and their relation with nucleophilicity and electrophilicity, with an emphasis towards the importance of these concepts for (...) chemical reactivity. (shrink)

The core structures of d 111 ¢ screw dislocations in bcc metals are studied using density functional theory in the local-density approximation. For Mo and Fe, direct calculations of the core structures show the cores to be symmetric with respect to 180° rotations around an axis perpendicular to the dislocation line. The magnetic moment in the Fe core is shown to be reduced relative to the bulk value. Calculations of n surfaces and the elastic constants B (...) , C ' and c 44 are reported for Fe and all group VB and VIB metals. Using a criterion suggested by Vitek and Duesbery the calculations point to symmetric core structures for all the studied metals. (shrink)

Hydrogen activation on the (100) surface of MoS2 structures was investigated by means of density functional theory calculations. Linear and quadratic synchronous transit methods with a conjugate gradient refinement of the saddle point were used to localize transition states. The calculations include heterolytic and homolytic dissociation of hydrogen; that is, an H2 molecule dissociates on an MoS2 catalyst surface into two hydrogen atoms, which react further with the catalyst surface under formation of either one Mo-H and one (...) S-H (heterolytic) or of two S-H surface groups (homolytic). Our results favor the heterolytic adsorption of hydrogen. Ni- and Co-promoted MoS2 have been considered to investigate the secondary promotional effect on the H2 dissociation. The authors observed a negative secondary promotional influence on the H2 dissociation in the case of Ni-promoted MoS2, whereas Co shows a positive effect. (shrink)

Douglas Hartree and Hilleth Thomas were graduate students together at Cambridge University in the mid-1920s. Each developed an important approximation method to calculate the electronic structure of atoms. Each went on to make significant contributions to numerical analysis and to the development of scientific computing. Their early efforts were fused in the mid-1960s with the development of an approach to the many-particle problem in quantum mechanics called density functional theory. This paper discusses the experiences which led Hartree (...) and Thomas to their approximations, outlines the similarities in their subsequent careers, and highlights the essential role their work played in the foundational papers of modern density functional theory. (shrink)

The theoretical solid-state physicist Walter Kohn was awarded one-half of the 1998 Nobel Prize in Chemistry for his mid-1960s creation of an approach to the many-particle problem in quantum mechanics called density functional theory (DFT). In its exact form, DFT establishes that the total charge density of any system of electrons and nuclei provides all the information needed for a complete description of that system. This was a breakthrough for the study of atoms, molecules, gases, liquids, (...) and solids. Before DFT, it was thought that knowledge of the vastly more complicated many-electron wave function was essential for a complete description of such systems. Today, 50 years after its introduction, DFT (in one of its approximate forms) is the method of choice used by most scientists to calculate the physical properties of materials of all kinds. In this paper, I present a biographical essay of Kohn’s educational experiences and professional career up to and including the creation of DFT. My account begins with Kohn’s student years in Austria, England, and Canada during World War II and continues with his graduate and postgraduate training at Harvard University and Niels Bohr’s Institute for Theoretical Physics in Copenhagen. I then study the research choices he made during the first 10 years of his career (when he was a faculty member at the Carnegie Institute of Technology and a frequent visitor to the Bell Telephone Laboratories) in the context of the theoretical solid-state physics agenda of the late 1950s and early 1960s. Subsequent sections discuss his move to the University of California, San Diego, identify the research issue which led directly to DFT, and analyze the two foundational papers of the theory. The paper concludes with an explanation of how the chemists came to award “their” Nobel Prize to the physicist Kohn and a discussion of why he was unusually well suited to create the theory in the first place. (shrink)

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation (...) invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

We provide an application of a sequent calculus framework to the formalization of definite descriptions. It is a continuation of research undertaken in [20, 22]. In the present paper a so-called free description theory is examined in the context of different kinds of free logic, including systems applied in computer science and constructive mathematics for dealing with partial functions. It is shown that the same theory in different logics may be formalised by means of different rules (...) and gives results of varying strength. For all presented calculi a constructive cut elimination is provided. (shrink)

