Bohmian mechanics in momentum representation and beyond

Bonilla-Licea, Moise; Schuch, Dieter

doi:10.1016/j.physleta.2020.126671

Cited by 16 publications

(20 citation statements)

References 28 publications

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“…8, we show the performance of the system optimized according to METHOD A with θ = 1 and METHOD B with P ref = 0.01 respectively. To get an insight into the impact of the approximations related to the global probability of avoidance imposed during the optimisation phase (see section V-B), in both figures, we plot P GP A in (14) (measured by simulations),P GP A in (16), P I in (17) (measured by simulations),P GP A in (20) andP I in (21). It is clear that for both METHOD A and METHOD B, our proposed approximationP I follows closely P I which validates this approximation.…”

Section: Simulations Resultsmentioning

confidence: 99%

“…To solve (7), as adopt an approach similar to that of [16]. For a fixed path's length j , the optimum shape is a straight line, see Fig.…”

Section: A Surveying Modementioning

confidence: 99%

“…Then, this approximation for P I , which we denoteP I , is used in (16). We denote the resulting approximation asP GP A :…”

Section: B Msn's Trajectory Configurationmentioning

confidence: 99%

“…In the literature, there has been little focus on WMSN due to its design and operation complexities. It has been shown that mobility alleviates several issues related to sensor network coverage and connectivity [15], [16], [17] but many challenges still remain unmet. The WMSN leverages dynamic coverage [18] to potentially achieve the same performance as SSN having much larger numbers of nodes.…”

Section: Introductionmentioning

confidence: 99%

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On Trajectory Design for Intruder Detection in Wireless Mobile Sensor Networks

Nurellari

Licea

Ghogho

et al. 2021

IEEE Trans. on Signal and Inf. Process. over Networks

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We address the problem of detecting the invasion of an intruder into a region of interest (ROI) which is monitored by a distributed bandwidth-constrained wireless mobile sensor network (WMSN). We design periodic trajectories for the mobile sensor nodes (MSNs) such that high detection probabilities are obtained while maintaining the MSNs' energy consumption low. To reduce the transmission and processing burden on the MSNs, we propose an operation algorithm based on two modes, surveying mode and conf irmation mode. In the former, to efficiently detect the intruder while using little mechanical energy, we optimize the surveying path such that the sensed area is maximized. During this mode, each MSN performs local detection and switches to the confirmation mode if and only if the intruder is suspected to be present. In the confirmation mode, each MSN collects further measurements over a predefined duration to reduce the detection uncertainly. A binary local hypothesis testing is performed at each MSN and only positive test statistics are transmitted to the FC where the ultimate decision is taken. Simulations results show the merits of the proposed two-mode operation algorithm in terms of detection performance and energy efficiency.

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Section: Simulations Resultsmentioning

confidence: 99%

“…To solve (7), as adopt an approach similar to that of [16]. For a fixed path's length j , the optimum shape is a straight line, see Fig.…”

Section: A Surveying Modementioning

confidence: 99%

“…Then, this approximation for P I , which we denoteP I , is used in (16). We denote the resulting approximation asP GP A :…”

Section: B Msn's Trajectory Configurationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Trajectory Design for Intruder Detection in Wireless Mobile Sensor Networks

Nurellari

Licea

Ghogho

et al. 2021

IEEE Trans. on Signal and Inf. Process. over Networks

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“…account motion and communications energy [17]; the minimization of energy consumption of a wireless sensor network using autonomous mobile robots [19].…”

Section: Bonilla Is With the Cinvestav-ipn Umi 3575 Cinvestav-cnrsmentioning

confidence: 99%

UAV Trajectory Planning for Delay Tolerant Communications

Licea

Bonilla

Ghogho

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this paper, we address the problem of optimizing a communication-aware trajectory for a quadrotor that must transfer periodically (with fixed period T) a maximum amount of data from a source node (SN) to a destination node (DN). The communications aspect is mathematically stated by linking the bit rate to the channel capacity concept from information theory. The trajectory is optimized using a parametric approach using Fourier series in order to reduce the computational load of the optimization process. We show that the proposed trajectory results in a large increase of the amount of transferred data, and can be easily tracked by the quadrotor. Index Terms-Trajectory planning, data ferry, delay tolerant communications. NOTATION A zero dimension subspace is denoted by {0}, and the identity operator is denoted by I, or In when its size, n×n, is specified. For a full row (column) rank matrix X ∈ R n×m , its right (left) inverses are denoted by X r (X), i.e. XX r = In (X X = Im). If X is square and invertible, its inverse is denoted by X −1. x T stands for the transpose of the matrix (or vector) x. s stands for the complex variable of Laplace transform. Given a pair of mappings (A, B), such that A : R n → R n and B : R m → R n , C (A, B) stands for the controllability matrix C (A, B) = B A B • • • A (n−1) B. Ψm(ξ) ∈ R n•m×m [ξ] stands for: Imξ Imξ 2 • • • Imξ n T. Further, c(ϑ) and s(ϑ) stand for cosine and sine of a given angle ϑ, respectively; and s −1 (ϑ) stands for arcsin(ϑ). The ceiling and the floor functions are denoted as • and • respectively.x stands for the estimate of the variable x; E[•] stands for the statistical expectation operator. A vector function f (ε, t) ∈ R n is said to be O(ε) over an interval [t1, t2] if there exist positive constants K and ε * such that f (ε, t) ≤ Kε for all ε ∈ [0, ε * ] and for all t ∈ [t1, t2], see [4]. CONFIDENTIAL. Limited circulation. For review only.

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Born’s rule in multiqubit Bohmian systems

Tzemos¹,

Contopoulos²

2022

Chaos, Solitons & Fractals

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Bohmian mechanics in momentum representation and beyond

Cited by 16 publications

References 28 publications

On Trajectory Design for Intruder Detection in Wireless Mobile Sensor Networks

On Trajectory Design for Intruder Detection in Wireless Mobile Sensor Networks

UAV Trajectory Planning for Delay Tolerant Communications

Born’s rule in multiqubit Bohmian systems

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