32,668 results
Search Results
2. Partner choice correlates with fine scale kin structuring in the paper wasp Polistes dominula
- Author
-
Paul J. Parsons, Jeremy Field, and Lena Grinsted
- Subjects
0106 biological sciences ,0301 basic medicine ,Topography ,Heredity ,Wasps ,NERC ,Social Sciences ,01 natural sciences ,Nesting Behavior ,Habits ,Nest ,Psychology ,Inbreeding ,Islands ,education.field_of_study ,Multidisciplinary ,Behavior, Animal ,biology ,Agricultural and Biological Sciences(all) ,Eusociality ,Spring ,Databases as Topic ,Physical Sciences ,NE/M003191/1 ,Medicine ,Female ,Seasons ,Research Article ,Statistical Distributions ,Kin recognition ,Permutation ,Science ,Population ,Cuticular Hydrocarbons ,Insect Physiology ,Polistes dominula ,NE/K00655X/1 ,010603 evolutionary biology ,Nesting Habits ,03 medical and health sciences ,Genetics ,Animal Physiology ,Animals ,Social Behavior ,education ,General ,Invertebrate Physiology ,Paper wasp ,Evolutionary Biology ,Behavior ,Landforms ,Population Biology ,Discrete Mathematics ,Biochemistry, Genetics and Molecular Biology(all) ,Biology and Life Sciences ,RCUK ,Geomorphology ,Probability Theory ,biology.organism_classification ,Statistical Dispersion ,030104 developmental biology ,Natal homing ,Combinatorics ,Evolutionary biology ,Earth Sciences ,Philopatry ,Zoology ,Entomology ,Population Genetics ,Mathematics - Abstract
Cooperation among kin is common in animal societies. Kin groups may form by individuals directly discriminating relatives based on kin recognition cues, or form passively through natal philopatry and limited dispersal. We describe the genetic landscape for a primitively eusocial wasp, Polistes dominula, and ask whether individuals choose cooperative partners that are nearby and/or that are genetic relatives. Firstly, we genotyped an entire sub-population of 1361 wasps and found genetic structuring on an extremely fine scale: the probability of finding genetic relatives decreases exponentially within just a few meters of an individual’s nest. At the same time, however, we found a lack of genetic structuring between natural nest aggregations within the population. Secondly, in a separate dataset where ~2000 wasps were genotyped, we show that wasps forced experimentally to make a new nest choice tended to choose new nests near to their original nests, and that these nests tended to contain some full sisters. However, a significant fraction of wasps chose nests that did not contain sisters, despite sisters being present in nearby nests. Although we cannot rule out a role for direct kin recognition or natal nest-mate recognition, our data suggest that kin groups may form via a philopatric rule-of-thumb, whereby wasps simply select groups and nesting sites that are nearby. The result is that most subordinate helpers obtain indirect fitness benefits by breeding cooperatively.
- Published
- 2019
3. Abelian powers in paper-folding words
- Author
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Holub, Štěpán
- Subjects
- *
ABELIAN groups , *PAPER arts , *VOCABULARY , *ARBITRARY constants , *ALGEBRA , *COMBINATORICS - Abstract
Abstract: We show that paper-folding words contain arbitrarily large abelian powers. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
4. Menon-type identities again: A note on a paper by Li, Kim and Qiao
- Author
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László Tóth, Pentti Haukkanen, Informaatioteknologian ja viestinnän tiedekunta - Faculty of Information Technology and Communication Sciences, and Tampere University
- Subjects
Combinatorics ,Identity (mathematics) ,Character (mathematics) ,Mathematics - Number Theory ,Simple (abstract algebra) ,General Mathematics ,Matematiikka - Mathematics ,Arithmetic function ,Function (mathematics) ,11A07, 11A25 ,Type (model theory) ,Mathematics - Group Theory ,Mathematics - Abstract
We give common generalizations of the Menon-type identities by Sivaramakrishnan (1969) and Li, Kim, Qiao (2019). Our general identities involve arithmetic functions of several variables, and also contain, as special cases, identities for gcd-sum type functions. We point out a new Menon-type identity concerning the lcm function. We present a simple character free approach for the proof., Comment: 14 pages
- Published
- 2019
5. A letter concerning Leonetti's paper 'Continuous Projections onto Ideal Convergent Sequences'
- Author
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Tomasz Kania
- Subjects
Mathematics::Functional Analysis ,Applied Mathematics ,010102 general mathematics ,46B20, 46B26 (primary), and 40A35 (secondary) ,Space (mathematics) ,Quotient space (linear algebra) ,01 natural sciences ,Functional Analysis (math.FA) ,010101 applied mathematics ,Combinatorics ,Mathematics - Functional Analysis ,Mathematics (miscellaneous) ,FOS: Mathematics ,Uncountable set ,Ideal (ring theory) ,Family of sets ,0101 mathematics ,Mathematics - Abstract
Leonetti proved that whenever $${\mathcal {I}}$$ is an ideal on $${\mathbb {N}}$$ such that there exists an uncountable family of sets that are not in $${\mathcal {I}}$$ with the property that the intersection of any two distinct members of that family is in $${\mathcal {I}}$$ , then the space $$c_{0,{\mathcal {I}}}$$ of sequences in $$\ell _\infty $$ that converge to 0 along $${\mathcal {I}}$$ is not complemented. We provide a shorter proof of a more general fact that the quotient space $$\ell _\infty / c_{0,{\mathcal {I}}}$$ does not even embed into $$\ell _\infty $$ .