We observe that Schrödinger’s equation may be written as two real coupled Hamilton–Jacobi (HJ)-like equations, each involving a quantum potential. Developing our established programme of representing the quantum state through exact free-standing deterministic trajectory models, it is shown how quantum evolution may be treated as the autonomous propagation of two coupled congruences. The wavefunction at a point is derived from two action functions, each generated by a single trajectory. The model shows that conservation as expressed through a continuity equation (...) is not a necessary component of a trajectory theory of state. Probability is determined by the difference in the action functions, not by the congruence densities. The theory also illustrates how time-reversal symmetry may be implemented through the collective behaviour of elements that individually disobey the conventional transformation (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}) of displacement (scalar) and velocity (reversal). We prove that an integral curve of the linear superposition of two vectors can be derived algebraically from the integral curves of one of the constituent vectors labelled by integral curves associated with the other constituent. A corollary establishes relations between displacement functions in diverse trajectory models, including where the functions obey different symmetry transformations. This is illustrated by showing that a (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}-obeying) de Broglie-Bohm trajectory is a sequence of points on the (non-T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}) HJ trajectories, and vice versa. (shrink)

The aim of this paper is twofold: (1) to assess whether the construct of neural representations plays an explanatory role under the variational free-energy principle and its corollary process theory, active inference; and (2) if so, to assess which philosophical stance - in relation to the ontological and epistemological status of representations - is most appropriate. We focus on non-realist (deflationary and fictionalist-instrumentalist) approaches. We consider a deflationary account of mental representation, according to which the explanatorily relevant contents (...) of neural representations are mathematical, rather than cognitive, and a fictionalist or instrumentalist account, according to which representations are scientifically useful fictions that serve explanatory (and other) aims. After reviewing the free-energy principle and active inference, we argue that the model of adaptive phenotypes under the free-energy principle can be used to furnish a formal semantics, enabling us to assign semantic content to specific phenotypic states (the internal states of a Markovian system that exists far from equilibrium). We propose a modified fictionalist account: an organism-centered fictionalism or instrumentalism. We argue that, under the free-energy principle, pursuing even a deflationary account of the content of neural representations licenses the appeal to the kind of semantic content involved in the aboutness or intentionality of cognitive systems; our position is thus coherent with, but rests on distinct assumptions from, the realist position. We argue that the free-energy principle thereby explains the aboutness or intentionality in living systems and hence their capacity to parse their sensory stream using an ontology or set of semantic factors. (shrink)

It is argued that some elusive “entropic” characteristics of chemical bonds, e.g., bond multiplicities (orders), which connect the bonded atoms in molecules, can be probed using quantities and techniques of Information Theory (IT). This complementary perspective increases our insight and understanding of the molecular electronic structure. The specific IT tools for detecting effects of chemical bonds and predicting their entropic multiplicities in molecules are summarized. Alternative information densities, including measures of the local entropy deficiency or its displacement relative to (...) the system atomic promolecule, and the nonadditive Fisher information in the atomic orbital resolution(called contragradience) are used to diagnose the bonding patterns in illustrative diatomic and polyatomic molecules. The elements of the orbital communication theory of the chemical bond are briefly summarized and illustrated for the simplest case of the two-orbital model. The information-cascade perspective also suggests a novel, indirect mechanism of the orbital interactions in molecular systems, through “bridges” (orbital intermediates), in addition to the familiar direct chemical bonds realized through “space”, as a result of the orbital constructive interference in the subspace of the occupied molecular orbitals. Some implications of these two sources of chemical bonds in propellanes, π-electron systems and polymers are examined. The current–density concept associated with the wave-function phase is introduced and the relevant phase-continuity equation is discussed. For the first time, the quantum generalizations of the classical measures of the information content, functionals of the probability distribution alone, are introduced to distinguish systems with the same electron density, but differing in their current(phase) composition. The corresponding information/entropy sources are identified in the associated continuity equations. (shrink)

We prove a number of results motivated by global questions of uniformity in computabi- lity theory, and universality of countable Borel equivalence relations. Our main technical tool is a game for constructing functions on free products of countable groups. We begin by investigating the notion of uniform universality, first proposed by Montalbán, Reimann and Slaman. This notion is a strengthened form of a countable Borel equivalence relation being universal, which we conjecture is equivalent to the usual notion. With (...) this additional uniformity hypothesis, we can answer many questions concerning how countable groups, probability measures, the subset relation, and increasing unions interact with universality. For many natural classes of countable Borel equivalence relations, we can also classify exactly which are uniformly universal. We also show the existence of refinements of Martin’s ultrafilter on Turing invariant Borel sets to the invariant Borel sets of equivalence relations that are much finer than Turing equivalence. For example, we construct such an ultrafilter for the orbit equivalence relation of the shift action of the free group on countably many generators. These ultrafilters imply a number of structural properties for these equivalence relations. (shrink)

