Entanglement of transverse modes in a pendular cavity

We study the phenomena that arise in the transverse structure of electromagnetic field impinging on a linear Fabry-Perot cavity with an oscillating end mirror. We find quantum correlations among transverse modes which can be considered as a signature of their entanglement.Comment: 10 pages, 4 eps figures, ReVTeX file, to appear in J. Opt. B: Quantum Semiclass. Op

Robust light transport in non-Hermitian photonic lattices

Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a two-dimensional structure, which break time reversal symmetry and enable one-way guiding at the edge of the medium. Here we suggest a different route toward robust transport of light in lower-dimensional (1D) photonic lattices, in which time reversal symmetry is broken because of the {\it non-Hermitian} nature of transport. While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport that is rather insensitive to disorder or imperfections in the structure. Non-Hermitian transport in two lattice models is considered: a tight-binding lattice with an imaginary gauge field (Hatano-Nelson model), and a non-Hermitian driven binary lattice. In the former case transport in spite of disorder is ensured by a mobility edge that arises because of a non-Hermitian delocalization transition. The possibility to observe non-Hermitian delocalization induced by a synthetic 'imaginary' gauge field is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.Comment: revised and extended version, to appear in Sci. Re

Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field

Unidirectional and robust transport is generally observed at the edge of two- or three-dimensional quantum Hall and topological insulator systems. A hallmark of these systems is topological protection, i.e. the existence of propagative edge states that cannot be scattered by imperfections or disorder in the system. A different and less explored form of robust transport arises in non-Hermitian systems in the presence of an {\it imaginary} gauge field. As compared to topologically-protected transport in quantum Hall and topological insulator systems, robust non-Hermitian transport can be observed in {\it lower} dimensional (i.e. one dimensional) systems. In this work the transport properties of one-dimensional tight-binding lattices with an imaginary gauge field are theoretically investigated, and the physical mechanism underlying robust one-way transport is highlighted. Back scattering is here forbidden because reflected waves are evanescent rather than propagative. Remarkably, the spectral transmission of the non-Hermitian lattice is shown to be mapped into the one of the corresponding Hermitian lattice, i.e. without the gauge field, {\it but} computed in the complex plane. In particular, at large values of the gauge field the spectral transmittance becomes equal to one, even in the presence of disorder or lattice imperfections. This phenomenon can be referred to as {\it one-way non-Hermitian transparency}. Robust one-way transport can be also realized in a more realistic setting, namely in heterostructure systems, in which a non-Hermitian disordered lattice is embedded between two homogeneous Hermitian lattices. Such a double heterostructure realizes asymmetric (non-reciprocal) wave transmission. A physical implementation of non-Hermtian transparency, based on light transport in a chain of optical microring resonators, is suggested.Comment: final version, to appear in Physical Review

Individual attitudes toward corruption: do social effects matter?

Using individual-level data for 35 countries, the authors investigate the microeconomic determinants of attitudes toward corruption. They find women, employed, less wealthy, and older individuals to be more averse to corruption. The authors also provide evidence that social effects play an important role in determining individual attitudes toward corruption, as these are robustly and significantly associated with the average level of tolerance of corruption in the region. This finding lends empirical support to theoretical models where corruption emerges in multiple equilibria and suggests that"big-push"policies might be particularly effective in combating corruption.Pharmaceuticals&Pharmacoeconomics,Environmental Economics&Policies,Poverty Monitoring&Analysis,Decentralization,Health Economics&Finance,Pharmaceuticals&Pharmacoeconomics,Governance Indicators,Environmental Economics&Policies,National Governance,Poverty Monitoring&Analysis

Unimodal Thompson Sampling for Graph-Structured Arms

We study, to the best of our knowledge, the first Bayesian algorithm for unimodal Multi-Armed Bandit (MAB) problems with graph structure. In this setting, each arm corresponds to a node of a graph and each edge provides a relationship, unknown to the learner, between two nodes in terms of expected reward. Furthermore, for any node of the graph there is a path leading to the unique node providing the maximum expected reward, along which the expected reward is monotonically increasing. Previous results on this setting describe the behavior of frequentist MAB algorithms. In our paper, we design a Thompson Sampling-based algorithm whose asymptotic pseudo-regret matches the lower bound for the considered setting. We show that -as it happens in a wide number of scenarios- Bayesian MAB algorithms dramatically outperform frequentist ones. In particular, we provide a thorough experimental evaluation of the performance of our and state-of-the-art algorithms as the properties of the graph vary

