scholarly journals Sums of standard uniform random variables

2019 ◽  
Vol 56 (3) ◽  
pp. 918-936 ◽  
Author(s):  
Tiantian Mao ◽  
Bin Wang ◽  
Ruodu Wang
Keyword(s):  
Random Variables ◽  
Complete Characterization ◽  
Partial Characterization ◽  
Challenging Problem ◽  
Marginal Distributions ◽  
Characterization Result ◽  
Full Characterization

AbstractIn this paper, we analyse the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are obtained for two distinct cases. In the case of dimension two, we obtain four partial characterization results. For dimension greater than or equal to three, we obtain a full characterization of the set of aggregate distributions, which is the first complete characterization result of this type in the literature for any choice of continuous marginal distributions.

Minimal Sets on Graphs and Dendrites

2003 ◽  
Vol 13 (07) ◽  
pp. 1721-1725 ◽  
Author(s):  
Francisco Balibrea ◽  
Roman Hric ◽  
L'ubomír Snoha
Keyword(s):  
Topological Structure ◽  
Partial Characterization ◽  
Minimal Set ◽  
Full Characterization ◽  
Minimal Sets ◽  
Continuous Maps

The topological structure of minimal sets of continuous maps on graphs, dendrites and dendroids is studied. A full characterization of minimal sets on graphs and a partial characterization of minimal sets on dendrites are given. An example of a minimal set containing an interval on a dendroid is given.

The structure of elementary pure birth processes

1982 ◽  
Vol 19 (3) ◽  
pp. 664-667 ◽  
Author(s):  
Dietmar Pfeifer
Keyword(s):  
Random Variables ◽  
Complete Characterization ◽  
Counting Processes ◽  
Birth Processes

A complete characterization of elementary pure birth processes is given by means of record counting processes from independent (non-identically) distributed random variables.

scholarly journals Graph Reconstruction from Unlabeled Edge Lengths

2021 ◽  
Author(s):  
Dániel Garamvölgyi ◽  
Tibor Jordán
Keyword(s):  
Complete Characterization ◽  
Partial Characterization ◽  
Reconstruction Problem ◽  
Global Rigidity ◽  
Generic Framework ◽  
Graph Reconstruction ◽  
The Family ◽  
Rigidity Property ◽  
Low Dimensional

AbstractA d-dimensional framework is a pair (G, p), where $$G=(V,E)$$ G = ( V , E ) is a graph and p is a map from V to $$\mathbb {R}^d$$ R d . The length of an edge $$uv\in E$$ u v ∈ E in (G, p) is the distance between p(u) and p(v). The framework is said to be globally rigid in $$\mathbb {R}^d$$ R d if every other d-dimensional framework (G, q), in which the corresponding edge lengths are the same, is congruent to (G, p). In a recent paper Gortler, Theran, and Thurston proved that if every generic framework (G, p) in $$\mathbb {R}^d$$ R d is globally rigid for some graph G on $$n\ge d+2$$ n ≥ d + 2 vertices (where $$d\ge 2$$ d ≥ 2 ), then already the set of (unlabeled) edge lengths of a generic framework (G, p), together with n, determine the framework up to congruence. In this paper we investigate the corresponding unlabeled reconstruction problem in the case when the above generic global rigidity property does not hold for the graph. We provide families of graphs G for which the set of (unlabeled) edge lengths of any generic framework (G, p) in d-space, along with the number of vertices, uniquely determine the graph, up to isomorphism. We call these graphs weakly reconstructible. We also introduce the concept of strong reconstructibility; in this case the labeling of the edges is also determined by the set of edge lengths of any generic framework. For $$d=1,2$$ d = 1 , 2 we give a partial characterization of weak reconstructibility as well as a complete characterization of strong reconstructibility of graphs. In particular, in the low-dimensional cases we describe the family of weakly reconstructible graphs that are rigid but not redundantly rigid.

scholarly journals NETWORK FORMATION UNDER HETEROGENEOUS COSTS: THE MULTIPLE GROUP MODEL

2007 ◽  
Vol 09 (04) ◽  
pp. 599-635 ◽  
Author(s):  
JURJEN KAMPHORST ◽  
GERARD VAN DER LAAN
Keyword(s):  
Network Formation ◽  
Group Model ◽  
Characterization Result ◽  
Full Characterization ◽  
Multiple Group ◽  
Aggregate Behavior ◽  
Multiple Groups ◽  
Do So

It is widely recognized that the shape of networks influences both individual and aggregate behavior. This raises the question which types of networks are likely to arise. In this paper we investigate a model of network formation, where players are divided into groups and the costs of a link between any pair of players are increasing in the distance between the groups that these players belong to. We give a full characterization of the networks induced by a minimal curb set for any number of groups. To do so, we show that in our multiple group model each minimal curb set is a so-called super-tight curb set, that is a minimal curb set satisfying the condition that in each state of the set every player has the same best reply. From the proof it follows that every recurrent class of an unperturbed best reply dynamics is a minimal (super-tight) curb set and reversely, which yields the characterization result. We show that in case of multiple groups networks in minimal curb sets may have features that can not occur in networks with at most two groups. Nevertheless, local centrality and center-sponsorship are still important characteristics of the networks in minimal curb sets.

scholarly journals Defining Coarsenings of Valuations

2017 ◽  
Vol 60 (3) ◽  
pp. 665-687 ◽  
Author(s):  
Franziska Jahnke ◽  
Jochen Koenigsmann
Keyword(s):  
Complete Characterization ◽  
Partial Characterization ◽  
Henselian Valuation

