Irreducible Properties Research Articles

The determinant of the stress matrix and restorability of hinged frameworks from self-stresses

We consider static-geometrical properties of planar hinged frameworks some of whose hinges are fastened. For such frameworks we establish some properties of the determinant of the stress matrix, including a necessary and sufficient condition for the irreducibility of this determinant as a polynomial. Using the irreducibility property, we prove the existence of uncancellable completely stressed frameworks with non-collinear fastened hinges for two infinite sequences of structure schemes. We give examples of frameworks such that the positions of all their free hinges can be restored knowing the space of self-stresses and the positions of the fastened hinges. However, this cannot be done knowing only one arbitrary stress instead of the whole space of self-stresses.

Entropy and the Self-Organization of Information and Value

Adam Smith, Charles Darwin, Rudolf Clausius, and Léon Brillouin considered certain “values” as key quantities in their descriptions of market competition, natural selection, thermodynamic processes, and information exchange, respectively. None of those values can be computed from elementary properties of the particular object they are attributed to, but rather values represent emergent, irreducible properties. In this paper, such values are jointly understood as information values in certain contexts. For this aim, structural information is distinguished from symbolic information. While the first can be associated with arbitrary physical processes or structures, the latter requires conventions which govern encoding and decoding of the symbols which form a message. As a value of energy, Clausius’ entropy is a universal measure of the structural information contained in a thermodynamic system. The structural information of a message, in contrast to its meaning, can be evaluated by Shannon’s entropy of communication. Symbolic information is found only in the realm of life, such as in animal behavior, human sociology, science, or technology, and is often cooperatively valuated by competition. Ritualization is described here as a universal scenario for the self-organization of symbols by which symbolic information emerges from structural information in the course of evolution processes. Emergent symbolic information exhibits the novel fundamental code symmetry which prevents the meaning of a message from being reducible to the physical structure of its carrier. While symbols turn arbitrary during the ritualization transition, their structures preserve information about their evolution history.

Irreducibility and strong Feller property for stochastic evolution equations in Banach spaces

The main goal of this paper is to generalize to Banach spaces the well-known results for diffusions on Hilbert spaces obtained in [Peszat, S. and Zabczyk, J. (1995). Strong Feller property and irreducibility for diffusions on Hilbert spaces. Ann. Probab. 23(1): 157-172.]. More precisely, we are aiming to prove the strong Feller property and irreducibility of the solutions to a stochastic evolution equations (SEEs) in Banach spaces. We give sufficient conditions on the path space and the coefficients of the SEEs for these aforementioned properties to hold. We apply our result to investigate the long-time behavior of a stochastic nonlinear heat equations on $L^p$-space with $p>4$. Our result implies the uniqueness of the invariant measure, if it exists, for the stochastic nonlinear heat equations on $L^p$-space with $p>4$.

Selfless Persons: Goodness in an Impersonal World?

AbstractMark Johnston takes reality to be wholly objective or impersonal, and aims to show that the inevitability of death does not obliterate goodness in such a naturalistic world. Crucial to his argument is the claim that there are no persisting selves. After critically discussing Johnston's arguments, I set out a view of persons that shares Johnston's view that there are no selves, but disagrees about the prospects of goodness in a wholly impersonal world. On my view, a wholly objective world is ontologically incomplete: Persons have irreducible first-person properties. My aim is to show that we can (and should) reject selves, but that we can (and should) retain persons and their essential first-person properties as ontologically significant.

Efficient algorithms for fourth and sixth-order two-point non-linear boundary value problems using non-polynomial spline approximations on a geometric mesh

An efficient algorithm for the numerical solution of linear and non-linear higher (even)-order two-point boundary value problems has been developed. The method is third-order accurate and applicable to both singular and non-singular cases. We have used non-polynomial spline basis and geometric mesh finite differences for the generation of new scheme. The irreducibility and monotone property of the iteration matrix have been established, that justify the convergence property of the proposed method. Some computational experiments have been carried out to demonstrate the efficiency in terms of convergence order and maximum absolute error estimates. The numerical results justify the reliability and efficiency of the method both in terms of order and accuracy.

