35 research outputs found
Diversities and the Geometry of Hypergraphs
The embedding of finite metrics in has become a fundamental tool for
both combinatorial optimization and large-scale data analysis. One important
application is to network flow problems in which there is close relation
between max-flow min-cut theorems and the minimal distortion embeddings of
metrics into . Here we show that this theory can be generalized
considerably to encompass Steiner tree packing problems in both graphs and
hypergraphs. Instead of the theory of metrics and minimal distortion
embeddings, the parallel is the theory of diversities recently introduced by
Bryant and Tupper, and the corresponding theory of diversities and
embeddings which we develop here.Comment: 19 pages, no figures. This version: further small correction
Constant distortion embeddings of Symmetric Diversities
Diversities are like metric spaces, except that every finite subset, instead
of just every pair of points, is assigned a value. Just as there is a theory of
minimal distortion embeddings of finite metric spaces into , there is a
similar, yet undeveloped, theory for embedding finite diversities into the
diversity analogue of spaces. In the metric case, it is well known that
an -point metric space can be embedded into with
distortion. For diversities, the optimal distortion is unknown. Here, we
establish the surprising result that symmetric diversities, those in which the
diversity (value) assigned to a set depends only on its cardinality, can be
embedded in with constant distortion.Comment: 14 pages, 3 figure
Hyperconvexity and tight-span theory for diversities, Adv
Abstract The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has applications to metric classification and data visualisation. Here we introduce a generalisation of metrics, called diversities, and demonstrate that the rich theory associated to metric tight spans and hyperconvexity extends to a seemingly richer theory of diversity tight spans and hyperconvexity
Hyperconvexity and Tight Span Theory for Diversities
The tight span, or injective envelope, is an elegant and useful construction
that takes a metric space and returns the smallest hyperconvex space into which
it can be embedded. The concept has stimulated a large body of theory and has
applications to metric classification and data visualisation. Here we introduce
a generalisation of metrics, called diversities, and demonstrate that the rich
theory associated to metric tight spans and hyperconvexity extends to a
seemingly richer theory of diversity tight spans and hyperconvexity.Comment: revised in response to referee comment
On the well-posedness of the stochastic Allen-Cahn equation in two dimensions
White noise-driven nonlinear stochastic partial differential equations
(SPDEs) of parabolic type are frequently used to model physical and biological
systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak
solutions to these equations are well established in one dimension, the
situation is different for d \geq 2. Despite their popularity in the applied
sciences, higher dimensional versions of these SPDE models are generally
assumed to be ill-posed by the mathematics community. We study this discrepancy
on the specific example of the two dimensional Allen-Cahn equation driven by
additive white noise. Since it is unclear how to define the notion of a weak
solution to this equation, we regularize the noise and introduce a family of
approximations. Based on heuristic arguments and numerical experiments, we
conjecture that these approximations exhibit divergent behavior in the
continuum limit. The results strongly suggest that a series of published
numerical studies are problematic: shrinking the mesh size in these simulations
does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics
(Dec 2011
The Marine light - mixed layer experiment cruise and data report, R/V Endeavor : cruise EN-224, mooring deployment, 27 April-1 May 1991, cruise EN-227, mooring recovery, 5-23 September 1991
The Marine Light - Mixed Layer experiment took place in the sub-Arctic North Atlantic ocean, approximately 275 miles
south of Reykjavik, Iceland. The field program included a central surface mooring to document the temporal evolution of physical,
biological and optical properties. The surface mooring was deployed at approximately 59°N, 21°W on 29 April 1991 and recovered
on 6 September 1991. The Upper Ocean Processes Group of the Woods Hole Oceanographic Institution was responsible for design,
preparation, deployment, and recovery of the mooring. The Group's contrbution to the field measurements included four different
types of sensors: a meteorological observation package on the surface buoy, a string of 15 temperature sensors along the mooring
line, an acoustic Doppler current profiler, and four instruments for measuring mooring tension and accelerations. The observations
obtained from the mooring are sufficient to describe the air-sea fluxes and the local physical response to surface forcing. The
objective in the analysis phase will be to determine the factors controlling this physical response and to work towards an understanding
of the links among physical, biological, and optical processes. This report describes the deployment and recovery of the
mooring, the meteorological data, and the subsurface temperature and current data.Funding was provided by the Office of Naval Research under Contract N00014-89-J-1683
A prenylated dsRNA sensor protects against severe COVID-19
Inherited genetic factors can influence the severity of COVID-19, but the molecular explanation underpinning a genetic association is often unclear. Intracellular antiviral defenses can inhibit the replication of viruses and reduce disease severity. To better understand the antiviral defenses relevant to COVID-19, we used interferon-stimulated gene (ISG) expression screening to reveal that OAS1, through RNase L, potently inhibits SARS-CoV-2. We show that a common splice-acceptor SNP (Rs10774671) governs whether people express prenylated OAS1 isoforms that are membrane-associated and sense specific regions of SARS-CoV-2 RNAs, or only express cytosolic, nonprenylated OAS1 that does not efficiently detect SARS-CoV-2. Importantly, in hospitalized patients, expression of prenylated OAS1 was associated with protection from severe COVID-19, suggesting this antiviral defense is a major component of a protective antiviral response
Para-infectious brain injury in COVID-19 persists at follow-up despite attenuated cytokine and autoantibody responses
To understand neurological complications of COVID-19 better both acutely and for recovery, we measured markers of brain injury, inflammatory mediators, and autoantibodies in 203 hospitalised participants; 111 with acute sera (1â11 days post-admission) and 92 convalescent sera (56 with COVID-19-associated neurological diagnoses). Here we show that compared to 60 uninfected controls, tTau, GFAP, NfL, and UCH-L1 are increased with COVID-19 infection at acute timepoints and NfL and GFAP are significantly higher in participants with neurological complications. Inflammatory mediators (IL-6, IL-12p40, HGF, M-CSF, CCL2, and IL-1RA) are associated with both altered consciousness and markers of brain injury. Autoantibodies are more common in COVID-19 than controls and some (including against MYL7, UCH-L1, and GRIN3B) are more frequent with altered consciousness. Additionally, convalescent participants with neurological complications show elevated GFAP and NfL, unrelated to attenuated systemic inflammatory mediators and to autoantibody responses. Overall, neurological complications of COVID-19 are associated with evidence of neuroglial injury in both acute and late disease and these correlate with dysregulated innate and adaptive immune responses acutely
Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19
IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19.
Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19.
DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 nonâcritically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022).
INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (nâ=â257), ARB (nâ=â248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; nâ=â10), or no RAS inhibitor (control; nâ=â264) for up to 10 days.
MAIN OUTCOMES AND MEASURES The primary outcome was organ supportâfree days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes.
RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ supportâfree days among critically ill patients was 10 (â1 to 16) in the ACE inhibitor group (nâ=â231), 8 (â1 to 17) in the ARB group (nâ=â217), and 12 (0 to 17) in the control group (nâ=â231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ supportâfree days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively).
CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes.
TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570
Diversities and the generalized circumradius
The generalized circumradius of a set of points A\subseteq R^d with respect to a convex body K equals the minimum value of \lambda\geq 0âsuch that a translate of â\lambda K contains A. Each choice of K gives a different function on the set of bounded subsets of R^d; we characterize which functions can arise in this way. Our characterization draws on the theory of diversities, a recently introduced generalization of metrics from functions on pairs to functions on finite subsets. We additionally investigate functions which arise by restricting the generalized circumradius to a finite subset of R^d. We obtain elegant characterizations in the case that K is a simplex or parallelotope