General Position Subsets and Independent Hyperplanes in d-Space

Erd\H{o}s asked what is the maximum number $\alpha(n)$ such that every set of $n$ points in the plane with no four on a line contains $\alpha(n)$ points in general position. We consider variants of this question for $d$-dimensional point sets and generalize previously known bounds. In particular, we prove the following two results for fixed $d$: - Every set $H$ of $n$ hyperplanes in $\mathbb{R}^d$ contains a subset $S\subseteq H$ of size at least $c \left(n \log n\right)^{1/d}$, for some constant $c=c(d)>0$, such that no cell of the arrangement of $H$ is bounded by hyperplanes of $S$ only. - Every set of $cq^d\log q$ points in $\mathbb{R}^d$, for some constant $c=c(d)>0$, contains a subset of $q$ cohyperplanar points or $q$ points in general position. Two-dimensional versions of the above results were respectively proved by Ackerman et al. [Electronic J. Combinatorics, 2014] and by Payne and Wood [SIAM J. Discrete Math., 2013].Comment: 8 page

Finding Multiple New Optimal Locations in a Road Network

We study the problem of optimal location querying for location based services in road networks, which aims to find locations for new servers or facilities. The existing optimal solutions on this problem consider only the cases with one new server. When two or more new servers are to be set up, the problem with minmax cost criteria, MinMax, becomes NP-hard. In this work we identify some useful properties about the potential locations for the new servers, from which we derive a novel algorithm for MinMax, and show that it is efficient when the number of new servers is small. When the number of new servers is large, we propose an efficient 3-approximate algorithm. We verify with experiments on real road networks that our solutions are effective and attains significantly better result quality compared to the existing greedy algorithms

Practical learning method for multi-scale entangled states

We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of measurements is polynomial in the number of particles. Data post-processing for state reconstruction uses standard tools, namely matrix diagonalisation and conjugate gradient method, and scales polynomially with the number of particles. Our method prevents the build-up of errors from both numerical and experimental imperfections

Chronic hindlimb ischemia impairs functional vasodilation and vascular reactivity in mouse feed arteries

Vasodilation of lower leg arterioles is impaired in animal models of chronic peripheral ischemia. In addition to arterioles, feed arteries are a critical component of the vascular resistance network, accounting for as much as 50% of the pressure drop across the arterial circulation. Despite the critical importance of feed arteries in blood flow control, the impact of ischemia on feed artery vascular reactivity is unknown. At 14 days following unilateral resection of the femoral–saphenous artery–vein pair, functional vasodilation of the profunda femoris artery was severely impaired, 11 ± 9 versus 152 ± 22%. Although endothelial and smooth muscle-dependent vasodilation were both impaired in ischemic arteries compared to control arteries (Ach: 40 ± 14 versus 81 ± 11%, SNP: 43 ± 12 versus and 85 ± 11%), the responses to acetylcholine and sodium nitroprusside were similar, implicating impaired smooth muscle-dependent vasodilation. Conversely, vasoconstriction responses to norepinephrine were not different between ischemic and control arteries, −68 ± 3 versus −66 ± 3%, indicating that smooth muscle cells were functional following the ischemic insult. Finally, maximal dilation responses to acetylcholine, ex vivo, were significantly impaired in the ischemic artery compared to control, 71 ± 9 versus 97 ± 2%, despite a similar generation of myogenic tone to the same intravascular pressure (80 mmHg). These data indicate that ischemia impairs feed artery vasodilation by impairing the responsiveness of the vascular wall to vasodilating stimuli. Future studies to examine the mechanistic basis for the impact of ischemia on vascular reactivity or treatment strategies to improve vascular reactivity following ischemia could provide the foundation for an alternative therapeutic paradigm for peripheral arterial occlusive disease

Audio-Visual Fusion for Emotion Recognition in the Valence-Arousal Space Using Joint Cross-Attention

