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In this work we first show that the classical Thompson sampling algorithm for multi-arm bandits is differentially private as-is, without any modification. We provide per-round privacy guarantees as a function of problem parameters and show composition over $T$ rounds; since the algorithm is unchanged, existing $O(\sqrt{NT\log N})$ regret bounds still hold and there is no loss in performance due to privacy. We then show that simple modifications -- such as pre-pulling all arms a fixed number of times, increasing the sampling variance -- can provide tighter privacy guarantees. We again provide privacy guarantees that now depend on the new parameters introduced in the modification, which allows the analyst to tune the privacy guarantee as desired. We also provide a novel regret analysis for this new algorithm, and show how the new parameters also impact expected regret. Finally, we empirically validate and illustrate our theoretical findings in two parameter regimes and demonstrate that tuning the new parameters substantially improve the privacy-regret tradeoff., Comment: Published at AISTATS 2023

We investigate the collective behavior of a system of social agents subject to the competition between two mass media influences considered as external fields. We study under what conditions either of two mass media with different intensities can impose its message to the majority. In addition to a collective state dominated by the stronger mass media and a disordered phase, we characterize two nontrivial effects as the parameters of the system are varied: (i) the appearance of a majority sharing the state of the weaker mass media, and (ii) the emergence of an alternative ordering in a state different from those of either media. We explore the dependence of both phenomena on the topology of the network of interactions. We show that the presence of long-range interactions rather than random connections is essential for the occurrence of both effects. The model can be extended to include multiple mass media and we illustrate it by considering three mass media fields acting on the system. Nontrivial collective behaviors persist for some ranges of parameters: the weakest mass media can convince the majority, and the system can spontaneously order against all applied fields., Comment: 8 pages, 15 figures, sent to Physical Review E

Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and retrieving information from quantum computers. Among the informationally complete sets of quantum measurements the tight ones provide a linear reconstruction formula and minimize the propagation of statistical errors. However, implementing tight measurements in the lab is challenging due to the high number of required measurement projections, involving a series of experimental setup preparations. In this work, we introduce the notion of cyclic tight measurements, that allow us to perform full quantum state tomography while considering only repeated application of a single unitary-based quantum device during the measurement stage process. This type of measurements significantly simplifies the complexity of the experimental setup required to retrieve the quantum state of a physical system. Additionally, we design feasible setup preparation procedure that produce well-approximated cyclic tight measurements, in every finite dimension., Comment: 22 pages, 2 figures

We derive the two-time linear response theory for out-of-equilibrium pumped systems, generic pump-probe delays and probe frequencies. Such a theory enormously simplifies the numerical calculations, for instance, of the optical conductivity with respect to the actual procedure, which requires computing the effect of the probe pulse for each time delay with respect to the pump pulse\textcolor{red}{.} The theory is given for a generic observable and pumped Hamiltonian and then specialized for a system with a quadratic Hamiltonian and its transient optical properties, exploiting the Dynamical Projective Operatorial Approach (DPOA). The theory is complemented by a set of crucial numerical guidelines that help perform actual calculations in a computationally affordable way. The optical response (differential transient reflectivity and absorption) of a prototypical three-band (core, valence, and conduction) model in the XUV regime is analyzed in detail to illustrate the theory and its application. Using some generalizations of the density of states, we provide a systematic approach to exploring the optical properties in terms of the system band structure features and the pump parameters. Such an analysis can be extremely helpful in understanding the actual results of experimental optical measurements. Moreover, we study the effects of inter-band and intra-band transitions, the local dipole coupling, and single and multi-photon processes. The latter is further investigated by varying the central frequency of the pump pulse to have different regions of the first Brillouin zone in resonance with it. We also study the effect of varying the pump pulse intensity. Finally, we study and analyze the transient optical properties in the probe pulse regime of IR and visible., Comment: 25 pages, 11 figures, 40 panels

We define a general strategy for finding new heavy-fermionic materials without rare-earth elements: doping a Hund metal with pronounced orbital-selective correlations towards half-filling. We argue that in general band structures a possible orbital-selective Mott transition is frustrated by inter-orbital hopping into heavy-fermion behaviour - where d-orbitals provide both the heavy and the light electrons - which is enhanced when approaching half-filling. This phase ultimately disappears due to magnetic correlations, as in a standard Doniach diagram. Experimentally we have further hole doped CsFe$_2$As$_2$, a Hund metal with 0.5 electrons/Fe away from half-filling, and obtained a heavy fermionic state with the highest Sommerfeld coefficient for Fe-pnictides to date (270 mJ/mol K$^2$), before signatures of an antiferromagnetic phase set in., Comment: 16 pages, 8 figures

