Notion Of Compatibility Research Articles

Compatibility of quantum instruments

Incompatibility of quantum devices is a useful resource in various quantum information theoretical tasks, and it is at the heart of some fundamental features of quantum theory. While the incompatibility of measurements and quantum channels is well studied, the incompatibility of quantum instruments has not been explored in much detail. In this work, we revise a notion of instrument compatibility introduced in the literature that we call traditional compatibility. Then, we introduce the notion of parallel compatibility and show that these two notions are inequivalent. We then argue that the notion of traditional compatibility is conceptually incomplete and prove that, while parallel compatibility captures measurement and channel compatibility, traditional compatibility does not capture channel compatibility. Hence, we propose parallel compatibility as the conceptually complete definition of the compatibility of quantum instruments.

Quantum channel marginal problem

Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems. These problems are strongly connected to the generalization of the no-signaling conditions to quantized inputs and outputs and can be understood as a general toolkit to study notions of quantum incompatibility. In fact, they include as special cases channel broadcasting, channel extendibility, measurement compatibility, and state marginal problems. After defining the notion of compatibility between global and local dynamics, we provide a solution to the channel marginal problem that takes the form of a semidefinite program. Using this formulation, we construct channel incompatibility witnesses, discuss their operational interpretation in terms of an advantage for a state-discrimination task, prove a gap between classical and quantum dynamical marginal problems and show that the latter is irreducible to state marginal problems.

Ordinal Bayesian incentive compatibility in random assignment model

We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is the uniform prior, then a large class of random mechanisms are OBIC with respect to this prior—this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent and identical priors in some neighborhood of a given independent and identical prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (J Econ Theory 100:295–328, 2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.

Social balance - a signed detour distance analysis

ABSTRACT In this paper, by defining two types of signed detour distances and corresponding detour distance matrices, we introduce the notion of detour distance compatibility for signed graphs and later applying these concepts, we give yet another characterization of balance in signed graphs. Further, we discuss signed detour spectra of certain classes of unbalanced signed graphs.

Integral operators defined “up to a polynomial”

We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these functions, the classical definition would lead to divergent expressions, thus we replace it with an appropriate framework obtained by a cut-off procedure. The notion obtained in this way quotients out the polynomials which produce the divergent pattern once the cut-off is removed. We also present results of stability under the appropriate notion of convergence and compatibility results between polynomials of different orders. Additionally, we address the solvability of the Dirichlet problem. The theory is developed in general in the pointwise sense. A viscosity counterpart is also presented under the additional assumption that the interaction kernel has a sign, in conformity with the maximum principle structure.

Fubini-Study metrics and Levi-Civita connections on quantum projective spaces

We introduce analogues of the Fubini-Study metrics and the corresponding Levi-Civita connections on quantum projective spaces. We define the quantum metrics as two-tensors, symmetric in the appropriate sense, in terms of the differential calculi introduced by Heckenberger and Kolb. We define connections on these calculi and show that they are torsion free and cotorsion free, where the latter condition uses the quantum metric and is a weaker notion of metric compatibility. Finally we show that these connections are bimodule connections and that the metric compatibility also holds in a stronger sense.

Ordinally Bayesian incentive compatible probabilistic voting rules

We study probabilistic voting rules in a two-voter model. The notion of incentive compatibility we consider is ordinal Bayesian incentive compatibility (OBIC) as introduced in d’Aspremont and Peleg (1988). We show that there exist anonymous and ex-post efficient probabilistic voting rules that are not random dictatorships and at the same time are OBIC with respect to an independently distributed generic prior. This contrasts with the results obtained for deterministic voting mechanisms obtained in Majumdar and Sen (2004) and in Mishra (2016). In case of neutral and efficient rules, there are two kinds of results. First we show that imposing OBIC with respect to some generic prior leads to random dictatorship when there are three alternatives. Second, we show that the result is no longer true when there are four or more alternatives and consequently we provide sufficient conditions on the priors for the result to be true.

Interface Automata for Shared Memory

Interface theories based on Interface Automata (IA) are formalisms for the component-based specification of concurrent systems. Extensions of their basic synchronization mechanism permit the modelling of data, but are studied in more complex settings involving modal transition systems or do not abstract from internal computation. In this article, we show how de Alfaro and Henzinger’s original IA theory can be conservatively extended by shared memory data, without sacrificing simplicity or imposing restrictions. Our extension IA for shared Memory (IAM) decorates transitions with pre- and post-conditions over algebraic expressions on shared variables, which are taken into account by IA’s notion of component compatibility. Simplicity is preserved as IAM can be embedded into IA and, thus, accurately lifts IA’s compatibility concept to shared memory. We also provide a ground semantics for IAM that demonstrates that our abstract handling of data within IA’s open systems view is faithful to the standard treatment of data in closed systems.

