Experimental Evidence for Quantum Structure in Cognition

We proof a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights can accomplish what classical membership weights cannot do.Comment: 12 pages, 3 figure

Effects of classification context on categorization in natural categories

The patterns of classification of borderline instances of eight common taxonomic categories were examined under three different instructional conditions to test two predictions: first, that lack of a specified context contributes to vagueness in categorization, and second, that altering the purpose of classification can lead to greater or lesser dependence on similarity in classification. The instructional conditions contrasted purely pragmatic with more technical/quasi-legal contexts as purposes for classification, and these were compared with a no-context control. The measures of category vagueness were between-subjects disagreement and within-subjects consistency, and the measures of similarity based categorization were category breadth and the correlation of instance categorization probability with mean rated typicality, independently measured in a neutral context. Contrary to predictions, none of the measures of vagueness, reliability, category breadth, or correlation with typicality were generally affected by the instructional setting as a function of pragmatic versus technical purposes. Only one subcondition, in which a situational context was implied in addition to a purposive context, produced a significant change in categorization. Further experiments demonstrated that the effect of context was not increased when participants talked their way through the task, and that a technical context did not elicit more all-or-none categorization than did a pragmatic context. These findings place an important boundary condition on the effects of instructional context on conceptual categorization

Ternary Mixed Magnetic Co/Mn/Ni Dichloride Dihydrate

Ternary mixed magnetic Co1-xMnyNix-yCl2 center dot 2H(2)O has as its components three well studied antiferromagnets. Each is characterized by MCl2MCl2M...chemical and structural chains, with intrachain exchange interactions antiferromagnetic for the Mn component but ferromagnetic for the other two components. Competing ferromagnetic and antiferromagnetic intrachain exchange interactions occur in two different pairwise combinations. Reported here is the magnetic behavior of an equimolar mixture of the three components. One maximum appears in the magnetic susceptibility vs temperature, at 4.85 +/- 0.05 K, a quite interesting result since decidedly lower than the locations of susceptibility maxima in the pure components. A pronounced upturn in the susceptibility below 2.3 K also appears. Magnetization vs field isotherms display increasingly strong convex upward curvature and associated hysteresis with decreasing temperature. All of these characteristics differ markedly from those of the pure components

Relationship between extensions and intensions in categorization: A match made in heaven?

The present study investigated the relationship between category extension and intension for 11 different semantic categories. It is often tacitly assumed that there is a (strong) extension–intension link. However, a recent study by Hampton and Passanisi (2016) examining the patterns of stable individual differences in concepts across participants called this hypothesis into question. To conceptually replicate their findings, two studies were conducted. We employed a category judgment task to measure category extensions, whereas a property generation (in Study 1) and property judgment task (Study 2) were used to measure intensions. Using their method, that is, correlating extension and intension similarity matrices, we found nonsignificant correlations in both studies, supporting their conclusion that similarity between individuals for extensional judgments does not map onto similarity between individuals for intensional judgments. However, multilevel logistic regression analyses showed that the properties a person generated (Study 1) or endorsed (Study 2) better predicted her own category judgments compared to other people’s category judgments. This result provides evidence in favor of a link between extension and intension at the subject level. The conflicting findings, resulting from two different approaches, and their theoretical repercussions are discussed

Pruning Algorithms for Pretropisms of Newton Polytopes

Pretropisms are candidates for the leading exponents of Puiseux series that represent solutions of polynomial systems. To find pretropisms, we propose an exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton polytopes. We prefer exact arithmetic not only because of the exact input and the degrees of the output, but because of the often unpredictable growth of the coordinates in the face normals, even for polytopes in generic position. We provide experimental results with our preliminary implementation in Sage that compare favorably with the pruning method that relies only on cone intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning, accepted for presentation at Computer Algebra in Scientific Computing, CASC 201

Global Opportunities to Increase Agricultural Independence Through Phosphorus Recycling

