Related papers: A new relationship between block designs
Graphical designs are subsets of vertices of a graph that perfectly average a selected set of eigenvectors of the Graph Laplacian. We show that in highly-structured graphs, graphical designs can coincide with highly structured and…
We say that a family of $k$-subsets of an $n$-element set is {\it intersecting}, if any two of its sets intersect. In this paper, we study the structure of large intersecting families. Several years ago, Han and Kohayakawa (Proc. AMS,…
We study the structure of personal relationships among 1068 high school students using a dataset that contains the network of self-reported friendly and conflictive relationships, with information on their directionality and intensity. We…
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…
In recent work, M. Just and the second author defined a class of "semi-modular forms" on $\mathbb C$, in analogy with classical modular forms, that are "half modular" in a particular sense; and constructed families of such functions as…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…
Let $v\geq6$ be an integer with $v\equiv2 \pmod 4$. In this paper, we introduce a new partitioning of the set of all $3$-subsets of a $v$-set into some simple trades.
Presented with a new machine with a specific interconnect topology, algorithm designers use intuition about the symmetry of the algorithm to design time and communication-efficient schedules that map the algorithm to the machine. Is there a…
Various models have been recently proposed to reflect and predict different properties of complex networks. However, the community structure, which is one of the most important properties, is not well studied and modeled. In this paper, we…
A new method for identifying communities in networks is proposed. Reference nodes, either selected using a priory information about the network or according to relevant node measurements, are obtained so as to indicate putative communities.…
A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…
We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are wound round of lattice-ordered groups. It follows that some results about cyclically ordered groups can be stated…
Every system of any significant size is created by composition from smaller sub-systems or components. It is thus fruitful to analyze the fault-tolerance of a system as a function of its composition. In this paper, two basic types of system…
Considering Schur positivity of differences of plethysms of homogeneous symmetric functions, we introduce a new relation on integer partitions. This relation is conjectured to be a partial order, with its restriction to one part partitions…
We demonstrate, using examples from $2$ and $3$-dimensions, a systematic method of finding all possible periodic arrangements of a given molecule or molecules such that the arrangements have the symmetry of a given space group. The…
A graph is $n$-existentially closed ($n$-e.c.) if for any disjoint subsets $A$, $B$ of vertices with $|{A \cup B}|=n$, there is a vertex $z \notin A \cup B$ adjacent to every vertex of $A$ and no vertex of $B$. For a block design with block…
We study the intersecting family process initially studied in \cite{BCFMR}. Here $k=k(n)$ and $E_1,E_2,\ldots,E_m$ is a random sequence of $k$-sets from $\binom{[n]}{k}$ where $E_{r+1}$ is uniformly chosen from those $k$-sets that are not…
In this short note we deal with a constructive scheme to decompose a continuous family of matrices $A(\rho)$ asymptotically as $\rho\to0$ into blocks corresponding to groups of eigenvalues of the limit matrix A(0). We also discuss the…
Minimal linear codes are algebraic objects which gained interest in the last twenty years, due to their link with Massey's secret sharing schemes. In this context, Ashikhmin and Barg provided a useful and a quite easy to handle sufficient…