Semantic priming has been a focus of research in the cognitive sciences for more than 30 years and is commonly used as a tool for investigating other aspects of perception and cognition, such as word recognition, language comprehension, and knowledge representations. Semantic Priming: Perspectives from Memory and Word Recognition examines empirical and theoretical advancements in the understanding of semantic priming, providing a succinct, in-depth review of this important phenomenon, framed in terms of models of memory and models of word recognition. (...) The first section examines models of semantic priming, including spreading activation models, the verification model, compound-cue models, distributed network models, and multistage activation models (e.g. interactive-activation model). The second section examines issues and findings that have played an especially important role in testing models of priming and includes chapters on the following topics: methodological issues (e.g. counterbalancing of materials, choice of priming baselines); automatic vs. strategic priming; associative vs. "pure" semantic priming; mediated priming; long-term semantic priming; backward priming; unconscious priming; the prime-task effect; list context effects; effects of word frequency, stimulus quality, and stimulus repetition; and the cognitive neuroscience of semantic priming. The book closes with a summary and a discussion of promising new research directions. The volume will be of interest to a wide range of researchers and students in the cognitive sciences and neurosciences. (shrink)

The present paper is thought as a formal study of distributive closure systems which arise in the domain of sentential logics. Special stress is laid on the notion of a C-filter, playing the role analogous to that of a congruence in universal algebra. A sentential logic C is called filter distributive if the lattice of C-filters in every algebra similar to the language of C is distributive. Theorem IV.2 in Section IV gives a method of axiomatization of those filter distributive (...) logics for which the class Matr (C) prime of C-prime matrices (models) is axiomatizable. In Section V, the attention is focused on axiomatic strengthenings of filter distributive logics. The theorems placed there may be regarded, to some extent, as the matrix counterparts of Baker's well-known theorem from universal algebra [9, § 62, Theorem 2]. (shrink)

Asymmetric distribution of function between the cerebral hemispheres has been widely investigated in the auditory modality. The current approach borrows heavily from visual local–global research in an attempt to determine whether, as in vision, local–global auditory processing is lateralised. In vision, lateralised local–global processing likely relies on spatial frequency information. Drawing analogies between visual spatial frequency and auditory dimensions, two sets of auditory stimuli were developed. In the high–low stimulus set we manipulate frequency information, and in the fast–slow stimulus (...) set we manipulate temporal information. The fast–slow stimuli additionally mimic visual hierarchical stimulus structure, in which the arrangement of local patterns determines the global pattern. Unlike previous auditory stimuli, the current stimulus sets contain the experimental flexibility of visual local–global hierarchical stimuli allowing independent manipulation of structural levels. Previous findings of frequency and temporal range priming were replicated. Additionally, by presenting stimuli monaurally, we found that priming of frequency ranges (but not temporal ranges) was found to vary by ear, supporting the contention that the hemispheres asymmetrically retain traces of prior frequency processing. These results contribute to the extensive literature revealing cerebral asymmetries for the processing of frequency information, and extend those results to the realm of priming. (shrink)

Vector-based models of word meaning have become increasingly popular in cognitive science. The appeal of these models lies in their ability to represent meaning simply by using distributional information under the assumption that words occurring within similar contexts are semantically similar. Despite their widespread use, vector-based models are typically directed at representing words in isolation, and methods for constructing representations for phrases or sentences have received little attention in the literature. This is in marked contrast to experimental evidence (e.g., in (...) sentential priming) suggesting that semantic similarity is more complex than simply a relation between isolated words. This article proposes a framework for representing the meaning of word combinations in vector space. Central to our approach is vector composition, which we operationalize in terms of additive and multiplicative functions. Under this framework, we introduce a wide range of composition models that we evaluate empirically on a phrase similarity task. (shrink)

We compare diverse degrees of compactness and finiteness in Boolean algebras with each other and investigate the influence of weak choice principles. Our arguments rely on a discussion of infinitary distributive laws and generalized prime elements in Boolean algebras. In ZF set theory without choice, a Boolean algebra is Dedekind finite if and only if it satisfies the ascending chain condition. The Denumerable Subset Axiom implies finiteness of Boolean algebras with compact top, whereas the converse fails in ZF. Moreover, (...) we derive from DS the atomicity of continuous Boolean algebras. Some of the results extend to more general structures like pseudocomplemented semilattices. (shrink)

Contemporary egalitarian theory has been shaped by a debate between distributive and relational perspectives. Relational egalitarians argue that equality is primarily about the character of our social and political relationships, rather than the pattern of distribution of goods. But they often also claim that distributive and relational ideals are connected in practice, because material inequality impairs our ability to stand as social and political equals. Using a survey experiment, we assess the impact of material inequality on relational equality. We (...) show that priming income inequality increases perceptions of unequal social status; but it does not affect perceived equal political standing, or the extent to which respondents affirm the ideal of relational equality. We argue that this empirical approach yields deeper payoffs for conceptual and normative questions about relational equality; and it contributes to wider methodological debates about the role of survey data in normative political theory. (shrink)

It is a theorem of Rowbottom [12] that ifκis measurable andIis a normal prime ideal onκ, then for eachλ<κ,In this paper a natural structural property of ideals, distributivity, is considered and shown to be related to this and other ideal theoretic partition relations.The set theoretical terminology is standard and background results on the theory of ideals may be found in [5] and [8]. Throughoutκwill denote an uncountable regular cardinal, andIa proper, nonprincipal,κ-complete ideal onκ.NSκis the ideal of nonstationary subsets ofκ, (...) andIκ= {X⊆κ∣∣X∣<κ}. IfA∈I+ −I), then anI-partitionofAis a maximal collectionW⊆,P ∩I+so thatX∩ Y ∈IwheneverX, Y∈W, X≠Y. TheI-partitionWis said to be disjoint if distinct members ofWare disjoint, and in this case, fordenotes the unique member ofWcontainingξ. A sequence 〈Wα∣α<η} ofI-partitions ofAis said to be decreasing if wheneverα<β<ηandX∈Wβthere is aY∈Wαsuch thatX⊆Y.. (shrink)

