Renyi entropies as a measure of the complexity of counting problems

Counting problems such as determining how many bit strings satisfy a given Boolean logic formula are notoriously hard. In many cases, even getting an approximate count is difficult. Here we propose that entanglement, a common concept in quantum information theory, may serve as a telltale of the difficulty of counting exactly or approximately. We quantify entanglement by using Renyi entropies S(q), which we define by bipartitioning the logic variables of a generic satisfiability problem. We conjecture that S(q\rightarrow 0) provides information about the difficulty of counting solutions exactly, while S(q>0) indicates the possibility of doing an efficient approximate counting. We test this conjecture by employing a matrix computing scheme to numerically solve #2SAT problems for a large number of uniformly distributed instances. We find that all Renyi entropies scale linearly with the number of variables in the case of the #2SAT problem; this is consistent with the fact that neither exact nor approximate efficient algorithms are known for this problem. However, for the negated (disjunctive) form of the problem, S(q\rightarrow 0) scales linearly while S(q>0) tends to zero when the number of variables is large. These results are consistent with the existence of fully polynomial-time randomized approximate algorithms for counting solutions of disjunctive normal forms and suggests that efficient algorithms for the conjunctive normal form may not exist.Comment: 13 pages, 4 figure

A Hox gene mutation that triggers Nonsense-mediated RNA decay and affects alternative splicing during Drosophila development

Nonsense mutations are usually assumed to affect protein function by generating truncated protein products. Nonetheless, it is now clear that these mutations affect not just protein synthesis but also messenger RNA stability. The surveillance mechanism responsible for the detection and degradation of 'nonsense' RNA messages is termed nonsense-mediated RNA decay (NMD). Essential biochemical components of the NMD machinery have been defined in several species. Here we identify the Drosophila orthologue of one of these factors, Upf1, and document its expression during embryogenesis. To test whether NMD acts during Drosophila development, we make use of a mutation that introduces a stop codon into a variably spliced exon of the Hox gene Ultrabithorax (Ubx). Using real-time quantitative RT-PCR we demonstrate that Ubx transcripts containing the premature stop codon are expressed at lower levels than their wild type counterpart. Unexpectedly, we also find that the same mutation significantly increases the levels of a Ubx splicing isoform that lacks the exon containing the premature termination codon. These findings indicate that NMD is operational during Drosophila development and suggest that nonsense mutations may affect development by altering the spectrum of splicing products formed, as well as by reducing or eliminating protein synthesis

The regulation of Hox gene expression during animal development

Hox genes encode a family of transcriptional regulators that elicit distinct developmental programmes along the head-to-tail axis of animals. The specific regional functions of individual Hox genes largely reflect their restricted expression patterns, the disruption of which can lead to developmental defects and disease. Here, we examine the spectrum of molecular mechanisms controlling Hox gene expression in model vertebrates and invertebrates and find that a diverse range of mechanisms, including nuclear dynamics, RNA processing, microRNA and translational regulation, all concur to control Hox gene outputs. We propose that this complex multi-tiered regulation might contribute to the robustness of Hox expression during development

Virtual Parallel Computing and a Search Algorithm using Matrix Product States

We propose a form of parallel computing on classical computers that is based on matrix product states. The virtual parallelization is accomplished by representing bits with matrices and by evolving these matrices from an initial product state that encodes multiple inputs. Matrix evolution follows from the sequential application of gates, as in a logical circuit. The action by classical probabilistic one-bit and deterministic two-bit gates such as NAND are implemented in terms of matrix operations and, as opposed to quantum computing, it is possible to copy bits. We present a way to explore this method of computation to solve search problems and count the number of solutions. We argue that if the classical computational cost of testing solutions (witnesses) requires less than $O(n^2)$ local two-bit gates acting on $n$ bits, the search problem can be fully solved in subexponential time. Therefore, for this restricted type of search problem, the virtual parallelization scheme is faster than Grover's quantum algorithmComment: 4 pages, 1 figure (published version

Thermal transport in nanocrystalline graphene investigated by approach-to-equilibrium molecular dynamics simulations

Approach-to-equilibrium molecular dynamics simulations have been used to study thermal transport in nanocrystalline graphene sheets. Nanostructured graphene has been created using an iterative process for grain growth from initial seeds with random crystallographic orientations. The resulting cells have been characterized by the grain size distribution based on the radius of gyration, by the number of atoms in each grain and by the number of atoms in the grain boundary. Introduction of nanograins with a radius of gyration of 1 nm has led to a significant reduction in the thermal conductivity to 3% of the value in single crystalline graphene. Analysis of the vibrational density of states has revealed a general reduction of the vibrational intensities and broadening of the peaks when nanograins are introduced which can be attributed to phonon scattering in the boundary layer. The thermal conductivity has been evaluated as a function of the grain size with increasing size up to 14 nm and it has been shown to follow an inverse rational function. The grain size dependent thermal conductivity could be approximated well by a function where transport is described by a connection in series of conducting elements and resistances (at boundaries).Comment: 9 pages, 9 figure

Exchange Rate Misalignment and Growth: Old and New Econometric Evidence

Several studies have tried to identify the relationship between growth and misaligned or overvalued currencies. Many works (Easterly (2001) and Fajnzylber et alii (2002)), find negative correlations between exchange rate misalignment and growth for a long list of developing countries since the seventies; the more overvalued the currency, the smaller the per capita growth rates. Even after controlling the regressions for several types of variables, the studies cannot reject the statistical significance of overvalued exchange rates in explaining growth. This paper presents new econometric evidence for the exchange rate levels and growth relation based on a panel data study for 58 developing countries from 1960 until 1999 using PPP deviation measures. Our main contribution here is to estimate growth regressions with a real exchange rate index that deals with changes in real GDP per capita levels. We use a new overvaluation index that takes into account variations in real per capita incomes, adjusting, thus, our exchange rate estimates for the so-called Balassa-Samuelson effect. By correcting traditional real exchange rate annual estimates for GDP per capita increases, we intend to control our whole series for appreciations due to productivity increases as many authors do for some specific years.Exchange Rate Levels, Overvaluations, Growth

Diversity-induced resonance

We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our analytical and numerical results show that when such systems are subjected to an external subthreshold signal, their response is optimized for an intermediate value of the diversity. These findings show that intrinsic diversity might have a constructive role and suggest that natural systems might profit from their diversity in order to optimize the response to an external stimulus.Comment: 4 pages, 3 figure

Social Exclusion Orderings

We consider the problem of measuring social exclusion using qualitative data. We suggest a class of social exclusion indicators deriving the partial orderings associated with dominace for these indicators. We characterize the set of transformations on the distribution of individual deprivation scores underlying the dominace conditions proposed.Social esclusion, dominance, measures.