We establish the global existence of classical solutions to a generalized chemotaxis model, which includes the volume filling effect expressed through a nonlinear squeezing probability. This novel choice of squeezing probability reflects the elastic properties of cells. Necessary and sufficient conditions for spatial pattern formation are given and the underlying bifurcations are analyzed. In n...

A method is proposed to compute the continuum of paths, from shortest paths to all random paths between all pairs of nodes at once in a unified way. The analysis is based on treating the network as a random walk with an additional absorbing state named evaporating state reachable with nonzero probability from any state (so called “evaporating random walk”). The probability of avoiding absorptio...

Motivated by experiments on splitting one-dimensional quasicondensates, we study the statistics of the work done by a quantum quench in a bosonic system. We discuss the general features of the probability distribution of the work and focus on its behavior at the lowest energy threshold, which develops an edge singularity. A formal connection between this probability distribution and the critica...

Quantum discord is the quantitative difference between two alternative expressions for bipartite mutual information, given respectively in terms of two distinct definitions for the conditional entropy. By constructing a stochastic model of shared states, classical discord can be similarly defined, quantifying the presence of some stochasticity in the measurement process. Therefore, discord can ...

Detailed measurements of the spin structure of the nucleon [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] have revealed that only a small fraction of the nucleon spin is carried by the quark spin. This result immediately raised the question, which degrees of freedom carry the rest. Unfortunately, both orbital angular momentum and the gluon spin are difficult to access experimentally, and therefore little ...

Let $A$ be a commutative ring with nonzero identity, and $1leq n

We propose a new adaptive L1 penalized quantile regression estimator for highdimensional sparse regression models with heterogeneous error sequences. We show that under weaker conditions compared with alternative procedures, the adaptive L1 quantile regression selects the true underlying model with probability converging to one, and the unique estimates of nonzero coefficients it provides have ...

Because of the mobility, computing power and changeable topology of dynamic networks, it is difficult for random linear network coding (RLNC) in static networks to satisfy the requirements of dynamic networks. To alleviate this problem, a minimal increase network coding (MINC) algorithm is proposed. By identifying the nonzero elements of an encoding vector, it selects blocks to be encoded on th...

The National Aeronautics and Space Administration (NASA) Cyclone Global Navigation Satellite System (CyGNSS) mission was launched in December 2016, which can remotely sense sea surface wind with a relatively high spatio-temporal resolution for tracking tropical cyclones. In recent years, the gradual development of geophysical model function (GMF) CyGNSS retrieval, different versions Level 2 pro...

We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-dimensional sparse signal based on a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column which is most correlated with the current residuals. In this paper, we present a fully data driven OMP algorithm with explicit stopping rules. It is shown t...