428 research outputs found
The f-vector of the descent polytope
For a positive integer n and a subset S of [n-1], the descent polytope DP_S
is the set of points x_1, ..., x_n in the n-dimensional unit cube [0,1]^n such
that x_i >= x_{i+1} for i in S and x_i <= x_{i+1} otherwise. First, we express
the f-vector of DP_S as a sum over all subsets of [n-1]. Second, we use certain
factorizations of the associated word over a two-letter alphabet to describe
the f-vector. We show that the f-vector is maximized when the set S is the
alternating set {1,3,5, ...}. We derive a generating function for the
f-polynomial F_S(t) of DP_S, written as a formal power series in two
non-commuting variables with coefficients in Z[t]. We also obtain the
generating function for the Ehrhart polynomials of the descent polytopes.Comment: 14 pages; to appear in Discrete & Computational Geometr
Regular Expression Matching and Operational Semantics
Many programming languages and tools, ranging from grep to the Java String
library, contain regular expression matchers. Rather than first translating a
regular expression into a deterministic finite automaton, such implementations
typically match the regular expression on the fly. Thus they can be seen as
virtual machines interpreting the regular expression much as if it were a
program with some non-deterministic constructs such as the Kleene star. We
formalize this implementation technique for regular expression matching using
operational semantics. Specifically, we derive a series of abstract machines,
moving from the abstract definition of matching to increasingly realistic
machines. First a continuation is added to the operational semantics to
describe what remains to be matched after the current expression. Next, we
represent the expression as a data structure using pointers, which enables
redundant searches to be eliminated via testing for pointer equality. From
there, we arrive both at Thompson's lockstep construction and a machine that
performs some operations in parallel, suitable for implementation on a large
number of cores, such as a GPU. We formalize the parallel machine using process
algebra and report some preliminary experiments with an implementation on a
graphics processor using CUDA.Comment: In Proceedings SOS 2011, arXiv:1108.279
Bistable molecular conductors with a field-switchable dipole group
A class of bistable "stator-rotor" molecules is proposed, where a stationary
bridge (stator) connects the two electrodes and facilitates electron transport
between them. The rotor part, which has a large dipole moment, is attached to
an atom of the stator via a single sigma bond. Hydrogen bonds formed between
the rotor and stator make the symmetric orientation of the dipole unstable. The
rotor has two potential minima with equal energy for rotation about the sigma
bond. The dipole orientation, which determines the conduction state of the
molecule, can be switched by an external electric field that changes the
relative energy of the two potential minima. Both orientation of the rotor
correspond to asymmetric current-voltage characteristics that are the reverse
of each other, so they are distinguishable electrically. Such bistable
stator-rotor molecules could potentially be used as parts of molecular
electronic devices.Comment: 8 pages, 7 figure
Structural Properties of Self-Attracting Walks
Self-attracting walks (SATW) with attractive interaction u > 0 display a
swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >=
2, analogous to the \Theta transition of polymers. We are interested in the
structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen
walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can
be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and
their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo
simulations, we find that for u<u_{\mathrm{c}}, the structures are in the
universality class of clusters generated by simple random walks. For
u>u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and
d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class.
The clusters are compact in both d=2 and d=3, but their interface is fractal:
d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In
d=1, where the walk is collapsed for all u and no swelling-collapse transition
exists, we derive analytical expressions for the average number of visited
sites and the mean time to visit S sites.Comment: 15 pages, 8 postscript figures, submitted to Phys. Rev.
Causes for Precipitation Increases in the Hills of Southern Illinois
Studies involving precipitation in Illinois have shown the presence of 10 to 15 percent more precipitation in the average annual precipitation pattern in the Shawnee Hills area of southern Illinois than in nearby ftatlands. Three methods differing in scale and time were used to delineate the hill anomaly and to determine the reasons for it. First, a series of climatic studies of precipitation distribution considering daily, monthly, and seasonal data for comparison of hill and fladand stations were performed during 1960-1963. Next, a 5-year project involving analysis of data from a special raingage network on the basis of individual rain periods, months, and seasons during 1965-1969 was planned to define the areal extent of the hill high. Finally, the results of these two studies were used to design a 1-month field study involving a weather radar, 3 cloud cameras, 5 weather (temperature-humidity) stations, 1 pilot balloon site, and aircraft sampling flights. Results of the three major studies show that the hill enhancement of precipitation is the addition of moisture due to greater evapotranspiration from the forested hills and the convergent wind field created over the western hills caused by the configuration of the hills and valleys.publishedpeer reviewedOpe
Diffuse Neutron Scattering Study of a Disordered Complex Perovskite Pb(Zn1/3Nb2/3)O3 Crystal
Diffuse scattering around the (110) reciprocal lattice point has been
investigated by elastic neutron scattering in the paraelectric and the relaxor
phases of the disordered complex perovskite crystal-Pb(Zn1/3Nb2/3)O3(PZN). The
appearance of a diffuse intensity peak indicates the formation of polar
nanoregions at temperature T*, approximately 40K above Tc=413K. The analysis of
this diffuse scattering indicates that these regions are in the shape of
ellipsoids, more extended in the direction than in the direction.
The quantitative analysis provides an estimate of the correlation length, \xi,
or size of the regions and shows that \xi ~1.2\xi , consistent with
the primary or dominant displacement of Pb leading to the low temperature
rhombohedral phase. Both the appearance of the polar regions at T*and the
structural transition at Tc are marked by kinks in the \xi curve but not
in the \xi one, also indicating that the primary changes take place in a
direction at both temperatures.Comment: REVTeX file. 4 pages, 3 figures embedded, New version after referee
cond-mat/010605
Hydrometeorological analysis of severe rainstorms in Illinois, 1956-1957, with summary of previous storms
Bibliography: p. 79.Enumeration continues through succeeding title
Hopf algebras and Markov chains: Two examples and a theory
The operation of squaring (coproduct followed by product) in a combinatorial
Hopf algebra is shown to induce a Markov chain in natural bases. Chains
constructed in this way include widely studied methods of card shuffling, a
natural "rock-breaking" process, and Markov chains on simplicial complexes.
Many of these chains can be explictly diagonalized using the primitive elements
of the algebra and the combinatorics of the free Lie algebra. For card
shuffling, this gives an explicit description of the eigenvectors. For
rock-breaking, an explicit description of the quasi-stationary distribution and
sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes
will only appear on the version on Amy Pang's website, the arXiv version will
not be updated.
Explicit solution of the (quantum) elliptic Calogero-Sutherland model
We derive explicit formulas for the eigenfunctions and eigenvalues of the
elliptic Calogero-Sutherland model as infinite series, to all orders and for
arbitrary particle numbers and coupling parameters. The eigenfunctions obtained
provide an elliptic deformation of the Jack polynomials. We prove in certain
special cases that these series have a finite radius of convergence in the nome
of the elliptic functions, including the two particle (= Lam\'e) case for
non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low
order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper
completely revised: the results of v1 and v2 are extended to all order
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