Results 1  10
of
132
Haplotyping as Perfect Phylogeny: Conceptual Framework and Efficient Solutions (Extended Abstract)
, 2002
"... The next highpriority phase of human genomics will involve the development of a full Haplotype Map of the human genome [12]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A prototype Haplotype Mapping strat ..."
Abstract

Cited by 121 (10 self)
 Add to MetaCart
The next highpriority phase of human genomics will involve the development of a full Haplotype Map of the human genome [12]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A prototype Haplotype Mapping strategy is presently being finalized by an NIH workinggroup. The biological key to that strategy is the surprising fact that genomic DNA can be partitioned into long blocks where genetic recombination has been rare, leading to strikingly fewer distinct haplotypes in the population than previously expected [12, 6, 21, 7]. In this paper
RASCAL: Calculation of Graph Similarity using Maximum Common Edge Subgraphs
, 2002
"... ..."
(Show Context)
Asymptotic enumeration and limit laws of planar graphs
"... Abstract. We present a complete analytic solution to the problem of counting planar graphs. We prove an estimate gn ∼ g ·n −7/2 γ n n! for the number gn of labelled planar graphs on n vertices, where γ and g are explicit computable constants. We show that the number of edges in random planar graphs ..."
Abstract

Cited by 45 (9 self)
 Add to MetaCart
(Show Context)
Abstract. We present a complete analytic solution to the problem of counting planar graphs. We prove an estimate gn ∼ g ·n −7/2 γ n n! for the number gn of labelled planar graphs on n vertices, where γ and g are explicit computable constants. We show that the number of edges in random planar graphs is asymptotically normal with linear mean and variance and, as a consequence, the number of edges is sharply concentrated around its expected value. Moreover we prove an estimate g(q) · n −4 γ(q) n n! for the number of planar graphs with n vertices and ⌊qn ⌋ edges, where γ(q) is an analytic function of q. We also show that the number of connected components in a random planar graph is distributed asymptotically as a shifted Poisson law 1+P(ν), where ν is an explicit constant. Additional Gaussian and Poisson limit laws for random planar graphs are derived. The proofs are based on singularity analysis of generating functions and on perturbation of singularities.
Modeling and assessing inference exposure in encrypted databases
 ACM Transactions on Information and System Security (TISSEC
, 2005
"... The scope and character of today’s computing environments are progressively shifting from traditional, oneonone clientserver interaction to the new cooperative paradigm. It then becomes of primary importance to provide means of protecting the secrecy of the information, while guaranteeing its ava ..."
Abstract

Cited by 42 (23 self)
 Add to MetaCart
The scope and character of today’s computing environments are progressively shifting from traditional, oneonone clientserver interaction to the new cooperative paradigm. It then becomes of primary importance to provide means of protecting the secrecy of the information, while guaranteeing its availability to legitimate clients. Operating online querying services securely on open networks is very difficult; therefore many enterprises outsource their data center operations to external application service providers. A promising direction toward prevention of unauthorized access to outsourced data is represented by encryption. However, data encryption is often supported for the sole purpose of protecting the data in storage while allowing access to plaintext values by the server, which decrypts data for query execution. In this paper, we present a simple yet robust singleserver solution for remote querying of encrypted databases on external servers. Our approach is based on the use of indexing information attached to the encrypted database, which can be used by the server to select the data to be This paper extends the previous work by the authors appeared under the title “Balancing
The number of labeled 2connected planar graphs
 Journal of Combinatorics
, 2000
"... We derive the asymptotic expression for the number of labeled 2connected planar graphs with respect to vertices and edges. We also show that almost all such graphs with n vertices contain many copies of any fixed planar graph, and this implies that almost all such graphs have large automorphism gro ..."
Abstract

