Lipschitz free spaces isomorphic to their infinite sums and geometric applications

Traffic congestion in parking lots is a common phenomenon across the world and larger commercial facilities with multiple parking areas may be particularly affected as many users struggle to gain access to sought-after parking spots close to their destinations. These popular zones often see traffic jams forming as many vehicles arrive within these regions, while less popular areas may remain free from congestion. This creates a very uneven distribution of traffic, with motorists in popular areas becoming trapped and unable to leave bottleneck regions. As a result, the car park management industry has taken an interest in research into parking guidance. Parking guidance has been developed to help improve efficiencies in car parks, guiding drivers to specific spaces using GPS technology to highlight free spaces near their location detailing the most efficient way to get to that spot. Associate Professor Akira Kawai, who is based at Shiga University in Japan, has been working on a KAKEN project that seeks to leverage real-time positional information to help guide drivers to free spaces within parking lots.

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Agoraphilic navigation algorithm in dynamic environment with obstacles motion tracking and prediction

Robotica ◽

10.1017/s0263574721000588 ◽

2021 ◽

pp. 1-19

Author(s):

H. S. Hewawasam ◽

M. Yousef Ibrahim ◽

Gayan Kahandawa ◽

T. A. Choudhury

Keyword(s):

Free Space ◽

Motion Tracking ◽

Dynamic Environment ◽

Experimental Tests ◽

Cluttered Environments ◽

Navigation Algorithm ◽

Prediction Module ◽

Future Space ◽

Free Spaces ◽

Advanced Development

Abstract This paper presents a new algorithm to navigate robots in dynamically cluttered environments. The proposed algorithm uses basic concepts of space attraction (hence the term Agoraphilic) to navigate robots through dynamic obstacles. The new algorithm in this paper is an advanced development of the original Agoraphilic navigation algorithm that was only able to navigate robots in static environments. The Agoraphilic algorithm does not look for obstacles (problems) to avoid but rather for a free space (solutions) to follow. Therefore, it is also described as an optimistic navigation algorithm. This algorithm uses only one attractive force created by the available free space. The free-space concept allows the Agoraphilic algorithm to overcome inherited challenges of general navigation algorithms. However, the original Agoraphilic algorithm has the limitation in navigating robots only in static, not in dynamic environments. The presented algorithm was developed to address this limitation of the original Agoraphilic algorithm. The new algorithm uses a developed object tracking module to identify the time-varying free spaces by tracking moving obstacles. The capacity of the algorithm was further strengthened by the new prediction module. Future space prediction allowed the algorithm to make decisions considering future growing/diminishing free spaces. This paper also includes a bench-marking study of the new algorithm compared with a recently published APF-based algorithm under a similar operating environment. Furthermore, the algorithm was validated based on experimental tests and simulation tests.

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Cigarette smoking and e-cigarette use among university students in Queensland, Australia and New Zealand: results of two cross-sectional surveys

BMJ Open ◽

10.1136/bmjopen-2020-041705 ◽

2021 ◽

Vol 11 (2) ◽

pp. e041705

Author(s):

Ben Wamamili ◽

Sheleigh Lawler ◽

Mark Wallace-Bell ◽

Coral Gartner ◽

David Sellars ◽

...

Keyword(s):

