Single-Server Multi-Message Private Information Retrieval with Side Information

We study the problem of single-server multi-message private information retrieval with side information. One user wants to recover $N$ out of $K$ independent messages which are stored at a single server. The user initially possesses a subset of $M$ messages as side information. The goal of the user is to download the $N$ demand messages while not leaking any information about the indices of these messages to the server. In this paper, we characterize the minimum number of required transmissions. We also present the optimal linear coding scheme which enables the user to download the demand messages and preserves the privacy of their indices. Moreover, we show that the trivial MDS coding scheme with $K-M$ transmissions is optimal if $N>M$ or $N^2+N \ge K-M$. This means if one wishes to privately download more than the square-root of the number of files in the database, then one must effectively download the full database (minus the side information), irrespective of the amount of side information one has available.Comment: 12 pages, submitted to the 56th Allerton conferenc

Cooperative Data Exchange based on MDS Codes

The cooperative data exchange problem is studied for the fully connected network. In this problem, each node initially only possesses a subset of the $K$ packets making up the file. Nodes make broadcast transmissions that are received by all other nodes. The goal is for each node to recover the full file. In this paper, we present a polynomial-time deterministic algorithm to compute the optimal (i.e., minimal) number of required broadcast transmissions and to determine the precise transmissions to be made by the nodes. A particular feature of our approach is that {\it each} of the $K-d$ transmissions is a linear combination of {\it exactly} $d+1$ packets, and we show how to optimally choose the value of $d.$ We also show how the coefficients of these linear combinations can be chosen by leveraging a connection to Maximum Distance Separable (MDS) codes. Moreover, we show that our method can be used to solve cooperative data exchange problems with weighted cost as well as the so-called successive local omniscience problem.Comment: 21 pages, 1 figur

QED Thermodynamics at Intermediate Coupling

We discuss reorganizing finite temperature perturbation theory using hard-thermal-loop (HTL) perturbation theory in order to improve the convergence of successive perturbative approximations to the free energy of a gauge theory. We briefly review the history of the technique and present new results for the three-loop HTL-improved approximation for the free energy of QED. We show that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at intermediate coupling, e ~ 2. The reorganization is gauge invariant by construction, and due to cancellation among various contributions, one can obtain a completely analytic result for the resummed thermodynamic potential at three loops.Comment: 8 pages, 3 figures, Proceedings contribution to "Three Days of Strong Interactions", Wroclaw (Poland), July 200

Charged current universality problem and NuTeV anomaly: is SUSY to blame?

We compute the complete one-loop contributions to low-energy charged current weak interaction observables in the Minimal Supersymmetric Standard Model (MSSM). We obtain the constraints on the MSSM parameter space which arise when precision low-energy charged current (CC) data are analyzed in tandem with measurements of the muon anomaly. The data imply a pattern of mass splittings among first and second generation sleptons and squarks which contradicts predictions of widely used models for supersymmetry breaking mediation. We also discuss the implications of these constraints on the SUSY one-loop contributions to the (anti)neutrino-nucleus deep inelastic scattering. We consider the ratios of neutral current to charged current cross sections, and compare with the deviations of these quantities from the Standard Model predictions implied by the recent NuTeV measurement. We discuss one scenario in which a right-sign effect arises, and show that it is ruled out by the CC data. We also study R parity-violating contributions. Although such effects can account for the violation of the first row CKM unitarity, they can not reproduce the NuTeV anomaly. If NuTeV anomaly is ultimately explained within the SM, R parity-violating resolution of the CKM unitarity problem can be tested in parity-violating electron scattering experiments at SLAC and TJNAF

Gas-Phase Photodegradation of Decane and Methanol on TiO_2: Dynamic Surface Chemistry Characterized by Diffuse Reflectance FTIR

Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) was used to study illuminated TiO2 surfaces under both vacuum conditions, and in the presence of organic molecules (decane and methanol). In the presence of hole scavengers, electrons are trapped at Ti(III)–OH sites, and free electrons are generated. These free electrons are seen to decay by exposure either to oxygen or to heat; in the case of heating, reinjection of holes into the lattice by loss of sorbed hole scavenger leads to a decrease in Ti(III)–OH centers. Decane adsorption experiments lend support to the theory that removal of surficial hydrocarbon contaminants is responsible for superhydrophilic TiO2 surfaces. Oxidation of decane led to a mixture of surface-bound organics, while oxidation of methanol leads to the formation of surface-bound formic acid

Voting for Committees in Agreeable Societies

We examine the following voting situation. A committee of $k$ people is to be formed from a pool of n candidates. The voters selecting the committee will submit a list of $j$ candidates that they would prefer to be on the committee. We assume that $j \leq k < n$. For a chosen committee, a given voter is said to be satisfied by that committee if her submitted list of $j$ candidates is a subset of that committee. We examine how popular is the most popular committee. In particular, we show there is always a committee that satisfies a certain fraction of the voters and examine what characteristics of the voter data will increase that fraction.Comment: 11 pages; to appear in Contemporary Mathematic