Acyclicity Condition Research Articles

Acyclicity Conditions on Pasting Diagrams

Acyclicity Conditions on Pasting Diagrams

Chase Termination Beyond Polynomial Time

The chase is a widely implemented approach to reason with tuple-generating dependencies (tgds), used in data exchange, data integration, and ontology-based query answering. However, it is merely a semi-decision procedure, which may fail to terminate. Many decidable conditions have been proposed for tgds to ensure chase termination, typically by forbidding some kind of "cycle'' in the chase process. We propose a new criterion that explicitly allows some such cycles, and yet ensures termination of the standard chase under reasonable conditions. This leads to new decidable fragments of tgds that are not only syntactically more general but also strictly more expressive than the fragments defined by prior acyclicity conditions. Indeed, while known terminating fragments are restricted to PTime data complexity, our conditions yield decidable languages for any k- ExpTime. We further refine our syntactic conditions to obtain fragments of tgds for which an optimised chase procedure decides query entailment in PSpace or k- ExpSpace, respectively.

On the efficiency and fairness of deferred acceptance with single tie-breaking

As a random allocation rule for indivisible object allocation under weak priorities, deferred acceptance with single tie-breaking (DA-STB) is not ex-post constrained efficient. We first observe that it also fails to satisfy equal-top fairness, which requires that two agents be assigned their common top choice with equal probability if they have equal priority for it. Then, it is shown that DA-STB is ex-post constrained efficient, if and only if it is equal-top fair, if and only if the priority structure satisfies a certain acyclic condition. We further characterize the priority structures under which DA-STB is ex-post stable-and-efficient. Based on the characterized priority domains, and using a weak fairness notion called local envy-freeness, new theoretical support is provided for the use of this rule: for any priority structure, among the class of strategy-proof, ex-post stable, symmetric, and locally envy-free rules, each of the above desiderata—ex-post constrained efficiency, ex-post stability-and-efficiency, and equal-top fairness—can be achieved if and only if it can be achieved by DA-STB.

Competition graphs of degree bounded digraphs

If each vertex of an acyclic digraph has indegree at most i and outdegree at most j, then it is called an (i,j) digraph, which was introduced by Hefner et al. (1991). Whereas Hefner et al. characterized (i,j) digraphs whose competition graphs are interval, characterizing the competition graphs of (i,j) digraphs is not an easy task. In this paper, we introduce the concept of 〈i,j〉 digraphs, which relax the acyclicity condition of (i,j) digraphs, and study their competition graphs. By doing so, we obtain quite meaningful results. Firstly, we give a necessary and sufficient condition for a loopless graph being an 〈i,j〉 competition graph for some positive integers i and j. Then we study on an 〈i,j〉 competition graph being chordal and present a forbidden subdigraph characterization. Finally, we study the family of 〈i,j〉 competition graphs, denoted by G〈i,j〉, and identify the set containment relation on {G〈i,j〉:i,j≥1}.

Conjunctive Queries with Comparisons

Conjunctive queries with predicates in the form of comparisons that span multiple relations have regained interest recently, due to their relevance in OLAP queries, spatiotemporal databases, and machine learning over relational data. The standard technique, predicate pushdown, has limited efficacy on such comparisons. A technique by Willard can be used to process short comparisons that are adjacent in the join tree in time linear in the input size plus output size. In this paper, we describe a new algorithm for evaluating conjunctive queries with both short and long comparisons, and identify an acyclic condition under which linear time can be achieved. We have also implemented the new algorithm on top of Spark, and our experimental results demonstrate order-of-magnitude speedups over SparkSQL on a variety of graph patterns and analytical queries.

