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We discuss the theory of equivariant localization focussing on applications relevant for holography. We consider geometries comprising compact and non-compact toric orbifolds, as well as more general non-compact toric Calabi–Yau singularities. A key object in our constructions is the equivariant volume, for which we describe two methods of evaluation: the Berline–Vergne fixed point formula and the Molien–Weyl formula, supplemented by the Jeffrey–Kirwan prescription. We present two applications in supersymmetric field theories. Firstly, we describe a method for integrating the anomaly polynomial of SCFTs on compact toric orbifolds. Secondly, we discuss equivariant orbifold indices that are expected to play a key role in the computation of supersymmetric partition functions. In the context of supergravity, we propose that the equivariant volume can be used to characterize universally the geometry of a large class of supersymmetric solutions. As an illustration, we employ equivariant localization to prove the factorization in gravitational blocks of various supergravity free energies, recovering previous results as well as obtaining generalizations. [ABSTRACT FROM AUTHOR]

We study the large N limit of the refined topologically twisted index of three-dimensional N = 2 gauge theories with a holographic dual, which is relevant for counting the number of microstates of rotating, magnetically charged and twisted AdS4 black holes. As a difference with previous computations, we perform a direct saddle point analysis of the relevant matrix model. Among other things we explicitly identify the distribution of gauge magnetic fluxes that contributes at large N. The index exhibits a large N factorized form in agreement with the supergravity expectations based on gravitational blocks and correctly reproduces the entropy of magnetically charged rotating AdS4× S7 black holes. [ABSTRACT FROM AUTHOR]

Obstructive sleep apnoea is a highly prevalent but under-diagnosed disorder. The gold standard for diagnosis of obstructive sleep apnoea is inpatient polysomnography. This is resource intensive and inconvenient for the patient, and the development of ambulatory diagnostic modalities has been identified as a key research priority. Sleep Minder ( Bianca Med, Nova UCD, Ireland) is a novel, non-contact, bedside sensor, which uses radio-waves to measure respiration and movement. Previous studies have shown it to be effective in measuring sleep and respiration. We sought to assess its utility in the diagnosis of obstructive sleep apnoea. Sleep Minder and polysomnographic assessment of sleep-disordered breathing were performed simultaneously on consecutive subjects recruited prospectively from our sleep clinic. We assessed the diagnostic accuracy of Sleep Minder in identifying obstructive sleep apnoea, and how Sleep Minder assessment of the apnoea-hypopnoea index correlated with polysomnography. Seventy-four subjects were recruited. The apnoea-hypopnoea index as measured by Sleep Minder correlated strongly with polysomnographic measurement ( r = 0.90; P ≤ 0.0001). When a diagnostic threshold of moderate-severe (apnoea-hypopnoea index ≥15 events h−1) obstructive sleep apnoea was used, Sleep Minder displayed a sensitivity of 90%, a specificity of 92% and an accuracy of 91% in the diagnosis of sleep-disordered breathing. The area under the curve for the receiver operator characteristic was 0.97. Sleep Minder correctly classified obstructive sleep apnoea severity in the majority of cases, with only one case different from equivalent polysomnography by more than one diagnostic class. We conclude that in an unselected clinical population undergoing investigation for suspected obstructive sleep apnoea, Sleep Minder measurement of sleep-disordered breathing correlates significantly with polysomnography. [ABSTRACT FROM AUTHOR]

We consider three-dimensional conformal field theories living on a stack of N anti-M2 branes at the tip of eight-dimensional supersymmetric cones. The corresponding supergravity solution is obtained by changing sign to the four-form in the Freund-Rubin solution representing M2 branes ("skew-whiffing" transformation) and it is known to be stable. The existence of these nonsupersymmetric, stable field theories, at least in the largeN limit, is a peculiarity of the AdS4/CFT3 correspondence with respect to the usual AdS5/CFT4, and it is worthwhile to study it.We analyze in detail the KK spectrum of the skew-whiffed solution associated with S7/ℤk and we speculate on the natural field content for a candidate non-supersymmetric dual field theory. [ABSTRACT FROM AUTHOR]

We give a short review on the study of the moduli space and the spectrum of chiral operators for gauge theories living on branes at singularities. We focus on theories with four real supercharges in 3 + 1 and 2 + 1 dimensions. The theories are holographically dual to AdS5 × H5 or AdS4 × H7 backgrounds, in Type-IIB or -M theory, respectively. We demonstrate that most of the information on the moduli space and spectrum of the quiver gauge theories is encoded in the concept of the “Master Space”, which isroughly the full moduli space for one brane, consisting of mesonic and baryonic degrees of freedom. We summarize the relevant information in generating functions for chiral operators, which can be computed using plethystics techniques and the language of complex geometry. [ABSTRACT FROM AUTHOR]