- Published
- 2018
6. Partner choice correlates with fine scale kin structuring in the paper wasp Polistes dominula.
- Author
-
Parsons, Paul John, Grinsted, Lena, and Field, Jeremy
- Subjects
- *
PHILOPATRY , *WASPS , *ANIMAL societies , *PHYSIOLOGY , *NESTS , *BIRD breeding - Abstract
Cooperation among kin is common in animal societies. Kin groups may form by individuals directly discriminating relatives based on kin recognition cues, or form passively through natal philopatry and limited dispersal. We describe the genetic landscape for a primitively eusocial wasp, Polistes dominula, and ask whether individuals choose cooperative partners that are nearby and/or that are genetic relatives. Firstly, we genotyped an entire sub-population of 1361 wasps and found genetic structuring on an extremely fine scale: the probability of finding genetic relatives decreases exponentially within just a few meters of an individual’s nest. At the same time, however, we found a lack of genetic structuring between natural nest aggregations within the population. Secondly, in a separate dataset where ~2000 wasps were genotyped, we show that wasps forced experimentally to make a new nest choice tended to choose new nests near to their original nests, and that these nests tended to contain some full sisters. However, a significant fraction of wasps chose nests that did not contain sisters, despite sisters being present in nearby nests. Although we cannot rule out a role for direct kin recognition or natal nest-mate recognition, our data suggest that kin groups may form via a philopatric rule-of-thumb, whereby wasps simply select groups and nesting sites that are nearby. The result is that most subordinate helpers obtain indirect fitness benefits by breeding cooperatively. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
7. Paper or and digital : A study on combinatorics in preschool class
- Author
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van Bommel, Jorryt and Palmér, Hanna
- Subjects
Matematik ,Combinatorics ,semi-concrete ,children’s documentation ,systematization ,digital application ,Educational Sciences ,Utbildningsvetenskap ,Mathematics - Abstract
In a design research study conducted in Swedish preschool class, children were asked: In how many ways can three toy bears sit in a sofa? In the initial design cycle the children who used pictographic representations seemed to make more systematic solutions with less duplications than children who used iconic representations. A later design cycle involved a digital application that was designed to provide an opportunity to work with pictographic representations on a semi-concrete level. In this paper, we make a comparison of paper and pencil documentation made by children who have used, respective not have used; the digital application. The results indicate that working with the digital application resulted in more systematic paper and pencil documentation with fewer duplications. Titelns "or" är i konferensbidraget genomstruket.
- Published
- 2018
8. Discussion of the paper: 'Sampling schemes for generalized linear Dirichlet process random effects models' by M. Kyung, J. Gill, and G. Casella
- Author
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Antonietta Mira, Mark Girolami, and Maurizio Filippone
- Subjects
Statistics and Probability ,Combinatorics ,Hierarchical Dirichlet process ,Dirichlet process ,Applied mathematics ,Sampling (statistics) ,Statistics, Probability and Uncertainty ,Random effects model ,Mathematics - Published
- 2018
9. Corrigendum to the paper 'On the K^2 of degenerations of surfaces and the multiple point formula'
- Author
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Alberto Calabri, Ciro Ciliberto, Richard Miranda, and Flaminio Flamini
- Subjects
Pure mathematics ,deformations, degenerations, enumerative problems, singularities ,deformations ,010102 general mathematics ,Minor (linear algebra) ,Socio-culturale ,01 natural sciences ,degenerations ,Combinatorics ,Multiple point ,Section (fiber bundle) ,Mathematics (miscellaneous) ,0103 physical sciences ,enumerative problems ,Gravitational singularity ,010307 mathematical physics ,Settore MAT/03 - Geometria ,0101 mathematics ,Statistics, Probability and Uncertainty ,singularities ,Mathematics - Abstract
We correct an error in the Multiple Point Formula (7.3) in the paper mentioned in the title. This correction propagates to formulas (7.5), (7.6), (7.23) and (8.18), and it affects minor results in Section 8, where few statements require an extra assumption, but it does not affect the main results of Section 8.
- Published
- 2017
10. Special Issue SELECTED PAPERS OF EUROCOMB'13 Preface
- Author
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Negetril Jaroslav and Pellegrini M.
- Subjects
Combinatorics - Abstract
This volume contains selected scientific papers related to the EUROCOMB'13 meeting held in Pisa, from September 9th to September 13th, 2013. Based on the suggestions of the program committee members, we solicited 19 contributions (17 research papers + 2 surveys) which we believe reflect the high quality of the meeting.
- Published
- 2015
11. Comments on Y. O. Hamidoune's Paper 'Adding Distinct Congruence Classes'
- Author
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Béla Bajnok
- Subjects
Statistics and Probability ,11B75 ,Lemma (mathematics) ,Mathematics - Number Theory ,Applied Mathematics ,Mistake ,Cyclic group ,Theoretical Computer Science ,Combinatorics ,Computational Theory and Mathematics ,Congruence (geometry) ,Order (group theory) ,Abelian group ,Argument (linguistics) ,Mathematics - Abstract
The main result in Y. O. Hamidoune's paper ‘Adding distinct congruence classes' (Combin. Probab. Comput.7 (1998) 81–87) is as follows. If S is a generating subset of a cyclic group G such that 0 ∉ S and |S| ⩾ 5, then the number of sums of the subsets of S is at least min(|G|, 2|S|). Unfortunately, the argument of the author, who, sadly, passed away in 2011, relies on a lemma whose proof is incorrect; in fact, the lemma is false for all cyclic groups of even order. In this short note we point out this mistake, correct the proof, and discuss why the main result is actually true for all finite abelian groups.
- Published
- 2015
12. Complete Bernstein functions and subordinators with nested ranges. A note on a paper by P. Marchal
- Author
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Chang-Song Deng and René L. Schilling
- Subjects
Statistics and Probability ,Measurable function ,Bernstein function ,Probability (math.PR) ,complete Bernstein function ,subordinator ,Lambda ,30E20 ,Combinatorics ,Probability space ,30H15 ,Exponent ,FOS: Mathematics ,Statistics, Probability and Uncertainty ,Mathematics - Probability ,60G51 ,Mathematics - Abstract
Let $\alpha:[0,1]\to [0,1]$ be a measurable function. It was proved by P. Marchal \cite{Mar15} that the function $$ \phi^{(\alpha)}(\lambda):=\exp\left[ \int_0^1\frac{\lambda-1}{1+(\lambda-1)x}\,\alpha(x)\,d x \right],\quad \lambda>0 $$ is a special Bernstein function. Marchal used this to construct, on a single probability space, a family of regenerative sets $\mathcal R^{(\alpha)}$ such that $\mathcal{R}^{(\alpha)} \stackrel{\text{law}}{=} \overline{\{S^{(\alpha)}_t:t\geq 0\}}$ ($S^{(\alpha)}$ is the subordinator with Laplace exponent $\phi^{(\alpha)}$) and $\mathcal R^{(\alpha)}\subset \mathcal R^{(\beta)}$ whenever $\alpha\leq\beta$. We give two simple proofs showing that $\phi^{(\alpha)}$ is a complete Bernstein function and extend Marchal's construction to all complete Bernstein functions., Comment: to appear in Electron. Comm. Probab
- Published
- 2016
13. Addendum to the paper: 'Artin prime producing quadratics', by P. Moree
- Author
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Pieter Moree and Yves Gallot
- Subjects
Combinatorics ,Algebra ,Number theory ,General Mathematics ,Addendum ,Algebra over a field ,Primitive root modulo n ,Prime (order theory) ,Mathematics - Abstract
A record mentioned in the paper by Moree (Abh Math Sem Univ Hamburg 77:109–127, 2007) was recently improved on by Akbary and Scholten. However, the record mentioned was not the then record. The then record, due to Gallot (2004), actually slightly improves on that obtained recently by Akbary and Scholten.
