Dynamical Linked Cluster Expansions: A Novel Expansion Scheme for Point-Link-Point-Interactions

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from 2-point to point-link-point interactions. We develop an associated graph theory with a generalized notion of connectivity and describe an algorithmic generation of the new multiple-line graphs. We indicate physical applications to spin glasses, partially annealed neural networks and SU(N) gauge Higgs systems. In particular the new expansion technique provides the possibility of avoiding the replica-trick in spin glasses. We consider variational estimates for the SU(2) Higgs model of the electroweak phase transition. The results for the transition line, obtained by dynamical linked cluster expansions, agree quite well with corresponding high precision Monte Carlo results.Comment: 41 pages, latex2e, 10 postscript figure

Structural validity of the MACI psychopathy and narcissism scales: Evidence of multidimensionality and implications for use in research and screening

This study investigated the psychometric properties and predictive validity of three self-report scales (the Psychopathy Content Scale, the Psychopathy-16 scale, and the Egotistic scale) derived from the Millon Adolescent Clinical Inventory (MACI) to screen for the presence of psychopathic and narcissistic personality characteristics. Exploratory and confirmatory factor analyses were performed in a sample of 173 clinic-referred adolescents (ages 12-17), results from which suggested that these scales are multidimensional in nature. The Psychopathy Content Scale was best captured by a two-factor structure, with personality-based items loading on one factor and antisocial/impulsive behaviors loading on the second. The most parsimonious solution for the Psychopathy-16 scale was a three-factor model, characterized by callous and egocentric features on the first two factors and antisocial behaviors on the third. The Egotistic scale of the MACI was best represented by three factors, depicting features of self-confidence, exhibitionistic tendencies, and social conceit, respectively. Regression analyses supported the multidimensionality of these scales by showing divergent patterns of association with violent and nonviolent outcomes among the factors that composed the scales

Study of resonance light scattering for remote optical probing

Enhanced scattering and fluorescence processes in the visible and UV were investigated which will enable improved remote measurements of gas properties. The theoretical relationship between scattering and fluorescence from an isolated molecule in the approach to resonance is examined through analysis of the time dependence of re-emitted light following excitation of pulsed incident light. Quantitative estimates are developed for the relative and absolute intensities of fluorescence and resonance scattering. New results are obtained for depolarization of scattering excited by light at wavelengths within a dissociative continuum. The experimental work was performed in two separate facilities. One of these utilizes argon and krypton lasers, single moded by a tilted etalon, and a 3/4 meter double monochromator. This facility was used to determine properties of the re-emission from NO2, I2 and O3 excited by visible light. The second facility involves a narrow-line dye laser, and a 3/4 meter single monochromator. The dye laser produces pulsed light with 5 nsec pulse duration and 0.005 nm spectral width

Stochastic learning in a neural network with adapting synapses

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are $n$-states variables which evolve in time according to Stochastic Learning rules; a parallel stochastic dynamics is assumed for neurons. Since the network maintains the same dynamics whether it is engaged in computation or in learning new memories, a very low probability of synaptic transitions is assumed. In the limit $N\to\infty$ with $K$ large and finite, the correlations of neurons and synapses can be neglected and the dynamics can be analitically calculated by flow equations for the macroscopic parameters of the system.Comment: 25 pages, LaTeX fil

A recurrent neural network with ever changing synapses

A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical study it is found that the fixed points of the dynamics of the net are time dependent, implying that the representation in the brain of a fixed piece of information (e.g., a word to be recognized) is not fixed in time.Comment: 17 pages, LaTeX, 4 figure

Hierarchical Self-Programming in Recurrent Neural Networks

We study self-programming in recurrent neural networks where both neurons (the `processors') and synaptic interactions (`the programme') evolve in time simultaneously, according to specific coupled stochastic equations. The interactions are divided into a hierarchy of $L$ groups with adiabatically separated and monotonically increasing time-scales, representing sub-routines of the system programme of decreasing volatility. We solve this model in equilibrium, assuming ergodicity at every level, and find as our replica-symmetric solution a formalism with a structure similar but not identical to Parisi's $L$-step replica symmetry breaking scheme. Apart from differences in details of the equations (due to the fact that here interactions, rather than spins, are grouped into clusters with different time-scales), in the present model the block sizes $m_i$ of the emerging ultrametric solution are not restricted to the interval $[0,1]$, but are independent control parameters, defined in terms of the noise strengths of the various levels in the hierarchy, which can take any value in [0,\infty\ket. This is shown to lead to extremely rich phase diagrams, with an abundance of first-order transitions especially when the level of stochasticity in the interaction dynamics is chosen to be low.Comment: 53 pages, 19 figures. Submitted to J. Phys.