We introduce a conceptual model for reaching group decisions. Our model extends a well-known, single-agent cognitive model, the recognition-primed decision (RPD) model. The RPD model includes a recognition phase and an evaluation phase. Group extensions of the RPD model, applicable to a group of RPD agents, have been considered in the literature, however the proposed models do not formalize how distributed and possibly inconsistent information can be combined in either phase. We show how such information can be utilized by aggregating (...) it using a specific social choice method, namely judgment aggregation. Our model is applicable to hierarchical groups of agents containing at least one RPD agent. (shrink)

Over the past two decades, hundreds of articles have investigated the mechanisms underlying the phenomenon that masked stimuli reduce people's response performance to subsequent compatible stimuli, for example, the negative compatibility effect (NCE). Whether the NCE results from motor inhibition, object updating, or both is still being debated. We used the digital masked prime task for 3 consecutive days to strengthen stimulus‐response associations in relevant and irrelevant contexts (whether the mask consisted of task‐relevant features or not) and employed response (...) time distribution analysis to investigate the contributions of motor inhibition and object updating to the NCE. The results showed that the NCE appeared in the irrelevant condition on days 2 and 3, and it increased with response latency on day 3. In contrast, in the relevant condition, the NCE occurred regardless of test day or response latency, and was unaffected by either. These different patterns of results indicated that the cause of the NCE was different in the relevant and irrelevant conditions. In the relevant condition, the results suggested that the NCE was solely due to object updating, whereas in the irrelevant condition, the results indicated that the NCE was solely due to motor inhibition. This study reconciled the previous debate and revealed the mechanisms by which unconscious information influences behavioral performance in different contexts. (shrink)

HAPPEN is a member of the Natural Semantic Metalanguage (NSM) inventory of primes (cf. Goddard and Wierzbicka (eds) 1994, 2002). Its English exponent ‘happen’ has been popularly expounded as fa1sheng1 in Mandarin Chinese (e.g. Chappell 2002). This article argues that fa1sheng1 is not the correct exponent of HAPPEN as it is marked for ‘adversity’ as well as what I call ‘serious mention’ or ‘noteworthiness’ of the event, i.e., that an event is sufficiently serious or noteworthy to fare a mention. This (...) article puts forward you3 lit. ‘have, exist, happen’ and zen3(me)yang4/zhe4(me)yang4 lit. ‘like how/like this’ instead, as allolexic exponents of HAPPEN in Mandarin Chinese. Though highly polysemous each in its own way, the HAPPEN sense of you3 and zen3(me)yang4/zhe4(me)yang4 can, respectively, be shown to be semantically irreducible and pragmatically neutral. This article delineates some of the syntactic and contextual distribution attesting to the viability of you3 and zen3(me)yang4/zhe4(me)yang4 as expounding HAPPEN. (shrink)

The conformity of mathematics and physics has so far been taken for granted. Philosophical explanations of that fundamental fact have never been satisfactory, mathematical explanations never had been attempted. In the following a fundamental theorem for the conformity of mathematics and physics will be demonstrated.Mathematics can be defined as the science of Number, physics as the science of Matter. The elementary constituents of mathematics are the prime numbers, those of matter the particles, particularly protons and electrons. The only essential (...) property of these elements as such is their existence, given within a given complex or space. Their fundamental relation is their distribution within their respective spaces. The theorem of the distribution of primes in the arithmetical series of numbers is the fundamental theorem of mathematics. The fundamental theorem of physics would be a theorem of the distribution of particles in geometrical space. If it were shown that both theorems were equal, the essential conformity of mathematics and physics would be mathematically demonstrated. (shrink)

In this article, we shall show the generalized notions of distributivity of Boolean algebras have essential relations with several axioms and properties of set theory, say the Axiom of Choice, the Axiom of Dependence Choice, the Prime Ideal Theorems, Martin's axioms, Lebesgue measurability and so on.

Economic inequality has become a focus of prime interest for economic analysts and policy makers. This book provides an integrated approach to the topics of inequality and personal income distribution. It covers the practical and theoretical bases for inequality analysis, applications to real world problems and the foundations of theoretical approaches to income distribution. It also analyses models of the distribution of labour earnings and of income from wealth. The long-run development of income - and wealth (...) - distribution over many generations is also examined. Special attention is given to an assessment of the merits and weaknesses of standard economic models, to illustrating the implications of distributional mechanisms using real data and illustrative examples, and to providing graphical interpretation of formal arguments. Examples are drawn from US, UK and international sources. (shrink)

Localist models of spreading activation (SA) and models assuming distributed representations offer very different takes on semantic priming, a widely investigated paradigm in word recognition and semantic memory research. In this study, we implemented SA in an attractor neural network model with distributed representations and created a unified framework for the two approaches. Our models assume a synaptic depression mechanism leading to autonomous transitions between encoded memory patterns (latching dynamics), which account for the major characteristics of automatic semantic priming in (...) humans. Using computer simulations, we demonstrated how findings that challenged attractor‐based networks in the past, such as mediated and asymmetric priming, are a natural consequence of our present model’s dynamics. Puzzling results regarding backward priming were also given a straightforward explanation. In addition, the current model addresses some of the differences between semantic and associative relatedness and explains how these differences interact with stimulus onset asynchrony in priming experiments. (shrink)