- Published
- 2015
14. Translation of Michael Sadowsky's paper 'An elementary proof for the existence of a developable M\'obius band and the attribution of the geometric problem to a variational problem'
- Author
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Eliot Fried and Denis F. Hinz
- Subjects
Combinatorics ,Mechanics of Materials ,Mechanical Engineering ,Philosophy ,Mathematics - History and Overview ,Elementary proof ,Physics - History and Philosophy of Physics ,General Materials Science ,Translation (geometry) - Abstract
This article is a translation of Michael Sadowsky's original paper "Ein elementarer Beweis f\"ur die Existenz eines abwickelbaren M\"obiusschen Bandes und die Zur\"uckf\"uhrung des geometrischen Problems auf ein Variationsproblem." which appeared in Sitzungsberichte der Preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 17. Juli 1930, Mitteilung vom 26. Juni, 412-415. Published on September 12, 1930., Comment: 5 pages, 3 figures, to appear in a special volume of the Journal of Elasticity entitled "The Mechanics of Ribbons and M\"obius Bands", citations of this translation should refer also to Sadowsky's original paper, as cited in the Abstract
- Published
- 2014
15. Coupled-Tasks in Presence of Bipartite Compatibilities Graphs : Third International Symposium, ISCO 2014, Lisbon, Portugal, March 5-7, 2014, Revised Selected Papers
- Author
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Gilles Simonin, Jean-Claude König, Rodolphe Giroudeau, Benoit Darties, Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i), Université de Bourgogne (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique (CNRS), Insight Centre for Data Analytics [Dublin], Dublin City University [Dublin] (DCU), Méthodes Algorithmes pour l'Ordonnancement et les Réseaux (MAORE), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Laboratoire Electronique, Informatique et Image ( Le2i ), Université de Bourgogne ( UB ) -AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique ( CNRS ), Dublin City University [Dublin] ( DCU ), Méthodes Algorithmes pour l'Ordonnancement et les Réseaux ( MAORE ), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier ( LIRMM ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Arts et Métiers (ENSAM), and HESAM Université (HESAM)-HESAM Université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement
- Subjects
021103 operations research ,Theoretical computer science ,Job shop scheduling ,0211 other engineering and technologies ,Approximation algorithm ,Context (language use) ,0102 computer and information sciences ,02 engineering and technology ,[INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO] ,Star (graph theory) ,01 natural sciences ,Combinatorics ,010201 computation theory & mathematics ,Constraint graph ,Knapsack problem ,Bipartite graph ,Minification ,Mathematics ,[ INFO.INFO-RO ] Computer Science [cs]/Operations Research [cs.RO] - Abstract
International audience; We tackle the makespan minimization coupled-tasks prob- lem in presence of incompatibility constraints. In particular, we focus on stretched coupled-tasks, i.e.coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in the framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain, ...). In such context, we design efficient polynomial-time approximation algorithms according to different parameters of the scheduling problem.
- Published
- 2014
16. Interfaces with internal structures in generalized rock-paper-scissors models
- Author
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P. P. Avelino, L. Losano, D. Bazeia, B. F. de Oliveira, and José C. Menezes
- Subjects
Competitive Behavior ,Work (thermodynamics) ,Interface (Java) ,Association (object-oriented programming) ,May-Leonard models ,Structure (category theory) ,Complex system ,FOS: Physical sciences ,Context (language use) ,Predator-prey models ,Decision Support Techniques ,Combinatorics ,Development (topology) ,Game Theory ,Animals ,Computer Simulation ,Field theory (psychology) ,Statistical physics ,Physics - Biological Physics ,Cooperative Behavior ,Quantitative Biology - Populations and Evolution ,Mathematics ,Models, Statistical ,Populations and Evolution (q-bio.PE) ,Nonlinear Sciences - Adaptation and Self-Organizing Systems ,Biological Physics (physics.bio-ph) ,Predatory Behavior ,FOS: Biological sciences ,Adaptation and Self-Organizing Systems (nlin.AO) - Abstract
In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships, in the context of cyclic predator-prey models with an even number of species $N \ge 8$. We use both stochastic and field theory simulations in one and two spatial dimensions, as well as analytical arguments, to describe the association at the interfaces of mutually neutral individuals belonging to enemy partnerships and to probe their role in the development of the dynamical structures at the interfaces. We identify an interesting behaviour associated to the symmetric or asymmetric evolution of the interface profiles depending on whether $N/2$ is odd or even, respectively. We also show that the macroscopic evolution of the interface network is not very sensitive internal structure of the interfaces. Although this work focus on cyclic predator prey-models with an even number of species, we argue that the results are expected to be quite generic in the context of spatial stochastic May-Leonard models., 7 pages, 9 figures; new version, to appear in PRE
- Published
- 2013
17. An aggregation method of Markov graphs for the reliability analysis of hybrid systems ☆ [☆] Revised version of the paper presented at QUALITA 2003.
- Author
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Schoenig, Raphaël, Aubry, Jean-François, Cambois, Thierry, and Hutinet, Tony
- Subjects
- *
AUTOMOBILE industry , *SYSTEMS design , *MARKOV processes , *COMBINATORICS , *PETRI nets - Abstract
Abstract: To meet always increasing safety requirements in car industry, design and safety assessment methods are developed in order to fit the complexity of new embedded mecatronic systems. Hybrid (discrete/continuous) and dynamic features, specific to these systems, require choosing a suitable formalism. These features should also be considered in safety studies made all through the system design. The aim of this paper is to propose a quantitative analysis method based on the construction of an aggregated Markov graph, which allows a limitation of the combinatorial expansion. This graph is directly deducted from the Petri net modelling of the system. It is composed by a set of functional modes and a set of transitions to which statistical information regarding the system dynamics has been added. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
18. Erratum for the paper ‘On the chain-level intersection pairing for PL manifolds’
- Author
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J E McClure
- Subjects
Lemma (mathematics) ,Pure mathematics ,010102 general mathematics ,Partial algebra ,intersection pairing ,01 natural sciences ,Combinatorics ,Chain (algebraic topology) ,Intersection ,18D50 ,Pairing ,0103 physical sciences ,57Q65 ,partial algebra ,010307 mathematical physics ,Geometry and Topology ,0101 mathematics ,General position ,Mathematics ,Sign (mathematics) ,general position - Abstract
Greg Friedman has pointed out that there are sign errors in our paper ‘On the chain-level intersection pairing for PL manifolds’, linked above, and in particular Lemma 10.5(b) (which is a key step in the proof of the main theorem) is not correct as stated. ¶ The purpose of this note is to provide a correction.
