15840170
Tetravalent edge-transitive Cayley graphs with odd number of vertices
A characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu [Automorphism groups and isomorphisms of Cayley graphs, Discrete Math. 182 (1998) 309-319] regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; constructing and characterising a new family of half-transitive graphs. Also this study leads to a construction of the first family of arc-transitive graphs of valency 4 which are non-Cayley graphs and have a 'nice' isomorphic 2-factorisation.
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.
35890566
On Isomorphisms of Minimal Cayley Graphs and Digraphs
Abstract. A Cayley graph or digraph Cay(G,S) is called a CI-graph of G if, for any T⊂G, Cay(G,S)≅Cay(G,T) if and only if Sσ=T for some σ∈Aut(G). The aim of this paper is to characterize finite abelian groups for which all minimal Cayley graphs and digraphs are CI-graphs.
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.
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.
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.
10820274
Simultaneous and exact interval estimates for the contrast of two groups based on an extremely high dimensional variable: application to mass spec data
MOTIVATION
Analysis of high-throughput proteomic/genomic data, in particular, surface-enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI-TOF MS) data and microarray data, has led to a multitude of techniques aimed at identifying potential biomarkers. Most of the statistical techniques for comparing two groups are based on qualitative measures such as P-value. A quantitative way such as interval estimation for the contrasts of two groups is more appealing.


RESULTS
We have devised a simultaneous confidence bands method capable of detecting potential biomarkers, while controlling for overall confidence coverage level, in high-dimensional datasets that discriminate two treatment groups using a permutation scheme. For example, for the SELDI-TOF MS data, we deal with the entire spectrum simultaneously and construct (1 - alpha) confidence bands for the mean differences between groups. Furthermore, peaks were identified based on the maximal differences between the groups as determined by the confidence bands. The analysis method herein described gives both qualitative (P-value) and quantitative data (magnitude of difference). The Clinical Proteomics Programs Databank's ovarian cancer dataset and data from in-house samples containing known spiked-in proteins were analyzed. We were able to identify potential biomarkers similar to those described in previous analysis of the ovarian cancer data, however, while these markers are highly significant between cancer and normal groups, our analysis indicated the absolute difference between the two groups was minimal. In addition, we found additional markers than those previously described with greater differences in average intensities. The proposed confidence bands method successfully detected the spiked-in peaks, as well as, secondary peaks generated by adducts and double-charged species. We also illustrate our method utilizing paired gene expression data from a prostate cancer microarray experiment by constructing confidence bands for the fold changes between cancer and normal samples.


AVAILABILITY
R-package, 'seie.zip' (license: GNU GPL), is publiclly available at http://research2.dfci.harvard.edu/dfci/MS_spike-in_data/
3731147
A Multi-tiered Model for Performance Analysis of Storage Area Network
14325657
An approach to reducing the labeling cost of Markov random fields within an infinite label space
This work proposes a novel idea, called SOIL, for reducing the computational complexity of the maximum a posteriori optimization problem using Markov random fields (MRFs). The local characteristics of MRFs are employed so that the searching in a virtually infinite label space is confined in a small finite space. Globally, the number of labels allowed is as many as the number of image sites while locally the optimal label is sampled from a space consisting of the labels assigned to the four-neighbor plus a random one. Neither the prior knowledge about the number of classes nor the estimation phase of the class number is required in this work. The proposed method is applied to the problem of texture segmentation and the result is compared with those obtained from conventional methods.
218270
Cryptanalysis of a multistage encryption system
This paper analyzes the security of a new multistage encryption system (MES) recently proposed in ISCAS'2004. It is found that MES is insecure against a differential chosen-plaintext/ciphertext attack. Experiments are given to support the proposed attack. It is also pointed out that the security of MES against brute-force attacks is not sufficiently high.
9181955
Answering Queries with Database Restrictions
I am a Ph.D. student in the Computer Science Department at Stanford University. My main research interests include query reformulation in the database domain. In particular, I work on the problems of how to do query planning and reformulation when relations have limited access patterns [7,9]. That is, the binding patterns of the relations require values to be specified for certain attributes in order to retrieve data from a relation. Most of my work is based on the TSIM-MIS project (http://www-db.stanford.edu/tsimmis/), a data-integration project [2,10,11] at Stanford.