We prove that all algebras P/IR, where the IR-'s are ideals generated by partitions of W into finite and arbitrary large elements, are isomorphic and homogeneous. Moreover, we show that the smallest size of a tower of such partitions with respect to the eventually-refining preordering is equal to the smallest size of a tower on ω.

Emotion recognition systems have been of interest to researchers for a long time. Improvement of brain-computer interface systems currently makes EEG-based emotion recognition more attractive. These systems try to develop strategies that are capable of recognizing emotions automatically. There are many approaches due to different features extractions methods for analyzing the EEG signals. Still, Since the brain is supposed to be a nonlinear dynamic system, it seems a nonlinear dynamic analysis tool may yield more convenient results. A novel approach in (...) Symbolic Time Series Analysis for signal phase space partitioning and symbol sequence generating is introduced in this study. Symbolic sequences have been produced by means of spherical partitioning of phase space; then, they have been compared and classified based on the maximum value of a similarity index. Obtaining the automatic independent emotion recognition EEG-based system has always been discussed because of the subject-dependent content of emotion. Here we introduce a subject-independent protocol to solve the generalization problem. To prove our method’s effectiveness, we used the DEAP dataset, and we reached an accuracy of 98.44% for classifying happiness from sadness. It was 93.75% for three, 89.06% for four, and 85% for five emotional groups. According to these results, it is evident that our subject-independent method is more accurate rather than many other methods in different studies. In addition, a subject-independent method has been proposed in this study, which is not considered in most of the studies in this field. (shrink)

Ontologies are the prime way of organizing data in the Semantic Web. Often, it is necessary to combine several, independently developed ontologies to obtain a complete representation of a domain of interest. The complementarity of existing ontologies can be leveraged by merging them. Existing approaches for ontology merging mostly implement a binary merge. However, with the growing number and size of relevant ontologies across domains, scalability becomes a central challenge. A multi-ontology merging technique offers a potential solution to this problem. (...) We present Co Merger, a scalable multiple ontologies merging method. It takes as input a set of source ontologies and existing mappings across them and generates a merged ontology. For efficient processing, rather than successively merging complete ontologies pairwise, we group related concepts across ontologies into partitions and merge first within and then across those partitions. In both steps, user-specified subsets of generic merge requirements (GMRs) are taken into account and used to optimize outputs. The experimental results on well-known datasets confirm the feasibility of our approach and demonstrate its superiority over binary strategies. A prototypical implementation is freely accessible through a live web portal. (shrink)

This "case study" examines the shaping of a research interest. It turns on the Partition of the South Asian subcontinent in 1947, leading to the Independence and establishment of the sovereign states of Pakistan and India. The Partition was a climax within a pattern of recurrent violence in the name of Hindus and Muslims for several generations before 1947, a pattern that recurs at lower intensity continually. This study explores the emerging of an interest in the social origins of the (...) Partition out of several decades of the author's personal experience. It tracks the origins of a sense of difference between the religiously defined social categories to the medieval period--though the Mughal period saw wide-ranging cooperative activity too. The colonial period saw a major change of phase, with heightened insecurities amidst large changes in polity, economy, and society, and the rise of influential institutions for religious revival on both sides. Amidst comprehensive enlargements in the scales of organisations, communications, and activities, the sense of opposition between groups, defined in religious terms, grew; and so too the frequency and intensity of aggression across the divide. The violence in 1947 was exceptionally brutal and large in scale; but the underlying attitudes had long been in the making. To take full measure of that long inception, one needs to summon the resources not only of history but also of a wide array of other social sciences. (shrink)

An important part of the Unified Medical Language System (UMLS) is its Semantic Network, consisting of 134 Semantic Types connected to each other by edges formed by one or more of 54 distinct Relation Types. This Network is however for many purposes overcomplex, and various groups have thus made attempts at simplification. Here we take this work further by simplifying the relations which involve the three Semantic Types – Diagnostic Procedure, Laboratory Procedure and Therapeutic or Preventive Procedure. We define operators (...) which can be used to generate terms instantiating types from this selected set when applied to terms designating certain other Semantic Types, including almost all the terms specifying clinical tasks. Usage of such operators thus provides a useful and economical way of specifying clinical tasks. The operators allow us to define a mapping between those types within the UMLS which do not represent clinical tasks and those which do. This mapping then provides a basis for an ontology of clinical tasks that can be used in the formulation of computer-interpretable clinical guideline models. (shrink)

We prove that for a finitely generated infinite nilpotent group $G$ with structure $(G,\cdot,\dots)$, the connected component ${G^*}^0$ of a sufficiently saturated extension $G^*$ of $G$ exists and equals \[ \bigcap_{n\in\N} \{g^n\colon g\in G^*\}. \] We construct an expansion of ${\mathbb Z}$ by a predicate $({\mathbb Z},+,P)$ such that the type-connected component ${{\mathbb Z}^*}^{00}_{\emptyset}$ is strictly smaller than ${{\mathbb Z}^*}^0$. We generalize this to finitely generated virtually solvable groups. As a corollary of our construction we obtain an optimality result for (...) the van der Waerden theorem for finite partitions of groups. (shrink)