In this study, we conducted a detailed investigation into the time evolution of the probability density within a 1D double-well potential hosting a Bose-Fermi mixture. This system comprised spinless bosons and spin one-half fermions with weak repulsive contact interactions. Notably, even at very low effective coupling constants, periodic probabilities were observed, indicating correlated tunneling of both bosons and fermions, leading to complete miscibility, which disappears when an external electric field is turned on. The electric field accentuated fermion-fermion interactions due to the Pauli exclusion principle, altering both boson density and interactions and leading to spatial redistribution of particles. These findings underscore the complex interplay between interactions, external fields, and spatial distributions within confined quantum systems. Our exploration of higher interaction strengths revealed conditions under which probability density functions are decoupled. Furthermore, we observed that increased fermion interaction, driven by the electric field, led to higher tunneling frequencies for both species because of the repulsive nature of the boson-fermion interaction. Conversely, increased boson-boson interaction resulted in complete tunneling of both species, especially when boson density was high, leading to effective fermion repulsion. Expanding our analysis to scenarios involving four bosons demonstrated that higher interaction values corresponded to increased oscillation frequencies in tunneling probabilities. Finally, by manipulating interaction parameters and activating the electric field, we achieved complete tunneling of both species, further increasing oscillation frequencies and resulting in intervals characterized by overlapping probability functions.

The climate change emergency calls for a reduction in energy consumption in all human activities and production processes. The radio broadcasting industry is no exception. However, reducing energy requirements by uniformly cutting the radiated power at every transmitter can potentially impair the quality of service. A careful evaluation and optimization study are in order. In this paper, by analyzing the Italian frequency modulation analog broadcasting service, we show that it is indeed possible to significantly reduce the energy consumption of the broadcasters without sacrificing the quality of the service, rather, even getting improvements.

Power posteriors "robustify" standard Bayesian inference by raising the likelihood to a constant fractional power, effectively downweighting its influence in the calculation of the posterior. Power posteriors have been shown to be more robust to model misspecification than standard posteriors in many settings. Previous work has shown that power posteriors derived from low-dimensional, parametric locally asymptotically normal models are asymptotically normal (Bernstein-von Mises) even under model misspecification. We extend these results to show that the power posterior moments converge to those of the limiting normal distribution suggested by the Bernstein-von Mises theorem. We then use this result to show that the mean of the power posterior, a point estimator, is asymptotically equivalent to the maximum likelihood estimator., Comment: 8 pages, In Proceedings of the 59th Annual Allerton Conference on Communication, Control, and Computing

Techniques based on classical and quantum correlations in light beams, such as ghost imaging, allow us to overcome many limitations of conventional imaging and sensing protocols. Despite their advantages, applications of such techniques are often limited in practical scenarios where the position and the longitudinal extension of the target object are unknown. In this work, we propose and experimentally demonstrate a novel imaging technique, named Light Field Ghost Imaging, that exploits light correlations and light field imaging principles to enable going beyond the limitations of ghost imaging in a wide range of applications. Notably, our technique removes the requirement to have prior knowledge of the object distance allowing the possibility of refocusing in post-processing, as well as performing 3D imaging while retaining all the benefits of ghost imaging protocols.

A comprehensive literature review on recently rediscovered Co- and/or CoNi-based superalloys, strengthened by the {\gamma}' phase, revealed a relationship between the configurational entropy of the system and the {\gamma}' solvus temperature. This study was conducted on a high Cr CoNi-based superalloy system with high configurational entropy to test our hypothesis based on the sustainable metallurgy framework. Thermodynamic calculations were performed to design the chemical compositions, followed by vacuum casting and heat treatments to produce the desired alloys. The microstructures were characterized using a scanning electron microscope, electron backscattered diffraction, transmission electron microscope, and differential thermal analysis. Microhardness and nanoindentation tests were employed to measure the mechanical properties. The results showed that both the configurational entropy and the type of alloying elements determine the final high-temperature performance of the alloys. We found that to enhance the higher {\gamma}' solvus temperature, the configurational entropy should be increased by adding {\gamma}' stabilizing elements. The microstructural and mechanical characteristics of the designed alloys before and after heat treatments are discussed in detail. The outcome of this study is beneficial for developing cobalt-based high-entropy superalloys with appropriate processing windows and freezing ranges for advanced sustainable manufacturing purposes, such as using powder bed fusion technologies.