- Published
- 2009
19. Corrigendum to the paper 'Quadratic Class Numbers Divisible by 3' (Functiones et Approximatio 37 (2007), 203--211)
- Author
-
D.R. Heath-Brown
- Subjects
Combinatorics ,Class (set theory) ,Quadratic equation ,11J70 ,11K60 ,General Mathematics ,Mathematics - Published
- 2010
20. Remarks on a paper of M. Ochiai
- Author
-
Alberto Cavicchioli and Fulvia Spaggiari
- Subjects
Combinatorics ,Fundamental group ,Sequence ,Reduction (recursion theory) ,Number theory ,Mathematics::Complex Variables ,General Mathematics ,Isotopy ,Order (group theory) ,Band sum ,Mathematics::Geometric Topology ,Heegaard splitting ,Mathematics - Abstract
This note is related to a nice short paper of M. Ochiai. We prove in a very fast way that the two-parameter family of Heegaard diagrams, constructed by Ochiai, encodes the genuine three-sphere. The result is obtained, up to isotopy, by using a sequence of only three moves in this order: a Whitehead–Zieschang reduction, a band sum and a cancellation of a handle.
- Published
- 2006
21. Note on a paper by A. Granville and K. Soundararajan
- Author
-
Jie Wu, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Wu, Jie
- Subjects
Discrete mathematics ,Algebra and Number Theory ,Distribution (number theory) ,010102 general mathematics ,Equal probability ,01 natural sciences ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,Combinatorics ,symbols.namesake ,Results on L(1,χ) ,\chi)$ ,0103 physical sciences ,symbols ,Results on $L(1 ,010307 mathematical physics ,11M20 ,0101 mathematics ,Random variable ,Euler product ,[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] ,Mathematics - Abstract
In this note, we improve some results of Granville and Soundararajan on the distribution of values of the truncated random Euler product L ( 1 , X ; y ) : = ∏ p ⩽ y ( 1 − X ( p ) / p ) −1 , where the X ( p ) are independent random variables, taking the values ±1 with equal probability p / 2 ( p + 1 ) and 0 with probability 1 / ( p + 1 ) .
- Published
- 2007
22. Plenary Papers A Priori Truncation Error Bounds for Continued Fractions
- Author
-
Lisa Lorentzen
- Subjects
Sequence ,40A15 ,convergence ,Truncation error (numerical integration) ,General Mathematics ,Mathematical analysis ,complementary error function ,incomplete gamma function ,30B10 ,Upper and lower bounds ,Limit periodic continued fractions ,Combinatorics ,Error function ,truncation error estimates ,Fraction (mathematics) ,Limit (mathematics) ,Incomplete gamma function ,Gamma function ,Mathematics - Abstract
Most of the known continued fraction expansions of special functions are limit periodic. This means that the classical approximants S n (0) are normally not the best ones to use for approximations. In this paper we suggest a number of approximants S n (w n ) which converge faster. The estimation of the improvement and bounds for the error |f - Sn(wn)| (which we still call the truncation error) are mainly obtained by means of Thron's parabola sequence theorem and the oval sequence theorem.
- Published
- 2003
23. Hierarchical package bidding: A paper & pencil combinatorial auction
- Author
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Goeree, Jacob K. and Holt, Charles A.
- Subjects
- *
COMBINATORICS , *EXPERIMENTS , *AUCTIONS , *COORDINATES , *GAME theory , *COMPUTATIONAL complexity - Abstract
Abstract: We introduce a new combinatorial auction format based on a simple, transparent pricing mechanism tailored for the hierarchical package structure proposed by Rothkopf, Pekeč, and Harstad to avoid computational complexity [Rothkopf, M., Pekeč, A., Harstad, R., 1998, Computationally manageable combinatorial auctions. Manage. Sci. 44, 1131–1147]. This combination provides the feedback necessary for bidders in multi-round auctions to discern winning bidding strategies for subsequent rounds and to coordinate responses to aggressive package bids. The resulting mechanism is compared to two leading alternatives in a series of laboratory experiments involving varying degrees of value synergies. Based on these “wind tunnel” tests the FCC has decided to use hierarchical package bidding in a segment of the upcoming 700 MHz auction. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
24. A REMARK ON A PAPER OF BLASCO
- Author
-
Z. Ercan
- Subjects
Discrete mathematics ,point evaluating homomorphism ,Algebra homomorphism ,General Mathematics ,Subalgebra ,Hausdorff space ,Mathematics::General Topology ,algebra homomorphisms ,Coimage ,54C35 ,Combinatorics ,countable evaluating homomorphism ,Bounded function ,Lindelöf space ,Homomorphism ,46E25 ,Group homomorphism ,Mathematics - Abstract
We generalize and give a simple proof of a Theorem of Blasco. For a topological space X , C(X) denotes the algebra of real valued continuous functions on X under the operation (αf + gh)(x) := αf(x) + h(x)g(x) for each f, g, h ∈ C(X) and α ∈ R. An algebra A on X means a subalgebra of C(X) which contains the constant functions. By a ∗-algebra A on X we mean an algebra on X and all bounded functions in A separate points from the closed sets. Let A be an algebra on X and π : A −→ R be a (algebra) homomorphism and α be a cardinal number. π is said to be α-evaluating if for each subset B of A with cardinality at most α there exits xB ∈ X such that π(f) = f(xB) for each f ∈ B. If α = |N|(=the cardinal number of the set of the natural numbers N), the α-evaluating homomorphism is called countable evaluating. Let α be a cardinal number. Recall that a topological space X is called αLindelof if for each open cover U has a subcover V such that the cardinality of V is at most α. A lindelof space means a |N|-Lindelof space. The following theorem is given in [1] as one of the main results. Theorem 1. Let X be a completely regular Hausdorff space. Then X is Lindelof if and only if each countable evaluating homomorphism π on a ∗-algebra A on X is point evaluating. Received June 9, 2004; accepted June 30, 2004. Communicated by Bor-Luh Lin. 2000 Mathematics Subject Classification: Primary 54C35, 46E25.
