Once more on the Witten index of 3d supersymmetric YM-CS theory

The problem of counting the vacuum states in the supersymmetric 3d Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy between its original calculation by Witten at large volumes and the calculation based on the evaluation of the effective Lagrangian in the small volume limit. We show that the latter calculation suffers from uncertainties associated with the singularities in the moduli space of classical vacua where the Born-Oppenheimer approximation breaks down. We also show that these singularities can be accurately treated in the Hamiltonian Born-Oppenheimer method, where one has to match carefully the effective wave functions on the Abelian valley and the wave functions of reduced non-Abelian QM theory near the singularities. This gives the same result as original Witten's calculation.Comment: 27 page

Ising Model Coupled to Three-Dimensional Quantum Gravity

We have performed Monte Carlo simulations of the Ising model coupled to three-dimensional quantum gravity based on a summation over dynamical triangulations. These were done both in the microcanonical ensemble, with the number of points in the triangulation and the number of Ising spins fixed, and in the grand canoncal ensemble. We have investigated the two possible cases of the spins living on the vertices of the triangulation (``diect'' case) and the spins living in the middle of the tetrahedra (``dual'' case). We observed phase transitions which are probably second order, and found that the dual implementation more effectively couples the spins to the quantum gravity.Comment: 11 page

A Computational Interpretation of Context-Free Expressions

We phrase parsing with context-free expressions as a type inhabitation problem where values are parse trees and types are context-free expressions. We first show how containment among context-free and regular expressions can be reduced to a reachability problem by using a canonical representation of states. The proofs-as-programs principle yields a computational interpretation of the reachability problem in terms of a coercion that transforms the parse tree for a context-free expression into a parse tree for a regular expression. It also yields a partial coercion from regular parse trees to context-free ones. The partial coercion from the trivial language of all words to a context-free expression corresponds to a predictive parser for the expression

Integrated plasmonic circuitry on a vertical-cavity surface-emitting semiconductor laser platform

Integrated plasmonic sources and detectors are imperative in the practical development of plasmonic circuitry for bio- and chemical sensing, nanoscale optical information processing, as well as transducers for high-density optical data storage. Here we show that vertical-cavity surface-emitting lasers (VCSELs) can be employed as an on-chip, electrically pumped source or detector of plasmonic signals, when operated in forward or reverse bias, respectively. To this end, we experimentally demonstrate surface plasmon polariton excitation, waveguiding, frequency conversion and detection on a VCSEL-based plasmonic platform. The coupling efficiency of the VCSEL emission to waveguided surface plasmon polariton modes has been optimized using asymmetric plasmonic nanostructures. The plasmonic VCSEL platform validated here is a viable solution for practical realizations of plasmonic functionalities for various applications, such as those requiring sub-wavelength field confinement, refractive index sensitivity or optical near-field transduction with electrically driven sources, thus enabling the realization of on-chip optical communication and lab-on-a-chip devices

Taming the zoo of supersymmetric quantum mechanical models

We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.Comment: final version published in JHE

Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM

The result for the six-loop anomalous dimension of twist-three operators in the planar N=4 SYM theory is presented. The calculations were performed along the paper arXiv:0912.1624. This result provides a new data for testing the proposed spectral equations for planar AdS/CFT correspondence.Comment: 19 pages, typos corrected, details adde

ABJ(M) Chiral Primary Three-Point Function at Two-loops

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%Article funded by SCOAP

Logarithmic mathematical morphology: a new framework adaptive to illumination changes

A new set of mathematical morphology (MM) operators adaptive to illumination changes caused by variation of exposure time or light intensity is defined thanks to the Logarithmic Image Processing (LIP) model. This model based on the physics of acquisition is consistent with human vision. The fundamental operators, the logarithmic-dilation and the logarithmic-erosion, are defined with the LIP-addition of a structuring function. The combination of these two adjunct operators gives morphological filters, namely the logarithmic-opening and closing, useful for pattern recognition. The mathematical relation existing between ``classical'' dilation and erosion and their logarithmic-versions is established facilitating their implementation. Results on simulated and real images show that logarithmic-MM is more efficient on low-contrasted information than ``classical'' MM

Single subject pharmacological-MRI (phMRI) study: Modulation of brain activity of psoriatic arthritis pain by cyclooxygenase-2 inhibitor

We use fMRI to examine brain activity for pain elicited by palpating joints in a single patient suffering from psoriatic arthritis. Changes in these responses are documented when the patient ingested a single dose of a selective cyclooxygenase-2 inhibitor (COX-2i). We show that mechanical stimulation of the painful joints exhibited a cortical activity pattern similar to that reported for acute pain, with activity primarily localized to the thalamus, insular, primary and secondary somatosensory cortices and the mid anterior cingulum. COX-2i resulted in significant decreased in reported pain intensity and in brain activity after 1 hour of administration. The anterior insula and SII correlated with pain intensity, however no central activation site for the drug was detected. We demonstrate the similarity of the activation pattern for palpating painful joints to brain activity in normal subjects in response to thermal painful stimuli, by performing a spatial conjunction analysis between these maps, where overlap is observed in the insula, thalamus, secondary somatosensory cortex, and anterior cingulate. The results demonstrate that one can study effects of pharmacological manipulations in a single subject where the brain activity for a clinical condition is delineated and its modulation by COX-2i demonstrated. This approach may have diagnostic and prognostic utility

Efficient FPT algorithms for (strict) compatibility of unrooted phylogenetic trees

In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$ and without degree-2 nodes -- called the "species tree". One common approach for reconstructing a species tree consists in first constructing several phylogenetic trees from primary data (e.g. DNA sequences originating from some species in $X$), and then constructing a single phylogenetic tree maximizing the "concordance" with the input trees. The so-obtained tree is our estimation of the species tree and, when the input trees are defined on overlapping -- but not identical -- sets of labels, is called "supertree". In this paper, we focus on two problems that are central when combining phylogenetic trees into a supertree: the compatibility and the strict compatibility problems for unrooted phylogenetic trees. These problems are strongly related, respectively, to the notions of "containing as a minor" and "containing as a topological minor" in the graph community. Both problems are known to be fixed-parameter tractable in the number of input trees $k$, by using their expressibility in Monadic Second Order Logic and a reduction to graphs of bounded treewidth. Motivated by the fact that the dependency on $k$ of these algorithms is prohibitively large, we give the first explicit dynamic programming algorithms for solving these problems, both running in time $2^{O(k^2)} \cdot n$, where $n$ is the total size of the input.Comment: 18 pages, 1 figur