Matches in SemOpenAlex for { <https://semopenalex.org/work/W2034145445> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W2034145445 abstract "In this paper we discuss the rigorous approach to the statistical mechanics of mean field desordered Ising model. The description of the thermodynamic behavior for the desordered systems is a formidable problem, and the mean field spin glass represents, for its complex behavior, a kind of paradigm for the study of complexity. The most advanced results in this direction have been obtained by means of the non—rigorous methods of physics, and are associated to the important discovery of spontaneous replica simmetry breaking and the Parisi ansatz. On the othe side, in order to improve the comprehension of complex systems, it is necessary to build suitable rigorous methods. We explain one of these techniques, the marginal martingale approach, and compare the theoretical physics results with the rigorous ones. In particular, we give a rigorous proof for the existence of a functional order parameter for the Sherringhton—Kirkpatrick model, and show how, by means of an suitable assumption, the ultrametric structure of the pure state space can be found. The tools developed for this mathematical study can be used to study in a rigorous way the neural network thermodynamics. In the next two paragraphs we compare the mean field spin glass model to the ferromagnetic and the neural network models and discuss the concept of functional order parameter for the desordered systems. Then, in the fourth paragraph the marginal martingale is defined and we give a representation theorem for it. Finally, by means of the cavity ansatz we find rigorously the Parisi expression of the ultrametric topology of the pure phases space. This work has been partially supported by MURST (Italian Ministry of University and Scientific and Technological Research) and INFN (Italian National Institute for Nuclear Physics). keywords spin glass, marginal martingale, neural network, ultrametric topology" @default.
- W2034145445 created "2016-06-24" @default.
- W2034145445 creator A5064791458 @default.
- W2034145445 creator A5067081611 @default.
- W2034145445 date "1996-03-22" @default.
- W2034145445 modified "2023-09-23" @default.
- W2034145445 title "<title>Statistical mechanics of neural networks: theory and applications</title>" @default.
- W2034145445 doi "https://doi.org/10.1117/12.235972" @default.
- W2034145445 hasPublicationYear "1996" @default.
- W2034145445 type Work @default.
- W2034145445 sameAs 2034145445 @default.
- W2034145445 citedByCount "0" @default.
- W2034145445 crossrefType "proceedings-article" @default.
- W2034145445 hasAuthorship W2034145445A5064791458 @default.
- W2034145445 hasAuthorship W2034145445A5067081611 @default.
- W2034145445 hasConcept C121332964 @default.
- W2034145445 hasConcept C121864883 @default.
- W2034145445 hasConcept C130979935 @default.
- W2034145445 hasConcept C150775274 @default.
- W2034145445 hasConcept C154945302 @default.
- W2034145445 hasConcept C28826006 @default.
- W2034145445 hasConcept C33923547 @default.
- W2034145445 hasConcept C41008148 @default.
- W2034145445 hasConcept C50644808 @default.
- W2034145445 hasConcept C51329190 @default.
- W2034145445 hasConcept C62520636 @default.
- W2034145445 hasConcept C99874945 @default.
- W2034145445 hasConceptScore W2034145445C121332964 @default.
- W2034145445 hasConceptScore W2034145445C121864883 @default.
- W2034145445 hasConceptScore W2034145445C130979935 @default.
- W2034145445 hasConceptScore W2034145445C150775274 @default.
- W2034145445 hasConceptScore W2034145445C154945302 @default.
- W2034145445 hasConceptScore W2034145445C28826006 @default.
- W2034145445 hasConceptScore W2034145445C33923547 @default.
- W2034145445 hasConceptScore W2034145445C41008148 @default.
- W2034145445 hasConceptScore W2034145445C50644808 @default.
- W2034145445 hasConceptScore W2034145445C51329190 @default.
- W2034145445 hasConceptScore W2034145445C62520636 @default.
- W2034145445 hasConceptScore W2034145445C99874945 @default.
- W2034145445 hasLocation W20341454451 @default.
- W2034145445 hasOpenAccess W2034145445 @default.
- W2034145445 hasPrimaryLocation W20341454451 @default.
- W2034145445 hasRelatedWork W1777236251 @default.
- W2034145445 hasRelatedWork W180587397 @default.
- W2034145445 hasRelatedWork W1963651811 @default.
- W2034145445 hasRelatedWork W1964677669 @default.
- W2034145445 hasRelatedWork W2024328365 @default.
- W2034145445 hasRelatedWork W2033360947 @default.
- W2034145445 hasRelatedWork W2034331330 @default.
- W2034145445 hasRelatedWork W2035843105 @default.
- W2034145445 hasRelatedWork W2047064695 @default.
- W2034145445 hasRelatedWork W2056052206 @default.
- W2034145445 hasRelatedWork W2091850602 @default.
- W2034145445 hasRelatedWork W2117332653 @default.
- W2034145445 hasRelatedWork W2133768745 @default.
- W2034145445 hasRelatedWork W2241294431 @default.
- W2034145445 hasRelatedWork W2356594524 @default.
- W2034145445 hasRelatedWork W2365155518 @default.
- W2034145445 hasRelatedWork W2380153983 @default.
- W2034145445 hasRelatedWork W2468915607 @default.
- W2034145445 hasRelatedWork W2538088269 @default.
- W2034145445 hasRelatedWork W2075669993 @default.
- W2034145445 isParatext "false" @default.
- W2034145445 isRetracted "false" @default.
- W2034145445 magId "2034145445" @default.
- W2034145445 workType "article" @default.