Defect Modes and Homogenization of Periodic Schr\"odinger Operators

We consider the discrete eigenvalues of the operator H_\eps=-\Delta+V(\x)+\eps^2Q(\eps\x), where V(\x) is periodic and Q(\y) is localized on $\R^d,\ \ d\ge1$. For \eps>0 and sufficiently small, discrete eigenvalues may bifurcate (emerge) from spectral band edges of the periodic Schr\"odinger operator, H_0 = -\Delta_\x+V(\x), into spectral gaps. The nature of the bifurcation depends on the homogenized Schr\"odinger operator L_{A,Q}=-\nabla_\y\cdot A \nabla_\y +\ Q(\y). Here, $A$ denotes the inverse effective mass matrix, associated with the spectral band edge, which is the site of the bifurcation.Comment: 26 pages, 3 figures, to appear SIAM J. Math. Ana

On Linear Congestion Games with Altruistic Social Context

We study the issues of existence and inefficiency of pure Nash equilibria in linear congestion games with altruistic social context, in the spirit of the model recently proposed by de Keijzer {\em et al.} \cite{DSAB13}. In such a framework, given a real matrix $\Gamma=(\gamma_{ij})$ specifying a particular social context, each player $i$ aims at optimizing a linear combination of the payoffs of all the players in the game, where, for each player $j$, the multiplicative coefficient is given by the value $\gamma_{ij}$. We give a broad characterization of the social contexts for which pure Nash equilibria are always guaranteed to exist and provide tight or almost tight bounds on their prices of anarchy and stability. In some of the considered cases, our achievements either improve or extend results previously known in the literature

Resistance Breeding in Apple at Dresden-Pillnitz

Resistance breeding in apple has a long tradition at the Institute of Fruit Breeding now Julius Kuehn-institute in Dresden-Pillnitz. The breeding was aimed at the production of multiple resistance cultivars to allow a more sustainable and environmentally friendly production of apple. In the last decades a series of resistant cultivars (Re®-cultivars) bred in Dresden-Pillnitz has been released, ‘Recolor’ and ‘Rekarda’ in 2006. The main topic in the resistance breeding programme was scab resistance and the donor of scab resistance in most cultivars was Malus x floribunda 821. Due to the development of strains that are able to overcome resistance genes inherited by M. x floribunda 821 and due to the fact that single resistance genes can be broken easily, pyramiding of resistance genes is necessary. Besides scab, fire blight and powdery mildew are the main disease for which a pyramiding of genes is aspired in Pillnitz. Biotechnical approaches are necessary for the early detection of pyramided resistance genes in breeding clones. This paper will give an overview of the resistance breeding of apple in Pillnitz and the methods used

Inelastic Decay of Electrons in the Shockley-type Metal-Organic Interface States

We present a theoretical study of lifetimes of interface states (IS) on metal-organic interfaces PTCDA/Ag(111), NTCDA/Ag(111), PFP/Ag(111), and PTCDA/Ag(100), describing and explaining the recent experimental data. By means of unfolding the band structure of one of the interfaces under study onto the Ag(111) Brillouin zone we demonstrate, that the Brillouin zone folding upon organic monolayer deposition plays a minor role in the phase space for electron decay, and hence weakly affects the resulting lifetimes. The presence of the unoccupied molecular states below the IS gives a small contribution to the IS decay rate mostly determined by the change of the phase space of bulk states upon the energy shift of the IS. The calculated lifetimes follow the experimentally observed trends. In particular, we explain the trend of the unusual increase of the IS lifetimes with rising temperature.Comment: 8 pages, 5 figure

The metaphysics of Machian frame-dragging

The paper investigates the kind of dependence relation that best portrays Machian frame-dragging in general relativity. The question is tricky because frame-dragging relates local inertial frames to distant distributions of matter in a time-independent way, thus establishing some sort of non-local link between the two. For this reason, a plain causal interpretation of frame-dragging faces huge challenges. The paper will shed light on the issue by using a generalized structural equation model analysis in terms of manipulationist counterfactuals recently applied in the context of metaphysical enquiry by Schaffer (2016) and Wilson (2017). The verdict of the analysis will be that frame-dragging is best understood in terms of a novel type of dependence relation that is half-way between causation and grounding

New Complexity Results and Algorithms for the Minimum Tollbooth Problem

The inefficiency of the Wardrop equilibrium of nonatomic routing games can be eliminated by placing tolls on the edges of a network so that the socially optimal flow is induced as an equilibrium flow. A solution where the minimum number of edges are tolled may be preferable over others due to its ease of implementation in real networks. In this paper we consider the minimum tollbooth (MINTB) problem, which seeks social optimum inducing tolls with minimum support. We prove for single commodity networks with linear latencies that the problem is NP-hard to approximate within a factor of $1.1377$ through a reduction from the minimum vertex cover problem. Insights from network design motivate us to formulate a new variation of the problem where, in addition to placing tolls, it is allowed to remove unused edges by the social optimum. We prove that this new problem remains NP-hard even for single commodity networks with linear latencies, using a reduction from the partition problem. On the positive side, we give the first exact polynomial solution to the MINTB problem in an important class of graphs---series-parallel graphs. Our algorithm solves MINTB by first tabulating the candidate solutions for subgraphs of the series-parallel network and then combining them optimally

Effekten av olika koncentrationer av Rotstop R och Rotstop S och ofullständig täckning av Rotstop S på sporinfektioner av rotticka på granstubbar

