We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are (...) shown to be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together. (shrink)

Recently, decomposition-based multiobjective evolutionary algorithms have good performances in the field of multiobjective optimization problems and have been paid attention by many scholars. Generally, a MOP is decomposed into a number of subproblems through a set of weight vectors with good uniformly and aggregate functions. The main role of weight vectors is to ensure the diversity and convergence of obtained solutions. However, these algorithms with uniformity of weight vectors cannot obtain a set of solutions with good diversity on some (...) MOPs with complex Pareto optimal fronts. To deal with this problem, an improved decomposition-based multiobjective evolutionary algorithm with adaptive weight adjustment is proposed. Firstly, a new method based on uniform design and crowding distance is used to generate a set of weight vectors with good uniformly. Secondly, according to the distances of obtained nondominated solutions, an adaptive weight vector adjustment strategy is proposed to redistribute the weight vectors of subobjective spaces. Thirdly, a selection strategy is used to help each subobjective space to obtain a nondominated solution. Comparing with six efficient state-of-the-art algorithms, for example, NSGAII, MOEA/D, MOEA/D-AWA, EMOSA, RVEA, and KnEA on some benchmark functions, the proposed algorithm is able to find a set of solutions with better diversity and convergence. (shrink)

This paper presents decomposition of the fourth-order Euler-type linear time-varying system as a commutative pair of two second-order Euler-type systems. All necessary and sufficient conditions for the decomposition are deployed to investigate the commutativity, sensitivity, and the effect of disturbance on the fourth-order LTVS. Some systems are commutative, and some are not commutative, while some are commutative under certain conditions. Based on this fact, the commutativity of fourth-order Euler-type LTVS is investigated by introducing the commutative requirements, theories, and (...) conditions. The fourth-order Euler-type LTVSs are investigated into commutative pairs of twice Euler-type second-order linear time-varying systems. The decomposition theories and conditions are derived, proved, and solved to simplify the use of commutativity for practical and industrial uses. Some fourth-order systems are sensitive toward change in initial conditions or parameters while others are not, and the effect due to disturbance also varies within systems. Furthermore, the stability and robustness of systems have so many issues. But we consider fourth-order Euler-type LTVS to observe, investigate, and tackle these issues. Lastly, the realization of fourth-order LTVS from cascaded two second-order systems can be laboratory experimented which is an open problem for future engineers to investigate. However, the theoretical results show a good agreement with the simulation results is considered in this work. Perhaps it might have unlimited physical applications in science and engineering as well as theoretical contribution. But beyond any reasonable doubt, the novelty is guaranteed because this study is the first of its kind that introduces the decomposition of the fourth-order Euler-type linear time-varying system as a commutative pair of two second-order Euler-type systems. Illustrative examples are presented to support the results. (shrink)

The concept of technical function is a key concept to describe technical artifacts and artifacts-to-be-designed. Engineers often give such descriptions in terms of functional decomposition models, which represent relationships between functions and sets of other functions. Despite the importance of the concept of function there is no consensus among engineers about its meaning. Models of functional decomposition are likewise conceptually divergent. Although this conceptual diversity hampers information exchange between engineers, they accept and maintain it. Engineers do not, by (...) and large, engage in a focused debate to establish commonly shared functional conceptualizations. This contrasts with science where both debates on the adequacy of key conceptualizations and convergence toward shared conceptualizations are common. This book investigates the side-by-side usage of different functional decomposition models in engineering. It explains this phenomenon by applying and extending the analysis of theory choice in terms of methodological incommensurability to engineering functional decomposition, rather than to science. This analysis shows that engineers’ usage of competing functional decomposition models is rational from a practical point of view. This book furthermore investigates the communication problems that the side-by-side usage of different models engenders and presents a strategy that supports the exchange and re-use of functional information between engineers. (shrink)

We focus on the decomposition problem for nonstationary multicomponent signals involving Big Data. We propose the kernel sparse learning, developed for the T-F reassignment algorithm by the path penalty function, to decompose the instantaneous frequencies ridges of the overlapped multicomponent from a time-frequency representation. The main objective of KSL is to minimize the error of the prediction process while minimizing the amount of training samples used and thus to cut the costs interrelated with the training sample collection. The (...) IFs first extraction is decided using the framework of the intrinsic mode polynomial chirp transform, which obtains a brief local orthogonal TFR of signals. Then, the IFs curves of the multicomponent signal can be easily reconstructed by the T-F reassignment. After the IFs are extracted, component decomposition is performed through KSL. Finally, the performance of the method is compared when applied to several simulated micro-Doppler signals, which shows its effectiveness in various applications. (shrink)