The effect of surface treatments on the interlaminar shear failure of GLARE laminates subjected to pre‐cyclic thermal loads

AbstractIn this study, both the individual and combined effect of thermal cycling and surface treatment on the interlaminar shear strength (ILSS) of glass laminate aluminum‐reinforced epoxy (GLARE) 3/2 sheet material are investigated experimentally. Three kinds of surface treatments including sandpapering, degreasing and both degreasing and sandpapering are applied to AA6061‐T6 sheets before manufacturing of hot‐pressed GLARE 3/2 sheet material. Two different cyclic thermal conditions, which are referred to the flight characteristics of a typical transport category aircraft, are then applied to short‐beam GLARE specimens by changing temperature limits and keeping the number of cycles the same. Three‐point bending tests are lastly performed to examine the effects of surface treatments on the ILSS of GLARE laminates under pre‐cyclic thermal conditions by comparing with the specimens under acyclic condition at room temperature. The results show that the ILSS of surface‐treated laminates have an increase by between 29% and 73% against untreated ones according to the cyclic thermal profile. If sandpapering and degreasing apply together as a combined mechanical–chemical surface treatment process, then ILSS is totally preserved or reduced by only 4% under certain thermal pre‐cyclic conditions.

Resource allocation on the basis of priorities under multi-unit demand

This paper considers resource allocation under multi-unit demand. We show that the deferred acceptance algorithm is efficient if and only if the priority structure satisfies an acyclicity condition introduced by Romero-Medina and Triossi (2020). It is also shown that such an acyclicity condition is sufficient but not necessary for the deferred acceptance algorithm to be consistent. In addition, under the acyclicity priority condition we obtain that the deferred acceptance algorithm satisfies a property of constrained respecting priority improvement, which partially extends a result of Balinski and Sönmez (1999) to resource allocation problems under multi-unit demand.

Robust group strategy‐proofness

Strategy‐proofness (SP) is a sought‐after property in social choice functions because it ensures that agents have no incentive to misrepresent their private information at both the interim and ex post stages. Group strategy‐proofness (GSP), however, is a notion that is applied to the ex post stage but not to the interim stage. Thus, we propose a new notion of GSP, coined robust group strategy‐proofness (RGSP), which ensures that no group benefits by deviating from truth telling at the interim stage. We show for the provision of a public good that the Minimum Demand rule (Serizawa (1999)) satisfies RGSP when the production possibilities set satisfies a particular topological property. In the problem of allocating indivisible objects, an acyclicity condition on the priorities is both necessary and sufficient for the Deferred Acceptance rule to satisfy RGSP, but is only necessary for the Top Trading Cycles rule. For the allocation of divisible private goods among agents with single‐peaked preferences (Sprumont (1991)), only free disposal, group replacement monotonic rules within the class of sequential allotment rules satisfy RGSP.

Acyclic Gambling Games

We consider two-player, zero-sum stochastic games in which each player controls the player’s own state variable living in a compact metric space. The terminology comes from gambling problems in which the state of a player represents its wealth in a casino. Under standard assumptions (e.g., continuous running payoff and nonexpansive transitions), we consider for each discount factor the value vλ of the λ-discounted stochastic game and investigate its limit when λ goes to zero. We show that, under a new acyclicity condition, the limit exists and is characterized as the unique solution of a system of functional equations: the limit is the unique continuous excessive and depressive function such that each player, if the player’s opponent does not move, can reach the zone when the current payoff is at least as good as the limit value without degrading the limit value. The approach generalizes and provides a new viewpoint on the Mertens–Zamir system coming from the study of zero-sum repeated games with lack of information on both sides. A counterexample shows that under a slightly weaker notion of acyclicity, convergence of (vλ) may fail.

Restricted Chase Termination for Existential Rules: A Hierarchical Approach and Experimentation

AbstractThe chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks. Most previous studies have focused on the skolem chase variant and its termination analysis. It is known that the restricted chase variant is a more powerful tool in termination analysis provided a database is given. But all-instance termination presents a challenge since the critical database and similar techniques do not work. In this paper, we develop a novel technique to characterize the activeness of all possible cycles of a certain length for the restricted chase, which leads to the formulation of a framework of parameterized classes of the finite restricted chase, called $k$-$\mathsf{safe}(\Phi)$ rule sets. This approach applies to any class of finite skolem chase identified with a condition of acyclicity. More generally, we show that the approach can be applied to the hierarchy of bounded rule sets previously only defined for the skolem chase. Experiments on a collection of ontologies from the web show the applicability of the proposed methods on real-world ontologies.