An MV-algebra A=(A,0,¬,⊕) is an abelian monoid (A,0,⊕) equipped with a unary operation ¬ such that ¬¬x=x,x⊕¬0=¬0, and y⊕¬(y⊕¬x)=x⊕¬(x⊕¬y). Chang proved that the equational class of MV-algebras is generated by the real unit interval [0,1] equipped with the operations ¬x=1−x and x⊕y=min(1,x+y). Therefore, the free n-generated MV-algebra Free n is the algebra of [0,1]-valued functions over the n-cube [0,1] n generated by the coordinate functions ξ i ,i=1, . . . ,n, with pointwise operations. Any such function f is a (...) McNaughton function, i.e., f is continuous, piecewise linear, and each piece has integer coefficients. Conversely, McNaughton proved that all McNaughton functions f: [0,1] n →[0,1] are in Free n . The elements of Free n are logical equivalence classes of n-variable formulas in the infinite-valued calculus of Łukasiewicz. The aim of this paper is to provide an alternative, representation-free, characterization of Free n. (shrink)

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying (...) phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed. (shrink)

The emergence of mental states from neural states by partitioning the neural phase space is analyzed in terms of symbolic dynamics. Well-defined mental states provide contexts inducing a criterion of structural stability for the neurodynamics that can be implemented by particular partitions. This leads to distinguished subshifts of finite type that are either cyclic or irreducible. Cyclic shifts correspond to asymptotically stable fixed points or limit tori whereas irreducible shifts are obtained from generating partitions of mixing hyperbolic (...) systems. These stability criteria are applied to the discussion of neural correlates of consiousness, to the definition of macroscopic neural states, and to aspects of the symbol grounding problem. In particular, it is shown that compatible mental descriptions, topologically equivalent to the neurodynamical description, emerge if the partition of the neural phase space is generating. If this is not the case, mental descriptions are incompatible or complementary. Consequences of this result for an integration or unification of cognitive science or psychology, respectively, will be indicated. (shrink)

The concept of contextual emergence has been proposed as a non-reductive, yet well- defined relation between different levels of description of physical and other systems. It is illustrated for the transition from statistical mechanics to thermodynamical properties such as temperature. Stability conditions are shown to be crucial for a rigorous implementation of contingent contexts that are required to understand temperature as an emergent property. Are such stability conditions meaningful for contextual emergence beyond physics as well? An affirmative example from cognitive (...) neuroscience addresses the relation between neurobiological and mental levels of description. For a particular class of partitions of the underlying neurobiological phase space, so-called generating partitions, the emergent mental states are stable under the dynamics. In this case, mental descriptions are (i) faithful representations of the neurodynamics and (ii) compatible with one another. (shrink)

The basic methodology of rough set theory depends on an equivalence relation induced from the generated partition by the classification of objects. However, the requirements of the equivalence relation restrict the field of applications of this philosophy. To begin, we describe two kinds of closure operators that are based on right and left adhesion neighbourhoods by any binary relation. Furthermore, we illustrate that the suggested techniques are an extension of previous methods that are already available in the literature. As a (...) result of these topological techniques, we propose extended rough sets as an extension of Pawlak’s models. We offer a novel topological strategy for making a topological reduction of an information system for COVID-19 based on these techniques. We provide this medical application to highlight the importance of the offered methodologies in the decision-making process to discover the important component for coronavirus infection. Furthermore, the findings obtained are congruent with those of the World Health Organization. Finally, we create an algorithm to implement the recommended ways in decision-making. (shrink)

A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted potentially infinite number of connectives and truth (...) values, therefore, it can be considered a general framework to provide semantics to several of the known logic systems (eg, LC, L3 LP, FDE). The presented semantics allow to converge to different standard semantics if the separation complexity procedure is annulled. Therefore, it can be understood as a framework that allows greater precision (in complexity terms) with respect to formula satisfaction. Naturally, because of how it is built, it can be incorporated into non-deterministic semantics. The presented procedure also allows generating valuations that grant a different truth value to each formula of propositional language. As a positive side effect, our method allows a constructive proof of the equipotence between N and N^n for all Natural n. (shrink)

Some partitions of Natural Number set are built through recursive processesgenerating in this manner countable examples of countable and disjoint sets whose unionis a set also countable. This process is constructive, so the Axiom of choice is not used.We provide a PC program that generates one of these special partitions and shows howto generate infinite of them. This line of reasoning can have multiple applications in Settheory and Model theory. We proved that the number of ways to make (...) these partitionsof natural numbers is not countable, there are more of these partitions (named doublycountable) than natural numbers. For each natural number greater than 1, we show aneffective procedure that generates these partitions -/- . (shrink)