Leadership in Singleton Congestion Games: What is Hard and What is Easy

We study the problem of computing Stackelberg equilibria Stackelberg games whose underlying structure is in congestion games, focusing on the case where each player can choose a single resource (a.k.a. singleton congestion games) and one of them acts as leader. In particular, we address the cases where the players either have the same action spaces (i.e., the set of resources they can choose is the same for all of them) or different ones, and where their costs are either monotonic functions of the resource congestion or not. We show that, in the case where the players have different action spaces, the cost the leader incurs in a Stackelberg equilibrium cannot be approximated in polynomial time up to within any polynomial factor in the size of the game unless P = NP, independently of the cost functions being monotonic or not. We show that a similar result also holds when the players have nonmonotonic cost functions, even if their action spaces are the same. Differently, we prove that the case with identical action spaces and monotonic cost functions is easy, and propose polynomial-time algorithm for it. We also improve an algorithm for the computation of a socially optimal equilibrium in singleton congestion games with the same action spaces without leadership, and extend it to the computation of a Stackelberg equilibrium for the case where the leader is restricted to pure strategies. For the cases in which the problem of finding an equilibrium is hard, we show how, in the optimistic setting where the followers break ties in favor of the leader, the problem can be formulated via mixed-integer linear programming techniques, which computational experiments show to scale quite well

Computing a Pessimistic Stackelberg Equilibrium with Multiple Followers: The Mixed-Pure Case

The search problem of computing a Stackelberg (or leader-follower)equilibrium (also referred to as an optimal strategy to commit to) has been widely investigated in the scientific literature in, almost exclusively, the single-follower setting. Although the optimistic and pessimistic versions of the problem, i.e., those where the single follower breaks any ties among multiple equilibria either in favour or against the leader, are solved with different methodologies, both cases allow for efficient, polynomial-time algorithms based on linear programming. The situation is different with multiple followers, where results are only sporadic and depend strictly on the nature of the followers' game. In this paper, we investigate the setting of a normal-form game with a single leader and multiple followers who, after observing the leader's commitment, play a Nash equilibrium. When both leader and followers are allowed to play mixed strategies, the corresponding search problem, both in the optimistic and pessimistic versions, is known to be inapproximable in polynomial time to within any multiplicative polynomial factor unless $$\textsf {P}=\textsf {NP}$$. Exact algorithms are known only for the optimistic case. We focus on the case where the followers play pure strategies—a restriction that applies to a number of real-world scenarios and which, in principle, makes the problem easier—under the assumption of pessimism (the optimistic version of the problem can be straightforwardly solved in polynomial time). After casting this search problem (with followers playing pure strategies) as a pessimistic bilevel programming problem, we show that, with two followers, the problem is NP-hard and, with three or more followers, it cannot be approximated in polynomial time to within any multiplicative factor which is polynomial in the size of the normal-form game, nor, assuming utilities in [0, 1], to within any constant additive loss stricly smaller than 1 unless $$\textsf {P}=\textsf {NP}$$. This shows that, differently from what happens in the optimistic version, hardness and inapproximability in the pessimistic problem are not due to the adoption of mixed strategies. We then show that the problem admits, in the general case, a supremum but not a maximum, and we propose a single-level mathematical programming reformulation which asks for the maximization of a nonconcave quadratic function over an unbounded nonconvex feasible region defined by linear and quadratic constraints. Since, due to admitting a supremum but not a maximum, only a restricted version of this formulation can be solved to optimality with state-of-the-art methods, we propose an exact ad hoc algorithm (which we also embed within a branch-and-bound scheme) capable of computing the supremum of the problem and, for cases where there is no leader's strategy where such value is attained, also an $$\alpha$$-approximate strategy where $$\alpha > 0$$ is an arbitrary additive loss (at most as large as the supremum). We conclude the paper by evaluating the scalability of our algorithms via computational experiments on a well-established testbed of game instances