Topological phase in a non-Hermitian PT symmetric system

In this work, we consider a tight binding lattice with two non-Hermitian impurities. The system is described by a non-Hermitian generalization of the Aubry Andre model. We show for the first time that there exists topologically nontrivial edge states with real spectra in the PT symmetric region.Comment: To Appear in PL

One pot domino synthesis of polyvicinalamine monomers

On a genere de l'imidazole par une reaction de type domino in situ entre le glyoxal, le formaldehyde et deux unites d'ammoniac aqueux. L'addition de bicarbonate aqueux et d'un anhydride carboxylique ou d'un dicarbonate de dialkyle conduit a la formation de la N,N'-diacyl- ou N,N'-dicarbalkoxy-2-hydroxyimidazoline correspondante. Il s'ensuit une reaction de clivage de cycle de Bamberger qui permet d'isoler facilement le cis-1,2-di(acetamido)ethene, le cis-1,2-di(propylamido)ethene, le cis-1,2-di(ethoxyamido)ethene, le cis-1,2-di(tert-butoxyamido)ethene ou le cis-1,2-di(benzamido)ethene sous la forme de solides. La facilite et la generalite offerte par cette approche monotope implique une voie efficace du point de vue des couts en vue de la synthese de routine de precurseurs d'amines oligo- et polyvicinales

Divided We Stand, United We Fall: The Hume-Weber-Jones Mechanism for the Rise of Europe

The "great divergence" in incomes between Europe and the rest of the world occurred relatively recently. Why was it that Western Europe, once a backward outpost on the fringes of the Eurasian continent, able to dominate in terms of income and technology the previously successful Eastern economies? Several mechanisms have been identifed to account for the rise of Europe. This paper formalizes one important mechanism, the intellectual origins of which can be traced back to Hume and Weber and which was fully, though informally, articulated by E.L. Jones. This mechanism emphasizes the contrast between the European states-system and the Eastern empires. Political competition for a mobile tax-base in a states-system forces rulers to expropriate less from their subjects and to supply relatively more "public services". By effectively limiting the "exit" options of the ruled, an empire rewards its ruler with a captive tax-base that can be subjected to relatively higher levels of expropriation without a similar rise in "public services" provided. The states-system thus encourages higher levels of capital accumulation, while the empire stifles it. The successes of the Eastern empires in their consolidation phase are due to the competition they initially faced from neighboring states. Since Europe escaped such consolidation, the process of accumulation there never faced the impediments its Eastern counterparts did. The paper, thus, also provides a structural explanation for the emergence of institutions in Europe that led to relatively secure property rights.public goods, inequality, redistribution, political economy

Commodity Chains, Unequal Exchange and Uneven Development

Research shows an uneven partition of value added along commodity chains between transnational firms and producers in developing countries. This paper briefly discusses how such a distribution occurs and how it leads to unequal exchange in trade. A North-South trade model reveals the uneven development consequences of this exchange. The terms of trade between North and South help maintain a gap in capital accumulation between the two regions. The model reveals that capital flows covering the trade deficit of the South with the North may help stimulate the unrequited transfer of real resources from South to North.Unequal exchange, development, commodity chains

Multi-objective Contextual Multi-armed Bandit with a Dominant Objective

In this paper, we propose a new multi-objective contextual multi-armed bandit (MAB) problem with two objectives, where one of the objectives dominates the other objective. Unlike single-objective MAB problems in which the learner obtains a random scalar reward for each arm it selects, in the proposed problem, the learner obtains a random reward vector, where each component of the reward vector corresponds to one of the objectives and the distribution of the reward depends on the context that is provided to the learner at the beginning of each round. We call this problem contextual multi-armed bandit with a dominant objective (CMAB-DO). In CMAB-DO, the goal of the learner is to maximize its total reward in the non-dominant objective while ensuring that it maximizes its total reward in the dominant objective. In this case, the optimal arm given a context is the one that maximizes the expected reward in the non-dominant objective among all arms that maximize the expected reward in the dominant objective. First, we show that the optimal arm lies in the Pareto front. Then, we propose the multi-objective contextual multi-armed bandit algorithm (MOC-MAB), and define two performance measures: the 2-dimensional (2D) regret and the Pareto regret. We show that both the 2D regret and the Pareto regret of MOC-MAB are sublinear in the number of rounds. We also compare the performance of the proposed algorithm with other state-of-the-art methods in synthetic and real-world datasets. The proposed model and the algorithm have a wide range of real-world applications that involve multiple and possibly conflicting objectives ranging from wireless communication to medical diagnosis and recommender systems.Comment: To appear in IEEE Transactions on Signal Processing, link: https://ieeexplore.ieee.org/document/8368272

Information-Theoretic Bounds for Adaptive Sparse Recovery

We derive an information-theoretic lower bound for sample complexity in sparse recovery problems where inputs can be chosen sequentially and adaptively. This lower bound is in terms of a simple mutual information expression and unifies many different linear and nonlinear observation models. Using this formula we derive bounds for adaptive compressive sensing (CS), group testing and 1-bit CS problems. We show that adaptivity cannot decrease sample complexity in group testing, 1-bit CS and CS with linear sparsity. In contrast, we show there might be mild performance gains for CS in the sublinear regime. Our unified analysis also allows characterization of gains due to adaptivity from a wider perspective on sparse problems.Comment: Accepted to IEEE ISIT 2014. Better presentation and fixed errors compared to the previous versio

Gambler's Ruin Bandit Problem

In this paper, we propose a new multi-armed bandit problem called the Gambler's Ruin Bandit Problem (GRBP). In the GRBP, the learner proceeds in a sequence of rounds, where each round is a Markov Decision Process (MDP) with two actions (arms): a continuation action that moves the learner randomly over the state space around the current state; and a terminal action that moves the learner directly into one of the two terminal states (goal and dead-end state). The current round ends when a terminal state is reached, and the learner incurs a positive reward only when the goal state is reached. The objective of the learner is to maximize its long-term reward (expected number of times the goal state is reached), without having any prior knowledge on the state transition probabilities. We first prove a result on the form of the optimal policy for the GRBP. Then, we define the regret of the learner with respect to an omnipotent oracle, which acts optimally in each round, and prove that it increases logarithmically over rounds. We also identify a condition under which the learner's regret is bounded. A potential application of the GRBP is optimal medical treatment assignment, in which the continuation action corresponds to a conservative treatment and the terminal action corresponds to a risky treatment such as surgery