- Published
- 2006
25. Higher-order tangents and Fefferman's paper on Whitney's extension problem
- Author
-
Wiesław Pawłucki, Edward Bierstone, and Pierre D. Milman
- Subjects
Combinatorics ,Mathematics (miscellaneous) ,Conjecture ,Continuous function ,Iterated function ,Whitney conditions ,Calculus ,Order (group theory) ,Function (mathematics) ,Extension (predicate logic) ,Statistics, Probability and Uncertainty ,Divided differences ,Mathematics - Abstract
Whitney [W2] proved that a function defined on a closed subset of R is the restriction of a Cm function if the limiting values of all mth divided differences form a continuous function. We show that Fefferman?s solution of Whitney?s problem for Rn [F, Th. 1] is equivalent to a variant of our conjecture in [BMP2] giving a criterion for Cm extension in terms of iterated limits of finite differences.
- Published
- 2006
26. Special Invited Paper: Geodesics And Spanning Tees For Euclidean First-Passage Percolaton
- Author
-
Charles M. Newman and C. Douglas Howard
- Subjects
Statistics and Probability ,Spanning tree ,Geodesic ,82D30 ,random surface ,First passage percolation ,Poisson process ,Infimum and supremum ,Euclidean distance ,Combinatorics ,random metric ,firstpassage percolation ,60K35 ,Lattice (order) ,minimal spanning tree ,shape theorem ,Almost surely ,combinatorial optimization ,60G55 ,Statistics, Probability and Uncertainty ,First-hitting-time model ,geodesic ,Mathematics ,60F10 - Abstract
The metric $D_{\alpha}(q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $\mathbb{R}^d$ , defined as the infimum of $(\sum_i |q_i - q_{i+1}|^{\alpha})^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending with $q'$ (where $|·|$ denotes Euclidean distance) has nontrivial geodesics when $\alpha>1$. The cases $1< \alpha
- Published
- 2001
27. Progressive nucleation mechanism for the growth behavior of items and its application to cumulative papers and citations of individual authors
- Author
-
Keshra Sangwal
- Subjects
Cumulative citations ,Computer science ,Nucleation ,General Social Sciences ,Social Sciences(all) ,Cumulative papers ,Function (mathematics) ,Library and Information Sciences ,Article ,Progressive nucleation mechanism (PNM) ,Computer Science Applications ,Combinatorics ,Statistics ,Individual authors ,Exponent ,Growth behavior of items ,Fraction (mathematics) ,General expression ,Law - Abstract
A general expression based on the concepts of the progressive nucleation mechanism is proposed in the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha (t) = \frac{N(t)}{C} = \left[ {1 - \exp \left\{ { - \left( {\frac{t}{\Uptheta }} \right)^{q} } \right\}} \right] $$\end{document} to describe the growth behavior of items in an individual system and a collective of systems. In the above relation, α(t) is the ratio of items N(t) at time t to the maximum number C of possible items for the system, Θ is the corresponding time constant and q is the exponent. The above relation is then used to analyze: (1) the growth behavior of cumulative number N(t) of papers published by individual authors and cumulative citations L(t) of N(t) papers of an author as a function of citation duration t, and (2) the relationship between cumulative citations L(t) of papers and cumulative number N(t) of papers. The proposed approach predicts that: (1) the fraction of items produced by successive systems is additive, (2) the cumulative fraction αsum(t) of maximum number of sites is the sum of contributions of fractions of maximum number of items produced by different systems, and (3) the values of time constants Θ and exponent q increase with the addition of fraction of items produced by subsequent systems, but their values are the lowest for individual systems. The approach is applied to explain the growth behavior of cumulative N(t) papers and L(t) citations of four selected Polish professors.
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28. Understanding normal and restricted normal products in soft directed graphs.
- Author
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Jose, Jinta, George, Bobin, Thumbakara, Rajesh K., and George, Sijo P.
- Subjects
DIRECTED graphs ,SOFT sets ,COMBINATORICS ,UNCERTAINTY ,GRAPH theory - Abstract
This paper extends the framework of soft set theory to directed graphs by introducing and analyzing the concepts of the normal product and restricted normal product of soft directed graphs. Building on Molodtsov’s foundational work in developing soft set theory to address uncertainty in data, this study presents new methods for modeling and understanding complex systems where uncertainty plays a significant role. Soft directed graphs, which enhance traditional graph models by incorporating parameters and uncertain relationships, serve as the foundation for this investigation. The normal product, defined as a combination of two soft directed graphs based on their respective parameter sets, and the restricted normal product, which combines soft directed graphs only where their parameter sets intersect, provide a comprehensive framework for these new operations. This paper also establishes the structural properties of these products, ensuring they are well-defined and retain the key features of soft directed graphs. Furthermore, we derive combinatorial identities related to vertex and arc counts, as well as degree sums, offering deeper insights into the composition and behavior of these graph products. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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29. Stepping Stone Problem on Graphs.
- Author
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O'Dwyer, Rory
- Subjects
SET functions ,GRAPH theory - Abstract
This paper formalizes the stepping stone problem introduced Ladoucer and Rebenstock [G] to the setting of simple graphs. This paper considers the set of functions from the vertices of our graph to N, which assign a fixed number of 1's to some vertices and assign higher numbers to other vertices by adding up their neighbors' assignments. The stepping stone solution is defined as an element obtained from the argmax of the maxima of these functions, and the maxima as its growth. This work is organized into work on the bounded and unbounded degree graph cases. In the bounded case, sufficient conditions are obtained for superlinear and sublinear stepping stone solution growth. Furthermore this paper demonstrates the existence of a basis of graphs which characterizes superlinear growth. In the unbounded case, properly sublinear and superlinear stepping stone solution growth are obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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30. A heuristic for the Minimum Score Separation Problem, a combinatorial problem associated with the cutting stock problem.
- Author
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Becker, Kai Helge and Appa, Gautam
- Subjects
HEURISTIC algorithms ,COMBINATORICS ,CUTTING stock problem ,PAPER industry ,COMPUTATIONAL complexity - Abstract
The Minimum Score Separation Problem (MSSP) is a combinatorial problem that was introduced in JORS 55 as an open problem in the paper industry arising in conjunction with the cutting stock problem. During the process of producing boxes, flat papers are prepared for folding by being scored with knives. The problem is to determine whether and how a given production pattern of boxes can be arranged such that a certain minimum distance between the knives can be kept. Introducing the concept of matching-based alternating Hamiltonian paths, this paper models the MSSP as the problem of finding an alternating Hamiltonian path on a graph that is the union of a matching and a type of graph known as a 'threshold graph'. On this basis, we find a heuristic that can quickly recognize a large percentage of feasible and infeasible instances of the MSSP. Detailed computational experiments demonstrate the efficiency of our approach. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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31. Addendum to our paper 'The Schwarz-Pick lemma for circle packings'
- Author
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Alan F. Beardon and Kenneth Stephenson
- Subjects
Combinatorics ,Lemma (mathematics) ,52C15 ,Circle packing ,General Mathematics ,57M15 ,30C80 ,Addendum ,31C20 ,Mathematics - Published
- 1992
32. SELECTION AND DESIGN OF HEURISTIC PROCEDURES FOR SOLVING ROLL TRIM PROBLEMS.
- Author
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Haessler, Robert W.