Automatic emotion recognition (ER) has recently gained lot of interest due to its potential in many real-world applications. In this context, multimodal approaches have been shown to improve performance (over unimodal approaches) by combining diverse and complementary sources of information, providing some robustness to noisy and missing modalities. In this paper, we focus on dimensional ER based on the fusion of facial and vocal modalities extracted from videos, where complementary audio-visual (A-V) relationships are explored to predict an individual's emotional states in valence-arousal space. Most state-of-the-art fusion techniques rely on recurrent networks or conventional attention mechanisms that do not effectively leverage the complementary nature of A-V modalities. To address this problem, we introduce a joint cross-attentional model for A-V fusion that extracts the salient features across A-V modalities, that allows to effectively leverage the inter-modal relationships, while retaining the intra-modal relationships. In particular, it computes the cross-attention weights based on correlation between the joint feature representation and that of the individual modalities. By deploying the joint A-V feature representation into the cross-attention module, it helps to simultaneously leverage both the intra and inter modal relationships, thereby significantly improving the performance of the system over the vanilla cross-attention module. The effectiveness of our proposed approach is validated experimentally on challenging videos from the RECOLA and AffWild2 datasets. Results indicate that our joint cross-attentional A-V fusion model provides a cost-effective solution that can outperform state-of-the-art approaches, even when the modalities are noisy or absent.Comment: arXiv admin note: substantial text overlap with arXiv:2203.14779, arXiv:2111.0522

LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

Mental health outcomes after SARS-CoV-2 vaccination in the United States: A national cross-sectional study.

Funder: NIHR Cambridge Biomedical Research CentreFunder: National Institute for Health Research (NIHR)BACKGROUND: Worsening of anxiety and depressive symptoms have been widely described during the COVID-19 pandemic. It can be hypothesized that vaccination could link to reduced symptoms of anxiety and/or depression. However, to date, no study has assessed this. This study aims to examine anxiety and depressive symptoms after vaccination in US adults, meanwhile test sociodemographic disparities in these outcomes. METHODS: Data from the January 6-June 7 2021, cross-sectional Household Pulse Survey were analyzed. Using survey-weighted logistic regression, we assessed the relationships between SARS-CoV-2 vaccination and anxiety and/or depressive symptoms, both on overall and sociodemographic subgroups. We controlled for a variety of potential socioeconomic and demographic confounding factors. RESULTS: Of the 453,167 participants studied, 52.2% of the participants had received the COVID-19 vaccine, and 26.5% and 20.3% of the participants reported anxiety and depression, respectively. Compared to those not vaccinated, the vaccinated participants had a 13% lower odds of anxiety (adjusted odds ratio [AOR] = 0.85, 95%CI 0.83-0.90) and 17% lower odds of depression (AOR = 0.83, 95%CI 0.79-0.85). Disparities on the above associations were identified in age, marital status, education level, ethnic/race, and income level, but not on gender. LIMITATIONS: The causal inference was not able to be investigated due to the cross-sectional study design. CONCLUSION: Being vaccinated for SARS-CoV-2 was associated with lower odds of anxiety and/or depressive symptoms. While those more middle-aged or more affluent, were more likely to show these negative associations, the contrary was observed in ethnic minorities and those with lower educational attainment. More strategic and demography-sensitive public health communications could perhaps temper these issues

The Pursuit of K: Reflections on the Current State-of-the-Art in Stress Intensity Factor Solutions for Practical Aerospace Applications

