Down the rabbit hole with theories of class S

We review some of the properties of 3d N=4 theories obtained by dimensionally reducing theories of class S. We study 3d partition functions, and certain limits thereof, for such theories, and the properties implied for these by 3d mirror symmetry

From 3d duality to 2d duality

In this paper we discuss $3d$ ${\cal N}=2$ supersymmetric gauge theories and their IR dualities when they are compactified on a circle of radius $r$, and when we take the $2d$ limit in which $r\to 0$. The $2d$ limit depends on how the mass parameters are scaled as $r\to 0$, and often vacua become infinitely distant in the $2d$ limit, leading to a direct sum of different $2d$ theories. For generic mass parameters, when we take the same limit on both sides of a duality, we obtain $2d$ dualities (between gauge theories and/or Landau-Ginzburg theories) that pass all the usual tests. However, when there are non-compact branches the discussion is subtle because the metric on the moduli space, which is not controlled by supersymmetry, plays an important role in the low-energy dynamics after compactification. Generally speaking, for IR dualities of gauge theories, we conjecture that dualities involving non-compact Higgs branches survive. On the other hand when there is a non-compact Coulomb branch on at least one side of the duality, the duality fails already when the $3d$ theories are compactified on a circle. Using the valid reductions we reproduce many known $2d$ IR dualities, giving further evidence for their validity, and we also find new $2d$ dualities

Differential utilization of CD134 as a functional receptor by diverse strains of feline immunodeficiency virus

The feline homologue of CD134 (fCD134) is the primary binding receptor for feline immunodeficiency virus (FIV), targeting the virus preferentially to activated CD4+ helper T cells. However, with disease progression, the cell tropism of FIV broadens such that B cells and monocytes/macrophages become significant reservoirs of proviral DNA, suggesting that receptor utilization may alter with disease progression. We examined the receptor utilization of diverse strains of FIV and found that all strains tested utilized CD134 as the primary receptor. Using chimeric feline x human CD134 receptors, the primary determinant of receptor function was mapped to the first cysteine-rich domain (CRD1) of fCD134. For the PPR and B2542 strains, the replacement of CDR1 of fCD134 (amino acids 1 to 64) with human CD134 (hCD134) alone was sufficient to confer nearly optimal receptor function. However, evidence of differential utilization of CD134 was revealed, since strains GL8, CPGammer (CPG41), TM2, 0827, and NCSU1 required determinants in the region spanning amino acids 65 to 85, indicating that these strains may require a more stringent interaction for infection to proceed

A Power-Enhanced Algorithm for Spatial Anomaly Detection in Binary Labelled Point Data Using the Spatial Scan Statistic [postprint]

This paper presents a novel modification to an existing algorithm for spatial anomaly detection in binary labeled point data sets, using the Bernoulli version of the Spatial Scan Statistic. We identify a potential ambiguity in p-values produced by Monte Carlo testing, which (by the selection of the most conservative p-value) can lead to sub-optimal power. When such ambiguity occurs, the modification uses a very inexpensive secondary test to suggest a less conservative p-value. Using benchmark tests, we show that this appears to restore power to the expected level, whilst having similarly retest variance to the original. The modification also appears to produce a small but significant improvement in overall detection performance when multiple anomalies are present

A spatial accuracy assessment of an alternative circular scan method for Kulldorff's spatial scan statistic

This paper concerns the Bernoulli version of Kulldorff’s spatial scan statistic, and how accurately it identifies the exact centre of approximately circular regions of increased spatial density in point data. We present an alternative method of selecting circular regions that appears to give greater accuracy. Performance is tested in an epidemiological context using manifold synthetic case-control datasets. A small, but statistically significant, improvement is reported. The power of the alternative method is yet to be assessed

A pilot inference study for a beta-Bernoulli spatial scan statistic

The Bernoulli spatial scan statistic is used to detect localised clusters in binary labelled point data, such as that used in spatial or spatio-temporal case/control studies. We test the inferential capability of a recently developed beta-Bernoulli spatial scan statistic, which adds a beta prior to the original statistic. This pilot study, which includes two test scenarios with 6,000 data sets each, suggests a marked increase in power for a given false alert rate. We suggest a more extensive study would be worthwhile to corroborate the findings. We also speculate on an explanation for the observed improvement

3d dualities from 4d dualities

Many examples of low-energy dualities have been found in supersymmetric gauge theories with four supercharges, both in four and in three space-time dimensions. In these dualities, two theories that are different at high energies have the same low-energy limit. In this paper we clarify the relation between the dualities in four and in three dimensions. We show that every four dimensional duality gives rise to a three dimensional duality between theories that are similar, but not identical, to the dimensional reductions of the four dimensional dual gauge theories to three dimensions. From these specific three dimensional dualities one can flow to many other low-energy dualities, including known three dimensional dualities and many new ones. We discuss in detail the case of three dimensional SU(N_c) supersymmetric QCD theories, showing how to derive new duals for these theories from the four dimensional duality.Comment: 84 pages, 3 figures, harvmac. v2: added an appendix on the reduction of the 4d index to the 3d partition function, added references, minor corrections and change