We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing (...) class='Hi'>decomposition trees. The resulting set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial letter-sharing condition. (shrink)

When solving a decision problem we want to determine an optimal policy for the decision variables of interest. A policy for a decision variable is in principle a function over its past; however, some of the past may be irrelevant and for both communicational as well as computational reasons it is important not to deal with redundant variables in the policies. In this paper we present a method to decompose a decision problem into a collection of smaller sub-problems (...) s.t. a solution to the original decision problem can be found by solving the sub-problems independently. The method is based on an operational characterization of the future variables being relevant for a decision variable, thereby also providing a characterization of those parts of a decision problem that are relevant for a particular decision. (shrink)

This paper examines the underdetermination between the Ptolemaic, Copernican, and the Tychonic theories of planetary motions and its attempted resolution by Kepler. I argue that past philosophical analyses of the problem of the planetary motions have not adequately grasped a method through which the underdetermination might have been resolved. This method involves a procedure of what I characterize as decomposition and identification. I show that this procedure is used by Kepler in the first half of the Astronomia Nova, (...) where he ultimately claims to have refuted the Ptolemaic theory, thus partially overcoming the underdetermination. Finally, I compare this method with other views of scientific inference such as bootstrapping. (shrink)

I discuss two subjects in Samir Okasha’s excellent book, Evolution and the Levels of Selection. In consonance with Okasha’s critique of the conventionalist view of the units of selection problem, I argue that conventionalists have not attended to what realists mean by group, individual, and genic selection. In connection with Okasha’s discussion of the Price equation and contextual analysis, I discuss whether the existence of these two quantitative frameworks is a challenge to realism.

In this paper we argue that an operational organism concept can help to overcome the structural deficiency of mathematical models in biology. In our opinion, the structural deficiency of mathematical models lies mainly in our inability to identify functionally relevant biological characters in biological systems, and not so much in a lack of adequate mathematical representations of biological processes. We argue that the problem of character identification in biological systems is linked to the question of a properly formulated organism (...) concept. Lastly, we demonstrate how a decomposition of an organism into independent characters in the context of a specific biological process--such as adaptation by means of natural selection--depends on the dynamical properties and invariance conditions of the equations that describe this process. (shrink)

The user data mining was introduced into the model construction process, and the user behavior was decomposed by analyzing various influencing factors through the factorization machine learning method. In the recommendation screening stage, the collaborative filtering recommendation is combined to screen the recommendation candidate set. The idea of user-based collaborative filtering is used for reference to obtain music works favored by similar users. On the other hand, we learn from item-based CF, which ensures that the candidate set covers user preference. (...) Firstly, the user’s interest value is predicted by using dynamic interest model. Then, the common problems such as cold start and hot items processing are fully considered. The frequent pattern growth algorithm is compared with the association rule algorithm based on the collaborative filtering recommendation algorithm and the content-based recommendation algorithm, which proves the superiority of the algorithm and its role in solving the recommendation problem after applying the recommendation. The music data in the database data conversion effectively improve the efficiency and accuracy of mining. According to the implementation of the algorithm described in this article, the accuracy of the music recommendation results used to recommend user satisfaction is proved. And the recommended music is indeed feasible and practical. (shrink)

De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.

De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.

This research work proposes an implementation of adept content-based music retrieval technique that attempts to address the demands of the rising availability of digital music. The primary objective of this research work is to balance the perilous impact of non-relevant songs through progressive filtering for query by humming music information retrieval system. The PF is a technique of searching in manifolds for problem solving through reduced search space. A new strategy for empirical mode decomposition analysis is adopted, and (...) outcomes are propelled as a significant source of information for multiresolution histogram representations. Finally, the concept of PF is realized through MRH to retrieve the desired song by humming. The proposed multiresolution QBH system is evaluated on a music database of 1200 fragments, and the experimental results effectively locate the humming patterns and recite the eminence of EMD analysis for retrieving the desired song through humming. (shrink)