In this work, a neo-classical relativistic mechanics theory is presented where the spin of an electron is an inherent part of its world space-time path as a point particle. The fourth-order equation of motion corresponds to the same covariant Lagrangian function in proper time as in special relativity except for an additional spin energy term. The theory provides a hidden-variable model of the electron where the dynamic variables give a complete description of its motion, giving a classical mechanics (...) explanation of the electron’s spin, its dipole moments, and Schrödinger’s zitterbewegung, These features are also described mathematically by quantum mechanics theory, of course, but without any physical picture of an underlying reality. The total motion of the electron can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called here the spin center. The global motion is sub-luminal and described by Newton’s Second Law in proper time, the time for a clock fixed at the spin center, while the total motion occurs at the speed of light c, consistent with the eigenvalues of Dirac’s velocity operators having magnitude c. The local spin motion is an inherent perpetual motion, which for a free electron is periodic at the ultra-high zitterbewegung frequency and its path is circular in a spin-center reference frame. In an electro-magnetic field, this spin motion generates magnetic and electric dipole energies through the Lorentz force on the electron’s point charge. The electric dipole energy corresponds to the spin-orbit coupling term involving the electric field that appears in the corrected Pauli non-relativistic Hamiltonian, which has long been used to explain the doublet structure of the spectral lines of the excited hydrogen atom. Pauli’s spin-orbit term is usually derived, however, from his magnetic dipole energy term, including also the effect of Thomas precession, which halves this energy. The magnetic dipole energy from Pauli’s and Dirac’s theory is twice that in the neo-classical theory, a discrepancy that has not been resolved. By defining a spin tensor as the angular momentum of the electron’s total motion about its spin center, the fundamental equations of motion can be re-written in an identical form to those of the Barut–Zanghi electron theory. This allows the equations of motion to be expressed in an equivalent form involving operators applied to a state function of proper time satisfying a neo-classical Dirac–Schrödinger spinor equation. This state function produces the dynamic variables from the same operators as in Dirac’s theory for the electron but without any probability implications. It leads to a neo-classical wave function that satisfies Dirac’s relativistic wave equation for the free electron by applying the Lorentz transformation to express proper time in the state function in terms of an observer’s space-time coordinates, showing that there is a close connection between the neo-classical theory and quantum mechanics theory for the electron’s dynamics. (shrink)

A possible atomic mechanism underlying the Re- and Ru-induced strengthening effects on the n - n ' interface in Ni-based single-crystal superalloys has been investigated using the DMol3 molecular orbital package based on density functional theory. The calculation of bonding properties has been performed on a cluster designed to model Re and Ru strengthening effects within the interface. The stronger Re--Ni bonds are formed mainly as a result of d- hybridization, while the Ni--Ni bonding become weaker (...) accompanying the Re substitution. The vertical and horizontal bond orders for a local environmental cluster are proposed and developed for the description of the strengthening effect on the n - n ' interface, with larger bond order values achieving better effect. Results show that both Re and Ru significantly strengthen the interface. It is also shown that the strengthening effect of Re is better than that of Ru, and this is explained in terms of the charge transfer of electrons between orbitals of Ru atom according to Mulliken population analysis. The calculation results provide a basis for understanding the atomic mechanism of Re- and Ru-induced n - n ' interfacial strengthening. (shrink)

