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We consider the four-dimensional $\mathcal{N}=2$ quiver gauge theory arising from a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills with gauge group $SU(2N)$. We study the integrated correlator between a half-BPS Wilson line and two Higgs branch operators of conformal dimension 2. Using supersymmetric localization, we resum the perturbative series for this observable and obtain exact expressions for both the planar and next-to-planar terms of its large $N$ expansion, valid for arbitrary values of the 't Hooft coupling. Finally, through a combination of analytical and numerical methods, we determine the leading terms of the corresponding strong-coupling expansions., Comment: 21 pages

In this paper, we address the development of a robotic rehabilitation system for the upper limbs based on collaborative end-effector solutions. The use of commercial collaborative robots offers significant advantages for this task, as they are optimized from an engineering perspective and ensure safe physical interaction with humans. However, they also come with noticeable drawbacks, such as the limited range of sizes available on the market and the standard control modes, which are primarily oriented towards industrial or service applications. To address these limitations, we propose an optimization-based design method to fully exploit the capability of the cobot in performing rehabilitation tasks. Additionally, we introduce a novel control architecture based on an admittance-type Virtual Fixture method, which constrains the motion of the robot along a prescribed path. This approach allows for an intuitive definition of the task to be performed via Programming by Demonstration and enables the system to operate both passively and actively. In passive mode, the system supports the patient during task execution with additional force, while in active mode, it opposes the motion with a braking force. Experimental results demonstrate the effectiveness of the proposed method., Comment: 11 pages, 15 Figures, submitted to Journal

The D theory is a $\mathcal{N}=2$ conformal SYM theory in four dimensions with gauge group SU($N$), four matter hypermultiplets in the fundamental and two in the anti-symmetric representation, and a flavor symmetry that contains a U(4) factor. Its holographic dual is obtained via a combination of orbifold and orientifold projections from Type II B string theory on $\mathrm{AdS}_5 \times S^5$ and possesses a sector of open strings attached to D7 branes with U(4) Chan-Paton factors. The AdS Veneziano amplitude of the U(4) gluons is dual to four-point correlators of moment-map operators of the U(4) flavor symmetry in the D theory. An integrated version of these correlators is captured by a deformation of the D theory in which the fundamental hypermultiplets acquire a mass. The partition function of this massive theory can be evaluated with matrix-model techniques using localization. In this paper we analyze the matrix model of the mass-deformed D theory arising from localization using the so-called "full Lie algebra" approach in a $1/N$ expansion. In particular, we study the partition function and its mass derivatives up to $O(1/N^2)$ corrections obtaining exact expressions that are valid for all values of the 't Hooft coupling. We also analyze their behavior at strong coupling where our results produce useful constraints on the dual open string scattering amplitudes in AdS., Comment: 31 pages, to be published in JHEP

We consider the $4d$ $\mathcal{N}=2$ superconformal quiver gauge theory obtained by a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills (SYM). By exploiting supersymmetric localization, we study the integrated correlator of two Coulomb branch and two moment map operators and the integrated correlator of four moment map operators, determining exact expressions valid for any value of the 't Hooft coupling in the planar limit. Additionally, for the second correlator, we obtain an exact expression also for the next-to-planar contribution. Then, we derive the leading terms of their strong-coupling expansions and outline the differences with respect to the $\mathcal{N}=4$ SYM theory.

Structurally anisotropic materials are ubiquitous in several application fields, yet their accurate optical characterization remains challenging due to the lack of general models linking their scattering coefficients to the macroscopic transport observables, and the need to combine multiple measurements to retrieve their direction-dependent values. Here, we present an improved method for the experimental determination of light transport tensor coefficients from the diffusive rates measured along all three directions, based on transient transmittance measurements and a generalized Monte Carlo model. We apply our method to the characterization of light transport properties in two common anisotropic materials - polytetrafluoroethylene (PTFE) tape and paper - highlighting the magnitude of systematic deviations that are typically incurred when neglecting anisotropy.

Anisotropic light transport is extremely common among scattering materials, yet a comprehensive picture of how macroscopic diffusion is determined by microscopic tensor scattering coefficients is not fully established yet. In this work, we present a theoretical and experimental study of diffusion in structurally anisotropic media with uniaxially symmetric scattering coefficients. Exact analytical relations are derived in the case of index-matched turbid media, unveiling the general relation between microscopic scattering coefficients and the resulting macroscopic diffusion tensor along different directions. Excellent agreement is found against anisotropic Monte Carlo simulations up to high degrees of anisotropy, in contrast with previously proposed approaches. The obtained solutions are used to analyze experimental measurements of anisotropic light transport in polystyrene foam samples under different degrees of uniaxial compression, providing a practical example of their applicability.