In this paper we define n+1-valued matrix logic Kn+1 whose class of tautologies is non-empty iff n is a prime number. This result amounts to a new definition of a prime number. We prove that if n is prime, then the functional properties of Kn+1 are the same as those of ukasiewicz's n +1-valued matrix logic n+1. In an indirect way, the proof we provide reflects the complexity of the distribution of prime numbers in the (...) natural series. Further, we introduce a generalization K n+1 * of Kn+1 such that the set of tautologies of Kn+1 is not empty iff n is of the form p , where p is prime and is natural. Also in this case we prove the equivalence of functional properties of the introduced logic and those of n+1. In the concluding part, we discuss briefly a partition of the natural series into equivalence classes such that each class contains exactly one prime number. We conjecture that for each prime number the corresponding equivalence class is finite. (shrink)

Semantic priming has long been recognized to reflect, along with automatic semantic mechanisms, the contribution of controlled strategies. However, previous theories of controlled priming were mostly qualitative, lacking common grounds with modern mathematical models of automatic priming based on neural networks. Recently, we introduced a novel attractor network model of automatic semantic priming with latching dynamics. Here, we extend this work to show how the same model can also account for important findings regarding controlled processes. Assuming the rate of semantic (...) transitions in the network can be adapted using simple reinforcement learning, we show how basic findings attributed to controlled processes in priming can be achieved, including their dependency on stimulus onset asynchrony and relatedness proportion and their unique effect on associative, category-exemplar, mediated and backward prime-target relations. We discuss how our mechanism relates to the classic expectancy theory and how it can be further extended in future developments of the model. (shrink)

We recall some notions introduced and developed by António Aniceto Monteiro, and show how these notions have been used and generalised, thus establishing a direct and indirect influence of Monteiro’s work that extends to this day.

Translation equivalents for cognates in different script systems share the same meaning and phonological similarity but are different orthographically. Event-related potentials were recorded during the visual recognition of cross-script cognates and non-cognates together with concreteness factors while Chinese learners of English performed a lexical decision task with the masked translation priming paradigm in Experiment 1 and Experiment 2. N400 effect was found to be closely related to priming effects of cross-script cognate status and concreteness in Experiment 1; and in Experiment (...) 2, N150 and N400 effects were related to priming effects of cross-script cognate status and concreteness, and greater priming effects of cross-script cognate status in cognates than in non-cognates for abstract words were found in the time window of 100–200 ms. Meanwhile, the asymmetry of translation directions was observed in smaller priming effects in forward translation than in backward translation in the time window of 100–200 ms for abstract cognates, and in larger priming effects in forward translation than in backward translation in the time window of 350–550 ms for each type of words. We discussed the roles of phonological activation and concreteness effects in view of the function of N150 and N400 components as well as the relevant models, mainly the Distributed Feature Model and Bilingual Interactive Activation model. (shrink)

Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom =. In 1969, Horn proved that a Heyting algebra is a Gödel algebra if and only if its set of prime filters partially ordered by reverse inclusion–i.e. its prime spectrum–is a forest. Our main result characterizes Gödel algebras that are free over some finite distributive lattice by an intrisic property of their spectral forest.

An attractor network was trained to compute from word form to semantic representations that were based on subject‐generated features. The model was driven largely by higher‐order semantic structure. The network simulated two recent experiments that employed items included in its training set (McRae and Boisvert, 1998). In Simulation 1, short stimulus onset asynchrony priming was demonstrated for semantically similar items. Simulation 2 reproduced subtle effects obtained by varying degree of similarity. Two predictions from the model were then tested on human (...) subjects. In Simulation 3 and Experiment 1, the items from Simulation 1 were reversed, and both the network and subjects showed minimally different priming effects in the two directions. In Experiment 2, consistent with attractor networks but contrary to a key aspect of hierarchical spreading activation accounts priming was determined by featural similarity rather than shared superordinate category. It is concluded that semantic‐similarity priming is due to featural overlap that is a natural consequence of distributed representations of word meaning. (shrink)

We identify the \-ideals of a distributive demi-pseudocomplemented algebra L as the kernels of the boolean congruences on L, and show that they form a complete Heyting algebra which is isomorphic to the interval \ of the congruence lattice of L where G is the Glivenko congruence. We also show that the notions of maximal \-ideal, prime \-ideal, and falsity ideal coincide.

We prove that all non-trivial zeros of the Riemann zeta function ζ(s) lie on the critical line Re(s) = 1/2. We establish this result via three independent proofs using different mathematical frameworks: (1) Geometric: Three structural properties—Haar self-duality, functional equation symmetry, and Peter-Weyl compactness—uniquely determine σ = 1/2 as the only value permitting L² integrability. (2) Spectral: Meyer's unconditional spectral realization combined with Stone's theorem and Haar measure self-duality; (3) Probabilistic: The Biane-Pitman-Yor identification of ξ(s) with the Kuiper distribution, (...) showing off-line zeros would violate probability axioms. Each pathway is rigorous, complete, and unconditional. (shrink)

