Two dimensional self-avoiding walk with hydrogen-like bonding: Phase diagram and critical behaviour

The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model displays a collapse transition. In contrast to the standard $\theta$-point model, the transition is first order. The phase diagram in the full fugacity-temperature plane displays an additional transition line, when compared to the $\theta$-point model, as well as a critical transition at finite temperature in the hamiltonian walk limit.Comment: 22 pages, 13 figures. To appear in Journal of Physics

Revised CPA method to compute Lyapunov functions for nonlinear systems

The CPA method uses linear programming to compute Continuous and Piecewise Affine Lyapunov function for nonlinear systems with asymptotically stable equilibria. In it was shown that the method always succeeds in computing a CPA Lyapunov function for such a system. The size of the domain of the computed CPA Lyapunov function is only limited by the equilibrium’s basin of attraction. However, for some systems, an arbitrary small neighborhood of the equilibrium had to be excluded from the domain a priori. This is necessary, if the equilibrium is not exponentially stable, because the existence of a CPA Lyapunov function in a neighborhood of the equilibrium is equivalent to its exponential stability as shown in. However, if the equilibrium is exponentially stable, then this was an artifact of the method. In this paper we overcome this artifact by developing a revised CPA method. We show that this revised method is always able to compute a CPA Lyapunov function for a system with an exponentially stable equilibrium. The only conditions on the system are that it is C² and autonomous. The domain of the CPA Lyapunov function can be any a priori given compact neighborhood of the equilibrium which is contained in its basin of attraction. Whereas in a previous paper we have shown these results for planar systems, in this paper we cover general n-dimensional systems

Febrile seizures and mechanisms of epileptogenesis: insights from an animal model.

Temporal lobe epilepsy (TLE) is the most prevalent type of human epilepsy, yet the causes for its development, and the processes involved, are not known. Most individuals with TLE do not have a family history, suggesting that this limbic epilepsy is a consequence of acquired rather than genetic causes. Among suspected etiologies, febrile seizures have frequently been cited. This is due to the fact that retrospective analyses of adults with TLE have demonstrated a high prevalence (20-->60%) of a history of prolonged febrile seizures during early childhood, suggesting an etiological role for these seizures in the development of TLE. Specifically, neuronal damage induced by febrile seizures has been suggested as a mechanism for the development of mesial temporal sclerosis, the pathological hallmark of TLE. However, the statistical correlation between febrile seizures and TLE does not necessarily indicate a causal relationship. For example, preexisting (genetic or acquired) 'causes' that result independently in febrile seizures and in TLE would also result in tight statistical correlation. For obvious reasons, complex febrile seizures cannot be induced in the human, and studies of their mechanisms and of their consequences on brain molecules and circuits are severely limited. Therefore, an animal model was designed to study these seizures. The model reproduces the fundamental key elements of the human condition: the age specificity, the physiological temperatures seen in fevers of children, the length of the seizures and their lack of immediate morbidity. Neuroanatomical, molecular and functional methods have been used in this model to determine the consequences of prolonged febrile seizures on the survival and integrity of neurons, and on hyperexcitability in the hippocampal-limbic network. Experimental prolonged febrile seizures did not lead to death of any of the seizure-vulnerable populations in hippocampus, and the rate of neurogenesis was also unchanged. Neuronal function was altered sufficiently to promote synaptic reorganization of granule cells, and transient and long-term alterations in the expression of specific genes were observed. The contribution of these consequences of febrile seizures to the epileptogenic process is discussed

Persistently modified h-channels after complex febrile seizures convert the seizure-induced enhancement of inhibition to hyperexcitability.

Febrile seizures are the most common type of developmental seizures, affecting up to 5% of children. Experimental complex febrile seizures involving the immature rat hippocampus led to a persistent lowering of seizure threshold despite an upregulation of inhibition. Here we provide a mechanistic resolution to this paradox by showing that, in the hippocampus of rats that had febrile seizures, the long-lasting enhancement of the widely expressed intrinsic membrane conductance Ih converts the potentiated synaptic inhibition to hyperexcitability in a frequency-dependent manner. The altered gain of this molecular inhibition-excitation converter reveals a new mechanism for controlling the balance of excitation-inhibition in the limbic system. In addition, here we show for the first time that h-channels are modified in a human neurological disease paradigm

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

A comparative investigation of marginal adaptation and surface defects of MTA and root MTA as two root end filling materials

Keywords: Marginal adaptation, Confocal microscope, Stereomicroscope, MTA, RMTA, Retrograde fillin

Synergist efficacy of piperonyl butoxide with deltamethrin as pyrethroid insecticide on culex tritaeniorhynchus (diptera: culicidae) and other mosquitoe species

Continuous and indiscriminate use of pesticides, especially in tropical countries for public health or agriculture purpose, has led many vector populations to become resistant to organochlorides, organophosphates, and even to carbamates and pyrethroids. Development of resistance by a vector population has been one of the reasons for the failure of the control measures in many countries. This investigation demonstrates the efficacy of piperonyl-butoxide (PBO) with deltamethrin, as pyrethroid insecticide, against the field-collected mosquitoe larvae of five species, Aedes aegypti, Anopheles culicifacies, An. stephensi, An. vagus, and Culex quinqufasciatus, and two morphological variants of Cx. tritaeniorhynchus (type A from grand pools of Mysore city and type B from rice fields of Mandya district). For testing the synergistic effect of 13130, stock solutions of deltamethrin and PBO were mixed in 1:6 ratio. The synergistic ratio and the percent suppression in deltamethrin tolerance were calculated by using LC50 values. From the results, it is clear that, PBO is an effective synergist with deltamethrin against all of species undertaken in this investigation. So, it is suggested that PBO is a good synergist in this area for decreasing the use of pesticides in environment in vector control. (C) 2008 Wiley Periodicals, Inc. Environ Toxicol 24: 19 24, 2009