The article studies radiant and coradiant sets of some normed space X from the point of view of separation properties between a set A⊆ X and a point x ∉ A; indeed they show striking similarities with the ones holding for convex sets and can be obtained by simply changing halfspaces (level sets of linear continuous functions), with level sets of continuous superlinear functions. In a geometric perspective one can say that radiant sets are separated by means of convex coradiant sets and coradiant sets are separated by means of convex radiant sets. The identification between the geometric and the analytic approach passes through the well-known Minkoski gauge and the study of concave continuous gauges of convex coradiant sets. The results are then applied to the study of abstract convexity with respect to the family L of continuous superlinear functions, to the characterization of evenly coradiant convex sets and to the subdifferentiability of positively homogeneous functions. Dedicated to D. Pallaschke on his 65th birthday. [ABSTRACT FROM AUTHOR]

In this work we characterize different types of solutions of a vector optimization problem by means of a scalarization procedure. Usually different scalarizing functions are used in order to obtain the various solutions of the vector problem. Here we consider different kinds of solutions of the same scalarized problem. Our results allow us to establish a parallelism between the solutions of the scalarized problem and the various efficient frontiers: stronger solution concepts of the scalar problem correspond to more restrictive notions of efficiency. Besides the usual notions of weakly efficient and efficient points, which are characterized as global and strict global solutions of the scalarized problem, we also consider some restricted notions of efficiency, such as strict and proper efficiency, which are characterized as Tikhonov well-posed minima and sharp minima for the scalarized problem. [ABSTRACT FROM AUTHOR]

We provide a universal microscopic counting for the microstates of the asymptotically AdS black holes and black strings that arise as solutions of the half-maximal gauged supergravity in 4 and 5 dimensions. These solutions can be embedded in all M-theory and type II string backgrounds with an AdS vacuum and 16 supercharges and provide an infinite set of examples dual to N=2 and N=4 conformal field theories in four and three dimensions, respectively. The counting is universal and it is performed by either studying the large N limit of the relevant supersymmetric index of the dual field theory or by using the charged Cardy formula. [ABSTRACT FROM AUTHOR]

I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimension equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS 4 black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS 5 black holes. [ABSTRACT FROM AUTHOR]

We discuss the large N factorization properties of five-dimensional supersymmetric partition functions for CFT with a holographic dual. We consider partition functions on manifolds of the form ℳ = ℳ 3 × S ϵ 2 , where ϵ is an equivariant parameter for rotation. We show that, when ℳ3 is a squashed three-sphere, the large N partition functions can be obtained by gluing elementary blocks associated with simple physical quantities. The same is true for various observables of the theories on ℳ 3 = Σ g × S 1 , where Σ g is a Riemann surface of genus 𝔤, and, with a natural assumption on the form of the saddle point, also for the partition function, corresponding to either the topologically twisted index or a mixed one. This generalizes results in three and four dimensions and correctly reproduces the entropy of known black objects in AdS6×wS4 and AdS7× S4. We also provide the supersymmetric background and explicitly perform localization for the mixed index on Σ g × S 1 × S ϵ 2 , filling a gap in the literature. [ABSTRACT FROM AUTHOR]

Some AdS3 × M7 type IIB vacua have been recently proposed to arise from D3-branes wrapped on a spindle, a sphere with conical singularities at the poles. We explicitly construct a generalization of these solutions corresponding to a class of electrically charged and rotating supersymmetric black strings in AdS5 × S5 with general magnetic fluxes on the spindle. We then perform a counting of their microstates using the charged Cardy formula. To this purpose, we derive the general form of the anomaly polynomial of the dual N = (0, 2) CFT in two dimensions and we show that it can be obtained via a simple gluing procedure. [ABSTRACT FROM AUTHOR]

We provide a unifying entropy functional and an extremization principle for black holes and black strings in AdS4 × S7 and AdS5 × S5 with arbitrary rotation and generic electric and magnetic charges. This is done by gluing gravitational blocks, basic building blocks that are directly inspired by the holomorphic blocks appearing in the factorization of supersymmetric partition functions in three and four dimensions. We also provide an explicit realization of the attractor mechanism by identifying the values of the scalar fields at the horizon with the critical points of the entropy functional. We give examples based on dyonic rotating black holes with a twist in AdS4 × S7, rotating black strings in AdS5 × S5, dyonic Kerr-Newman black holes in AdS4 × S7 and Kerr-Newman black holes in AdS5 × S5. In particular, our entropy functional extends existing results by adding rotation to the twisted black holes in AdS4 and by adding flavor magnetic charges for the Kerr-Newman black holes in AdS4. We also discuss generalizations to higher-dimensional black objects. [ABSTRACT FROM AUTHOR]

