Glassy phases in Random Heteropolymers with correlated sequences

We develop a new analytic approach for the study of lattice heteropolymers, and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a ``frozen glass'' phase. The presence of the new intermediate ``soft glass'' phase is predicted for instance in the case of polyampholytes with sequences that favor the alternation of monomers. Our approach is based on the cavity method, a refined Bethe Peierls approximation adapted to frustrated systems. It amounts to a mean field treatment in which the nearest neighbor correlations, which are crucial in the dense phases of heteropolymers, are handled exactly. This approach is powerful and versatile, it can be improved systematically and generalized to other polymeric systems

HOPF BIFURCATION ANALYSIS FOR SIMPLE THIRD-ORDER QUADRATIC SYSTEMS

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GENE REGULATION BY MYC DURING B CELL ACTIVATION

c-Myc is a transcriptional regulator required for the cellular response to proliferative stimuli. The gene expression programs regulated by Myc in physiological settings remain to be clarified. Here, we provide a complete characterization of Myc-dependent regulatory events in primary mouse B cells following activation by bacterial lipopolysaccharide (LPS). Taking advantage of cells homozygous for a conditional knockout allele of c-myc, we induced deletion before LPS stimulation, followed by genome wide profiling of mRNA levels and Myc-DNA interactions. In contrast with previous studies, in which Myc was proposed to directly drive transcriptional amplification at all active loci (Nie et al. 2012, Lin et al. 2012), our study revealed that Myc is required for the up- and down-regulation of distinct subsets of genes early after stimulation, occurring prior to the global increase in RNA production. These gene expression programs where partially overlapping with those regulated by Myc upon oncogenic activation, a distinction made not only in B-cells, but also in fibroblasts (Sab\uf2 et al., 2014, Perna et al. 2012). Our data also show that Myc dependent regulation can occur at the level of RNA Polymerase II loading, as well as elongation. Altogether these data provide an extensive picture of Myc' s action in response to a mitogenic stimulus, highlighting the importance of Myc-target genes in the remodeling of cellular physiology and metabolism. Systematic work will be needed to unravel which, among all the Myc-regulated genes, are critical in mediating this chain of events

First integrals can explain coexistence of attractors, multistability, and loss of ideality in circuits with memristors

In this paper a systematic procedure to compute the first integrals of the dynamics of a circuit with an ideal memristor is presented. In this perspective, the state space results in a layered structure of manifolds generated by first integrals, which are associated, via the choice of the initial conditions, to different exhibited behaviors. This feature turns out to be a powerful investigation tool, and it can be used to disclose the coexistence of attractors and the so called “extreme multistability,” which are typical of the circuits with ideal memristors. The first integrals can also be exploited to study the energetic behavior of both the circuit and of the memristor itself. How to extend these results to the other ideal memelements and to more complex circuit configurations is shortly mentioned. Moreover, a class of ideal memristive devices capable of inducing the same first integrals layered in the state space is introduced. Finally, a mechanism for the loss of the ideality is conceived in terms of spoiling the first integrals structure, which makes it possible to develop a non-ideal memristive model. Notably, this latter can be interpreted as an ideal memristive device subject to a dynamic nonlinear feedback, thus highlighting that the non-ideal model is still affected by the first integrals influence, and justifying the importance of studying the ideal devices in order to understand the non-ideal ones

Harmonic Balance Design of Oscillatory Circuits Based on Stanford Memristor Model

Oscillatory circuits with real memristors have attracted a lot of interest in recent years. The vast majority of circuits involve volatile memristors, while less explored is the use of non-volatile ones. This paper considers a circuit composed by the interconnection of a two-terminal (one port) element, based on the linear part of Chua's circuit, and a non-volatile memristor obeying the Stanford model. A peculiar feature of such a memristor is that its state displays negligible time-variations under some voltage threshold. Exploiting this feature, the memristor is modeled below threshold as a programmable nonlinear resistor whose resistance depends on the gap distance. Then, the first-order Harmonic Balance (HB) method is employed to derive a procedure to select the parameters of the two-terminal element in order to generate programmable subthreshold oscillatory behaviors, within a given range of the gap, via a supercritical Hopf bifurcation. Finally, the dynamic behaviors of the designed circuits as well as the sensitivity of the procedure with respect to the location of the bifurcating equilibrium point and the range of the gap are discussed and illustrated via some application examples

Drift of invariant manifolds and transient chaos in memristor Chua's circuit

The article shows that transient chaos phenomena can be observed in a generalized memristor Chua's circuit where a nonlinear resistor is introduced to better model the real memristor behaviour. The flux-charge analysis method is used to explain the origin of transient chaos, that is attributed to the drift of the index of the memristor circuit invariant manifolds caused by the charge flowing into the nonlinear resistor

Snap-back repellers and chaos in a class of discrete-time memristor circuits

In the last decade the flux-charge analysis method (FCAM) has been successfully used to show that continuous-time (CT) memristor circuits possess for structural reasons first integrals (invariants of motion) and their state space can be foliated in invariant manifolds. Consequently, they display an initial condition dependent dynamics, extreme multistability (coexistence of infinitely many attractors) and bifurcations without parameters. Recently, a new discretization scheme has been introduced for CT memristor circuits, guaranteeing that the first integrals are preserved exactly in the discretization. On this basis, FCAM has been extended to discrete-time (DT) memristor circuits showing that they also are characterized by invariant manifolds and they display extreme multistability and bifurcations without parameters. This manuscript considers the maps obtained via DT-FCAM for a circuit with a flux-controlled memristor and a capacitor and it provides a thorough and rigorous investigation of the presence of chaotic dynamics. In particular, parameter ranges are obtained where the maps have snap-back repellers at some fixed points, thus implying that they display chaos in the Marotto and also in the Li-Yorke sense. Bifurcation diagrams are provided where it is possible to analytically identify relevant points in correspondence with the appearance of snap-back repellers and the onset of chaos. The dependence of the bifurcation diagrams and snap-back repellers upon the circuit initial conditions and the related manifold is also studied

Convergence of Discrete-Time Cellular Neural Networks with Application to Image Processing

The paper considers a class of discrete-time cellular neural networks (DT-CNNs) obtained by applying Euler's discretization scheme to standard CNNs. Let T be the DT-CNN interconnection matrix which is defined by the feedback cloning template. The paper shows that a DT-CNN is convergent, i.e. each solution tends to an equilibrium point, when T is symmetric and, in the case where T + En is not positive-semidefinite, the step size of Euler's discretization scheme does not exceed a given bound (En is the n × n unit matrix). It is shown that two relevant properties hold as a consequence of the local and space-invariant interconnecting structure of a DT-CNN, namely: (1) the bound on the step size can be easily estimated via the elements of the DT-CNN feedback cloning template only; (2) the bound is independent of the DT-CNN dimension. These two properties make DT-CNNs very effective in view of computer simulations and for the practical applications to high-dimensional processing tasks. The obtained results are proved via Lyapunov approach and LaSalle's Invariance Principle in combination with some fundamental inequalities enjoyed by the projection operator on a convex set. The results are compared with previous ones in the literature on the convergence of DT-CNNs and also with those obtained for different neural network models as the Brain-State-in-a-Box model. Finally, the results on convergence are illustrated via the application to some relevant 2D and 1D DT-CNNs for image processing tasks