Results for 'Convexity'

31 found
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  1. Uniformly convex Banach spaces are reflexive—constructively.Douglas S. Bridges, Hajime Ishihara & Maarten McKubre-Jordens - 2013 - Mathematical Logic Quarterly 59 (4-5):352-356.
    We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman-Pettis theorem that uniformly convex Banach spaces are reflexive.
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  2. Naturalness and Convex Class Nominalism.Ben Blumson - 2019 - Dialectica 73 (1-2):65-81.
    In this paper I argue that the analysis of natural properties as convex subsets of a metric space in which the distances are degrees of dissimilarity is incompatible with both the definition of degree of dissimilarity as number of natural properties not in common and the definition of degree of dissimilarity as proportion of natural properties not in common, since in combination with either of these definitions it entails that every property is a natural property, which is absurd. I suggest (...)
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  3.  92
    Optimized Energy Numbers Continued.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:12.
    In this paper, we explore the properties and optimization techniques related to polyhedral cones and energy numbers with a focus on the cone of positive semidefinite matrices and efficient computation strategies for kernels. In Part (a), we examine the polyhedral nature of the cone of positive semidefinite matrices, , establishing that it does not form a polyhedral cone for due to its infinite dimensional characteristics. In Part (b), we present an algorithm for efficiently computing the kernel function on-the-fly, leveraging a (...)
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  4. A potential theory approach to an algorithm of conceptual space partitioning.Roman Urban & Magdalena Grzelińska - 2017 - Cognitive Science 17:1-10.
    This paper proposes a new classification algorithm for the partitioning of a conceptual space. All the algorithms which have been used until now have mostly been based on the theory of Voronoi diagrams. This paper proposes an approach based on potential theory, with the criteria for measuring similarities between objects in the conceptual space being based on the Newtonian potential function. The notion of a fuzzy prototype, which generalizes the previous definition of a prototype, is introduced. Furthermore, the necessary conditions (...)
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  5. Topology and Leibniz's principle of the Identity of Indiscernibles.Mormann Thomas - manuscript
    The aim of this paper is to show that topology has a bearing on Leibniz’s Principle of the Identity of Indiscernibles (PII). According to (PII), if, for all properties F, an object a has property F iff object b has property F, then a and b are identical. If any property F whatsoever is permitted in PII, then Leibniz’s principle is trivial, as is shown by “identity properties”. The aim of this paper is to show that topology can make a (...)
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  6. Risk aversion over finite domains.Jean Baccelli, Georg Schollmeyer & Christoph Jansen - 2021 - Theory and Decision 93 (2):371-397.
    We investigate risk attitudes when the underlying domain of payoffs is finite and the payoffs are, in general, not numerical. In such cases, the traditional notions of absolute risk attitudes, that are designed for convex domains of numerical payoffs, are not applicable. We introduce comparative notions of weak and strong risk attitudes that remain applicable. We examine how they are characterized within the rank-dependent utility model, thus including expected utility as a special case. In particular, we characterize strong comparative risk (...)
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  7. Continuity and completeness of strongly independent preorders.David McCarthy & Kalle Mikkola - 2018 - Mathematical Social Sciences 93:141-145.
    A strongly independent preorder on a possibly in finite dimensional convex set that satisfi es two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfi es two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (iii') completeness. Applications (...)
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  8. Universal Agent Mixtures and the Geometry of Intelligence.Samuel Allen Alexander, David Quarel, Len Du & Marcus Hutter - 2023 - Aistats.
    Inspired by recent progress in multi-agent Reinforcement Learning (RL), in this work we examine the collective intelligent behaviour of theoretical universal agents by introducing a weighted mixture operation. Given a weighted set of agents, their weighted mixture is a new agent whose expected total reward in any environment is the corresponding weighted average of the original agents' expected total rewards in that environment. Thus, if RL agent intelligence is quantified in terms of performance across environments, the weighted mixture's intelligence is (...)
