Quantum Weakly Nondeterministic Communication Complexity

We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this model of quantum nondeterministic communication complexity for a total function. This separation is quadratic.Comment: 12 pages. v3: minor correction

Snudebiller i hvidkløver til frø

Kløversnudebiller og kløvergnavere kan forårsage udbyttetab i hvidkløver til frø. Ved Danmarks JordbrugsForskning er der de sidste fem år lavet et forsøg, der har til formål at bestemme snudebillernes skadevirkning. Der blev i gennemsnit af de fem års forsøg målt et merudbytte på ca. 40 pct. ved at bekæmpe snudebiller. Forsøgene kan ikke bruges til at belyse, hvor mange sprøjtninger det er nødvendigt at udføre mod snudebiller

Refining a Bayesian network using a chain event graph

The search for a useful explanatory model based on a Bayesian Network (BN) now has a long and successful history. However, when the dependence structure between the variables of the problem is asymmetric then this cannot be captured by the BN. The Chain Event Graph (CEG) provides a richer class of models which incorporates these types of dependence structures as well as retaining the property that conclusions can be easily read back to the client. We demonstrate on a real health study how the CEG leads us to promising higher scoring models and further enables us to make more refined conclusions than can be made from the BN. Further we show how these graphs can express causal hypotheses about possible interventions that could be enforced

Permeability and conductivity of platelet-reinforced membranes and composites

We present large scale simulations of the diffusion constant $D$ of a random composite consisting of aligned platelets with aspect ratio $a/b>>1$ in a matrix (with diffusion constant $D_0$) and find that $D/D_0 = 1/(1+ c_1 x + c_2 x^2)$, where $x= a v_f/b$ and $v_f$ is the platelet volume fraction. We demonstrate that for large aspect ratio platelets the pair term ($x^2$) dominates suggesting large property enhancements for these materials. However a small amount of face-to-face ordering of the platelets markedly degrades the efficiency of platelet reinforcement.Comment: RevTeX, 5 pages, 4 figures, submitted to PR

Unitary Gate Synthesis for Continuous Variable Systems

We investigate the synthesis of continuous-variable two-mode unitary gates in the setting where two modes A and B are coupled by a fixed quadratic Hamiltonian H. The gate synthesis consists of a sequence of evolutions governed by Hamiltonian H interspaced by local phase shifts applied to A and B. We concentrate on protocols that require the minimum necessary number of steps and we show how to implement the beam splitter and the two-mode squeezer in just three steps. Particular attention is paid to the Hamiltonian x_A p_B that describes the effective off-resonant interaction of light with the collective atomic spin.Comment: 7 pages, minor text modifications, references adde

Bregman Voronoi Diagrams: Properties, Algorithms and Applications

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures

Relative sit-to-stand power: aging trajectories, functionally relevant cut-off points, and normative data in a large European cohort

Background: A validated, standardized, and feasible test to assess muscle power in older adults has recently been reported: the sit-to-stand (STS) muscle power test. This investigation aimed to assess the relationship between relative STS power and age and to provide normative data, cut-off points, and minimal clinically important differences (MCID) for STS power measures in older women and men. Methods: A total of 9320 older adults (6161 women and 3159 men) aged 60–103 years and 586 young and middle-aged adults (318 women and 268 men) aged 20–60 years were included in this cross-sectional study. Relative (normalized to body mass), allometric (normalized to height squared), and specific (normalized to legs muscle mass) muscle power values were assessed by the 30 s STS power test. Body composition was evaluated by dual energy X-ray absorptiometry and bioelectrical impedance analysis, and legs skeletal muscle index (SMI; normalized to height squared) was calculated. Habitual and maximal gait speed, timed up-and-go test, and 6 min walking distance were collected as physical performance measures, and participants were classified into two groups: well-functioning and mobility-limited older adults. Results: Relative STS power was found to decrease between 30–50 years (-0.05 W·kg-1·year-1; P > 0.05), 50–80 years (-0.10 to -0.13 W·kg-1·year-1; P < 0.001), and above 80 years (-0.07 to -0.08 W·kg-1·year-1; P < 0.001). A total of 1129 older women (18%) and 510 older men (16%) presented mobility limitations. Mobility-limited older adults were older and exhibited lower relative, allometric, and specific power; higher body mass index (BMI) and legs SMI (both only in women); and lower legs SMI (only in men) than their well-functioning counterparts (all P < 0.05). Normative data and cut-off points for relative, allometric, and specific STS power and for BMI and legs SMI were reported. Low relative STS power occurred below 2.1 W·kg-1 in women (area under the curve, AUC, [95% confidence interval, CI] = 0.85 [0.84–0.87]) and below 2.6 W·kg-1 in men (AUC [95% CI] = 0.89 [0.87–0.91]). The age-adjusted odds ratios [95% CI] for mobility limitations in older women and men with low relative STS power were 10.6 [9.0–12.6] and 14.1 [10.9–18.2], respectively. MCID values for relative STS power were 0.33 W·kg-1 in women and 0.42 W·kg-1 in men. Conclusions: Relative STS power decreased significantly after the age of 50 years and was negatively and strongly associated with mobility limitations. Our study provides normative data, functionally relevant cut-off points, and MCID values for STS power for their use in daily clinical practice. © 2021 The Authors. Journal of Cachexia, Sarcopenia and Muscle published by John Wiley & Sons Ltd on behalf of Society on Sarcopenia, Cachexia and Wasting Disorders