176 research outputs found
The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus
We present necessary and sufficient conditions for the generic rigidity of
body-bar frameworks on the three-dimensional fixed torus. These frameworks
correspond to infinite periodic body-bar frameworks in with a
fixed periodic lattice.Comment: 31 pages, 12 figure
When is a symmetric pin-jointed framework isostatic?
Maxwell's rule from 1864 gives a necessary condition for a framework to be
isostatic in 2D or in 3D. Given a framework with point group symmetry, group
representation theory is exploited to provide further necessary conditions.
This paper shows how, for an isostatic framework, these conditions imply very
simply stated restrictions on the numbers of those structural components that
are unshifted by the symmetry operations of the framework. In particular, it
turns out that an isostatic framework in 2D can belong to one of only six point
groups. Some conjectures and initial results are presented that would give
sufficient conditions (in both 2D and 3D) for a framework that is realized
generically for a given symmetry group to be an isostatic framework.Comment: 24 pages, 10 figures; added references, minor changes, revised last
paragrap
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
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
Algorithms for 3D rigidity analysis and a first order percolation transition
A fast computer algorithm, the pebble game, has been used successfully to
study rigidity percolation on 2D elastic networks, as well as on a special
class of 3D networks, the bond-bending networks. Application of the pebble game
approach to general 3D networks has been hindered by the fact that the
underlying mathematical theory is, strictly speaking, invalid in this case. We
construct an approximate pebble game algorithm for general 3D networks, as well
as a slower but exact algorithm, the relaxation algorithm, that we use for
testing the new pebble game. Based on the results of these tests and additional
considerations, we argue that in the particular case of randomly diluted
central-force networks on BCC and FCC lattices, the pebble game is essentially
exact. Using the pebble game, we observe an extremely sharp jump in the largest
rigid cluster size in bond-diluted central-force networks in 3D, with the
percolating cluster appearing and taking up most of the network after a single
bond addition. This strongly suggests a first order rigidity percolation
transition, which is in contrast to the second order transitions found
previously for the 2D central-force and 3D bond-bending networks. While a first
order rigidity transition has been observed for Bethe lattices and networks
with ``chemical order'', this is the first time it has been seen for a regular
randomly diluted network. In the case of site dilution, the transition is also
first order for BCC, but results for FCC suggest a second order transition.
Even in bond-diluted lattices, while the transition appears massively first
order in the order parameter (the percolating cluster size), it is continuous
in the elastic moduli. This, and the apparent non-universality, make this phase
transition highly unusual.Comment: 28 pages, 19 figure
The orbit rigidity matrix of a symmetric framework
A number of recent papers have studied when symmetry causes frameworks on a
graph to become infinitesimally flexible, or stressed, and when it has no
impact. A number of other recent papers have studied special classes of
frameworks on generically rigid graphs which are finite mechanisms. Here we
introduce a new tool, the orbit matrix, which connects these two areas and
provides a matrix representation for fully symmetric infinitesimal flexes, and
fully symmetric stresses of symmetric frameworks. The orbit matrix is a true
analog of the standard rigidity matrix for general frameworks, and its analysis
gives important insights into questions about the flexibility and rigidity of
classes of symmetric frameworks, in all dimensions.
