3,076 research outputs found
A structural approach to kernels for ILPs: Treewidth and Total Unimodularity
Kernelization is a theoretical formalization of efficient preprocessing for
NP-hard problems. Empirically, preprocessing is highly successful in practice,
for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this,
previous work studied the existence of kernelizations for ILP related problems,
e.g., for testing feasibility of Ax <= b. In contrast to the observed success
of CPLEX, however, the results were largely negative. Intuitively, practical
instances have far more useful structure than the worst-case instances used to
prove these lower bounds.
In the present paper, we study the effect that subsystems with (Gaifman graph
of) bounded treewidth or totally unimodularity have on the kernelizability of
the ILP feasibility problem. We show that, on the positive side, if these
subsystems have a small number of variables on which they interact with the
remaining instance, then we can efficiently replace them by smaller subsystems
of size polynomial in the domain without changing feasibility. Thus, if large
parts of an instance consist of such subsystems, then this yields a substantial
size reduction. We complement this by proving that relaxations to the
considered structures, e.g., larger boundaries of the subsystems, allow
worst-case lower bounds against kernelization. Thus, these relaxed structures
can be used to build instance families that cannot be efficiently reduced, by
any approach.Comment: Extended abstract in the Proceedings of the 23rd European Symposium
on Algorithms (ESA 2015
A discrete slug population model determined by egg production
Slugs are significant pests in agriculture (as well as a nuisance to gardeners), and it is therefore important to understand their population dynamics for the construction of efficient and effective control measures. Differential equation models of slug populations require the inclusion of large (variable) temporal delays, and strong seasonal forcing results in a non-autonomous system. This renders such models open to only a limited amount of rigorous analysis. In this paper, we derive a novel batch model based purely upon the quantity of eggs produced at different times of the year. This model is open to considerable reduction; from the resulting two variable discrete-time system it is possible to reconstruct the dynamics of the full population across the year and give conditions for extinction or global stability and persistence. Furthermore, the steady state temporal population distribution displays qualitatively different behavior with only small changes in the survival probability of slugs. The model demonstrates how small variations in the favorability of different years may result in widely different slug population fluctuations between consecutive years, and is in good agreement with field data
Nosocomial infections: A further assault on patients in a high-volume urban trauma centre in South Africa
Background. Hospital-acquired infections (HAIs) are a major cause of morbidity and mortality. Surgical site infection (SSI) rates are reported to range from 2.5% to 41%. HAI increases the risk of death by 2 - 11%, and three-quarters of these deaths are directly attributable to SSIs.Objectives. To determine the incidence of HAI and to identify risk factors amenable to modification with a resultant reduction in infection rates.Methods. An analysis of HAIs was performed between January and April 2018 in the trauma centre surgical wards at Groote Schuur Hospital, Cape Town, South Africa.Results. There were 769 admissions during the study period. Twenty-two patients (0.03%) developed an HAI. The majority were men, and the mean age was 32 years (range 18 - 57). The mean length of hospital stay (LoS) was 9 days, higher than the mean LoS for the hospital of 6 days. Fourteen patients underwent emergency surgery, 3 patients underwent abbreviated damage control surgery, and 9 patients were admitted to the critical care unit. Most patients with nosocomial sepsis were treated with appropriate culture-based antibiotics (82%). Four patients were treated with amoxicillin/clavulanic acid presumptively prior to culture and sensitivity results, after which antibiotic therapy was tailored. All but 1 patient received antibiotics.Conclusions. A combination of measures is required to prevent trauma-related infections. By determining the incidence of nosocomial infections in our trauma patients, uniform policies to reduce infection rates further could be determined. Our low incidence of infection may be explained by established preventive care bundles already in place.
A new displacement-based approach to calculate stress intensity factors with the boundary element method
The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs). The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has be-come very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM) in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes
Picosecond timescale tracking of pentacene triplet excitons with chemical sensitivity
Singlet fission is a photophysical process in which an optically excited singlet exciton is converted into two triplet excitons. Singlet fission sensitized solar cells are expected to display a greatly enhanced power conversion efficiency compared to conventional singlejunction cells, but the efficient design of such devices relies on the selection of materials capable of harvesting triplets generated in the fission chromophore. To this aim, the possibility of measuring triplet exciton ynamics with chemical selectivity paves the way for the rational design of complex heterojunctions, with optimized triplet conversion. Here we exploit the chemical sensitivity of X-ray absorption spectroscopy to track triplet exciton dynamics at the picosecond timescale in multilayer films of pentacene, the archetypal singlet fission material. We experimentally identify the signature of the triplet exciton in the Carbon K-edge absorption spectrum and measure its lifetime of about 300 ps. Our results are supported by state-of-the-art ab initio calculations
Modular and duality properties of surface operators in N=2* gauge theories
We calculate the instanton partition function of the four-dimensional N = 2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure
N = 2 or to N = 2* gauge theories
The Dynamics of Poor Systems of Galaxies
We assemble and observe a sample of poor galaxy systems that is suitable for
testing N-body simulations of hierarchical clustering (Navarro, Frenk, & White
1997; NFW) and other dynamical halo models (e.g., Hernquist 1990). We (1)
determine the parameters of the density profile rho(r) and the velocity
dispersion profile sigma(R), (2) separate emission-line galaxies from
absorption-line galaxies, examining the model parameters and as a function of
spectroscopic type, and (3) for the best-behaved subsample, constrain the
velocity anisotropy parameter, beta, which determines the shapes of the galaxy
orbits.
The NFW universal profile and the Hernquist (1990) model both provide good
descriptions of the spatial data. In most cases an isothermal sphere is ruled
out. Systems with declining sigma(R) are well-matched by theoretical profiles
in which the star-forming galaxies have predominantly radial orbits (beta > 0);
many of these galaxies are probably falling in for the first time. There is
significant evidence for spatial segregation of the spectroscopic classes
regardless of sigma(R).Comment: 36 pages, 20 figures, and 5 tables. To appear in the Astrophysical
Journa
Asymptotics for the number of eigenvalues of three-particle Schr\"{o}dinger operators on lattices
We consider the Hamiltonian of a system of three quantum mechanical particles
(two identical fermions and boson)on the three-dimensional lattice and
interacting by means of zero-range attractive potentials. We describe the
location and structure of the essential spectrum of the three-particle discrete
Schr\"{o}dinger operator being the total quasi-momentum
and the ratio of the mass of fermion and boson.
We choose for the interaction in such a way the system
consisting of one fermion and one boson has a zero energy resonance.
We prove for any the existence infinitely many eigenvalues of the
operator We establish for the number of
eigenvalues lying below the following asymptotics Moreover,
for all nonzero values of the quasi-momentum we establish the
finiteness of the number of eigenvalues of
below the bottom of the essential spectrum and we give an asymptotics for the
number of eigenvalues below zero.Comment: 25 page
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