Deciding first-order properties of nowhere dense graphs

Nowhere dense graph classes, introduced by Nesetril and Ossona de Mendez, form a large variety of classes of "sparse graphs" including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and graph classes of bounded expansion. We show that deciding properties of graphs definable in first-order logic is fixed-parameter tractable on nowhere dense graph classes. At least for graph classes closed under taking subgraphs, this result is optimal: it was known before that for all classes C of graphs closed under taking subgraphs, if deciding first-order properties of graphs in C is fixed-parameter tractable, then C must be nowhere dense (under a reasonable complexity theoretic assumption). As a by-product, we give an algorithmic construction of sparse neighbourhood covers for nowhere dense graphs. This extends and improves previous constructions of neighbourhood covers for graph classes with excluded minors. At the same time, our construction is considerably simpler than those. Our proofs are based on a new game-theoretic characterisation of nowhere dense graphs that allows for a recursive version of locality-based algorithms on these classes. On the logical side, we prove a "rank-preserving" version of Gaifman's locality theorem.Comment: 30 page

On the Parameterized Intractability of Monadic Second-Order Logic

One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms, where the parameter is the tree-width plus the size of the formula. An immediate question is whether this is best possible or whether the result can be extended to classes of unbounded tree-width. In this paper we show that in terms of tree-width, the theorem cannot be extended much further. More specifically, we show that if C is a class of graphs which is closed under colourings and satisfies certain constructibility conditions and is such that the tree-width of C is not bounded by \log^{84} n then MSO_2-model checking is not fpt unless SAT can be solved in sub-exponential time. If the tree-width of C is not poly-logarithmically bounded, then MSO_2-model checking is not fpt unless all problems in the polynomial-time hierarchy can be solved in sub-exponential time

In search of virus carriers of the 1988 and 2002 phocine distemper virus outbreaks in European harbour seals

European harbour seal (Phoca vitulina) populations decreased substantially during the phocine distemper virus (PDV) outbreaks of 1988 and 2002. Different hypotheses have stated that various seals and terrestrial carnivore species might be the source of infection. To further analyse these hypotheses, grey (Halichoerus grypus) and ringed (Phoca hispida) seals, polar bears (Ursus maritimus) and minks (Mustela lutreola) were sampled from the North Sea and East Greenland coasts between 1988 and 2004 and investigated by RT-PCR using a panmorbillivirus primer pair. However, all samples were negative for morbillivirus nucleic acid

Natural-gradient learning for spiking neurons

In many normative theories of synaptic plasticity, weight updates implicitly depend on the chosen parametrization of the weights. This problem relates, for example, to neuronal morphology: synapses which are functionally equivalent in terms of their impact on somatic firing can differ substantially in spine size due to their different positions along the dendritic tree. Classical theories based on Euclidean gradient descent can easily lead to inconsistencies due to such parametrization dependence. The issues are solved in the framework of Riemannian geometry, in which we propose that plasticity instead follows natural gradient descent. Under this hypothesis, we derive a synaptic learning rule for spiking neurons that couples functional efficiency with the explanation of several well-documented biological phenomena such as dendritic democracy, multiplicative scaling and heterosynaptic plasticity. We therefore suggest that in its search for functional synaptic plasticity, evolution might have come up with its own version of natural gradient descent.Comment: Joint senior authorship: Walter M. Senn and Mihai A. Petrovic

Technical note:On the reliability of laboratory beta-source calibration for luminescence dating

