Error tolerance of two-basis quantum key-distribution protocols using qudits and two-way classical communication

We investigate the error tolerance of quantum cryptographic protocols using $d$-level systems. In particular, we focus on prepare-and-measure schemes that use two mutually unbiased bases and a key-distillation procedure with two-way classical communication. For arbitrary quantum channels, we obtain a sufficient condition for secret-key distillation which, in the case of isotropic quantum channels, yields an analytic expression for the maximally tolerable error rate of the cryptographic protocols under consideration. The difference between the tolerable error rate and its theoretical upper bound tends slowly to zero for sufficiently large dimensions of the information carriers.Comment: 10 pages, 1 figur

Understanding Adoption of Internet Technologies Among SMEs

The Internet has been viewed as a powerful tool enabling small firms to "level the playing field" when competing with larger firms. Yet, the benefits of e-business are accruing to larger, rather than smaller, firms. While numerous studies have been conducted in other countries to examine the use of the Internet by small and medium-sized enterprises (SMEs), similar studies focused on U.S. small firms have not yet emerged. Using the Commission of the European Communities' stringent definition of SMEs, this paper identifies significantly different patterns in e-business usage among 395 micro, small, and medium-sized firms. While using the Internet to find information and to enhance the company/image brand is important for all firms, the smallest of firms attach greater importance to using the Internet for research purposes and lesser for communication reasons (i.e., e-mail). This pattern is reversed for larger (i.e., small and medium sized) firms

Portal protein functions akin to a DNA-sensor that couples genome-packaging to icosahedral capsid maturation.

Tailed bacteriophages and herpesviruses assemble infectious particles via an empty precursor capsid (or \u27procapsid\u27) built by multiple copies of coat and scaffolding protein and by one dodecameric portal protein. Genome packaging triggers rearrangement of the coat protein and release of scaffolding protein, resulting in dramatic procapsid lattice expansion. Here, we provide structural evidence that the portal protein of the bacteriophage P22 exists in two distinct dodecameric conformations: an asymmetric assembly in the procapsid (PC-portal) that is competent for high affinity binding to the large terminase packaging protein, and a symmetric ring in the mature virion (MV-portal) that has negligible affinity for the packaging motor. Modelling studies indicate the structure of PC-portal is incompatible with DNA coaxially spooled around the portal vertex, suggesting that newly packaged DNA triggers the switch from PC- to MV-conformation. Thus, we propose the signal for termination of \u27Headful Packaging\u27 is a DNA-dependent symmetrization of portal protein

Mixing Times in Quantum Walks on Two-Dimensional Grids

Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.Comment: 11 page

Hitting time for quantum walks on the hypercube

Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as well as unitary evolution. We derive an expression for hitting time using superoperators, and numerically evaluate it for the discrete walk on the hypercube. The values found are compared to other analogues of hitting time suggested in earlier work. The dependence of hitting times on the type of unitary ``coin'' is examined, and we give an example of an initial state and coin which gives an infinite hitting time for a quantum walk. Such infinite hitting times require destructive interference, and are not observed classically. Finally, we look at distortions of the hypercube, and observe that a loss of symmetry in the hypercube increases the hitting time. Symmetry seems to play an important role in both dramatic speed-ups and slow-downs of quantum walks.Comment: 8 pages in RevTeX format, four figures in EPS forma

Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing

We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to the question of tripartite to bipartite entanglement transformations

LINVIEW: Incremental View Maintenance for Complex Analytical Queries

Many analytics tasks and machine learning problems can be naturally expressed by iterative linear algebra programs. In this paper, we study the incremental view maintenance problem for such complex analytical queries. We develop a framework, called LINVIEW, for capturing deltas of linear algebra programs and understanding their computational cost. Linear algebra operations tend to cause an avalanche effect where even very local changes to the input matrices spread out and infect all of the intermediate results and the final view, causing incremental view maintenance to lose its performance benefit over re-evaluation. We develop techniques based on matrix factorizations to contain such epidemics of change. As a consequence, our techniques make incremental view maintenance of linear algebra practical and usually substantially cheaper than re-evaluation. We show, both analytically and experimentally, the usefulness of these techniques when applied to standard analytics tasks. Our evaluation demonstrates the efficiency of LINVIEW in generating parallel incremental programs that outperform re-evaluation techniques by more than an order of magnitude.Comment: 14 pages, SIGMO

Adenomatoid odontogenic tumor with impacted mandibular canine: a case report

The Adenomatoid Odontogenic Tumor (AOT) is a rare, slow growing, benign, odontogenic epithelial tumor with characteristic clinical and histological features; which usually arise in the second or third decade. It is a tumor composed of odontogenic epithelium in a variety of histoarchitectural patterns which are embedded in a mature connective tissue stroma. It is mostly encountered in young patients with a greater predilection for females. Maxilla is the predilection site of occurrence, most commonly associated with an unerupted maxillary canine. It presents as a symptom-free lesion and is frequently discovered during routine radiographic examination. This case report describes an unusual case of 20 year old male with only a one month history of tumor in the anterior mandible. The tumor was a well circumscribed intraosseous lesion with an embedded tooth. Histological evidence of calcification was present. The present case lends support to the categorization of AOT as a mixed odontogenic tumo

On Profit-Maximizing Pricing for the Highway and Tollbooth Problems

In the \emph{tollbooth problem}, we are given a tree \bT=(V,E) with $n$ edges, and a set of $m$ customers, each of whom is interested in purchasing a path on the tree. Each customer has a fixed budget, and the objective is to price the edges of \bT such that the total revenue made by selling the paths to the customers that can afford them is maximized. An important special case of this problem, known as the \emph{highway problem}, is when \bT is restricted to be a line. For the tollbooth problem, we present a randomized $O(\log n)$-approximation, improving on the current best $O(\log m)$-approximation. We also study a special case of the tollbooth problem, when all the paths that customers are interested in purchasing go towards a fixed root of \bT. In this case, we present an algorithm that returns a $(1-\epsilon)$-approximation, for any $\epsilon > 0$, and runs in quasi-polynomial time. On the other hand, we rule out the existence of an FPTAS by showing that even for the line case, the problem is strongly NP-hard. Finally, we show that in the \emph{coupon model}, when we allow some items to be priced below zero to improve the overall profit, the problem becomes even APX-hard

Thresholded Covering Algorithms for Robust and Max-Min Optimization

The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? Feige et al. and Khandekar et al. considered the k-robust model where the possible outcomes tomorrow are given by all demand-subsets of size k, and gave algorithms for the set cover problem, and the Steiner tree and facility location problems in this model, respectively. In this paper, we give the following simple and intuitive template for k-robust problems: "having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold, augment the anticipatory solution to cover this demand as well, and repeat". In this paper we show that this template gives us improved approximation algorithms for k-robust Steiner tree and set cover, and the first approximation algorithms for k-robust Steiner forest, minimum-cut and multicut. All our approximation ratios (except for multicut) are almost best possible. As a by-product of our techniques, we also get algorithms for max-min problems of the form: "given a covering problem instance, which k of the elements are costliest to cover?".Comment: 24 page