324,748 research outputs found

    New perspectives on the Ising model

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    The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which holds for any dimensionality of the system. The Hamiltonian of the model is solved in terms of a complete finite set of eigenoperators and eigenvalues. The Green's function and the correlation functions of the fermionic model are exactly known and are expressed in terms of a finite small number of parameters that have to be self-consistently determined. By using the equation of the motion method, we derive a set of equations which connect different spin correlation functions. The scheme that emerges is that it is possible to describe the Ising model from a unified point of view where all the properties are connected to a small number of local parameters, and where the critical behavior is controlled by the energy scales fixed by the eigenvalues of the Hamiltonian. By using algebra and symmetry considerations, we calculate the self-consistent parameters for the one-dimensional case. All the properties of the system are calculated and obviously agree with the exact results reported in the literature.Comment: 19 RevTeX pages, 9 panels, to be published in Eur. Phys. J.

    Predictive brains: forethought and the levels of explanation

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    Is any unified theory of brain function possible? Following a line of thought dat- ing back to the early cybernetics (see, e.g., Cordeschi, 2002), Clark (in press) has proposed the action-oriented Hierarchical Predictive Coding (HPC) as the account to be pursued in the effort of gain- ing the “Grand Unified Theory of the Mind”—or “painting the big picture,” as Edelman (2012) put it. Such line of thought is indeed appealing, but to be effectively pursued it should be confronted with experimental findings and explana- tory capabilities (Edelman, 2012). The point we are making in this note is that a brain with predictive capa- bilities is certainly necessary to endow the agent situated in the environment with forethought or foresight, a crucial issue to outline the unified account advocated by Clark. But the capacity for fore- thought is deeply entangled with the capacity for emotions and when emotions are brought into the game, cogni- tive functions become part of a large-scale functional brain network. However, for such complex networks a consistent view of hierarchical organization in large-scale functional networks has yet to emerge (Bressler and Menon, 2010), whilst heterarchical organization is likely to play a strategic role (Berntson et al., 2012). This raises the necessity of a multilevel approach that embraces causal relations across levels of explanation in either direc- tion (bottom–up or top–down), endorsing mutual calibration of constructs across levels (Berntson et al., 2012). Which, in turn, calls for a revised perspective on Marr’s levels of analysis framework (Marr, 1982). In the following we highlight some drawbacks of Clark’s proposal in address- ing the above issues

    Towards a shared ontology: a generic classification of cognitive processes in conceptual design

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    Towards addressing ontological issues in design cognition research, this paper presents the first generic classification of cognitive processes investigated in protocol studies on conceptual design cognition. The classification is based on a systematic review of 47 studies published over the past 30 years. Three viewpoints on the nature of design cognition are outlined (search, exploration and design activities), highlighting considerable differences in the concepts and terminology applied to describe cognition. To provide a more unified view of the cognitive processes fundamentally under study, we map specific descriptions of cognitive processes provided in protocol studies to more generic, established definitions in the cognitive psychology literature. This reveals a set of 6 categories of cognitive process that appear to be commonly studied and are therefore likely to be prevalent in conceptual design: (1) long-term memory; (2) semantic processing; (3) visual perception; (4) mental imagery processing; (5) creative output production and (6) executive functions. The categories and their constituent processes are formalised in the generic classification. The classification provides the basis for a generic, shared ontology of cognitive processes in design that is conceptually and terminologically consistent with the ontology of cognitive psychology and neuroscience. In addition, the work highlights 6 key avenues for future empirical research: (1) the role of episodic and semantic memory; (2) consistent definitions of semantic processes; (3) the role of sketching from alternative theoretical perspectives on perception and mental imagery; (4) the role of working memory; (5) the meaning and nature of synthesis and (6) unidentified cognitive processes implicated in conceptual design elsewhere in the literature

    Few-body semiclassical approach to nucleon transfer and emission reactions

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    A three-body semiclassical model is proposed to describe the nucleon transfer and emission reactions in a heavy-ion collision. In this model the two heavy particles, i.e. nuclear cores A1(ZA1,MA1)_1(Z_{A_1}, M_{A_1}) and A2(ZA2,MA2)_2(Z_{A_2}, M_{A_2}), move along classical trajectories R1(t)\vec R_1(t) and R2(t)\vec R_2(t) respectively, while the dynamics of the lighter neutron, n, is considered from a quantum mechanical point of view. Here, MiM_i are the nucleon masses and ZiZ_i are the Coulomb charges of the heavy nuclei (i=1,2i=1,2). A Faddeev-type semiclassical formulation using realistic paired nuclear-nuclear potentials is applied so that all three channels (elastic, rearrangement and break-up) are described in an unified manner. In order to solve these time-dependent equations the Faddeev components of the total three-body wave-function are expanded in terms of the input and output channel target eigenfunctions. In the special case when the nuclear cores are identical (A1_1 \equiv A2_2) and the two-level approximation in the expansion over target functions the time-dependent semiclassical Faddeev equations are resolved in an explicit way. To determine the realistic R1(t)\vec R_1(t) and R2(t)\vec R_2(t) trajectories of the nuclear cores a self-consistent approach based on the Feynman path integral theory is applied.Comment: 15 pages, 1 figur

    Cycle-Consistent Deep Generative Hashing for Cross-Modal Retrieval

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    In this paper, we propose a novel deep generative approach to cross-modal retrieval to learn hash functions in the absence of paired training samples through the cycle consistency loss. Our proposed approach employs adversarial training scheme to lean a couple of hash functions enabling translation between modalities while assuming the underlying semantic relationship. To induce the hash codes with semantics to the input-output pair, cycle consistency loss is further proposed upon the adversarial training to strengthen the correlations between inputs and corresponding outputs. Our approach is generative to learn hash functions such that the learned hash codes can maximally correlate each input-output correspondence, meanwhile can also regenerate the inputs so as to minimize the information loss. The learning to hash embedding is thus performed to jointly optimize the parameters of the hash functions across modalities as well as the associated generative models. Extensive experiments on a variety of large-scale cross-modal data sets demonstrate that our proposed method achieves better retrieval results than the state-of-the-arts.Comment: To appeared on IEEE Trans. Image Processing. arXiv admin note: text overlap with arXiv:1703.10593 by other author

    Boson-fermion unification, superstrings, and Bohmian mechanics

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    Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmian interpretation of particle quantum mechanics more appealing. The superstring current allows a consistent Bohmian interpretation of superstrings themselves, including a Bohmian description of string creation and destruction in terms of string splitting. The Bohmian equations of motion and the corresponding probabilistic predictions are fully relativistic covariant and do not depend on the preferred foliation.Comment: 30 pages, 1 figure, revised, to appear in Found. Phy
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