Machine generated contents note: Prelude -- Introduction -- Part I: A Cabinet of Diversity -- 1. Object 1: Diversity Doesn't Work? -- 2. Object 2: Dominance -- 3. Object 3: From Wunderkammner to the Majors -- 4. Object 4: Patrol/Willy -- 5. Object 5: Accumulation/Difference that Makes No Difference -- 6. Object 6: Colorblindness/Federalist Paper no.6 -- 7. Object 7: Partition/No. 76-811: A Grievance Not of Their Making -- 8. Object 8: The Morrill Acts: "The Land Grab University" -- 9. (...) Afterthoughts -- Part II: The Constellation of Reparation -- 10. Star 1: Attempted Remedies -- 11. Star 2: Outlines of Epistemic Reparation -- 12. Star 3: How is a University like a Light Switch? -- 13. Afterthoughts -- Part III: Reparative Endeavors -- 14. Thread 1: Why Poetics? -- 15. Thread 2: Breath-Taking Landscapes: Place based interventions -- 16. Thread 3: Counter-space as the dramatization of a poetics of refusal -- 17. Thread 4: Gates/Gatekeeping -- 18. Thread 5: Unraveling Patrol -- 19. Thread 6: From Rank to Rhizome -- 20. Afterthoughts -- Acknowledgements -- Bibliography -- Notes -- Index. (shrink)

We study ultrafilters onω2produced by forcing with the quotient of${\cal P}$(ω2) by the Fubini square of the Fréchet filter onω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically generated but (...) that it shares with basically generated ultrafilters the property of not being at the top of the Tukey ordering. In fact, it is not Tukey-above [ω1]<ω, and it has only continuum many ultrafilters Tukey-below it. A tool in our proofs is the analysis of similar (but not the same) properties for ultrafilters obtained as the sum, over a selective ultrafilter, of nonisomorphic selective ultrafilters. (shrink)

The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to (...) infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue). (shrink)

Asymmetric cell division generates cell diversity and contributes to cellular aging and rejuvenation. Here, we review the molecular mechanisms enabling budding yeast to recognize spindle pole bodies (SPB, centrosome equivalent) based on their age, and guide their non‐random mitotic segregation: SPB inheritance requires the distinction of old from new SPBs and is regulated by the SPB‐inheritance network (SPIN) and the mitotic exit network (MEN). The SPIN marks the pre‐existing SPB as old and the MEN recognizes these marks translating them into (...) spindle orientation. We next revisit other molecules and structures that partition depending on their age rather than their abundance at mitosis as, for example, DNA, centrosomes, mitochondria, and histones in yeast and other systems. The recurrence of this differential behavior suggests a functional significance for numerous cell types, which we then discuss. We conclude that non‐random segregation may facilitate asymmetric cell fate determination and thereby indirectly aging and rejuvenation. (shrink)

The Hamiltonian for n relativistic electrons without interaction but in a Coulomb potential is well known. If in this Hamiltonian we take r ′ u =r′, P ′ u =P′ with u=1,2,..., n, we obtain a one-body problem in a Coulomb field, but the appearance of n of the α u , u=1,..., n, each of which corresponds to spin $\tfrac{1}{2}$ , indicates that we may have spins up to (n/2). We analyze this last problem first by denoting the 4×4 (...) matrices α, β as direct products of 2×2 matrices which correspond to the ordinary spin, and a new concept, also related to the SU(2) group, which we call sign spin. In this new notation our problem depends on the sixteen generators of a U(4) group reduced along the chain Û(2)⊗Ŭ(2) sub-groups associated with the ordinary and sign spins. We now make a change of variables in our Hamiltonian so a term ε related to the frequency ω of an oscillator, which will be our variational parameter, appears in it, and later construct the full states of the problem with a harmonic oscillator of frequency 1 and ordinary and sign spin parts. Finally we obtain the matrix representation of our Hamiltonian with respect to the states mentioned and discuss the energy spectra of the problem where the partition {h} representing the irrep of U(4) and j the total angular momentum, take the values {h}=[1], j= $\tfrac{1}{2}$ ; {h}=[11], j=0; {h}=[2], j=0. (shrink)

Schoenflies point groups are presented in terms of spatial partitions and Laue classes based on abstract groups. A much simpler system using only a minimal set of generators for three dimensional groups is then presented in the same form. This simplified treatment allows group operations of a given Laue class to be correlated to a greatly simplified Mulliken-style notation for irreducible representations of that class. Transformation matrix representations of point groups in the simplified style can then be manipulated according (...) to their position in the class or to their sub-groups in very clear procedures. Simple rules can replace the large numbers of tables necessary in the Schoenflies approach. Some applications of the method are described. (shrink)

David Lewis (1969) introduced sender-receiver games as a way of investigating how meaningful language might evolve from initially random signals. In this report I investigate the conditions under which Lewis signaling games evolve to perfect signaling systems under various learning dynamics. While the 2-state/2- term Lewis signaling game with basic urn learning always approaches a signaling system, I will show that with more than two states suboptimal pooling equilibria can evolve. Inhomogeneous state distributions increase the likelihood of pooling equilibria, but (...) learning strategies with negative reinforcement or certain sorts of mutation can decrease the likelihood of, and even eliminate, pooling equilibria. Both Moran and APR learning strategies (Bereby-Meyer and Erev 1998) are shown to promote successful convergence to signaling systems. A model is presented that illustrates how a language that codes state-act pairs in an order-based grammar might evolve in the context of a Lewis signaling game. The terms, grammar, and the corresponding partitions of the state space co-evolve to generate a language whose structure appears to reflect canonical natural kinds. The evolution of these apparent natural kinds, however, is entirely in service of the rewards that accompany successful distinctions between the sender and receiver. Any metaphysics grounded on the structure of a natural language that evolved in this way would track arbitrary, but pragmatically useful distinctions. (shrink)

