Fast Discovery of Reliable k-terminal Subgraphs

Peer reviewe

Minimal Obstructions for Partial Representations of Interval Graphs

Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. Two linear-time algorithms are known for solving this problem. In this paper, we characterize the minimal obstructions which make partial representations non-extendible. This generalizes Lekkerkerker and Boland's characterization of the minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible if and only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to a linear-time certifying algorithm for partial representation extension

Orthogonal Arrays of Strength Three from Regular 3-Wise Balanced Designs

The construction given in Kreher, J Combin Des 4 (1996) 67 is extended to obtain new infinite families of orthogonal arrays of strength 3. Regular 3-wise balanced designs play a central role in this construction

Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels

The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when e.g., d=6 or d=10. In contrast to their result, we show that the King's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.Comment: REVTeX4, 4 page

Entanglement-assisted quantum low-density parity-check codes

This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes (EAQECCs) with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error correction performance, high rates, and low decoding complexity. The proposed method produces infinitely many new codes with a wide variety of parameters and entanglement requirements. Our framework encompasses various codes including the previously known entanglement-assisted quantum LDPC codes having the best error correction performance and many new codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.Comment: 20 pages, 5 figures. Final version appearing in Physical Review

Partial Covering Arrays: Algorithms and Asymptotics

A covering array $\mathsf{CA}(N;t,k,v)$ is an $N\times k$ array with entries in $\{1, 2, \ldots , v\}$, for which every $N\times t$ subarray contains each $t$-tuple of $\{1, 2, \ldots , v\}^t$ among its rows. Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems. A central question is to determine or bound $\mathsf{CAN}(t,k,v)$, the minimum number $N$ of rows of a $\mathsf{CA}(N;t,k,v)$. The well known bound $\mathsf{CAN}(t,k,v)=O((t-1)v^t\log k)$ is not too far from being asymptotically optimal. Sensible relaxations of the covering requirement arise when (1) the set $\{1, 2, \ldots , v\}^t$ need only be contained among the rows of at least $(1-\epsilon)\binom{k}{t}$ of the $N\times t$ subarrays and (2) the rows of every $N\times t$ subarray need only contain a (large) subset of $\{1, 2, \ldots , v\}^t$. In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two. In each case, a randomized algorithm constructs such arrays in expected polynomial time

Community-linked maternal death review (CLMDR) to measure and prevent maternal mortality: a pilot study in rural Malawi.

In Malawi, maternal mortality remains high. Existing maternal death reviews fail to adequately review most deaths, or capture those that occur outside the health system. We assessed the value of community involvement to improve capture and response to community maternal deaths

What is the probability of connecting two points ?

The two-terminal reliability, known as the pair connectedness or connectivity function in percolation theory, may actually be expressed as a product of transfer matrices in which the probability of operation of each link and site is exactly taken into account. When link and site probabilities are $p$ and $\rho$, it obeys an asymptotic power-law behavior, for which the scaling factor is the transfer matrix's eigenvalue of largest modulus. The location of the complex zeros of the two-terminal reliability polynomial exhibits structural transitions as $0 \leq \rho \leq 1$.Comment: a few critical polynomials are at the end of the .tex source fil

Coarse-grained entanglement classification through orthogonal arrays

Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of $N$ subsystems with an arbitrary number of internal levels each, based on properties of orthogonal arrays with $N$ columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four and five qubits, as well as heterogeneous tripartite systems consisting of two qubits and one qutrit or one qubit and two qutrits.Comment: 38 pages, 1 figur

Surface Screening Charge and Effective Charge

The charge on an atom at a metallic surface in an electric field is defined as the field-derivative of the force on the atom, and this is consistent with definitions of effective charge and screening charge. This charge can be found from the shift in the potential outside the surface when the atoms are moved. This is used to study forces and screening on surface atoms of Ag(001) c$(2\times 2)$ -- Xe as a function of external field. It is found that at low positive (outward) fields, the Xe with a negative effective charge of -0.093 $|{e}|$ is pushed into the surface. At a field of 2.3 V \AA$^{-1}$ the charge changes sign, and for fields greater than 4.1 V \AA$^{-1}$ the Xe experiences an outward force. Field desorption and the Eigler switch are discussed in terms of these results.Comment: 4 pages, 1 figure, RevTex (accepted by PRL