Competing logics in a hybrid organization: ICT service provision in the Italian health care sector

PurposeThis paper reports an investigation of a hybrid ex-state-owned enterprise (ex-SOE) providing ICT (Information and Communication Technology) services in the Italian healthcare sector (in-house provision). The authors aim to offer a framing that reflects the concerns expressed in the interdisciplinary literature on hybrid SOEs from management, public administration and, more recently, accounting.Design/methodology/approachThis study operationalizes Besharov and Smith’s (2014) theoretical model on multiple logics to analyze institutional structures and organizational outcomes at an ICT in-house provider. It builds on extensive textual analysis of regulatory, archival, survey and interview data.FindingsThe study results show that the combination of hybridity in the form of layering of multiple logics in the health care sector (Polzer et al., 2016) creates problems for the effectiveness of ICT provision. In particular, the hybrid organization the authors study remained stuck in established competing relationships despite a restructure of regional health care governance. The study findings also reflect on the design of organizational control mechanisms when balancing different logics.Research limitations/implicationsThe identified case-study accountability practices and performance system add to the debate on hybrid organizations in the case of ex-SOEs and facilitate the understanding and management of hybrids in the public sector. The authors note policymaking implications.Originality/valueThe authors’ operationalization of Besharov and Smith's (2014) model adds clarity to key elements of their model, notably how to identify evidence in order to disentangle notions of centrality and compatibility. By doing this, the authors’ analysis offers potential insights into both managerial design and policy prescription. The authors provide cautionary tales around institutional reorganization regarding the layered synthesis of logics within these organizations.

Jordan products of quantum channels and their compatibility

Given two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

Weak existence and uniqueness for McKean–Vlasov SDEs with common noise

This paper concerns the McKean–Vlasov stochastic differential equation (SDE) with common noise. An appropriate definition of a weak solution to such an equation is developed. The importance of the notion of compatibility in this definition is highlighted by a demonstration of its role in connecting weak solutions to McKean–Vlasov SDEs with common noise and solutions to corresponding stochastic partial differential equations (SPDEs). By keeping track of the dependence structure between all components in a sequence of approximating processes, a compactness argument is employed to prove the existence of a weak solution assuming boundedness and joint continuity of the coefficients (allowing for degenerate diffusions). Weak uniqueness is established when the private (idiosyncratic) noise’s diffusion coefficient is nondegenerate and the drift is regular in the total variation distance. This seems sharp when one considers using finite-dimensional noise to regularise an infinite dimensional problem. The proof relies on a suitably tailored cost function in the Monge–Kantorovich problem and representation of weak solutions via Girsanov transformations.

On Intuitionistic Fuzzy Soft Ideal Topological Spaces

In this paper, we introduce the notion of intuitionistic fuzzy soft ideal in intuitionistic fuzzy soft set theory. Also we introduce the concept of intuitionistic fuzzy soft local function. These concepts are discussed with a view to find new intuitionistic fuzzy soft topologies from the original one. The basic structure, especially a basis for such generated intuitionistic fuzzy soft topologies also studied here. The notion of compatibility of intuitionistic fuzzy soft ideals with intuitionistic fuzzy soft topologies is introduced and some equivalent conditions concerning this topic are established here. Finally we introduce intuitionistic fuzzy soft-I-open set, intuitionistic fuzzy soft pre-I-open set, intuitionistic fuzzy soft semi-I-open set, intuitionistic fuzzy soft-α-Iopen set and intuitionistic fuzzy soft-β-I-open set and discuss some of their properties.

Incentive compatibility under ambiguity

The paper examines notions of incentive compatibility in an environment with ambiguity-averse agents. In particular, we propose the notion of maxmin transfer coalitional incentive compatibility, which is immune to coalitional manipulations and thus more stable than the individual incentive compatibility condition. The main result characterizes the set of allocations that satisfy the maxmin transfer coalitional incentive compatibility condition. We show that an allocation satisfies maxmin transfer coalitional incentive compatibility if and only if it is maxmin interim efficient. This result extends that of De Castro and Yannelis (J Econ Theory 177:678–707, 2018) in the sense that ambiguity not only resolves the conflict between efficiency and incentive compatibility, it also accommodates stability. Furthermore, this result is false in a finite economy where agents are subjective expected utility maximizers.