On the Efficiency and Fairness of Deferred Acceptance With Single Tie-Breaking

As a random allocation rule for indivisible object allocation problems under weak priorities, deferred acceptance with single tie-breaking (DA-STB) is not ex-post constrained efficient. We first observe that it also fails to satisfy a natural fairness notion, symmetry at the top, which requires that two agents be assigned their common top choice with equal probability if they have equal claim to it. Then it is shown that DA-STB is ex-post constrained efficient, if and only if it is symmetric at the top, if and only if the priority structure satisfies a certain acyclic condition. We further characterize the priority structures under which DA-STB is ex-post fully efficient. Based on the characterized priority domains, and using a mild fairness notion called local envy-freeness, some new theoretical support is provided for this widely used rule in practice. Among strategy-proof, symmetric and locally envy-free rules, there exists an ex-post constrained efficient (ex-post stable and efficient) one if and only if DA-STB is ex-post constrained efficient (ex-post stable and efficient). Among strategy-proof, ex-post stable and locally envy-free rules, there exists one that is symmetric at the top if and only if DA-STB is symmetric at the top.

On Responsiveness of Two Competing Mechanisms to Affirmative Action in School Choice

For school choice problems with affirmative action, responsiveness is used as a measure of how a matching mechanism performs in terms of a certain type of affirmative action policy. We know that the Deferred Acceptance (DA) mechanism is not responsive to the priority-based affirmative action on the universal domain of school choice. As a further study, we show in this paper that, the DA mechanism is responsive to the priority-based affirmative action if and only if the schools' priority structure satisfies an acyclicity condition characterized in this paper. This acyclicity condition is stronger than Dogan's acyclicity, which is the necessary and sufficient condition for the DA mechanism to be responsive to the reserved-based affirmative action.

Top trading cycles, consistency, and acyclic priorities for house allocation with existing tenants

We study the house allocation with existing tenants model (Abdulkadiroğlu and Sönmez, 1999) and consider rules that allocate houses based on priorities. We introduce a new acyclicity requirement and show that for house allocation with existing tenants a top trading cycles (TTC) rule is consistent if and only if its underlying priority structure satisfies our acyclicity condition. Next we give an alternative description of TTC rules based on ownership-adapted acyclic priorities in terms of two specific rules, YRMH-IGYT (you request my house - I get your turn) and efficient priority rules, that are applied in two steps. Moreover, even if no priority structure is a priori given, we show that a rule is a top trading cycles rule based on ownership-adapted acyclic priorities if and only if it satisfies Pareto-optimality, individual-rationality, strategy-proofness, consistency, and either reallocation-proofness or non-bossiness.

Perturbation Theory and Singular Perturbations for Input-to-State Multistable Systems on Manifolds

We consider the notion of input-to-state multistability, which generalizes input-to-state stability to nonlinear systems evolving on Riemannian manifolds and possessing a finite number of compact, globally attractive, invariant sets, and in addition satisfies a specific condition of acyclicity. We prove that a parameterized family of dynamical systems whose solutions converge to those of a limiting system inherits such input-to-state multistability property from the limiting system in a semiglobal practical fashion. A similar result is also established for singular perturbation models whose boundary-layer subsystem is uniformly asymptotically stable and whose reduced subsystem is input-to-state multistable. Known results in the theory of perturbations, singular perturbations, averaging, and highly oscillatory control systems are here generalized to the multistable setting by replacing the classical asymptotic stability requirement of a single invariant set with attractivity and acyclicity of a decomposable invariant one.

On responsiveness of top trading cycles mechanism to priority-based affirmative action

In school choice, priority-based affirmative action favors minority students by means of promoting their priority ranking at schools. This paper investigates the responsiveness of the top trading cycles mechanism to priority-based affirmative action when schools’ priority structure satisfies a certain acyclicity condition. When schools’ priority under the problem without affirmative action satisfies virtual homogeneity condition, a weak responsiveness result is obtained.