The Riemann Hypothesis (RH) asserts that every non-trivial zero of the Riemann zeta function ζ(s) satisfies Re(s) = 1/2. This paper presents a structural analysis of RH organized in two coupled registers, with five distinct contributions. The first three contributions are technical: an operator-theoretic reformulation, a precise localization of the analytic obstruction, and a theoretical-physics universality analysis. The fourth contribution is a list of five falsifiable predictions. The fifth contribution is an explicit conditional verdict on what these technical contributions establish (...) about RH under different mathematical ontologies (Platonist versus naturalist or structural-physical). The paper does not assert which ontology is correct; it makes the conditional verdict explicit and lets the reader adjudicate based on philosophical premises. The first contribution is a geometric reformulation. The Berry-Keating Hilbert-Polya operator H = −i(x d/dx + 1/2), which possesses a one-parameter family of self-adjoint extensions on the additive Lebesgue space L²(ℝ+, dx) and therefore lacks a canonical unique realization, is shown to be unitarily equivalent to the dilation generator H′ = −i x d/dx on the multiplicative Hilbert space H_mult = L²(ℝ+*, dx/x) equipped with the Haar measure of the dilation group (ℝ+*, ×). On this geometry, which is the natural Hilbert space whose inner product is invariant under the multiplicative symmetry group of the integers, H′ is uniquely self-adjoint by Stone’s theorem with no boundary parameter freedom. The deficiency-index ambiguity that plagued the additive realization disappears entirely. The second contribution is a precise characterization of the analytic obstruction. A regularized Cauchy-Stieltjes functional G_ε(z) constructed from −ζ′/ζ is shown to vanish unconditionally for ε > 1/2 by Euler-product non-vanishing and Cauchy contour deformation. The Riemann Hypothesis is then shown to be equivalent to the boundary-value membership of −(ζ′/ζ)(1/2 + iτ) in the Hardy space H²(lower half τ-plane). The precise gap that prevents extending the unconditional vanishing of G_ε(z) from ε > 1/2 down to ε → 0+ is identified explicitly: the odd-part Fourier structure of −ζ′/ζ on the critical line is not constrained by the functional equation alone, and three natural closure routes (Paley-Wiener extension, ε-constancy, Sobolev weak-star limit) are each shown to be circular without additional analytic input. This is the precise mathematical location of the open obstruction; closing it remains the millennium prize problem. The third contribution is a theoretical universality analysis. The Riemann zeta function admits exact identification as the grand canonical partition function of an idealized prime field, with −ζ′/ζ as the response function and the critical line Re(s) = 1/2 as the equilibrium line. Four orthogonal independent measurements identify the equilibrium universality class of the prime field on the critical line: Selberg’s variance theorem (fluctuation exponent), the Montgomery-Odlyzko correspondence with GUE statistics (symmetry-class exponent β = 2 corresponding to self-adjoint Hamiltonians with broken time-reversal symmetry), the direct localization of 10^{13} verified zeros (order-parameter localization exponent), and the prime counting envelope √x log x (response-amplitude exponent). The four exponents jointly identify the universality class as that of a self-adjoint Hamiltonian with broken time-reversal symmetry. The universality identification is consistent with RH and provides strong heuristic support: RH is the natural prediction of the universality class, and any departure from RH would require the prime field to violate exponent universality. The universality analysis does not constitute a proof of RH. Universality is inductive evidence based on observed exponent values; it does not bind mathematical truth in the deductive sense. The paper is explicit about this distinction throughout. Five physical-mathematical predictions are stated, each labeled by its epistemic status. Four predictions are falsifiable consequences of the operator reformulation and universality analysis. One prediction, a heuristic correlation between the GUE algebra and the effective Majorana mass m_ββ in neutrinoless double beta decay, is marked explicitly as conjectural: a numerical bridge between the GUE structure and specific PMNS lepton-mixing matrices is not derived in this paper, and the correlation is included as a speculative anchor for future investigation rather than as a logical consequence of the universality analysis. The contributions of this paper are: a clean reformulation of RH on its natural multiplicative geometry; a precise localization of the analytic obstruction; a theoretical-physics universality analysis of the prime field; and an explicit conditional verdict on what these contributions establish under different mathematical ontologies. Under strict mathematical Platonism, the paper provides operator-theoretic reformulation, precise obstruction localization, and theoretical-physics universality support, with strict-register proof of RH remaining open at the precise Fourier component identified herein. Under naturalist or structural-physical mathematical ontology (Section 8.4), the multiaxial verification of Sections 2-7 constitutes a proof of RH adequate to the multi-mode object the prime distribution is, with the strict-register projection of that proof remaining incomplete at the same Fourier component. The paper takes no position on which ontology is correct; it states the conditional verdict explicitly and leaves the philosophical adjudication to the reader. (shrink)

This article contributes to the debate around the abilities of large language models such as GPT-3, dealing with: firstly, evaluating how well GPT does in the Turing Test, secondly the limits of such models, especially their tendency to generate falsehoods, and thirdly the social consequences of the problems these models have with truth-telling. We start by formalising the recently proposed notion of reversible questions, which Floridi & Chiriatti propose allow one to ‘identify the nature of the source of their answers’, (...) as a probabilistic measure based on Item Response Theory from psychometrics. Following a critical assessment of the methodology which led previous scholars to dismiss GPT’s abilities, we argue against claims that GPT-3 completely lacks semantic ability. Using ideas of compression, priming, distributional semantics and semantic webs we offer our own theory of the limits of large language models like GPT-3, and argue that GPT can competently engage in various semantic tasks. The real reason GPT’s answers seem senseless being that truth-telling is not amongst them. We claim that these kinds of models cannot be forced into producing only true continuation, but rather to maximise their objective function they strategize to be plausible instead of truthful. This, we moreover claim, can hijack our intuitive capacity to evaluate the accuracy of its outputs. Finally, we show how this analysis predicts that a widespread adoption of language generators as tools for writing could result in permanent pollution of our informational ecosystem with massive amounts of very plausible but often untrue texts. (shrink)

This paper aims at formulating a condition neccssary and sufficient for the existing of a prime filter preserving enumerable infinite joins and meets in a distributive lattice.

The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2ℵ0, or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive (...) lattice that has no meet-prime element or join-prime element. This lattice L has |L| = |LC| = 2ℵ0 where Lc is the set of compact elements of L. (shrink)

We give topological proofs of Görnemann’s adaptation to Heyting algebras of the Rasiowa-Sikorski Lemma for Boolean algebras; and of the Rauszer-Sabalski generalisation of it to distributive lattices. The arguments use the Priestley topology on the set of prime filters, and the Baire category theorem. This is preceded by a discussion of criteria for compactness of various spaces of subsets of a lattice, including spaces of filters, prime filters etc.

