Ising spin glass in a random network with a Gaussian random field

We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable parameter in our theory, allowing us to answer what the differences are between this description and the mean-field theory i.e., the fully connected theory. We have considered the random network random field Ising model where the spin exchange interaction as well as the RF are random variables following a Gaussian distribution. The results were found within the replica symmetric (RS) approximation, whose stability is obtained using the two-replica method. This also puts our work in the context of a broader discussion, which is the RS stability as a function of the connectivity. In particular, our results show that for small connectivity there is a region at zero temperature where the RS solution remains stable above a given value of the magnetic field no matter the strength of RF. Consequently, our results show important differences with the crossover between the RF and SG regimes predicted by the fully connected theory

Model architecture for associative memory in a neural network of spiking neurons

AbstractA synaptic connectivity model is assembled on a spiking neuron network aiming to build up a dynamic pattern recognition system. The connection architecture includes gap junctions and both inhibitory and excitatory chemical synapses based on Hebb’s hypothesis. The network evolution resulting from external stimulus is sampled in a properly defined frequency space. Neurons’ responses to different current injections are mapped onto a subspace using Principal Component Analysis. Departing from the base attractor, related to a quiescent state, different external stimuli drive the network to different fixed points through specific trajectories in this subspace

Implantação por recuo de antimônio em silício por bombardeamento com íons de argônio e germânio

Estudamos o processo de dopagem de silício com antimônio por recuo promovido por bombardeamento iônico. Em nossas experiências o sistema filme fino de antimônio de 60 nm de espessura depositado sobre silício monocristalino de orientação foi bombardeado com Ar+ ou Ge+ com energias entre 40 e 800 KeV e doses entre 1,0X1014 e 1,0X1017 cm². As amostras foram submetidas e recozimento térmico rápido a temperaturas entre 950 e 1150 ºC por tempos entre 20 e 60 s ou a recozimento prolongado em forno a 600 ºC por 1h. Algumas amostras foram submetidas a recozimento em duas etapas: prolongado a 600ºC por 1h seguido de recozimento rápido a 1200ºC por 5s. A análise das amostras foi feita empregando-se retroespalhamento Rutherford (RBS), espectrometria Auger e medidas em dispositivos Van der Pauw. Os principais resultados são: i) O processo que governa a implantação por recuo e a mistura balística induzida por colisões secundárias. ii) A concentração máxima de dopante situa-se na superfície e toda região dopada localiza-se a profundidade inferior a 0,1 um. iii) A largura do perfil de implantação independo da energia do projétil, e é função da dose incidente. Doses crescentes geram perfis mais profundos. iv) O bombardeamento com Ar+ resulta em recristalização inadequado do silício. O bombardeamento com Ge+ viabiliza perfeita recristalização do silício e boa substitucionalidade do dopante.We investigated the doping process of silicon with antimony by means of the recoil implantation method. I our experiments a film of antimony deposited over single cristal silicon was bombarded with Ar+ or Ge+ with energies between 40 and 800 KeV and doses ranging from 1,30C1014 to 1,0X1017 cm². Single step annealing of the bombarded samples was performed either in a Rapid Thermal Annealing (RTA) system or in a conventional furnace. IN the former case temperatures ranged from 950 to 1150 ºC and annealing times from 20 to 60s. In the latter case samples were annealed at 600ºC for 1 hour. The samples were analyzed by means of the Rutherford Backscattering spectrometry (RBS) technique Auger spectrometry and electrical measurements in Van der Pauw devices. The main results are: i) Recoil implantation ir governed by ballistic mixing process of collision cascades generated by the incident ions. ii) The maximum antimony concentration occours at the surface and decays rapidly with depth. The profile extends up to a maximum depth of 0,1um, even after annealing. iii) Antimony depth profile are independent of the bombarding particle’s energy, but are dependent on the dose. iv) Ar + bombardment yields imperfect recrystallization at the silicon substrate. Ge+ bombardment yields perfect recrystallization and good substitutionality of antimony atoms after annealing

El Telegrama del Rif: El Telegrama del Rif - Año XV Número 9833 - 1916 octubre 24 (24/10/1916)

