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Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other…
We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes…
Boolean functions are important primitives in different domains of cryptology, complexity and coding theory. In this paper, we connect the tools from cryptology and complexity theory in the domain of Boolean functions with low polynomial…
We model a particulate flow of constant velocity through confined geometries, ranging from a single channel to a bundle of $N_c$ identical coupled channels, under conditions of reversible blockage. Quantities of interest include the exiting…
Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This…
We consider entanglement negativity for two disjoint intervals in 1+1 dimensional CFT in the limit of large central charge. As the two intervals get close, the leading behavior of negativity is given by the logarithm of the conformal block…
Detection of hydroacoustic transmissions is a key enabling technology in applications such as depth measurements, detection of objects, and undersea mapping. To cope with the long channel delay spread and the low signal-to-noise ratio,…
A system of soft ellipsoid molecules confined between two planar walls is studied using classical Density Functional Theory (DFT). Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different…
Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of…
We generalize the factorization method for inverse medium scattering using a particular factorization of the difference of two far field operators. Whilst the factorization method been used so far mainly to identify the shape of a…
Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size $m \times n$) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix…
We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove new bounds on the number of relevant variables for boolean functions in terms of a variety of complexity measures. Our approach unifies and refines…
A rate-dependent upper bound of the best achievable block error probability of polar codes with successive-cancellation decoding is derived.
Power line communications (PLC) is the central communications technology for the realization of smart power grids. As the designated band for smart grid communications is the narrowband (NB) power line channel, NB-PLC has been receiving…
It is shown that a large class of events in a product probability space are highly sensitive to noise, in the sense that with high probability, the configuration with an arbitrary small percent of random errors gives almost no prediction…
Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced,…
Martingale concentration inequalities constitute a powerful mathematical tool in the analysis of problems in a wide variety of fields ranging from probability and statistics to information theory and machine learning. Here we apply…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
Constraint "at most one" is a basic cardinality constraint which requires that at most one of its $n$ boolean inputs is set to $1$. This constraint is widely used when translating a problem into a conjunctive normal form (CNF) and we…
We consider several transitions between narrow lines that have an enhanced sensitivity to a possible variation of the fine structure constant, alpha. This enhancement may allow a search to be performed with an effective suppression of the…