With this narrower focus on fully symmetric infinitesimal motions, comes the
power to predict symmetry-preserving finite mechanisms - giving a simplified
analysis which covers a wide range of the known mechanisms, and generalizes the
classes of known mechanisms. This initial exploration of the properties of the
orbit matrix also opens up a number of new questions and possible extensions of
the previous results, including transfer of symmetry based results from
Euclidean space to spherical, hyperbolic, and some other metrics with shared
symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure
Acute Surgical Pulmonary Embolectomy: A 9-Year Retrospective Analysis
Acute pulmonary embolism is a substantial cause of morbidity and death. Although the American College of Chest Physicians Evidence-Based Clinical Practice Guidelines recommend surgical pulmonary embolectomy in patients with acute pulmonary embolism associated with hypotension, there are few reports of 30-day mortality rates. We performed a retrospective review of acute pulmonary embolectomy procedures performed in 96 consecutive patients who had severe, globally hypokinetic right ventricular dysfunction as determined by transthoracic echocardiography. Data on patients who were treated from January 2003 through December 2011 were derived from health system databases of the New York State Cardiac Surgery Reporting System and the Society of Thoracic Surgeons. The data represent procedures performed at 3 tertiary care facilities within a large health system operating in the New York City metropolitan area. The overall 30-day mortality rate was 4.2%. Most patients (68 [73.9%]) were discharged home or to rehabilitation facilities (23 [25%]). Hemodynamically stable patients with severe, globally hypokinetic right ventricular dysfunction had a 30-day mortality rate of 1.4%, with a postoperative mean length of stay of 9.1 days. Comparable findings for hemodynamically unstable patients were 12.5% and 13.4 days, respectively. Acute pulmonary embolectomy can be a viable procedure for patients with severe, globally hypokinetic right ventricular dysfunction, with or without hemodynamic compromise; however, caution is warranted. Our outcomes might be dependent upon institutional capability, experience, surgical ability, and careful patient selection
Nonlinear Integer Programming
Research efforts of the past fifty years have led to a development of linear
integer programming as a mature discipline of mathematical optimization. Such a
level of maturity has not been reached when one considers nonlinear systems
subject to integrality requirements for the variables. This chapter is
dedicated to this topic.
The primary goal is a study of a simple version of general nonlinear integer
problems, where all constraints are still linear. Our focus is on the
computational complexity of the problem, which varies significantly with the
type of nonlinear objective function in combination with the underlying
combinatorial structure. Numerous boundary cases of complexity emerge, which
sometimes surprisingly lead even to polynomial time algorithms.
We also cover recent successful approaches for more general classes of
problems. Though no positive theoretical efficiency results are available, nor
are they likely to ever be available, these seem to be the currently most
successful and interesting approaches for solving practical problems.
It is our belief that the study of algorithms motivated by theoretical
considerations and those motivated by our desire to solve practical instances
should and do inform one another. So it is with this viewpoint that we present
the subject, and it is in this direction that we hope to spark further
research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G.
Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50
Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art
Surveys, Springer-Verlag, 2009, ISBN 354068274
Predictors of long-term pain and disability in patients with low back pain investigated by magnetic resonance imaging: A longitudinal study
<p>Abstract</p> <p>Background</p> <p>It is possible that clinical outcome of low back pain (LBP) differs according to the presence or absence of spinal abnormalities on magnetic resonance imaging (MRI), in which case there could be value in using MRI findings to refine case definition of LBP in epidemiological research. We therefore conducted a longitudinal study to explore whether spinal abnormalities on MRI for LBP predict prognosis after 18 months.</p> <p>Methods</p> <p>A consecutive series of patients aged 20-64 years, who were investigated by MRI because of mechanical LBP (median duration of current episode 16.2 months), were identified from three radiology departments, and those who agreed completed self-administered questionnaires at baseline and after a mean follow-up period of 18.5 months (a mean of 22.2 months from MRI investigation). MRI scans were assessed blind to other clinical information, according to a standardised protocol. Associations of baseline MRI findings with pain and disability at follow-up, adjusted for treatment and for other potentially confounding variables, were assessed by Poisson regression and summarised by prevalence ratios (PRs) with their 95% confidence intervals (CIs).</p> <p>Results</p> <p>Questionnaires were completed by 240 (74%) of the patients who had agreed to be followed up. Among these 111 men and 129 women, 175 (73%) reported LBP in the past four weeks, 89 (37%) frequent LBP, and 72 (30%) disabling LBP. In patients with initial disc degeneration there was an increased risk of frequent (PR 1.3, 95%CI 1.0-1.9) and disabling LBP (PR 1.7, 95%CI 1.1-2.5) at follow-up. No other associations were found between MRI abnormalities and subsequent outcome.</p> <p>Conclusions</p> <p>Our findings suggest that the MRI abnormalities examined are not major predictors of outcome in patients with LBP. They give no support to the use of MRI findings as a way of refining case definition for LBP in epidemiological research.</p
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