- Subjects
PAPER industry ,PROBLEM solving ,HEURISTIC ,COMBINATORICS ,DECISION making ,METHODOLOGY ,OPERATIONS research ,MANAGEMENT science ,LINEAR programming ,PAPER mills ,MANAGEMENT - Abstract
This paper discusses the selection and design of heuristic procedures for solving one-dimensional roll trim problems. These are well-defined combinatorial problems which are too large to optimize. Five different roll trim problems from the paper and film industries are described along with the heuristic procedures that have been used successfully to improve the quality of the solutions generated. The paper concludes with some general guidelines for developing "industrial-grade" heuristic problem solving procedures. [ABSTRACT FROM AUTHOR]
- Published
- 1988
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33. Some Basic Properties of the Second Multiplicative Zagreb Eccentricity Index.
- Author
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Azari, Mahdieh
- Subjects
GRAPH grammars ,INDEXES ,GRAPH theory ,COMBINATORICS ,EXTREMAL problems (Mathematics) ,TOPOLOGICAL dynamics - Abstract
The second multiplicative Zagreb eccentricity index E*
2 (G) of a simple connected graph G is expressed as the product of the weights ε(a)εG(b) over all edges ab of G, where ε(a) stands for the eccentricity of the vertex a in G. In this paper, some extremal problems on the E*2 index over some special graph classes including trees, unicyclic graphs and bicyclic graphs are examined, and the corresponding extremal graphs are characterized. Besides, the relationships between this vertex-eccentricity-based graph invariant and some well-known parameters of graphs and existing graph invariants such as the number of vertices, number of edges, minimum vertex degree, maximum vertex degree, eccentric connectivity index, connective eccentricity index, first multiplicative Zagreb eccentricity index and second multiplicative Zagreb index are investigated. [ABSTRACT FROM AUTHOR]- Published
- 2024
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34. Fuzzy logics – quantitatively.
- Author
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Kostrzycka, Zofia and Zaionc, Marek
- Subjects
FUZZY logic ,MANY-valued logic ,REAL numbers ,COMBINATORICS ,GENERATING functions - Abstract
The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length built with exactly one variable. Then, we investigate such proportion for satisfiable formulas. Second, we generalise our investigation on formulas written with $ k\ge 1 $ k ≥ 1 variables. The primary goal of the paper is the research on the asymptotic behaviour of these fractions when the length n tends to infinity. If such limits exists, they are real numbers between 0 and 1, which are called the density of truth or the density of SAT. To compare the density of truth and the density of satisfiable formulas for both fragments of 3-valued Gödel–Dummett's and Łukasiewicz's logics we use the powerful theory of analytic combinatorics. This paper is a natural continuation of the previous brief conference note by Kostrzycka and Zaionc (2020) as well as enriched with some previous results from Kostrzycka and Zaionc (2003). In the conference note we computed analytically the density of truth and the density of SAT (with a determined precision) for 3-valued Łukasiewicz's logic restricted to a language with only one variable. In Kostrzycka and Zaionc (2003) we computed the same values for exactly the same fragment of the 3-valued Gödel–Dummett logic. This paper answers the more general questions of the existence of density of truth and density of SAT for both many-valued logics with an arbitrary finite number of variables. Therefore this paper gives an an interesting picture of two main families of finite-valued fuzzy logics problems treated quantitatively. This picture is taken from the perspective of classical logic. It shows that unexpectedly there is quantitatively a little distance between these two approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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35. SOME CRITICAL REMARKS ON THE PAPER: "AN ESSENTIAL REMARK ON FIXED POINT RESULTS ON MULTIPLICATIVE METRIC SPACES".
- Author
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DOŠENOVIĆ, TATJANA and RADENOVIĆ, STOJAN
- Subjects
- *
FIXED point theory , *MULTIPLICATION , *METRIC spaces , *TOPOLOGY , *COMBINATORICS - Abstract
In this short note we generalize, complement and improve recent result on multiplicative metric spaces established by R.P. Agarwal et al. [Ravi P. Agarwal, Erdal Karapinar and Bessem Samet: An essential remark on fixed point results on multiplicative metric spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2017
36. FASHION, PAPER DOLLS AND MULTIPLICATIVES.
- Author
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Ura, Suzana Kaori, Stein-Barana, Alzira C. M., and Munhoz, Deisy P.
- Subjects
- *
MULTIPLICATION , *PAPER dolls , *CREATIVE teaching , *COMBINATORICS , *MATHEMATICS teachers - Abstract
The article focuses on the proposal to utilize fashion and paper dolls to assist mathematics teachers in teaching the students on multiplicative principle in Great Britain. The proposal aims to help the children understand multiplication much easier through integrating fashion and paper cut outs which are entertaining and an enjoying activity. It notes that the method enhance the child's imagination, creativity, combinatorics and logic.
- Published
- 2011
37. A performance investigation of small-bore sewers.
- Author
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Memon, F. A., Fidar, A., Littlewood, K., Butler, D., Makropoulos, C., and Liu, S.
- Subjects
SEWERAGE ,HYDRAULIC models ,PERFORMANCE ,INDUSTRIAL efficiency ,WASTEWATER treatment ,PLUMBING industry ,TOILET paper ,COMBINATORICS ,INDUSTRIAL wastes - Abstract
This paper describes a full-scale physical model and its application to investigate the effectiveness/performance of small-bore sewers for a range of operational and design parameters. The implementation methodology involves observing the movement of synthetic gross solids in three small bore sewers (150, 100 and 75 mm diameter) for different volumes of simulated flush waves and gradients. The simulated flush waves were generated, using an automated wave sequencer, for three different flush volumes (3, 4.5 and 6 likes). To investigate the impact of solid shape factor, a number of tests were carried out using synthetic solids in combination with toilet tissue paper. In total, more than 1,000 tests were performed for different operational and design parameter combinations. Results obtained to date have confirmed earlier studies, particularly with respect to the role of flush volume in solids transport, and identified the impact of gradient variation and its significance particularly in small-bore sewers receiving low flush volume. Results from the physical model application exercise will be used to propose new design guidelines for wastewater collection systems with specific consideration to new developments and inform the decision support system, currently being developed as pan of a research project on water cycle management for new developments (WAND). [ABSTRACT FROM AUTHOR]
- Published
- 2007
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38. Multi-Population-Based Algorithm with an Exchange of Training Plans Based on Population Evaluation.
