Displaying 21 – 40 of 117

Showing per page

Commuting contractive families

Luka Milićević (2015)

Fundamenta Mathematicae

A family f₁,..., fₙ of operators on a complete metric space X is called contractive if there exists a positive λ < 1 such that for any x,y in X we have d ( f i ( x ) , f i ( y ) ) λ d ( x , y ) for some i. Austin conjectured that any commuting contractive family of operators has a common fixed point, and he proved this for the case of two operators. We show that Austin’s conjecture is true for three operators, provided that λ is sufficiently small.

Composition and structure of social networks

Ove Frank (1997)

Mathématiques et Sciences Humaines

Social networks representing one or more relationships between individuals and one or more categorical characteristics of the individuals exhibit both structure and composition. Probabilistic models of such networks can be used for analyzing the interrelations between structural and compositional variables, for instance in order to find how structure can be explained by composition or how structure explains composition. Different models are discussed and different statistical methods are employed...

Dürer polyhedra: the dark side of melancholia

Patrick W. Fowler, Peter E. John (2002)

Discussiones Mathematicae Graph Theory

Dürer's engraving Melencolia I famously includes a perspective view of a solid polyhedral block of which the visible portion is an 8-circuit bounding a pentagon-triple+triangle patch. The polyhedron is usually taken to be a cube truncated on antipodal corners, but an infinity of others are compatible with the visible patch. Construction of all cubic polyhedra compatible with the visible portion (i.e., Dürer Polyhedra) is discussed, explicit graphs and symmetries are listed for small cases ( ≤ 18...

Embedding complete ternary trees into hypercubes

S.A. Choudum, S. Lavanya (2008)

Discussiones Mathematicae Graph Theory

We inductively describe an embedding of a complete ternary tree Tₕ of height h into a hypercube Q of dimension at most ⎡(1.6)h⎤+1 with load 1, dilation 2, node congestion 2 and edge congestion 2. This is an improvement over the known embedding of Tₕ into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of Tₕ into its optimal hypercube with load 1 and dilation 2. The optimal hypercube has dimension ⎡(log₂3)h⎤ ( = ⎡(1.585)h⎤) or ⎡(log₂3)h⎤+1....

Existence of graphs with sub exponential transitions probability decay and applications

Clément Rau (2010)

Bulletin de la Société Mathématique de France

In this paper, we recall the existence of graphs with bounded valency such that the simple random walk has a return probability at time n at the origin of order exp ( - n α ) , for fixed α [ 0 , 1 [ and with Følner function exp ( n 2 α 1 - α ) . This result was proved by Erschler (see [4], [3]); we give a more detailed proof of this construction in the appendix. In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random walk on...

Fatgraph models of RNA structure

Fenix Huang, Christian Reidys, Reza Rezazadegan (2017)

Molecular Based Mathematical Biology

In this review paper we discuss fatgraphs as a conceptual framework for RNA structures. We discuss various notions of coarse-grained RNA structures and relate them to fatgraphs.We motivate and discuss the main intuition behind the fatgraph model and showcase its applicability to canonical as well as noncanonical base pairs. Recent discoveries regarding novel recursions of pseudoknotted (pk) configurations as well as their translation into context-free grammars for pk-structures are discussed. This...

Food Webs, Competition Graphs, and Habitat Formation

M. Cozzens (2011)

Mathematical Modelling of Natural Phenomena

One interesting example of a discrete mathematical model used in biology is a food web. The first biology courses in high school and in college present the fundamental nature of a food web, one that is understandable by students at all levels. But food webs as part of a larger system are often not addressed. This paper presents materials that can be used in undergraduate classes in biology (and mathematics) and provides students with the opportunity...

Frequency planning and ramifications of coloring

Andreas Eisenblätter, Martin Grötschel, Arie M.C.A. Koster (2002)

Discussiones Mathematicae Graph Theory

This paper surveys frequency assignment problems coming up in planning wireless communication services. It particularly focuses on cellular mobile phone systems such as GSM, a technology that revolutionizes communication. Traditional vertex coloring provides a conceptual framework for the mathematical modeling of many frequency planning problems. This basic form, however, needs various extensions to cover technical and organizational side constraints. Among these ramifications are T-coloring and...

Currently displaying 21 – 40 of 117