On the exactness of the cavity method for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs

We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution both for synchronous and asynchronous updating

Exactness of Belief Propagation for Some Graphical Models with Loops

It is well known that an arbitrary graphical model of statistical inference defined on a tree, i.e. on a graph without loops, is solved exactly and efficiently by an iterative Belief Propagation (BP) algorithm convergent to unique minimum of the so-called Bethe free energy functional. For a general graphical model on a loopy graph the functional may show multiple minima, the iterative BP algorithm may converge to one of the minima or may not converge at all, and the global minimum of the Bethe free energy functional is not guaranteed to correspond to the optimal Maximum-Likelihood (ML) solution in the zero-temperature limit. However, there are exceptions to this general rule, discussed in \cite{05KW} and \cite{08BSS} in two different contexts, where zero-temperature version of the BP algorithm finds ML solution for special models on graphs with loops. These two models share a key feature: their ML solutions can be found by an efficient Linear Programming (LP) algorithm with a Totally-Uni-Modular (TUM) matrix of constraints. Generalizing the two models we consider a class of graphical models reducible in the zero temperature limit to LP with TUM constraints. Assuming that a gedanken algorithm, g-BP, funding the global minimum of the Bethe free energy is available we show that in the limit of zero temperature g-BP outputs the ML solution. Our consideration is based on equivalence established between gapless Linear Programming (LP) relaxation of the graphical model in the $T\to 0$ limit and respective LP version of the Bethe-Free energy minimization.Comment: 12 pages, 1 figure, submitted to JSTA

The number of matchings in random graphs

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical Mechanic

Decline in subarachnoid haemorrhage volumes associated with the first wave of the COVID-19 pandemic

BACKGROUND: During the COVID-19 pandemic, decreased volumes of stroke admissions and mechanical thrombectomy were reported. The study\u27s objective was to examine whether subarachnoid haemorrhage (SAH) hospitalisations and ruptured aneurysm coiling interventions demonstrated similar declines. METHODS: We conducted a cross-sectional, retrospective, observational study across 6 continents, 37 countries and 140 comprehensive stroke centres. Patients with the diagnosis of SAH, aneurysmal SAH, ruptured aneurysm coiling interventions and COVID-19 were identified by prospective aneurysm databases or by International Classification of Diseases, 10th Revision, codes. The 3-month cumulative volume, monthly volumes for SAH hospitalisations and ruptured aneurysm coiling procedures were compared for the period before (1 year and immediately before) and during the pandemic, defined as 1 March-31 May 2020. The prior 1-year control period (1 March-31 May 2019) was obtained to account for seasonal variation. FINDINGS: There was a significant decline in SAH hospitalisations, with 2044 admissions in the 3 months immediately before and 1585 admissions during the pandemic, representing a relative decline of 22.5% (95% CI -24.3% to -20.7%, p\u3c0.0001). Embolisation of ruptured aneurysms declined with 1170-1035 procedures, respectively, representing an 11.5% (95%CI -13.5% to -9.8%, p=0.002) relative drop. Subgroup analysis was noted for aneurysmal SAH hospitalisation decline from 834 to 626 hospitalisations, a 24.9% relative decline (95% CI -28.0% to -22.1%, p\u3c0.0001). A relative increase in ruptured aneurysm coiling was noted in low coiling volume hospitals of 41.1% (95% CI 32.3% to 50.6%, p=0.008) despite a decrease in SAH admissions in this tertile. INTERPRETATION: There was a relative decrease in the volume of SAH hospitalisations, aneurysmal SAH hospitalisations and ruptured aneurysm embolisations during the COVID-19 pandemic. These findings in SAH are consistent with a decrease in other emergencies, such as stroke and myocardial infarction

Decline in subarachnoid haemorrhage volumes associated with the first wave of the COVID-19 pandemic

