324,748 research outputs found
New perspectives on the Ising model
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
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
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
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 A and A, move along classical trajectories and
respectively, while the dynamics of the lighter neutron, n, is considered from
a quantum mechanical point of view. Here, are the nucleon masses and
are the Coulomb charges of the heavy nuclei (). 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 (A A) 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 and 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
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
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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