Strongly Monotone Research Articles

Distillability for non-full-rank coherent states in the probabilistic framework

We adequately characterize the distillability of quantum coherence under the maximally incoherent operations (MIO) in the probabilistic distillation’s framework. In particular, we prove that every non-full-rank coherent state exhibits a nonzero probability in the task of probabilistic deterministic distillation. Moreover, we find that the maximal coherence, a computable coherence monotone under strictly incoherent operations (SIO), is a coherence monotone under incoherent operations (IO) and add the proof that the maximal coherence fulfills strong monotonicity under SIO. It is suggested that the maximal success probability of distillation from all coherent states whose density matrix does not contain any rank-one submatrix is less than 1 under IO and equals 0 under SIO. Finally, we present an explicit example for probabilistic distillation under IO and show that a class of non-full rank 3-dimensional states possesses the probabilistic distillability.

How numeric advice precision affects advice taking

AbstractAdvice is a powerful means to improve peoples' judgments and decisions. Because advice quality is rarely apparent, decision‐makers must infer it from the characteristics of the advisor or the advice itself. Here, we focus on a largely neglected advice characteristic that should signal quality: advice precision. In a preregistered, high‐powered study (N = 195), we tested the effects of advice precision on advice taking. Drawing from past research and theorizing on anchor precision, we derived and tested two competing hypotheses for the relation of advice precision and advice taking—one predicting a monotone increase in advice taking when advice precision increases and the other predicting a backfiring effect of overly precise advice resulting in an inverted U‐shape. Our results support the notion of a monotone, albeit not a strong monotone, relationship. Higher perceived advice quality correlated with individuals' advice taking. Consistent with the idea that advice precision serves as a cue for advice quality, the effect of advice precision on advice taking was statistically mediated by perceived advice quality. Although the mediation analysis does not allow for causal interpretation because we did not manipulate the mediating variable, it shows that the effect of advice precision on advice taking is not merely a demand effect. Implications of our findings for theory and practice are discussed.

Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory

A wide class of coupled-cluster methods is introduced, based on Arponen's extended coupled-cluster theory. This class of methods is formulated in terms of a coordinate transformation of the cluster operators. The mathematical framework for the error analysis of coupled-cluster methods based on Arponen's bivariational principle is presented, in which the concept of local strong monotonicity of the flipped gradient of the energy is central. A general mathematical result is presented, describing sufficient conditions for coordinate transformations to preserve the local strong monotonicity. The result is applied to the presented class of methods, which include the standard and quadratic coupled-cluster methods, and also Arponen's canonical version of extended coupled-cluster theory. Some numerical experiments are presented, and the use of canonical coordinates for diagnostics is discussed.

Single-Timescale Distributed GNE Seeking for Aggregative Games Over Networks via Forward–Backward Operator Splitting

We consider aggregative games with affine coupling constraints, where agents have partial information on the aggregate value and can only communicate with neighbouring agents. We propose a single-layer distributed algorithm that reaches a variational generalized Nash equilibrium, under constant step sizes. The algorithm works on a single timescale, i.e., does not require multiple communication rounds between agents before updating their action. The convergence proof leverages an invariance property of the aggregate estimates and relies on a forward-backward splitting for two preconditioned operators and their restricted (strong) monotonicity properties on the consensus subspace.

Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency

A solution on a set of transferable utility (TU) games satisfies strong aggregate monotonicity (SAM) if every player can improve when the grand coalition becomes richer. It satisfies equal surplus division (ESD) if the solution allows the players to improve equally. We show that the set of weight systems generating weighted prenucleoli that satisfy SAM is open, which implies that for weight systems close enough to any regular system, the weighted prenucleolus satisfies SAM. We also provide a necessary condition for SAM for symmetrically weighted nucleoli. Moreover, we show that the per capita nucleolus on balanced games is characterized by single-valuedness (SIVA), translation covariance (TCOV) and scale covariance (SCOV), and equal adjusted surplus division (EASD), a property that is comparable to but stronger than ESD. These properties together with ESD characterize the per capita prenucleolus on larger sets of TU games. EASD and ESD can be transformed to independence of (adjusted) proportional shifting, and these properties may be generalized for arbitrary weight systems p to I(A)Sp. We show that the p-weighted prenucleolus on the set of balanced TU games is characterized by SIVA, TCOV, SCOV, and IASp and on larger sets by additionally requiring ISp.