The so-called Granovetter-Watts model was introduced to capture a situation in which the adoption of new ideas or technologies requires a certain redundancy in the social environment of each agent to take effect. This model has become a paradigm for complex contagion. Here we investigate a symmetric version of the model: agents may be in two states that can spread equally through the system via complex contagion. We find three possible phases: a mixed one (dynamically active disordered state), an ordered one, and a heterogeneous frozen phase. These phases exist for several configurations of the contact network. Then we consider the effect of introducing aging as a non-Markovian mechanism in the model, where agents become increasingly resistant to change their state the longer they remain in it. We show that when aging is present, the mixed phase is replaced, for sparse networks, by a new phase with different dynamical properties. This new phase is characterized by an initial disordering stage followed by a slow ordering process towards a fully ordered absorbing state. In the ordered phase, aging modifies the dynamical properties. For random contact networks, we develop a theoretical description based on an Approximate Master Equation that describes with good accuracy the results of numerical simulations for the model with and without aging., Comment: 17 pages, 15 figures

Efficiently simulating real materials under the application of a time-dependent field and computing reliably the evolution over time of relevant response functions, such as the TR-ARPES signal or differential transient optical properties, has become one of the main concerns of modern condensed matter theory in response to the recent developments in all areas of experimental out-of-equilibrium physics. In this manuscript, we propose a novel model-Hamiltonian method, the dynamical projective operatorial approach (DPOA), designed and developed to overcome some of the limitations and drawbacks of currently available methods. Relying on (i) many-body second-quantization formalism and composite operators, DPOA is in principle capable of handling both weakly and strongly correlated systems, (ii) tight-binding approach and wannierization of DFT band structures, DPOA naturally deals with the complexity and the very many degrees of freedom of real materials, (iii) dipole gauge and Peierls substitution, DPOA is built to address pumped systems and, in particular, pump-probe spectroscopies, (iv) a Peierls expansion we have devised ad hoc, DPOA is numerically extremely efficient and fast. The latter expansion clarifies how single- and multi-photon resonances, rigid shifts, band dressings, and different types of sidebands emerge and allows understanding the related phenomenologies. Comparing DPOA to the single-particle density-matrix approach and the Houston method (this latter is generalized to second-quantization formalism), we show how it can compute multi-particle multi-time correlation functions and go well beyond these approaches for real materials. We also propose protocols for evaluating the strength of single- and multi-photon resonances and for assigning the residual excited electronic population at each crystal momentum and band to a specific excitation process. The expression for ..., Comment: 27 pages, 15 figures, 38 panels

We investigate an agent-based model for the emergence of corruption in public contracts. There are two types of agents: business people and public servants. Both business people and public servants can adopt two strategies: corrupt or honest behavior. Interactions between business people and public servants take place through defined payoff rules. Either type of agent can switch between corrupt or honest strategies by comparing their payoffs after interacting. We measure the level of corruption in the system by the fractions of corrupt and honest agents for asymptotic times. We study the effects of the group size of the interacting agents, the dispersion with respect to the average salary of the public servants, and a parameter representing the institutional control of corruption. We characterize the fractions of honest and corrupt agents as functions of these variables. We construct phase diagrams for the level of corruption in the system in terms of these variables, where three collective states can be distinguished: i) a phase where corruption dominates; ii) a phase where corruption remains in less than $50\%$ of the agents; and iii) a phase where corruption disappear. Our results indicate that a combination of large group sizes of interacting servants and business people and small dispersion of the salaries of public servants, contributes to the decrease of systemic corruption in public contracts., Comment: Submitted to Heliyon Journal

Bell inequalities are one of the cornerstones of quantum foundations, and fundamental tools for quantum technologies. Recently, the scientific community worldwide has put a lot of effort towards them, which culminated with loophole-free experiments. Nonetheless, none of the experimental tests so far was able to extract information on the full inequality from each entangled pair, since the wave function collapse forbids performing, on the same quantum state, all the measurements needed for evaluating the entire Bell parameter. We present here the first single-pair Bell inequality test, able to obtain a Bell parameter value for every entangled pair detected. This is made possible by exploiting sequential weak measurements, allowing to measure non-commuting observables in sequence on the same state, on each entangled particle. Such an approach not only grants unprecedented measurement capability, but also removes the need to choose between different measurement bases, intrinsically eliminating the freedom-of-choice loophole and stretching the concept of counterfactual-definiteness (since it allows measuring in the otherwise not-chosen bases). We also demonstrate how, after the Bell parameter measurement, the pair under test still presents a noteworthy amount of entanglement, providing evidence of the absence of (complete) wave function collapse and allowing to exploit this quantum resource for further protocols., Comment: 14 pages, 3 figures