In this series of papers I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Papers I and II were devoted to system A theory of the outer planets and of the planet Venus. In this third and last paper I will study system A theory of the planet Mercury. Our knowledge of the Babylonian theory of Mercury is at present based on twelveEphemeridesand sevenProcedure Texts. (...) Three computational systems of Mercury are known, all of system A. System A1is represented by nineEphemeridescovering the years 190 BC to 100 BC and system A2by twoEphemeridescovering the years 310 to 290 BC. System A3is known from aProcedure Textand from Text M, anEphemerisof the last evening visibility of Mercury for the years 424 to 403 BC. From an analysis of the Babylonian observations of Mercury preserved in theAstronomical DiariesandPlanetary Textswe find: (1) that dates on which Mercury reaches its stationary points are not recorded, (2) that Normal Star observations on or near dates of first and last appearance of Mercury are rare (about once every twenty observations), and (3) that about one out of every seven pairs of first and last appearances is recorded as “omitted” when Mercury remains invisible due to a combination of the low inclination of its orbit to the horizon and the attenuation by atmospheric extinction. To be able to study the way in which the Babylonian scholars constructed their system A models of Mercury from the available observational material I have created a database of synthetic observations by computing the dates and zodiacal longitudes of all first and last appearances and of all stationary points of Mercury in Babylon between 450 and 50 BC. Of the data required for the construction of an ephemeris synodic time intervals Δt can be directly derived from observed dates but zodiacal longitudes and synodic arcs Δλ must be determined in some other way. Because for Mercury positions with respect to Normal Stars can only rarely be determined at its first or last appearance I propose that the Babylonian scholars used the relation Δλ = Δt −3;39,40, which follows from the period relations, to compute synodic arcs of Mercury from the observed synodic time intervals. An additional difficulty in the construction of System A step functions is that most amplitudes are larger than the associated zone lengths so that in the computation of the longitudes of the synodic phases of Mercury quite often two zone boundaries are crossed. This complication makes it difficult to understand how the Babylonian scholars managed to construct System A models for Mercury that fitted the observations so well because it requires an excessive amount of computational effort to find the best possible step function in a complicated trial and error fitting process with four or five free parameters. To circumvent this difficulty I propose that the Babylonian scholars used an alternative more direct method to fit System A-type models to the observational data of Mercury. This alternative method is based on the fact that after three synodic intervals Mercury returns to a position in the sky which is on average only 17.4° less in longitude. Using reduced amplitudes of about 14°–25° but keeping the same zone boundaries, the computation of what I will call 3-synarc system A models of Mercury is significantly simplified. A full ephemeris of a synodic phase of Mercury can then be composed by combining three columns of longitudes computed with 3-synarc step functions, each column starting with a longitude of Mercury one synodic event apart. Confirmation that this method was indeed used by the Babylonian astronomers comes from Text M (BM 36551+), a very early ephemeris of the last appearances in the evening of Mercury from 424 to 403 BC, computed in three columns according to System A3. Based on an analysis of Text M I suggest that around 400 BC the initial approach in system A modelling of Mercury may have been directed towards choosing “nice” sexagesimal numbers for the amplitudes of the system A step functions while in the later final models, dating from around 300 BC onwards, more emphasis was put on selecting numerical values for the amplitudes such that they were related by simple ratios. The fact that different ephemeris periods were used for each of the four synodic phases of Mercury in the later models may be related to the selection of a best fitting set of System A step function amplitudes for each synodic phase. (shrink)

The Uniformly Reflexive Structure was introduced by E. G. Wagner who showed that the theory of such structures generalized much of recursive function theory. In this paper Uniformly Reflexive Structures are constructed as factor algebras of Free nonassociative algebras. Wagner's question about the existence of a model with no computable splinter ("successor set") is answered in the affirmative by the construction of a model whose only computable sets are the finite sets and their complements. Finally, for each (...) countable Boolean algebra R of subsets of a countable set which contains the finite subsets, a model is constructed with R as its family of computable sets. (shrink)

The paper puts forward the proposal to do relativistic quantum theory without a position operator and without a position probability amplitude. The proposed scheme employs space and time in a fundamental manner and treats them equitably as in special relativity by defining the state vectors as functions of configuration spacetime. From a discussion of the conceptual structure and of the problem of measurement of quantum theory, there emerges an understanding which shows that the absence of a satisfactory position (...) probability density in important cases like that of the photon, in the usual scheme of quantum theory, poses a fundamental difficulty, but that the scheme proposed here is free from the same difficulty and promises, instead, to lead in a natural manner to a fundamentally more satisfactory description of the observations. (shrink)

The human brain shows neuroplastic adaptations induced by motor skill training. However, the description of the plastic architecture of the whole-brain network in resting-state is still limited. In the present study, we aimed to detect how motor training affected the density distribution of whole-brain resting-state functional connectivity (FC) brain in fast-ball student-athletes using resting-state functional magnetic resonance imaging (fMRI) data of student-athletes (SA), and non-athlete healthy controls (NC). The voxel-wise data-driven graph theory approach, namely global (...) class='Hi'>functional connectivity density (gFCD) mapping was applied. The results showed that the SA group exhibited significantly decreased gFCD in brain regions centered at left triangular part of inferior frontal gyrus (IFG), extending to opercular part of left IFG and middle frontal gyrus (MFG) compared with NC group. The findings supported the idea of an increased neural efficiency of athletes’ brain in the brain regions associated with attentional-motor modulation and executive control. Furthermore, the behavioral results demonstrated that in the SA group, faster executive control reaction time was associated with smaller gFCD values in left IFG. The findings implied that the motor skill training would decrease the numbers of FC in IFG to accelerate the execution control with high attentional demands, and focus the attention to the target detection the athletes are interested in. (shrink)

