Related papers: A traffic approach for profiled Pennington-Worah m…
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Anomaly detection in road networks is vital for traffic management and emergency response. However, existing approaches do not directly address multiple anomaly types. We propose a tensor-based spatio-temporal model for detecting multiple…
We study a general transition operator, generated by a random walk on a graph $X$; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transition probablilities) to be a bounded operator from…
We perform statistical analysis of the single-vehicle data measured on the Dutch freeway A9 and discussed in Ref. [2]. Using tools originating from the Random Matrix Theory we show that the significant changes in the statistics of the…
We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…
Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend…
Within the formalism of matrix product ansatz, we study a two-species asymmetric exclusion process with backward and forward site-ordered sequential update. This model, which was originally introduced with the random sequential update,…
Interacting random matrix systems are fundamental to modern theoretical physics and data science, yet a unified framework for their analysis has been lacking. This work introduces such a universal framework, built upon two novel concepts:…
The research paper addresses linear decomposition of time series of non-additive metrics that allows for the identification and interpretation of contributing factors (input features) of variance. Non-additive metrics, such as ratios, are…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing…
Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…
Based on simulations with the ``intelligent driver model'', a microscopic traffic model, we explain the recently discovered transition from free over ``synchronized'' traffic to stop-and-go patterns [B. S. Kerner, Phys. Rev. Lett. 81, 3797…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
A new phenomenon, entrainment of chaos, which is understood as a seizure of an irregular behavior by limit cycles, is discussed. As a result, chaotic cycles appear if the chaos amplitude is small. Otherwise, the chaos is not necessarily…
We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior of arbitrary order transport moments. The theory is applied to different kinds of one-dimensional intermittent maps, and Lorentz gas with…
Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding…
We characterize real functions $f$ on an interval $(-\alpha,\alpha)$ for which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional…
For any family of $N\times N$ random matrices $(\mathbf{A}_k)_{k\in K}$ which is invariant, in law, under unitary conjugation, we give general sufficient conditions for central limit theorems for random variables of the type…