Counterexamples in multimarginal optimal transport with Coulomb cost and spherically symmetric data

We disprove a conjecture in Density Functional Theory, relative to multimarginal optimal transport maps with Coulomb cost. In the case of spherically symmetric data, which model for instance Lithium and Beryllium atoms, we show that some special maps, introduced by Seidl, Gori-Giorgi and Savin are not always optimal in the corresponding transport problem. We also provide examples of maps satisfying optimality conditions for special classes of data

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Entropy solutions of mildly singular non-local scalar conservation laws with congestion via deterministic particle method

We develop deterministic particle schemes to solve nonlocal scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution under more general assumptions than the existing literature: the velocity fields are allowed to be timedependent (with no regularity in time), they are allowed to be less regular in space (in particular the interaction force can have a discontinuity at the origin), no prescribed attractive/repulsive regimes or symmetry are required, and the mobility can have unbounded support. We treat in a unified manner two different schemes, with sampled and integrated interaction, showing that they both converge to the entropy solution, albeit with different trade-offs between accuracy and computational effort. We complement our results with some numerical simulations, among which we show the applicability to the multispecies setting, for which the integrated scheme appears to be the better choice

Lagrangian discretization of crowd motion and linear diffusion

We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density constraint of the resulting particles is enforced by means of a partial optimal transport problem at each time step. We prove the convergence of the discrete measures to a solution of the continuous PDE describing the crowd motion in dimension one. In a second part, we show how a similar approach can be used to construct a Lagrangian discretization of a linear advection-diffusion equation. Both discretizations rely on the interpretation of the two equations (crowd motion and linear diffusion) as gradient flows in Wasserstein space. We provide also a numerical implementation in 2 dimensions to demonstrate the feasibility of the computations

A PDE approach to a 2-dimensional matching problem

We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by Caracciolo et al. (Phys Rev E 90:012118, 2014) that linearizes the Monge–Ampère equation

Linear Lipschitz and C1 extension operators through random projection

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C1 extension theorem by Whitney [8] to Banach spaces

Allosteric Inhibition as a New Mode of Action for BAY 1213790, a Neutralizing Antibody Targeting the Activated Form of Coagulation Factor XI

Factor XI FXI , the zymogen of activated FXI FXIa , is an attractive target for novel anticoagulants because FXI inhibition offers the potential to reduce thrombosis risk while minimizing the risk of bleeding. BAY 1213790, a novel anti FXIa antibody, was generated using phage display technology. Crystal structure analysis of the FXIa BAY 1213790 complex demonstrated that the tyrosine rich complementarity determining region 3 loop of the heavy chain of BAY 1213790 penetrated deepest into the FXIa binding epitope, forming a network of favorable interactions including a direct hydrogen bond from Tyr102 to the Gln451 sidechain 2.9 . The newly discovered binding epitope caused a structural rearrangement of the FXIa active site, revealing a novel allosteric mechanism of FXIa inhibition by BAY 1213790. BAY 1213790 specifically inhibited FXIa with a binding affinity of 2.4 nM, and in human plasma, prolonged activated partial thromboplastin time and inhibited thrombin generation in a concentration dependent manne

Effectiveness of mask and helmet interfaces to deliver noninvasive ventilation in a human model of resistive breathing

The helmet, a transparent latex-free polyvinyl chloride cylinder linked by a metallic ring to a soft collar that seals the helmet around the neck, has been recently proposed as an effective alternative to conventional face mask to deliver pressure support ventilation (PSV) during noninvasive ventilation in patients with acute respiratory failure. We tested the hypothesis that mechanical characteristics of the helmet (large internal volume and high compliance) might impair patient-ventilator interactions compared with standard face mask. Breathing pattern, CO(2) clearance, indexes of inspiratory muscle effort and patient-ventilator asynchrony, and dyspnea were measured at different levels of PSV delivered by face mask and helmet in six healthy volunteers before (load-off) and after (load-on) application of a linear resistor. During load-off, no differences in breathing pattern and inspiratory muscle effort were found. During load-on, the use of helmet to deliver pressure support increased inspiratory muscle effort and patient-ventilator asynchrony, worsened CO(2) clearance, and increased dyspnea compared with standard face mask. Autocycled breaths accounted for 12 and 25% of the total minute ventilation and for 10 and 23% of the total inspiratory muscle effort during mask and helmet PSV, respectively. We conclude that PSV delivered by helmet interface is less effective in unloading inspiratory muscles compared with PSV delivered by standard face mask. Other ventilatory assist modes should be tested to exploit to the most the potential benefits offered by the helmet