When Alain Locke developed a philosophy of valuation that he termed “functional relativism,” he contrasted his position to “value realism,” apparently because he wanted to keep valuations free from being bound to status quo existence. This article considers Locke's philosophy of valuation in relation to the “realism” of Charles S. Peirce in order to show that there is an approach to realism that answers to requirements of dynamic, evolutionary growth and creativity. The argument begins by placing Locke's cardinal (...) values onto a compass-like diagram inspired by Black Elk's ritual acknowledgment of cardinal directions. The illustration of a hoop of valuation is used to explore the usefulness of thinking in terms of diagrams, with explicit reference to Peircean semiotics. Next the article pursues a context of valuation developed through the psychical philosophy of George Herbert Mead and recent work on Peircean realism. It shows how valuation may be viewed as an exercise in freedom, not confined to status quo existence. Sources of error are acknowledged and reviewed. In the end, Peirce's choice of realism versus nominalism is found to be consistent with Lockean commitments to shared living in communities of inquiry. A Lockean philosophy of valuation, therefore, is not necessarily antirealist. (shrink)

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories (...) with a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research. (Bibliographic note: the thesis was submitted for the Master of Science in mathematics at Rutgers University.). (shrink)

Alcohol use disorder is one of the most common substance use disorders contributing to both behavioral and cognitive impairments in patients with AUD. Recent neuroimaging studies point out that AUD is a typical disorder featured by altered functional connectivity. However, the details about how voxel-wise functional coordination remain unknown. Here, we adopted a newly proposed method named functional connectivity density to depict altered voxel-wise functional coordination in AUD. The novel functional imaging technique, FCD, provides (...) a comprehensive analytical method for brain's “scale-free” networks. We applied resting-state functional MRI toward subjects to obtain their FCD, including global FCD, local FCD, and long-range FCD. Sixty-one patients with AUD and 29 healthy controls were recruited, and patients with AUD were further divided into alcohol-related cognitive impairment group and non-cognitive impairment group. All subjects were asked to stay stationary during the scan in order to calculate the resting-state gFCD, lFCD, and lrFCD values, and further investigate the abnormal connectivity alterations among AUD-NCI, ARCI, and HC. Compared to HC, both AUD groups exhibited significantly altered gFCD in the left inferior occipital lobe, left calcarine, altered lFCD in right lingual, and altered lrFCD in ventromedial frontal gyrus. It is notable that gFCD of the ARCI group was found to be significantly deviated from AUD-NCI and HC in left medial frontal gyrus, which changes probably contributed by the impairment in cognition. In addition, no significant differences in gFCD were found between ARCI and HC in left parahippocampal, while ARCI and HC were profoundly deviated from AUD-NCI, possibly reflecting a compensation of cognition impairment. Further analysis showed that within patients with AUD, gFCD values in left medial frontal gyrus are negatively correlated with MMSE scores, while lFCD values in left inferior occipital lobe are positively related to ADS scores. In conclusion, patients with AUD exhibited significantly altered functional connectivity patterns mainly in several left hemisphere brain regions, while patients with AUD with or without cognitive impairment also demonstrated intergroup FCD differences which correlated with symptom severity, and patients with AUD cognitive impairment would suffer less severe alcohol dependence. This difference in symptom severity probably served as a compensation for cognitive impairment, suggesting a difference in pathological pathways. These findings assisted future AUD studies by providing insight into possible pathological mechanisms. (shrink)

The wavefunction is the central mathematical entity of quantum mechanics, but it still lacks a universally accepted interpretation. Much effort is spent on attempts to probe its fundamental nature. Here I investigate the consequences of a matter ontology applied to spherical masses of constant bulk density. The governing equation for the center-of-mass wavefunction is derived and solved numerically. The ground state wavefunctions and resulting matter densities are investigated. A lowering of the density from its bulk value is found (...) for low masses due to increased spatial spreading. A discussion of the possibility to experimentally observe these effects is given and the possible consequences for choosing an ontological interpretation for quantum mechanics are commented upon. (shrink)