In many assessment problems—aptitude testing, hiring decisions, appraisals of the risk of recidivism, evaluation of the credibility of testimonial sources, and so on—the fair treatment of different groups of individuals is an important goal. But individuals can be legitimately grouped in many different ways. Using a framework and fairness constraints explored in research on algorithmic fairness, I show that eliminating certain forms of bias across groups for one way of classifying individuals can make it impossible to eliminate such bias across (...) groups for another way of dividing people up. And this point generalizes if we require merely that assessments be approximately bias-free. Moreover, even if the fairness constraints are satisfied for some given partitions of the population, the constraints can fail for the coarsest common refinement, that is, the partition generated by taking intersections of the elements of these coarser partitions. This shows that these prominent fairness constraints admit the possibility of forms of intersectional bias. (shrink)

The modern abundance and prominence of data have led to the development of “data science” as a new field of enquiry, along with a body of epistemological reflections upon its foundations, methods, and consequences. This article provides a systematic analysis and critical review of significant open problems and debates in the epistemology of data science. We propose a partition of the epistemology of data science into the following five domains: (i) the constitution of data science; (ii) the kind of enquiry (...) that it identifies; (iii) the kinds of knowledge that data science generates; (iv) the nature and epistemological significance of “black box” problems; and (v) the relationship between data science and the philosophy of science more generally. (shrink)

Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics were generated (...) by "trivalent" matrices. This paper will show that contrary to these intuitions, logical two-valuedness has more to do with the geometrical properties of the deduction relation of a logical structure than with the algebraic properties embedded on it. (shrink)

Continuing prior work by the author, a simple classical system for personal obligation is integrated with a fairly rich system for aretaic (agent-evaluative) appraisal. I then explore various relationships between definable aretaic statuses such as praiseworthiness and blameworthiness and deontic statuses such as obligatoriness and impermissibility. I focus on partitions of the normative statuses generated ("normative positions" but without explicit representation of agency). In addition to being able to model and explore fundamental questions in ethical theory about the connection (...) between blame, praise, permissibility and obligation, this allows me to carefully represent schemes for supererogation and kin. These controversial concepts have provided challenges to both ethical theory and deontic logic, and are among deontic logic's test cases. (shrink)

This essay examines the origin of genotype-environment interaction, or G×E. "Origin" and not "the origin" because the thesis is that there were actually two distinct concepts of G×E at this beginning: a biometric concept, or \[G \times E_B\], and a developmental concept, or \[G \times E_D \]. R. A. Fisher, one of the founders of population genetics and the creator of the statistical analysis of variance, introduced the biometric concept as he attempted to resolve one of the main problems in (...) the biometric tradition of biology - partitioning the relative contributions of nature and nurture responsible for variation in a population. Lancelot Hogben, an experimental embryologist and also a statistician, introduced the developmental concept as he attempted to resolve one of the main problems in the developmental tradition of biology - determining the role that developmental relationships between genotype and environment played in the generation of variation. To argue for this thesis, I outline Fisher and Hogben's separate routes to their respective concepts of G × E; then these separate interpretations of G × E are drawn on to explicate a debate between Fisher and Hogben over the importance of G × E, the first installment of a persistent controversy. Finally, Fisher's \[G \times E_B\] and Hogben's \[G \times E_D \] are traced beyond their own work into mid-2Oth century population and developmental genetics, and then into the infamous IQ Controversy of the 1970s. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue that (...) it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing the (...) Pudlák–Rödl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraïssé classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor generating p-points which are k-arrow but not \-arrow, and in a partial order of Blass producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra \\). If the number of Fraïssé classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly \. In contrast, the set of isomorphism types of any product of finitely many Fraïssé classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template. (shrink)

We obtain an algorithm to compute finite coproducts of finitely generated Gödel algebras, i.e. Heyting algebras satisfying the prelinearity axiom =1. We achieve this result using ordered partitions of finite sets as a key tool to investigate the category opposite to finitely generated Gödel algebras . We give two applications of our main result. We prove that finitely presented Gödel algebras have free products with amalgamation; and we easily obtain a recursive formula for the cardinality of the free Gödel (...) algebra over a finite number of generators first established by A. Horn. (shrink)

This paper offers an explanation of how collaboration leads to abstract and flexible problem solving. We asked the individual and paired subjects to indicate 3/4 of 2/3 of the area of a square sheet of paper and found that (1) they primarily folded or partitioned the paper rather than algorithmically calculating the answer, (2) they strongly tendened to backtrack and confirm their proto‐plans on externalized traces such as creases on the paper, and (3) only the paired subjects shifted to the (...) mathematical strategy in their second trials. Based on these results, we propose that two factors, individuals' activeness in choosing and confirming the initial strategies and the frequent role exchange between task‐doing and monitoring in collaborative situations, interact in collaboration to generate various solutions differing in the degree of abstraction, which are then reflected upon by the participants to lead them to abstraction. (shrink)