The elastic stress intensity factor (SIF, commonly denoted as K) is the foundation of practical fracture mechanics (FM) analysis for aircraft structures. This single parameter describes the first-order effects of stress magnitude and distribution as well as the geometry of both structure/component and crack. Hence, the calculation of K is often the most significant step in fatigue analysis based on FM. This presentation will provide several reflections on the current state-of-the-art in SIF solution methods used for practical aerospace applications, including a brief historical perspective, descriptions of some recent and ongoing advances, and comments on some remaining challenges. Newman and Raju made significant early contributions to practical structural analysis by developing closed-form SIF equations for surface and corner cracks in simplified geometries, often based on empirical fits of finite element (FE) solutions. Those solutions (and others like them) were sometimes revised as new analyses were conducted or limitations discovered. The foundational solutions have exhibited striking longevity, despite the relatively "coarse" FE models employed many decades ago. However, in recent years, the accumulation of different generations of solutions for the same nominal geometry has led to some confusion (which solution is correct?), and steady increases in computational capabilities have facilitated the discovery of inaccuracies in some (not all!) of the legacy solutions. Some examples of problems and solutions are presented and discussed, including the challenge of maintaining consistency with legacy design applications. As computational power has increased, the prospect of calculating large numbers of SIF solutions for specific complex geometries with advanced numerical methods has grown more attractive. Fawaz and Andersson, for example, have been generating literally millions of new SIF solutions for different combinations of multiple cracks under simplified loading schemes using p-version FE methods. These data are invaluable, but questions remain about their practical use, because the tabular databases of key results needed to support practical life analysis can occupy gigabytes of storage for only a few classes of geometries. The prospect of using such advanced numerical methods to calculate in real time only those K solutions actually needed to support a specific crack growth analysis is also tempting, but the stark reality is that the computational cost is still so high that the approach is not practical except for specific, critical application problems. Some thoughts are offered about alternative paradigms. Compounding approaches are some of the earliest building blocks of SIF development for more complex geometries. These approaches are especially attractive because of their very low computational cost and their conceptual robustness; they are, in some ways, an intriguing contrast and complement to the brute-force numerical methods. In recent years, researchers at NRC-Canada have published remarkable results showing how compounding approaches can be used to generate accurate solutions for very difficult problems. Examples are provided of some successes--and some limitations--using this approach. These closed-form, tabulated numerical, and compounding approaches have typically been used for simple remote loading with simple load paths to the crack. However, many significant cracks occur in complex stress gradient fields. This is a job for weight function (WF) methods, where the arbitrary stress distribution on the crack plane in the corresponding uncracked body (typically determined using FE methods) is used to determine K. Several significant recent advances in WF methods and solutions are highlighted here. Fueled by advanced 3D numerical methods, many new solutions have been generated for classic geometries such as surface and corner cracks with wide ranges of geometrical validity. A new WF formulation has also be developed for part-through cracks considering the arbitrary stress gradients in all directions in the crack plane (so-called bivariant solutions). Basic WF methods have recently been combined with analytical expressions for crack plane stresses to develop a large family of accurate SIF solutions for corner, surface, and through cracks at internal or external notches with very wide ranges of shapes, sizes, acuities, and offsets. Finally, WF solutions are much faster than FE or boundary element solutions, but can still be much slower than simple closed-form solutions, especially for bivariant solutions that can require 2D numerical integration. Novel pre-integration and dynamic tabular methods have been developed that substantially increase the speed of these advanced WF solutions. The practical utility of advanced SIF methods, including both WF and direct numerical methods, is greatly enhanced if the FM life analysis can be directly and efficiently linked with digital models of the actual structure or component (e.g., FE models for stress analysis). Two recent advances of this type will be described. One approach directly interfaces the FM life analysis with the FE model of the uncracked component (including stress results). Through a powerful graphical user interface, simplified FM life models can be constructed (and visualized) directly on the component model, with the computer collecting the geometry and stress gradient information needed for the life calculation. An even more powerful paradigm uses expert logic to automatically build an optimum simple fracture model at any and every desired location in the component model, perform the life calculation, and even generate fatigue crack growth life contour maps, all with minimal user intervention. This paradigm has also been extended to the automatic calculation of fracture risk, considering uncertainty or variability in key input parameters such as initial crack size or location. Another new integrated approach links the engineering life analysis, the component model, and a 3D numerical fracture analysis built with the same component model to generate a table of SIF values at a specific location that can then be employed efficiently to perform the life calculation. Some attention must be given to verification and validation (V&V) issues and challenges: how good are these SIF solutions, how good is good enough, and does anyone believe the life answer? It is important to think critically about the different sources of error or uncertainty and to perform V&V in a hierarchal, building-block manner. Some accuracy issues for SIF solutions, for example, may actually involve independent material behavior issues, such as constraint loss effects for crack fronts near component surfaces, and can be a source of confusion. Recommendations are proposed for improved V&V approaches. This presentation will briefly but critically survey the range of issues and advances mentioned above, with a particular view towards assembling an integrated approach that combines different methods to create practical tools for real-world design and analysis problems. Examples will be selectively drawn from the recent literature, from recent enhancements in the NASGRO and DARWIN computer codes, and from previously unpublished researc