Alien Registration- Bosse, Marie I. (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/30584/thumbnail.jp

Topological Correlations in a Layer Adsorbed on a Crystal Surface

The incoherent scattering of electrons by a layer adsorbed at a single crystal surface is determined by the topological correlations of elements forming the adsorbed layer. The model for the description of atoms or molecules adsorbed on the surface is formulated in terms of occupation operators which are expressed in terms of pseudospin operators with a given spin value. The correlations can be determined by the fluctuation dissipation theorem in connection with the susceptibility or given directly by means of the Green functions properly chosen. An example of the topological or chemical disorder of two components is considered in detail. The calculations of the topological correlations allow us to find the incoherent scattering amplitude as a function of the surface coverage which can be experimentally detected.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Approximate well-supported Nash equilibria in symmetric bimatrix games

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed strategy. The smallest constant $\varepsilon$ currently known for which there is a polynomial-time algorithm that computes an $\varepsilon$-well-supported Nash equilibrium in bimatrix games is slightly below $2/3$. In this paper we study this problem for symmetric bimatrix games and we provide a polynomial-time algorithm that gives a $(1/2+\delta)$-well-supported Nash equilibrium, for an arbitrarily small positive constant $\delta$

Polylogarithmic Supports are required for Approximate Well-Supported Nash Equilibria below 2/3

In an epsilon-approximate Nash equilibrium, a player can gain at most epsilon in expectation by unilateral deviation. An epsilon well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with positive probability must have payoff within epsilon of the best response payoff. Daskalakis, Mehta and Papadimitriou conjectured that every win-lose bimatrix game has a 2/3-well-supported Nash equilibrium that uses supports of cardinality at most three. Indeed, they showed that such an equilibrium will exist subject to the correctness of a graph-theoretic conjecture. Regardless of the correctness of this conjecture, we show that the barrier of a 2/3 payoff guarantee cannot be broken with constant size supports; we construct win-lose games that require supports of cardinality at least Omega((log n)^(1/3)) in any epsilon-well supported equilibrium with epsilon < 2/3. The key tool in showing the validity of the construction is a proof of a bipartite digraph variant of the well-known Caccetta-Haggkvist conjecture. A probabilistic argument shows that there exist epsilon-well-supported equilibria with supports of cardinality O(log n/(epsilon^2)), for any epsilon> 0; thus, the polylogarithmic cardinality bound presented cannot be greatly improved. We also show that for any delta > 0, there exist win-lose games for which no pair of strategies with support sizes at most two is a (1-delta)-well-supported Nash equilibrium. In contrast, every bimatrix game with payoffs in [0,1] has a 1/2-approximate Nash equilibrium where the supports of the players have cardinality at most two.Comment: Added details on related work (footnote 7 expanded

Navigating Uncertainty - Evaluating Human and Model-Based Forecasting of COVID-19

Infectious disease modelling and forecasting has garnered broad interest throughout the COVID-19 pandemic. Accurate forecasts for the trajectory of the pandemic can be useful for informing public policy and public health interventions. In this, forecast evaluation plays a crucial role. Forecasts are only useful if they are accurate. Evaluating the performance of different forecasting approaches can provide information about their trustworthiness, as well as on how to improve them. This thesis makes contributions in two areas related to forecasting and forecast evaluation in an epidemiological context. Firstly, it advances the tools available as well as our theoretical understanding of how to evaluate forecasts of infectious diseases. Secondly, it investigates the relative performance and interplay of human judgement and mathematical modelling in the context of short-term forecasts of COVID-19. With respect to forecast evaluation, the first contribution made by this thesis is scoringutils, an R package that facilitates the evaluation process. The package provides a coherent framework for forecast evaluation in R and implements a selection of scoring rules, helper functions and visualisations. In particular, it supports evaluating forecasts in a quantile-based format that has recently been used by several COVID-19 Forecast Hubs in the US, Europe, and Germany and Poland. The second contribution to the field of forecast evaluation is a novel approach to evaluating forecasts in an epidemiological context. Scores like the continuous ranked probability score (CRPS) or the weighted interval score (WIS), which are common in epidemiology, represent a generalisation of the absolute error to predictive distributions. However, determining predictive performance based on the absolute distance between forecast and observation neglects the exponential nature of infectious disease processes. Transforming forecasts and observations using the natural logarithm before applying the CRPS or WIS may be more adequate in an epidemiological context. The resulting score can be understood as a probabilistic version of the relative error. It measures predictive performance in terms of the exponential growth rate and can serve as a variance-stabilising transformation assuming that the underlying disease process has a quadratic mean-variance relationship. This thesis motivates the idea of transforming forecasts before evaluating them and illustrates the behaviour of these scores using data from the European COVID-19 Forecast Hub. Log-transforming forecasts before scoring them changed the ranking between forecasters and resulted in scores that were more evenly distributed across time and space. With respect to the role of human judgement in infectious disease forecasting, this thesis contributes two studies that analyse and compare the predictive performance of human judgement forecasts and model-based predictions. It starts from the understanding that computational modelling, which has been the predominant way to obtain infectious disease forecasts in the past, represents a synthesis between epidemiological and mathematical assumptions and the expertise and judgement of the researchers fine-tuning the models. Understanding the interplay between human judgement and mathematical modelling better, as well as trade-offs between the two, may help make future forecasting efforts more efficient and improve predictive accuracy. This thesis uses the newly developed forecast evaluation tools to investigate the interplay between human judgement and mathematical modelling in the context of infectious disease forecasting, specifically of COVID-19. In a first study, it elicited forecasts from researchers and laypersons and compared these human judgement forecasts against predictions from a minimally-tuned mathematical model, as well as from an ensemble of several computational models submitted to the German and Polish COVID-19 Forecast Hub. It found that human judgement forecasts generally performed on par with the ensemble of computational models, performing slightly better when predicting cases and slightly worse when predicting deaths. Adding more forecasts to the ensemble was generally advantageous, even if the model to be added performed worse than the already existing ensemble. A second study replicates the basic set-up and compared human judgement forecasts of COVID-19 in the UK, elicited as part of a public “UK Crowd Forecasting Challenge”, against the ensemble of all forecasts submitted to the European COVID-19 Forecast Hub. Again, forecasts performed broadly on par with the ensemble forecasts. We did not find a strong difference between self-selected “experts” and “non-experts” in terms of predictive performance. Results should generally be interpreted carefully, due to small sample sizes and susceptibility to choices made in the evaluation process. We explored a novel way to combine human judgement and mathematical modelling by asking forecasters to predict the effective reproduction number Rt which then got mapped to case and death numbers using an epidemiological model. Due to various limitations, the initial performance with this new approach was worse than that of direct human forecasts. Nevertheless, approaches that combine human judgement and mathematical modelling are promising as they could help reduce the cognitive burden of the forecasters and increase accuracy