In this paper we argue that an operational organism concept can help to overcome the structural deficiency of mathematical models in biology. In our opinion, the structural deficiency of mathematical models lies mainly in our inability to identify functionally relevant biological characters in biological systems, and not so much in a lack of adequate mathematical representations of biological processes. We argue that the problem of character identification in biological systems is linked to the question of a properly formulated organism (...) concept. Lastly, we demonstrate how a decomposition of an organism into independent characters in the context of a specific biological process—such as adaptation by means of natural selection—depends on the dynamical properties and invariance conditions of the equations that describe this process. (shrink)

This paper proposes a constrained solution update strategy for multiobjective evolutionary algorithm based on decomposition, in which each agent aims to optimize one decomposed subproblem. Different from the existing approaches that assign one solution to each agent, our approach allocates the closest solutions to each agent and thus the number of solutions in an agent may be zero and no less than one. Regarding the agent with no solution, it will be assigned one solution in priority, once offspring are (...) generated closest to its subproblem. To keep the same population size, the agent with the largest number of solutions will remove one solution showing the worst convergence. This improves diversity for one agent, while the convergence of other agents is not lowered. On the agent with no less than one solution, offspring assigned to this agent are only allowed to update its original solutions. Thus, the convergence of this agent is enhanced, while the diversity of other agents will not be affected. After a period of evolution, our approach may gradually reach a stable status for solution assignment; i.e., each agent is only assigned with one solution. When compared to six competitive multiobjective evolutionary algorithms with different population selection or update strategies, the experiments validated the advantages of our approach on tackling two sets of test problems. (shrink)

The constraint-handling methods using multiobjective techniques in evolutionary algorithms have drawn increasing attention from researchers. This paper proposes an efficient conical area differential evolution algorithm, which employs biased decomposition and dual populations for constrained optimization by borrowing the idea of cone decomposition for multiobjective optimization. In this approach, a conical subpopulation and a feasible subpopulation are designed to search for the global feasible optimum, along the Pareto front and the feasible segment, respectively, in a cooperative way. In particular, (...) the conical subpopulation aims to efficiently construct and utilize the Pareto front through a biased cone decomposition strategy and conical area indicator. Neighbors in the conical subpopulation are fully exploited to assist each other to find the global feasible optimum. Afterwards, the feasible subpopulation is ranked and updated according to a tolerance-based rule to heighten its diversity in the early stage of evolution. Experimental results on 24 benchmark test cases reveal that CADE is capable of resolving the constrained optimization problems more efficiently as well as producing solutions that are significantly competitive with other popular approaches. (shrink)

In this paper we attempt to develop a problem representation technique which enables the decomposition of a problem into subproblems such that their solution in sequence constitutes a strategy for solving the problem. An important issue here is that the subproblems generated should be easier than the main problem. We propose to represent a set of problem states by a statement which is true for all the members of the set. A statement itself is (...) just a set of atomic statements which are binary predicates on state variables. Then, the statement representing the set of goal states can be partitioned into its subsets each of which becomes a subgoal of the resulting strategy. The techniques involved in partitioning a goal into its subgoals are presented with examples. (shrink)

“On the Problem of Action” contrasts two conceptions of the task of action theory: the dominant conception, which I call the decompositional approach, and an alternative, non-decompositional approach that is implicit in the tradition of action theory descending from Aristotle. Decompositionalists seek to characterize intentional action as a composite of something inward and something outward, bound together by some generic kind of causal relation. I show that this approach is committed to characterizing action in terms that treat the agent’s (...) own standpoint on her action as a separable factor, not integral to the worldly happening that constitutes her action proper, and I argue that this commitment leads decompositionalists to focus their theorizing not on actions-in-progress, but on cases of completed action. I then show how the neo-Aristotelian approach to understanding action contrasts with the decompositional approach in each of these respects: it seeks, not to explain what intentional action is by decomposing action into several not-intrinsically-agential factors, but rather to characterize the understanding of what it is to act implicit in the agent’s knowledge of her own action-in-progress. The main aim of this paper is simply to show that there is an alternative to the decompositional project, one that resists the demand for an explanation of action in non-agential terms, while not simply treating the notion of intentional agency as an unexplained primitive. To see the possibility of this sort of understanding of action is, I argue, to see how action could turn out to be, not a worldly event with certain psychological causes, but a distinctive form of material process, one that is not simply caused by an exercise of reason but is itself a exercise of reason, it is itself the exercise of a power of practical cognition. (shrink)

