2,974 research outputs found
Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces
We consider the problem of enumerating spanning trees on lattices.
Closed-form expressions are obtained for the spanning tree generating function
for a hypercubic lattice of size N_1 x N_2 x...x N_d in d dimensions under
free, periodic, and a combination of free and periodic boundary conditions.
Results are also obtained for a simple quartic net embedded on two
non-orientable surfaces, a Moebius strip and the Klein bottle. Our results are
based on the use of a formula expressing the spanning tree generating function
in terms of the eigenvalues of an associated tree matrix. An elementary
derivation of this formula is given.Comment: latex, 9 pages, no figures, to appear in Lett. Appl. Mat
The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
We consider the dimer-monomer problem for the rectangular lattice. By mapping
the problem into one of close-packed dimers on an extended lattice, we rederive
the Tzeng-Wu solution for a single monomer on the boundary by evaluating a
Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by
identifying it as the product of the nonzero eigenvalues of the Kasteleyn
matrix.Comment: 4 Pages to appear in the Physical Review E (2006
Revisiting the Equivalence Problem for Finite Multitape Automata
The decidability of determining equivalence of deterministic multitape
automata (or transducers) was a longstanding open problem until it was resolved
by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability
yields a co_NP upper bound, but apparently not much more is known about the
complexity of the problem. In this paper we give an alternative proof of
decidability, which follows the basic strategy of Harju and Karhumaki but
replaces their use of group theory with results on matrix algebras. From our
proof we obtain a simple randomised algorithm for deciding language equivalence
of deterministic multitape automata and, more generally, multiplicity
equivalence of nondeterministic multitape automata. The algorithm involves only
matrix exponentiation and runs in polynomial time for each fixed number of
tapes. If the two input automata are inequivalent then the algorithm outputs a
word on which they differ
Spanning Trees on Graphs and Lattices in d Dimensions
The problem of enumerating spanning trees on graphs and lattices is
considered. We obtain bounds on the number of spanning trees and
establish inequalities relating the numbers of spanning trees of different
graphs or lattices. A general formulation is presented for the enumeration of
spanning trees on lattices in dimensions, and is applied to the
hypercubic, body-centered cubic, face-centered cubic, and specific planar
lattices including the kagom\'e, diced, 4-8-8 (bathroom-tile), Union Jack, and
3-12-12 lattices. This leads to closed-form expressions for for these
lattices of finite sizes. We prove a theorem concerning the classes of graphs
and lattices with the property that
as the number of vertices , where is a finite
nonzero constant. This includes the bulk limit of lattices in any spatial
dimension, and also sections of lattices whose lengths in some dimensions go to
infinity while others are finite. We evaluate exactly for the
lattices we considered, and discuss the dependence of on d and the
lattice coordination number. We also establish a relation connecting to the free energy of the critical Ising model for planar lattices .Comment: 28 pages, latex, 1 postscript figure, J. Phys. A, in pres
Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss
The dissipation associated with nonequilibrium flow processes is reflected by
the formation of strange attractor distributions in phase space. The
information dimension of these attractors is less than that of the equilibrium
phase space, corresponding to the extreme rarity of nonequilibrium states. Here
we take advantage of a simple model for heat conduction to demonstrate that the
nonequilibrium dimensionality loss can definitely exceed the number of
phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte
Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle
Closed-form expressions are obtained for the partition function of the Ising
model on an M x N simple-quartic lattice embedded on a Moebius strip and a
Klein bottle for finite M and N. The finite-size effects at criticality are
analyzed and compared with those under cylindrical and toroidal boundary
conditions. Our analysis confirms that the central charge is c=1/2.Comment: 8 pages, 3 eps figure
Retention or defection? Chinese consumers’ decision-making styles for domestic and global brands
This study explores consumers’ decision-making in terms of intention to switch to foreign brands from domestic brands when purchasing cell phones and sports shoes. A survey of 584 undergraduates in Guangdong, China, shows that domestic brands retain their low quality-conscious, low fashion-and-recreational-conscious and low price-conscious customers and attract low brand-conscious and high choice-confused buyers from foreign brands. Foreign brands typically retain their consumers who are highly conscious of fashion and recreation and keep and draw customers with low choice confusion. High-price-conscious consumers and those who are highly brand-confused will assess foreign and domestic brands when searching for bargains. Regarding managerial implications, local brands should offer products of high quality at low prices
and constantly invest in R&D; foreign brands may expand their customer bases and build interactive brand channels; all companies can retain brand-confused customers with preferential packages and design their marketing strategies based on decision-making styles of their target consumers
DPRP: a database of phenotype-specific regulatory programs derived from transcription factor binding data
Gene expression profiling has been extensively used in the past decades, resulting in an enormous amount of expression data available in public databases. These data sets are informative in elucidating transcriptional regulation of genes underlying various biological and clinical conditions. However, it is usually difficult to identify transcription factors (TFs) responsible for gene expression changes directly from their own expression, as TF activity is often regulated at the posttranscriptional level. In recent years, technical advances have made it possible to systematically determine the target genes of TFs by ChIP-seq experiments. To identify the regulatory programs underlying gene expression profiles, we constructed a database of phenotype-specific regulatory programs (DPRP, http://syslab.nchu.edu.tw/DPRP/) derived from the integrative analysis of TF binding data and gene expression data. DPRP provides three methods: the Fisher's Exact Test, the Kolmogorov-Smirnov test and the BASE algorithm to facilitate the application of gene expression data for generating new hypotheses on transcriptional regulatory programs in biological and clinical studies
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