Cited by 40 (2 self)
 Add to MetaCart
We derive the asymptotic expression for the number of labeled 2connected planar graphs with respect to vertices and edges. We also show that almost all such graphs with n vertices contain many copies of any fixed planar graph, and this implies that almost all such graphs have large automorphism groups.
Detection of functional modules from protein interaction networks
 PROTEINS
, 2004
"... Complex cellular processes are modular and are accomplished by the concerted action of functional modules (Ravasz et al., Science 2002;297:1551–1555; Hartwell et al., Nature 1999;402: C47–52). These modules encompass groups of genes or proteins involved in common elementary biological functions. O ..."
Abstract

Cited by 39 (1 self)
 Add to MetaCart
Complex cellular processes are modular and are accomplished by the concerted action of functional modules (Ravasz et al., Science 2002;297:1551–1555; Hartwell et al., Nature 1999;402: C47–52). These modules encompass groups of genes or proteins involved in common elementary biological functions. One important and largely unsolved goal of functional genomics is the identification of functional modules from genomewide information, such as transcription profiles or protein interactions. To cope with the everincreasing volume and complexity of protein interaction data (Bader et al., Nucleic Acids Res 2001;29:242–245; Xenarios et al., Nucleic Acids Res 2002;30:303–305), new automated approaches for pattern discovery in these densely connected interaction networks are required
The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density
 SOCIOLOGICAL METHODOLOGY
, 2001
"... This study shows various ways that formal graph theoretic statements map patterns of network ties into substantive hypotheses about social cohesion. If network cohesion is enhanced by multiple connections between members of a group, for example, then the higher the global minimum of the number of ..."
Abstract

Cited by 23 (4 self)
 Add to MetaCart
(Show Context)
This study shows various ways that formal graph theoretic statements map patterns of network ties into substantive hypotheses about social cohesion. If network cohesion is enhanced by multiple connections between members of a group, for example, then the higher the global minimum of the number of independent paths that connect every pair of nodes in the network, the higher the social cohesion. The cohesiveness of a group is also measured by the extent to which it is not disconnected by removal of 1, 2, 3,..., n actors. Menger's Theorem proves that these two measures are equivalent. Within this graph theoretic framework, we evaluate the family of concepts of cohesion and establish the validity of a pair of related measures: 1. Connectivity  the minimum number k of its actors whose removal would not allow the group to remain connected or would reduce the group to but a single member  measures the social cohesion of a group at a general level. 2. Conditional density measures cohesion on a finer scale as a proportion of ties beyond that required by a graph's connectivity k over the number of ties that would force it to k + 1. Calibrated for successive values of k, these two measures combine into an aggregate measure of social cohesion, suitable for both smalland largescale network studies. Using these measures to define the core of a new methodology of cohesive blocking, we offer hypotheses about the consequences of cohesive blocks for social groups and their members, and explore empirical examples that illustrate the significance, theoretical relevance, and predictiveness of cohesive blocking in a variety of substantively important applications in sociology.
The number of planar graphs and properties of random planar graphs
 J. Amer. Math. Soc
"... We show an asymptotic estimate for the number of labelled planar graphs on n vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in random planar graphs. ..."
Abstract

Cited by 22 (7 self)
 Add to MetaCart
(Show Context)
We show an asymptotic estimate for the number of labelled planar graphs on n vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in random planar graphs.
On the History of Combinatorial Optimization (till 1960)
"... As a coherent mathematical discipline, combinatorial optimization is relatively young. When studying the history of the field, one observes a number of independent lines of research, separately considering problems like optimum assignment, shortest spanning tree, transportation, and the traveling ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
(Show Context)
As a coherent mathematical discipline, combinatorial optimization is relatively young. When studying the history of the field, one observes a number of independent lines of research, separately considering problems like optimum assignment, shortest spanning tree, transportation, and the traveling salesman problem. Only in the 1950's, when the unifying tool of linear and integer programming became available and the area of operations research got intensive attention, these problems were put into one framework, and relations between them were laid. Indeed, linear programming forms the hinge in the history of combinatorial optimization. Its initial conception by Kantorovich and Koopmans was motivated by combinatorial applications, in particular in transportation and transshipment. After the formulation of linear programming as generic problem, and the development in 1947 by Dantzig of the simplex method as a tool, one has tried to attack about all combinatorial opti