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We construct a bounded degree graph $G$, such that a simple random walk on it is transient but the random walk path (i.e., the subgraph of all the edges the random walk has crossed) has only finitely many cutpoints, almost surely. We also…
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…
We use techniques from the theory of electrical networks to give nearly tight bounds for the transience class of the Abelian sandpile model on the two-dimensional grid up to polylogarithmic factors. The Abelian sandpile model is a discrete…
We derive the form of reciprocal generalized radiative transfer (RGRT) that includes the Levermore-Pomraning attenuation law for paths leaving a deterministic origin. The resulting model describes linear transport within multi-dimensional…
Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure…
This paper is concerned with the existence and uniqueness of transition fronts of a general reaction-diffusion-advection equation in domains with multiple branches. In this paper, every branch in the domain is not necessary to be straight…
Dickson's Lemma is a simple yet powerful tool widely used in termination proofs, especially when dealing with counters or related data structures. However, most computer scientists do not know how to derive complexity upper bounds from such…
Resistive wall tearing modes (RWTM) can cause major disruptions. A signature of RWTMs is that the rational surface is sufficiently close to the wall. For $(m,n) = (2,1)$ modes, at normalized minor radius $\rho = 0.75$, the value of $q$ is…
This paper contains the proofs of Theorems 2 and 3 of the article entitled Random Electrical Networks on Complete Graphs, written by the same authors and published in the Journal of the London Mathematical Society, vol. 30 (1984), pp.…
With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…
Interest in studying the conductive properties of networks made from randomly distributed nanowires is due to their numerous technological applications. Although the sheet resistance of such networks can be calculated directly, the…
We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…
We generalize normal mode expansion of Green's tensor $\bar{\bar{G}}(\bf{r},\bf{r}')$ to lossy resonators in open systems, resolving a longstanding open challenge. We obtain a simple yet robust formulation, whereby radiation of energy to…
We show that if the sum of the resistances of an electrical network $N$ is finite, then there is a unique electrical current in $N$ provided we do not allow, in a sense, any flow to escape to infinity.
Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the…
The possibility of the resonance reflection (100 % at maximum) is revealed. The corresponding exactly solvable models with the controllable numbers of resonances, their positions and widths are presented.
We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…
We outline a recently developed theory of impedance-matching, or reflectionless excitation of arbitrary finite photonic structures in any dimension. It describes the necessary and sufficient conditions for perfectly reflectionless…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…