Rules for Minimal Atomic Multipole Expansion of Molecular Fields

A non-empirical minimal atomic multipole expansion (MAME) defines atomic charges or higher multipoles that reproduce electrostatic potential outside molecules. MAME eliminates problems associated with redundancy and with statistical sampling, and produces atomic multipoles in line with chemical intuition.Comment: 3.5 pages, 3 color PS figures embedde

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions or projects from a fixed set P. Each project k is characterized by a valuation function; v_k(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.Comment: Under Revie

Blended delivery of imagery rescripting for childhood ptsd:A case study during the covid 19 pandemic

[Background] Despite the growing evidence that trauma-focused treatments can be applied as first-line approaches for individuals with childhood trauma-related PTSD (Ch-PTSD), many therapists are still reluctant to provide trauma-focused treatments as a first-choice intervention for individuals with Ch-PTSD, especially by telehealth. The current manuscript will therefore give an overview of the evidence for the effectiveness of trauma-focused therapies for individuals with Ch-PTSD, the delivery of trauma-focused treatments via telehealth, and a case example on how a specific form of trauma focused therapy: Imagery Rescripting (ImRs) can be applied by telehealth. [Method] This article presents a clinical illustration of a blended telehealth trajectory of imagery rescripting (ImRs) Ch-PTSD delivered during the COVID-19 pandemic. [Results] The presented case shows that ImRs can be safely and effectively performed by telehealth for ch-PTSD, no stabilization phase was needed and only seven sessions were needed to drastically reduce Ch-PTSD and depressive symptoms, and to increase quality of life. [Conclusion] This case report shows the effectiveness of ImRs by telehealth for Ch-PTSD, which gives hope and additional possibilities to reach out to patients with ch-PTDS. Telehealth treatment might have some of advantages for specific patients, especially, but certainly not only, during the pandemic

The Inverse Shapley Value Problem

For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice theory as a measure of the "influence" of voters. The \emph{Inverse Shapley Value Problem} is the problem of designing a weighted voting scheme which (approximately) achieves a desired input vector of values for the Shapley-Shubik indices. Despite much interest in this problem no provably correct and efficient algorithm was known prior to our work. We give the first efficient algorithm with provable performance guarantees for the Inverse Shapley Value Problem. For any constant \eps > 0 our algorithm runs in fixed poly$(n)$ time (the degree of the polynomial is independent of \eps) and has the following performance guarantee: given as input a vector of desired Shapley values, if any "reasonable" weighted voting scheme (roughly, one in which the threshold is not too skewed) approximately matches the desired vector of values to within some small error, then our algorithm explicitly outputs a weighted voting scheme that achieves this vector of Shapley values to within error \eps. If there is a "reasonable" voting scheme in which all voting weights are integers at most \poly(n) that approximately achieves the desired Shapley values, then our algorithm runs in time \poly(n) and outputs a weighted voting scheme that achieves the target vector of Shapley values to within error $\eps=n^{-1/8}.

Comparative Perspectives on History and Historians: Essays in Memory of Bryce Lyon (1920-2007)

Comparative Perspectives on History and Historians: Essays in Memory of Bryce Lyon (1920-2007) features a section of appreciations of Bryce Lyon from the three editors, R. C. Van Caenegem, and Walter Prevenier, followed by three sections on the major areas on which Lyon\u27s research concentrated: the legacy of Henri Pirenne, constitutional and legal history of England and the Continent, and the economic history of the Low Countries. Original essays by Bernard S. Bachrach, David S. Bachrach, Jan Dumolyn, Caroline Dunn, Jelle Haemers, John H. A. Munro, James M. Murray, Anthony Musson, David Nicholas, W. Mark Ormrod, Walter Prevenier, Jeff Rider, Don C. Skemer, and Marci Sortor deepen our understanding of Lyon\u27s career and significance and further our knowledge of the areas in which he worked.https://scholarworks.wmich.edu/mip_fopl/1001/thumbnail.jp

Triggering And Maintaining Interest In Early Phases Of Interest Development

This article reports on the complexities of triggering and maintaining interest, a process that is initiated when something catches the attention of a learner. Triggering interest (the initiation of the psychological state of interest) can occur in both earlier and later phases of interest development. However, in this study we focus on this process in earlier phases of interest development. Findings from a study of the activity of eight, Black, inner-city, middle school-age participants in an out-of-school biology workshop are described. We address the identification and generalizability of potential triggers for interest across activities and explore the relationship between triggers for interest and learner characteristics. Taken together, findings from the study suggest that learners do not perceive and respond identically to potential triggers for interest; and that the triggering process is nuanced by particular activity, and the readiness of the learner to respond