scholarly journals Gel’fand-N-width in probabilistic setting

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xin Tan ◽  
Yanan Wang ◽  
Lu Sun ◽  
Xingfeng Shao ◽  
Guanggui Chen
Keyword(s):  
Probabilistic Setting

scholarly journals Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs

2000 ◽  
Vol 9 (6) ◽  
pp. 489-511 ◽  
Author(s):  
JOSEP DÍAZ ◽  
MATHEW D. PENROSE ◽  
JORDI PETIT ◽  
MARÍA SERNA
Keyword(s):  
Constant Factor ◽  
Geometric Graphs ◽  
Convergence Theorems ◽  
Linear Arrangement ◽  
Random Lattice ◽  
Random Geometric Graphs ◽  
Unit Square ◽  
Subcritical Regime ◽  
Probabilistic Setting ◽  
Lattice Graphs

This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. Specifically, we consider the following problems: Minimum Linear Arrangement, Cutwidth, Sum Cut, Vertex Separation, Edge Bisection and Vertex Bisection. For full square lattices, we give optimal layouts for the problems still open. For arbitrary lattice graphs, we present best possible bounds disregarding a constant factor. We apply percolation theory to the study of lattice graphs in a probabilistic setting. In particular, we deal with the subcritical regime that this class of graphs exhibits and characterize the behaviour of several layout measures in this space of probability. We extend the results on random lattice graphs to random geometric graphs, which are graphs whose nodes are spread at random in the unit square and whose edges connect pairs of points which are within a given distance. We also characterize the behaviour of several layout measures on random geometric graphs in their subcritical regime. Our main results are convergence theorems that can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidean TSP on random points in the unit square.

Axial Impact Buckling of a Column With Random Initial Imperfections

1978 ◽  
Vol 45 (2) ◽  
pp. 361-365 ◽  
Author(s):  
I. Elishakoff
Keyword(s):  
Critical Time ◽  
Initial Imperfection ◽  
Random Variable ◽  
Axial Impact ◽  
Absolute Value ◽  
Initial Imperfections ◽  
Total Displacement ◽  
Probabilistic Setting ◽  
Probabilistic Nature ◽  
First Time

Axial impact buckling of perfectly elastic bars with initial imperfections is considered in a probabilistic setting. It is assumed that the initial imperfection function involved a single parameter, which in turn is a continuous random variable with given probability distribution function. The structure is said to buckle if the absolute value of the total displacement exceeds a prescribed value. The probabilistic nature of the random, critical time when such a failure occurs for the first time, is studied.

scholarly journals Sample-path analysis of the proportional relation and its constant for discrete-time single-server queues

2006 ◽  
Vol 2006 ◽  
pp. 1-10
Author(s):  
Fumio Ishizaki ◽  
Naoto Miyoshi
Keyword(s):  
Discrete Time ◽  
Queue Length ◽  
Length Distribution ◽  
Sample Path ◽  
General Setting ◽  
Single Server ◽  
Sample Path Analysis ◽  
Stochastic Version ◽  
Queue Length Distribution ◽  
Probabilistic Setting

In the previous work, the authors have considered a discrete-time queueing system and they have established that, under some assumptions, the stationary queue length distribution for the system with capacity K1 is completely expressed in terms of the stationary distribution for the system with capacity K0 (>K1). In this paper, we study a sample-path version of this problem in more general setting, where neither stationarity nor ergodicity is assumed. We establish that, under some assumptions, the empirical queue length distribution (along through a sample path) for the system with capacity K1 is completely expressed only in terms of the quantities concerning the corresponding system with capacity K0 (>K1). Further, we consider a probabilistic setting where the assumptions are satisfied with probability one, and under the probabilistic setting, we obtain a stochastic version of our main result. The stochastic version is considered as a generalization of the author's previous result, because the probabilistic assumptions are less restrictive.

scholarly journals A Unifying Framework for Probabilistic Belief Revision

2017 ◽  
Author(s):  
Zhiqiang Zhuang ◽  
James Delgrande ◽  
Abhaya Nayak ◽  
Abdul Sattar
Keyword(s):  
Belief Revision ◽  
Representation Theorem ◽  
Probabilistic Logic ◽  
Basic Principles ◽  
Probabilistic Information ◽  
Probabilistic Setting ◽  
Revision Function

