Lattice determination of the critical point of QCD at finite T and \mu

Based on universal arguments it is believed that there is a critical point (E) in QCD on the temperature (T) versus chemical potential (\mu) plane, which is of extreme importance for heavy-ion experiments. Using finite size scaling and a recently proposed lattice method to study QCD at finite \mu we determine the location of E in QCD with n_f=2+1 dynamical staggered quarks with semi-realistic masses on $L_t=4$ lattices. Our result is T_E=160 \pm 3.5 MeV and \mu_E= 725 \pm 35 MeV. For the critical temperature at \mu=0 we obtained T_c=172 \pm 3 MeV.Comment: misprints corrected, version to appear in JHE

The Breakdown of Topology at Small Scales

We discuss how a topology (the Zariski topology) on a space can appear to break down at small distances due to D-brane decay. The mechanism proposed coincides perfectly with the phase picture of Calabi-Yau moduli spaces. The topology breaks down as one approaches non-geometric phases. This picture is not without its limitations, which are also discussed.Comment: 12 pages, 2 figure

The local Gromov-Witten theory of CP^1 and integrable hierarchies

In this paper we begin the study of the relationship between the local Gromov-Witten theory of Calabi-Yau rank two bundles over the projective line and the theory of integrable hierarchies. We first of all construct explicitly, in a large number of cases, the Hamiltonian dispersionless hierarchies that govern the full descendent genus zero theory. Our main tool is the application of Dubrovin's formalism, based on associativity equations, to the known results on the genus zero theory from local mirror symmetry and localization. The hierarchies we find are apparently new, with the exception of the resolved conifold O(-1) + O(-1) -> P1 in the equivariantly Calabi-Yau case. For this example the relevant dispersionless system turns out to be related to the long-wave limit of the Ablowitz-Ladik lattice. This identification provides us with a complete procedure to reconstruct the dispersive hierarchy which should conjecturally be related to the higher genus theory of the resolved conifold. We give a complete proof of this conjecture for genus g<=1; our methods are based on establishing, analogously to the case of KdV, a "quasi-triviality" property for the Ablowitz-Ladik hierarchy at the leading order of the dispersive expansion. We furthermore provide compelling evidence in favour of the resolved conifold/Ablowitz-Ladik correspondence at higher genus by testing it successfully in the primary sector for g=2.Comment: 30 pages; v2: an issue involving constant maps contributions is pointed out in Sec. 3.3-3.4 and is now taken into account in the proofs of Thm 1.3-1.4, whose statements are unchanged. Several typos, formulae, notational inconsistencies have been fixed. v3: typos fixed, minor textual changes, version to appear on Comm. Math. Phy

A Note on Conserved Charges of Asymptotically Flat and Anti-de Sitter Spaces in Arbitrary Dimensions

The calculation of conserved charges of black holes is a rich problem, for which many methods are known. Until recently, there was some controversy on the proper definition of conserved charges in asymptotically anti-de Sitter (AdS) spaces in arbitrary dimensions. This paper provides a systematic and explicit Hamiltonian derivation of the energy and the angular momenta of both asymptotically flat and asymptotically AdS spacetimes in any dimension D bigger or equal to 4. This requires as a first step a precise determination of the asymptotic conditions of the metric and of its conjugate momentum. These conditions happen to be achieved in ellipsoidal coordinates adapted to the rotating solutions.The asymptotic symmetry algebra is found to be isomorphic either to the Poincare algebra or to the so(D-1, 2) algebra, as expected. In the asymptotically flat case, the boundary conditions involve a generalization of the parity conditions, introduced by Regge and Teitelboim, which are necessary to make the angular momenta finite. The charges are explicitly computed for Kerr and Kerr-AdS black holes for arbitrary D and they are shown to be in agreement with thermodynamical arguments.Comment: 27 pages; v2 : references added, minor corrections; v3 : replaced to match published version forthcoming in General Relativity and Gravitatio

Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is selected to capture the slow, macroscopic behavior of the system, and the family of quasi-equilibrium probability densities on phase space corresponding to these resolved variables is employed as a statistical model. The macroscopic dynamics of the mean resolved variables is determined by optimizing over paths of these probability densities. Specifically, a cost function is introduced that quantifies the lack-of-fit of such paths to the underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of the residual that results from submitting a path of trial densities to the Liouville equation. The evolution of the macrostate is estimated by minimizing the time integral of the cost function. The value function for this optimization satisfies the associated Hamilton-Jacobi equation, and it determines the optimal relation between the statistical parameters and the irreversible fluxes of the resolved variables, thereby closing the reduced dynamics. The resulting equations for the macroscopic variables have the generic form of governing equations for nonequilibrium thermodynamics, and they furnish a rational extension of the classical equations of linear irreversible thermodynamics beyond the near-equilibrium regime. In particular, the value function is a thermodynamic potential that extends the classical dissipation function and supplies the nonlinear relation between thermodynamics forces and fluxes

Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur

Sensitivity analysis of the primary endpoint from the N-MOmentum study of inebilizumab in NMOSD

BACKGROUND: In the N-MOmentum trial, the risk of an adjudicated neuromyelitis optica spectrum disorder (NMOSD) attack was significantly reduced with inebilizumab compared with placebo. OBJECTIVE: To demonstrate the robustness of this finding, using pre-specified sensitivity and subgroup analyses. METHODS: N-MOmentum is a prospective, randomized, placebo-controlled, double-masked trial of inebilizumab, an anti-CD19 monoclonal B-cell-depleting antibody, in patients with NMOSD. Pre-planned and post hoc analyses were performed to evaluate the primary endpoint across a range of attack definitions and demographic groups, as well as key secondary endpoints. RESULTS: In the N-MOmentum trial (ClinicalTrials.gov: NCT02200770), 174 participants received inebilizumab and 56 received placebo. Attack risk for inebilizumab versus placebo was consistently and significantly reduced, regardless of attack definition, type of attack, baseline disability, ethnicity, treatment history, or disease course (all with hazard ratios < 0.4 favoring inebilizumab, p < 0.05). Analyses of secondary endpoints showed similar trends. CONCLUSION: N-MOmentum demonstrated that inebilizumab provides a robust reduction in the risk of NMOSD attacks regardless of attack evaluation method, attack type, patient demographics, or previous therapy.The N-MOmentum study is registered at ClinicalTrials.gov: NCT2200770

Disability outcomes in the N-MOmentum trial of inebilizumab in neuromyelitis optica spectrum disorder

OBJECTIVE: To assess treatment effects on Expanded Disability Status Scale (EDSS) score worsening and modified Rankin Scale (mRS) scores in the N-MOmentum trial of inebilizumab, a humanized anti-CD19 monoclonal antibody, in participants with neuromyelitis optica spectrum disorder (NMOSD). METHODS: Adults (N = 230) with aquaporin-4 immunoglobulin G-seropositive NMOSD or -seronegative neuromyelitis optica and an EDSS score ≤8 were randomized (3:1) to receive inebilizumab 300 mg or placebo on days 1 and 15. The randomized controlled period (RCP) was 28 weeks or until adjudicated attack, with an option to enter the inebilizumab open-label period. Three-month EDSS-confirmed disability progression (CDP) was assessed using a Cox proportional hazard model. The effect of baseline subgroups on disability was assessed by interaction tests. mRS scores from the RCP were analyzed by the Wilcoxon-Mann-Whitney odds approach. RESULTS: Compared with placebo, inebilizumab reduced the risk of 3-month CDP (hazard ratio [HR]: 0.375; 95% CI: 0.148-0.952; p = 0.0390). Baseline disability, prestudy attack frequency, and disease duration did not affect the treatment effect observed with inebilizumab (HRs: 0.213-0.503; interaction tests: all p > 0.05, indicating no effect of baseline covariates on outcome). Mean EDSS scores improved with longer-term treatment. Inebilizumab-treated participants were more likely to have a favorable mRS outcome at the end of the RCP (OR: 1.663; 95% CI: 1.195-2.385; p = 0.0023). CONCLUSIONS: Disability outcomes were more favorable with inebilizumab vs placebo in participants with NMOSD