3,561 research outputs found
Bovine tuberculosis in Swedish farmed deer
Bovine tuberculosis (BTB) was introduced into Swedish farmed deer herds in 1987. Epidemiological investigations showed that 10 deer herds had become infected (July 1994) and a common source of infection, a consignment of 168 imported farmed fallow deer, was identified (I). As trace-back of all imported and in-contact deer was not possible, a control program, based on tuberculin testing, was implemented in July 1994. As Sweden has been free from BTB since 1958, few practising veterinarians had experience in tuberculin testing. In this test, result relies on the skill, experience and conscientiousness of the testing veterinarian. Deficiencies in performing the test may adversely affect the test results and thereby compromise a control program. Quality indicators may identify possible deficiencies in testing procedures. For that purpose, reference values for measured skin fold thickness (prior to injection of the tuberculin) were established (II) suggested to be used mainly by less experienced veterinarians to identify unexpected measurements. Furthermore, the within-veterinarian variation of the measured skin fold thickness was estimated by fitting general linear models to data (skin fold measurements) (III). The mean square error was used as an estimator of the within-veterinarian variation. Using this method, four (6%) veterinarians were considered to have unexpectedly large variation in measurements. In certain large extensive deer farms, where mustering of all animals was difficult, meat inspection was suggested as an alternative to tuberculin testing. The efficiency of such a control was estimated in paper IV and V. A Reed Frost model was fitted to data from seven BTB-infected deer herds and the spread of infection was estimated (< 0.6 effective contacts per deer and year) (IV). These results were used to model the efficiency of meat inspection in an average extensive Swedish deer herd. Given a 20% annual slaughter and meat inspection, the model predicted that BTB would be either detected or eliminated in most herds (90%) 15 years after introduction of one infected deer. In 2003, an alternative control for BTB in extensive Swedish deer herds, based on the results of paper V, was implemented
Compression via Matroids: A Randomized Polynomial Kernel for Odd Cycle Transversal
The Odd Cycle Transversal problem (OCT) asks whether a given graph can be
made bipartite by deleting at most of its vertices. In a breakthrough
result Reed, Smith, and Vetta (Operations Research Letters, 2004) gave a
\BigOh(4^kkmn) time algorithm for it, the first algorithm with polynomial
runtime of uniform degree for every fixed . It is known that this implies a
polynomial-time compression algorithm that turns OCT instances into equivalent
instances of size at most \BigOh(4^k), a so-called kernelization. Since then
the existence of a polynomial kernel for OCT, i.e., a kernelization with size
bounded polynomially in , has turned into one of the main open questions in
the study of kernelization.
This work provides the first (randomized) polynomial kernelization for OCT.
We introduce a novel kernelization approach based on matroid theory, where we
encode all relevant information about a problem instance into a matroid with a
representation of size polynomial in . For OCT, the matroid is built to
allow us to simulate the computation of the iterative compression step of the
algorithm of Reed, Smith, and Vetta, applied (for only one round) to an
approximate odd cycle transversal which it is aiming to shrink to size . The
process is randomized with one-sided error exponentially small in , where
the result can contain false positives but no false negatives, and the size
guarantee is cubic in the size of the approximate solution. Combined with an
\BigOh(\sqrt{\log n})-approximation (Agarwal et al., STOC 2005), we get a
reduction of the instance to size \BigOh(k^{4.5}), implying a randomized
polynomial kernelization.Comment: Minor changes to agree with SODA 2012 version of the pape
Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model
The collective dynamics in populations of magnetic spin torque oscillators
(STO) is an intensely studied topic in modern magnetism. Here, we show that
arrays of STO coupled via dipolar fields can be modeled using a variant of the
Kuramoto model, a well-known mathematical model in non-linear dynamics. By
investigating the collective dynamics in arrays of STO we find that the
synchronization in such systems is a finite size effect and show that the
critical coupling-for a complete synchronized state-scales with the number of
oscillators. Using realistic values of the dipolar coupling strength between
STO we show that this imposes an upper limit for the maximum number of
oscillators that can be synchronized. Further, we show that the lack of long
range order is associated with the formation of topological defects in the
phase field similar to the two-dimensional XY model of ferromagnetism. Our
results shed new light on the synchronization of STO, where controlling the
mutual synchronization of several oscillators is considered crucial for
applications.Comment: Accepted for publication in Scientific Reports. Corrected typo in
Eq.(9) from previous versio
Discretizing stochastic dynamical systems using Lyapunov equations
Stochastic dynamical systems are fundamental in state estimation, system
identification and control. System models are often provided in continuous
time, while a major part of the applied theory is developed for discrete-time
systems. Discretization of continuous-time models is hence fundamental. We
present a novel algorithm using a combination of Lyapunov equations and
analytical solutions, enabling efficient implementation in software. The
proposed method circumvents numerical problems exhibited by standard algorithms
in the literature. Both theoretical and simulation results are provided
Half-integrality, LP-branching and FPT Algorithms
A recent trend in parameterized algorithms is the application of polytope
tools (specifically, LP-branching) to FPT algorithms (e.g., Cygan et al., 2011;
Narayanaswamy et al., 2012). However, although interesting results have been
achieved, the methods require the underlying polytope to have very restrictive
properties (half-integrality and persistence), which are known only for few
problems (essentially Vertex Cover (Nemhauser and Trotter, 1975) and Node
Multiway Cut (Garg et al., 1994)). Taking a slightly different approach, we
view half-integrality as a \emph{discrete} relaxation of a problem, e.g., a
relaxation of the search space from to such that
the new problem admits a polynomial-time exact solution. Using tools from CSP
(in particular Thapper and \v{Z}ivn\'y, 2012) to study the existence of such
relaxations, we provide a much broader class of half-integral polytopes with
the required properties, unifying and extending previously known cases.
In addition to the insight into problems with half-integral relaxations, our
results yield a range of new and improved FPT algorithms, including an
-time algorithm for node-deletion Unique Label Cover with
label set and an -time algorithm for Group Feedback Vertex
Set, including the setting where the group is only given by oracle access. All
these significantly improve on previous results. The latter result also implies
the first single-exponential time FPT algorithm for Subset Feedback Vertex Set,
answering an open question of Cygan et al. (2012).
Additionally, we propose a network flow-based approach to solve some cases of
the relaxation problem. This gives the first linear-time FPT algorithm to
edge-deletion Unique Label Cover.Comment: Added results on linear-time FPT algorithms (not present in SODA
paper
Breaking the PPSZ Barrier for Unique 3-SAT
The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane (FOCS 1998) is the
fastest known algorithm for (Promise) Unique k-SAT. We give an improved
algorithm with exponentially faster bounds for Unique 3-SAT.
For uniquely satisfiable 3-CNF formulas, we do the following case
distinction: We call a clause critical if exactly one literal is satisfied by
the unique satisfying assignment. If a formula has many critical clauses, we
observe that PPSZ by itself is already faster. If there are only few clauses
allover, we use an algorithm by Wahlstr\"om (ESA 2005) that is faster than PPSZ
in this case. Otherwise we have a formula with few critical and many
non-critical clauses. Non-critical clauses have at least two literals
satisfied; we show how to exploit this to improve PPSZ.Comment: 13 pages; major revision with simplified algorithm but slightly worse
constant
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