We report an empirical study of elementary algebra errors, conducted in three separate schools. The errors are diagnosed using mal‐rules, as proposed by Sleeman (1984, 1,985). Our analysis uncovers the following properties of algebra mal‐rules: The frequency of mal‐rules is severely skewed, there are many infrequent mal‐rules and few frequent ones; mal‐rules are very unstable, students typically use mal‐rules very irregularly; different mal‐rules have explanatory power in different schools (many of our most powerful mal‐rules are previously unreported); mal‐rule diagnosis Is (...) more successful with more skilled students; students' confidence ratings do not partition the total set of mal‐rules, every mal‐rule we find is associated with high confidence ratings by at least one student. The Implications of our data for cognitive theories of error generation are discussed. Contrary to commonplace assumptions, we argue that It is impossible to make a clear distinction between slips and mistakes; most errors depend on properties of the knowledge base and the cognitive architecture. Errors In a procedural skill cannot be assumed to be purely syntactic In orgin. (shrink)

In this paper, an efficient chaos-based image encryption scheme is proposed, which uses the imitating jigsaw method containing revolving and shifting operations. In this scheme, there are three processes in encryption: preprocessing, encryption process, and postprocessing. In the preprocessing, the original image is partitioned into 64 × 64 pixel image blocks and then randomly revolved and shifted under control sequences which are generated by the hyperchaotic Lorenz system whose initial conditions are calculated by original image and keys. Therefore, the preprocessing (...) is sensitive to plain image against differential attacks. In the encryption process, the after-preprocessing image is partitioned into 32 × 32 pixel image blocks; next they are randomly revolved and encrypted by control sequence and key blocks which are generated by the skew tent map. In postprocessing, the after-encryption image is partitioned into 16 × 16 pixels’ image blocks, and they are randomly revolved and shifted again under control sequences which are related with encrypted image and keys. The postprocessing further increases the diffusion characteristics. Moreover, the test experiment and security analyses are given; the results show that our proposed cryptosystem has both security and speed performance. (shrink)

We analyze the cognitive strategies underlying performance in the Number task, a Math game that requires both arithmetic fluency and mathematical creativity. In this game all elements in a set of numbers have to be used precisely once to create a target number with basic arithmetic operations. We argue that some instances of this game are NP complete, by showing its relation to the well-known Partition problem. We propose heuristics based on the distinction in forward and backward reasoning. The Number (...) Game is part of Math Garden, a popular online educational platform for practicing and monitoring math skills using innovations in computerized adaptive testing. These educational games generate enormous amounts of rich data on children's cognitive development. We found converging evidence for the use of forward proximity heuristics in the data of Math Garden, consisting of more than 20 million answers to 1,700 items. Item difficulties and the structure of correct answers were analyzed. (shrink)

The automated parsing of 130,213 news articles about the 2012 US presidential elections produces a network formed by the key political actors and issues, which were linked by relations of support and opposition. The nodes are formed by noun phrases and links by verbs, directly expressing the action of one node upon the other. This network is studied by applying insights from several theories and techniques, and by combining existing tools in an innovative way, including: graph partitioning, centrality, assortativity, hierarchy (...) and structural balance. The analysis yields various patterns. First, we observe that the fundamental split between the Republican and Democrat camps can be easily detected by network partitioning, which provides a strong validation check of the approach adopted, as well as a sound way to assign actors and topics to one of the two camps. Second, we identify the most central nodes of the political camps. We also learnt that Clinton played a more central role than Biden in the Democrat camp; the overall campaign was much focused on economy and rights; the Republican Party is the most divisive subject in the campaign, and is portrayed more negatively than the Democrats; and, overall, the media reported positive statements more frequently for the Democrats than the Republicans. This is the first study in which political positions are automatically extracted and derived from a very large corpus of online news, generating a network that goes well beyond traditional word-association networks by means of richer linguistic analysis of texts. (shrink)

It is commonly accepted that people can, and regularly do, deceive themselves. Yet closer examination reveals a set of conceptual puzzles that make self-deception difficult to explain. Applying the conditions for other-deception to self-deception generates what are known as the ‘paradoxes’ of belief and intention. Simply put, the central problem is how it is possible for me to believe one thing, and yet intentionally cause myself to simultaneously believe its contradiction. There are two general approaches taken by philosophers to account (...) for these puzzles about the self-deceptive state and the process of self-deception. ‘Partitioning’ strategies try to resolve the paradoxes by proposing that the mind is divided in some way that allows self-deception to occur. ‘Reformulation’ strategies suggest that the conditions we use to define self-deception should be modified so that the paradoxes do not arise at all. Both approaches are subject to criticism about the consequences of the strategies philosophers use, but recent cross-disciplinary analyses of self-deception may help shed light on the puzzles that underlie this phenomenon. (shrink)

