14389597
Symmetrical path-cycle covers of a graph and polygonal graphs
A near-polygonal graph is a graph @C which has a set C of m-cycles for some positive integer m such that each 2-path of @C is contained in exactly one cycle in C. If m is the girth of @C then the graph is called polygonal. We introduce a method for constructing near-polygonal graphs with 2-arc transitive automorphism groups. As special cases, we obtain several new infinite families of polygonal graphs.
10480954
Isomorphisms of Finite Cayley Digraphs of Bounded Valency
LetGbe a finite group,Sa subset ofG\{1}, and let Cay(G,S) denote the Cayley digraph ofGwith respect toS. If, for all subsetsS,TofG\{1} of size at mostm, Cay(G,S)?Cay(G,T) implies thatS?=Tfor some??Aut(G), thenGis called anm-DCI-group. In this paper, we prove that, form?2, allm-DCI-groups are of the formU×V, where (|U|, |V|)=1,Uis abelian andVbelongs to an explicitly determined list of groups. Moreover Sylow subgroups of such groups satisfy some very restrictive conditions.
27555290
Constructing Homogeneous Factorisations of Complete Graphs and Digraphs
Abstract. A homogeneous factorisation of a complete graph Kn is a partition of the edge set that is invariant under a subgroup G of Sn such that G is transitive on the parts of the partition and induces a vertex-transitive automorphism group on the graph corresponding to each part. A product construction is given for such factorisations.
206571122
On Half-Transitive Metacirculant Graphs of Prime-Power Order
In this paper, infinitely many graphs of large valency which are half-transitive (that is vertex- and edge-transitive but not arc-transitive) are constructed, and a complete classification is given of half-transitive metacirculant graphs of order a p-power and valency less than 2p, where p is a prime. In particular, it is shown that, for any odd prime p, integers n?3 and k?2 such that k divides p?1, there are exactly (pn?2?1)/2+pn?3?1 nonisomorphic connected half-transitive metacirculants of order pn and valency 2k.
16649809
Relative difference sets fixed by inversion and Cayley graphs
Using graph theoretical technique, we present a construction of a (30, 2, 29, 14)-relative difference set fixed by inversion in the smallest finite simple group--the alternating group A5. To our knowledge this is the first example known of relative difference sets in the finite simple groups with a non-trivial forbidden subgroup. A connection is then established between some relative difference sets fixed by inversion and certain antipodal distance-regular Cayley graphs. With the connection, several families of antipodal distance-regular Cayley graphs which are coverings of complete graphs are presented.
23350440
On Isomorphisms of Connected Cayley Graphs, II
A Cayley graph or digraph Cay(G, S) of a finite groupGis called aCI-graphofGif, for anyT?G, Cay(G, S)?Cay(G, T) if and only ifS?=Tfor some??Aut(G). We study the problem of determining which Cayley graphs and digraphs for a given group are CI-graphs. A finite groupGis called aconnected m-DCI-group(orconnected m-CI-group) if all connected Cayley digraphs (or connected Cayley graphs, respectively) ofGof (out)-valency at most m are CI-graphs. For a groupG, letp(G) be the smallest prime divisor of |G|. It was previously shown that all finite groupsGare connected (p(G)?1)-DCI-groups and all finite groupsGare connected 2(p(G)?1)-CI-groups. In this paper, for every primep, we construct infinitely many finite groupsGsuch thatp(G)=pandGis neither a connectedp-DCI-group nor a connected 2p-CI-group, which provides solutions for several open problems in this area.
8267935
Structural Modeling and Analysis of Signaling Pathways Based on Petri Nets
The purpose of this paper is to discuss how to model and analyze signaling pathways by using Petri net. Firstly, we propose a modeling method based on Petri net by paying attention to the molecular interactions and mechanisms. Then, we introduce a new notion "activation transduction component" in order to describe an enzymic activation process of reactions in signaling pathways and shows its correspondence to a so-called elementary T-invariant in the Petri net models. Further, we design an algorithm to effectively find basic enzymic activation processes by obtaining a series of elementary T-invariants in the Petri net models. Finally, we demonstrate how our method is practically used in modeling and analyzing signaling pathway mediated by thrombopoietin as an example.
2028079
Strong uniqueness of the restricted Chebyshev center with respect to an RS-set in a Banach space
Let G be a strict RS-set (resp. an RS-set) in X and let F be a bounded (resp. totally bounded) subset of X satisfying rG (F) < rx (F), where rG (F) is the restricted Chebyshev radius of F with respect to G. It is shown that the restricted Chebyshev center of F with respect to G is strongly unique in the case when X is a real Banach space, and that, under some additional convexity assumptions, the restricted Chebyshev center of F with respect to G is strongly unique of order α ≥ 2 in the case when X is a complex Banach space.
6907477
Achieving Communication Efficiency through Push-Pull Partitioning of Semantic Spaces to Disseminate Dynamic Information
Many database applications that need to disseminate dynamic information from a server to various clients can suffer from heavy communication costs. Data caching at a client can help mitigate these costs, particularly when individual PUSH-PULL decisions are made for the different semantic regions in the data space. The server is responsible for notifying the client about updates in the PUSH regions. The client needs to contact the server for queries that ask for data in the PULL regions. We call the idea of partitioning the data space into PUSH-PULL regions to minimize communication cost data gerrymandering. In this paper, we present solutions to technical challenges in adopting this simple but powerful idea. We give a provably optimal-cost dynamic programming algorithm for gerrymandering on a single query attribute. We propose a family of efficient heuristics for gerrymandering on multiple query attributes. We handle the dynamic case in which the workloads of queries and updates evolve over time. We validate our methods through extensive experiments on real and synthetic data sets
39573011
The adaptive modulated wavelet transform image representation
In this paper, a new, called the adaptive modulated wavelet transform (AMWT) image representation is presented. One of the attractive features is that the informative instantaneous frequencies of images can be taken into account to improve the representation performance via adaptation of the modulating frequencies involved. The transform coefficients in both wavelet and modulated wavelet domains are uniformly quantized with several quantization levels. The computed peak signal-to-noise ratio values and entropies are used as rate distortion curves for performance comparison. Experimental results show that AMWT out performs wavelet transform for representing images containing textures with rapid variation in grays.
15797731
A Novel Indexing Approach for Efficient and Fast Similarity Search of Captured Motions
Indexing of motion data is important for quickly searching similar motions for sign language recognition and gait analysis and rehabilitation. This paper proposes a simple and efficient tree structure for indexing motion data with dozens of attributes. Feature vectors are extracted for indexing by using singular value decomposition (SVD) properties of motion data matrices. By having similar motions with large variations indexed together, searching for similar motions of a query needs only one node traversal at each tree level, and only one feature needs to be considered at one tree level. Experiments show that the majority of irrelevant motions can be pruned while retrieving all similar motions, and one traversal of the indexing tree takes only several microseconds with the existence of motion variations.