Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons

We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of the oscillatory rhythm, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcations, each with its own characteristic scaling laws. The discontinuous bifurcations exhibit a new kind of phase transition that may be viewed as intermediate between continuous and first order, while tangent bifurcations behave like continuous transitions with a diverging coherence scale.Comment: 4 pages, 5 figure

Capture zones of the family of functions lambda z^m exp(z)

We consider the family of entire transcendental maps given by $F_{\lambda,m}= \lambda z^m exp(z)$ where m>=2. All functions $F_{\lambda,m}$ have a superattracting fixed point at z=0, and a critical point at z=-m. In the dynamical plane we study the topology of the basin of attraction of z=0. In the parameter plane we focus on the capture behaviour, i.e., \lambda values such that the critical point belongs to the basin of attraction of z=0. In particular, we find a capture zone for which this basin has a unique connected component, whose boundary is then non-locally connected. However, there are parameter values for which the boundary of the immediate basin of z=0 is a quasicircle.Comment: 25 pages, 14 figures. Accepted for publication in the International Journal of bifurcation and Chao

Hash Functions Using Chaotic Iterations

International audienceIn this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proven that, under some conditions, these iterations have a chaotic behavior as defined by Devaney. This chaotic behavior allows us to propose a way to generate new hash functions. An illustrative example is detailed in order to show how to use our theoretical study in practice

Nambu-Hamiltonian flows associated with discrete maps

For a differentiable map $(x_1,x_2,..., x_n)\to (X_1,X_2,..., X_n)$ that has an inverse, we show that there exists a Nambu-Hamiltonian flow in which one of the initial value, say $x_n$, of the map plays the role of time variable while the others remain fixed. We present various examples which exhibit the map-flow correspondence.Comment: 19 page

Stability of Intercelular Exchange of Biochemical Substances Affected by Variability of Environmental Parameters

Communication between cells is realized by exchange of biochemical substances. Due to internal organization of living systems and variability of external parameters, the exchange is heavily influenced by perturbations of various parameters at almost all stages of the process. Since communication is one of essential processes for functioning of living systems it is of interest to investigate conditions for its stability. Using previously developed simplified model of bacterial communication in a form of coupled difference logistic equations we investigate stability of exchange of signaling molecules under variability of internal and external parameters.Comment: 11 pages, 3 figure

Cutting and Shuffling a Line Segment: Mixing by Interval Exchange Transformations

We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing processes. Illustrative examples of the mixing behaviors, including pathological cases that violate the assumptions of the known governing theorems and lead to poor mixing, are shown. Since the mathematical theory applies as the number of iterations of the map goes to infinity, we introduce practical measures of mixing (the percent unmixed and the number of intermaterial interfaces) that can be computed over given (finite) numbers of iterations. We find that good mixing can be achieved after a finite number of iterations of a one-dimensional cutting and shuffling map, even though such a map cannot be considered chaotic in the usual sense and/or it may not fulfill the conditions of the ergodic theorems for interval exchange transformations. Specifically, good shuffling can occur with only six or seven intervals of roughly the same length, as long as the rearrangement order is an irreducible permutation. This study has implications for a number of mixing processes in which discontinuities arise either by construction or due to the underlying physics.Comment: 21 pages, 10 figures, ws-ijbc class; accepted for publication in International Journal of Bifurcation and Chao

Discrete Dynamical Systems Embedded in Cantor Sets

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $N$ variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit $N\to\infty$. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological entropy and Lyapunov exponents through the concept of error-profile. We made explicit calculations both numerical and analytic for well known discrete dynamical models.Comment: 36 pages, 13 figures: minor text amendments in places, time running top to bottom in figures, to appear in J. Math. Phy

A repurposing strategy for Hsp90 inhibitors demonstrates their potency against filarial nematodes

Novel drugs are required for the elimination of infections caused by filarial worms, as most commonly used drugs largely target the microfilariae or first stage larvae of these infections. Previous studies, conducted in vitro, have shown that inhibition of Hsp90 kills adult Brugia pahangi. As numerous small molecule inhibitors of Hsp90 have been developed for use in cancer chemotherapy, we tested the activity of several novel Hsp90 inhibitors in a fluorescence polarization assay and against microfilariae and adult worms of Brugia in vitro. The results from all three assays correlated reasonably well and one particular compound, NVP-AUY922, was shown to be particularly active, inhibiting Mf output from female worms at concentrations as low as 5.0 nanomolar after 6 days exposure to drug. NVP-AUY922 was also active on adult worms after a short 24 h exposure to drug. Based on these in vitro data, NVP-AUY922 was tested in vivo in a mouse model and was shown to significantly reduce the recovery of both adult worms and microfilariae. These studies provide proof of principle that the repurposing of currently available Hsp90 inhibitors may have potential for the development of novel agents with macrofilaricidal properties