AbstractWe study the question of which Henselian fields admit definable Henselian valuations (with or without parameters). We show that every field that admits a Henselian valuation with non-divisible value group admits a parameter-definable (non-trivial) Henselian valuation. In equicharacteristic 0, we give a complete characterization of Henselian fields admitting a parameter-definable (non-trivial) Henselian valuation. We also obtain partial characterization results of fields admitting -definable (non-trivial) Henselian valuations. We then draw some Galois-theoretic conclusions from our results.

scholarly journals Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 2
Author(s):  
Serena Doria ◽  
Radko Mesiar ◽  
Adam Šeliga
Keyword(s):  
Linear Space ◽  
Random Variables ◽  
Aggregation Function ◽  
Full Characterization ◽  
Aggregation Functions ◽  
Bounded Below

In this paper, we explore the use of aggregation functions in the construction of coherent upper previsions. Sub-additivity is one of the defining properties of a coherent upper prevision defined on a linear space of random variables and thus we introduce a new sub-additive transformation of aggregation functions, called a revenue transformation, whose output is a sub-additive aggregation function bounded below by the transformed aggregation function, if it exists. Method of constructing coherent upper previsions by means of shift-invariant, positively homogeneous and sub-additive aggregation functions is given and a full characterization of shift-invariant, positively homogeneous and idempotent aggregation functions on [0,∞[n is presented. Lastly, some concluding remarks are added.

The structure of elementary pure birth processes

1982 ◽  
Vol 19 (03) ◽  
pp. 664-667 ◽  
Author(s):  
Dietmar Pfeifer
Keyword(s):  
Random Variables ◽  
Complete Characterization ◽  
Counting Processes ◽  
Birth Processes

A complete characterization of elementary pure birth processes is given by means of record counting processes from independent (non-identically) distributed random variables.

scholarly journals Partially-honest Nash implementation: a full characterization

2019 ◽  
Vol 70 (3) ◽  
pp. 871-904 ◽  
Author(s):  
Michele Lombardi ◽  
Naoki Yoshihara
Keyword(s):  
Social Choice ◽  
Complete Characterization ◽  
Choice Rule ◽  
Social Choice Rule ◽  
Nash Implementation ◽  
Full Characterization ◽  
Material Interest ◽  
Welfare Implications ◽  
Social Choice Rules

Abstract A partially-honest individual is a person who follows the maxim, “Do not lie if you do not have to”, to serve your material interest. By assuming that the mechanism designer knows that there is at least one partially-honest individual in a society of $$ n\ge 3$$ n ≥ 3 individuals, a social choice rule that can be Nash implemented is termed partially-honestly Nash implementable. The paper offers a complete characterization of the (unanimous) social choice rules that are partially-honestly Nash implementable. When all individuals are partially-honest, then any (unanimous) rule is partially-honestly Nash implementable. An account of the welfare implications of partially-honest Nash implementation is provided in a variety of environments.

scholarly journals A method for complete characterization of complex germline rearrangements from long DNA reads

2019 ◽  
Author(s):  
Satomi Mitsuhashi ◽  
Sachiko Ohori ◽  
Kazutaka Katoh ◽  
Martin C Frith ◽  
Naomichi Matsumoto
Keyword(s):  
Chromosomal Rearrangements ◽  
Complete Characterization ◽  
Chromosomal Translocations ◽  
Full Characterization ◽  
Complex Chromosomal Rearrangements ◽  
Copy Number Changes ◽  
Genomic Disorders ◽  
Different Order ◽  
Automatic Algorithm

AbstractMany genetic/genomic disorders are caused by genomic rearrangements. Standard methods can often characterize these variations only partly, e.g. copy number changes. We describe full characterization of complex chromosomal rearrangements, based on whole-genome-coverage sequencing of long DNA reads from four patients with chromosomal translocations. We developed a new analysis pipeline, which filters out rearrangements seen in humans without the same disease, reducing the number of loci per patient from a few thousand to a few dozen. For one patient with two reciprocal chromosomal translocations, we find that the translocation points have complex rearrangements of multiple DNA fragments involving 5 chromosomes, which we could order and orient by an automatic algorithm, thereby fully reconstructing the rearrangement. Some important properties of these rearrangements, such as sequence loss, are holistic: they cannot be inferred from any part of the rearrangement, but only from the fully-reconstructed rearrangement. In this patient, the rearrangements were evidently caused by shattering of the chromosomes into multiple fragments, which rejoined in a different order and orientation with loss of some fragments. Our approach promises to fully characterize many congenital germline rearrangements, provided they do not involve poorly-understood loci such as centromeric repeats.

Full Characterization of a Tool Steel Texture and Microstructure by Using Fast Simultaneous EBSD/EDS Measurements

2011 ◽  
Vol 172-174 ◽  
pp. 1290-1295 ◽  
Author(s):  
Daniel Goran
Keyword(s):  
Tool Steel ◽  
Electron Backscatter Diffraction ◽  
Complete Characterization ◽  
Full Characterization ◽  
Multiphase Materials ◽  
Submicron Scale ◽  
Different Types ◽  
The Matrix ◽  
Backscatter Diffraction

The study presents the latest developments in terms of speed and integration of theelectron backscatter diffraction(EBSD) and energy dispersive spectroscopy (EDS) techniques. The microstructural features and texture of a commercially available tool steel have been analyzed by simultaneous EBSD/EDS measurements. The EDS data was used for confirming/correcting the EBSD results as well as for detecting the presence of ultrafine carbide precipitates. The results indicate the formation of two different types of carbides inside a ferritic matrix. Most of the matrix was found to be composed of fully recrystallized grains with average diameters around 10 microns. Zones characterized by finer submicron scale grains could also be identified locally as well as grains containing networks of subgrain boundaries. This study demonstrates that the combination of the two techniques, i.e. EBSD and EDS, results in a powerful tool for a fast, reliable and complete characterization of multiphase materials.

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