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a (...) class='Hi'>decomposition result involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

We examined how children’s strategy choices in solving complex subtraction problems are related to grade and to variations in problem complexity. In two studies, third- and fifth-grade children (N≈160 each study) solved multi-digit subtraction problems (e.g., 34 - 18) and described their solution strategies. In the first experiment, strategy selection was investigated by means of a free-choice paradigm, whereas in the second study a discrete-choice approach was implemented. In both experiments, analyses of strategy repertoire indicated that third-grade children were (...) more likely to report less-efficient strategies (i.e., counting) and relied more on the right-to-left solution algorithm compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e., decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems. (shrink)

New mechanical philosophy posits that explanations in the life sciences involve the decomposition of a system into its entities and their respective activities and organization that are responsible for the explanandum phenomenon. This mechanistic account of explanation has proven problematic in its application to mathematical models, leading the mechanists to suggest different ways of aligning abstract models with the mechanist program. Initially, the discussion centered on whether the Hodgkin-Huxley model is explanatory. Network models provided another complication, as they apply (...) to a wide number of materially diverse systems. In this article, we examine the various attempts to integrate abstract models within the mechanist program, also presenting a further challenge: the Heimburg-Jackson model, which was introduced as an alternative to the Hodgkin-Huxley model. We argue that although the notion of abstraction as the omission of irrelevant mechanistic details appears to give a mechanistic solution for accommodating abstract models, this notion does not suit models whose epistemic strategy is not decompositional. As a result, the mechanist has to choose whether to dilute the mechanistic approach nearly beyond recognition or to claim that many, if not most, abstract theoretical models do not deliver mechanistic explanations, or qualify as explanatory at all. (shrink)

New mechanical philosophy posits that explanations in the life sciences involve the decomposition of a system into its entities and their respective activities and organization that are responsible for the explanandum phenomenon. This mechanistic account of explanation has proven problematic in its application to mathematical models, leading the mechanists to suggest different ways of aligning abstract models with the mechanist program. Initially, the discussion centered on whether the Hodgkin-Huxley model is explanatory. Network models provided another complication, as they apply (...) to a wide number of materially diverse systems. In this article, we examine the various attempts to integrate abstract models within the mechanist program, also presenting a further challenge: the Heimburg-Jackson model, which was introduced as an alternative to the Hodgkin-Huxley model. We argue that although the notion of abstraction as the omission of irrelevant mechanistic details appears to give a mechanistic solution for accommodating abstract models, this notion does not suit models whose epistemic strategy is not decompositional. As a result, the mechanist has to choose whether to dilute the mechanistic approach nearly beyond recognition or to claim that many, if not most, abstract theoretical models do not deliver mechanistic explanations, or qualify as explanatory at all. (shrink)

There is compelling linguistic evidence that many words (e.g., boil) are derived from phrasal sources (e.g., cause to boil). Among causation, typical semantic primitives composing word meanings are becoming, having and getting. While linguists have argued that word meanings contain semantic knowledge that we can grasp but cannot express linguistically, Fodor and his colleagues maintain that words express primitive, semantically unanalysable concepts. Under this view, putative linguistic semantic decompositions express nonsemantic metaphysical regularities. After reviewing the debate, it is suggested in (...) this article that semantic features that are linguistically salient and unspeakable emerge neither from the analytical connections between words, nor from the metaphysical structure of the world, but from the logical syntax of the grammar. (shrink)

Because methodical doubt is a process of demarcation of scientific (clear) and non-scientific constructions, then in this process Descartes affirmed truly neo-positivistic principle. Descartes` rational transformation of thinking is usage methods of mechanical sciences to «sciences about spirit» attaching to them also natural status. But Descartes had not noticed that scientific obviousnesses with time turns into dogmas. That is why Husserl offered to describe phenomena after riching «epoche» about natural-scientific beliefs. Search of pretheoretical grounds of obviousness has led to loss (...) of clarity and of its apodictic weight. Because «obviousnesses» were always founded on historico-philosophical invariant, then needed either reconsider Descartes «technique» or kernel of decomposition and reconstruct «laws of thinking» in respect to it. (shrink)

Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized eigenvalues problem of sparse matrices, with automatic parallelization of calculations on modern parallel computers with graphics processors. Peculiarities of realization of parallel algorithms for different structures of sparse matrices are presented. The times of solving the problem of stability of composite materialsusing a three-dimensional model of "finite size fibers" on computers of different architectures are given. In mathematical modeling of physical (...) and technical processes in many cases there is a need to solve problems of algebraic problem of eigenvalues with sparse matrices of large volumes. In particular, such problems arise in the analysis of the strength of structures in civil and industrial construction, aircraft construction, electric welding, etc. The solving to these problems is to determine the eigenvalues and eigenvectors of sparse matrices of different structure. The efficiency of solving these problems largely depends on the effectiveness of mathematical modeling of the problem as a whole. Continuous growth of task parameters, calculation of more complete models of objects and processes on computers require an increase in computer productivity. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. Today, this problem is solved by using powerful supercomputers of hybrid architecture, such as computers with multicore processors and graphics processors, which combine MIMD and SIMD architectures. But the potential of high-performance computers can be used to the fullest only with algorithmic software that takes into account both the properties of the task and the features of the hybrid architecture. Complicating the architecture of modern high-performance supercomputers of hybrid architecture, which are actively used for mathematical modeling means a significant complication of efficient use of these resources in creating parallel algorithms and programs. here are problems with the creation of algorithmic software with automatic execution of stages of work, which are associated with the efficient use of computing resources, ways to store and process sparse matrices, analysis of the reliability of computer results. This makes it possible to significantly increase the efficiency of mathematical modeling of practical problems on modern high-performance computers, as well as free users from the problems of parallelization of complex problems. he developed algorithmic software automatically implements all stages of parallel computing and processing of sparse matrices on a hybrid computer. It was used at the Institute of Mechanics named after S.P. Tymoshenko NAS of Ukraine in modeling the strength problems of composite material. A significant improvement in the time characteristics of mathematical modeling was obtained. Problems of mathematical modeling of the properties of composite materials has an important role in designing the processes of deformation and destruction of products in various subject areas. Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized problem of eigen values of sparse matrices of different structure of large orders, with automatic parallelization of calculations on modern parallel computers with graphics processors. The main methodological principles and features of implementation of parallel algorithms for different structures of sparse matrices are presented, which ensure effective implementation of multilevel parallelism of a hybrid system and reduce data exchange time during the computational process. As an example of these approaches, a hybrid algorithm of the iteration method in subspace for tape and block-diagonal matrices with a frame for computers of hybrid architecture is given. Peculiarities of data decomposition for matrices of profile structure at realization of parallel algorithms are considered. The proposed approach provides automatic determination of the required topology of the hybrid computer and the optimal amount of resources for the organization of an efficient computational process. The results of testing the developed algorithmic software for problems from the collection of the University of Florida, as well as the times of solving the problem of stability of composite materials using a three-dimensional model of "finite size fibers" on computers of different architectures. The results show a significant improvement in the time characteristics of solving problems. (shrink)

One aspect of the Micro-Macro-Problem is the analysis of the principles of composition and decomposition. Since these principles play a considerable role in everyday life whenever people identify parts of large social units, they can be derived by way of reconstruction from everyday knowledge. On this basis a definition of micro-macro-relations is developed. According to this definition there are empirical and conceptual relations between the macro-phenomenon and its constituent parts, although the micro-phenomena are also independent entities in their (...) own right. Two different forms of ascription of macro-attributes are distinguished and the limits of 'upward'-composition and 'downward'- decomposition are discussed. Finally, consequences of this perspective are presented concerning the explanation of social facts. (shrink)

The present study aims to elucidate whether insight problem solving could be facilitated by the cognitive component of humour. The authors take interest in whether the logical mechanisms of humour can affect how fast insight problems are solved. To that end, the authors conducted two experiments where participants solved insight problems after watching visual humorous stimuli such as videos and slideshows. The first experiment demonstrated the overall impact of facilitation by humour on insight problem solving; however, it did (...) not show any difference in how particular logical mechanisms of humour affect the solution time of insight problems. The second experiment showed that the cognitive component of humour could selectively affect insight problems whose difficulty stems from different sources. These results suggest that the cognitive component of humour, when operationalised as logical mechanisms and schema switching, contributes to solving insight problems. (shrink)