The dose rate of the 90Sr / 90Y beta source used in most luminescence readers is a laboratory key parameter. There is a well-established body of knowledge about parameters controlling accuracy and precision of the calibration value but some hard-to-explain inconsistencies still exist. Here, we have investigated the impact of grain size, aliquot size and irradiation geometry on the resulting calibration value through experiments and simulations. The resulting data indicate that the dose rate of an individual beta source results from the interplay of a number of parameters, most of which are well established by previous studies. Our study provides evidence for the impact of aliquot size on the absorbed dose in particular for grain sizes of 50–200 µm. For this grain-size fraction, the absorbed dose is enhanced by ∼ 10 %–20 % as aliquot size decreases due to the radial increase of dose rate towards the centre of the aliquot. The enhancement is most variable for 50–100 µm grains mounted as aliquots of &lt; 8 mm size. The enhancement is reversed when large grains are mounted as small aliquots due to the edge effect by which the dose induced by backscattered electrons is reduced. While the build-up of charge dictates the increase of absorbed dose with the increase of grain size, this principle becomes more variable with changing irradiation geometry. We conclude that future calibration samples should consist of subsamples composed of small, medium, large and very large quartz grains, each obtaining several gamma doses. The calibration value measured with small, medium and large aliquots is then obtained from the inverse slope of the fitted line, not from a single data point. In this way, all possible irradiation geometries of an individual beta source are covered, and the precision of the calibration is improved.</p

Transportable system enabling multiple irradiation studies under simultaneous hypoxia in vitro

BackgroundCells in solid tumours are variably hypoxic and hence resistant to radiotherapy - the essential role of oxygen in the efficiency of irradiation has been acknowledged for decades. However, the currently available methods for performing hypoxic experiments in vitro have several limitations, such as a limited amount of parallel experiments, incapability of keeping stable growth conditions and dependence on CO2 incubator or a hypoxia workstation. The purpose of this study was to evaluate the usability of a novel portable system (Minihypoxy) in performing in vitro irradiation studies under hypoxia, and present supporting biological data.Materials and methodsThis study was conducted on cancer cell cultures in vitro. The cells were cultured in normoxic (similar to 21% O-2) or in hypoxic (1% O-2) conditions either in conventional hypoxia workstation or in the Minihypoxy system and irradiated at dose rate 1.28Gy/min2.9%. The control samples were sham irradiated. To study the effects of hypoxia and irradiation on cell viability and DNA damage, western blotting, immunostainings and clonogenic assay were used. The oxygen level, pH, evaporation rate and osmolarity of the culturing media on cell cultures in different conditions were followed.ResultsThe oxygen concentration in interest (5, 1 or 0% O-2) was maintained inside the individual culturing chambers of the Minihypoxy system also during the irradiation. The radiosensitivity of the cells cultured in Minihypoxy chambers was declined measured as lower phosphorylation rate of H2A.X and increased clonogenic capacity compared to controls (OER similar to 3).Conclusions The Minihypoxy system allows continuous control of hypoxic environment in multiple wells and is transportable. Furthermore, the system maintains the low oxygen environment inside the individual culturing chambers during the transportation and irradiation in experiments which are typically conducted in separate facilities.Peer reviewe

A numerical technique to simulate display pixels based on electrowetting

We present a numerical simulation technique to calculate the deformation of interfaces between a conductive and non-conductive fluid as well as the motion of liquid–liquid–solid three-phase contact lines under the influence of externally applied electric fields in electrowetting configuration. The technique is based on the volume of fluid method as implemented in the OpenFOAM framework, using a phase fraction parameter to track the different phases. We solve the combined electrohydrodynamic problem by coupling the equations for electric effects—Gauss’s law and a charge transport equation—to the Navier–Stokes equations of fluid flow. Specifically, we use a multi-domain approach to solving for the electric field in the solid and liquid dielectric parts of the system. A Cox–Voinov boundary condition is introduced to describe the dynamic contact angle of moving contact lines. We present several benchmark problems with analytical solutions to validate the simulation model. Subsequently, the model is used to study the dynamics of an electrowetting-based display pixel. We demonstrate good qualitative agreement between simulation results of the opening and closing of a pixel with experimental tests of the identical reference geometry

The heavy quark decomposition of the S-matrix and its relation to the pinch technique

We propose a decomposition of the S-matrix into individually gauge invariant sub-amplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompsition is obtained by considering limits of the S-matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic $n$-point functions is briefly discussed.Comment: 11 uuencoded pages, NYU-TH-94/10/0