P-Selectivity, Immunity, and the Power of One Bit

We prove that P-sel, the class of all P-selective sets, is EXP-immune, but is not EXP/1-immune. That is, we prove that some infinite P-selective set has no infinite EXP-time subset, but we also prove that every infinite P-selective set has some infinite subset in EXP/1. Informally put, the immunity of P-sel is so fragile that it is pierced by a single bit of information. The above claims follow from broader results that we obtain about the immunity of the P-selective sets. In particular, we prove that for every recursive function f, P-sel is DTIME(f)-immune. Yet we also prove that P-sel is not \Pi_2^p/1-immune

The Shield that Never Was: Societies with Single-Peaked Preferences are More Open to Manipulation and Control

Much work has been devoted, during the past twenty years, to using complexity to protect elections from manipulation and control. Many results have been obtained showing NP-hardness shields, and recently there has been much focus on whether such worst-case hardness protections can be bypassed by frequently correct heuristics or by approximations. This paper takes a very different approach: We argue that when electorates follow the canonical political science model of societal preferences the complexity shield never existed in the first place. In particular, we show that for electorates having single-peaked preferences, many existing NP-hardness results on manipulation and control evaporate.Comment: 38 pages, 2 figure

Credimus

We believe that economic design and computational complexity---while already important to each other---should become even more important to each other with each passing year. But for that to happen, experts in on the one hand such areas as social choice, economics, and political science and on the other hand computational complexity will have to better understand each other's worldviews. This article, written by two complexity theorists who also work in computational social choice theory, focuses on one direction of that process by presenting a brief overview of how most computational complexity theorists view the world. Although our immediate motivation is to make the lens through which complexity theorists see the world be better understood by those in the social sciences, we also feel that even within computer science it is very important for nontheoreticians to understand how theoreticians think, just as it is equally important within computer science for theoreticians to understand how nontheoreticians think

The Complexity of Computing Minimal Unidirectional Covering Sets

Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08] proved that it is NP-hard to decide whether an alternative is contained in some inclusion-minimal upward or downward covering set. For both problems, we raise this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other natural problems regarding minimal or minimum-size covering sets are hard or complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of our results is that neither minimal upward nor minimal downward covering sets (even when guaranteed to exist) can be computed in polynomial time unless P=NP. This sharply contrasts with Brandt and Fischer's result that minimal bidirectional covering sets (i.e., sets that are both minimal upward and minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure

Inclusive One Jet Production With Multiple Interactions in the Regge Limit of pQCD

DIS on a two nucleon system in the regge limit is considered. In this framework a review is given of a pQCD approach for the computation of the corrections to the inclusive one jet production cross section at finite number of colors and discuss the general results.Comment: 4 pages, latex, aicproc format, Contribution to the proceedings of "Diffraction 2008", 9-14 Sep. 2008, La Londe-les-Maures, Franc

On the Complexity of Query Result Diversification

Query result diversification is a bi-criteria optimization problem for ranking query results. Given a database D, a query Q and a positive integer k, it is to find a set of k tuples from Q(D) such that the tuples are as relevant as possible to the query, and at the same time, as diverse as possible to each other. Subsets of Q(D) are ranked by an objective function defined in terms of relevance and diversity. Query result diversification has found a variety of applications in databases, information retrieval and operations research. This paper studies the complexity of result diversification for relational queries. We identify three problems in connection with query result diversification, to determine whether there exists a set of k tuples that is ranked above a bound with respect to relevance and diversity, to assess the rank of a given k-element set, and to count how many k-element sets are ranked above a given bound. We study these problems for a variety of query languages and for three objective functions. We establish the upper and lower bounds of these problems, all matching, for both combined complexity and data complexity. We also investigate several special settings of these problems, identifying tractable cases. 1

A common algebraic description for probabilistic and quantum computations

AbstractThrough the study of gate arrays we develop a unified framework to deal with probabilistic and quantum computations, where the former is shown to be a natural special case of the latter. On this basis we show how to encode a probabilistic or quantum gate array into a sum-free tensor formula which satisfies the conditions of the partial trace problem, and vice-versa; that is, given a tensor formula F of order n×1 over a semiring S plus a positive integer k, deciding whether the kth partial trace of the matrix valSn,n(F·FT) fulfills a certain property. We use this to show that a certain promise version of the sum-free partial trace problem is complete for the class pr- BPP (promise BPP) for formulas over the semiring (Q+,+,·) of the positive rational numbers, for pr-BQP (promise BQP) in the case of formulas defined over the field (Q+,+,·), and if the promise is given up, then completeness for PP is shown, regardless whether tensor formulas over positive rationals or rationals in general are used. This suggests that the difference between probabilistic and quantum polytime computers may ultimately lie in the possibility, in the latter case, of having destructive interference between computations occurring in parallel. Moreover, by considering variants of this problem, classes like ⊕P, NP, C=P, its complement co-C=P, the promise version of Valiant's class UP, its generalization promise SPP, and unique polytime US can be characterized by carrying the problem properties and the underlying semiring

Comparison of five commercial serological tests for the detection of anti-Chlamydia trachomatis antibodies.

Screening for Chlamydia trachomatis-specific antibodies is valuable in investigating recurrent miscarriage, tubal infertility and extrauterine pregnancy. We compared here the performance of immunofluorescence (IF) to four other commercial tests in detecting IgG antibodies directed against C. trachomatis: two enzyme-linked immunosorbent assays (ELISAs) using the major outer membrane protein (MOMP) as the antigen, commercialised respectively by Medac and R-Biopharm (RB), one ELISA using the chlamydial heat shock protein 60 (cHSP60) as the antigen (Medac), as well as a new automated epifluorescence immunoassay (InoDiag). A total of 405 patients with (n = 251) and without (n = 154) miscarriages were tested by all five tests. The prevalence of C. trachomatis-specific IgG antibodies as determined by the IF, cHSP60-Medac, MOMP-Medac, MOMP-RB and InoDiag was 14.3, 23.2, 14.3, 11.9 and 26.2%, respectively. InoDiag exhibited the highest sensitivity, whereas MOMP-RB showed the best specificity. Cross-reactivity was observed with C. pneumoniae using IF, MOMP-RB and InoDiag, and Parachlamydia acanthamoebae using the cHSP60 ELISA test. No cross-reactivity was observed between C. trachomatis and the other Chlamydiales (Neochlamydia hartmannellae, Waddlia chondrophila and Simkania negevensis). Given its high sensitivity, the new automated epifluorescence immunoassay from InoDiag represents an interesting alternative. The MOMP-based ELISA of R-Biopharm should be preferred for large serological studies, given the high throughput of ELISA and its excellent specificity