The interpretation of unsolvable λ-terms in models of untyped λ-calculus

1998 ◽  
Vol 63 (4) ◽  
pp. 1529-1548 ◽  
Author(s):  
Rainer Kerth
Keyword(s):  
Graph Model ◽  
Stable Model ◽  
Graph Models ◽  
Stable Models

AbstractOur goal in this paper is to analyze the interpretation of arbitrary unsolvable λ-terms in a given model of λ-calculus. We focus on graph models and (a special type of) stable models. We introduce the syntactical notion of a decoration and the semantical notion of a critical sequence. We conjecture that any unsolvable term β-reduces to a term admitting a decoration. The main result of this paper concerns the interconnection between those two notions: given a graph model or stable model , we show that any unsolvable term admitting a decoration and having a non-empty interpretation in generates a critical sequence in the model.In the last section, we examine three classical graph models, namely the model of Plotkin and Scott, Engeler's model and Park's model . We show that and do not contain critical sequences whereas does.

Unsatisfiable Core Analysis and Aggregates for Optimum Stable Model Search

2020 ◽  
Vol 176 (3-4) ◽  
pp. 271-297
Author(s):  
Mario Alviano ◽  
Carmine Dodaro
Keyword(s):  
State Of The Art ◽  
Answer Set Programming ◽  
Efficient Algorithms ◽  
Satisfiability Problem ◽  
Core Analysis ◽  
Stable Model ◽  
Maximum Satisfiability ◽  
Model Search ◽  
Unsatisfiable Core ◽  
Stable Models

Many efficient algorithms for the computation of optimum stable models in the context of Answer Set Programming (ASP) are based on unsatisfiable core analysis. Among them, algorithm OLL was the first introduced in the context of ASP, whereas algorithms ONE and PMRES were first introduced for solving the Maximum Satisfiability problem (MaxSAT) and later on adapted to ASP. In this paper, we present the porting to ASP of another state-of-the-art algorithm introduced for MaxSAT, namely K, which generalizes ONE and PMRES. Moreover, we present a new algorithm called OLL-IN-ONE that compactly encodes all aggregates of OLL by taking advantage of shared aggregate sets propagators. The performance of the algorithms have been empirically compared on instances taken from the latest ASP Competition.

Graph methods for the investigation of metabolic networks in parasitology

Parasitology ◽  
2010 ◽  
Vol 137 (9) ◽  
pp. 1393-1407 ◽  
Author(s):  
LUDOVIC COTTRET ◽  
FABIEN JOURDAN
Keyword(s):  
Metabolic Network ◽  
Large Scale ◽  
Metabolic Networks ◽  
Graph Model ◽  
New Drugs ◽  
Mathematical Methods ◽  
Graph Models ◽  
Metabolic Network Reconstruction ◽  
Network Analyses ◽  
Genome Scale

SUMMARYRecently, a way was opened with the development of many mathematical methods to model and analyze genome-scale metabolic networks. Among them, methods based on graph models enable to us quickly perform large-scale analyses on large metabolic networks. However, it could be difficult for parasitologists to select the graph model and methods adapted to their biological questions. In this review, after briefly addressing the problem of the metabolic network reconstruction, we propose an overview of the graph-based approaches used in whole metabolic network analyses. Applications highlight the usefulness of this kind of approach in the field of parasitology, especially by suggesting metabolic targets for new drugs. Their development still represents a major challenge to fight against the numerous diseases caused by parasites.

scholarly journals A Unification of Heterogeneous Data Sources into a Graph Model in E-commerce

2021 ◽  
Author(s):  
Sonal Tuteja ◽  
Rajeev Kumar
Keyword(s):  
Large Scale ◽  
Graph Model ◽  
Heterogeneous Data ◽  
Data Models ◽  
Graph Models ◽  
Query Performance ◽  
Source Models ◽  
Database Size ◽  
Modelling Techniques ◽  
Heterogeneous Source

AbstractThe incorporation of heterogeneous data models into large-scale e-commerce applications incurs various complexities and overheads, such as redundancy of data, maintenance of different data models, and communication among different models for query processing. Graphs have emerged as data modelling techniques for large-scale applications with heterogeneous, schemaless, and relationship-centric data. Models exist for mapping different types of data to a graph; however, the unification of data from heterogeneous source models into a graph model has not received much attention. To address this, we propose a new framework in this study. The proposed framework first transforms data from various source models into graph models individually and then unifies them into a single graph. To justify the applicability of the proposed framework in e-commerce applications, we analyse and compare query performance, scalability, and database size of the unified graph with heterogeneous source data models for a predefined set of queries. We also access some qualitative measures, such as flexibility, completeness, consistency, and maturity for the proposed unified graph. Based on the experimental results, the unified graph outperforms heterogeneous source models for query performance and scalability; however, it falls behind for database size.