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  9. Identity and Aboutness.Benjamin Brast-McKie - 2021 - Journal of Philosophical Logic 50 (6):1471-1503.
    This paper develops a theory of propositional identity which distinguishes necessarily equivalent propositions that differ in subject-matter. Rather than forming a Boolean lattice as in extensional and intensional semantic theories, the space of propositions forms a non-interlaced bilattice. After motivating a departure from tradition by way of a number of plausible principles for subject-matter, I will provide a Finean state semantics for a novel theory of propositions, presenting arguments against the convexity and nonvacuity constraints which Fine (2016, 2017a,b) introduces. (...)
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  10. Risk-taking and tie-breaking.Ryan Doody - 2023 - Philosophical Studies 180 (7):2079-2104.
    When you are indifferent between two options, it’s rationally permissible to take either. One way to decide between two such options is to flip a fair coin, taking one option if it lands heads and the other if it lands tails. Is it rationally permissible to employ such a tie-breaking procedure? Intuitively, yes. However, if you are genuinely risk-averse—in particular, if you adhere to risk-weighted expected utility theory (Buchak in Risk and rationality, Oxford University Press, 2013) and have a strictly (...)
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  11. Aggregation for potentially infinite populations without continuity or completeness.David McCarthy, Kalle M. Mikkola & J. Teruji Thomas - 2019 - arXiv:1911.00872 [Econ.TH].
    We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to (...)
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  12. La Neutro-Geometría y la Anti-Geometría como Alternativas y Generalizaciones de las Geometrías no Euclidianas.Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 20 (1):91-104.
    In this paper we extend Neutro-Algebra and Anti-Algebra to geometric spaces, founding Neutro/Geometry and AntiGeometry. While Non-Euclidean Geometries resulted from the total negation of a specific axiom (Euclid's Fifth Postulate), AntiGeometry results from the total negation of any axiom or even more axioms of any geometric axiomatic system (Euclidean, Hilbert, etc. ) and of any type of geometry such as Geometry (Euclidean, Projective, Finite, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.), and Neutro-Geometry results from the partial negation of one (...)
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  13. How to Define 'Prioritarianism' and Distinguish It from (Moderate) Egalitarianism.Christoph Lumer - 2021 - In Michael Schefczyk & Christoph Schmidt-Petri (eds.), Utility, Progress, and Technology: Proceedings of the 15th Conference of the International Society for Utilitarian Studies. Karlsruhe: KIT Scientific Publishing. pp. 153-166.
    In this paper, first the term 'prioritarianism' is defined, with some mathematical precision, on the basis of intuitive conceptions of prioritarianism, especially the idea that "benefiting people matters more the worse off these people are". (The prioritarian weighting function is monotonously ascending and concave, while its first derivation is smoothly descending and convex but positive throughout.) Furthermore, (moderate welfare) egalitarianism is characterized. In particular a new symmetry condition is defended, i.e. that egalitarianism evaluates upper and lower deviations from the social (...)
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  14. Differential Calculus Based on the Double Contradiction.Kazuhiko Kotani - 2016 - Open Journal of Philosophy 6 (4):420-427.
    The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the (...)
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  15. Sensitivity to three-dimensional orientation in visual search.James T. Enns & Ronald A. Rensink - 1990 - Psychological Science 1 (5):323-326.
    Previous theories of early vision have assumed that visual search is based on simple two-dimensional aspects of an image, such as the orientation of edges and lines. It is shown here that search can also be based on three-dimensional orientation of objects in the corresponding scene, provided that these objects are simple convex blocks. Direct comparison shows that image-based and scene-based orientation are similar in their ability to facilitate search. These findings support the hypothesis that scene-based properties are represented at (...)
