Computation of the Vortex Free Energy in SU(2) Gauge Theory

We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the vacuum tends to unity. This is rigorously known to provide a necessary and sufficient condition for maintaining confinement at weak coupling in SU(N) gauge theories.Comment: 7 pages, LaTeX with 3 eps figures, minor changes, replacement of Fig.

Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature

We investigate the Anderson transition found in the spectrum of the Dirac operator of Quantum Chromodynamics (QCD) at high temperature, studying the properties of the critical quark eigenfunctions. Applying multifractal finite-size scaling we determine the critical point and the critical exponent of the transition, finding agreement with previous results, and with available results for the unitary Anderson model. We estimate several multifractal exponents, finding also in this case agreement with a recent determination for the unitary Anderson model. Our results confirm the presence of a true Anderson localization-delocalization transition in the spectrum of the quark Dirac operator at high-temperature, and further support that it belongs to the 3D unitary Anderson model class.Comment: 10 pages, 6 figure

Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

A new problem with cross-species amplification of microsatellites: Generation of non-homologous products

Microsatellites have been widely used in studies on population genetics, ecology and evolutionary biology. However, microsatellites are not always available for the species to be studied and their isolation could be time-consuming. In order to save time and effort researchers often rely on cross-species amplification. We revealed a new problem of microsatellite cross-species amplification in addition to size homoplasy by analyzing the sequences of electromorphs from seven catfish species belonging to three different families (Clariidae, Heteropneustidae and Pimelodidae). A total of 50 different electromorphs were amplified from the seven catfish species by using primers for 4 microsatellite loci isolated from the species Clarias batrachus. Two hundred and forty PCR-products representing all 50 electromorphs were sequenced and analyzed. Primers for two loci amplified specific products from orthologous loci in all species tested, whereas primers for the other two loci produced specific and polymorphic bands from some non-orthologous loci, even in closely related non-source species. Size homoplasy within the source species was not obvious, whereas extensive size homoplasy across species were detected at three loci, but not at the fourth one. These data suggest that amplification of products from non-orthologous loci and appearance of size homoplasy by cross-amplification are locus dependent, and do not reflect phylogenetic relationship. Amplification of non-orthologous loci and appearance of size homoplasy will lead to obvious complications in phylogenetic interference, population genetic and evolutionary studies. Therefore, we propose that sequence analysis of cross-amplification products should be conducted prior to application of cross-species amplification of microsatellites