Convex Rank Tests and Semigraphoids

Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. Each class consists of the linear extensions of a partially ordered set specified by data. Our methods refine existing rank tests of non-parametric statistics, such as the sign test and the runs test, and are useful for exploratory analysis of ordinal data. We establish a bijection between convex rank tests and probabilistic conditional independence structures known as semigraphoids. The subclass of submodular rank tests is derived from faces of the cone of submodular functions, or from Minkowski summands of the permutohedron. We enumerate all small instances of such rank tests. Of particular interest are graphical tests, which correspond to both graphical models and to graph associahedra

Thouless Pumps and Bulk-Boundary Correspondence in Higher-Order Symmetry-Protected Topological Phases

The bulk-boundary correspondence relates quantized edge states to bulk topological invariants in topological phases of matter. In one-dimensional symmetry-protected topological systems (SPTs), quantized topological Thouless pumps directly reveal this principle and provide a sound mathematical foundation. Symmetry-protected higher-order topological phases of matter (HOSPTs) also feature a bulk-boundary correspondence, but its connection to quantized charge transport remains elusive. Here we show that quantized Thouless pumps connecting $C_4$-symmetric HOSPTs can be described by a tuple of four Chern numbers that measure quantized bulk charge transport in a direction-dependent fashion. Moreover, this tuple of Chern numbers allows to predict the sign and value of fractional corner charges in the HOSPTs. We show that the topologically non-trivial phase can be characterized by both quadrupole and dipole configurations, shedding new light on current debates about the multi-pole nature of the HOSPT bulk. By employing corner-periodic boundary conditions, we generalize Restas's theory to HOSPTs. Our approach provides a simple framework for understanding topological invariants of general HOSPTs and paves the way for an in-depth description of future dynamical experiments.Comment: 4 pages, 4 figures plus supplement

Спосіб пошарової побудови виробів на базі тріангуляційної 3D моделі за заданою стратегією обробки лазерним промінням

Спосіб пошарової побудови виробів на базі тріангуляційної 3D моделі за заданою стратегією обробки лазерним промінням включає періодичне опускання столу на величину кроку побудови і подальше формування шарів. При формуванні кожного наступного шару матеріалу змінюють стратегію обробки лазерним промінням шляхом задання напрямку одиничних треків випадковим чином

From intensive care to rehabilitation: survey on the satisfaction with care received during prolonged hospitalization for COVID-19 at a northern Italian university hospital

Objective: Investigating the experiences perceived by COVID-19 inpatients is a fundamental research area that is starting to be explored. For this reason, our objective was to provide the first Italian survey on COVID-19 inpatients' satisfaction, obtained through a self-completed questionnaire previously used in a reference study in a UK cohort of COVID-19 patients. Subjects and methods: Hospitalized COVID-19 patients (>20 days) admitted to Ferrara University Hospital who underwent rehabilitation during their hospital stay were invited to complete an anonymous questionnaire. The survey's questions explored the patients' satisfaction with the health services received, and their completion took place approximately one year after hospitalization. Information on sex, number of wards, ICU stays, and hospital discharge dates was collected. Results: Sixty-two completed questionnaires were analyzed. The average overall satisfaction score obtained from the answers indicated by the participants in the tenth question was 4.7 out of 5.0. Very positive responses were observed for information about discharge plans, privacy, management of pain, sleep quality, and feeling of safety. The possibility of being consulted about medications and side effects received a very low satisfaction score. Considering overall satisfaction, no significant differences were noted for sex or ICU stay. The obtained results were almost superimposable to those reported in the cohort of COVID-19 patients of the reference study. Conclusions: This survey suggested that COVID-19 patients' healthcare satisfaction was high. Nevertheless, some areas must be improved, such as the communication and involvement of the patients in the decision-making of care and the discussion about medications or possible side effects