On the Positive Definiteness of Limiting Coderivative for Set-Valued Mappings

This paper concerns the interconnection between the positive definiteness of limiting coderivative and the local strong maximal monotonicity of set-valued mappings suspected in Mordukhovich and Nghia (SIAM J. Optim. 26, 1032–1059, 2016, Conjecture 3.6). We disprove the conjecture by a counterexample and provide some special classes at which it is true. However, the positive definiteness of limiting coderivative characterizes a new property called nearly strong monotonicity. Consequently, we show that the strong metric regularity of set-valued mappings could be obtained under the positive definiteness of limiting coderivative.

Some Impossibility Results on the Converse Consistency Principle in Bargaining

We present two impossibility results on the converse consistency principle in the context of bargaining. First, we show that there is no solution satis-fying Pareto optimality, contraction independence, and converse consistency. Next, we show that there is no solution satisfying Pareto optimality, strong individual rationality, individual monotonicity, and converse consistency.

A Well-Defined Composite Indicator: An Application to Corporate Social Responsibility

This paper introduces a model to construct composite indicators for performance evaluation of decision making units, which is based upon the determination of the least distance from each assessed unit to a frontier estimated by data envelopment analysis. This generates less demanding targets from a benchmarking point of view. The model also makes it possible to account for the existence of slacks in all the considered dimensions (sub-indicators), playing with the notion of Pareto efficiency. Additionally, our approach satisfies units invariance, translation invariance and strong monotonicity and ensures that the weights used for the aggregation of the sub-indicators are always strictly positive. All previous approaches based on data envelopment analysis have failed to satisfy at least one of these properties. We also implement a new version of the Russell output measure of technical efficiency working with full-dimensional efficient facets. Finally, the new approach is illustrated by an application to the sphere of corporate social responsibility, showing the main empirical implications of the theoretical properties.

Single projection algorithm for variational inequalities in Banach spaces with application to contact problem

We study the single projection algorithm of Tseng for solving a variational inequality problem in a 2-uniformly convex Banach space. The underline cost function of the variational inequality is assumed to be monotone and Lipschitz continuous. A weak convergence result is obtained under reasonable assumptions on the variable step-sizes. We also give the strong convergence result for when the underline cost function is strongly monotone and Lipchitz continuous. For this strong convergence case, the proposed method does not require prior knowledge of the modulus of strong monotonicity and the Lipschitz constant of the cost function as input parameters, rather, the variable step-sizes are diminishing and non-summable. The asymptotic estimate of the convergence rate for the strong convergence case is also given. For completeness, we give another strong convergence result using the idea of Halpern’s iteration when the cost function is monotone and Lipschitz continuous and the variable step-sizes are bounded by the inverse of the Lipschitz constant of the cost function. Finally, we give an example of a contact problem where our proposed method can be applied.

Quantum coherence, discord and correlation measures based on Tsallis relative entropy

Several ways have been proposed in the literature to define a coherence measure based on Tsallis relative entropy. One of them is defined as a distance between a state and a set of incoherent states with Tsallis relative entropy taken as a distance measure. Unfortunately, this measure does not satisfy the required strong monotonicity, but a modification of this coherence has been proposed that does. We introduce three new Tsallis coherence measures coming from a more general definition that also satisfy the strong monotonicity, and compare all five definitions between each other. Using three coherence measures that we discuss, one can also define a discord. Two of these have been used in the literature, and another one is new. We also discuss two correlation measures based on Tsallis relative entropy. We provide explicit expressions for all three discord and two correlation measure on pure states. Lastly, we provide tight upper and lower bounds on two discord and correlations measures on any quantum state, with the condition for equality.