A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, thus eliminating some of the difficulties involved in following the known indirect reduction.Comment: 21 page

Scoring epidemiological forecasts on transformed scales

Forecast evaluation is essential for the development of predictive epidemic models and can inform their use for public health decision-making. Common scores to evaluate epidemiological forecasts are the Continuous Ranked Probability Score (CRPS) and the Weighted Interval Score (WIS), which can be seen as measures of the absolute distance between the forecast distribution and the observation. However, applying these scores directly to predicted and observed incidence counts may not be the most appropriate due to the exponential nature of epidemic processes and the varying magnitudes of observed values across space and time. In this paper, we argue that transforming counts before applying scores such as the CRPS or WIS can effectively mitigate these difficulties and yield epidemiologically meaningful and easily interpretable results. Using the CRPS on log-transformed values as an example, we list three attractive properties: Firstly, it can be interpreted as a probabilistic version of a relative error. Secondly, it reflects how well models predicted the time-varying epidemic growth rate. And lastly, using arguments on variance-stabilizing transformations, it can be shown that under the assumption of a quadratic mean-variance relationship, the logarithmic transformation leads to expected CRPS values which are independent of the order of magnitude of the predicted quantity. Applying a transformation of log(x + 1) to data and forecasts from the European COVID-19 Forecast Hub, we find that it changes model rankings regardless of stratification by forecast date, location or target types. Situations in which models missed the beginning of upward swings are more strongly emphasised while failing to predict a downturn following a peak is less severely penalised when scoring transformed forecasts as opposed to untransformed ones. We conclude that appropriate transformations, of which the natural logarithm is only one particularly attractive option, should be considered when assessing the performance of different models in the context of infectious disease incidence

Dynamic stability control in younger and older adults during stair descent.

The purpose of this study was to examine dynamic stability control in older and younger adults while descending stairs. Thirteen older (aged 64-77years) and 13 younger (aged 22-29years) adults descended a staircase at their preferred speed. A motion capture system and three force plates were used to determine locomotion mechanics. Dynamic stability was investigated by using the margin of stability, calculated as the instantaneous difference between anterior boundary of the base of support and extrapolated centre of mass. At the initiation of the single support phase, older adults demonstrated a more negative (p<.05) margin of stability value. The component responsible for the lower margin of stability in the elderly was the higher velocity of the centre of mass (p<.05). Before the initiation of the single support phase, the older adults showed a lower (p<.05) ankle and knee joint angular impulse compared to the younger ones. We found a significant correlation (r=.729, p<.05) between centre of mass velocity and joint angular impulse. These results indicate that older adults are at greater risk of falls while descending stairs potentially due to a reduced ability to generate adequate leg-extensor muscular output to safely control the motion of the body's centre of mass while stepping down

Sound-propagation gap in fluid mixtures

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.Comment: Published; withdrawn since ordering in archive gives misleading impression of new publicatio