We present a counting of microstates of a class of dyonic BPS black holes in AdS 4 which precisely reproduces their Bekenstein–Hawking entropy. The counting is performed in the dual boundary description, that provides a non-perturbative definition of quantum gravity, in terms of a twisted and mass-deformed ABJM theory. We evaluate its twisted index and propose an extremization principle to extract the entropy, which reproduces the attractor mechanism in gauged supergravity. [ABSTRACT FROM AUTHOR]

We evaluate the topologically twisted index of a general four-dimensional $$ \mathcal{N}=1 $$ gauge theory in the 'high-temperature' limit. The index is the partition function for $$ \mathcal{N}=1 $$ theories on S × T , with a partial topological twist along S , in the presence of background magnetic fluxes and fugacities for the global symmetries. We show that the logarithm of the index is proportional to the conformal anomaly coefficient of the two-dimensional $$ \mathcal{N}=\left(0,2\right) $$ SCFTs obtained from the compactification on S . We also present a universal formula for extracting the index from the four-dimensional conformal anomaly coefficient and its derivatives. We give examples based on theories whose holographic duals are black strings in type IIB backgrounds AdS × SE, where SE are five-dimensional Sasaki-Einstein spaces. [ABSTRACT FROM AUTHOR]

Ambulatory monitoring is of major clinical interest in the diagnosis of obstructive sleep apnoea syndrome. We compared a novel non-contact biomotion sensor, which provides an estimate of both sleep time and sleep-disordered breathing, with wrist actigraphy in the assessment of total sleep time in adult humans suspected of obstructive sleep apnoea syndrome. Both systems were simultaneously evaluated against polysomnography in 103 patients undergoing assessment for obstructive sleep apnoea syndrome in a hospital-based sleep laboratory (84 male, aged 55 ± 14 years and apnoea-hypopnoea index 21 ± 23). The biomotion sensor demonstrated similar accuracy to wrist actigraphy for sleep/wake determination (77.3%: biomotion; 76.5%: actigraphy), and the biomotion sensor demonstrated higher specificity (52%: biomotion; 34%: actigraphy) and lower sensitivity (86%: biomotion; 94%: actigraphy). Notably, total sleep time estimation by the biomotion sensor was superior to actigraphy (average overestimate of 10 versus 57 min), especially at a higher apnoea-hypopnoea index. In post hoc analyses, we assessed the improved apnoea-hypopnoea index accuracy gained by combining respiratory measurements from polysomnography for total recording time (equivalent to respiratory polygraphy) with total sleep time derived from actigraphy or the biomotion sensor. Here, the number of misclassifications of obstructive sleep apnoea severity compared with full polysomnography was reduced from 10/103 (for total respiratory recording time alone) to 7/103 and 4/103 (for actigraphy and biomotion sensor total sleep time estimate, respectively). We conclude that the biomotion sensor provides a viable alternative to actigraphy for sleep estimation in the assessment of obstructive sleep apnoea syndrome. As a non-contact device, it is suited to longitudinal assessment of sleep, which could also be combined with polygraphy in ambulatory studies. [ABSTRACT FROM AUTHOR]

The large N limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS5 black holes only in the particular case of equal angular momenta. Using the Bethe ansatz formulation, we compute the index at large N with arbitrary chemical potentials for all charges and angular momenta, for general four-dimensional conformal theories with a holographic dual. We conjecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large N. For SYM, this contribution correctly leads to the entropy of BPS Kerr–Newman black holes in AdS5 × S5 for arbitrary values of the conserved charges, thus completing the microscopic derivation of their microstates. We also consider theories dual to AdS5 × SE5, where SE5 is a Sasaki–Einstein manifold. We first check our results against the so-called universal black hole. We then explicitly construct the near-horizon geometry of BPS Kerr–Newman black holes in AdS5 × T1,1, charged under the baryonic symmetry of the conifold theory and with equal angular momenta. We compute the entropy of these black holes using the attractor mechanism and find complete agreement with the field theory predictions. [ABSTRACT FROM AUTHOR]

In this note we show that the entropy of BPS, rotating, electrically charged AdS7 × S4 black holes can be obtained by an extremization principle involving a particular combination of anomaly coefficients of the six-dimensional N=20 theory. This result extends our previous finding for BPS, rotating AdS5 × S5 black holes. [ABSTRACT FROM AUTHOR]