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  16. Capitalmud, or Akyn's Song about the Nibelungs, paradigms and simulacra.Valentin Grinko - manuscript
    ...If, in some places, backward science determines the remaining period by the lack of optimism only by the number 123456789, then our progressive science expands it to 987654321, which is eight times more advanced than theirs. However, due to the inherent caution of scientists, both sides do not specify the measuring unit of reference — year, day, hour or minute are meant. Leonid Leonov. Collected Op. in ten volumes. Volume ten. M.: IHL, 1984, p.583. -/- The modern men being as (...)
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  17. Three concepts of decidability for general subsets of uncountable spaces.Matthew W. Parker - 2003 - Theoretical Computer Science 351 (1):2-13.
    There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, in: R.S. (...)
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  18. In the chaos of today's society: The dynamics of collapse as another shift in the quantum anthropology of Heidi Ann Russell.Radek Trnka - 2015 - Prague: Togga.
    The presented study introduces a new theoretical model of collapse for social, cultural, or political systems. Based on the current form of quantum anthropology conceptualized by Heidi Ann Russell, further development of this field is provided. The new theoretical model is called the spiral model of collapses, and is suggested to provide an analytical framework for collapses in social, cultural, and political systems. The main conclusions of this study are: 1) The individual crises in the period before a collapse of (...)
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  19. Representation of strongly independent preorders by vector-valued functions.David McCarthy, Kalle M. Mikkola & Teruji Thomas - 2017 - Mpra.
    We show that without assuming completeness or continuity, a strongly independent preorder on a possibly infinite dimensional convex set can always be given a vector-valued representation that naturally generalizes the standard expected utility representation. More precisely, it can be represented by a mixture-preserving function to a product of lexicographic function spaces.
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  20. The aesthetic appeal of minimal structures: Judging the attractiveness of solutions to traveling salesperson problems.D. Vickers, M. Lee, M. Dry, P. Hughes & Jennifer A. McMahon - 2007 - Perception and Psychophysics 68 (1):32-42.
    Ormerod and Chronicle reported that optimal solutions to traveling salesperson problems were judged to be aesthetically more pleasing than poorer solutions and that solutions with more convex hull nodes were rated as better figures. To test these conclusions, solution regularity and the number of potential intersections were held constant, whereas solution optimality, the number of internal nodes, and the number of nearest neighbors in each solution were varied factorially. The results did not support the view that the convex hull is (...)
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  21. Two Forms of Inconsistency in Quantum Foundations.Jer Steeger & Nicholas Teh - 2021 - British Journal for the Philosophy of Science 72 (4):1083-1110.
    Recently, there has been some discussion of how Dutch Book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory. In this paper, we argue that the 'form of inconsistency' underlying this alleged irrationality is deeply and comprehensively related to the more familiar 'inconsistency' phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger corresponds to a hierarchy of additivity/convexity-violations which yields formal Dutch Books of (...)
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  22. Type-2 Fuzzy Sets and Newton’s Fuzzy Potential in an Algorithm of Classification Objects of a Conceptual Space.Adrianna Jagiełło, Piotr Lisowski & Roman Urban - 2022 - Journal of Logic, Language and Information 31 (3):389-408.
    This paper deals with Gärdenfors’ theory of conceptual spaces. Let S{\mathcal {S}} be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes P~1,,P~nS\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S} be given. Our main result is the construction of a classification algorithm. That is, given an element A~S,{\tilde{A}}\in \mathcal {S}, our algorithm classifies it into the conceptual field determined by one of the given prototypes P~i.\tilde{P}_i. The construction of our algorithm uses some physical analogies (...)
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  23. The value of up-hill skiing.Ignace Haaz - 2022 - In Ignace Haaz & Amélé Adamavi-Aho Ekué (eds.), Walking with the Earth: Intercultural Perspectives on Ethics of Ecological Caring. Geneva, Switzerland: Globethics Publications. pp. 181-222.