De Finetti was a strong proponent of allowing 0 credal probabilities to be assigned to serious possibilities. I have sought to show that (pace Shimony) strict coherence can be obeyed provided that its scope of applicability is restricted to partitions into states generated by finitely many ultimate payoffs. When countable additivity is obeyed, a restricted version of ISC can be applied to partitions generated by countably many ultimate payoffs. Once this is appreciated, perhaps the compelling character of the (...) Shimony argument will be less overwhelming and the attractiveness of de Finetti's more permissive attitude will become more apparent.I want to push the permissive tendency in de Finetti still further. It seems doubtful that RUIWC should be required as de Finetti apparently suggested. It is also excessively dogmatic and restrictive to require that the credal states of ideally situated rational agents be numerically definite (Levi 1974, 1980). And de Finetti's rejection of objectivism in statistics overreached itself when he dismissed objective probabilities as meaningless metaphysical artefacts (Levi 1986). In this respect, the philosophically most important lessons de Finetti has to teach us are to be found not in his celebrated representation theorem but in his discussions of the relations between 0-probability and possibility, conditional probability and countable additivity. Perhaps, the technical issues involved are remote and pedantic. But the attitude de Finetti sought to inculcate is of profound importance. (shrink)

In the human cognitive economy there are four grades of epistemic involvement. Knowledge partitions into distinct sorts, each in turn subject to gradations. This gives a fourwise partition on ignorance, which exhibits somewhat different coinstantiation possibilities. The elements of these partitions interact with one another in complex and sometimes cognitively fruitful ways. The first grade of knowledge I call “anselmian” to echo the famous declaration credo ut intelligam, that is, “I believe in order that I may come to (...) know”. As construed here, one knows in this anselmian way that E = mc2 just in case one knows that sentence expresses a true statement, but without having to understand the proposition it expresses. Most epistemologists ignore the significance of this grade of epistemic involvement. In a second grade of epistemic involvement, knowing that E = mc2 is knowing what that sentence means and understanding the proposition it express. This is knowledge in the propositional or semantic sense, and is the dominant target of epistemological investigation. Tacit and implicit knowledge occupies another tier. A typical example would be something that someone has “known all along” but, until now, hasn’t had occasion to put her mind to it or formulate in words. TI-knowledge remains a minority interest in today’s epistemology. Operating at a fourth grade of epistemic involvement is what I call “impact”-knowledge, which is the knowledge of a matter at its deepest and most widespread. An example, to be discussed below, is the knowledge that was generated by the Wiles proof of Fermat’s last theorem. Its true importance lies not only, or even mainly, in its verification of a commonly accepted fact about numbers, but rather in its enrichment of the mathematics of elliptical curves and the promise it holds for greater advancement into the mathematical unknown. Knowledge of this fourth grade has yet to find a seat in the parliaments of epistemology. Knowledge of the anselmian sort is independent of the other three. Tacit and implicit knowledge is incompatible with anselmian and semantic knowledge but coinstantiable with impact-knowledge. Semantic knowledge is incompatible with tacit and implicit knowledge but coinstantiable with the others. Impact-knowledge is pairwise coinstantiable with the others. Below I will bring the ignorance partitions into such alignment as they have with these ones. In doing so, I’ll propose a naturalized causal response epistemology designed to give these interactive distinctions the theoretical air they need to breathe. (shrink)

This article engages with the production and government of migrant multiplicities in border zones of Europe, arguing that the specificity of migrant multiplicities consists in their temporary and divisible character. It is argued that there are three different forms of migrant multiplicities: (1) the multiplicity produced due to migrants’ spatial proximity; (2) the virtual multiplicity generated through data; and (3) the visualized and narrated multiplicity that emerges from media portraits of the ‘spectacle’ of the arrivals of migrants. It is claimed (...) that multiplicities are made to divide and partition the migrants and thus prevent the formation of a collective political subject. In the concluding section, the article deals with the ambivalent character of the term ‘the mob’, addressing the twofold dimension of migrant multiplicities: these are in fact generated by techniques of power, at the same time exceeding them and representing potential emerging political subjects. (shrink)

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. -/- Another consequence of (...) vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper. (shrink)

How have contemporary media artworks been proposing hybrid experiences, discussing the ontological implications from the experimentation with emerging techniques that alter our way of being-in-the-world? These experiences dialectically articulate aesthetic relations between real and virtual, visible and invisible, human and technological. In this article, we develop a participant observation of two specific works: Generation 244 (2011), by Scott Draves, and Zee (2008), by Kurt Hentschläger. This observation establishes a dialogue with phenomenology as it considers experience and perception as needed prerequisites (...) for the analysis, as proposed by Merleau-Ponty. In this scenario, we have observed that a whole way of partitioning the sensible resets itself and points in the direction of a trans-immanence, generating an integrated knowledge that not only relies on reason, but in a collective wisdom where we can find, according to Didi-Huberman, a ‘light of survival’. (shrink)