- Author
-
Łapa, Krystian, Cpałka, Krzysztof, Kisiel-Dorohinicki, Marek, Paszkowski, Józef, Dębski, Maciej, and Le, Van-Hung
- Subjects
ALGORITHMS ,ARTIFICIAL neural networks ,COMPUTER simulation ,MATHEMATICAL formulas ,COMBINATORICS - Abstract
Population Based Algorithms (PBAs) are excellent search tools that allow searching space of parameters defined by problems under consideration. They are especially useful when it is difficult to define a differentiable evaluation criterion. This applies, for example, to problems that are a combination of continuous and discrete (combinatorial) problems. In such problems, it is often necessary to select a certain structure of the solution (e.g. a neural network or other systems with a structure usually selected by the trial and error method) and to determine the parameters of such structure. As PBAs have great application possibilities, the aim is to develop more and more effective search formulas used in them. An interesting approach is to use multiple populations and process them with separate PBAs (in a different way). In this paper, we propose a new multi-population-based algorithm with: (a) subpopulation evaluation and (b) replacement of the associated PBAs subpopulation formulas used for their processing. In the simulations, we used a set of typical CEC2013 benchmark functions. The obtained results confirm the validity of the proposed concept. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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- View/download PDF
39. IPDPS 2014 Selected Papers on Numerical and Combinatorial Algorithms.
- Author
-
Benoit, Anne
- Subjects
- *
PUBLISHING , *PERIODICAL publishing , *PERIODICAL articles , *COMBINATORICS , *MATHEMATICAL periodicals - Published
- 2015
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40. Recognizing brittle graphs: remarks on a paper of Hoàng and Khouzam
- Author
-
Alejandro A. Schäffer
- Subjects
Combinatorics ,Discrete mathematics ,Indifference graph ,Pathwidth ,Clique-sum ,Chordal graph ,Applied Mathematics ,Strong perfect graph theorem ,Discrete Mathematics and Combinatorics ,Cograph ,Split graph ,1-planar graph ,Mathematics - Abstract
A graph is perfect if the size of the maximum clique equals the chromatic number in every induced subgraph. Chvatal defined a subclass of perfect graphs known as perfectly-orderable graphs, which have the property that a special ordering on the vertices leads to a trivial algorithm to find an optimum coloring. He also identified a subclass of the perfectly-orderable graphs, which he called brittle graphs, characterized by the property that every nonempty induced subgraph contains a vertex x such that x is either not an endpoint of a P 4 or is not in the middle of a P 4 . The brittle graphs were studied in a recent paper of Hoang and Khouzam [J. Graph Theory 12 (1988) 391-404] where the authors gave alternate characterizations one of which leads to an O( n 3 m ) time recognition algorithm for brittle graphs, where n is the number of vertices and m is the number of edges. In contrast, no polynomial-time recognition algorithms are known for either perfect graphs or perfectly-orderable graphs. We point out that an O( n 2 m ) time recognition algorithm for brittle graphs can be derived from Chvatal's definition, and we present a more complicated O( m 2 ) time recognition algorithm.
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41. Enumeration of the Multiple-Outage Missed-Thrust Problem.
- Author
-
Pekosh, Jeffrey and Longuski, James M.
- Abstract
Enumeration of the problem space for the multiple-outage missed-thrust problem is a significant factor for determining what types of analysis is feasible to conduct. An exhaustive examination of the multiple-outage problem is one method for conducting missed-thrust analysis. In this paper, we explore the combinatorics of the problem, providing methods of calculating and estimating the number of possible missed-thrust cases when discretizing a trajectory to consider the effects of multiple missed-thrust events. We examine the difficulties of enumerating all possible cases, and examine when it may be desirable to conduct an exhaustive enumeration rather than a stochastic Monte-Carlo-type analysis. For missions which cover large time scales or feature high resolutions for their analysis, the combinatorics of the problem quickly grow excessively large, but the exhaustive formulation can still provide useful insight for smaller problems or with the right assumptions. We also explore various sub-problems, and their enumeration, such as the partial-thrust problem and the consideration of only critical regions of the trajectory, their potential applicability to the field of missed-thrust analysis, and connections to mathematical topics. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Ranks of compositionally closed minimal reaction systems.
- Author
-
Intekhab, Husain, Lim, Johnny, and Teh, Wen Chean
- Abstract
A reaction system is a computational model motivated by the functioning of living cells. In previous studies, Ehrenfeucht et al. have classified the functions specified by minimal reaction systems. Several studies have focused on the reaction system ranks of functions specified by minimal reaction systems, where the rank pertains to the minimum size of a specifying reaction system. This paper focuses on reaction system rank for a class of union-additive functions specified by minimal reaction systems introduced by Salomaa, which are closed under composition. More precisely, we establish a sufficient condition for the equality of reaction system ranks for functions belonging to the class. Then we study the reaction system ranks of such functions with signature sizes one and two, as well as those with one-to-one signatures, specifically over ternary and quaternary alphabets. Lastly, we establish a lower upper bound of reaction system ranks of such functions with one-to-one signatures for | S | ≥ 5. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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43. Infinite families of minimal binary codes via Krawtchouk polynomials.
- Author
-
Du, Xiaoni, Rodríguez, René, and Wu, Hao
- Subjects
BINARY codes ,LINEAR codes ,BOOLEAN functions ,POLYNOMIALS ,COMBINATORICS ,DATA warehousing ,QUANTUM cryptography - Abstract
Linear codes play a crucial role in various fields of engineering and mathematics, including data storage, communication, cryptography, and combinatorics. Minimal linear codes, a subset of linear codes, are particularly essential for designing effective secret sharing schemes. In this paper, we introduce several classes of minimal binary linear codes by carefully selecting appropriate Boolean functions. These functions belong to a renowned class of Boolean functions, namely, the general Maiorana–McFarland class. We employ a method first proposed by Ding et al. (IEEE Trans Inf Theory 64(10):6536–6545, 2018) to construct minimal codes violating the Ashikhmin–Barg bound (wide minimal codes) by using Krawtchouk polynomials. The lengths, dimensions, and weight distributions of the obtained codes are determined using the Walsh spectrum distribution of the chosen Boolean functions. Our findings demonstrate that a vast majority of the newly constructed codes are wide minimal. Furthermore, our proposed codes exhibit a significantly larger minimum distance, in some cases, compared to some existing similar constructions. Finally, we address this method, based on Krawtchouk polynomials, more generally, and highlight certain generic properties related to it. These general results offer insights into the scope of this approach. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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44. Approximating the α-permanent
- Author
-
KOU, S. C. and McCULLAGH, P.
