random walks on infinite graphs and groups

... models on (finite) digraphs We also study the random walk on the set of single-chip-and-rotor states which is induced by the random walk on a strongly connected digraph We show that its stationary ... operation: Is there an infinite family of non-Eulerian strongly connected digraphs such that the rotor-router operation on each digraph has a single orbit? It turns out that on a strongly connected ... performs a random walk on G The structure of this paper is as follows In Section 2 we will give some background on the rotor-router model and the random walk The definitions and the results on the

Ngày tải lên: 14/10/2015, 15:20

... of any unproved assertions below 2.1 Understanding Random Walks on Graphs in the Context of Markov Chains Weappeal to [No] for the following association of random walks on graphs to discrete timeMarkov ... undirected, strongly connected graphs The rest of the thesis is organized asfollows: Section 2 constructs a theoretical conceptualization of hitting times for randomwalks on graphs, Section 3 uses ... both supports ural observations about random walks on graphs and allows us to move toward our goal nat-of calculating expected hitting times for random walks on finite graphs The reader isinstructed

Ngày tải lên: 21/09/2015, 21:23

... the transposition of the remaining two vertices This implies that the only graphs which have fix(G) = n − 1 are the complete graphs and the empty graphs On the other hand, the graphs with fix(G) ... vertex-transitive actions of Γ on all possible sets of vertices V is in one-to-one correspondence with the conjugacy classes of subgroups of Γ Specifically, if v is any vertex in V , the action of Γ on V is ... shown on the right Note that for two finite non-trivial groups Γ1 and Γ2, 1 ∈ fix(Γ1× Γ2) but 1 6∈ fix(Γ1) + fix(Γ2) Open Question Is it true that for all finite non-trivial groups Γ1 and Γ2,

Ngày tải lên: 07/08/2014, 21:21

... al [13] constructed functional synergistic regulatory interactions between miRNAs by considering common target genes in the context of gene ontology and prox-imity in a protein interaction network ... In addition, we downloaded predicted human miRNA-target gene associations from TargetScan with non-conserved site context++ scores, and constructed a second heterogeneous miRNA network consisting ... AccessRandom walks on mutual microRNA-target gene interaction network improve the prediction of disease-associated microRNAs Duc-Hau Le1, Lieven Verbeke2, Le Hoang Son3, Dinh-Toi Chu4,5and Van-Huy

Ngày tải lên: 25/11/2020, 16:28

... M(x,y) and N(x,y) are continuous functions and have continuous first partial derivatives on some rectangle of the xy-plane, then Equation (27) is exact if and only if x y x 3.3 Solution: To solve ... M(x,y) and N(x,y) are continuous functions and have continuous first partial derivatives on some rectangle of the xy-plane, then Equation (27) is exact if and only if x y x 3.3 Solution: To solve ... relationship governing the electrical charge (q in coulombs) on the capacitor is defined by a specific equation.Definitions and Related Concepts2.1 Definition differential equationA is an equation

Ngày tải lên: 11/03/2022, 15:46

... Z 4 × Z 5 × Z 5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson’s pentagon- pentagram definition of the Hoffman-Singleton graph and is obtained ... Section 13. In the remainder of this introduction, we give a brief overview of some constructions of the Higman-Sims graph, and establish the notational conventions for the rest of the paper. Constructions ... construction is visible in Fig. 4, if one considers only H 3 ∪ H 2 . In a variation on this theme, [2] begins with the projective plane of order 4 and effectively incorporates some of the construction

Ngày tải lên: 07/08/2014, 08:22

... toedges, and so condition 4 of Definition 2.1 is satisfied Let us check the conditions ofDefinition 2.2 Conditions 1 and 2 are clearly satisfied and we have to check condition 3.Proposition 2.9 ... example and we also omit verifications of theconditions of Definitions 2.1 and 2.2 which are easy With the exception of Example 6,each set R(K, B) of 2 of Definition 2.2 has only one element and condition ... restrictions of the type1–4 on growths of other classes of structures besides permutations and ordered graphs We shall generalize only 1 and 3, i.e., the constant dichotomy (Theorem 3.1) and theFibonacci