Coupling a system to two different baths can lead to novel phenomena escaping the constraints of thermal equilibrium. In quantum materials inside optical cavities, this feature can be exploited as electrons and cavity-photons are easily pulled away from their mutual equilibrium, even in the steady state. This offers new routes for a non-invasive control of material properties and functionalities. We show that the absence of thermal equilibrium between electrons and photons leads to reduced symmetries of the steady-state electronic distribution function. Moreover, by defining an effective temperature from the on-shell distribution function, we find a non-monotonic behaviour as a function of cavity frequency, consistent with recent experimental findings. Finally, we show that, the non-thermal behaviour leads to qualitative modifications of the material's properties, as the standard Sommerfeld expansion for observables is modified by a leading-order correction linearly proportional to the temperature difference between the two baths and to the frequency-derivative of the electron damping.

We provide a comprehensive theoretical study of the radio-frequency (rf) spectra of a two-component Fermi gas with balanced populations in the normal region of the temperature-vs-coupling phase diagram. In particular, rf spectra are analyzed in terms of two characteristic peaks, which can be either distinct or overlapping. On the BEC side of the crossover, these two contributions are associated with a fermionic quasi-particle peak and a bosonic-like contribution due to pairing. On the BCS side of the crossover, the two peaks are instead associated with interactions between particles occurring, respectively, at high or low relative momenta. Through this two-peak analysis, we show how and to what extent the correlation between the widths of the rf spectra and the pair size, previously identified in the superfluid phase at low temperature, can be extended to the normal phase, as well as how the temperature-vs-coupling phase diagram of the BCS-BEC crossover can be partitioned in a number of distinct physical sectors. Several analytic results for the shape and widths of the rf spectra are also derived in appropriate temperature and coupling limits., Comment: 23 pages, 16 figures

We consider 4-dimensional $\mathcal{N} = 2$ superconformal quiver theories with $SU(N)^M$ gauge group and bi-fundamental matter and we evaluate correlation functions of $n$ coincident Wilson loops in the planar limit of the theory. Exploiting specific untwisted/twisted combinations of these operators and using supersymmetric localization, we are able to resum the whole perturbative expansion and find exact expressions for these correlators that are valid for all values of the 't Hooft coupling. Moreover, we analytically derive the leading strong coupling behaviour of the correlators, showing that they obey a remarkable simple rule. Our analysis is complemented by numerical checks based on a Pad\'e resummation of the perturbative series.

Low-carbon dispatchable power underpins a sustainable energy system, providing load balancing complementing wide-scale deployment of intermittent renewable power. In this new context, fossil fuel-fired power plants must be coupled with a post-combustion carbon capture (PCC) process capable of highly transient operation. To tackle design and operational challenges simultaneously, we have developed a computational framework that integrates process design with techno-economic assessment. The backbone of this is a high-fidelity PCC mathematical model of a pressure-vacuum swing adsorption process. We demonstrate that the cost-optimal design has limited process flexibility, challenging reactiveness to disturbances, such as those in the flue gas feed conditions. The results illustrate that flexibility can be introduced by relaxing the CO$_2$ recovery constraint on the operation, albeit at the expense of the capture efficiency of the process. We discover that adsorption-based processes can accommodate for significant flexibility and improved performance with respect to the operational constraints on CO$_2$ recovery and purity. The results herein demonstrate a trade-off between process economics and process operability, which must be effectively rationalised to integrate CO$_2$ capture units in the design of low-carbon energy systems., Comment: Pre-print paper currently under review. 32 pages, 6 figures. The first two authors contributed equally to this work

Pini and Vantini (2017) introduced the interval-wise testing procedure which performs local inference for functional data defined on an interval domain, where the output is an adjusted p-value function that controls for type I errors. We extend this idea to a general setting where domain is a Riemannian manifolds. This requires new methodology such as how to define adjustment sets on product manifolds and how to approximate the test statistic when the domain has non-zero curvature. We propose to use permutation tests for inference and apply the procedure in three settings: a simulation on a "chameleon-shaped" manifold and two applications related to climate change where the manifolds are a complex subset of $S^2$ and $S^2 \times S^1$, respectively. We note the tradeoff between type I and type II errors: increasing the adjustment set reduces the type I error but also results in smaller areas of significance. However, some areas still remain significant even at maximal adjustment.