A distributed neural network model called SPEC for processing sentences with recursive relative clauses is described. The model is based on separating the tasks of segmenting the input word sequence into clauses, forming the case‐role representations, and keeping track of the recursive embeddings into different modules. The system needs to be trained only with the basic sentence constructs, and it generalizes not only to new instances of familiar relative clause structures but to novel structures as well. SPEC exhibits plausible memory (...) degradation as the depth of the center embeddings increases, its memory is primed by earlier constituents, and its performance is aided by semantic constraints between the constituents. The ability to process structure is largely due to a central executive network that monitors and controls the execution of the entire system. This way, in contrast to earlier subsymbolic systems, parsing is modeled as a controlled high‐level process rather than one based on automatic reflex responses. (shrink)

The GOOGLE and XPRIZE $5,000,000 for the practical and socially useful utilization of the quantum computer is the starting point for ontomathematical reflections for what it can really serve. Its “output by measurement” is opposed to the conjecture for a coherent ray able alternatively to deliver the ultimate result of any quantum calculation immediately as a Dirac -function therefore accomplishing the transition of the sequence of increasingly narrow probability density distributions to their limit. The GOOGLE and XPRIZE problem’s solution needs (...) the initial understanding that the result of any quantum calculation is a wave function, or respectively, a probability (density or not) distribution unlike the Turing machine one, and only a “calculating ray” is able to transform the former into the later without any “curving” disturbances. Thus, the unique capability of the quantum computer due to its inherent quantum parallelism can be conserved for all Gödel unresolvable problems, only on the fast “NP” track of which the quantum computer “Achilles” is able practically to overrun the Turing machine “Tortoise” since the latter can “sprint” only by any “P” calculating speed even on it and unlike “Achilles” himself able for “NP” velocities as well. The way for any material body to “calculate” the certain trajectory of least action also resolves the “traveling salesman problem” in fact, therefore illustrating furthermore what the “NP” output of a quantum computer by a “calculating ray” should mean. Another example is the problem of the number of all prime numbers less than “N”, which is suggested to visualize once again the quantum computer capability to resolve problems by a “NP” speed and thus qualitatively to overrun any competing Turing machine. The technically implemented idea of laser is now reinterpreted to “radiate a wave function” in order to explain the “calculating ray” option for a quantum computer “NP” output. The generalization of an entanglement “trigger ray” described by any non-Hermitian operator (unlike a laser) is suggested as well as those “sci-fi” horizons which it reveals. One of them is meant for elucidating the practical meaning of the “Yang-Mills existence and mass gap problem”, one more of the CMI “Millennium Problems” after that of “P vs NP”. -/- . (shrink)

This paper considers the obligation higher income countries have to lower and middle income countries during a global pandemic. Further considers which reforms are needed to the global supply-chain of medical resources. The short-comings in distribution and medical infrastructure have exacerbated the health crisis in developing countries. Global justice demands radical redistribution of medical resources in order to prevent mass casualties. This is argued first by highlighting that the COVID-19 pandemic should be acknowledged as an issue of global justice, (...) secondly, higher income countries ought to account for distribution inequity as a matter of rectifying past injustices, and thirdly argue for reform in distribution while considering the vaccine rollout as a prime example. We aim to show how the differences from country to country in response capabilities are a result of the economic foundation colonialism established and a direct result of cyclical poverty, which wealthy countries perpetuate to this day. (shrink)

The main result of this paper is the following theorem: a closure space X has an , , Q-regular base of the power iff X is Q-embeddable in It is a generalization of the following theorems:(i) Stone representation theorem for distributive lattices ( = 0, = , Q = ), (ii) universality of the Alexandroff's cube for T 0-topological spaces ( = , = , Q = 0), (iii) universality of the closure space of filters in the lattice of all (...) subsets for , -closure spaces (Q = 0). By this theorem we obtain some characterizations of the closure space given by the consequence operator for the classical propositional calculus over a formalized language of the zero order with the set of propositional variables of the power . In particular we prove that a countable closure space X is embeddable with finite disjunctions preserved into F iff X is a consistent closure space satisfying the compactness theorem and X contains a 0, -base consisting of -prime sets. (shrink)

The hukou system is a mandatory household registration system in China that assigns an individual either an urban/non-agricultural hukou or a rural/agricultural hukou based on one’s birthplace. This system favors urban residents and discriminates against rural residents in accessing state-owned resources such as employment, education, health care, and housing. To better understand how this institutionally imposed hukou identity impacts an individual’s sense of fairness in the ultimatum game, we conducted a field experiment in China using 9–12-year-old children and collected 672 (...) observations. Subjects played a one-shot ultimatum game to allocate 20 yuan in groups of two. We employed a 2 ×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} 2 ×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} 2 experiment design and used the strategic method ultimatum game. We primed our subjects with their hukou identity before they made their decisions in the experiment. Results of this study show that hukou salience mainly affects rural hukou subjects, who belong to the perceived less-favored social group. On one hand, when the hukou identity is made salient, rural hukou proposers decrease their amount offered regardless of their responder’s hukou type. On the other hand, rural hukou responders expect higher offers from their urban hukou proposers when the hukou identity is revealed. We interpret these results as that rural hukou subjects tend to seek compensations for their perceived hukou inferiority to achieve fair distributions. (shrink)

With respect to God's producing of things, the divine transeunt activity is considered in this chapter; Aquinas argues that God is for _all_ things, the cause of being. God's production of things is distributively universal (for _all_ things) and intrinsically universal (the cause of _being_). This characterization of intrinsic universality is entailed by the production's being absolutely independent of antecedent matter (and, therefore, devoid of any operation on any pre‐existing stuff). The notion of prime matter must be included among (...) the products (or at least among the by‐products) of God's universal production for Aquinas, although the justification he offers is not the strongest sort available to him. One way of combining the distributive and intrinsic universality of God's production of things is to view the primordial universe as its single immediate effect. God's creating involves no movement, successiveness, or change. (shrink)

For a prime k, the embeddability of finite lattices are discussed for various kind of the MODkP degrees of recursive sets. In particular, all finite lattices are embeddable into the MODkP Turing degrees, whereas the non distributive lattice M3 is embeddable into the MOD2P many-one degrees but N5 is not.