On the irreducibility of irreducible characters of simple Lie algebras

We establish an irreducibility property for the characters of finite dimensional, irreducible representations of simple Lie algebras (or simple algebraic groups) over the complex numbers, i.e., that the characters of irreducible representations are irreducible after dividing out by (generalized) Weyl denominator type factors. For S L ( r ) SL(r) the irreducibility result is the following: let λ = ( a 1 ≥ a 2 ≥ ⋯ ≥ a r − 1 ≥ 0 ) \lambda =(a_1\geq a_2\geq \cdots \geq a_{r-1}\geq 0) be the highest weight of an irreducible rational representation V λ V_{\lambda } of S L ( r ) SL(r) . Assume that the integers a 1 + r − 1 , a 2 + r − 2 , ⋯ , a r − 1 + 1 a_1+r-1, ~a_2+r-2, \cdots , a_{r-1}+1 are relatively prime. Then the character χ λ \chi _{\lambda } of V λ V_{\lambda } is strongly irreducible in the following sense: for any natural number d d , the function χ λ ( g d ) , g ∈ S L ( r , C ) \chi _{\lambda }(g^d), ~g\in SL(r,\mathbb {C}) is irreducible in the ring of regular functions of S L ( r , C ) SL(r,\mathbb {C}) .

The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Nonlinear Higher Order Two-Point Boundary Value Problems

An efficient algorithm for the numerical solution of higher (even) orders two-point nonlinear boundary value problems has been developed. The method is third order accurate and applicable to both singular and nonsingular cases. We have used cubic spline polynomial basis and geometric mesh finite difference technique for the generation of this new scheme. The irreducibility and monotone property of the iteration matrix have been established and the convergence analysis of the proposed method has been discussed. Some numerical experiments have been carried out to demonstrate the computational efficiency in terms of convergence order, maximum absolute errors, and root mean square errors. The numerical results justify the reliability and efficiency of the method in terms of both order and accuracy.

Ideality, Divine Reality, and Realism

Ideality, Divine Reality, and Realism

Dimensional Analysis of Psychosocial Barriers to Prevention of Early Childhood Caries Among Recent Immigrants

The objective of this article is to define the underlying dimensions of psychosocial barriers to obtaining and providing dental care for young children among recent immigrants. Fifteen focus groups were conducted with 99 primary caregivers from African, South Asian, and Chinese recent immigrants. A secondary analysis of identified barriers using dimensional analysis methodology was performed to determine dimensions and properties of barriers. The analysis continued until irreducible properties were found or emerging dimensions were not relevant to the study. Identified dimensions were associated with barriers and individuals. Type, number, level, objectiveness, nature, and impact were barrier-related; awareness and controllability were individual-related dimensions. Type refers to barriers themselves. Number and level indicate the amount and location of barriers, respectively. Objectiveness refers to the extent that perceived barrier reflects reality and nature indicates its intrinsic characteristic. Impact concerns behaviors, goals, and outcomes compromised by barriers. Awareness alludes to the extent that individuals are aware of the barriers and controllability explains how much control people perceive to have over barriers. Identified dimensions are useful for better understanding and addressing existing barriers to children’s optimal oral health.

The organism – reality or fiction?

What is an ‘organism’? A state of matter, or a particular type of living being chosen as an experimental object, like the fruit fly or the roundworm c. elegans, which are ‘model organisms’? Organisms are real, in a trivial sense, since flies and Tasmanian tigers and Portuguese men-o-war are (or were, in the case of the Tasmanian tiger) as real as tables and chairs and planets. But at the same time, they are meaningful constructs, as when we describe Hegel or Whitehead as philosophers of organism in the sense that they insist on the irreducible properties of wholes – sometimes, living wholes in particular. In addition, the idea of organism is sometimes appealed to in a polemical way, as when biologists or philosophers angrily oppose a more ‘holistic’ sense of organism to a seemingly cold-hearted, analytic and dissective attitude associated with ‘mechanism’ and ‘reductionism’. We murder to dissect, or as the famous physicist Niels Bohr warned, we may kill the organism with our too-detailed measurements.

