discrete space
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2022 ◽  
Vol 4 ◽  
Author(s):  
Reuth Mirsky ◽  
Ran Galun ◽  
Kobi Gal ◽  
Gal Kaminka

Plan recognition deals with reasoning about the goals and execution process of an actor, given observations of its actions. It is one of the fundamental problems of AI, applicable to many domains, from user interfaces to cyber-security. Despite the prevalence of these approaches, they lack a standard representation, and have not been compared using a common testbed. This paper provides a first step towards bridging this gap by providing a standard plan library representation that can be used by hierarchical, discrete-space plan recognition and evaluation criteria to consider when comparing plan recognition algorithms. This representation is comprehensive enough to describe a variety of known plan recognition problems and can be easily used by existing algorithms in this class. We use this common representation to thoroughly compare two known approaches, represented by two algorithms, SBR and Probabilistic Hostile Agent Task Tracker (PHATT). We provide meaningful insights about the differences and abilities of these algorithms, and evaluate these insights both theoretically and empirically. We show a tradeoff between expressiveness and efficiency: SBR is usually superior to PHATT in terms of computation time and space, but at the expense of functionality and representational compactness. We also show how different properties of the plan library affect the complexity of the recognition process, regardless of the concrete algorithm used. Lastly, we show how these insights can be used to form a new algorithm that outperforms existing approaches both in terms of expressiveness and efficiency.


Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2283
Author(s):  
Garnet Ord

Minkowski spacetime provides a background framework for the kinematics and dynamics of classical particles. How the framework implements the motion of matter is not specified within special relativity. In this paper we specify how Minkowski space can implement motion in such a way that ’quantum’ propagation occurs on appropriate scales. This is done by starting in a discrete space and explicitly taking a continuum limit. The argument is direct and illuminates the special tension between ’rest’ and ’uniform motion’ found in Minkowski space, showing how the formal analytic continuations involved in Minkowski space and quantum propagation arise from the same source.


2021 ◽  
Author(s):  
Chaoliang Dang ◽  
Fei Wang ◽  
Xiangqian Tong ◽  
Ding Liu ◽  
Xiaoyu Mu ◽  
...  

2021 ◽  
Author(s):  
Charlotte M. Jones‐Todd ◽  
Enrico Pirotta ◽  
John W. Durban ◽  
Diane E. Claridge ◽  
Robin W. Baird ◽  
...  

2021 ◽  
Vol 22 (2) ◽  
pp. 303
Author(s):  
Igor V. Protasov

<p>Given a coarse space (X, E), we endow X with the discrete topology and denote X ♯ = {p ∈ βG : each member P ∈ p is unbounded }. For p, q ∈ X ♯ , p||q means that there exists an entourage E ∈ E such that E[P] ∈ q for each P ∈ p. We say that (X, E) is orbitally discrete if, for every p ∈ X ♯ , the orbit p = {q ∈ X ♯ : p||q} is discrete in βG. We prove that every orbitally discrete space is almost finitary and scattered.</p>


2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Žiga Krajnik ◽  
Enej Ilievski ◽  
Tomaz Prosen ◽  
Vincent Pasquier

We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this explicit discrete symplectic integration scheme to compute the spin Drude weight and diffusion constant as functions of anisotropy and chemical potential. We demonstrate qualitatively different behavior in the easy-axis and the easy-plane regimes in the non-magnetized sector. Upon approaching the isotropic point we also find an algebraic divergence of the diffusion constant, signaling a crossover to spin superdiffusion.


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Irappa Basappa Hunagund ◽  
V. Madhusudanan Pillai ◽  
Kempaiah U.N.

Purpose The purpose of this paper is to review, evaluate and classify the academic research that has been published in facility layout problems (FLPs) and to analyse how researches and practices on FLPs are. Design/methodology/approach The review is based on 166 papers published from 1953 to 2021 in international peer-reviewed journals. The literature review on FLPs is presented under broader headings of discrete space and continuous space FLPs. The important formulations of FLPs under static and dynamic environments represented in the discrete and continuous space are presented. The articles reported in the literature on various representations of facilities for the continuous space Unequal Area Facility Layout Problems (UA-FLPs) are summarized. Discussed and commented on adaptive and robust approaches for dynamic environment FLPs. Highlighted the application of meta-heuristic solution methods for FLPs of a larger size. Findings It is found that most of the earlier research adopted the discrete space for the formulation of FLPs. This type of space representation for FLPs mostly assumes an equal area for all facilities. UA-FLPs represented in discrete space yield irregular shape facilities. It is also observed that the recent works consider the UA-FLPs in continuous space. The solution of continuous space UA-FLPs is more accurate and realistic. Some of the recent works on UA-FLPs consider the flexible bay structure (FBS) due to its advantages over the other representations. FBS helps the proper design of aisle structure in the detailed layout plan. Further, the recent articles reported in the literature consider the dynamic environment for both equal and unequal area FLPs to cope with the changing market environment. It is also found that FLPs are Non-deterministic Polynomial-complete problems, and hence, they set the challenges to researchers to develop efficient meta-heuristic methods to solve the bigger size FLPs in a reasonable time. Research limitations/implications Due to the extremely large number of papers on FLPs, a few papers may have inadvertently been missed. The facility layout design research domain is extremely vast which covers other areas such as cellular layouts, pick and drop points and aisle structure design. This research review on FLPs did not consider the papers published on cellular layouts, pick and drop points and aisle structure design. Despite the possibility of not being all-inclusive, the authors firmly believe that most of the papers published on FLPs are covered and the general picture presented on various approaches and parameters of FLPs in this paper are precise and trustworthy. Originality/value To the best of the authors’ knowledge, this paper reviews and classifies the literature on FLPs for the first time under the broader headings of discrete space and continuous space representations. Many important formulations of FLPs under static and dynamic environments represented in the discrete and continuous space are presented. This paper also provides the observations from the literature review and identifies the prospective future directions.


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