A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models

Collective behavior of animals: swarming and complex patterns

En esta nota repasamos algunos modelos basados en individuos para describir el movimiento colectivo de agentes, a lo que nos referimos usando la voz inglesa swarming. Estos modelos se basan en EDOs (ecuaciones diferenciales ordinarias) y muestran un comportamiento asintótico complejo y rico en patrones, que mostramos numéricamente. Además, comentamos cómo se conectan estos modelos de partículas con las ecuaciones en derivadas parciales para describir la evolución de densidades de individuos de forma continua. Las cuestiones matemáticas relacionadas con la estabilidad de de estos modelos de EDP's (ecuaciones en derivadas parciales) despiertan gran interés en la investigación en biología matemáticaIn this short note we review some of the individual based models of the collective motion of agents, called swarming. These models based on ODEs (ordinary differential equations) exhibit a complex rich asymptotic behavior in terms of patterns, that we show numerically. Moreover, we comment on how these particle models are connected to partial differential equations to describe the evolution of densities of individuals in a continuum manner. The mathematical questions behind the stability issues of these PDE (partial differential equations) models are questions of actual interest in mathematical biology researc

Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions $d\geq 2$ and in all of space for $d\geq 3$, the uniqueness being a result previously not known for PKS with degenerate diffusion. We generalize the notion of criticality for PKS and show that subcritical problems are globally well-posed. For a fairly general class of problems, we prove the existence of a critical mass which sharply divides the possibility of finite time blow up and global existence. Moreover, we compute the critical mass for fully general problems and show that solutions with smaller mass exists globally. For a class of supercritical problems we prove finite time blow up is possible for initial data of arbitrary mass.Comment: 31 page

In vivo cholinergic basal forebrain degeneration and cognition in Parkinson's disease: Imaging results from the COPPADIS study

COPPADIS Study Group.[Introduction] We aimed to assess associations between multimodal neuroimaging measures of cholinergic basal forebrain (CBF) integrity and cognition in Parkinson's disease (PD) without dementia.[Methods] The study included a total of 180 non-demented PD patients and 45 healthy controls, who underwent structural MRI acquisitions and standardized neurocognitive assessment through the PD-Cognitive Rating Scale (PD-CRS) within the multicentric COPPADIS-2015 study. A subset of 73 patients also had Diffusion Tensor Imaging (DTI) acquisitions. Volumetric and microstructural (mean diffusivity, MD) indices of CBF degeneration were automatically extracted using a stereotactic CBF atlas. For comparison, we also assessed multimodal indices of hippocampal degeneration. Associations between imaging measures and cognitive performance were assessed using linear models.[Results] Compared to controls, CBF volume was not significantly reduced in PD patients as a group. However, across PD patients lower CBF volume was significantly associated with lower global cognition (PD-CRStotal: r = 0.37, p < 0.001), and this association remained significant after controlling for several potential confounding variables (p = 0.004). Analysis of individual item scores showed that this association spanned executive and memory domains. No analogue cognition associations were observed for CBF MD. In covariate-controlled models, hippocampal volume was not associated with cognition in PD, but there was a significant association for hippocampal MD (p = 0.02).[Conclusions] Early cognitive deficits in PD without dementia are more closely related to structural MRI measures of CBF degeneration than hippocampal degeneration. In our multicentric imaging acquisitions, DTI-based diffusion measures in the CBF were inferior to standard volumetric assessments for capturing cognition-relevant changes in non-demented PD.This work was supported by the Alzheimer Forschung Initiative e.V. (AFI International Training Grant to MJG), the Instituto de Salud Carlos III-Fondo Europeo de Desarrollo Regional (ISCIII-FEDER) [PI14/01823, PI16/01575, PI18/01898, PI19/01576, PI20/00613], the Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía [CVI-02526, CTS-7685], the Consejería de Salud y Bienestar Social de la Junta de Andalucía [PI-0471-2013, PE-0210-2018, PI-0459-2018, PE-0186-2019], the Fundación Alicia Koplowitz and the Fundación “Curemos el Parkinson” (https://www.curemoselparkinson.org). MJG is supported by the “Miguel Servet” program [CP19/00031], MALE by the University of Seville [USE-20046-J], JFM by the “Sara Borrell” program [CD13/00229] and VI-PPIT-US from the University of Seville [USE-18817-A], SJ by the “Acción B-Clínicos-Investigadores” program [B-0007-2019], and DMG by the “Río Hortega” program [CM18/00142].Peer reviewe

