Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

Sequential injection system with higher dimensional electrochemical sensor signals Part 1. Voltammetric e-tongue for the determination of oxidizable compounds

A sequential injection analysis (SIA) system was developed with the aim of obtaining an automatic and versatile way to prepare standards needed in the study of systems with higher dimensional sensor signals. To illustrate this, different analytical techniques were used in determinations of several analytes. Automated potentiometric calibrations of different potentiometric sensors, with and without interference, were carried out. Useful determinations of selectivity coefficients with two degrees of freedom were obtained. Simultaneous voltammetric determinations have also been done. Firstly, simultaneous determinations of lead and cadmium, using epoxy-graphite composite as the working electrode, have enabled a separate calibration for each metal to be obtained. Next, a voltammetric electronic tongue was designed and applied to the determination of oxidizable species. The use of artificial neural networks has solved the overlapped signal of ascorbic acid, 4-aminophenol and 4-acetamidophenol (paracetamol). A set of 63 data points was prepared automatically and has facilitated the training of an electronic tongue for these three analytes. Accurate predictions of test solutions, in the range of 12–410 μM for ascorbic acid, 17–530 μM for 4-aminophenol and 10–420 μM for paracetamol, have been achieved with RMSEs lower than 0.10 μM.     

Sorption of binary liquid mixtures on polymer networks Part I. Determination of surface excess isotherms and free energy functions

Two groups of polymer networks (polymer resins) are investigated by selective liquid sorption fromn-propanol-water mixtures. Group 1 consists of gel polymerized polar (hydrophilic) ion exchangers which swell in the binary liquid mixture. Group 2 consists of non-polar, non-swelling, macroporous resins. The free energy isotherms accompanying the sorption processes are calculated from the excess isotherms and the bulk activities. The adsorption excess free energies reveal the differences in polarity of the polymer network.     

Light traffic for workload in queues

General exact light traffic limit theorems are given for the distribution of steadystate workloadV, in open queueing networks having as input a general stationary ergodic marked point process {(t _n ,K _n )n0 (where t_n denotes the arrival time and K_n the routing and service times of the nth customer). No independence assumptions of any kind are required of the input. As the light traffic regime, it is only required that the Palm distribution for the exogenous interarrival time converges weakly to infinity (while the service mechanism is not allowed to change much). As is already known in the context of a single-server queue, work is much easier to deal with mathematically in light traffic than is customer delayD, and consequently, our results are far more general than existing results forD. We obtain analogous results for multi-channel and infinite-channel queues. In the context of open queueing networks, we handle both the total workload in the network as well as the workload at isolated nodes.Research supported in part by the Japan Society for the Promotion of Science during the author's fellowship in Tokyo, and by NSF Grant DDM 895 7825.     

A multineuron interaction model for neural networks

A multineuron interaction model (RS model) with an energy function given by the product of the squared distances in phase space between the state of the net and the stored patterns is studied in detail within a mean-field approach. Two limits are considered: when the patterns and antipatterns are stored (as in the Hopfield model), PAS case, and when only the patterns are taken into account, OPS case. TheT=0 solutions for the proper memories are exactly obtained for all finite values of, as a consequence of the energy function: whenever one of the overlaps is exactly one the corresponding equations decouple and no configuration average is required. Special interest is focused on the OPS situation, which presents a peculiar phase space topology. On the other hand, the PAS configuration recovers the Hopfield model in the appropriate limit, while keeping associative memory abilities far beyond the critical values of other models when the full Hamiltonian is considered.     

Phenomenology of nonlocal cellular automata

Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting edge-of-chaos nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled selectors or multiplexers. It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.     

Solid-State NMR Study of Phase Separation and Order of Water Molecules and Silanol Groups in Polysiloxane Networks

Homogeneity and structure of organically modified polysiloxane networks prepared by sol-gel co-condensation, as well as location and nature of water molecules and silanol groups were studied by 1D and 2D solid-state NMR. ¹H–²⁹Si and ¹H–¹H interatomic distances were estimated from variable contact-time CP/MAS experiments, ¹H NMR chemical shifts and off-resonance WISE NMR. A structure model of these networks is proposed and discussed. The fraction of proton-inaccessible units Q⁴ in the networks decreases with increasing amounts of dimethylsiloxane (D) and methylsiloxane (T) units. In contrast to systems prepared by co-condensation of tetraethoxysilane (TEOS) with dimethyl(diethoxy)silane (DMDEOS), proton-inaccessible units form essential fraction in networks prepared by co-condensation of TEOS with methyl(triethoxy)silane (MTEOS). The proton-accessible part of the networks with high O/Si ratios is nano-heterogeneous phase, which is composed of water containing Q ⁱ particles separated by copolymer domains. The overall homogeneity and uniformity of binding sites around silanol groups increases by co-condensation TEOS with DMDEOS or MTEOS, while the amount of physisorbed water as well as the hydrogen bond strength decreases, as compared with neat silica gel prepared by polycondensation of TEOS.     

A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and “ruggedness”. As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population’s evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.     

A Note on ＂Global Exponential Convergence Analysis of Hopfield Neural Networks with Continuously Distributed Delays＂

In this note, we would like to point out that （i） of Corollary 1 given by Zhang et al. （cf Commun. Theor. Phys. 39 （2003） 381） is incorrect in general.