This paper analyzes the performance of five well-known off-the-shelf optimization solvers on a set of congested capacitated facility location problems formulated as mixed-integer conic programs (MICPs). We aim to compare the computational efficiency of the solvers and examine the solution strategies they adopt when solving instances with different sizes and complexity. The solvers we compare are Gurobi, Cplex, Mosek, Xpress, and Scip. We run extensive numerical tests on a testbed of 30 instances from the literature. Our results show that Mosek and Gurobi are the most competitive solvers, as they achieve better time and gap performance, solving most instances within the time limit. Mosek outperforms Gurobi in large-size problems and provides more accurate solutions in terms of feasibility. Xpress solves to optimality about half of the instances tested within the time limit, and in this half, it achieves performance similar to that of Gurobi and Mosek. Cplex and Scip emerge as the least competitive solvers. The results provide guidelines on how each solver behaves on this class of problems and highlight the importance of choosing a solver suited to the problem type.

We propose and experimentally demonstrate a general method allowing us to unravel microscopic noise events that affect a continuous quantum variable. Such unraveling is achieved by frequent measurements of a discrete variable coupled to the continuous one. The experimental realization involves photons traversing a noisy channel. There, their polarization, whose coupling to the photons spatial wavepacket is subjected to stochastic noise, is frequently measured in the quantum Zeno regime. The measurements not only preserve the polarization state, but also enable the recording of the full noise statistics from the spatially-resolved detection of the photons emerging from the channel. This method proves the possibility of employing photons as quantum noise sensors and robust carriers of information., Comment: 6 pages, 3 figures

The route towards manipulation of the optoelectronic properties of matter beyond the current limits of electronics starts from a comprehensive study of the ultrafast dynamics triggered by interaction with light. Among them, a fundamental role is played by charge photoinjection, a complex process that stems from the interplay of many different physical phenomena, which cannot be easily disentangled. Single- and multi-photon absorption, diabatic tunnelling, intra-band motion, and field-driven band dressing, all concur in determining the overall excited electron population, dictating the electro-optical properties of a material. Here we investigate ultrafast photoinjection in a prototypical semiconductor (monocrystalline germanium) by using attosecond transient reflection spectroscopy. The precise pump-field characterization ensured by a simultaneous attosecond streaking experiment, in tandem with a comprehensive theoretical approach, allowed us to disentangle the different physical phenomena unfolding at different positions in the reciprocal space and at different timing within the envelope of the pump pulse. Moreover, we found that intra-band phenomena hinder charge injection, in contrast to what was previously observed for resonant, direct band-gap semiconductors. Therefore, besides other known parameters as the central wavelength and peak intensity, our results indicate that the pulse temporal envelope and the local band structure probed by intra-band effects are of key importance to achieve an optimal control over the ultrafast carrier injection process and tailor the complex optical and electronic properties of a semiconductor on the few- to sub-femtosecond time scale.

We propose kernel PCA as a method for analyzing the dependence structure of multivariate extremes and demonstrate that it can be a powerful tool for clustering and dimension reduction. Our work provides some theoretical insight into the preimages obtained by kernel PCA, demonstrating that under certain conditions they can effectively identify clusters in the data. We build on these new insights to characterize rigorously the performance of kernel PCA based on an extremal sample, i.e., the angular part of random vectors for which the radius exceeds a large threshold. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure in extreme value theory and provide a careful analysis in the case where the extremes are generated from a linear factor model. We give theoretical guarantees on the performance of kernel PCA preimages of such extremes by leveraging their asymptotic distribution together with Davis-Kahan perturbation bounds. Our theoretical findings are complemented with numerical experiments illustrating the finite sample performance of our methods.

This paper addresses the site and power assignment problem arising in the optimal design of wireless networks. It is well-known that natural formulations of this problem are sources of numerical instabilities and make the optimal solution challenging for state-of-the-art solvers, even in small-sized instances. We tackle this limitation from a computational perspective by suggesting two implementation procedures that can speed up the solution of this problem. The first is an extremely effective branching rule for a compact reformulation of this problem. Presolve operations are used as a second strategy to manage numerical instability. The approaches are validated using realistic LTE instances kindly provided by Fondazione Ugo Bordoni. The proposed implementation techniques have proved capable of significantly accelerating the solution of the problem, beating the performance of a standard solution.