We consider superconformal and supersymmetric field theories on four-dimensional Lorentzian curved space-times, and their five-dimensional holographic duals. As in the Euclidean signature case, preserved supersymmetry for a superconformal theory is equivalent to the existence of a charged conformal Killing spinor. Differently from the Euclidean case, we show that the existence of such spinors is equivalent to the existence of a null conformal Killing vector. For a supersymmetric field theory with an R-symmetry, this vector field is further restricted to be Killing. We demonstrate how these results agree with the existing classification of supersymmetric solutions of minimal gauged supergravity in five dimensions. [ABSTRACT FROM AUTHOR]

We studied a novel non-contact biomotion sensor, which has been developed for identifying sleep/wake patterns in adult humans. The biomotion sensor uses ultra low-power reflected radiofrequency waves to determine the movement of a subject during sleep. An automated classification algorithm has been developed to recognize sleep/wake states on a 30-s epoch basis based on the measured movement signal. The sensor and software were evaluated against gold-standard polysomnography on a database of 113 subjects [94 male, 19 female, age 53 ± 13 years, apnoea-hypopnea index (AHI) 22 ± 24] being assessed for sleep-disordered breathing at a hospital-based sleep laboratory. The overall per-subject accuracy was 78%, with a Cohen's kappa of 0.38. Lower accuracy was seen in a high AHI group (AHI >15, 63 subjects) than in a low AHI group (74.8% versus 81.3%); however, most of the change in accuracy can be explained by the lower sleep efficiency of the high AHI group. Averaged across subjects, the overall sleep sensitivity was 87.3% and the wake sensitivity was 50.1%. The automated algorithm slightly overestimated sleep efficiency (bias of +4.8%) and total sleep time (TST; bias of +19 min on an average TST of 288 min). We conclude that the non-contact biomotion sensor can provide a valid means of measuring sleep-wake patterns in this patient population, and also allows direct visualization of respiratory movement signals. [ABSTRACT FROM AUTHOR]

Supersymmetric gauge theories have an important but perhaps under-appreciated notion of a master space, which controls the full moduli space. For world-volume theories of D-branes probing a Calabi-Yau singularity $${\mathcal X}$$ the situation is particularly illustrative. In the case of one physical brane, the master space $${\mathcal F^b}$$ is the space of F-terms and a particular quotient thereof is $${\mathcal X}$$ itself. We study various properties of $${\mathcal F^b}$$ which encode such physical quantities as Higgsing, BPS spectra, hidden global symmetries, etc. Using the plethystic program we also discuss what happens at higher number N of branes. [ABSTRACT FROM AUTHOR]

Summary: The high prevalence of obstructive sleep apnea has led to increasing interest in ambulatory diagnosis. The SleepMinder™ (SM) is a novel non‐contact device that employs radiofrequency wave technology to assess the breathing pattern, and thereby estimate obstructive sleep apnea severity. We assessed the performance of SleepMinder™ in the home diagnosis of obstructive sleep apnea. One‐hundred and twenty‐two subjects were prospectively recruited in two protocols, one from an unselected sleep clinic cohort (n = 67, mean age 51 years) and a second from a hypertension clinic cohort (n = 55, mean age 58 years). All underwent 7 consecutive nights of home monitoring (SMHOME) with the SleepMinder™ as well as inpatient‐attended polysomnography in the sleep clinic cohort or cardiorespiratory polygraphy in the hypertension clinic cohort with simultaneous SleepMinder™ recordings (SMLAB). In the sleep clinic cohort, median SMHOME apnea–hypopnea index correlated significantly with polysomnography apnea–hypopnea index (r =.68; p <.001), and in the hypertension clinic cohort with polygraphy apnea–hypopnea index (r =.7; p <.001). The median SMHOME performance against polysomnography in the sleep clinic cohort showed a sensitivity and specificity of 72% and 94% for apnea–hypopnea index ≥ 15. Device performance was inferior in females. In the hypertension clinic cohort, SMHOME showed a 50% sensitivity and 72% specificity for apnea–hypopnea index ≥ 15. SleepMinder™ classified 92% of cases correctly or within one severity class of the polygraphy classification. Night‐to‐night variability in home testing was relatively high, especially at lower apnea–hypopnea index levels. We conclude that the SleepMinder™ device provides a useful ambulatory screening tool, especially in a population suspected of obstructive sleep apnea, and is most accurate in moderate–severe obstructive sleep apnea. [ABSTRACT FROM AUTHOR]