Traditionalists affirm that in self-deception I intend to deceive myself; but, on the standard account of interpersonal deception, according to which deceiver intend to make their target believe a falsehood, traditionalism generates paradoxes, arising from the fact that I will surely know that I want to make myself believe a falsehood. In this thesis, I argue that these well-known paradoxes need not arise under my manipulativist account of deception. In particular, I defend traditionalism about self-deception by showing that what causes (...) paradoxes is not the idea that self-deception is an intrapersonal analogue of interpersonal deception but rather our incorrect conceptions of deception, interpersonal deception, and lying. I show, by way of counterexamples, that the essence of deception is not ending up epistemically worse off but rather being intentionally manipulated into forming or retaining a certain truth-evaluable mental state. Vitally, contra the standard view, the deceiver need not hold that the mental state he intends to produce in the deceived involves a falsehood; in fact, the targeted effect may involve a proposition believed by the deceiver to be true or about whose truth the deceiver suspends belief. Any phenomenon rightly called self-deception, I argue, involves an action in which the person intentionally manipulates (by way of a trick) her own way of forming or retaining some truth-evaluable mental state of her own (belief or a belief-like thought). Thus, on the manipulativist view, a self-deceiver may non-paradoxically intend to deceive himself: the relevant intention is to affect a particular truth-evaluable thought by way of non-deviantly manipulating his agential use of his own cognitive capacities. While all cases of self-deception involve intentional manipulation of the self by the self, how this manipulative trick works out varies in different kinds of cases. In some cases, the self-deceptive manipulative trick is not intentional under that description, a description that captures the so-called deflationary view. Although the manipulativist account allows for numerous different strategies of self-deception, and is consistent with both traditionalism and deflationism, it cannot, by itself, vindicate the idea of lying to oneself. On the standard conception, lying to myself is practically impossible (if the mind is not partitioned) and this is because the very forming the intention to lie to myself – as including the intention to make myself believe my own lie – seems very unlikely. Arguably, people will not φ if they think that φ-ing is impossible. I argue that some kinds of behaviour typically understood as self-deception are actually cases in which the person is lying to herself without the intention to deceive herself; rather, she avoids legitimising an unfavourable state of affairs by openly affirming its contrary. It may also be the case, however, that some lies to oneself are aimed at deceiving – this is because, as I argue, liars need not assert what they believe is false; hence, by lying to myself, I may intend to increase my confidence in the belief I already hold. Finally, the motive for self-deception is always a matter of preserving the person’s endorsed idealised picture of reality. This account allows me to explain all possible cases of self-deception. In the last chapter, I apply my theory to some paradigmatic cases first outlined in my introduction. (shrink)

This article examines eight “gaps” in order to clarify why the quantitative genetics methods of partitioning variation of a trait into heritability and other components has very limited power to show anything clear and useful about genetic and environmental influences, especially for human behaviors and other traits. The first two gaps should be kept open; the others should be bridged or the difficulty of doing so should be acknowledged: 1. Key terms have multiple meanings that are distinct; 2. Statistical patterns (...) are distinct from measurable underlying factors; 3. Translation from statistical analyses to hypotheses about measurable factors is difficult; 4. Predictions based on extrapolations from existing patterns of variation may not match outcomes; 5. The partitioning of variation in human studies does not reliably estimate the intended quantities; 6. Translation from statistical analyses to hypotheses about the measurable factors is even more difficult in light of the possible heterogeneity of underlying genetic or environmental factors; 7. Many steps lie between the analysis of observed traits and interventions based on well-founded claims about the causal influence of genetic or environmental factors; 8. Explanation of variation within groups does not translate to explanation of differences among groups. At the start, I engage readers’ attention with three puzzles that have not been resolved by past debates. The puzzles concern generational increases in IQ test scores, the possibility of underlying heterogeneity, and the translation of methods from selective breeding into human genetics. After discussing the gaps, I present each puzzle in a new light and point to several new puzzles that invite attention from analysts of variation in quantitative genetics and in social science more generally. The article’s critical perspectives on agricultural, laboratory, and human heritability studies are intended to elicit further contributions from readers across the fields of history, philosophy, sociology, and politics of biology and in the sciences. (shrink)

The BPR assumes that we already know how sentences are partitioned into focused and backgrounded material, and this is quite legitimate, given the literature on the topic , von Stechow ). If the BPR was true, no more would have to be said about the meaning of focus. The behavior of whatever inferences are generated by backgrounding could be taken care of by theories dealing with the projection of presuppositions of the familiar kind, the presuppositions of definite descriptions, clefts, or (...) factives, for example. This is a non-trivial and interesting claim. (shrink)

According to the Aristotelian account of substantial change, that is, the corruption of one substance and the generation of another, prime matter must be found at the starting and at the end point of change, as that which persists throughout the change. But knowing that matter remains as the substrate of change tells us little about the nature of this matter, which constitutes both the corrupted substance and the new generated substance. Among the questions we can ask about its nature (...) are whether prime matter is an entity of its own apart from form; whether it is one in all those individual material substances or is somehow divided or partitioned into different parts. Early commentaries on the Physics and Metaphysics were interested in precisely these questions about the unity and divisibility of prime matter and about what kind of unity this may be. This article aims to investigate how authors from the English commentary tradition in the period 1250–1270 answered these questions. (shrink)