Variance-Based Modified Backward-Forward Algorithm with Line Search for Stochastic Variational Inequality Problems and Its Applications

We propose a variance-based modified backward-forward algorithm with a stochastic approximation version of Armijo’s line search, which is robust with respect to an unknown Lipschitz constant, for solving a class of stochastic variational inequality problems. A salient feature of the proposed algorithm is to compute only one projection and two independent queries of a stochastic oracle at each iteration. We analyze the proposed algorithm for its asymptotic convergence, sublinear convergence rate in terms of the mean natural residual function, and optimal oracle complexity under moderate conditions. We also discuss the linear convergence rate with finite computational budget for the proposed algorithm without strong monotonicity. Preliminary numerical experiments indicate that the proposed algorithm is competitive with some existing algorithms. Furthermore, we consider an application in dealing with an equilibrium problem in stochastic natural gas trading market.

Benchmarking with data envelopment analysis: An agency perspective

Most studies on benchmarking in data envelopment analysis (DEA) focus on setting targets on the “best practice frontier”, few of them pay attention to motivating decision-making units (DMUs) to realize these benchmarks. Moreover, such “DEA-based best practice” may not be the actual “best practice” of evaluated DMUs. In this paper, subordinates’ strategy behaviors are first considered to realize the actual “best practice” during the benchmarking process, and agency theory is employed to reveal subordinates’ strategy behaviors. A novel incentive game with yardstick competition theory is established. Together with the ex-post targets (“DEA-based best practice”) and the actual production, we propose a reimbursement scheme to motivate DMUs to realize their “best practice”. In addition, we prove that DMUs’ best responses to our incentive game are just to realize their “best practice” when the reimbursement scheme satisfies strong monotonicity in outputs, and these responses constitute the strong Nash equilibrium of our incentive game. Finally, several DEA models are provided to hold the reimbursement scheme's strong monotonicity in outputs and minimize the compensations paid to all DMUs.

Dynamic NE Seeking for Multi-Integrator Networked Agents With Disturbance Rejection

In this paper, we consider game problems played by (multi)-integrator agents, subject to external disturbances. We propose Nash equilibrium seeking dynamics based on gradient-play, augmented with a dynamic internal-model based component, which is a reduced-order observer of the disturbance. We consider single-, double- and extensions to multi-integrator agents, in a partial-information setting, where agents have only partial knowledge on the others' decisions over a network. The lack of global information is offset by each agent maintaining an estimate of the others' states, based on local communication with its neighbours. Each agent has an additional dynamic component that drives its estimates to the consensus subspace. In all cases, we show convergence to the Nash equilibrium irrespective of disturbances. Our proofs leverage input-to-state stability under strong monotonicity of the pseudo-gradient and Lipschitz continuity of the extended pseudo-gradient.

Sample complexity of single-parameter revenue maximization

The sample complexity of learning Myerson's optimal auction from i.i.d. samples of bidders' values has received much attention since its introduction by Cole and Roughgarden (STOC 2014). This letter gives a brief introduction of a recent work that settles the sample complexity by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the literature. The upper bounds are unified under a novel framework, which builds on the strong revenue monotonicity by Devanur, Huang, and Psomas (STOC 2016), and an information theoretic argument. This is fundamentally different from the previous approaches that rely on either constructing an ∈-net of the mechanism space, either explicitly, or implicitly via statistical learning theory, or learning an approximately accurate version of the virtual values. To our knowledge, it is the first time information theoretical arguments are used to show sample complexity upper bounds, instead of lower bounds. The lower bounds are also unified under a meta construction of hard instances.

Global error bounds for mixed Quasi-Hemivariational inequality problems on Hadamard manifolds

ABSTRACT In this paper, we introduce and study a class of mixed quasi-hemivariational inequality problems on Hadamard manifolds (in short, (MQHIP)). Some regularized gap functions for (MQHIP) are proposed under suitable conditions. Finally, global error bounds for (MQHIP) in terms of regularized gap functions are derived by employing some strong monotonicity conditions and using the properties of Clarke's generalized directional derivative. The main results presented in this paper improve and generalize corresponding results in literature.

