An optimal transportation approach for assessing almost stochastic order

When stochastic dominance $F\leq_{st}G$ does not hold, we can improve agreement to stochastic order by suitably trimming both distributions. In this work we consider the $L_2-$Wasserstein distance, $\mathcal W_2$, to stochastic order of these trimmed versions. Our characterization for that distance naturally leads to consider a $\mathcal W_2$-based index of disagreement with stochastic order, $\varepsilon_{\mathcal W_2}(F,G)$. We provide asymptotic results allowing to test $H_0: \varepsilon_{\mathcal W_2}(F,G)\geq \varepsilon_0$ vs $H_a: \varepsilon_{\mathcal W_2}(F,G)<\varepsilon_0$, that, under rejection, would give statistical guarantee of almost stochastic dominance. We include a simulation study showing a good performance of the index under the normal model

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

BackgroundBiochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities.ResultsIn this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler ?-leap, as well as two more recent ?-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments.ConclusionsThe Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations

The two gap transitions in Ge1−x_{1-x}Snx_x: effect of non-substitutional complex defects

The existence of non-substitutional $\beta$-Sn defects in Ge$_{1-x}$Sn$_{x}$ was confirmed by emission channeling experiments [Decoster et al., Phys. Rev. B 81, 155204 (2010)], which established that although most Sn enters substitutionally ($\alpha$-Sn) in the Ge lattice, a second significant fraction corresponds to the Sn-vacancy defect complex in the split-vacancy configuration ( $\beta$-Sn ), in agreement with our previous theoretical study [Ventura et al., Phys. Rev. B 79, 155202 (2009)]. Here, we present our electronic structure calculation for Ge$_{1-x}$Sn$_{x}$, including substitutional $\alpha$-Sn as well as non-substitutional $\beta$-Sn defects. To include the presence of non-substitutional complex defects in the electronic structure calculation for this multi-orbital alloy problem, we extended the approach for the purely substitutional alloy by Jenkins and Dow [Jenkins and Dow, Phys. Rev. B 36, 7994 (1987)]. We employed an effective substitutional two-site cluster equivalent to the real non-substitutional $\beta$-Sn defect, which was determined by a Green's functions calculation. We then calculated the electronic structure of the effective alloy purely in terms of substitutional defects, embedding the effective substitutional clusters in the lattice. Our results describe the two transitions of the fundamental gap of Ge$_{1-x}$Sn$_{x}$ as a function of the total Sn-concentration: namely from an indirect to a direct gap, first, and the metallization transition at higher $x$. They also highlight the role of $\beta$-Sn in the reduction of the concentration range which corresponds to the direct-gap phase of this alloy, of interest for optoelectronics applications.Comment: 11 pages, 9 Figure

Non-substitutional single-atom defects in the Ge_(1-x)Sn_x alloy

Ge_(1-x)Sn_x alloys have proved difficult to form at large x, contrary to what happens with other group IV semiconductor combinations. However, at low x they are typical examples of well-behaved substitutional compounds, which is desirable for harnessing the electronic properties of narrow band semiconductors. In this paper, we propose the appearance of another kind of single-site defect ($\beta-Sn$), consisting of a single Sn atom in the center of a Ge divacancy, that may account for these facts. Accordingly, we examine the electronic and structural properties of these alloys by performing extensive numerical ab-initio calculations around local defects. The results show that the environment of the $\beta$ defect relaxes towards a cubic octahedral configuration, facilitating the nucleation of metallic white tin and its segregation, as found in amorphous samples. Using the information stemming from these local defect calculations, we built a simple statistical model to investigate at which concentration these $\beta$ defects can be formed in thermal equilibrium. These results agree remarkably well with experimental findings, concerning the critical concentration above which the homogeneous alloys cannot be formed at room temperature. Our model also predicts the observed fact that at lower temperature the critical concentration increases. We also performed single site effective-field calculations of the electronic structure, which further support our hypothesis.Comment: 12 pages, 1 table, 16 figure

Assessment of methods for estimating wild rabbit population abundance in agricultural landscapes

Various methods have been used to estimate rabbit abundance, but comparisons of standard methods are still lacking, and thus, results remain roughly comparable across studies. Ideally, a method should be applicable over a wide range of situations, such as differing abundances or habitat types. Comparisons of methods are required to evaluate the benefits of each of them, and survey methods should be validated for the conditions in which they will be used. In this study, we compare the performance of direct methods (kilometric abundance index and distance sampling) in two seasons and at two times of day (dusk and night) for estimating wild rabbit abundances in agricultural landscapes. Estimates based on direct methods were highly correlated and detected similar seasonal population changes. Night counts provided better estimates than did dusk counts and exhibited more precision. Results are discussed within the context of rabbit behaviour and their implications for rabbit population surveys.Funding was provided by FEDENCA. ICB was supported by a PhD fellowship from the Spanish Ministry of Science and Innovation. PA is currently enjoying a Juan de la Cierva research contract awarded by the Spanish Ministry of Science and Innovation and is supported by the project CGL2006-09567/BOS.Peer Reviewe

Using the Sound Card as a Timer

Experiments in mechanics can often be timed by the sounds they produce. In such cases, digital audio recordings provide a simple way of measuring time intervals with an accuracy comparable to that of photogate timers. We illustrate this with an experiment in the physics of sports: to measure the speed of a hard-kicked soccer ball.Comment: 3 pages, 4 figures, Late

Sucrose homeostasis: Mechanisms and opportunity in crop yield improvement

Sugar homeostasis is a critical feature of biological systems. In humans, raised and dysregulated blood sugar is a serious health issue. In plants, directed changes in sucrose homeostasis and allocation represent opportunities in crop improvement. Plant tissue sucrose varies more than blood glucose and is found at higher concentrations (cytosol and phloem ca. 100 mM v 3.9–6.9 mM for blood glucose). Tissue sucrose varies with developmental stage and environment, but cytosol and phloem exhibit tight sucrose control. Sucrose homeostasis is a consequence of the integration of photosynthesis, synthesis of storage end products such as starch, transport of sucrose to sinks and sink metabolism. Trehalose 6-phosphate (T6P)-SnRK1 and TOR play central, still emerging roles in regulating and coordinating these processes. Overall, tissue sucrose levels are more strongly related to growth than to photosynthesis. As a key sucrose signal,T6P regulates sucrose levels, transport and metabolic pathways to coordinate source and sink at a whole plant level. Emerging evidence shows that T6P interacts with meristems. With careful targeting, T6P manipulation through exploiting natural variation, chemical intervention and genetic modification is delivering benefits for crop yields. Regulation of cereal grain set, filling and retention may be the most strategically important aspect of sucrose allocation and homeostasis for food security