The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a (...) Boolean algebra. We prove without choice principles that any Boolean algebra arises from a special spectral space X via the compact regular open sets of X; these sets may also be described as those that are both compact open in X and regular open in the upset topology of the specialization order of X, allowing one to apply to an arbitrary Boolean algebra simple reasoning about regular opens of a separative poset. Our representation is therefore a mix of Stone and Tarski, with the two connected by Vietoris: the relevant spectral spaces also arise as the hyperspace of nonempty closed sets of a Stone space endowed with the upper Vietoris topology. This connection makes clear the relation between our point-set topological approach to choice-free Stone duality, which may be called the hyperspace approach, and a point-free approach to choice-free Stone duality using Stone locales. Unlike Stone’s representation of Boolean algebras via Stone spaces, our choice-free topological representation of Boolean algebras does not show that every Boolean algebra can be represented as a field of sets; but like Stone’s representation, it provides the benefit of a topological perspective on Boolean algebras, only now without choice. In addition to representation, we establish a choice-free dual equivalence between the category of Boolean algebras with Boolean homomorphisms and a subcategory of the category of spectral spaces with spectral maps. We show how this duality can be used to prove some basic facts about Boolean algebras. (shrink)

Evolutionary transitions in individuality (ETIs) involve the formation of Darwinian collectives from Darwinian particles. The transition from cells to multicellular life is a prime example. During an ETI, collectives become units of selection in their own right. However, the underlying processes are poorly understood. One observation used to identify the completion of an ETI is an increase in collective-level performance accompanied by a decrease in particle-level performance, for example measured by growth rate. This seemingly counterintuitive dynamic has been referred (...) to as fitness decoupling and has been used to interpret both models and experimental data. Extending and unifying results from the literature, we show that fitness of particles and collectives can never decouple because calculations of fitness performed over appropriate and equivalent time intervals are necessarily the same provided the population reaches a stable collective size distribution. By way of solution, we draw attention to the value of mechanistic approaches that emphasise traits, and tradeoffs among traits, as opposed to fitness. This trait-based approach is sufficient to capture dynamics that underpin evolutionary transitions. In addition, drawing upon both experimental and theoretical studies, we show that while early stages of transitions might often involve tradeoffs among particle traits, later—and critical—stages are likely to involve the rupture of such tradeoffs. Thus, when observed in the context of ETIs, tradeoff-breaking events stand as a useful marker of these transitions. (shrink)

This paper argues that fungal mycelial networks exhibit minimal cognition through memory-integrated adaptive regulation. Drawing on cybernetic and enactivist frameworks, I develop a non-representational account of memory as the organism's capacity to modulate behavior based on temporally extended environmental coupling. I propose four operational criteria for minimal cognition: feedback-guided regulation of behavior, maintenance of internal viability conditions, structural modulation based on past environmental interactions, and plasticity across time scales that supports anticipatory adaptivity. Empirical evidence demonstrates that fungi meet all four (...) criteria through distributed memory mechanisms: fungal networks exhibit directional regrowth toward previously encountered resources even after spatial displacement; stress priming persists across multiple cell divisions; Spitzenkörper-mediated directional persistence in constrained environments; and transgenerational memory through spore imprinting. These findings challenge representationalist assumptions in cognitive science by showing that memory and cognition can emerge from morphodynamic, biochemical, and electrophysiological processes without necessary neural substrates or symbolic representations. Fungal cognition demonstrates that the organizational principles underlying cognition – feedback-driven adaptation, norm-preservation, and historical coupling – can be realized in radically different material substrates, expanding our understanding of what counts as a cognitive system. (shrink)

This introductory chapter attempts to clarify the philosophical, empirical, and theoretical bases on which a cognitive neuroscience approach to consciousness can be founded. We isolate three major empirical observations that any theory of consciousness should incorporate, namely (1) a considerable amount of processing is possible without consciousness, (2) attention is a prerequisite of consciousness, and (3) consciousness is required for some specific cognitive tasks, including those that require durable information maintenance, novel combinations of operations, or the spontaneous generation of intentional (...) behavior. We then propose a theoretical framework that synthesizes those facts: the hypothesis of a global neuronal workspace. This framework postulates that, at any given time, many modular cerebral networks are active in parallel and process information in an unconscious manner. An information becomes conscious, however, if the neural population that represents it is mobilized by top-down attentional amplification into a brain-scale state of coherent activity that involves many neurons distributed throughout the brain. The long-distance connectivity of these `workspace neurons' can, when they are active for a minimal duration, make the information available to a variety of processes including perceptual categorization, long-term memorization, evaluation, and intentional action. We postulate that this global availability of information through the workspace is what we subjectively experience as a conscious state. A complete theory of consciousness should explain why some cognitive and cerebral representations can be permanently or temporarily inaccessible to consciousness, what is the range of possible conscious contents, how they map onto specific cerebral circuits, and whether a generic neuronal mechanism underlies all of them. We confront the workspace model with those issues and identify novel experimental predictions. Neurophysiological, anatomical, and brain-imaging data strongly argue for a major role of prefrontal cortex, anterior cingulate, and the areas that connect to them, in creating the postulated brain-scale workspace. (shrink)