New Zealand ◽

Cigarette Smoking ◽

University Students ◽

Multinomial Logistic Regression ◽

Smoking Status ◽

Cigarette Use ◽

Dual Use ◽

Cross Sectional ◽

Free Spaces ◽

And Gender

ObjectivesExamine the patterns of cigarette smoking and e-cigarette use (vaping), the perceived harm of e-cigarettes compared with tobacco cigarettes, and associations between smoking and vaping with student characteristics.DesignCross-sectional studies.SettingThe University of Queensland (UQ), Australia and eight New Zealand (NZ) universities.ParticipantsStudents at UQ: 4957 (70.8% aged <25 years, 63.0% women) and NZ: 1854 (82.5% aged <25 years, 60.1% women).MethodsΧ2 tests compared smoking by age and gender, and vaping by age, gender and smoking status. Two-sided p<0.05 was considered significant and 95% CIs reported where appropriate. Multinomial logistic regression examined associations between smoking and vaping (exclusive smoking, exclusive vaping, dual use and non-use) with age, gender and student type (domestic vs international).ResultsSmoking (UQ vs NZ, 95% CI): ever 45.2% (43.8% to 46.6%) vs 50.0% (47.7% to 52.3%), current 8.9% (8.1% to 9.7%) vs 10.4% (9.1% to 11.9%) and daily 5.2% (4.6% to 5.8%) vs 5.6% (4.6% to 6.7%), and not smoking in indoor 98.3% vs 87.7% or outdoor smoke-free spaces 83.8% vs 65.3%.Vaping (UQ vs NZ, 95% CI): ever 20.9% (19.8% to 22.1%) vs 37.6% (35.4% to 39.9%), current 1.8% (1.5% to 2.2%) vs 6.5% (5.4% to 7.7%) and daily 0.7% (0.5% to 1.0%) vs 2.5% (1.9% to 3.4%), and not vaping in indoor 91.4% vs 79.6% or outdoor smoke-free spaces 84.4% vs 71.3%. Of respondents, 71.7% (70.3% to 73.2%) vs 75.3% (72.9% to 77.6%) perceived e-cigarettes as less harmful than tobacco cigarettes.Men were more likely than women to smoke and vape, and to believe that e-cigarettes are less harmful. Regression models containing all predictors for smoking and vaping were significant and the effect of gender was significant for dual use, exclusive smoking and exclusive vaping (all p<0.01). Men had higher odds for smoking, vaping or dual use.ConclusionsResults suggest significant differences in patterns of smoking and vaping of university students in Australia and NZ, and a strong influence of gender on smoking and vaping.

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A VISIBILITY-BASED PURSUIT-EVASION PROBLEM

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195999000273 ◽

1999 ◽

Vol 09 (04n05) ◽

pp. 471-493 ◽

Cited By ~ 163

Author(s):

LEONIDAS J. GUIBAS ◽

JEAN-CLAUDE LATOMBE ◽

STEVEN M. LAVALLE ◽

DAVID LIN ◽

RAJEEV MOTWANI

Keyword(s):

Finite Graph ◽

Initial Position ◽

Moving Target ◽

Multiply Connected ◽

Pursuit Evasion ◽

Minimum Number ◽

Evasion Problem ◽

Free Spaces ◽

Simply Connected ◽

Motion Strategy

This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simply-connected free spaces, it is shown that the minimum number of pursuers required is Θ( lg n). For multiply-connected free spaces, the bound is [Formula: see text] pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a finite graph that is constructed on the basis of critical information changes. It has been implemented and computed examples are shown.

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Mixing for stationary processes with finite-order multiple Wiener-Itô integral representation

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700010191 ◽

1996 ◽

Vol 16 (5) ◽

pp. 1087-1100

Author(s):

Eric Slud ◽

Daniel Chambers

Keyword(s):

Large Class ◽

Order Term ◽

Sufficient Conditions ◽

Polynomial Form ◽

Itô Integral ◽

Ito Integral ◽

Weakly Mixing ◽

Subordinated Processes ◽

Infinite Sums ◽

Necessary And Sufficient

abstractNecessary and sufficient analytical conditions are given for homogeneous multiple Wiener-Itô integral processes (MWIs) to be mixing, and sufficient conditions are given for mixing of general square-integrable Gaussian-subordinated processes. It is shown that every finite or infinite sum Y of MWIs (i.e. every real square-integrable stationary polynomial form in the variables of an underlying weakly mixing Gaussian process) is mixing if the process defined separately by each homogeneous-order term is mixing, and that this condition is necessary for a large class of Gaussian-subordinated processes. Moreover, for homogeneous MWIs Y1, for sums of MWIs of order ≤ 3, and for a large class of square-integrable infinite sums Y1, of MWIs, mixing holds if and only if Y2 has correlation-function decaying to zero for large lags. Several examples of the criteria for mixing are given, including a second-order homogeneous MWI, i.e. a degree two polynomial form, orthogonal to all linear forms, which has auto-correlations tending to zero for large lags but is not mixing.

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