Emergence, Closure and Inter-level Causation in Biological Systems

In this paper, we advocate the idea that an adequate explanation of biological systems requires appealing to organizational closure as an emergent causal regime. We first develop a theoretical justification of emergence in terms of relatedness, by arguing that configurations, because of the relatedness among their constituents, possess ontologically irreducible properties, providing them with distinctive causal powers. We then focus on those emergent causal powers exerted as constraints, and we claim that biological systems crucially differ from other natural systems in that they realize a closure of constraints, i.e. a second-order emergent regime of causation such that the constituents, each of them acting as a constraint, realize a mutual dependence among them, and are collectively able to self-maintain. Lastly, we claim that closure can be justifiably taken as an emergent regime of causation, without admitting that it inherently involves whole-parts causation, which would require to commit to stronger ontological and epistemological assumptions.

Nominalism and Systemism: On the Non-Reductionist Nature of Methodological Individualism

This paper investigates the systemic nature of methodological individualism. According to widespread belief, the notion of autonomy of the actor that is defended by methodological individualism is mistaken because it is incompatible with the study of society in terms of its organized structure. We argue that this viewpoint must be rejected. In our opinion, it stems from confusion between ontological nominalism – the idea that superhuman collective entities do not exist – and reductionism. In contrast, we would argue that methodological individualism is a form of nominalist structuralism. Following Hayek, Popper and Boudon, we will maintain that methodological individualism is not incompatible with the reference to systemic and irreducible properties. As these authors stressed, the history of methodological individualism is full of examples of non-reductionist explanations that undermine the widespread theory of the equivalence between methodological individualism and reductionism. We will state, therefore, that the current debate about methodological individualism is often based on a caricature of the concept of methodological individualism that does not match its correct meaning. In addition, we will provide a criticism of the notion of “structural individualism” that is becoming increasingly popular among social scientists.

The Content and Phenomenology of Perceptual Experience

The paper’s main target is strong and reductive “representationalism”. What we claim is that even though this position looks very appealing in so far as it does not postulate intrinsic and irreducible experiential properties, the attempt it pursues of accounting for the phenomenology of experience in terms of representational content runs the risk of providing either an inadequate phenomenological account or an inadequate account of the content of the experience.

Response to “Emergence in Sociology”

Jens Greve has accurately summarized nonreductive individualism (NRI) and has made an important contribution to an ongoing discussion concerning individualism, reductionism, and emergentism. Greve’s primary criticism is of my account of downward causation, and he cites Kim’s critique of Fodor by analogy. I argue that my original paper already addressed Kim’s critique, by drawing on other philosophers of mind that Greve does not engage with, to make an argument for downward causation based on wild disjunction. Further, I argue that Greve does not successfully make the case that the issue of the autonomy of the mental level is distinct from the autonomy of the social level. As empirical examples of irreducible emergent group properties, I cite studies of improvisational theater dialogues, and studies of social networks.

Une représentation galoisienne universelle attachée aux formes modulaires modulo 2

Let A be the algebra of Hecke operators acting on mod 2 cusp forms of level 1 and any weight. Nicolas and Serre have determined the structure of A: one has A≃F2〚x,y〛. Let GQ,2 be the Galois group of the maximal extension of Q unramified outside 2 and ∞, and let G be its maximal pro-2-quotient. One constructs a continuous Galois representation r:G→SL2(A) such that trr(Frobp)=Tp for all odd prime p. One also proves its uniqueness and one studies its irreducibility properties.

English No Matter Construction: A Construction-based Perspective

The expression no matter, combining with an interrogative clause X, expresses ‘it doesn’t matter what the value is of X’ and displays many syntactic and semantic peculiarities. To better understand the grammatical properties of the construction in question, we investigate English corpora available online and suggest that some of the irreducible properties the construction displays can be best captured by the inheritance mechanism which plays a central role in the HPSG and Construction Grammar. We show that the construction in question has its own constructional properties, but also inherits properties from related major head constructions.

Irreducible Divisor Graphs and Factorization Properties of Domains

This article examines the connections between the factorization properties of a domain, e.g., unique factorization domain (UFD), finite factorization domain (FFD), and the domain's irreducible divisor graphs. In particular, we show that although there are some nice correlations between the properties of the domain D and the set of irreducible divisor graphs {G(x): x ∈ D* \\ U(D)} when D is an FFD, it is very unlikely that any information about the domain D can be gleaned from the collection {G(x): x ∈ D* \\ U(D)} when D is not an FFD. We also introduce an alternate irreducible divisor graph called the compressed irreducible divisor graph and study some of its properties.