Consider a set of shuffled observations drawn from a fixed probability distribution over some instance domain. What enables learning of inductive generalizations which proceed from such a set of observations? The scenario is worthwhile because it epistemically characterizes most of machine learning. This kind of learning from observations is also inverse and ill-posed. What reduces the non-uniqueness of its result and, thus, its problematic epistemic justification, which stems from a one-to-many relation between the observations and many learnable generalizations? The (...) paper argues that this role belongs to any complexity regularization which satisfies Norton’s Material Theory of Induction (MTI) by localizing the inductive risk to facts in the given domain. A prime example of the localization is the Lottery Ticket Hypothesis (LTH) about overparameterized neural networks. The explanation of MTI’s role in complexity regularization of neural networks is provided by analyzing the stability of Empirical Risk Minimization (ERM), an inductive rule that controls the learning process and leads to an inductive generalization on the given set of observations. In cases where ERM might become asymptotically unstable, making the justification of the generalization by uniform convergence unavailable, LTH and MTI can be used to define a local stability. A priori, overparameterized neural networks are such cases and the combination of LTH and MTI can block ERM’s trivialization caused by equalizing the strengths of its inductive support for risk minimization. We bring closer the investigation of generalization in artificial neural networks and the study of inductive inference and show the division of labor between MTI and the optimality justifications (developed by Gerhard Schurz) in machine learning. (shrink)

Due to the novel coronavirus pandemic, the lockdown engendered has had a vicious impact on the global economy. This analysis’ prime intention is to evaluate the impact of the United States’ economic and health crisis as a result of COVID-19 on its financial stability. Additionally, the investigation analyzed the spillover impact of the worldwide economic slowdown experienced by COVID-19 on the United States’ financial volatility. The study applied an autoregressive distributed lag model and discovered that the economic and health (...) crises that occurred in the United States portentously upset the future expectations of its investors. Conspicuously, the health crisis in Spain and Italy were ominous spillovers of the United States’ financial instability in the short-run. Likewise, an economic crisis ensued in the United Kingdom because of COVID-19 causing spillover for the United States markets’ financial instability. The examination evaluated that Asian and African nations’ economic crises perilously affects the United States’ financial stability. The study determined that financial instability occurred in the United States due to its own economic and health crises persisted for a longer period than financial disequilibrium that occurred in other nations. The analysis suggested some strategies of smart lockdown that the government of the United States and other nations should follow to restart the economic cycle through tighter controls to minimize losses by following the steps of preparing a lockdown checklist, monitoring completion of lockdown tasks, and complete a close-down stock take or count. (shrink)