Effect of Superior Ovarian Nerve and Plexus Nerve Sympathetic Denervation on Ovarian-Derived Infertility Provoked by Estradiol Exposure to Rats.

Sympathetic innervation of the ovary in rodents occurs via two routes: the superior ovarian nerve (SON), which runs along the ovarian ligament, and the plexus nerve (PN), which is mainly associated with the vasculature. SON and ovarian norepinephrine (NE) levels play a major role in regulating ovarian cystic health. Although it was previously described that the polycystic ovarian phenotype (PCO) is causally related to hyperstimulation of the sympathetic nerves of the ovary, much less is known, however, regarding the role of PN in ovarian physiology. We studied the role of SON and PN in relation to the maintenance of the PCO phenotype induced in the rat by exposure to estradiol valerate (EV). EV exposure at 24 days old (juvenile exposure) increases NE in the ovary for up to 90 days after EV injection. SON or PN denervation (SONX and PNX) decreased NE. SONXreversed the acyclic condition from 30 days after surgery (p < 0.05), but PNXdid not. SONX was more effective than PNX to downregulate the increased number of cysts induced by EV, with the presence of the corpora lutea (CL, signifying ovulation) in the SONX group. Seventy percent of SONX rats presented with pregnancy at 60 days post-EV (6 of the 7 sperm-positive rats were pregnant); however, SONX rats had a reduced number (half) of pups compared with vehicle-treated rats and 60% more pups than EV rats. These data suggest that the SON plays a predominant role in follicular development, ovulation and pregnancy during ovarian diseases.

OBVIOUSLY STRATEGY‐PROOF IMPLEMENTATION OF TOP TRADING CYCLES

AbstractAlthough there is a rich theoretical literature extolling the virtues of the top trading cycles (TTCs) mechanism, it is rarely used in practice. Anecdotal evidence suggests that one possible explanation is that TTC is difficult for participants to understand. This article formalizes this intuition by asking whether it is possible to implement TTC in an obviously strategy‐proof (OSP) way. I identify an acyclicity condition that is both necessary and sufficient for OSP implementation of TTC. The condition is unlikely to hold in most applications, which may explain why TTC is rarely used, despite its many appealing theoretical properties.

Learning dynamics with social comparisons and limited memory

We study models of learning in games where agents with limited memory use social information to decide when and how to change their play. When agents only observe the aggregate distribution of payoffs and only recall information from the last period, aggregate play comes close to Nash equilibrium for generic games, and pure equilibria are generally more stable than mixed equilibria. When agents observe both the payoff distribution of other agents and the actions that led to those payoffs and can remember this for some time, the length of their memory plays a key role: With short memories, aggregate play may not come close to Nash equilibrium unless the game satisfies an acyclicity condition. When agents have sufficiently long memory generically aggregate play comes close to Nash equilibrium. However, unlike in the model where social information is solely about how well other agents are doing, mixed equilibria can be favored over pure ones.

Distributed Circular Formation Control of Nonholonomic Vehicles Without Direct Distance Measurements

This note presents a static distributed formation control law for nonholonomic vehicles subject to velocity constraints, such that the controlled vehicles travel along a common circle with the given center and radius, while maintaining a desired spaced formation. The center is assumed to be known to only some vehicles. The proposed controller does not require any communication and only uses local measurements based on a sensor graph of which the topology is modeled by a directed graph satisfying a certain acyclic condition. Moreover, direct distance measurements are not needed. Finally, the simulation results of an example verify the effectiveness of the proposed controller.

Gaming the deferred acceptance when message spaces are restricted

We consider school choice problems where students may submit only restricted length of preference lists. We propose an acyclicity condition for the priority structure of schools. When schools’ priorities are substitutable, we show that a Pareto efficient and stable assignment rule is Nash implementable by the deferred acceptance mechanism if and only if schools’ priority structures are acyclic in our sense.