Wall-Crossing from Boltzmann Black Hole Halos

A key question in the study of N=2 supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound states as multi-centered black hole solutions in N=2 supergravity, we provide two fully general and explicit formulae for the change in the (refined) index across the wall. The first, "Higgs branch" formula relies on Reineke's results for invariants of quivers without oriented loops, specialized to the Abelian case. The second, "Coulomb branch" formula results from evaluating the symplectic volume of the classical phase space of multi-centered solutions by localization. We provide extensive evidence that these new formulae agree with each other and with the mathematical results of Kontsevich and Soibelman (KS) and Joyce and Song (JS). The main physical insight behind our results is that the Bose-Fermi statistics of individual black holes participating in the bound state can be traded for Maxwell-Boltzmann statistics, provided the (integer) index \Omega(\gamma) of the internal degrees of freedom carried by each black hole is replaced by an effective (rational) index \bar\Omega(\gamma)= \sum_{m|\gamma} \Omega(\gamma/m)/m^2. A similar map also exists for the refined index. This observation provides a physical rationale for the appearance of the rational Donaldson-Thomas invariant \bar\Omega(\gamma) in the works of KS and JS. The simplicity of the wall crossing formula for rational invariants allows us to generalize the "semi-primitive wall-crossing formula" to arbitrary decays of the type \gamma\to M\gamma_1+N\gamma_2 with M=2,3.Comment: 71 pages, 1 figure; v3: changed normalisation of symplectic form 3.22, corrected 3.35, other cosmetic change

Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

From Black Holes to Quivers

Middle cohomology states on the Higgs branch of supersymmetric quiver quantum mechanics - also known as pure Higgs states - have recently emerged as possible microscopic candidates for single-centered black hole micro-states, as they carry zero angular momentum and appear to be robust under wall-crossing. Using the connection between quiver quantum mechanics on the Coulomb branch and the quantum mechanics of multi-centered black holes, we propose a general algorithm for reconstructing the full moduli-dependent cohomology of the moduli space of an arbitrary quiver, in terms of the BPS invariants of the pure Higgs states. We analyze many examples of quivers with loops, including all cyclic Abelian quivers and several examples with two loops or non-Abelian gauge groups, and provide supporting evidence for this proposal. We also develop methods to count pure Higgs states directly.Comment: 56 pages; v2: added Eqs 4.28-30, 5.35-36, 5.55; v3: journal version; v4: Misprints corrected, improved discussion of Higgs branch for non-Abelian 3-node quiver, see around Eq. (6.22) and (6.37

Quiver Structure of Heterotic Moduli

We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.Comment: 38 pages, 5 figures, 1 tabl

Heterologous expression screens in Nicotiana benthamiana identify a candidate effector of the wheat Yellow Rust Pathogen that associates with processing bodies

Rust fungal pathogens of wheat (Triticum spp.) affect crop yields worldwide. The molecular mechanisms underlying the virulence of these pathogens remain elusive, due to the limited availability of suitable molecular genetic research tools. Notably, the inability to perform high-throughput analyses of candidate virulence proteins (also known as effectors) impairs progress. We previously established a pipeline for the fast-forward screens of rust fungal candidate effectors in the model plant Nicotiana benthamiana. This pipeline involves selecting candidate effectors in silico and performing cell biology and protein-protein interaction assays in planta to gain insight into the putative functions of candidate effectors. In this study, we used this pipeline to identify and characterize sixteen candidate effectors from the wheat yellow rust fungal pathogen Puccinia striiformis f sp tritici. Nine candidate effectors targeted a specific plant subcellular compartment or protein complex, providing valuable information on their putative functions in plant cells. One candidate effector, PST02549, accumulated in processing bodies (P-bodies), protein complexes involved in mRNA decapping, degradation, and storage. PST02549 also associates with the P-body-resident ENHANCER OF mRNA DECAPPING PROTEIN 4 (EDC4) from N. benthamiana and wheat. We propose that P-bodies are a novel plant cell compartment targeted by pathogen effectors

How to Compute Worst-Case Execution Time by Optimization Modulo Theory and a Clever Encoding of Program Semantics