International audienceBACKGROUND: During the COVID-19 pandemic, decreased volumes of stroke admissions and mechanical thrombectomy were reported. The study's objective was to examine whether subarachnoid haemorrhage (SAH) hospitalisations and ruptured aneurysm coiling interventions demonstrated similar declines. METHODS: We conducted a cross-sectional, retrospective, observational study across 6 continents, 37 countries and 140 comprehensive stroke centres. Patients with the diagnosis of SAH, aneurysmal SAH, ruptured aneurysm coiling interventions and COVID-19 were identified by prospective aneurysm databases or by International Classification of Diseases, 10th Revision, codes. The 3-month cumulative volume, monthly volumes for SAH hospitalisations and ruptured aneurysm coiling procedures were compared for the period before (1 year and immediately before) and during the pandemic, defined as 1 March-31 May 2020. The prior 1-year control period (1 March-31 May 2019) was obtained to account for seasonal variation. FINDINGS: There was a significant decline in SAH hospitalisations, with 2044 admissions in the 3 months immediately before and 1585 admissions during the pandemic, representing a relative decline of 22.5% (95% CI -24.3% to -20.7%, p\textless0.0001). Embolisation of ruptured aneurysms declined with 1170-1035 procedures, respectively, representing an 11.5% (95%CI -13.5% to -9.8%, p=0.002) relative drop. Subgroup analysis was noted for aneurysmal SAH hospitalisation decline from 834 to 626 hospitalisations, a 24.9% relative decline (95% CI -28.0% to -22.1%, p\textless0.0001). A relative increase in ruptured aneurysm coiling was noted in low coiling volume hospitals of 41.1% (95% CI 32.3% to 50.6%, p=0.008) despite a decrease in SAH admissions in this tertile. INTERPRETATION: There was a relative decrease in the volume of SAH hospitalisations, aneurysmal SAH hospitalisations and ruptured aneurysm embolisations during the COVID-19 pandemic. These findings in SAH are consistent with a decrease in other emergencies, such as stroke and myocardial infarction

Global impact of COVID-19 on stroke care

BACKGROUND: The COVID-19 pandemic led to profound changes in the organization of health care systems worldwide. AIMS: We sought to measure the global impact of the COVID-19 pandemic on the volumes for mechanical thrombectomy, stroke, and intracranial hemorrhage hospitalizations over a three-month period at the height of the pandemic (1 March-31 May 2020) compared with two control three-month periods (immediately preceding and one year prior). METHODS: Retrospective, observational, international study, across 6 continents, 40 countries, and 187 comprehensive stroke centers. The diagnoses were identified by their ICD-10 codes and/or classifications in stroke databases at participating centers. RESULTS: The hospitalization volumes for any stroke, intracranial hemorrhage, and mechanical thrombectomy were 26,699, 4002, and 5191 in the three months immediately before versus 21,576, 3540, and 4533 during the first three pandemic months, representing declines of 19.2% (95%CI, -19.7 to -18.7), 11.5% (95%CI, -12.6 to -10.6), and 12.7% (95%CI, -13.6 to -11.8), respectively. The decreases were noted across centers with high, mid, and low COVID-19 hospitalization burden, and also across high, mid, and low volume stroke/mechanical thrombectomy centers. High-volume COVID-19 centers (-20.5%) had greater declines in mechanical thrombectomy volumes than mid- (-10.1%) and low-volume (-8.7%) centers (p < 0.0001). There was a 1.5% stroke rate across 54,366 COVID-19 hospitalizations. SARS-CoV-2 infection was noted in 3.9% (784/20,250) of all stroke admissions. CONCLUSION: The COVID-19 pandemic was associated with a global decline in the volume of overall stroke hospitalizations, mechanical thrombectomy procedures, and intracranial hemorrhage admission volumes. Despite geographic variations, these volume reductions were observed regardless of COVID-19 hospitalization burden and pre-pandemic stroke/mechanical thrombectomy volumes

Global impact of COVID-19 on stroke care

Background: The COVID-19 pandemic led to profound changes in the organization of health care systems worldwide. Aims: We sought to measure the global impact of the COVID-19 pandemic on the volumes for mechanical thrombectomy, stroke, and intracranial hemorrhage hospitalizations over a three-month period at the height of the pandemic (1 March–31 May 2020) compared with two control three-month periods (immediately preceding and one year prior). Methods: Retrospective, observational, international study, across 6 continents, 40 countries, and 187 comprehensive stroke centers. The diagnoses were identified by their ICD-10 codes and/or classifications in stroke databases at participating centers. Results: The hospitalization volumes for any stroke, intracranial hemorrhage, and mechanical thrombectomy were 26,699, 4002, and 5191 in the three months immediately before versus 21,576, 3540, and 4533 during the first three pandemic months, representing declines of 19.2% (95%CI, −19.7 to −18.7), 11.5% (95%CI, −12.6 to −10.6), and 12.7% (95%CI, −13.6 to −11.8), respectively. The decreases were noted across centers with high, mid, and low COVID-19 hospitalization burden, and also across high, mid, and low volume stroke/mechanical thrombectomy centers. High-volume COVID-19 centers (−20.5%) had greater declines in mechanical thrombectomy volumes than mid- (−10.1%) and low-volume (−8.7%) centers (p &lt; 0.0001). There was a 1.5% stroke rate across 54,366 COVID-19 hospitalizations. SARS-CoV-2 infection was noted in 3.9% (784/20,250) of all stroke admissions. Conclusion: The COVID-19 pandemic was associated with a global decline in the volume of overall stroke hospitalizations, mechanical thrombectomy procedures, and intracranial hemorrhage admission volumes. Despite geographic variations, these volume reductions were observed regardless of COVID-19 hospitalization burden and pre-pandemic stroke/mechanical thrombectomy volumes. © 2021 World Stroke Organization