Ngày tải lên: 07/08/2014, 21:20

... Corol-lary 2.1, and Propositions 3.3, 3.1 and 3.4; further results which bound Diam C(G, X) are given in Propositions 3.2 and 3.5 From Table 1 when a = (123)(45) and n = 9, Diam C(G, X) = 5 and when ... permutation in question is even The next result shows that we can guarantee this if m is even In the proofs of Propositions 3.8 and 3.9, the permutations appearing there are acting upon the ‘positions’; ... = 4 (see Table 1) We remark that, as a consequence of Theorems 1 and 2 of [5], all the commuting graphs in Theorems 1.1, 1.2 and 1.3 are connected Section 2 is devoted to the proof of Theorem

Ngày tải lên: 07/08/2014, 21:21

... row-operations, consisting of symplectic scalar multiplications, symplectic row-swaps, and symplectic row-additions/subtractions. We also characterize the conditions under which quadratic unitary graphs ... avaluation of the functions S n and D n . We may evaluate these functions for n a prime power, through a straightforward generalization of standard results on patterns of quadratic residues and non-residues ... > 0 odd and r ∈ Z n , we ha v e S n (r) = 0 if and only if at least one of the followin g conditions hold: (i) n is a multiple of 3, and r ≡ 2 (mod 3 ); (ii) n is a multiple of 5, and r ≡ ±1

Ngày tải lên: 08/08/2014, 12:22

... operations with ∆Y γ (Op) > 0 , apart from the increase s due to the first operation. The operations in the first summation can only be performed, in view of condition (B), when Y γ = 0, and so ... LP 1 (Op init ). There are still O(1/n) variations in the right hand side constants in t he constraints, depending on n and on the initial operation Op init . To remove these, define the linear ... chain by one edge and the final component in the chain is connected back to the first as indicated As each component... to find a solution, we use one that also gives a solution to the

Ngày tải lên: 08/08/2014, 12:23

... Classification: 05C80 Abstract We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erd ˝ os-R ´ enyi random graphs, ... Proposition 2.15. Every vertex random graph is isomorphism-invariant. 2.3 Vertex-edge random graphs A generalization both of vertex random graphs and of edge random graphs are the vertex-edge random graphs ... vertex random graphs are generalizations of geometric random graphs, and vertex- edge random graphs generalize both. The names of these three types of random graphs describe where the randomness

Ngày tải lên: 08/08/2014, 14:23

... 2.2.18 (and variations of it—see Corollary 2.2.33 and Lemma 2.2.35): Let G and H be groups and ϕ be an iso-morphism between G and H Let G(1), G(2) and H(1), H(2) be the first andsecond derived groups ... 19Free Groups And PresentationsWe begin with a collection of facts, concepts, and notational conventions used throughout this thesis 1.1 Preliminaries Definition 1.1.1 Let X be a set, and G be ... in context of some associations with subgroups of the additive group of rational numbers 2.1 Historical background and motivation We focus our attention on the special class of 1-relator groups

Ngày tải lên: 13/11/2014, 09:08

... 3.1 Effect of monomer concentration and reaction time on gel content of PAM-gel When the monomer concentration increases from 15% to 30%, the gel content increases and the reaction time decreases ... coefficient of copolymerization process, controlled the conversion of reactions ≤ 10% (by reacting at very low concentration condition, experimented several times to conversion reached ≤ 10%) Synthesis ... published on articles of national scientific journals and international conferences THE CONTRIBUTES OF DISERTATION This dissertation studied the conditions to synthesis two resins for ion exchanging:

Ngày tải lên: 09/01/2020, 15:30

... theo-rem, based on U (t), thus requires this additional condition and, thus, cannot hold for all random walks under consideration A final argument is that somevery important random time points considered ... a theory on the (limiting)behavior of randomly indexed random walks Furthermore, in view of theimmense interest and effort that has been spent on ordinary random walks,in particular, on the classical ... process Among the oldest results for random walks are perhaps the Bernoulli law oflarge numbers and the De Moivre–Laplace central limit theorem for Bernoullirandom walks and simple random walks,