In this paper we provide a general, unifying framework for probabilistic belief revision. We first introduce a probabilistic logic called p-logic that is capable of representing and reasoning with basic probabilistic information. With p-logic as the background logic, we define a revision function called p-revision that resembles partial meet revision in the AGM framework. We provide a representation theorem for p-revision which shows that it can be characterised by the set of basic AGM revision postulates. P-revision represents an "all purpose" method for revising probabilistic information that can be used for, but not limited to, the revision problems behind Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis's imaging. Importantly, p-revision subsumes all three approaches indicating that Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis' imaging all obey the basic principles of AGM revision. As well our investigation sheds light on the corresponding operation of AGM expansion in the probabilistic setting.

scholarly journals A probabilistic setting for prime number theory

1974 ◽  
Vol 26 (1) ◽  
pp. 59-81 ◽  
Author(s):  
M. Wunderlich
Keyword(s):  
Number Theory ◽  
Prime Number ◽  
Probabilistic Setting

scholarly journals Strength and life estimation for assigning the useful life of wheelpairs of high-speed flat wagons

Dependability ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 26-30
Author(s):  
G. M. Volokhov ◽  
E. S. Oganian ◽  
G. I. Gajimetov ◽  
D. A. Knyazev ◽  
V. V. Chunin ◽  
...  
Keyword(s):  
High Speed ◽  
Crack Nucleation ◽  
Conformity Assessment ◽  
Rolling Stock ◽  
Fatigue Crack Nucleation ◽  
Probabilistic Setting ◽  
Gauge Space ◽  
Standards And Regulations ◽  
Useful Life ◽  
Strength And Durability

Aim. The most vital unit of railway rolling stock is a wheelpair, as a broken wheel or axle may have catastrophic consequences. Therefore, before the production of a highspeed flat wagon designed for operation at speeds of up to 140 km/h, which is unique for the 1520 mm gauge space, could commence, it was required to research the applicability of the standard wheelpair for high-speed movement. Ensuring the safe operation of a wheelpair involves compliance with the requirements that are to be confirmed by means of assessment of strength and durability parameters [1]. Product conformity assessment may be based on the requirements of standards, whose voluntary fulfilment ensures compliance with [1], or other documents. Methods. The paper describes the computational and experimental methods used for confirming the strength and estimating the life (durability) of wheelpair elements in the probabilistic setting. As experimental data, the authors used the results of full-scale bench testing of wheelpairs for fatigue using the method of rotational bending as it best approximates the loading conditions in operation. The results confirmed the endurance limits of the axle and wheel as parts of an assembled wheelpair. Using design analysis, the authors examined the stress-strain state of the wheelpair caused by installation and operational loads in various running modes. Results. The conducted studies confirmed the wheelpair’s compliance with the requirements of [1–3] in terms of safety factors of fatigue strength and endurance, which eliminates the possibility of hazardous situations in the course of high-speed flat wagon operation. The time to fatigue crack nucleation in wheelpair components was evaluated using the fatigue resistance figures of the parts and equivalent amplitudes of dynamic stress caused by operational loads. It appears that this assessment allows establishing – with the assumed probability of destruction – the assigned useful life of a wheelpair axle at 32 years, which corresponds to the assigned useful life of the flat wagon according to the combined criterion. Corresponding standards and regulations required for developing the container-carrying flat wagon are being updated and a new State Standard is being developed. Conclusion. The conducted conformity assessment established that the flat wagon wheelpair meets the safety requirements of [1] and ensures the absence of unacceptable risks associated with harm to life and health of people, animals and plants, the environment and property of individuals and companies in the course of flat wagon operation.

Anti-Optimization Versus Probability in an Applied Mechanics Problem: Vector Uncertainty

2000 ◽  
Vol 67 (3) ◽  
pp. 472-484 ◽  
Author(s):  
M. Zingales ◽  
I. Elishakoff
Keyword(s):  
Smooth Boundary ◽  
Optimization Method ◽  
Rectangular Domain ◽  
Probability Density Functions ◽  
Alternative Methods ◽  
Applied Mechanics ◽  
Mechanical Problem ◽  
Uncertain Variables ◽  
Advantages And Disadvantages ◽  
Probabilistic Setting

In this study probabilistic and nonprobabilistic anti-optimization approaches are contrasted to evaluate their relative advantages and disadvantages while solving a mechanical problem in presence of vector uncertainty. The different cases that are analyzed in probabilistic setting that deal with either uniform or generic probability density functions for the uncertain variables varying in a rectangular domain. This case has been compared with interval analysis, a particular case of anti-optimization. The presence of a convex, smooth boundary of the uncertain domain has been also considered for comparing results obtained with these two alternative methods. It is shown that in case of vector uncertainty the anti-optimization method yields the same solution for the design problem as is provided by means of more complex probabilistic considerations. [S0021-8936(00)03103-2]

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