The extensive use of petroleum-based plastics has led to severe environmental pollution, emphasizing the need for sustainable alternatives such as biodegradable polyhydroxybutyrate (PHB). Conventional PHB production using heterotrophic microorganisms requires external organic carbon sources, contributing high costs. Additionally, separation biomass growth phase and accumulation in conventional systems limits efficiency. This study introduces a dual-phase hybrid cultivation system designed...

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The is defined with the rate p(n) = n(delta) at which particles hop out of nodes n particles. show analytically that complete condensation occurs when delta < or delta(c) triple bond 1/(gamma-1) where gamma degree distribution exponent underlying networks. In condensation, those whose higher than threshold are occupied by macroscopic numbers particles, while other...

We present an analytic study of the three-urn model for separation sand, which can be regarded as a zero-range process. solve analytically master equation and first-passage problem. find that stationary probability distribution obeys detailed balance is governed by free energy. characteristic lifetime cluster diverges algebraically with exponent $1∕3$ at limit stability. also give general argument scaling behavior robust respect to different expressions flux.

The thermodynamic and retrieval properties of fully connected Q-Ising networks are studied in the replica-symmetric mean-field approximation. In particular, capacity-gain parameter capacity-temperature phase diagrams derived for Q=3, 4 Q= infinity different distributions stored patterns. Furthermore, optimal gain function is determined order to obtain best performance. Where appropriate, results compared with diluted layered versions these models.

We present an analytic study of the urn model for separation sand recently introduced by Lipowski and Droz [Phys. Rev. E 65, 031307 (2002)]. solve analytically master equation first-passage problem. The results confirm numerical obtained Droz. find that stationary probability distribution shortest one among characteristic times are governed same free energy. also derive form critical on line, which supports their numerically calculating Binder cumulants (A. M. Droz, e-print cond-mat/0201472).

A dynamic model for neural networks that explicitly takes into account the existence of several time scales without discretizing is studied analytically via use path integrals. The maximum capacity network found to be Hopfield divided by 1+${\mathit{a}}^{2}$, with a ratio refractory period action-potential duration. We obtain phase diagram as function a, capacity, and temperature. overall rich in structure, exhibiting first-order transitions well continuous ones.

The layered feedforward neural network is extended to a q-state Potts-glass model. version of the realized by imposing local inhibition on group Ising spins and introducing competitive updating rules them. dynamics such system solved exactly, storage capacity found be proportional ${\mathit{q}}^{\mathrm{\ensuremath{\Delta}}}$, with \ensuremath{\Delta}\ensuremath{\approxeq}1.85 in case storing unbiased patterns. For biased patterns, we obtain phase diagram for q=3 as function bias parameters,...

Using the replica-symmetric mean-field theory approach thermodynamic and retrieval properties of extremely diluted {\it symmetric} $Q$-Ising neural networks are studied. In particular, capacity-gain parameter capacity-temperature phase diagrams derived for $Q=3, 4$ $Q=\infty$. The zero-temperature results compared with those obtained from a study dynamics model. Furthermore, de Almeida-Thouless line is determined. Where appropriate, difference other architectures outlined.

A Blume-Emery-Griffiths perceptron model is introduced and its optimal capacity calculated within the replica-symmetric Gardner approach, as a function of pattern activity embedding stability parameter. The approximation studied via analog de Almeida-Thouless line. comparison made with other three-state perceptrons.

The stochastic dynamics of Q-phasor neural networks is discussed using a probabilistic approach. For layered feedforward architectures and Hebbian learning, exact evolution equations are given for arbitrary Q at both zero finite temperatures. capacity-temperature diagram presented. At temperature nonmonotonic behavior the capacity found as function number phases Q, contrary to other multistate network models.

AbstractThe effects of nonlinear modulation the Hebbian learning rule on performance a perceptron are investigated. Both random classification and provided by teacher considered. It is seen that both generalization rate depend overlap between student signal-to-noise ratio in local field. Furthermore, they independent specific distribution when number training examples size small. An analytic expression obtained for optimal function different schemes. For Gaussian classifications best choice...

The Willshaw model is a neural network with binary synaptic strengths. In the local inhibition, only one neuron in each block of q neurons active. We formulate using Potts spin variables and extend dynamics to stochastic one. equilibrium states system are characterized by set representing overlap between group patterns state. Stable Mattis-like solutions exist at zero temperature, phase transition found be first order. A related whose Hamiltonian linear interaction also studied. does not...

Gardner's analysis (1989) of the optimal storage capacity neural networks is extended to study finite-temperature effects. The typical volume space interactions calculated for strongly diluted as a function ratio alpha , temperature T and tolerance parameter m, from which c obtained m. At zero it found that c=2 regardless m while in general increases with at finite temperatures. authors show how best performance given obtained, reveals first-order transition high-quality low-quality one low...

We consider the behaviour of multi-state neural networks averaged over an extended monitoring period their dynamics. Pattern reconstruction by clipping activities is proposed, leading to improvement in retrieval precision.

A replica-symmetric mean-field theory approach is presented to the multi-neuron interaction model introduced by de Almeida and Iglesias (1990 Phys. Lett. 146A 239). Fixed-point equations are derived for relevant order parameters of model, extended include biased patterns, without truncating interaction. The capacity-bias temperature-capacity phase diagrams discussed. Compared with truncated version it found that capacity at zero temperature infinite retrieval states satisfy Almeida-Thouless...

The authors investigate the effects of synaptic noise in neural networks at finite temperatures. analytic results are obtained through use path-integral formulation which facilitates performing quenched average over random patterns and noises. We consider diluted Hopfield model, fully-connected model dynamic laying emphasis on interplay with temperature. In phase diagrams drawn as functions temperature, storage, strength, interesting features including re-entrance, first-order transitions...

The effects of nonlinear modulation the Hebbian learning rule on performance a perceptron are investigated. Both random classification and provided by teacher considered. It is seen that both generalization rate depend overlap between student signal-to-noise ratio in local field. Furthermore, they independent specific distribution when number training examples size small. An analytic expression obtained for optimal function different schemes. For Gaussian classifications best choice appears...

The time evolution of the local field in symmetric Q-Ising neural networks is studied for arbitrary Q. In particular, structure noise and appearance gaps probability distribution are discussed. Results presented several values Q compared with numerical simulations.