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Sep 08, 2010
Information Theory

Two-Way Transmission Capacity of Wireless Ad-hoc Networks

The transmission capacity of an ad-hoc network is the maximum density of active transmitters per unit area, given an outage constraint at each receiv…
Mar 03, 2012
Statistical Finance
General Finance
Portfolio Management

Incorporating fat tails in financial models using entropic divergence…

In the existing financial literature, entropy based ideas have been proposed in portfolio optimization, in model calibration for options pricing as w…
Feb 20, 2014
Networking and Internet Architecture
Data Structures and Algorithms
Information Theory

Sub-Modularity of Waterfilling with Applications to Online Basestatio…

We show that the popular water-filling algorithm for maximizing the mutual information in parallel Gaussian channels is sub-modular. The sub-modulari…
Oct 30, 2012
Statistics Theory

Generalized Network Tomography (journal version)

Generalized network tomography (GNT) deals with estimation of link performance parameters for networks with arbitrary topologies using only end-to-en…
Aug 04, 2015
Discrete Mathematics

Popular Edges and Dominant Matchings

Given a bipartite graph G = (A u B, E) with strict preference lists and and edge e*, we ask if there exists a popular matching in G that contains the…
Jan 08, 2008
Information Theory

Capacity of the Discrete-Time AWGN Channel Under Output Quantization

We investigate the limits of communication over the discrete-time Additive White Gaussian Noise (AWGN) channel, when the channel output is quantized …
May 26, 2018
Discrete Mathematics

Popular Matchings and Limits to Tractability

We consider popular matching problems in both bipartite and non-bipartite graphs with strict preference lists. It is known that every stable matching…
Feb 21, 2018
Data Structures and Algorithms

Max-size popular matchings and extensions

We consider the max-size popular matching problem in a roommates instance G = (V,E) with strict preference lists. A matching M is popular if there is…
May 30, 2011
Information Theory

Percolation and Connectivity on the Signal to Interference Ratio Graph

A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater th…
Apr 06, 2011
Information Theory

Super Critical and Sub Critical Regimes of Percolation with Secure …

Percolation in an information-theoretically secure graph is considered where both the legitimate and the eavesdropper nodes are distributed as Poisso…
Oct 08, 2010
Information Theory

Communicating Under Channel Uncertainty

For a single transmit and receive antenna system, a new constellation design is proposed to combat errors in the phase estimate of the channel coeffi…
Mar 05, 2012
Probability

Efficient simulation of density and probability of large deviations o…

We consider the problem of efficient simulation estimation of the density function at the tails, and the probability of large deviations for a sum of…
Jun 18, 2010
Molecular Networks
Commutative Algebra

Catalysis in Reaction Networks

We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is on in the presence of certain…
Jan 10, 2013
Data Structures and Algorithms

On Pairwise Spanners

Given an undirected $n$-node unweighted graph $G = (V, E)$, a spanner with stretch function $f(\cdot)$ is a subgraph $H\subseteq G$ such that, if two…
Jul 13, 2014
Computational Complexity

The author would like to thank Arkadev Chattopadhyay and Prahladh Harsha for many helpful discussions. The author is thankful to Prahladh Harsha for his help in improving the presentation of this article significantly.

Sub-linear Upper Bounds on Fourier dimension of Boolean Functions in …

We prove that the Fourier dimension of any Boolean function with Fourier sparsity $s$ is at most $O\left(s^{2/3}\right)$. Our proof method yields an …
Nov 14, 2017
Information Theory

Energy-Delay-Distortion Problem

An energy-limited source trying to transmit multiple packets to a destination with possibly different sizes is considered. With limited energy, the s…
Apr 26, 2010
Information Theory

Throughput-Delay-Reliability Tradeoff with ARQ in Wireless Ad Hoc N…

Delay-reliability (D-R), and throughput-delay-reliability (T-D-R) tradeoffs in an ad hoc network are derived for single hop and multi-hop transmissio…
Jul 19, 2013
Networking and Internet Architecture
Data Structures and Algorithms

Optimally Approximating the Coverage Lifetime of Wireless Sensor Ne…

We consider the problem of maximizing the lifetime of coverage (MLCP) of targets in a wireless sensor network with battery-limited sensors. We first …
Jul 23, 2018

I thank Ashley Montanaro for pointing me to his work [HMS11] on compression of quantum states and Johnson Lindenstrauss lemma during a talk given on a preliminary version of this work at a workshop in CRM, Montréal, Canada, October 2011.

A quantum Johnson-Lindenstrauss lemma via unitary t-designs

The famous Johnson-Lindenstrauss lemma states that for any set of n vectors, there is a linear transformation into a space of dimension O(log n) that…
Dec 01, 2015
Data Structures and Algorithms

Online Budgeted Repeated Matching

A basic combinatorial online resource allocation problem is considered, where multiple servers have individual capacity constraints, and at each time…
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