    The value of up-hill skiing is double, it is first a sport and artistic expression, second it incorporates functional dependencies related to the natural obstacles which the individual aims to overcome. On the artistic side, M. Dufrenne shows the importance of living movement in dance, and we can compare puppets with dancers in order to grasp the lack of intentional spiritual qualities in the former. The expressivity of dance, as for, Chi Gong, ice skating or ski mountaineering is a particular (...)
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  24. NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited).Florentin Smarandache - 2021 - Neutrosophic Sets and Systems 46 (1):456-477.
    In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom or even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.) and from any type of geometry such as (Euclidean, Projective, Finite, Affine, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.) Geometry, and the (...)
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  25. Coherent choice functions without Archimedeanity.Enrique Miranda & Arthur Van Camp - 2022 - In Thomas Augustin, Fabio Gagliardi Cozman & Gregory Wheeler (eds.), Reflections on the Foundations of Probability and Statistics: Essays in Honor of Teddy Seidenfeld. Springer.
    We study whether it is possible to generalise Seidenfeld et al.’s representation result for coherent choice functions in terms of sets of probability/utility pairs when we let go of Archimedeanity. We show that the convexity property is necessary but not sufficient for a choice function to be an infimum of a class of lexicographic ones. For the special case of two-dimensional option spaces, we determine the necessary and sufficient conditions by weakening the Archimedean axiom.
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  26. Exposing some points of interest about non-exposed points of desirability.Arthur Van Camp & Teddy Seidenfeld - 2022 - International Journal of Approximate Reasoning 144:129-159.
    We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) (...)
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  27. Will I die (decease)? – I immortal (deathless) (how to realize immortality (deathlessness) in first person perspective) (Скончаюсь? – я бессмертен (как осознать бессмертие «от первого лица»)).Aleksandr Zhikharev - manuscript
    Will I die? As a hypothesis, in my natural scientific understanding, the psyche, is nothing more than, and exclusively just some states of my living brain – I will die as a result of his death. -/- In presented answer, psyche – itself own immediate reality itself, that is – undoubted. -/- This work was performed in reality “in the first person” (“subjective reality”, “phenomenal consciousness”). To realize, how, what it is the reality of the “in the first person” let’s (...)
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  28. Needs as Reference Points – When Marginal Gains to the Poor do not Matter.Arne Robert Weiß, Alexander Max Bauer & Stefan Traub - manuscript
    Imagine that only the state can meet the need for housing but decides not to do so. Unsurprisingly, participants in a vignette experiment deem this scenario unjust. Hence, justice ratings increase when the living situation improves. To a lesser extent, this also holds beyond the need threshold, understood as the minimum amount necessary for a decent life. Surprisingly, however, the justice evaluation function is highly convex below this point. The resulting S-shaped curve is akin to the value function in prospect (...)
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  29. Operational axioms for diagonalizing states.Giulio Chiribella & Carlo Maria Scandolo - 2015 - EPTCS 195:96-115.
    In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that (...)
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  30. Preliminary Science.U. M. Goraya - manuscript
    The term falak applies to any round quantity of a globular body or surface or of the surface (area) of the circumfrance of a circale,' the body surrounding the world, which turns about the centre(viz.' of Earth) is called in particular falak, and this falak is divided into many parts, but first and foremost into seven parts, which are sphereical bodies(i.e shalls) contiguous with one another in such a way that each one of them surrounds the next one, the concave (...)
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  31. Leibniz's Calculus Proof of Snell's Laws Violates Ptolemy's Theorem. Radhakrishanamurty - manuscript
    Leibniz proposed the ‘Most Determined Path Principle’ in seventeenth century. According to it, ‘ease’ of travel is the end purpose of motion. Using this principle and his calculus method he demonstrated Snell’s Laws of reflection and refraction. This method shows that light follows extremal (local minimum or maximum) time path in going from one point to another, either directly along a straight line path or along a broken line path when it undergoes reflection or refraction at plane or spherical (concave (...)
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