250 research outputs found
Symmetric, Hankel-symmetric, and Centrosymmetric Doubly Stochastic Matrices
We investigate convex polytopes of doubly stochastic matrices having special
structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric
and Hankel symmetric. We determine dimensions of these polytopes and classify
their extreme points. We also determine a basis of the real vector spaces
generated by permutation matrices with these special structures
Exchange coupling between magnetic layers across non-magnetic superlattices
The oscillation periods of the interlayer exchange coupling are investigated
when two magnetic layers are separated by a metallic superlattice of two
distinct non-magnetic materials. In spite of the conventional behaviour of the
coupling as a function of the spacer thickness, new periods arise when the
coupling is looked upon as a function of the number of cells of the
superlattice. The new periodicity results from the deformation of the
corresponding Fermi surface, which is explicitly related to a few controllable
parameters, allowing the oscillation periods to be tuned.Comment: 13 pages; 5 figures; To appear in J. Phys.: Cond. Matte
Derandomized Construction of Combinatorial Batch Codes
Combinatorial Batch Codes (CBCs), replication-based variant of Batch Codes
introduced by Ishai et al. in STOC 2004, abstracts the following data
distribution problem: data items are to be replicated among servers in
such a way that any of the data items can be retrieved by reading at
most one item from each server with the total amount of storage over
servers restricted to . Given parameters and , where and
are constants, one of the challenging problems is to construct -uniform CBCs
(CBCs where each data item is replicated among exactly servers) which
maximizes the value of . In this work, we present explicit construction of
-uniform CBCs with data items. The
construction has the property that the servers are almost regular, i.e., number
of data items stored in each server is in the range . The
construction is obtained through better analysis and derandomization of the
randomized construction presented by Ishai et al. Analysis reveals almost
regularity of the servers, an aspect that so far has not been addressed in the
literature. The derandomization leads to explicit construction for a wide range
of values of (for given and ) where no other explicit construction
with similar parameters, i.e., with , is
known. Finally, we discuss possibility of parallel derandomization of the
construction
First-Digit Law in Nonextensive Statistics
Nonextensive statistics, characterized by a nonextensive parameter , is a
promising and practically useful generalization of the Boltzmann statistics to
describe power-law behaviors from physical and social observations. We here
explore the unevenness of the first digit distribution of nonextensive
statistics analytically and numerically. We find that the first-digit
distribution follows Benford's law and fluctuates slightly in a periodical
manner with respect to the logarithm of the temperature. The fluctuation
decreases when increases, and the result converges to Benford's law exactly
as approaches 2. The relevant regularities between nonextensive statistics
and Benford's law are also presented and discussed.Comment: 11 pages, 3 figures, published in Phys. Rev.
Model category extensions of the Pirashvili-S{\l}omi\'{n}ska theorems
We describe the class of semi-stable model categories, which generalize the
equivalence of finite products and coproducts in abelian and stable model
categories, and use this to establish Morita equivalences among categories of
functors. We provide a construction of pairs of small categories--known as
conjugate pairs--whose associated categories of diagrams are Quillen equivalent
in the semi-stable setting. We frame our development in the context of Morita
theory, following Slominska's work on similar questions for categories of
functors enriched over and taking values in R-modules.Comment: 27 pages, submitted to Journal of Homotopy and Related Structure
Parameterized Edge Hamiltonicity
We study the parameterized complexity of the classical Edge Hamiltonian Path
problem and give several fixed-parameter tractability results. First, we settle
an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT
parameterized by vertex cover, and that it also admits a cubic kernel. We then
show fixed-parameter tractability even for a generalization of the problem to
arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set.
We also consider the problem parameterized by treewidth or clique-width.
Surprisingly, we show that the problem is FPT for both of these standard
parameters, in contrast to its vertex version, which is W-hard for
clique-width. Our technique, which may be of independent interest, relies on a
structural characterization of clique-width in terms of treewidth and complete
bipartite subgraphs due to Gurski and Wanke
Sign patterns for chemical reaction networks
Most differential equations found in chemical reaction networks (CRNs) have
the form , where lies in the nonnegative orthant, where
is a real matrix (the stoichiometric matrix) and is a column vector
consisting of real-valued functions having a special relationship to . Our
main interest will be in the Jacobian matrix, , of , in particular
in whether or not each entry has the same sign for all in the
orthant, i.e., the Jacobian respects a sign pattern. In other words species
always acts on species in an inhibitory way or its action is always
excitatory.
In Helton, Klep, Gomez we gave necessary and sufficient conditions on the
species-reaction graph naturally associated to which guarantee that the
Jacobian of the associated CRN has a sign pattern. In this paper, given we
give a construction which adds certain rows and columns to , thereby
producing a stoichiometric matrix corresponding to a new CRN with
some added species and reactions. The Jacobian for this CRN based on
has a sign pattern. The equilibria for the and the based CRN are
in exact one to one correspondence with each equilibrium for the original
CRN gotten from an equilibrium for the new CRN by removing its added
species. In our construction of a new CRN we are allowed to choose rate
constants for the added reactions and if we choose them large enough the
equilibrium is locally asymptotically stable if and only if the
equilibrium is locally asymptotically stable. Further properties of the
construction are shown, such as those pertaining to conserved quantities and to
how the deficiencies of the two CRNs compare.Comment: 23 page
SimRank*: effective and scalable pairwise similarity search based on graph topology
Given a graph, how can we quantify similarity between two nodes in an effective and scalable way? SimRank is an attractive measure of pairwise similarity based on graph topologies. Its underpinning philosophy that “two nodes are similar if they are pointed to (have incoming edges) from similar nodes” can be regarded as an aggregation of similarities based on incoming paths. Despite its popularity in various applications (e.g., web search and social networks), SimRank has an undesirable trait, i.e., “zero-similarity”: it accommodates only the paths of equal length from a common “center” node, whereas a large portion of other paths are fully ignored. In this paper, we propose an effective and scalable similarity model, SimRank*, to remedy this problem. (1) We first provide a sufficient and necessary condition of the “zero-similarity” problem that exists in Jeh and Widom’s SimRank model, Li et al. ’s SimRank model, Random Walk with Restart (RWR), and ASCOS++. (2) We next present our treatment, SimRank*, which can resolve this issue while inheriting the merit of the simple SimRank philosophy. (3) We reduce the series form of SimRank* to a closed form, which looks simpler than SimRank but which enriches semantics without suffering from increased computational overhead. This leads to an iterative form of SimRank*, which requires O(Knm) time and O(n2) memory for computing all (n2) pairs of similarities on a graph of n nodes and m edges for K iterations. (4) To improve the computational time of SimRank* further, we leverage a novel clustering strategy via edge concentration. Due to its NP-hardness, we devise an efficient heuristic to speed up all-pairs SimRank* computation to O(Knm~) time, where m~ is generally much smaller than m. (5) To scale SimRank* on billion-edge graphs, we propose two memory-efficient single-source algorithms, i.e., ss-gSR* for geometric SimRank*, and ss-eSR* for exponential SimRank*, which can retrieve similarities between all n nodes and a given query on an as-needed basis. This significantly reduces the O(n2) memory of all-pairs search to either O(Kn+m~) for geometric SimRank*, or O(n+m~) for exponential SimRank*, without any loss of accuracy, where m~≪n2 . (6) We also compare SimRank* with another remedy of SimRank that adds self-loops on each node and demonstrate that SimRank* is more effective. (7) Using real and synthetic datasets, we empirically verify the richer semantics of SimRank*, and validate its high computational efficiency and scalability on large graphs with billions of edges
- …