scholarly journals A Multilayer Approach to Subgraph Matching in HP-graphs

2021 ◽  
Vol 33 (4) ◽  
pp. 163-176
Author(s):  
Nikolai Mikhailovich Suvorov ◽  
Lyudmila Nickolaevna Lyadova
Keyword(s):  
Graph Model ◽  
Main Element ◽  
User Requirements ◽  
Visual Languages ◽  
Graph Models ◽  
Visual Modeling ◽  
Subgraph Matching ◽  
Graph Pattern ◽  
Visual Models ◽  
Search Field

Visual modeling is widely used nowadays, but the existing modeling platforms cannot meet all the user requirements. Visual languages are usually based on graph models, but the graph types used have significant restrictions. A new graph model, called HP-graph, whose main element is a set of poles, the subsets of which are combined into vertices and edges, has been previously presented to solve the problem of insufficient expressiveness of the existing graph models. Transformations and many other operations on visual models face a problem of subgraph matching, which slows down their execution. A multilayer approach to subgraph matching can be a solution for this problem if a modeling system is based on the HP-graph. In this case, the search is started on the higher level of the graph model, where vertices and hyperedges are compared without revealing their structures, and only when a candidate is found, it moves to the level of poles, where the comparison of the decomposed structures is performed. The description of the idea of the multilayer approach is given. A backtracking algorithm based on this approach is presented. The Ullmann algorithm and VF2 are adapted to this approach and are analyzed for complexity. The proposed approach incrementally decreases the search field of the backtracking algorithm and helps to decrease its overall complexity. The paper proves that the existing subgraph matching algorithms except ones that modify a graph pattern can be successfully adapted to the proposed approach.

scholarly journals The generalized centrality method for analyzing network cyberspace

2019 ◽  
pp. 55-64
Author(s):  
Natalia Nikolaevna Gorlushkina ◽  
Sergei Evgenievich Ivanov ◽  
Lubov Nikolaevna Ivanova
Keyword(s):  
Mathematical Model ◽  
Social Networks ◽  
Information Dissemination ◽  
Relative Weight ◽  
Graph Model ◽  
Graph Models ◽  
Number Of Factors ◽  
The Subject ◽  
Comparison Of The Results ◽  
Centrality Analysis

The subject of the research is the methods of network cyberspace analysis based on graph models. The analysis allows to find leaders of groups and communities, to find cohesive groups and visualize the results. The main methods of the graph theory used for cyberspace social networks are the methods of analyzing the centrality to determine the relative weight or importance of the vertices of the graph. There are known methods for analyzing centralities: by degree, by proximity, by mediation, by radiality, by eccentricity, by status, eigenvector, referential ranking. The disadvantage of these methods is that they are based only on one or several properties of the network participant. Based on the centrality analysis methods, a new generalized centrality method is proposed, taking into account such participant properties as the participant's popularity, the importance and speed of information dissemination in the cyberspace network. A mathematical model of a new method of generalized centrality has been developed. Comparison of the results of the presented method with the methods of the analysis of centralities is performed. As a visual example, a subgroup of cyberspace consisting of twenty participants, represented by a graph model, is analyzed. Comparative analysis showed the accuracy of the method of generalized centrality, taking into account at once a number of factors and properties of the network participant.

scholarly journals Simple Formulas for Pricing and Hedging European Options in the Finite Moment Log-Stable Model

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 36 ◽  
Author(s):  
Jean-Philippe Aguilar ◽  
Jan Korbel
Keyword(s):  
Stable Model ◽  
European Options ◽  
Finite Moment ◽  
Stable Models

We provide ready-to-use formulas for European options prices, risk sensitivities, and P&L calculations under Lévy-stable models with maximal negative asymmetry. Particular cases, efficiency testing, and some qualitative features of the model are also discussed.

