113 research outputs found
Structure of Cubic Lehman Matrices
A pair of square -matrices is called a \emph{Lehman pair} if
for some integer . In this case and
are called \emph{Lehman matrices}. This terminology arises because Lehman
showed that the rows with the fewest ones in any non-degenerate minimally
nonideal (mni) matrix form a square Lehman submatrix of . Lehman
matrices with are essentially equivalent to \emph{partitionable graphs}
(also known as -graphs), so have been heavily studied as part
of attempts to directly classify minimal imperfect graphs. In this paper, we
view a Lehman matrix as the bipartite adjacency matrix of a regular bipartite
graph, focusing in particular on the case where the graph is cubic. From this
perspective, we identify two constructions that generate cubic Lehman graphs
from smaller Lehman graphs. The most prolific of these constructions involves
repeatedly replacing suitable pairs of edges with a particular -vertex
subgraph that we call a -rung ladder segment. Two decades ago, L\"{u}tolf \&
Margot initiated a computational study of mni matrices and constructed a
catalogue containing (among other things) a listing of all cubic Lehman
matrices with of order up to . We verify their catalogue
(which has just one omission), and extend the computational results to matrices. Of the cubic Lehman matrices (with ) of order
up to , only two do not arise from our -rung ladder
construction. However these exceptions can be derived from our second
construction, and so our two constructions cover all known cubic Lehman
matrices with
Vertex adjacencies in the set covering polyhedron
We describe the adjacency of vertices of the (unbounded version of the) set
covering polyhedron, in a similar way to the description given by Chvatal for
the stable set polytope. We find a sufficient condition for adjacency, and
characterize it with similar conditions in the case where the underlying matrix
is row circular. We apply our findings to show a new infinite family of
minimally nonideal matrices.Comment: Minor revision, 22 pages, 3 figure
An extension of Lehman's theorem and ideal set functions
Lehman’s theorem on the structure of minimally nonideal clutters is a fundamental result in polyhedral combinatorics. One approach to extending it has been to give a common generalization with the characterization of minimally imperfect clutters (Sebő, 1998; Gasparyan et al., 2003). We give a new generalization of this kind, which combines two types of covering inequalities and works well with the natural definition of minors. We also show how to extend the notion of idealness to unit-increasing set functions, in a way that is compatible with minors and blocking operations
Flux corrected transport applied to hydrodynamics for heavy ion collisions
Includes abstract.Includes bibliographical references (p.145-154).This thesis presents FCTHydro, a ROOT package, and its application to hydrodynamic simulations through the packages RelHydro and Nonideal xy. These packages aim to provide the broader heavy ion collision community with access to hydrodynamic simulation software which is now accessible from within the primary analysis framework, ROOT. Tests are performed and show how well the high-order, monotone, conservative, positivity preserving routines within FCTHydro simulate hydrodynamic systems with harsh initial conditions. RelHydro illustrates the application of FCTHydro to relativistic systems and Nonideal xy the application to causal non-ideal hydrodynamic systems. Nonideal xy is also used to obtain a first order understanding of the effects of the relaxation times in causal non-ideal hydrodynamics. In addition, a semi-analytic solution for the particle rapidity spectra obtained by combining Landau hydrodynamics and the Cooper-Frye freezeout formalism is given. The results are compared with the Landau Gaussian and a known approximation for midrapidies. The Landau Gaussian provides the best approximation to experimental data. Furthermore, the chemical freezeout results for preliminary data from AGS for central Au-Au collisions at nominal beam energies 2, 4, 6 and 8 AGeV are shown to agree with the E/N = 1 GeV freezeout criteria. These data allow access to a previously unexplored region in the T-μB phase space
On the foundations of thermodynamics
On the basis of new, concise foundations, this paper establishes the four
laws of thermodynamics, the Maxwell relations, and the stability requirements
for response functions, in a form applicable to global (homogeneous), local
(hydrodynamic) and microlocal (kinetic) equilibrium.
The present, self-contained treatment needs very little formal machinery and
stays very close to the formulas as they are applied by the practicing
physicist, chemist, or engineer. From a few basic assumptions, the full
structure of phenomenological thermodynamics and of classical and quantum
statistical mechanics is recovered.
Care has been taken to keep the foundations free of subjective aspects (which
traditionally creep in through information or probability). One might describe
the paper as a uniform treatment of the nondynamical part of classical and
quantum statistical mechanics ``without statistics'' (i.e., suitable for the
definite descriptions of single objects) and ``without mechanics'' (i.e.,
independent of microscopic assumptions). When enriched by the traditional
examples and applications, this paper may serve as the basis for a course on
thermal physics.Comment: 78 page
Distributed Detection and Estimation in Wireless Sensor Networks
In this article we consider the problems of distributed detection and
estimation in wireless sensor networks. In the first part, we provide a general
framework aimed to show how an efficient design of a sensor network requires a
joint organization of in-network processing and communication. Then, we recall
the basic features of consensus algorithm, which is a basic tool to reach
globally optimal decisions through a distributed approach. The main part of the
paper starts addressing the distributed estimation problem. We show first an
entirely decentralized approach, where observations and estimations are
performed without the intervention of a fusion center. Then, we consider the
case where the estimation is performed at a fusion center, showing how to
allocate quantization bits and transmit powers in the links between the nodes
and the fusion center, in order to accommodate the requirement on the maximum
estimation variance, under a constraint on the global transmit power. We extend
the approach to the detection problem. Also in this case, we consider the
distributed approach, where every node can achieve a globally optimal decision,
and the case where the decision is taken at a central node. In the latter case,
we show how to allocate coding bits and transmit power in order to maximize the
detection probability, under constraints on the false alarm rate and the global
transmit power. Then, we generalize consensus algorithms illustrating a
distributed procedure that converges to the projection of the observation
vector onto a signal subspace. We then address the issue of energy consumption
in sensor networks, thus showing how to optimize the network topology in order
to minimize the energy necessary to achieve a global consensus. Finally, we
address the problem of matching the topology of the network to the graph
describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R.
Chellapa and S. Theodoridis, Eds., Elsevier, 201
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