Nondeterministic Instance Complexity and Proof Systems with Advice

Motivated by strong Karp-Lipton collapse results in bounded arithmetic, Cook and Krajíček [1] have recently introduced the notion of propositional proof systems with advice. In this paper we investigate the following question: Given a language L , do there exist polynomially bounded proof systems with advice for L ? Depending on the complexity of the underlying language L and the amount and type of the advice used by the proof system, we obtain different characterizations for this problem. In particular, we show that the above question is tightly linked with the question whether L has small nondeterministic instance complexity

Percolation of satisfiability in finite dimensions

The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though there is a logical connectivity transition. In part of the disconnected phase, rare regions lead to a divergent running time for optimization algorithms. The thermodynamic ground state for the NP-hard two-dimensional maximum-satisfiability problem is typically unique. These results have implications for the computational study of disordered materials.Comment: 4 pages, 4 fig

A Taxonomy of Objectives for the Training of Financial Aid Administrators

The training of financial aid administrators is mostly informal and is accomplished by the workshop and apprenticeship method. There are few training programs specifically for financial aid administrators and these in­clude occasional two-week summer school institutes which have been sponsor­ed by the U.S. Office of Education in coordination with a university or the various state financial aid associations. Occasionally, a financial aid admin­istrator is able to wing a financial aid training program in a Master\u27s or Doctoral program in the Student Personnel area; but, beyond having a few specific courses in financial aid administration, the candidate may engage in a practicum in financial aid or write a major paper on some financial aid related subject in order to complete the degree requirements. The void in formal degree or training programs for financial aid administrators (see: Schiesz, Journal of Student Financial Aid, March, 1974) i& not surprising for a relatively new and emerging profession; but it is clearly one which must be responded to by universities, educational leadership, and ·profes­sional associations at the local and the national levels with the development of formal training programs, degree programs, and ultimately a national examination for the certification of financial aid administrators

A Two-loop Test of Buscher's T-duality I

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.Comment: 28 pp, Latex, references adde

MIMO free-space optical communication employing subcarrier intensity modulation in atmospheric turbulence channels

In this paper, we analyse the error performance of transmitter/receiver array free-space optical (FSO) communication system employing binary phase shift keying (BPSK) subcarrier intensity modulation (SIM) in clear but turbulent atmospheric channel. Subcarrier modulation is employed to eliminate the need for adaptive threshold detector. Direct detection is employed at the receiver and each subcarrier is subsequently demodulated coherently. The effect of irradiance fading is mitigated with an array of lasers and photodetectors. The received signals are linearly combined using the optimal maximum ratio combining (MRC), the equal gain combining (EGC) and the selection combining (SelC). The bit error rate (BER) equations are derived considering additive white Gaussian noise and log normal intensity fluctuations. This work is part of the EU COST actions and EU projects

Subtropical Real Root Finding

We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients. Then we employ linear programming to heuristically find roots. There is a specialized variant for roots with exclusively positive coordinates, which is of considerable interest for applications in chemistry and systems biology. An implementation of our method combining the computer algebra system Reduce with the linear programming solver Gurobi has been successfully applied to input data originating from established mathematical models used in these areas. We have solved several hundred problems with up to more than 800000 monomials in up to 10 variables with degrees up to 12. Our method has failed due to its incompleteness in less than 8 percent of the cases

Practical Evaluation of Lempel-Ziv-78 and Lempel-Ziv-Welch Tries

We present the first thorough practical study of the Lempel-Ziv-78 and the Lempel-Ziv-Welch computation based on trie data structures. With a careful selection of trie representations we can beat well-tuned popular trie data structures like Judy, m-Bonsai or Cedar

The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Testing Consumer Rationality using Perfect Graphs and Oriented Discs

Given a consumer data-set, the axioms of revealed preference proffer a binary test for rational behaviour. A natural (non-binary) measure of the degree of rationality exhibited by the consumer is the minimum number of data points whose removal induces a rationalisable data-set.We study the computational complexity of the resultant consumer rationality problem in this paper. This problem is, in the worst case, equivalent (in terms of approximation) to the directed feedback vertex set problem. Our main result is to obtain an exact threshold on the number of commodities that separates easy cases and hard cases. Specifically, for two-commodity markets the consumer rationality problem is polynomial time solvable; we prove this via a reduction to the vertex cover problem on perfect graphs. For three-commodity markets, however, the problem is NP-complete; we prove thisusing a reduction from planar 3-SAT that is based upon oriented-disc drawings

Scaling Limits for Internal Aggregation Models with Multiple Sources

We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, all three models are found to have the same scaling limit, which we describe as the solution to a certain PDE free boundary problem in R^d. In particular, internal DLA has a deterministic scaling limit. We find that the scaling limits are quadrature domains, which have arisen independently in many fields such as potential theory and fluid dynamics. Our results apply both to the case of multiple point sources and to the Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in v2: added "least action principle" (Lemma 3.2); small corrections in section 4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version); expanded section 6.