How, in a discretized model, to utilize the duality and complementarity of two saddle point variational principles is considered in the paper. A homology family of optimality conditions, different from the conventional saddle point conditions of the domain-decomposed Hellinger–Reissner principle, is derived to enhance stability of hybrid finite element schemes. Based on this, a stabilized hybri...

We consider low scale slow roll inflation driven by the gauge invariant flat directions udd and LLe of the Minimally Supersymmetric Standard Model at the vicinity of a saddle point of the scalar potential. We study the stability of saddle point and the slow roll regime by considering radiative and supergravity corrections. The latter are found to be harmless, but the former require a modest fin...

A plausible model for coherent perception is the synchronization of chaotically distributed neural spike trains over wide cortical areas. A recently introduced propensity criterion provides a tool for a quantitative comparison of different neuron models in terms of their ability to synchronize to an applied perturbation. We explore the propensity of several systems and indicate the requirements...

We extend recent work on the connection between loopy belief propagation and the Bethe free energy. Constrained minimization of the Bethe free energy can be turned into an unconstrained saddle-point problem. Both converging double-loop algorithms and standard loopy belief propagation can be interpreted as attempts to solve this saddle-point problem. Stability analysis then leads us to conclude ...

One of the important medical problems is infectious diseases such as HIV and hepatitis which annually causes the death of many people. So it is important to study infectious diseases parametric models. In this paper, we investigate differential equations system of HIV and hepatitis (with delay and without delay) from the stability and codimension-one bifurcation point of view. We show that thei...

A path integral associated with a dynamical system is an integral of a memoryless function of the system variables which, when integrated along trajectories of the system, depends only on the value of the trajectory and its derivatives at the endpoints of the integration interval. In this paper we study path independence for linear systems and integrals of quadratic diierential forms. These not...

We discuss the rate of an elementary chemical reaction. We use the reaction path and especially its saddle point on the potential energy surface. The reaction path connects reactant and product of a reaction over the transition state (TS). Usually, the TS is assumed near or at the single saddle point of the reaction path. By means of comparison of the statistics of states at the reactant and at...

Path integral formulation of Brownian trajectories is employed to re-derive the steepest descent path (SDP). An analogy between the mechanics of overdamped tra-jectories and a Hamiltonian system is found and exploited. The SDP is a special path selected from the curves that connect two predetermined xed conngurations. One xed connguration is the reactant and the second is the product. It is the...

An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented. In systems where the force along the minimum energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the minimum energ...