EXPRESS: Global Impact of the COVID-19 Pandemic on Stroke Hospitalizations and Mechanical Thrombectomy Volumes.

BACKGROUND The COVID-19 pandemic led to profound changes in the organization of health care systems worldwide. AIMS We sought to measure the global impact of the COVID-19 pandemic on the volumes for mechanical thrombectomy (MT), stroke, and intracranial hemorrhage (ICH) hospitalizations over a 3-month period at the height of the pandemic (March 1 to May 31, 2020) compared with two control 3-month periods (immediately preceding and one year prior). METHODS Retrospective, observational, international study, across 6 continents, 40 countries, and 187 comprehensive stroke centers. The diagnoses were identified by their ICD-10 codes and/or classifications in stroke databases at participating centers. RESULTS The hospitalization volumes for any stroke, ICH, and MT were 26,699, 4,002, and 5,191 in the 3 months immediately before versus 21,576, 3,540, and 4,533 during the first 3 pandemic months, representing declines of 19.2% (95%CI,-19.7 to -18.7), 11.5% (95%CI,-12.6 to -10.6), and 12.7% (95%CI,-13.6 to -11.8), respectively. The decreases were noted across centers with high, mid, and low COVID-19 hospitalization burden, and also across high, mid, and low volume stroke/MT centers. High-volume COVID-19 centers (-20.5%) had greater declines in MT volumes than mid- (-10.1%) and low-volume (-8.7%) centers (p<0.0001). There was a 1.5% stroke rate across 54,366 COVID-19 hospitalizations. SARS-CoV-2 infection was noted in 3.9% (784/20,250) of all stroke admissions. CONCLUSION The COVID-19 pandemic was associated with a global decline in the volume of overall stroke hospitalizations, MT procedures, and ICH admission volumes. Despite geographic variations, these volume reductions were observed regardless of COVID-19 hospitalization burden and pre-pandemic stroke/MT volumes

Global impact of COVID-19 on stroke care.

BACKGROUND: The COVID-19 pandemic led to profound changes in the organization of health care systems worldwide. AIMS: We sought to measure the global impact of the COVID-19 pandemic on the volumes for mechanical thrombectomy, stroke, and intracranial hemorrhage hospitalizations over a three-month period at the height of the pandemic (1 March-31 May 2020) compared with two control three-month periods (immediately preceding and one year prior). METHODS: Retrospective, observational, international study, across 6 continents, 40 countries, and 187 comprehensive stroke centers. The diagnoses were identified by their ICD-10 codes and/or classifications in stroke databases at participating centers. RESULTS: The hospitalization volumes for any stroke, intracranial hemorrhage, and mechanical thrombectomy were 26,699, 4002, and 5191 in the three months immediately before versus 21,576, 3540, and 4533 during the first three pandemic months, representing declines of 19.2% (95%CI, -19.7 to -18.7), 11.5% (95%CI, -12.6 to -10.6), and 12.7% (95%CI, -13.6 to -11.8), respectively. The decreases were noted across centers with high, mid, and low COVID-19 hospitalization burden, and also across high, mid, and low volume stroke/mechanical thrombectomy centers. High-volume COVID-19 centers (-20.5%) had greater declines in mechanical thrombectomy volumes than mid- (-10.1%) and low-volume (-8.7%) centers (p \u3c 0.0001). There was a 1.5% stroke rate across 54,366 COVID-19 hospitalizations. SARS-CoV-2 infection was noted in 3.9% (784/20,250) of all stroke admissions. CONCLUSION: The COVID-19 pandemic was associated with a global decline in the volume of overall stroke hospitalizations, mechanical thrombectomy procedures, and intracranial hemorrhage admission volumes. Despite geographic variations, these volume reductions were observed regardless of COVID-19 hospitalization burden and pre-pandemic stroke/mechanical thrombectomy volumes