Combinatorics of BB-orbits and Bruhat--Chevalley order on involutions

Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\in B$, $f\in\mathfrak{u}^*$, $x\in\mathfrak{u}$. To each involution $\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\Omega_{\sigma}\in\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is given in terms of rook placements and is dual to A. Melnikov's results on $B$-orbits on $\mathfrak{u}$. Using results of F. Incitti, we also prove that this partial order coincides with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page

Comparison of Information Structures and Completely Positive Maps

A theorem of Blackwell about comparison between information structures in classical statistics is given an analogue in the quantum probabilistic setup. The theorem provides an operational interpretation for trace-preserving completely positive maps, which are the natural quantum analogue of classical stochastic maps. The proof of the theorem relies on the separation theorem for convex sets and on quantum teleportation.Comment: 12 pages. Substantial changes. Accepted for publication in Journal of Physics

Choosing face: The curse of self in profile image selection.

People draw automatic social inferences from photos of unfamiliar faces and these first impressions are associated with important real-world outcomes. Here we examine the effect of selecting online profile images on first impressions. We model the process of profile image selection by asking participants to indicate the likelihood that images of their own face ("self-selection") and of an unfamiliar face ("other-selection") would be used as profile images on key social networking sites. Across two large Internet-based studies (n = 610), in line with predictions, image selections accentuated favorable social impressions and these impressions were aligned to the social context of the networking sites. However, contrary to predictions based on people's general expertise in self-presentation, other-selected images conferred more favorable impressions than self-selected images. We conclude that people make suboptimal choices when selecting their own profile pictures, such that self-perception places important limits on facial first impressions formed by others. These results underscore the dynamic nature of person perception in real-world contexts

Participatory Analysis, Monitoring and Evaluation for Fishing Communities: A Manual

While there are many manuals available on participatory rapid appraisal approaches to monitoring and evaluation, there were none easily used by field officers attempting to aid and encourage fishing community level participation in monitoring and evaluating activities of projects and programmes in rural fishing communities.This manual is prepared in cook book fashion with easily followed instructions for 26 participatory monitoring tools to allow use by both local field staff acting as facilitators and directly by community members engaged in the evaluation process

Asymptotically optimal quantum channel reversal for qudit ensembles and multimode Gaussian states

We investigate the problem of optimally reversing the action of an arbitrary quantum channel C which acts independently on each component of an ensemble of n identically prepared d-dimensional quantum systems. In the limit of large ensembles, we construct the optimal reversing channel R* which has to be applied at the output ensemble state, to retrieve a smaller ensemble of m systems prepared in the input state, with the highest possible rate m/n. The solution is found by mapping the problem into the optimal reversal of Gaussian channels on quantum-classical continuous variable systems, which is here solved as well. Our general results can be readily applied to improve the implementation of robust long-distance quantum communication. As an example, we investigate the optimal reversal rate of phase flip channels acting on a multi-qubit register.Comment: 17 pages, 3 figure

Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

A Christian Guide to Body Stewardship, Diet and Exercise - 3rd Edition

This free textbook provides readers with a wealth of practical information regarding body stewardship, nutrition, and exercise, all written from a Christian worldview. While other textbooks provide readers with the why proper nutrition and regular exercise is important, this textbook takes it one step further and provides readers with the how . Each chapter is filled with helpful charts, tables, and figures that equip readers with tangible resources and recommendations they can use to put into practice the various concepts being introduced. Additionally, each chapter is written from a Christian worldview recognizing that the human body was created for a purpose, and through Godly stewardship of our bodies, we can more effectively worship our creator.https://digitalcommons.cedarville.edu/cedrus_press_publications/1024/thumbnail.jp

Self-Reporting Technologies for Supporting Epilepsy Treatment

Epilepsy diagnosis and treatment relies heavily on patient self-reporting for informing clinical decision-making. These self-reports are traditionally collected from handwritten patient journals and tend to be either incomplete or inaccurate. Recent mobile and wearable health tracking developments stand to dramatically impact clinical practice through supporting patient and caregiver data collection activities. However, the specific types and characteristics of the data that clinicians need for patient care are not well known. In this study, we conducted interviews, a literature review, an expert panel, and online surveys to assess the availability and quality of patient-reported data that is useful but reported as being unavailable, difficult for patients to collect, or unreliable during epilepsy diagnosis and treatment, respectively. The results highlight important yet underexplored data collection and design opportunities for supporting the diagnosis, treatment, and self-management of epilepsy and expose notable gaps between clinical data needs and current patient practices