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We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
Video compression systems must support increasing bandwidth and data throughput at low cost and power, and can be limited by entropy coding bottlenecks. Efficiency can be greatly improved by parallelizing coding, which can be done at much…
Locks are a standard mechanism for synchronizing concurrent threads. The standard lock set construction assumes that critical sections are confined to a single thread, and therefore only accounts for locks acquired within that thread.…
Applications running in modern multithreaded environments are sometimes \emph{over-threaded}. The excess threads do not improve performance, and in fact may act to degrade performance via \emph{scalability collapse}. Often, such software…
In this note, I revisit the problem of computing the entanglement entropy of a single interval in the ground state of a 2d CFT. I write the leading-order result in three different ways: once by doing the replica trick with the…
Characterizing the capacity region of multi-source wireless relay networks is one of the fundamental issues in network information theory. The problem is, however, quite challenging due to inter-user interference when there exist multiple…
We establish a relation between the boundary and the topological entropies for the conformal minimal models in some of the simplest models of the unitary A-A series. We show that in these models the boundary entropy is a difference of…
The Ryu-Takayanagi (RT) formula is a crucial concept in current theory of gauge-gravity duality and emergent phenomena of geometry. Recent reinterpretation of this formula in terms of a set of "bit threads" is an interesting effort in…
The Ryu-Takayanagi conjecture establishes a remarkable connection between quantum systems and geometry. Specifically, it relates the entanglement entropy to minimal surfaces within the setting of AdS/CFT correspondence. This Letter shows…
Motivated by bit threads, we introduce a new prescription for computing entropy vectors outside the holographic entropy cone. By utilizing cycle flows on directed graphs, we show that the maximum cycle flow associated to any subset of…
When a spacetime has boundaries, the entangling surface does not have to be necessarily compact and it may have boundaries as well. Then there appear a new, boundary, contribution to the entanglement entropy due to the intersection of the…
We use the 'bit thread' formulation of holographic entanglement entropy to highlight the distinction between the universally-valid strong subadditivity and the more restrictive relation called monogamy of mutual information (MMI), known to…
Real-world graphs often manifest as a massive temporal stream of edges. The need for real-time analysis of such large graph streams has led to progress on low memory, one-pass streaming graph algorithms. These algorithms were designed for…
Quantities computed by minimal cuts, such as entanglement entropies achievable by the Ryu-Takayanagi proposal in the AdS/CFT correspondence, are constrained by linear inequalities. We prove a previously conjectured property of all such…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each…
We give a scheme to geometrize the partial entanglement entropy (PEE) for holographic CFT in the context of AdS/CFT. More explicitly, given a point $\textbf{x}$ we geometrize the two-point PEEs between $\textbf{x}$ and any other points in…
Communities in networks are commonly considered as highly cohesive subgraphs which are well separated from the rest of the network. However, cohesion and separation often cannot be maximized at the same time, which is why a compromise is…
In holographic duality, if a boundary state has a geometric description that realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey certain inequalities that together define the so-called holographic entropy cone. A…
The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space. It is interesting to ask if there is also an information theoretic interpretation of…