Estudamos os efeitos gerais que a 'correlação', definida como superposição entre os padrões exerce sobre as propriedades de equilíbrio de redes neurais atratoras. Inicialmente, estudamos analiticamente o modelo de Hopfield de memória associativa, com um número finito de padrões armazenados de acordo com a regra de Hebb. Determinamos as propriedades de recuperação dos estados que apresentam uma superposição assimétrica com mais de um padrão (estados mistos assimétricos). Os diagramas de fase demonstram que estes estados são relevantes se a quantidade de ruido na rede e a correlação entre os padrões não são ambas demasiado grandes. Estudamos a capacidade de armazenamento a = P/N em uma rede com a inclusão de P — p padrões não correlacionados, e obtivemos resultados para a, crítico, que corresponde ao valor de a acima do qual não há mais estados de recuperação. Efetuamos simulações numéricas para discutir a qualidade da recuperação e a dimensão das bacias de atração. Na segunda parte do trabalho, estudamos as propriedades de armazenamento de padrões correlacionados acima do limite de saturação, em redes neurais de Gardner—Derrida com sinapses contínuas ótimas. Utilizando o método de réplicas para calcular médias configuracionais na rede de neurônios, determinamos, na teoria de simetria de réplicas, a fração mínima de padrões erroneamente armazenados por neurônio e a capacidade de armazenamento crítica como função das correlações. Estudamos a estabilidade destas soluções, e verificamos que a quebra de simetria de réplicas é relevante. Finalmente, apresentamos um estudo preliminar dos efeitos de quebra de simetria de réplicas na ordem mais baixa do esquema iterativo de Parisi para vidros de spin.We studied here the general effects that the 'correlation', defined as the overlap among the set of stored patterns causes to the equilibrium properties of atractor neural networks. Initially, the Hopfield model for associative memory was studied analitically with a finite number of patterns stored according to the Hebb learning rule. The retrieval properties of states that show an asymmetric overlap with more than one stored pattern (asymmetric mixed states) were determined. The phase diagrams for the overlaps demonstrate that these states are relevant if the amount of thermal noise is not too large and the correlations are not too strong. The storage capacity a = P/N is considered in a network with the adition of P — p uncorrelated patterns and results are given for the critical ac. This corresponds to the value of cx above wich the retrieval state is no longer present. Numerical simulations are carried out to discuss the retrieval quality and the size of the basins of attraction of the network. In the second part of the work, we studied the storage properties of correlated patterns, in the saturation regime, in Gardner—Derrida neural networks with optimal, continuous synapses. The average over quenched disorder were performed with the replica method, and the minimal fraction of storage errors 'per neuron' and the critical storage capacity in function of the corelations were calculated in the replica symmetry theory. We studied the stability in the space of replicas of these solutions, verifying that the symmetry breaking is relevant. Finally, we show a preliminar study of the replica symmetry breaking effects in the first order of the iterative Parisi's scheme for spin glasses

Canonical ensemble approach to graded-response perceptrons

Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner- Derrida canonical ensemble approach. Soft non-negative error measures are introduced allowing for extended retrieval properties. In particular, the performance of these systems for a linear (quadratic) error measure, corresponding to the perceptron (adaline) learning algorithm, is compared with the performance for a rigid error measure, simply counting the number of errors. Replica-symmetry-breaking effects are evaluated, and the analytic results are compared with numerical simulations. [S1063-651X(99)04503-1

Canonical ensemble approach to graded-response perceptrons

Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner- Derrida canonical ensemble approach. Soft non-negative error measures are introduced allowing for extended retrieval properties. In particular, the performance of these systems for a linear (quadratic) error measure, corresponding to the perceptron (adaline) learning algorithm, is compared with the performance for a rigid error measure, simply counting the number of errors. Replica-symmetry-breaking effects are evaluated, and the analytic results are compared with numerical simulations. [S1063-651X(99)04503-1

Simulação de neurônios de Fitzhugh-Nagumo

04

Phase transitions in the three-state Ising spin-glass model with finite connectivity

The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase transitions in the three-state Ghatak-Sherrington (or random Blume-Capel) model of a spin glass with a crystal-field term. The replica symmetry ansatz for the order function is expressed in terms of a two-dimensional effective-field distribution, which is determined numerically by means of a population dynamics procedure. Phase diagrams are obtained exhibiting phase boundaries that have a reentrance with both a continuous and a genuine first-order transition with a discontinuity in the entropy. This may be seen as “inverse freezing,” which has been studied extensively lately, as a process either with or without exchange of latent heat

La correspondencia de Valencia : diario de noticias : eco imparcial de la opinión y de la prensa: Año XXXII Número 10748 - 1909 Mayo 21

Copia digital. Madrid : Ministerio de Cultura. Subdirección General de Coordinación Bibliotecaria, 200