The mean-field theory with the use of the slave-boson functional method has been generalized to take account of the spin- and/or orbital-ordered state in the doubly degenerate Hubbard model. Numerical calculations are presented of the antiferromagnetic orbital-ordered state in the half-filled simple-cubic model. The orbital order in the present theory is much reduced compared with that in the Hartree–Fock approximation because of the large orbital fluctuations. From a comparison of the ground-state energy, the (...) antiferromagnetic orbital state is shown to be unstable against the antiferromagnetic spin state, although the situation becomes reversed when the exchange interaction is negative. (shrink)

This paper explores whether human proactivity can be considered an expression of free will. The discussion involves two paradigms, which are mutually complementary and encompass psychological proactivity and reactivity. Both paradigms raise the question of linear and non-linear determinism, which inevitably leads to the issue of free will. The analysis attempts to find a compromise between linear and non-linear determinism through the approach of human dialectical complexity (Lebed & Bar-Eli, 2013). This refers to the relationships of two types (...) of complex subsystems within a human: the perceptual-motor dynamic system (PMDS), which is mostly determined by linear impacts and expressed through reactive behavior, and the “free-will”11. The authors employ the term “free will” in a metaphorical sense and do not put forth philosophical arguments for this consideration. complex system (FCS), which is mostly determined by non-linear redundant determinism and expressed through proactive dynamics. In summary, it is concluded that there cannot be a categorical assertion of the permanent existence of free will in human functioning. The human dialectical complexity expressed by both proactivity and reactivity causes the “floating” presence of free will depending on the prevalence of proactive control factors and the non-linear determination of a living human system. (shrink)

In this paper we prove that the preordering $\lesssim $ of provable implication over any recursively enumerable theory $T$ containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function $F$ for $\lesssim $. A recursive function $F$ is a density function if it computes, for $A$ and $B$ with $A\lnsim B$, an element $C$ such that $A\lnsim C\lnsim B$. The function is extensional if it preserves $T$-provable equivalence. Secondly, (...) we prove a general result that implies that, for extensions of elementary arithmetic, the ordering $\lesssim $ restricted to $\Sigma_{n}$-sentences is uniformly dense. In the last section we provide historical notes and background material. (shrink)

The aim of UK-REACH (“The United Kingdom Research study into Ethnicity And COVID-19 outcomes in Healthcare workers”) is to understand if, how, and why healthcare workers (HCWs) in the United Kingdom (UK) from ethnic minority groups are at increased risk of poor outcomes from COVID-19. In this article, we present findings from the ethical and legal stream of the study, which undertook qualitative research seeking to understand and address legal, ethical, and social acceptability issues around data protection, privacy, and information (...) governance associated with the linkage of HCWs’ registration data and healthcare data. We interviewed 22 key opinion leaders in healthcare and health research from across the UK in two-to-one semi-structured interviews. Transcripts were coded using qualitative thematic analysis. Participants told us that a significant aspect of Big Data research in public health is varying drivers of mistrust—of the research itself, research staff and funders, and broader concerns of mistrust within participant communities, particularly in the context of COVID-19 and those situated in more marginalised community settings. However, despite the challenges, participants also identified ways in which legally compliant and ethically informed approaches to research can be crafted to mitigate or overcome mistrust and establish greater confidence in Big Data public health research. Overall, our research indicates that a “Big Data Ethics by Design” approach to research in this area can help assure (1) that meaningful community and participant engagement is taking place and that extant challenges are addressed, and (2) that any new challenges or hitherto unknown unknowns can be rapidly and properly considered to ensure potential (but material) harms are identified and minimised where necessary. Our findings indicate such an approach, in turn, will help drive better scientific breakthroughs that translate into medical innovations and effective public health interventions, which benefit the publics studied, including those who are often marginalised in research. (shrink)

A metric approach to Popper's verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some (...) of the difficulties arising from the known definitions of verisimilitude. (shrink)

Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schrödinger and Born, are in tension with one another but are not incompatible. Schrödinger’s idea that the nucleus of an atom is surrounded by a spread-out electron charge density is supported by a variety of evidence from quantum chemistry, including two methods that are used to determine atomic (...) and molecular structure: the Hartree-Fock method and density functional theory. Taking this evidence as a clue to the foundations of quantum physics, Schrödinger’s electron charge density can be incorporated into many different interpretations of quantum mechanics. (shrink)