Rank and duality in representation theory

There is both theoretical and numerical evidence that the set of irreducible representations of a reductive group over local or finite fields is naturally partitioned into families according to analytic properties of representations. Examples of such properties are the rate of decay at infinity of “matrix coefficients” in the local field setting, and the order of magnitude of “character ratios” in the finite field situation. In these notes we describe known results, new results, and conjectures in the theory of “size” of representations of classical groups over finite fields (when correctly stated, most of them hold also in the local field setting), whose ultimate goal is to classify the above mentioned families of representations and accordingly to estimate the relevant analytic properties of each family. Specifically, we treat two main issues: the first is the introduction of a rigorous definition of a notion of size for representations of classical groups, and the second issue is a method to construct and obtain information on each family of representation of a given size. In particular, we propose several compatible notions of size that we call U-rank, tensor rank and asymptotic rank, and we develop a method called eta correspondence to construct the families of representation of each given rank. Rank suggests a new way to organize the representations of classical groups over finite and local fields—a way in which the building blocks are the “smallest” representations. This is in contrast to Harish-Chandra’s philosophy of cusp forms that is the main organizational principle since the 60s, and in it the building blocks are the cuspidal representations which are, in some sense, the “largest”. The philosophy of cusp forms is well adapted to establishing the Plancherel formula for reductive groups over local fields, and led to Lusztig’s classification of the irreducible representations of such groups over finite fields. However, the understanding of certain analytic properties, such as those mentioned above, seems to require a different approach.

A Pragmatic Logic for Expressivism

AbstractThis article aims to show that the incompatibility between the application of logic to norms and values and the expressive conception of these notions – basically summed up by the Frege–Geach problem – can be overcome. To this end, a logic is constructed for the expressive conception of norms and values which provides a solution to the Frege–Geach problem and is not affected by the limitations that occur in some previous attempts. More specifically, a pragmatic language LP is introduced which is an extension of the language L of standard propositional logic, obtained by adding two categories of logical‐pragmatic signs to the vocabulary of L: the signs of pragmatic mood (, , , standing for assertion, obligation and approval, respectively) and the pragmatic connectives (∼, ∩, ∪, ⊃, ≡, standing for pragmatic negation, conjunction, disjunction, implication and bi‐implication, respectively). The notions of pragmatic validity, consistency (satisfiability), compatibility, equivalence and inference are then defined, and some criteria of pragmatic validity are given. It is thus possible to carry out in LP inferences on norms and values expressively understood, adequately formalizing Geach's problematic inferences.

Equilibrium as compatibility of plans

This paper uses a game-theoretic framework to formalize the Hayekian notion of equilibrium as the compatibility of plans. To do so, it imposes more structure on the conventional model of strategic games. For each player, it introduces goals, goal-oriented strategies, and the goals’ probabilities of success, from which players’ payoffs are derived. The differences between the compatibility of plans and Nash equilibrium are identified and discussed. Furthermore, it is shown that the notion of compatibility of plans, in general, differs from the notion of Pareto efficiency. Since the compatibility of plans across all players can rarely be achieved in reality, a measurement is introduced to determine various degrees of plan compatibility. Several possible extensions and applications of the model are discussed.

Local vs. global strategy-proofness: A new equivalence result for ordinal mechanisms

We study two incentive compatibility notions of ordinal mechanisms: strategy-proofness and a new notion of local strategy-proofness, called block-adjacent strategy-proofness, which requires no gain by a flip of two adjacent blocks. A condition on the preference domain called path-nestedness is identified as sufficient for the equivalence between these two notions.

Ordinal Bayesian Incentive Compatibility in Random Assignment Model

We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is a uniform prior, then a large class of random mechanisms are OBIC with respect to this prior - this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent priors in some neighborhood of a given independent prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.

Skew Poincaré–Birkhoff–Witt extensions over weak compatible rings

In this paper, we introduce weak [Formula: see text]-compatible rings and study skew Poincaré–Birkhoff–Witt extensions over these rings. We characterize the weak notion of compatibility for several noncommutative rings appearing in noncommutative algebraic geometry and some quantum algebras of theoretical physics. As a consequence of our treatment, we unify and extend results in the literature about Ore extensions and skew PBW extensions over compatible rings.

Fuzzy neutrosophic Soft Ideal Theory Fuzzy neutrosophic Soft Local Function and Generated Fuzzy neutrosophic Soft Topological Spaces

The purpose of this paper is to introduce the notion of fuzzy neutrosophic soft ideal in fuzzy neutrosophic soft set theory. The concept of fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new fuzzy neutrosophic soft topologies from the original one. The basic structure, especially a basis for such generated fuzzy neutrosophic soft topologies also studied here. Finally, the notion of compatibility of fuzzy neutrosophic soft ideals with fuzzy neutrosophic soft topologies is introduced and some equivalent conditions concerning this topic are established here