This paper examines an insoluble Cartesian problem for classical AI, namely, how linguistic understanding involves knowledge and awareness of u’s meaning, a cognitive process that is irreducible to algorithms. As analyzed, Descartes’ view about reason and intelligence has paradoxically encouraged certain classical AI researchers to suppose that linguistic understanding suffices for machine intelligence. Several advocates of the Turing Test, for example, assume that linguistic understanding only comprises computational processes which can be recursively decomposed into algorithmic mechanisms. Against this background, (...) in the first section, I explain Descartes’ view about language and mind. To show that Turing bites the bullet with his imitation game, in the second section I analyze this method to assess intelligence. Then, in the third section, I elaborate on Schank and Abelsons’ Script Applier Mechanism (SAM, hereby), which supposedly casts doubt on Descartes’ denial that machines can think. Finally, in the fourth section, I explore a challenge that any algorithmic decomposition of linguistic understanding faces. This challenge, I argue, is the core of the Cartesian problem: knowledge and awareness of meaning require a first-person viewpoint which is irreducible to the decomposition of algorithmic mechanisms. (shrink)

A comparison is made between the Bohm trajectory and Feynman path approaches to the long-standing problem of determining the average lime taken for a particle described by the Schrödinger wave function ψ to tunnel through a potential barrier. The former approach follows simply and uniquely from the basic postulates of Bohm's causal interpretation of quantum mechanics; the latter is intimately related to the most frequently cited approaches based on conventional interpretations. Emphasis is given to the fact that fundamentally different (...) transmission (T)-reflection (R) decompositions, particlelike and wavelike respectively, are central to the two methods: ¦ψ¦2=[¦ψ¦2]T+[¦ψ¦2]R (Bohm trajectory approach); ψ=ψT+ψR (Feynman path approach). (shrink)

The paper examines Davidson′s discussion of Frege on the problem of predication. Simple declarative sentences are unities that are true or false; how do predicates contribute to this kind of semantic unity? According to Davidson, the problem cannot be solved by assigning referents to predicates, since this leads to an infinite regress. Frege famously contributes the idea that predicates are “incomplete” or “unsaturated” functional expressions, mapping objects to truth-values. However, he takes predicates to refer to concepts and thus (...) is exposed to Davidson′s argument. I will show that Davidson is only right with regards to “Frege′s semantics”. Yet Frege′s logical doctrine of the decomposition of a sentence – I shall argue – allows for a resolution of this problem. (shrink)

This paper argues that historical research is an important tool for modeling problem-solving in scientific invention and discovery. Two important cases in the history of modern physics—the invention of the transistor by John Bardeen and Walter Brattain and the development of the theory of superconductivity by Bardeen, Leon Cooper, and J. Robert Schrieffer—reveal factors essential to include in such a model. The focus is on problem-solving practices: problem decomposition, analogy, bridging principles, team-work, empirical tinkering, and library (...) research. A complete framework must encompass the full range of factors, including contingent individual traits and environmental circumstances. (shrink)

Levelt et al. describe a model of speech production in which lemma access is achieved via input from nondecompositional conceptual representations. They claim that existing decompositional theories are unable to account for lexical retrieval because of the so-called hyperonym problem. However, existing decompositional models have solved a formally equivalent problem.

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering (...) and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics. (shrink)

Theories of diagrams and diagrammatic reasoning typically seek to account for either the formal semantics of diagrams, or for the advantages which diagrammatic representations hold for the reasoner over other forms of representation. Regrettably, almost no theory exists which accounts for both of these issues together, nor how they affect one another. We do not attempt to provide such an account here. We do, however, seek to lay out larger context than is generally used for examining the processes of using (...) diagrams in reasoning or communication. A context in which detailed studies of sub-problems, such as the formal semantics or cognitive impact of specific diagrammatic systems, may be embedded.Accounts of the embedding of sentential logics in the computational processes of reasoners and communicators are relatively well developed from several decades of research in AI. Analogies between the sentential and the graphical cases are quite revealing about both similarities and differences. To provide a structure for the 'grand context' of diagrammatic representation and reasoning, and to clarify the relations between its component problems, we examine carefully these analogies and the decomposition they provide of subproblems for analysing diagrammatic reasoning. (shrink)

In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the 3-ball B, i.e., a piecewise isometry from B onto two copies of B. This article answers a question of de Groot from 1958 by showing that there is a paradoxical decomposition of B in which the pieces move continuously while remaining disjoint to yield two copies of B. More generally, we show that if n ≥ 2, any two bounded sets in.