The reduction of the lambda calculus to the theory of combinators in [Sch¨ onfinkel, 1924] applies to positive implicational logic, i.e. to the typed lambda calculus, where the types are built up from atomic types by means of the operation A −→ B, to show that the lambda operator can be eliminated in favor of combinators K and S of each type A −→ (B −→ A) and (A −→ (B −→ C)) −→ ((A −→ B) −→ (A −→ (...) C)), respectively.1 I will extend that result to the case in which the types are built up by means of the general function type ∀x : A.B(x) as well as the disjoint union type ∃x : A.B(x)– essentially to the theory of [Howard, 1980]. To extend the treatment of −→ to ∀ we shall need a generalized form of the combinators K and S, and to deal with ∃ we will need to introduce a new form of the combinator S.. (shrink)

Technology used in online marketing has advanced to a state where collection, enhancement and aggregation of information are instantaneous. This proliferation of customer information focused technology brings with it a host of issues surrounding customer privacy. This article makes two key contributions to the debate concerning digital privacy. First, we use theories of justice to help understand the way consumers conceive of, and react to, privacy concerns. Specifically, it is argued that an important component of consumers' privacy concerns relates to (...) fairness judgments, which in turn comprise of the two primary components of distributive and procedural justice. Second, we make a number of prescriptions, aimed at both firms and regulators, based on the notion that consumers respond to perceived privacy violations in much the same way they would respond to an unfair exchange. (shrink)

We show that any formula with two free variables in a Vapnik–Chervonenkis (VC) minimal theory has VC-codensity at most 2. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where acleq= dcleq, the VC-codensity of a formula is at most the number of free variables (from the work of Aschenbrenner et al., the author, and Laskowski).

I argue for a soft compatibilist theory of free will, i.e., such that free will is compatible with both determinism and indeterminism, directly opposite hard incompatibilism, which holds free will incompatible both with determinism and indeterminism. My intuitions in this book are primarily based on an analysis of meditation, but my arguments are highly syncretic, deriving from many fields, including behaviorism, psychology, conditioning and deconditioning theory, philosophy of language, philosophy of mind, simulation theory, etc. (...) I offer a causal/functional analysis of meta-mental control, or 'metacausality', cashed out in counterfactual terms, to solve what I call the easy problem of free will. (shrink)

Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure one represented by a density matrix. I characterize and elaborate on Density Matrix Realism, the thesis that the universal quantum state is objective but can be impure. To clarify the thesis, I compare it with Wave Function Realism, explain the conditions under which they are empirically (...) equivalent, consider two generalizations of Density Matrix Realism, and answer some frequently asked questions. I end by highlighting an implication for scientific realism. (shrink)

The following result is an approximation to the answer of the question of Kokorin about decidability of a quantifier-free theory of field of rational numbers. Let Q0 be a subset of the set of all rational numbers which contains integers 1 and −1. Let be a set containing Q0 and closed by the functions of addition, subtraction and multiplication. For example coincides with Q0 if Q0 is the set of all binary rational numbers or the set of all (...) decimal rational numbers. It is clear that , where Z is the set of all integers and Q is the set of all rational numbers. A negationless theory uses only conjunction and disjunction as logical connectives. Let T be a quantifier-free negationless elementary theory of signature , where Pol is the list of all polynomials with rational coefficients from Q0 in which exponent of the polynomials and rational coefficients are written in binary number system. Theorem 1. Theory T is NP-hard and if is everywhere dense then the theory T is decidable by an algorithm which belongs to EXPTIME. The set of all rational numbers or the set of all binary rational numbers may be taken instead of . The quantifier-free negationless theory of the field of rational numbers may be regarded as a base of constructive mathematics. (shrink)

BackgroundThe pursuit of a cure for HIV is a high priority for researchers, funding agencies, governments and people living with HIV (PLWH). To date, over 250 biomedical studies worldwide are or have been related to discovering a safe, effective, and scalable HIV cure, most of which are early translational research and experimental medicine. As HIV cure research increases, it is critical to identify and address the ethical challenges posed by this research.MethodsWe conducted a scoping review of the growing HIV cure (...) research ethics literature, focusing on articles published in English peer-reviewed journals from 2013 to 2021. We extracted and summarized key developments in the ethics of HIV cure research. Twelve community advocates actively engaged in HIV cure research provided input on this summary and suggested areas warranting further ethical inquiry and foresight via email exchange and video conferencing.DiscussionDespite substantial scholarship related to the ethics of HIV cure research, additional attention should focus on emerging issues in six categories of ethical issues: (1) social value (ongoing and emerging biomedical research and scalability considerations); (2) scientific validity (study design issues, such as the use of analytical treatment interruptions and placebos); (3) fair selection of participants (equity and justice considerations); (4) favorable benefit/risk balance (early phase research, benefit-risk balance, risk perception, psychological risks, and pediatric research); (5) informed consent (attention to language, decision-making, informed consent processes and scientific uncertainty); and (6) respect for enrolled participants and community (perspectives of people living with HIV and affected communities and representation).ConclusionHIV cure research ethics has an unfinished agenda. Scientific research and bioethics should work in tandem to advance ethical HIV cure research. Because the science of HIV cure research will continue to rapidly advance, ethical considerations of the major themes we identified will need to be revisited and refined over time. (shrink)

