Related papers: Crossing versus locking: Bit threads and continuum…

In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a…

The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…

Destructive interference of single-electron tunneling between three quantum dots can trap an electron in a coherent superposition of charge on two of the dots. Coupling to external charges causes decoherence of this superposition, and in…

In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi…

Quantum corrections to holographic entanglement entropy require knowledge of the bulk quantum state. In this paper, we derive a novel dual prescription for the generalized entropy that allows us to interpret the leading quantum corrections…

The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow problem, which considers flow of a single commodity. We study a multiple commodity generalization of Max-Flow in which flows are composed of real-valued k-vectors…

The number of linear regions is one of the distinct properties of the neural networks using piecewise linear activation functions such as ReLU, comparing with those conventional ones using other activation functions. Previous studies showed…

The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…

Let $G=(V,E)$ be a supply graph and $H=(V,F)$ a demand graph defined on the same set of vertices. An assignment of capacities to the edges of $G$ and demands to the edges of $H$ is said to satisfy the \emph{cut condition} if for any cut in…

The entanglement entropy in one dimensional critical systems with boundaries has been associated with the noninteger ground state degeneracy. This quantity, being a characteristic of boundary fixed points, decreases under renormalization…

We consider in this paper the problem of computing the entropy of a braid. We recall its definition and construct, for each braid, a sequence of real numbers, whose limit is its entropy. We state one conjecture about the convergence speed,…

Bubble curtains are line bubble plumes that are used to mitigate saltwater intrusion in shipping locks. When the lock gate that separates the saline seawater from the fresh river water is opened, a lock-exchange flow is initiated. Placing a…

We consider a network multicast example that relates the solvability of the multicast problem with the existence of an entropy function. As a result, we provide an alternative approach to the proving of the insufficiency of linear (and…

Network coding is a new technique to transmit data through a network by letting the intermediate nodes combine the packets they receive. Given a network, the network coding solvability problem decides whether all the packets requested by…

We describe an algorithm for studying the entanglement entropy and spectrum of 2D systems, as a coupled array of $N$ one dimensional chains in their continuum limit. Using the algorithm to study the quantum Ising model in 2D, (both in its…

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…

We study a class of quantum states involving multiple entangled CFTs in AdS$_3$/CFT$_2$, associated with multi-boundary black hole geometries, and demonstrate that the Ryu-Takayanagi (RT) formula for entanglement entropy can be derived…

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a…

We study tunneling of electrons into and between interacting wires in the spin-incoherent regime subject to a magnetic field. The tunneling currents follow power laws of the applied voltage with exponents that depend on whether the electron…

Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…