Related papers: On Network Coding Capacity - Matroidal Networks an…
Characterizing the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterizing all information inequalities. The majority of…
This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells and other neurons with convex receptive fields. In Chapter 4,…
We introduce the families of solvable and nilpotent matroids, examining their realization spaces, closures, and associated matroid and circuit varieties. We study their realizability, as well as the irreducible decomposition of their…
Satellite networks provide unique challenges that can restrict users' quality of service. For example, high packet erasure rates and large latencies can cause significant disruptions to applications such as video streaming or voice-over-IP.…
Reed-Solomon codes are a classic family of error-correcting codes consisting of evaluations of low-degree polynomials over a finite field on some sequence of distinct field elements. They are widely known for their optimal unique-decoding…
Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…
In this paper, we completely characterize the deterministic capacity region of a four-node relay network with no direct links between the nodes, where each node communicates with the three other nodes via a relay. Towards this end, we…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
In networks, there are often more than one source of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity and…
This paper provides a link between matroid theory and locally repairable codes (LRCs) that are either linear or more generally almost affine. Using this link, new results on both LRCs and matroid theory are derived. The parameters…
For a wide class of multi-user systems, a subset of capacity region which includes the corner points and the sum-capacity facet has a special structure known as polymatroid. Multiaccess channels with fixed input distributions and…
Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…
Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic…
We investigate the two unicast flow problem over layered linear deterministic networks with arbitrary number of nodes. When the minimum cut value between each source-destination pair is constrained to be 1, it is obvious that the triangular…
We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with…
The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. The channel state is unknown at the transmitter, but observations of…
The concept of dispatchable region is useful in quantifying how much renewable generation power the system can handle. In this paper, we aim to provide an improved dispatchable region approximation method in distribution networks. First,…
A classical result in undirected wireline networks is the near optimality of routing (flow) for multiple-unicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a…
This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…