242 research outputs found
An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains
It is known that the First-Fit algorithm for partitioning a poset P into
chains uses relatively few chains when P does not have two incomparable chains
each of size k. In particular, if P has width w then Bosek, Krawczyk, and
Szczypka (SIAM J. Discrete Math., 23(4):1992--1999, 2010) proved an upper bound
of ckw^{2} on the number of chains used by First-Fit for some constant c, while
Joret and Milans (Order, 28(3):455--464, 2011) gave one of ck^{2}w. In this
paper we prove an upper bound of the form ckw. This is best possible up to the
value of c.Comment: v3: referees' comments incorporate
An Improved Upper Bound for the Ring Loading Problem
The Ring Loading Problem emerged in the 1990s to model an important special
case of telecommunication networks (SONET rings) which gained attention from
practitioners and theorists alike. Given an undirected cycle on nodes
together with non-negative demands between any pair of nodes, the Ring Loading
Problem asks for an unsplittable routing of the demands such that the maximum
cumulated demand on any edge is minimized. Let be the value of such a
solution. In the relaxed version of the problem, each demand can be split into
two parts where the first part is routed clockwise while the second part is
routed counter-clockwise. Denote with the maximum load of a minimum split
routing solution. In a landmark paper, Schrijver, Seymour and Winkler [SSW98]
showed that , where is the maximum demand value. They
also found (implicitly) an instance of the Ring Loading Problem with . Recently, Skutella [Sku16] improved these bounds by showing that , and there exists an instance with .
We contribute to this line of research by showing that . We
also take a first step towards lower and upper bounds for small instances
On 1-factorizations of Bipartite Kneser Graphs
It is a challenging open problem to construct an explicit 1-factorization of
the bipartite Kneser graph , which contains as vertices all -element
and -element subsets of and an edge between any
two vertices when one is a subset of the other. In this paper, we propose a new
framework for designing such 1-factorizations, by which we solve a nontrivial
case where and is an odd prime power. We also revisit two classic
constructions for the case --- the \emph{lexical factorization} and
\emph{modular factorization}. We provide their simplified definitions and study
their inner structures. As a result, an optimal algorithm is designed for
computing the lexical factorizations. (An analogous algorithm for the modular
factorization is trivial.)Comment: We design the first explicit 1-factorization of H(2,q), where q is a
odd prime powe
Bounding biomass in the Fisher equation
The FKPP equation with a variable growth rate and advection by an
incompressible velocity field is considered as a model for plankton dispersed
by ocean currents. If the average growth rate is negative then the model has a
survival-extinction transition; the location of this transition in the
parameter space is constrained using variational arguments and delimited by
simulations. The statistical steady state reached when the system is in the
survival region of parameter space is characterized by integral constraints and
upper and lower bounds on the biomass and productivity that follow from
variational arguments and direct inequalities. In the limit of
zero-decorrelation time the velocity field is shown to act as Fickian diffusion
with an eddy diffusivity much larger than the molecular diffusivity and this
allows a one-dimensional model to predict the biomass, productivity and
extinction transitions. All results are illustrated with a simple growth and
stirring model.Comment: 32 Pages, 13 Figure
A study on the radiation hardness of lead tungstate crystals
This report presents recent progress of a study on the radiation damage in lead tungstate (PbWO_4) crystals. The dose rate dependence of radiation damage in PbWO_4 has been observed, confirming our early prediction based upon a kinetic model of color centers. An optimization of the oxygen compensation through post-growth thermal annealing, carried out in Shanghai Institute of Ceramics, has led to PbWO_4 crystals with significantly improved radiation hardness. A comparison between front versus uniform irradiations revealed that the later caused a factor of 2 to 6 times more severe damage. A measurement of a preliminary batch of lanthanum doped PbWO_4 crystals indicates that the La doping seems not a determine factor for PbWO_4 radiation hardness improvement. Finally, a TEM/EDS analysis confirmed our previous conjecture that the radiation damage in PbWO_4 crystals is caused by oxygen vacancies
Microwave Spectroscopy
Contains research objectives and reports on four research projects.Signal Corps Contract DA36-039-sc-7489
A study of the optical and radiation damage properties of lead tungstate crystals
A study has been made of the optical and radiation damage properties of undoped and niobium doped lead tungstate crystals. Data were obtained on the optical absorbance, the intensity and decay time of the scintillation light output, and the radioluminescence and photoluminescence emission spectra. Radiation damage was studied in several undoped and niobium doped samples using ^(60)Co gamma ray irradiation. The change in optical absorption and observed scintillation light output was measured as a function of dose up to total cumulative doses on the order of 800 krad. The radiation induced phosphorescence and thermoluminescence was also measured, as well as recovery from damage by optical bleaching and thermal annealing. An investigation was also made to determine trace element impurities in several samples
Influence of turbulent advection on a phytoplankton ecosystem with nonuniform carrying capacity
In this work we study a plankton ecosystem model in a turbulent flow. The plankton model we consider contains logistic growth with a spatially varying background carrying capacity and the flow dynamics are generated using the two-dimensional (2D) Navier-Stokes equations. We characterize the system in terms of a dimensionless parameter, γ TB / TF, which is the ratio of the ecosystem biological time scales TB and the flow time scales TF. We integrate this system numerically for different values of γ until the mean plankton reaches a statistically stationary state and examine how the steady-state mean and variance of plankton depends on γ. Overall we find that advection in the presence of a nonuniform background carrying capacity can lead to very different plankton distributions depending on the time scale ratio γ. For small γ the plankton distribution is very similar to the background carrying capacity field and has a mean concentration close to the mean carrying capacity. As γ increases the plankton concentration is more influenced by the advection processes. In the largest γ cases there is a homogenization of the plankton concentration and the mean plankton concentration approaches the harmonic mean, 1/K -1. We derive asymptotic approximations for the cases of small and large γ. We also look at the dependence of the power spectra exponent, β, on γ where the power spectrum of plankton is k-β. We find that the power spectra exponent closely obeys β=1+2/γ as predicted by earlier studies using simple models of chaotic advection
Photonics
Contains reports on seven research projects.Air Force Rome Air Development Center (in collaboration with C.C. Leiby, Jr.)U.S. Air Force-Rome Air Development Center (Contract F19628-80-C-0077)National Science Foundation (Grant PHY79-09739)Joint Services Electronics Program (Contract DAAG29-80-C-0104)U.S. Air Force Geophysics Laboratory (Contract F19628-79-C-0082
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