Related papers: Coordination and Discoordination in Linear Algebra…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
To increase the information capacity of DNA storage, composite DNA letters were introduced. We propose a novel channel model for composite DNA in which composite sequences are decomposed into ordered standard non-composite sequences. The…
Chain-of-thought reasoning is often treated as a monotone way to improve language-model accuracy by letting a model think longer. We identify a countervailing effect, the coupling tax: when reasoning traces and final answers share one…
This paper considers vector network coding based on rank-metric codes and subspace codes. Our main result is that vector network coding can significantly reduce the required field size compared to scalar linear network coding in the same…
Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem…
Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
We consider the problem of linear network coding over communication networks, representable by directed acyclic graphs, with multiple groupcast sessions: the network comprises of multiple destination nodes, each desiring messages from…
The decomposition theory of matroids initiated by Paul Seymour in the 1980's has had an enormous impact on research in matroid theory. This theory, when applied to matrices over the binary field, yields a powerful decomposition theory for…
Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann…
Distribution matching is the process of invertibly mapping a uniformly distributed input sequence onto sequences that approximate the output of a desired discrete memoryless source. The special case of a binary output alphabet and…
Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in $d$-space into constant-complexity subcells. In this paper, we settle in the affirmative a few long-standing open…
Coded caching and delivery is studied taking into account the correlations among the contents in the library. Correlations are modeled as common parts shared by multiple contents; that is, each file in the database is composed of a group of…
In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given $p,\epsilon>0$, we study (i) The $p$-bounded constraint: a binary vector of size $m$ is said to be $p$-bounded if its weight is at most…
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…
Generative models that learn disentangled representations for different factors of variation in an image can be very useful for targeted data augmentation. By sampling from the disentangled latent subspace of interest, we can efficiently…
Coded caching is an effective technique to decongest the amount of traffic in the backhaul link. In such a scheme, each file hosted in the server is divided into a number of packets to pursue a low transmission rate based on the delicate…