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Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
Measurements have been made of the probability distribution of total transmission of microwave radiation in waveguides filled with randomly positioned scatterers which would have values of the dimensionless conductance g near unity. The…
We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior…
Estimates based on 2x2 tables of frequencies are widely used in statistical applications. However, in many cases these tables are incomplete in the sense that the data required to compute the frequencies for a subset of the cells defining…
The polarization position angles (PA) of pulsar radio emission occupy a distribution that can be much wider than what is expected from the average linear polarization and the off-pulse instrumental noise. Contrary to our limited…
We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…
Almost-dispersionless pulse transfer between the extremal masses of a uniform harmonic spring-mass chain of arbitrary length can be induced by suitably modifying two masses and their spring's elastic constant at both extrema of the chain.…
The study of complex networks sheds light on the relation between the structure and function of complex systems. One remarkable result is the absence of an epidemic threshold in infinite-size scale-free networks, which implies that any…
The time-dependent diffusion spreadability $\mathcal{S}(t)$ is a powerful dynamical probe of the microstructure of two-phase heterogeneous media across length scales [Torquato, S., \emph{Phys. Rev. E.}, 104 054102 (2021)]. It has been shown…
Estimating the prevalence of a disease is necessary for evaluating and mitigating risks of its transmission within or between populations. Estimates that consider how prevalence changes with time provide more information about these risks…
Total absorption, defined as the net flux of energy out of a bounded region averaged over one cycle for time harmonic motion, must be non-negative when there are no sources of energy within the region. This passivity condition places…
One of the most striking features of quantum theory is that it allows distant observers to share correlations that resist local hidden variable (classical) explanations, a phenomenon referred to as Bell nonlocality. Besides their…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
The completeness of the quasinormal modes of the wave equation with Poeschl-Teller potential is investigated. A main result is that after a large enough time $t_0$, the solutions of this equation corresponding to $C^{\infty}$-data with…
A statistical framework is presented for the study of the orthogonally polarized modes of radio pulsar emission via the covariances between the Stokes parameters. To accommodate the typically heavy-tailed distributions of single-pulse radio…
Short-time human travel behaviour can be described by a power law with respect to distance. We incorporate this information in space-time models for infectious disease surveillance data to better capture the dynamics of disease spread. Two…
The availability of high-throughput parallel methods for sequencing microbial communities is increasing our knowledge of the microbial world at an unprecedented rate. Though most attention has focused on determining lower-bounds on the…
The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the…