The ability to ensure proteostasis is critical for maintaining proper cell function and organismal viability but is mitigated by aging. We analyzed the role of the endoplasmic reticulum unfolded protein response (UPR(ER)) in aging of C. elegans and found that age-onset loss of ER proteostasis could be reversed by expression of a constitutively active form of XBP-1, XBP-1s. Neuronally derived XB...

The basic method for the stability analysis of nonlinear time-discrete systems is the Lyapunov functions one, cf. [1,2]. By this method many very strong results are obtained, but finding Lyapunov’s functions is often connected with serious mathematical difficulties. Explicit stability stability conditions for nonlinear multivariable systems are established mainly in the case of autonomous linea...

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance ...

Given a nonautonomous and nonlinear differential equation(0.1)x′=A(t)x+f(t,x)t≥0, on an arbitrary Banach space X, we formulate very general conditions for the associated linear equation x′=A(t)x term f:[0,+∞)×X→X under which above system satisfies appropriate version of shadowing property. More precisely, require that admits type dichotomy, includes classical hyperbolic behavior as particular c...

in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

We propose a theory of how the speech gesture determines change in a functionally relevant variable of vocal tract state (e.g., constriction degree). A core postulate of the theory is that the gesture determines how the variable evolves in time independently of any executive time-keeper. That is, the theory involves intrinsic timing of speech gestures. We compare the theory against others in wh...

It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a superposition of time-periodic functions with incommensurate frequencies. Furthermore, such systems are constrained by one fewer integral of motion than is required to...

We derive a numerical scheme to compute invariant manifolds for timevariant discrete dynamical systems, i.e., nonautonomous difference equations. Our universally applicable method is based on a truncated Lyapunov-Perron operator and computes invariant manifolds using a system of nonlinear algebraic equations which can be solved both locally using (nonsmooth) inexact Newton, and globally using c...