447 research outputs found
Drawing graphs with vertices and edges in convex position
A graph has strong convex dimension , if it admits a straight-line drawing
in the plane such that its vertices are in convex position and the midpoints of
its edges are also in convex position. Halman, Onn, and Rothblum conjectured
that graphs of strong convex dimension are planar and therefore have at
most edges. We prove that all such graphs have at most edges
while on the other hand we present a class of non-planar graphs of strong
convex dimension . We also give lower bounds on the maximum number of edges
a graph of strong convex dimension can have and discuss variants of this
graph class. We apply our results to questions about large convexly independent
sets in Minkowski sums of planar point sets, that have been of interest in
recent years.Comment: 15 pages, 12 figures, improved expositio
On the Complexity of Hilbert Refutations for Partition
Given a set of integers W, the Partition problem determines whether W can be
divided into two disjoint subsets with equal sums. We model the Partition
problem as a system of polynomial equations, and then investigate the
complexity of a Hilbert's Nullstellensatz refutation, or certificate, that a
given set of integers is not partitionable. We provide an explicit construction
of a minimum-degree certificate, and then demonstrate that the Partition
problem is equivalent to the determinant of a carefully constructed matrix
called the partition matrix. In particular, we show that the determinant of the
partition matrix is a polynomial that factors into an iteration over all
possible partitions of W.Comment: Final versio
Similarity classes of 3x3 matrices over a local principal ideal ring
In this paper similarity classes of three by three matrices over a local
principal ideal commutative ring are analyzed. When the residue field is
finite, a generating function for the number of similarity classes for all
finite quotients of the ring is computed explicitly.Comment: 14 pages, final version, to appear in Communications in Algebr
A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs
In this paper we generalize N-fold integer programs and two-stage integer
programs with N scenarios to N-fold 4-block decomposable integer programs. We
show that for fixed blocks but variable N, these integer programs are
polynomial-time solvable for any linear objective. Moreover, we present a
polynomial-time computable optimality certificate for the case of fixed blocks,
variable N and any convex separable objective function. We conclude with two
sample applications, stochastic integer programs with second-order dominance
constraints and stochastic integer multi-commodity flows, which (for fixed
blocks) can be solved in polynomial time in the number of scenarios and
commodities and in the binary encoding length of the input data. In the proof
of our main theorem we combine several non-trivial constructions from the
theory of Graver bases. We are confident that our approach paves the way for
further extensions
Hot electron injection into dense argon, nitrogen, and hydrogen
Hot electrons have been injected into very dense argon, nitrogen, and hydrogen gases and liquids. The current‐voltage characteristics are experimentally determined for densities (N) of argon, nitrogen, and hydrogen ranging from about 10²⁰ to 10²² cm⁻³ and applied fields (E) ranging from about 10 to 10⁴ V cm⁻¹. The argon data show a square root E∕N dependence of the current. The nitrogen and hydrogen data show a complicated dependence of the current on E∕N due to the rapid thermalization in the region of the image potential of the injected electrons through inelastic collision processes not present in argon. A hydrodynamic‐two‐fluid model is developed to analyze the nitrogen and hydrogen data. From the analysis of our data, we obtain the density dependence of the momentum exchange scattering cross section and the energy relaxation time for the injected hot electrons
Patients with ovarian carcinoma excrete different altered levels of urine CD59, kininogen-1 and fragments of inter-alpha-trypsin inhibitor heavy chain H4 and albumin
CD59, kininogen-1 and fragments of ITIH4 and albumin may be used as complementary biomarkers in the development of new noninvasive protocols for diagnosis and screening of ovarian carcinoma
Learning intrinsic excitability in medium spiny neurons
We present an unsupervised, local activation-dependent learning rule for
intrinsic plasticity (IP) which affects the composition of ion channel
conductances for single neurons in a use-dependent way. We use a
single-compartment conductance-based model for medium spiny striatal neurons in
order to show the effects of parametrization of individual ion channels on the
neuronal activation function. We show that parameter changes within the
physiological ranges are sufficient to create an ensemble of neurons with
significantly different activation functions. We emphasize that the effects of
intrinsic neuronal variability on spiking behavior require a distributed mode
of synaptic input and can be eliminated by strongly correlated input. We show
how variability and adaptivity in ion channel conductances can be utilized to
store patterns without an additional contribution by synaptic plasticity (SP).
The adaptation of the spike response may result in either "positive" or
"negative" pattern learning. However, read-out of stored information depends on
a distributed pattern of synaptic activity to let intrinsic variability
determine spike response. We briefly discuss the implications of this
conditional memory on learning and addiction.Comment: 20 pages, 8 figure
A polynomial oracle-time algorithm for convex integer minimization
In this paper we consider the solution of certain convex integer minimization
problems via greedy augmentation procedures. We show that a greedy augmentation
procedure that employs only directions from certain Graver bases needs only
polynomially many augmentation steps to solve the given problem. We extend
these results to convex -fold integer minimization problems and to convex
2-stage stochastic integer minimization problems. Finally, we present some
applications of convex -fold integer minimization problems for which our
approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur
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