The effectiveness of treatment with two Phlebiopsis gigantea based preparations (Rotstop® and RotstopS) in different concentrations against the root and butt rot causing fungus Heterobasidion annosum s.l. on Norway spruce (Picea abies) thinning stumps in southern Sweden was compared. The trees were cut on three sites during the summer 2004 and 285 stumps were treated manually with 100% cover with two different amounts of spores in solution corresponding to approximately 5×106 spores/l and 10×106 spores/l. 31 stumps received mechanical part cover with the highest spore concentrations of Phlebiopsis gigantea, i.e. approximately 20×106 spores/l. Mechanical treatment was assessed for satisfactory treatment effect. Three months later, samples were collected and analyzed. There was a significant reduction in frequency and relative areas of Heterobasidion spp. infections on stumps with manual application of control agents compared to untreated stumps. On average 10 to 23% of stumps subjected to manual treatments were infected compared to 52% for the untreated stumps. However, none of the concentration solutions of Rotstop® and RotstopS differed from the others in reduction of Heterobasidion spp. infections. Mechanical treatment failed to control the Heterobasidion spp. infections, but there was a tendency for the 85.1-95.0% cover class to provide better result than the others. Thus, despite of the incomplete control of the pathogen, stump treatment with different concentrations of Phlebiopsis gigantea oidia in suspensions provided equal effects at the present spore loads of Heterobasidion spp.Effektiviteten av behandling med två pergamentsvampsbaserade (Phlebiopsis gigantea) lösningar (Rotstop® och RotstopS) i olika koncentrationer mot sporinfektioner av rotticka (Heterobasidion spp.) på gallringsstubbar av gran (Picea abies) i södra Sverige jämfördes. Träd avverkades på tre olika lokaler under sommaren 2004 och sammanlagt 285 stubbar behandlades manuellt med en hundraprocentig täckning i två olika koncentrationer motsvarande ungefär 5×106 sporer/l respektive 10×106 sporer/l lösning. 31 stubbar på en av lokalerna behandlades maskinellt med en ofullständig täckning men med den högsta koncentrationen av pergamentsvamp (RotstopS), ca 20×106 sporer/l lösning. Effekten av den mekaniska behandlingens partiella täckning jämfördes med den manuella fullständiga. Tre månader efter behandlingen samlades prover in för analys med avseende på förekomsten av rotticka. Alla manuella behandlingar gav en signifikant reducering av frekvensen av och relativa arean av rottickeinfektioner jämfört med obehandlade stubbar. I genomsnitt var 10 till 23 % av de manuellt behandlade stubbarna infekterade jämfört med 52 % av de obehandlade. Ingen av de manuella applikationerna skiljde sig dock från varandra. Den mekaniska behandlingen gav inte ett tillfredsställande resultat men det fanns en tendens till att täckningsgradsklass 85,1- 95,0 % fungerade bättre än de andra. Således, trots att ingen behandling gav en 100 % -ig minskning av antalet rottickeinfektioner, verkar olika koncentrationer av Rotstop® och RotstopS ge ett likvärdigt resultat under de förhållanden i sportryck som rådde vid behandlingen

On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, eg. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with the three dimensional experiment show that three and two dimensional approximations are in excellent agreement and one dimensional approximations are in good qualitative agreement. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.Comment: 24 pages, 28 figures, submitted to Phys Rev

Physics in the Real Universe: Time and Spacetime

The Block Universe idea, representing spacetime as a fixed whole, suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This view is however based on time-reversible microphysical laws and does not represent macro-physical behaviour and the development of emergent complex systems, including life, which do indeed exist in the real universe. When these are taken into account, the unchanging block universe view of spacetime is best replaced by an evolving block universe which extends as time evolves, with the potential of the future continually becoming the certainty of the past. However this time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world linesComment: 28 pages, including 9 Figures. Major revision in response to referee comment

Temporal Evolution of Serum Concentrations of High-Sensitivity Cardiac Troponin During 1 Year After Acute Coronary Syndrome Admission

BACKGROUND: Detailed insights in temporal evolution of high-sensitivity cardiac troponin following acute coronary syndrome (ACS) are currently missing. We aimed to describe and compare the post-ACS kinetics of high-sensitivity cardiac troponin I (hs-cTnI) and high-sensitivity cardiac troponin T (hs-cTnT), and to determine their intra- and interindividual variation in clinically stable patients. METHODS AND RESULTS: We determined hs-cTnI (Abbott) and hs-cTnT (Roche) in 1507 repeated blood samples, derived from 191 patients with ACS (median, 8/patient) who remained free from adverse cardiac events during 1-year follow-up. Post-ACS kinetics were studied by linear mixed-effect models. Using the samples collected in the 6- to 12-month post-ACS time frame, patients were then considered to have chronic coronary syndrome. We determined (differences between) the average hs-cTnI and average hs-cTnT concentration, and the intra- and interindividual variation for both biomarkers. Compared with hs-cTnT, hs-cTnI peaked higher (median 3506 ng/L versus 494 ng/L; P<0.001) and was quicker below the biomarker-specific upper reference limit (16 versus 19 days; P<0.001). In the post–6-month samples, hs-cTnI and hs-cTnT showed modest correlation (rspearman=0.60), whereas the average hs-cTnT concentration was 5 times more likely to be above the upper reference limit than hs-cTnI. The intraindividual variations of hs-cTnI and hs-cTnT were 14.0% and 18.1%, while the interindividual variations were 94.1% and 75.9%. CONCLUSIONS: Hs-cTnI peaked higher after ACS and was quicker below the upper reference limit. In the post–6-month samples, hs-cTnI and hs-cTnT were clearly not interchangeable, and average hs-cTnT concentrations were much more often above the upper reference limit than hs-cTnI. For both markers, the within-patient variation fell largely below beween-patient variation. REGISTRATION: URL: https://www.trialregister.nl; unique identifiers: NTR1698 and NTR1106