Graph Models for Optimization Problems in Road Networks

2021 ◽  
pp. 275-336
Author(s):  
Vadim Zverovich
Keyword(s):  
Urban Areas ◽  
Optimization Problems ◽  
Optimal Path ◽  
Road Networks ◽  
Graph Model ◽  
Pedestrian Safety ◽  
Graph Models ◽  
Battery Charge ◽  
Domination Problem ◽  
Charging Stations

Here two applications of graph theory are considered. The first is devoted to pedestrian safety, and the focus is on pedestrian safety in urban areas with respect to pedestrian-vehicle crashes. In particular, an algorithm for automated construction of a graph model for pavement networks is discussed. Then, an algorithm for finding a user-optimal path in a given pavement network is presented. This algorithm is based on three criteria: path safety, distance, and path complexity. The second part of this chapter is devoted to optimizing the placement of charging stations for electric vehicles in road networks. The placement of charging stations in road networks is modelled as a multiple domination problem on reachability graphs. This model takes into account a threshold for the remaining battery charge and provides some minimal choice for a travel direction to recharge the battery. Experimental evaluation and simulations for the proposed facility location model are given for real road networks of the cities of Boston and Dublin.

scholarly journals On the existence of stable models of non-stratified logic programs

2006 ◽  
Vol 6 (1-2) ◽  
pp. 169-212 ◽  
Author(s):  
STEFANIA COSTANTINI
Keyword(s):  
Canonical Form ◽  
Logic Program ◽  
Practical Importance ◽  
The Body ◽  
Fundamental Result ◽  
Stable Model ◽  
Logic Programs ◽  
Truth Value ◽  
Answer Sets ◽  
Stable Models

In this paper we analyze the relationship between cyclic definitions and consistency in Gelfond-Lifschitz's answer sets semantics (originally defined as ‘stable model semantics’). This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is given a syntactic characterization. This condition may have a practical importance both for defining new algorithms for checking consistency and computing answer sets, and for improving the existing systems. The approach of this paper is to introduce a new canonical form (to which any logic program can be reduced to), to focus the attention on cyclic dependencies. The technical result is then given in terms of programs in canonical form (canonical programs), without loss of generality: the stable models of any general logic program coincide (up to the language) to those of the corresponding canonical program. The result is based on identifying the cycles contained in the program, showing that stable models of the overall program are composed of stable models of suitable sub-programs, corresponding to the cycles, and on defining the Cycle Graph. Each vertex of this graph corresponds to one cycle, and each edge corresponds to one handle, which is a literal containing an atom that, occurring in both cycles, actually determines a connection between them. In fact, the truth value of the handle in the cycle where it appears as the head of a rule, influences the truth value of the atoms of the cycle(s) where it occurs in the body. We can therefore introduce the concept of a handle path, connecting different cycles. Cycles can be even, if they consist of an even number of rules, or vice versa they can be odd. Problems for consistency, as it is well-known, originate in the odd cycles. If for every odd cycle we can find a handle path with certain properties, then the existence of stable model is guaranteed. We will show that based on this results new classes of consistent programs can be defined, and that cycles and cycle graphs can be generalized to components and component graphs.

The intricacies of three-valued extensional semantics for higher-order logic programs

2017 ◽  
Vol 17 (5-6) ◽  
pp. 974-991
Author(s):  
PANOS RONDOGIANNIS ◽  
IOANNA SYMEONIDOU
Keyword(s):  
Infinite Number ◽  
Higher Order ◽  
Order Logic ◽  
Stable Model ◽  
Logic Programs ◽  
Higher Order Logic ◽  
Truth Values ◽  
Positive Side ◽  
Stable Models

AbstractM. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated by Rondogiannis and Symeonidou that Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values. Rondogiannis and Symeonidou also demonstrated that Bezem's technique, when extended under the stable model semantics, does not in general lead to extensional stable models. In this paper, we consider the problem of extending Bezem's technique under the well-founded semantics. We demonstrate that the well-founded extensionfailsto retain extensionality in the general case. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved. We analyze the reasons of the failure of extensionality in the general case, arguing that a three-valued setting cannot distinguish between certain predicates that appear to have a different behaviour inside a program context, but which happen to be identical as three-valued relations.

scholarly journals A note on perfect simulation for Exponential Random Graph Models

2020 ◽  
Vol 24 ◽  
pp. 138-147 ◽  
Author(s):  
Andressa Cerqueira ◽  
Aurélien Garivier ◽  
Florencia Leonardi
Keyword(s):  
Markov Chain ◽  
Random Graph ◽  
Mixing Time ◽  
Graph Model ◽  
Glauber Dynamics ◽  
Perfect Simulation ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Model ◽  
Exponential Random Graph

In this paper, we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling from the past method of Propp and Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the monotonicity of the ERGM for a subset of the parametric space. We also obtain an upper bound on the running time of the algorithm that depends on the mixing time of the Markov chain.

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