International audienceIn systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive control loops with a fixed clock; the WCET of the loop body must not exceed the clock period. We compute the WCET (or at least a close upper bound thereof) as the solution of an optimization modulo theory problem that takes into account the semantics of the program, in contrast to other methods that compute the longest path whether or not it is feasible according to these semantics. Optimization modulo theory extends satisfiability modulo theory (SMT) to maximization problems. Immediate encodings of WCET problems into SMT yield formulas intractable for all current production-grade solvers; this is inherent to the DPLL(T) approach to SMT implemented in these solvers. By conjoining some appropriate "cuts" to these formulas, we considerably reduce the computation time of the SMT-solver. We experimented our approach on a variety of control programs, using the OTAWA analyzer both as baseline and as underlying microarchitectural analysis for our analysis, and show notable improvement on the WCET bound on a variety of benchmarks and control programs

Mixed Hodge polynomials of character varieties

We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,C)-character variety. The calculation also leads to several conjectures about the cohomology of M_n: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious Hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n = 2.Comment: with an appendix by Nicholas M. Katz; 57 pages. revised version: New definition for homogeneous weight in Definition 4.1.6, subsequent arguments modified. Some other minor changes. To appear in Invent. Mat

Prevention and Intervention Studies with Telmisartan, Ramipril and Their Combination in Different Rat Stroke Models

The effects of AT1 receptor blocker, telmisartan, and the ACE inhibitor, ramipril, were tested head-to head and in combination on stroke prevention in hypertensive rats and on potential neuroprotection in acute cerebral ischemia in normotensive rats. Normotensive Wistar rats were treated s.c. 5 days prior to middle cerebral artery occlusion (MCAO) for 90 min with reperfusion. Groups (n = 10 each): (1) sham, (2) vehicle (V; 0,9% NaCl), (3) T (0,5 mg/kg once daily), (4) R (0,01 mg/kg twice daily), (5) R (0,1 mg/kg twice daily) or (6) T (0,5 mg/kg once daily) plus R (0,01 mg/kg twice daily). Twenty-four and 48 h after MCAO, neurological outcome (NO) was determined. Forty-eight h after MCAO, infarct volume by MRI, neuronal survival, inflammation factors and neurotrophin receptor (TrkB) were analysed.Stroke incidence was reduced, survival was prolonged and neurological outcome was improved in all treated SHR-SP with no differences between treated groups. In the acute intervention study, T and T+R, but not R alone, improved NO, reduced infarct volume, inflammation (TNFα), and induced TrkB receptor and neuronal survival in comparison to V.T, R or T+R had similar beneficial effects on stroke incidence and NO in hypertensive rats, confirming BP reduction as determinant factor in stroke prevention. In contrast, T and T+R provided superior neuroprotection in comparison to R alone in normotensive rats with induced cerebral ischemia

Nanooptics of molecular-shunted plasmonic nanojunctions.

Gold nanoparticles are separated above a planar gold film by 1.1 nm thick self-assembled molecular monolayers of different conductivities. Incremental replacement of the nonconductive molecules with a chemically equivalent conductive version differing by only one atom produces a strong 50 nm blue-shift of the coupled plasmon. With modeling this gives a conductance of 0.17G(0) per biphenyl-4,4'-dithiol molecule and a total conductance across the plasmonic junction of 30G(0). Our approach provides a reliable tool quantifying the number of molecules in each plasmonic hotspot, here <200.We acknowledge financial support from EPSRC grant EP/ G060649/1, EP/I012060/1, EP/L027151/1, EP/K028510/1, ERC grant LINASS 320503. F.B. acknowledges support from the Winton Programme for the Physics of Sustainability. C.T. and J.A. acknowledge financial support from Project FIS2013- 41184-P from MINECO, ETORTEK 2014-15 of the Basque Department of Industry and IT756-13 from the Basque consolidated groups.This paper was originally published in Nano Letters under a CC-BY licence (F Benz, C Tserkezis, LO Herrmann, B de Nijs, A Sanders, DO Sigle, L Pukenas, SD Evans, J Aizpurua, JJ Baumberg, Nano Letters 2015, 15, 669−674