Various methods have been employed to investigate different aspects of the brain activity modulation related to the performance of a cycling task. In our study we examined how functional connectivity and brain network efficiency varied during an endurance cycling task. To this purpose, we reconstructed EEG signals at source level: we computed current densities in 28 anatomical regions of interest (ROIs) through the eLORETA algorithm, then we calculated the Lagged Coherence of the 28 current density signals to define (...) the adjacency matrix. To quantify changes of functional network efficiency during an exhaustive cycling task, we computed three graph theoretical indices: local efficiency (LE), global efficiency (GE) and Density (D) in two different frequency bands, Alpha and Beta bands, that indicate alertness processes and motor binding/fatigue respectively. This analysis was conducted for six different task intervals: pre-cycling, initial, intermediate and final stages of cycling, active recovery and passive recovery. Fourteen participants performed an incremental cycling task with simultaneous EEG recording and RPE monitoring to detect participants’ exhaustion. LE remained constant during the endurance cycling task in both bands. Therefore, we speculate that fatigue processes did not affect segregated neural processing. We observed an increase of GE in the Alpha band only during cycling, that could be due to greater alertness processes and preparedness to stimuli during exercise. Conversely, although D did not change significantly over time in the Alpha band, its general reduction in the Beta bands during cycling could be interpreted within the framework of the neural efficiency hypothesis, which posits a reduced neural activity for expert/automated performances. We argue that the use of graph theoretical indices represents a clear methodological advancement in studying endurance performance. (shrink)

Technology used in online marketing has advanced to a state where collection, enhancement and aggregation of information are instantaneous. This proliferation of customer information focused technology brings with it a host of issues surrounding customer privacy. This article makes two key contributions to the debate concerning digital privacy. First, we use theories of justice to help understand the way consumers conceive of, and react to, privacy concerns. Specifically, it is argued that an important component of consumers’ privacy concerns relates to (...) fairness judgments, which in turn comprise of the two primary components of distributive and procedural justice. Second, we make a number of prescriptions, aimed at both firms and regulators, based on the notion that consumers respond to perceived privacy violations in much the same way they would respond to an unfair exchange. (shrink)

The threat simulation theory of dreaming states that dream consciousness is essentially an ancient biological defence mechanism, evolutionarily selected for its capacity to repeatedly simulate threatening events. Threat simulation during dreaming rehearses the cognitive mechanisms required for efficient threat perception and threat avoidance, leading to increased probability of reproductive success during human evolution. One hypothesis drawn from TST is that real threatening events encountered by the individual during wakefulness should lead to an increased activation of the system, a threat (...) simulation response, and therefore, to an increased frequency and severity of threatening events in dreams. Consequently, children who live in an environment in which their physical and psychological well-being is constantly threatened should have a highly activated dream production and threat simulation system, whereas children living in a safe environment that is relatively free of such threat cues should have a weakly activated system. We tested this hypothesis by analysing the content of dream reports from severely traumatized and less traumatized Kurdish children and ordinary, non-traumatized Finnish children. Our results give support for most of the predictions drawn from TST. The severely traumatized children reported a significantly greater number of dreams and their dreams included a higher number of threatening dream events. The dream threats of traumatized children were also more severe in nature than the threats of less traumatized or non-traumatized children. (shrink)

I argue for a possible Buddhist theory of free will that combines Frankfurt's hierarchical analysis of meta-volitional/volitional accord with elements of the Buddhist eightfold path that prescribe that Buddhist aspirants cultivate meta-volitional wills that promote the mental freedom that culminates in enlightenment, as well as a causal/functional analysis of how Buddhist meditative methodology not only plausibly makes that possible, but in ways that may be applied to undermine Galen Strawson's impossibility argument, along with most of the other (...) major arguments for free will skepticism. (shrink)