Marginality and Myerson values

The aim of this paper is to analyze the relationship between marginality and the Myerson value, the within groups Myerson value (WG-Myerson value) and the between groups Myerson value (BG-Myerson value). We enlarge the idea of the classical marginal contribution of a player to a coalition in a cooperative game. Besides this type of contribution, in games with cooperation restricted by a graph, a player can contribute to a coalition in other ways. For example, lending his links to the coalition but without joining it. We will call it the marginal contribution of the player’s links (L-marginal contribution). Also he can contribute to a coalition by joining it with his communication possibilities. This is the marginal contribution of the player with his links (PL-marginal contribution). According to this, we define the strong monotonicity of the allocation rules with respect to the L-marginal contributions (and the L-marginality); and similarly, the strong monotonicity with respect to the PL-marginal contributions (and the PL-marginality). We prove that the Myerson value, the WG-Myerson value and the BG-Myerson value can be characterized using as requirement PL-marginality, marginality and L-marginality, respectively (as well as other properties).

General regularized nonconvex mixed equilibrium problems: iterative methods by auxiliary principle technique

This paper introduces a new class of equilibrium problems named general regularized nonconvex mixed equilibrium problem. By using the auxiliary principle technique, some predictor–corrector methods for solving such class of general regularized nonconvex mixed equilibrium problems are suggested and analyzed. The study of convergence analysis of the proposed iterative algorithms requires either jointly pseudomonotonicity or partially mixed relaxed and strong monotonicity property of the operator and bifunction involved in the considered problem. As a consequence of our main results, we provide the correct versions of the algorithms and results presented in the literature.

Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set

We present new axiomatic characterizations of five classes of TU-values, the classes of the weighted, positively weighted, and multiweighted Shapley values, random order values, and the Harsanyi set. The axiomatizations are given in parallel, i.e., they differ only in one axiom. In conjunction with marginality, a new property, called coalitional differential dependence, is the key that allows us to dispense with additivity. In addition, we propose new axiomatizations of the above five classes, in which, in part new, different versions of monotonicity, associated with the strong monotonicity in Young (1985), are decisive.

Property testing in high-dimensional Ising models

This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property testing is more fundamental than graph recovery, any necessary conditions for property testing imply corresponding conditions for graph recovery, while custom property tests can be statistically and/or computationally more efficient than graph recovery based algorithms. Understanding the statistical complexity of property testing requires the distinction of ferromagnetic (i.e., positive interactions only) and general Ising models. Using combinatorial constructs such as graph packing and strong monotonicity, we characterize how target properties affect the corresponding minimax upper and lower bounds within the realm of ferromagnets. On the other hand, by studying the detection of an antiferromagnetic (i.e., negative interactions only) Curie–Weiss model buried in Rademacher noise, we show that property testing is strictly more challenging over general Ising models. In terms of methodological development, we propose two types of correlation based tests: computationally efficient screening for ferromagnets, and score type tests for general models, including a fast cycle presence test. Our correlation screening tests match the information-theoretic bounds for property testing in ferromagnets in certain regimes.

Uniqueness results for strongly monotone operators related to Gauss measure

In the present paper we prove some uniqueness results for weak solutions to a class of problems, whose prototype is $$\begin{cases}-\rm{div} & ((\varepsilon+|\triangledown{u}|^2)\frac{p-2}{2}\triangledown{u}\varphi)=f\varphi\;\;\;\;\;\rm{in}\;\;\Omega\\u=0 &\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \rm{on}\;\partial\Omega,\end{cases}$$ where e ≥ 0, 1 1) with Gauss measure less than one and datum f belongs to the natural dual space. When p ≤ 2 we obtain a uniqueness result for e = 0, while for p > 2 we have to consider e > 0 unless the sign of f is constant. Some counterexamples are given too.