Finitely Materialisable Datalog Programs with Metric Temporal Operators

Mapping Intimacies ◽

10.24963/kr.2021/59 ◽

2021 ◽

Author(s):

Przemysław A. Wałęga ◽

Michał Zawidzki ◽

Bernardo Cuenca Grau

Keyword(s):

Sufficient Conditions ◽

Large Fragment ◽

Exponential Time ◽

Forward Chaining ◽

Rule Application ◽

Temporal Intervals ◽

Significant Attention

DatalogMTL is an extension of Datalog with metric temporal operators that has recently received significant attention. In contrast to plain Datalog, where scalable implementations are often based on materialisation (a.k.a. forward chaining), reasoning algorithms for recursive fragments of DatalogMTL are automata-based and not well suited for practice. In this paper we propose the class of finitely materialisable DatalogMTL programs, for which forward chaining reasoning terminates after finitely many rounds of rule application. We show that, for bounded programs (a large fragment of DatalogMTL where temporal intervals are restricted to not mention infinity), checking whether a program is finitely materialisable is feasible in exponential time, and propose sufficient conditions for finite materialisability that can be checked more efficiently. We finally show that fact entailment over finitely materialisable bounded programs is ExpTime-complete, and hence no harder than Datalog reasoning.

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Impulsive Switching Epidemic Model with Benign Worm Defense and Quarantine Strategy

Complexity ◽

10.1155/2020/3578390 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Jiying Lai ◽

Shujing Gao ◽

Yujiang Liu ◽

Xinzhu Meng

Keyword(s):

Numerical Simulation ◽

Periodic Solution ◽

Epidemic Model ◽

Sufficient Conditions ◽

Propagation Model ◽

The Internet ◽

Worm Propagation ◽

Worm Defense ◽

Benign Worm ◽

Significant Attention

The issue on how to effectively control Internet malicious worms has been drawn significant attention owing to enormous threats to the Internet. Due to the rapid spreading of malicious worms, it is necessary to explore the integrated measures to automatically mitigate the propagation on the Internet. In this paper, a novel worm propagation model is established, which combines both impulsive quarantine and benign worm implementation. Then, sufficient conditions for the global stability of worm-free periodic solution and the permanence of the benign worm are obtained. Finally, the effects of quarantine strategy are assessed and some feasible strategies that can constrain the propagation of malicious worm are provided by numerical simulation.

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Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

Journal of Applied Probability ◽

10.1017/s0021900200003119 ◽

2007 ◽

Vol 44 (02) ◽

pp. 492-505

Author(s):

M. Molina ◽

M. Mota ◽

A. Ramos

Keyword(s):

Branching Process ◽

Branching Processes ◽

Sufficient Conditions ◽

Positive Probability ◽

Limit Laws ◽

Bisexual Branching Processes ◽

Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

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The extinction time of a general birth and death process with catastrophes

Journal of Applied Probability ◽

10.1017/s0021900200116031 ◽

1986 ◽

Vol 23 (04) ◽

pp. 851-858 ◽

Cited By ~ 1

Author(s):

P. J. Brockwell

Keyword(s):

Laplace Transform ◽

Size Distribution ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Death Process ◽

Extinction Time ◽

Birth And Death Process ◽

Different Types ◽

The Laplace Transform ◽

Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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Normal approximations to discrete unimodal distributions

Journal of Applied Probability ◽

10.1017/s0021900200115931 ◽

1986 ◽

Vol 23 (04) ◽

pp. 1013-1018

Author(s):

B. G. Quinn ◽

H. L. MacGillivray

Keyword(s):

Stationary Distribution ◽

Sufficient Conditions ◽

Random Variables ◽

Hypergeometric Distribution ◽

Death Process ◽

Normal Approximations ◽

Discrete Random Variables ◽

Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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The Prediction of Problem-Solving Assessed Via Microworlds

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000263 ◽

2016 ◽

Vol 32 (4) ◽

pp. 298-306 ◽

Cited By ~ 7

Author(s):

Samuel Greiff ◽

Katarina Krkovic ◽

Jarkko Hautamäki

Keyword(s):

Working Memory ◽

Problem Solving ◽

Complex Problem ◽

Two Dimensions ◽

Assessment Instruments ◽

Complex Problem Solving ◽

Visual Spatial ◽

Rule Knowledge ◽

Rule Application ◽

Fluid Reasoning

Abstract. In this study, we explored the network of relations between fluid reasoning, working memory, and the two dimensions of complex problem solving, rule knowledge and rule application. In doing so, we replicated the recent study by Bühner, Kröner, and Ziegler (2008) and the structural relations investigated therein [ Bühner, Kröner, & Ziegler, (2008) . Working memory, visual-spatial intelligence and their relationship to problem-solving. Intelligence, 36, 672–680]. However, in the present study, we used different assessment instruments by employing assessments of figural, numerical, and verbal fluid reasoning, an assessment of numerical working memory, and a complex problem solving assessment using the MicroDYN approach. In a sample of N = 2,029 Finnish sixth-grade students of which 328 students took the numerical working memory assessment, the findings diverged substantially from the results reported by Bühner et al. Importantly, in the present study, fluid reasoning was the main source of variation for rule knowledge and rule application, and working memory contributed only a little added value. Albeit generally in line with previously conducted research on the relation between complex problem solving and other cognitive abilities, these findings directly contrast the results of Bühner et al. (2008) who reported that only working memory was a source of variation in complex problem solving, whereas fluid reasoning was not. Explanations for the different patterns of results are sought, and implications for the use of assessment instruments and for research on interindividual differences in complex problem solving are discussed.

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