- Published
- 2009
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45. 2005 Information Theory Society Paper Award.
- Subjects
- *
INFORMATION theory , *ASSOCIATIONS, institutions, etc. , *PERIODICALS , *CODING theory , *COMBINATORICS , *INFORMATION science , *AWARDS - Abstract
The article presents information on the 2005 Information Theory Society Paper Award, which is given annually to for a valuable publication in the field of information theory. This year the award was jointly awarded to researchers Shuo-Yen Robert Li, Raymond W. Yeung, and Ning Cai for their paper "Linear Network Coding" which appeared in the February 2003 issue of the journal "IEEE Transactions on Information Theory." Shuo-Yen Robert Li has done his B.S. in mathematics from National Taiwan University in 1970 and Ph.D. in mathematics from the University of California, Berkeley, in 1974. Yeung was born in Hong Kong on June 3, 1962. He has done B.S., M.Eng., Ph.D. in electrical engineering from Cornell University in Ithaca, New York. His research work include information theory and network coding. Ning Cai has done his B.S. in mathematics from the Normal College of Beijing in Beijing, China in 1982. He completed his Ph.D. in mathematics from the University of Bielefeld in Bielefeld, Germany in 1988. He has done research in the field of combinatorics, information theory and their applications.
- Published
- 2006
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46. On a paper of Lang and Maslamani
- Author
-
L. Andrew Campbell
- Subjects
Combinatorics ,Algebra ,Polynomial (hyperelastic model) ,symbols.namesake ,Monomial ,Algebra and Number Theory ,Degree (graph theory) ,Jacobian matrix and determinant ,symbols ,Field (mathematics) ,Automorphism ,Constant (mathematics) ,Mathematics - Abstract
Let k be a field of characteristic 0, and let f : k n →k n be a polynomial map with components of the form f i = x i + h i , where the h i are monomials. If the Jacobian determinant of the map f is a nonzero constant, then f is a tame automorphism. If, in addition, each h i is either constant or of degree 2 or more, then f is linearly triangularizable.
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47. First passage times of general sequences of random vectors: A large deviations approach11Some of the results in this paper were originally contained in the author’s Ph.D. dissertation, written at the University of Wisconsin-Madison under the supervision of Professor Peter Ney
- Author
-
Jeffrey F. Collamore
- Subjects
Statistics and Probability ,Sequence ,Applied Mathematics ,Combinatorics ,Large deviations ,Law of large numbers ,Modeling and Simulation ,Modelling and Simulation ,Probability distribution ,Large deviations theory ,First-hitting-time model ,Random variable ,Rate function ,Scaling ,First passage times ,Mathematics - Abstract
Suppose Y1;Y2;:::R d is a sequence of random variables such that the probability law of Yn=n satises the large deviation principle and suppose AR d . Let T(A)=inffn:Yn 2Ag be the rst passage time and, to obtain a suitable scaling, let T(A)=inffn: Yn 2A=g. We consider the asymptotic behavior of T(A )a s !0. We show that the the probability law of T(A) satises the large deviation principle; in particular, PfT(A)2Cgexpf inf2CIA()=g as !0, where IA() is a large deviation rate function and C is any open or closed subset of [0;1): We then establish conditional laws of large numbers for the normalized rst passage time T(A) and normalized rst passage place YT(A). c 1998 Elsevier Science B.V. All rights reserved. AMS classication: primary 60F10; secondary 60K10
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48. NEW COMBINATORIAL PROOF OF THE MULTIPLE BINOMIAL COEFFICIENT IDENTITY.
- Author
-
Stojiljković, Vuk N.
- Subjects
BINOMIAL coefficients ,COMBINATORICS - Abstract
Copyright of Military Technical Courier / Vojnotehnicki Glasnik is the property of Military Technical Courier / Vojnotehnicki Glasnik and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2022
- Full Text
- View/download PDF
49. Special Issue dedicated to Workshop on Graph Spectra, Combinatorics and Optimization (WGSCO2018).
- Author
-
Elster, Rosalind, Tchemisova, Tatiana, and Weber, Gerhard-Wilhelm
- Subjects
GRAPH theory ,COMBINATORICS ,LINEAR programming ,SEMIDEFINITE programming ,NONSTANDARD mathematical analysis ,CONSTRAINT programming - Published
- 2020
- Full Text
- View/download PDF
50. Note on a paper by H. S. Qin
- Author
-
André Vanderbauwhede
- Subjects
Scalar (mathematics) ,Mathematical analysis ,Banach space ,Codimension ,Combinatorics ,Simple eigenvalue ,Computational Mathematics ,Bifurcation theory ,Computational Theory and Mathematics ,Modeling and Simulation ,Modelling and Simulation ,Bifurcation ,Eigenvalues and eigenvectors ,Subspace topology ,Mathematics - Abstract
In a recent paper entitled "Some sufficient conditions for occurring bifurcation" [1], H. S. Qin claims to have obtained sufficient conditions for bifurcation from multiple eigenvalues. The setting is that of an equation F(x,/~) = 0, (1) where F: R" x R--, R" is smooth, with F(0,/~) = 0, V# e R. It is assumed that for some Poe R we have rank DxF(O, ~) = n - rn, with 1 l, is misleading and gives a false impression that the results have to do with "higher multiplicities". What happens is that one looks for solutions in a subspace with codimension m - 1, while assuming that: (a) m - 1 of the n scalar equations in equation (1) are automatically satisfied for x in this subspace; (b) zero is a simple eigenvalue of DxF(O, ~o) when the nonrelevant dimensions are taken out of the picture. Condition (a) is especially severe when m > 1, except when it is a consequence of symmetry considerations (e.g. Ref. [3]). To be more precise let us formulate the following "generalized" version of the Crandall- Rabinowitz theorem. Theorem I Let X and Y be Banach spaces, X 0 a closed subspace of X and Y0 a closed subspace of Y. Let F: Y x R --* Y be a smooth mapping such that and
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- View/download PDF
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