Mitochondrial function is achieved through the cooperative interaction of two genomes: one nuclear (nuDNA) and the other mitochondrial (mtDNA). The unusual transmission of mtDNA, predominantly maternal without recombination is predicted to affect the fitness of male offspring. Recent research suggests the strong sexual dimorphism in aging is one such fitness consequence. The uniparental inheritance of mtDNA results in a selection asymmetry; mutations that affect only males will not respond to natural selection, imposing a male‐specific mitochondrial mutation load. Prior work has (...) implicated this male‐specific mutation load in disease and infertility, but new data from fruit flies suggests a prominent role for mtDNA in aging; across many taxa males almost invariably live shorter lives than females. Here we discuss this new work and identify some areas of future research that might now be encouraged to explore what may be the underpinning cause of the strong sexual dimorphism in aging.Editor's suggested further reading in BioEssays: Mitonuclear match: Optimizing fitness and fertility over generations drives ageing within generations AbstractMitochondrial manoeuvres: Latest insights and hypotheses on mitochondrial partitioning during mitosis in Saccharomyces cerevisiae AbstractMitochondria and the culture of the Borg Abstract. (shrink)

We consider Geanakoplos and Polemarchakis’s generalization of Aumman’s famous result on “agreeing to disagree", in the context of imprecise probability. The main purpose is to reveal a connection between the possibility of agreeing to disagree and the interesting and anomalous phenomenon known as dilation. We show that for two agents who share the same set of priors and update by conditioning on every prior, it is impossible to agree to disagree on the lower or upper probability of a hypothesis unless (...) a certain dilation occurs. With some common topological assumptions, the result entails that it is impossible to agree not to have the same set of posterior probabilities unless dilation is present. This result may be used to generate sufficient conditions for guaranteed full agreement in the generalized Aumman-setting for some important models of imprecise priors, and we illustrate the potential with an agreement result involving the density ratio classes. We also provide a formulation of our results in terms of “dilation-averse” agents who ignore information about the value of a dilating partition but otherwise update by full Bayesian conditioning. (shrink)

One lists the distinct pairs of categorical premises formulable via only the positive terms, S,P,M, by constructing a six by six matrix obtained by pairing the six categorical P-premises, A, O, A, O, where P* ∈ {P,P′}, with the six, similar, categorical S-premises. One shows how five rules of valid syllogism, select only 15 distinct PCPs that entail logical consequences belonging to the set L+: = {A, O, A, E, O, I}. The choice of admissible LCs can be regarded as (...) a condition separated from the conditions contained in the RofVS: the usual eight PCPs that generate valid syllogisms are obtained when the only admissible LCs belong to the set L: = {A, E, O, I} and no existential imports are addressed. A 64 PCP-matrix obtains when both PCPs and LCs may contain indefinite terms—the positive, S,P,M, terms, and their complementary sets, S′,P′, M′, in the universe of discourse, U, called the negative terms. Now one can accept eight LCs: A, I, where P* ∈ {P,P′}, S* ∈ {S,S′}, and there are 32 conclusive PCPs, entailing precise, “one partitioning subset of U” LCs. The four rules of conclusive syllogisms predict the less precise LCs, left after eliminating the middle term from the exact LCs. The RofCS also predict that the other 32 PCPs of the 64 PCP-matrix are non-conclusive. The RofVS and the RofCS are generalized, and arguments are given, for also accepting as valid syllogisms the conclusive syllogisms formulable via positive terms which entail the LCs A and O. (shrink)

We summarize the essential ingredients, which enabled us to derive the path-integral for a system of harmonically interacting spin-polarized identical particles in a parabolic confining potential, including both the statistics (Bose–Einstein or Fermi–Dirac) and the harmonic interaction between the particles. This quadratic model, giving rise to repetitive Gaussian integrals, allows to derive an analytical expression for the generating function of the partition function. The calculation of this generating function circumvents the constraints on the summation over the cycles of (...) the permutation group. Moreover, it allows one to calculate the canonical partition function recursively for the system with harmonic two-body interactions. Also, static one-point and two-point correlation functions can be obtained using the same technique, which make the model a powerful trial system for further variational treatments of realistic interactions. (shrink)

In his pioneering work on Abstract Argumentation, P.M. Dung set a wide scenario by connecting stable models in Logic and Game Theory to simple Abstract Argumentation Frameworks ( AAF), which are essentially directed graphs in which arguments are represented as nodes, and the attack relation is represented by arrows. From such abstraction and simplicity, it is possible to capture important properties in many different fields. The Stable Marriage ( SM) problem is exactly one of such representable problems. Given two sets (...) of individuals partitioned into men and women, a matching is stable when there does not exist any man-woman match by which both man and woman would be individually better off than they are with the person to which they are currently matched. Stable matchings correspond to stable extensions if an AAF is correctly generated from the given SM problem. In this paper we elaborate on the original formulation by Dung, by also encoding SM problems with ties and incomplete preference lists into AAFs. Moreover, we use Weighted Abstract Argumentation to represent optimality criteria in the optimal extension of SM problems, where some matchings are better than others: criteria may consider only the preference of either men, or women, or a more global view obtained by combining the preferences of both. (shrink)

The main result of the present article is the following: Let N be an infinite subset of,, and let be a matrix with infinitely many rows of completely Ramsey subsets of such that for every n,. Then there exist, a sequence of nonempty finite subsets of N, and an infinite subset T of such that for every infinite subset I of. We also give an application of this result to partitions of an uncountable analytic subset of a Polish space (...) X into sets belonging to the σ‐algebra generated by the analytic subsets of X. (shrink)