Bimodal distributions of protein activities in signaling systems are often interpreted as indicators of underlying switch-like responses and bistable dynamics. We investigate the emergence of bimodal protein distributions by analyzing a less appreciated mechanism: oscillating signaling systems with varying amplitude, phase and frequency due to cell-to-cell variability. We support our analysis b...

We establish necessary and sufficient conditions, in the language of bidiagonal decompositions, for a matrix V to be an eigenvector matrix of a totally positive matrix. Namely, this is the case if and only if V and V −T are lowerly totally positive. These conditions translate into easy positivity requirements on the parameters in the bidiagonal decompositions of V and V −T . Using these decompo...

The particular properties of synchronization are discussed for coupled auto-oscillating systems, which are characterized by non-quadratic law of potential dependence on the coordinate. In particular, structure of the parameter plane (frequency mismatch – coupling value) is considered for coupled van der Pol – Duffing oscillators. The arrangement of synchronization tongues and the particular pro...

The problem of system identification from a time series of measurements is solved by using nonparametric additive models. Having only few structural information about the system, a nonparametric approach may be more appropriate than a parametric one for which detailed prior knowledge is needed. Based on nonparametric regression, the functions in the additive models are estimated by a penalized ...

We present cointegration analysis as a method to infer the network structure of a linearly phase coupled oscillating system. By defining a class of oscillating systems with interacting phases, we derive a data generating process where we can specify the coupling structure of a network that resembles biological processes. In particular we study a network of Winfree oscillators, for which we pres...

If a discrete elastic system with frictional interfaces is subjected to periodic loading, the eventual steady-state response may depend on the initial condition or an initial transient phase of the loading history. In cases where shakedown is possible, it is known that it will occur for all initial conditions if there is no coupling between slip displacements and normal contact tractions, but t...

As a novel biomimetic polymer, we have developed polymer gels with an autonomous self-oscillating function. This was achieved by utilizing oscillating chemical reactions, called the Belousov-Zhabotinsky (BZ) reaction, which is recognized as a chemical model for understanding several autonomous phenomena in biological systems. Under the coexistence of the reactants, the polymer gel undergoes spo...

We investigate the dynamics of a first order transition when the order parameter field undergoes resonant oscillations, driven by a periodically varying parameter of the free energy. This parameter could be a background oscillating field as in models of pre-heating after inflation. In the context of condensed matter systems, it could be temperature T , or pressure, external electric/magnetic fi...

The peroxidase-oxidase (PO) reaction is an important example of how oscillating reactions arise in living organisms. The reaction is important mathematically because exhibits many characteristics of chaos. Of these characteristics, sensitive dependence on initial conditions illustrates how predicting the future state of the PO reaction is next to impossible. For this reason, chaotic behavior in...