Ngày tải lên: 20/01/2020, 08:06

... theo-rem, based on U (t), thus requires this additional condition and, thus, cannot hold for all random walks under consideration A final argument is that somevery important random time points considered ... a theory on the (limiting)behavior of randomly indexed random walks Furthermore, in view of theimmense interest and effort that has been spent on ordinary random walks,in particular, on the classical ... process Among the oldest results for random walks are perhaps the Bernoulli law oflarge numbers and the De Moivre–Laplace central limit theorem for Bernoullirandom walks and simple random walks,

Ngày tải lên: 03/03/2020, 10:10

... question is raised: What are the differences in terms of complexity and inapproxamability of several optimization problems between on general graphs and on PLG? Many experimental results on random ... L-reduction from MDS on d-bounded graph Gd to MDS on power law graph G(α,β) Let φ and ϕ be a feasible solution on Gd and G(α,β) respectively Trang 7We first consider MDS on different graphs Notice ... L-reduction from MVC on d-bounded graph Gd to MVC on power law graph G(α,β) Let φ be a feasible solution on Gd and ϕ be a feasible solution on G(α,β) However, MVC on K2, cycle, d-Regular Cycle and

Ngày tải lên: 17/10/2022, 16:40

... P. Diaconis, R. L. Graham and J. A. Morrison, Asymptotic analysis of a random walk on a hypercube with many dimensions, Random Structures and Algorithms, 1 (1990), 51–72. [6] P. Diaconis and L. ... =inf f=constant  e∈E f 2 (e)  x f 2 (x)d x log f 2 (x)  y f 2 (y)π(y) (8) where f ranges over all non-constant functions f : V → R and π is the stationary distribution of the nearest neighbor random walk on Γ. In a recent paper [9], Diaconis and Saloffe-Coste show that ∆ TV (t)≤e 1−c if ... most c r n 2 log n where the constant c r depends only on the order r of G . 1. Introduction One method often used in computational group theory for generating random elements from a given (non-trivial) finite...

Ngày tải lên: 07/08/2014, 06:22

... this section, we deal with an abstract graph G satisfying certain conditions listed below. In the next sections, concrete examples of G will be considered. Our assumptions and conventions concerning ... are equal to 1; graphs with nontrivial multiplicities are considered in Đ 3and 4.) A complex function (à)onG is called a harmonic function on the graph G if it satisfies the relation (à)= : à (à, ... summation formula. Proposition 2.5. The function ϕ zz  afforded by Theorem 2.1 is a nondegenerate function from H + 1 (Y) if and only if the parameters satisfy one of the following two conditions: ã...

Ngày tải lên: 07/08/2014, 06:20

... numbers within the vertices and the permutation corresponding to each vertex. Let S 4 act on X by conjugation. (This action does consist of graph automorphisms since conjugation preserves inverses.) ... the action of S n on itself by conjugation since relatively prime orbits can be constructed in that case. Theorem 2.5. Let X be the set of permutations S n with the group action of S n upon X given ... X given by conjugation. Then D S n (S n )=2. Proof. The orbits of S n acting on itself by conjugation are the conjugacy classes of S n and are characterized by cycle type, that is by partitions of...

Ngày tải lên: 07/08/2014, 08:20

... National Bank for Agriculture and Rural Development A HANDBOOK ON FORMING SELF-HELP GROUPS (SHGs) 1414 1414 14 !! !! ! Functions of SHGs :Functions of SHGs : Functions of SHGs :Functions of ... SELF -HELP GROUPS- HELP GROUPS -HELP GROUPS- HELP GROUPS -HELP GROUPS The Articles of Agreement made on this day of 199- at By and Between M/s. [name of SHG] an unregistered association of persons/individuals ... (Rupees only) for onlending to its members. And whereas the Bank has agreed to grant the *loan/extend credit facility to the borrower on certain terms and conditions. And whereas the Bank and the...

Ngày tải lên: 16/02/2014, 10:20