Exponential ergodicity and regularity for equations with Lévy noise

We prove exponential convergence to the invariant measure, in the total variation norm, for solutions of SDEs driven by α -stable noises in finite and in infinite dimensions. Two approaches are used. The first one is based on Liapunov’s function approach by Harris, and the second on Doeblin’s coupling argument in [8]. Irreducibility and uniform strong Feller property play an essential role in both approaches. We concentrate on two classes of Markov processes: solutions of finite dimensional equations, introduced in [27], with Hölder continuous drift and a general, non-degenerate, symmetric α -stable noise, and infinite dimensional parabolic systems, introduced in [29], with Lipschitz drift and cylindrical α -stable noise. We show that if the nonlinearity is bounded, then the processes are exponential mixing. This improves, in particular, an earlier result established in [28], with a different method.

Ungrounded Dispositions in Quantum Mechanics

General metaphysical arguments have been proposed in favour of the thesis that all dispositions have categorical bases (Armstrong; Prior, Pargetter, Jackson). These arguments have been countered by equally general arguments in support of ungrounded dispositions (Molnar, Mumford). I believe that this controversy cannot be settled purely on the level of abstract metaphysical considerations. Instead, I propose to look for ungrounded dispositions in specific physical theories, such as quantum mechanics. I explain why non-classical properties such as spin are best interpreted as irreducible dispositional properties, and I give reasons why even seemingly classical properties, for instance position or momentum, should receive a similar treatment when interpreted in the quantum realm. Contrary to the conventional wisdom, I argue that quantum dispositions should not be limited to probabilistic dispositions (propensities) by showing reasons why even possession of well-defined values of parameters should qualify as a dispositional property. I finally discuss the issue of the actuality of quantum dispositions, arguing that it may be justified to treat them as potentialities whose being has a lesser degree of reality than that of classical categorical properties, due to the incompatibility relations between non-commuting observables.

The Explanatory Role of Irreducible Properties

I aim to reconcile two apparently conflicting theses: 1. Everything that can be explained, can be explained in purely physical terms, that is, using the machinery of fundamental physics, and 2. Some properties that play an explanatory role in the higher-level sciences are irreducible in the strong sense that they are physically undefinable: their nature cannot be described using the vocabulary of physics. I investigate the contribution that physically undefinable properties typically make to explanations in the high-level sciences, and I show that when they are explanatorily relevant, it is in virtue of their extension (or something close) alone. They are irreducible because physics cannot capture their nature; this is no obstacle, however, to physics’ more or less capturing their extension, which is all that it need do to duplicate their explanatory power. In the course of the argument, I sketch the outlines of an account of the explanation of physically contingent regularities, such as the regularities found in most branches of biological inquiry, at the center of which is an account of the nature of contingent, empirical “bridge principles”. Science and philosophy are fighting a battle over reduction, or so it seems. On the one hand, for any “high-level” phenomenon—chemical, biological, psychological, economic—science claims to be able to provide, in the long term if not quite yet, a lower-level explanation, and ultimately a physicallevel explanation. The enormous progress that has been made towards this goal can hardly be ignored. On the other hand, philosophers have recently claimed with increasing confidence that many explanatory properties cited by higher-level sciences—being water, being a gene, being a species, being a belief, being currency—are irreducible. The aim of this paper is to show that both sides may be correct. I will characterize very strong versions of both the scientific and the philosophical claims—strong versions of explanatory physicalism and explanatory irreducibility—and I will argue that there exists an explanatory relevance relation, a conception of the explanatory role played by irreducible properties, that allows the two to coexist. I will provide no arguments for either explanatory physicalism or explanatory irreducibility; I will rather simply suppose that both doctrines are correct and attempt a reconciliation. Further, in contrast with much of the recent literature on reductionism, this paper will not be especially concerned with functionally defined or multiply realizable higher-level properties; the explanatory role I find for irreducible properties can be played by functional and non-functional properties, by multiply and singly realizable properties, alike. 1. Explanatory Physicalism Everything that can be explained, can be explained physically; that is the doctrine of explanatory physicalism. More fancifully, if there were a race that only spoke and thought in the language of fundamental physics, and so could not conceive of non-physical properties, they could understand the world as