Mortality and pulmonary complications in patients undergoing surgery with perioperative sars-cov-2 infection: An international cohort study

Background The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (740%) had emergency surgery and 280 (248%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (261%) patients. 30-day mortality was 238% (268 of 1128). Pulmonary complications occurred in 577 (512%) of 1128 patients; 30-day mortality in these patients was 380% (219 of 577), accounting for 817% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 175 [95% CI 128-240], p&lt;00001), age 70 years or older versus younger than 70 years (230 [165-322], p&lt;00001), American Society of Anesthesiologists grades 3-5 versus grades 1-2 (235 [157-353], p&lt;00001), malignant versus benign or obstetric diagnosis (155 [101-239], p=0046), emergency versus elective surgery (167 [106-263], p=0026), and major versus minor surgery (152 [101-231], p=0047). Interpretation Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research

Search for top squark production in fully hadronic final states in proton-proton collisions at s\sqrt{s} =13 TeV

A search for production of the supersymmetric partners of the top quark, top squarks, is presented. The search is based on proton-proton collision events containing multiple jets, no leptons, and large transverse momentum imbalance. The data were collected with the CMS detector at the CERN LHC at a center-of-mass energy of 13 TeV, and correspond to an integrated luminosity of 137  fb$^{-1}$. The targeted signal production scenarios are direct and gluino-mediated top squark production, including scenarios in which the top squark and neutralino masses are nearly degenerate. The search utilizes novel algorithms based on deep neural networks that identify hadronically decaying top quarks and W bosons, which are expected in many of the targeted signal models. No statistically significant excess of events is observed relative to the expectation from the standard model, and limits on the top squark production cross section are obtained in the context of simplified supersymmetric models for various production and decay modes. Exclusion limits as high as 1310 GeV are established at the 95% confidence level on the mass of the top squark for direct top squark production models, and as high as 2260 GeV on the mass of the gluino for gluino-mediated top squark production models. These results represent a significant improvement over the results of previous searches for supersymmetry by CMS in the same final state

Mortality and pulmonary complications in patients undergoing surgery with perioperative SARS-CoV-2 infection: an international cohort study

Background: The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods: This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings: This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (74·0%) had emergency surgery and 280 (24·8%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (26·1%) patients. 30-day mortality was 23·8% (268 of 1128). Pulmonary complications occurred in 577 (51·2%) of 1128 patients; 30-day mortality in these patients was 38·0% (219 of 577), accounting for 81·7% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 1·75 [95% CI 1·28–2·40], p\textless0·0001), age 70 years or older versus younger than 70 years (2·30 [1·65–3·22], p\textless0·0001), American Society of Anesthesiologists grades 3–5 versus grades 1–2 (2·35 [1·57–3·53], p\textless0·0001), malignant versus benign or obstetric diagnosis (1·55 [1·01–2·39], p=0·046), emergency versus elective surgery (1·67 [1·06–2·63], p=0·026), and major versus minor surgery (1·52 [1·01–2·31], p=0·047). Interpretation: Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding: National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research

Search for top squark production in fully hadronic final states in proton-proton collisions at root s=13 TeV

A search for production of the supersymmetric partners of the top quark, top squarks, is presented. The search is based on proton-proton collision events containing multiple jets, no leptons, and large transverse momentum imbalance. The data were collected with the CMS detector at the CERN LHC at a center-of-mass energy of 13 TeV, and correspond to an integrated luminosity of 137 fb(-1). The targeted signal production scenarios are direct and gluino-mediated top squark production, including scenarios in which the top squark and neutralino masses are nearly degenerate. The search utilizes novel algorithms based on deep neural networks that identify hadronically decaying top quarks and W bosons, which are expected in many of the targeted signal models. No statistically significant excess of events is observed relative to the expectation from the standard model, and limits on the top squark production cross section are obtained in the context of simplified supersymmetric models for various production and decay modes. Exclusion limits as high as 1310 GeVare established at the 95% confidence level on the mass of the top squark for direct top squark production models, and as high as 2260 GeV on the mass of the gluino for gluino-mediated top squark production models. These results represent a significant improvement over the results of previous searches for supersymmetry by CMS in the same final state.Peer reviewe