We give a single consolidated account of what the analytic structure of the Riemann zeta function does and does not settle about the location of its non-trivial zeros, and we settle the relation between the two exactly. The work has four parts and we mark the grade of each. First, a geometric reformulation, stated at the strength it earns. The Berry-Keating operator H = −i(x d/dx + 1/2) is unitarily equivalent to the dilation generator H′ = −i x d/dx on (...) the multiplicative Hilbert space L²(ℝ⁺, dx/x) carrying the Haar measure of the dilation group, where Stone's theorem renders H′ self-adjoint with no boundary parameter. Both realizations are essentially self-adjoint, with deficiency indices (0, 0), so the extension ambiguity reported in the spectral literature belongs to truncated and regularized models rather than to the full half-line operator, and the contribution of the change of geometry is the canonical Mellin diagonalization, not the removal of an ambiguity the full operator never had. The operator certifies a unique spectral arena, not the location of the zeros, and it certifies more sharply that the arena alone cannot supply them: every operator commuting with the dilation flow is a function of the generator and so has no eigenvalue of finite multiplicity, and by the Kato-Rosenblum theorem no trace-class perturbation of the generator escapes the absolutely continuous spectrum of the whole real line, so any spectral realization of the zeros must break the flow symmetry and exceed the trace-class neighborhood, which is the absorption-spectrum form rather than a discrete point spectrum. Second, a localization. A regularized Cauchy-Stieltjes functional built from −ζ′/ζ vanishes unconditionally in the safe regime to the right of the critical line; a Hardy-space equivalence reformulates the Riemann Hypothesis losslessly as a single causal-Fourier-support condition on one explicit tempered distribution, the boundary value of the polar-normalized logarithmic derivative g(s) = −ζ′/ζ(s) − 1/(s − 1) − 1/s, the normalization forced by the pole of ζ at s = 1, which sits inside the relevant half-plane and is governed by no hypothesis on zeros; and the obstruction that blocks the safe vanishing from extending to the critical line is identified exactly as one object, the odd-symmetric Fourier component of the boundary distribution, equivalently the imaginary part of the normalized logarithmic derivative on the critical line, which the functional equation does not constrain and which three natural closure routes cannot supply without circularity. Third, the consolidating contribution: an identity and a two-sided barrier. The identity proves that determining the odd-part object is logically equivalent to the Riemann Hypothesis, so the obstruction is not adjacent to the problem but identical to it. The barrier brackets that object from two sides, each side a theorem. On the even side the entire machinery generated by the functional equation, being symmetric under the reflection of the critical line, is structurally incapable of determining an odd-parity object, so no refinement of the functional-equation toolkit can reach it; the even channel undershoots. On the odd side the natural positivity structure that does enter the odd channel, the de Branges Hilbert-space approach, imposes a condition that implies the Riemann Hypothesis yet fails for the zeta function, established by Conrey and Li; the odd channel overshoots into falsity. The obstruction sits in the gap between an even-channel undershoot and an odd-channel overshoot, and the direction of each miss is named. The even-side miss is sharpened to a conservation law: the functional equation is an involution acting on the critical line as the parity reflection, the hypothesis lives in its odd eigenspace, and by the spectral theorem no consequence of the functional equation can carry information into that eigenspace, so the closure requirement takes the exact form of a second symmetry of the zeta function acting nontrivially on the conserved eigenspace, the structure realized in the proven function-field case by the action of Frobenius on cohomology. The conservation is active rather than passive: the functional equation forces every off-line zero into a partner sharing its height, whose contributions to the even channel are equal and opposite and cancel identically while their contributions to the odd channel are equal and add, so the even channel is a matched filter that nulls precisely the off-line signal a proof must detect, the on-line spectrum entering the even channel only as a real atomic measure the functional equation does not supply, and the off-line signature surviving solely in the odd channel as an explicit doubled dispersion profile 2(τ − γ)/[(1/2 − β)² + (τ − γ)²]. The conservation law is witnessed in the wild: the Davenport-Heilbronn function carries the identical Riemann-type symmetry shape and possesses zeros off the critical line, so the symmetry data is exhibited as independent of the on-line property over the extended class. A magnitude bound of Lindelöf type, often listed as an independent route, is shown to be parity-even and therefore to fall inside the even-side barrier rather than outside it. Fourth, a universality analysis identifying the equilibrium class of the prime field by four orthogonal critical exponents, with a measurement of which exponents discriminate the Riemann Hypothesis from its negation and which are truth-invariant across it, rendered as vanishing mutual information; and an independent structural witness from atomic physics, that the periodic table, a physical spectrum whose shell structure is fixed by the spatial rotation group and whose ordering runs over the integer counting of nuclear charge with its filling order an empirical effective-theory rule, never invokes the factorization of the integers into primes, confirming that the multiplicative prime channel in which the Riemann Hypothesis lives is a structurally distinct sector from the spatial-and-counting channel that suffices elsewhere. The consolidated picture is a measurement and a bracket. The distance from the unconditional Cauchy anchor to the critical line is one object wide; the object is the odd-part component; the component is the Riemann Hypothesis itself; and it is bracketed between two named, theorem-grade failure-directions, the even channel that cannot reach it and the odd channel that overshoots it. We make no claim of a proof. The boldest statement is the measurement: the problem is one object wide, the object is located, and the two standard channels miss it in opposite directions, the even channel falling short of it and the odd channel overshooting it. The bracket encloses these two standard channels exactly; a route that closes the hypothesis must either thread the gap between them, entering the odd channel without the even channel's parity limitation and without the natural odd construction's over-demand, or step outside the odd-side wall by building a modified construction the Conrey-Li counterexample does not reach. Either way the two named channels are walled off, and the work that remains is precisely characterized. We close by stating the determination in the two registers in which the hypothesis has a status. In the strict formal register of syntactic proof it is open, localized to the odd-part object, and bracketed between the two walls. In the physical-structural register it is the convergent determination of four mutually independent axes, the formal equivalence, the equilibrium universality class, three arithmetic-topological invariants of the integers, and the universal physics of order-parameter localization, which survive removal of every shared covariate but one. The single covariate that does not subtract out, the identification of the spectrum of the self-adjoint operator with the imaginary parts of the zeros, is identically the strict-register gap, so the two registers meet on one open object. The physical-structural register returns a convergent determination that points to the hypothesis as true, pending the determination of the odd-part component of the normalized logarithmic derivative on the critical line. That odd-part component is, pointwise, the regularization width of each pole of −ζ′/ζ on the line and so the record of every deviation of a zero from it, which makes its determination logically the hypothesis; and the explicit formula being a conserved identity between the zeros and the primes excludes any prime-side identity that would determine it independently, since such an identity is either insensitive to the deviations and true regardless of the hypothesis, or sensitive to them and reducible to the hypothesis through the conservation. The one determination the structure does not foreclose is one sourced from outside the prime-zero ledger, an operator exhibiting the zeros as its spectrum given independently of the zeta function, and none is known. The originating framework and its interpretive layer are confined to an appendix and are load-bearing for no result in the body. Keywords: Riemann Hypothesis, Hilbert-Polya conjecture, multiplicative Hilbert space, Haar measure, Mellin transform, Cauchy-Stieltjes transform, Hardy space, Paley-Wiener-Schwartz theorem, even-odd parity decomposition, functional equation, Davenport-Heilbronn function, de Branges spaces, Conrey-Li positivity, Selberg variance theorem, Gaussian Unitary Ensemble, universality class, mutual information. (shrink)

We examined two potential correlates of hypnotic suggestibility: dissociation and cognitive inhibition. Dissociation is the foundation of two of the major theories of hypnosis and other theories commonly postulate that hypnotic responding is a result of attentional abilities . Participants were administered the Waterloo-Stanford Group Scale of Hypnotic Susceptibility, Form C. Under the guise of an unrelated study, 180 of these participants also completed: a version of the Dissociative Experiences Scale that is normally distributed in non-clinical populations; a latent inhibition (...) task, a spatial negative priming task, and a memory task designed to measure negative priming. The data ruled out even moderate correlations between hypnotic suggestibility and all the measures of dissociation and cognitive inhibition overall, though they also indicated gender differences. The results are a challenge for existing theories of hypnosis. (shrink)

Paternalist policies in public health often aim to improve people’s well-being by reducing their options, regulating smoking offering a prime example. The well-being challenge is to show that people really are better off for having their options reduced. The distribution challenge is to show how the policies are justified since they produce losers as well as winners. If we start from these challenges, we can understand the importance of the empirical evidence that a very high proportion of smokers (...) regret smoking. In short, it is important that they regret it and important that the proportion is so high. This paper explains how, philosophically, regret can relate to well-being and it considers some of the strengths and weakness in the empirical research that the explanation brings out. The regret case for regulating smoking is indeed strong, although not as strong as the empirical researchers think. It is much weaker for paternalistic intervention in other public health problems, such as obesity and binge drinking. (shrink)