A Simple Holographic Model of a Charged Lattice

We use holography to compute the conductivity in an inhomogeneous charged scalar background. We work in the probe limit of the four-dimensional Einstein-Maxwell theory coupled to a charged scalar. The background has zero charge density and is constructed by turning on a scalar source deformation with a striped profile. We solve for fluctuations by making use of a Fourier series expansion. This approach turns out to be useful for understanding which couplings become important in our inhomogeneous background. At zero temperature, the conductivity is computed analytically in a small amplitude expansion. At finite temperature, it is computed numerically by truncating the Fourier series to a relevant set of modes. In the real part of the conductivity along the direction of the stripe, we find a Drude-like peak and a delta function with a negative weight. These features are understood from the point of view of spectral weight transfer.Comment: 25 pages, 5 figures. v2: minor revision

Holographic Superconductors from Gauged Supergravity

We consider minimal setups arising from different truncations of N=8 five-dimensional SO(6) gauged supergravity to study phase transitions involving spontaneous breaking of any of the U(1) symmetries in U(1)xU(1)xU(1)in SO(6). These truncations only keep the three relevant vector fields, four complex scalar fields carrying U(1) charges, plus two neutral scalar fields required by consistency. By considering thermal ensembles with different fixed U(1) charge densities and solving the complete equations including the full back-reaction, in some cases we find instabilities towards the formation of hairy black holes, which lead to second order transitions, resulting from a thermodynamical competition between different sectors. We argue that these should be the dominant thermodynamical instabilities in the full ten-dimensional type IIB theory. In other cases we find unstable branches of hairy black holes that extend to temperatures above a critical temperature (`retrograde condensation'). The results can be used as a first step to understand new aspects of the phase diagram of large N, N=4 SU(N) super Yang-Mills theory with fixed charge densities.Comment: 25 pages, 10 figures. v3: typo corrected in eq. (2.18

Multipoint fishnet Feynman diagrams: sequential splitting

We study fishnet Feynman diagrams defined by a certain triangulation of a planar n-gon, with massless scalars propagating along and across the cuts. Our solution theory uses the technique of Separation of Variables, in combination with the theory of symmetric polynomials and Mellin space. The n-point split-ladders are solved by a recursion where all building blocks are made fully explicit. In particular, we find an elegant formula for the coefficient functions of the light-cone leading logs. When the diagram grows into a fishnet, we obtain new results exploiting a Cauchy identity decomposition of the measure over separated variables. This leads to an elementary proof of the Basso-Dixon formula at 4-points, while at n-points it provides a natural OPE-like stratification of the diagram. Finally, we propose an independent approach based on ``stampede" combinatorics to study the light-cone behaviour of the diagrams as the partition function of a certain vertex model.Comment: Letter: 5 pages, 5 figures; Supplemental material: 21 pages, 8 figure

Outlier admissions of medical patients: Prognostic implications of outlying patients. The experience of the Hospital of Mestre

ABSTRACT The admission of a patient in wards other than the appropriate ones, known as the patient outlying phenomenon, involves both Medicine and Geriatric Units of many Hospitals. The aims were to learn more about the prognosis of the outlying patients, we investigated 3828 consecutive patients hospitalized in Medicine and Geriatrics of our hub Hospital during the year 2012. We compared patients\u2019 mean hospital length of stay, survival, and early readmission according to their outlying status. The mean hospital length of stay did not significantly differ between the two groups, either for Medicine (9.8 days for outliers and 10.0 for in-ward) or Geriatrics (13.0 days for both). However, after adjustment for age and sex, the risk of death was about twice as high for outlier patients admitted into surgical compared to medical areas (hazard ratio 1.8, 1.2-2.5 95% confidence interval). Readmission within 90 days from the first discharge was more frequent for patients admitted as outliers (26.1% vs 14.2%, P<0.0001). We highlight some critical aspects of an overcrowded hospital, as the shortage of beds in Medicine and Geriatrics and the potential increased clinical risk denoted by deaths or early readmission for medical outlier patients when assigned to inappropriate wards. There is the need to reorganize beds allocation involving community services, improve in-hospital bed management, an extent diagnostic procedures for outlier patients admitted in nonmedical wards

Models of Holographic superconductivity

We construct general models for holographic superconductivity parametrized by three couplings which are functions of a real scalar field and show that under general assumptions they describe superconducting phase transitions. While some features are universal and model independent, important aspects of the quantum critical behavior strongly depend on the choice of couplings, such as the order of the phase transition and critical exponents of second-order phase transitions. In particular, we study a one-parameter model where the phase transition changes from second to first order above some critical value of the parameter and a model with tunable critical exponents.Comment: 15 pages, 6 figure

Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles

We consider T[SU(N)] and its mirror, and we argue that there are two more dual frames, which are obtained by adding flipping fields for the moment maps on the Higgs and Coulomb branch. Turning on a monopole deformation in T[SU(N)], and following its effect on each dual frame, we obtain four new daughter theories dual to each other. We are then able to construct pairs of 3d spectral dual theories by performing simple operations on the four dual frames of T[SU(N)]. Engineering these 3d spectral pairs as codimension-two defect theories coupled to a trivial 5d theory, via Higgsing, we show that our 3d spectral dual theories descends from the 5d spectral duality, or fiber base duality in topological string. We provide further consistency checks about the web of dualities we constructed by matching partition functions on the three sphere, and in the case of spectral duality, matching exactly topological string computations with holomorphic blocks.Comment: 74 pages, 15 picture

On some problems related to 2-level polytopes

In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes of perfect graphs, and despite their apparently simple structure, are at the center of many open problems ranging from information theory to semidefinite programming. The extension complexity of a polytope P is a measure of the complexity of representing P: it is the smallest size of an extended formulation of P, which in turn is a linear description of a polyhedron that projects down to P. In the first chapter, we examine several classes of 2-level polytopes arising in combinatorial settings and we prove a relation between the number of vertices and facets of such polytopes, which is conjectured to hold for all 2-level polytopes. The proofs are obtained through an improved understanding of the combinatorial structure of such polytopes, which in some cases leads to results of independent interest. In the second chapter, we study the extension complexity of a restricted class of 2-level polytopes, the stable set polytopes of bipartite graphs, for which we obtain non-trivial lower and upper bounds. In the third chapter we study slack matrices of 2-level polytopes, important combinatorial objects related to extension complexity, defining operations on them and giving algorithms for the following recognition problem: given a matrix, determine whether it is a slack matrix of some special class of 2-level polytopes. In the fourth chapter we address the problem of explicitly obtaining small size extended formulations whose existence is guaranteed by communication protocols. In particular we give an algorithm to write down extended formulations for the stable set polytope of perfect graphs, making a well known result by Yannakakis constructive, and we extend this to all deterministic protocols

Holography and Correlation Functions of Huge Operators: Spacetime Bananas

We initiate the study of holographic correlators for operators whose dimension scales with the central charge of the CFT. Differently from light correlators or probes, the insertion of any such maximally heavy operator changes the AdS metric, so that the correlator itself is dual to a backreacted geometry with marked points at the Poincar\'e boundary. We illustrate this new physics for two-point functions. Whereas the bulk description of light or probe operators involves Witten diagrams or extremal surfaces in an AdS background, the maximally heavy two-point functions are described by nontrivial new geometries which we refer to as "spacetime bananas". As a universal example, we discuss the two-point function of maximally heavy scalar operators described by the Schwarzschild black hole in the bulk and we show that its onshell action reproduces the expected CFT result. This computation is nonstandard, and adding boundary terms to the action on the stretched horizon is crucial. Then, we verify the conformal Ward Identity from the holographic stress tensor and discuss important aspects of the Fefferman-Graham patch. Finally we study a Heavy-Heavy-Light-Light correlator by using geodesics propagating in the banana background. Our main motivation here is to set up the formalism to explore possible universal results for three- and higher-point functions of maximally heavy operators.Comment: 45 pages, 14 figure

Rationally Designed Bicyclic Peptides Prevent the Conversion of Aβ42 Assemblies Into Fibrillar Structures.

There is great interest in drug discovery programs targeted at the aggregation of the 42-residue form of the amyloid β peptide (Aβ42), since this molecular process is closely associated with Alzheimer's disease. The use of bicyclic peptides may offer novel opportunities for the effective modification of Aβ42 aggregation and the inhibition of its cytotoxicity, as these compounds combine the molecular recognition ability of antibodies with a relatively small size of about 2 kD. Here, to pursue this approach, we rationally designed a panel of six bicyclic peptides targeting various epitopes along the sequence of Aβ42 to scan its most amyloidogenic region (residues 13-42). Our kinetic analysis and structural studies revealed that at sub-stoichiometric concentrations the designed bicyclic peptides induce a delay in the condensation of Aβ42 and the subsequent transition to a fibrillar state, while at higher concentrations they inhibit such transition. We thus suggest that designed bicyclic peptides can be employed to inhibit amyloid formation by redirecting the aggregation process toward amorphous assemblies.This work was supported by the Japan Society for the Promotion of Science (JSPS) oversea research fellowships. Francesco A. Aprile is supported by UK Research and Innovation (MR/S033947/1) and the Alzheimer’s Society, UK (317, 511)