Food production hinges largely upon access to phosphorus (P) fertilizer. Most fertilizer P used in the global agricultural system comes from mining of nonrenewable phosphate rock deposits located within few countries. However, P contained in livestock manure or urban wastes represents a recyclable source of P. To inform development of P recycling technologies and policies, we examined subnational, national, and global spatial patterns for two intersections of land use affording high P recycling potential: (a) manure‐rich cultivated areas and (b) populous cultivated areas. In turn, we examined overlap between P recycling potential and nation‐level P fertilizer import dependency. Populous cultivated areas were less abundant globally than manure‐rich cultivated areas, reflecting greater segregation between crops and people compared to crops and livestock, especially in the Americas. Based on a global hexagonal grid (290‐km2 grid cell area), disproportionately large shares of subnational “hot spots” for P recycling potential occurred in India, China, Southeast Asia, Europe, and parts of Africa. Outside of China, most of the remaining manure‐rich or populous cultivated areas occurred within nations that had relatively high imports of P fertilizer (net P import:consumption ratios ≥0.4) or substantial increases in fertilizer demand between the 2000s (2002–2006) and 2010s (2010–2014). Manure‐rich cultivated grid cells (those above the 75th percentiles for both manure and cropland extent) represented 12% of the global grid after excluding cropless cells. Annually, the global sum of animal manure P was at least 5 times that contained in human excreta, and among cultivated cells the ratio was frequently higher (median = 8.9). The abundance of potential P recycling hot spots within nations that have depended on fertilizer imports or experienced rising fertilizer demand could prove useful for developing local P sources and maintaining agricultural independence

Meaning-focused and Quantum-inspired Information Retrieval

In recent years, quantum-based methods have promisingly integrated the traditional procedures in information retrieval (IR) and natural language processing (NLP). Inspired by our research on the identification and application of quantum structures in cognition, more specifically our work on the representation of concepts and their combinations, we put forward a 'quantum meaning based' framework for structured query retrieval in text corpora and standardized testing corpora. This scheme for IR rests on considering as basic notions, (i) 'entities of meaning', e.g., concepts and their combinations and (ii) traces of such entities of meaning, which is how documents are considered in this approach. The meaning content of these 'entities of meaning' is reconstructed by solving an 'inverse problem' in the quantum formalism, consisting of reconstructing the full states of the entities of meaning from their collapsed states identified as traces in relevant documents. The advantages with respect to traditional approaches, such as Latent Semantic Analysis (LSA), are discussed by means of concrete examples.Comment: 11 page

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Classical Logical versus Quantum Conceptual Thought: Examples in Economics, Decision theory and Concept Theory

Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a layer given form by an underlying classical deterministic process, incorporating essentially logical thought and its indeterministic version modeled by classical probability theory; (ii) a layer given form under influence of the totality of the surrounding conceptual landscape, where the different concepts figure as individual entities rather than (logical) combinations of others, with measurable quantities such as 'typicality', 'membership', 'representativeness', 'similarity', 'applicability', 'preference' or 'utility' carrying the influences. We call the process in this second layer 'quantum conceptual thought', which is indeterministic in essence, and contains holistic aspects, but is equally well, although very differently, organized than logical thought. A substantial part of the 'quantum conceptual thought process' can be modeled by quantum mechanical probabilistic and mathematical structures. We consider examples of three specific domains of research where the effects of the presence of quantum conceptual thought and its deviations from classical logical thought have been noticed and studied, i.e. economics, decision theory, and concept theories and which provide experimental evidence for our hypothesis.Comment: 14 page

Seven-body central configurations: a family of central configurations in the spatial seven-body problem

The main result of this paper is the existence of a new family of central configurations in the Newtonian spatial seven-body problem. This family is unusual in that it is a simplex stacked central configuration, i.e the bodies are arranged as concentric three and two dimensional simplexes.Comment: 15 pages 5 figure