Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in $L^\infty$ in space and time.Comment: 23 pages, 2 fugure

Optimal lower exponent for the higher gradient integrability of solutions to two-phase elliptic equations in two dimensions

We study the higher gradient integrability of distributional solutions u to the equation div(σ∇u) = 0 in dimension two, in the case when the essential range of σ consists of only two elliptic matrices, i.e., σ ∈ {σ1,σ2} a.e. in Ω. In [9], for every pair of elliptic matrices σ1 and σ2 exponents pσ1,σ2 ∈ (2,+∞) and qσ1,σ2 ∈ (1,2) have been found so that if u ∈ W1,qσ1,σ2(Ω) is solution to the elliptic equation then ∇u ∈ Lpσ1,σ2(Ω) and the optimality of the upper exponent pσ1,σ2 has been proved. In this paper we complement the above result by proving the optimality of the lower exponent qσ1,σ2. Precisely, we show that for every arbitrarily small δ, one can find a particular microgeometry, i.e. an arrangement of the sets σ-1(σ1) and σ-1(σ2), for which there exists a solution u to the corresponding elliptic equation such that ∇u ∈ Lqσ1,σ2-δ, but ∇u Ɇ Lqσ1,σ2-δ. The existence of such optimal microgeometries is achieved by convex integration methods, adapting to the present setting the geometric constructions provided in [2] for the isotropic case

An NMR-based scoring function improves the accuracy of binding pose predictions by docking by two orders of magnitude

Low-affinity ligands can be efficiently optimized into high-affinity drug leads by structure based drug design when atomic-resolution structural information on the protein/ligand complexes is available. In this work we show that the use of a few, easily obtainable, experimental restraints improves the accuracy of the docking experiments by two orders of magnitude. The experimental data are measured in nuclear magnetic resonance spectra and consist of protein-mediated NOEs between two competitively binding ligands. The methodology can be widely applied as the data are readily obtained for low-affinity ligands in the presence of non-labelled receptor at low concentration. The experimental inter-ligand NOEs are efficiently used to filter and rank complex model structures that have been pre-selected by docking protocols. This approach dramatically reduces the degeneracy and inaccuracy of the chosen model in docking experiments, is robust with respect to inaccuracy of the structural model used to represent the free receptor and is suitable for high-throughput docking campaigns

Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques

Neutrophil-lymphocyte ratio kinetics in patients with advanced solid tumours on phase I trials of PD-1/PD-L1 inhibitors.

BACKGROUND:Although the neutrophil-lymphocyte ratio (NLR) is prognostic in many oncological settings, its significance in the immunotherapy era is unknown. Mechanistically, PD-1/PD-L1 inhibitors may alter NLR. We sought to characterise NLR kinetics in patients with advanced solid tumours treated with PD-1/PD-L1 inhibitors. METHODS:Electronic records of patients treated with PD-1/PD-L1 inhibitors on phase I trials across three sites were reviewed. A high NLR (hNLR) was predefined as >5. Univariate logistic regression models were used for toxicity, response analyses and Cox models for overall survival (OS) and progression-free survival analyses. Landmark analyses were performed (cycle two, three). Longitudinal analysis of NLR was performed utilising a mixed effect regression model. RESULTS:The median OS for patients with hNLR was 8.5 months and 19.4 for patients with low NLR, (hazard ratio [HR] = 1.85, 95% confidence interval [CI] 1.15-2.96, p = 0.01). On landmark analysis, hNLR was significantly associated with inferior OS at all time points with a similar magnitude of effect over time (p < 0.05). On multivariate analysis, NLR was associated with OS (HR 1.06, 95% CI 1.01-1.11, p = 0.01). NLR did not correlate with increased immune toxicity. Longitudinally, NLR correlated with response: NLR decreased by 0.09 (95% CI: -0.15 to -0.02; p = 0.01) per month in responders compared with non-responders. CONCLUSIONS:hNLR at baseline and during treatment is adversely prognostic in patients with advanced malignancies receiving PD-1/PD-L1 blockade. Importantly, NLR reduced over time in responders to immunotherapy. Taken together, these data suggest that baseline and longitudinal NLR may have utility as a unique biomarker to aid clinical decision-making in patients receiving immunotherapy

On the automatic identification of unobserved components models

Automatic identi cation of time series models is a necessity once the big data era has come and is staying among us. This has become obvious for many companies and public entities that has passed from a crafted analysis of each individual problem to handle a tsunami of information that has to be processed e ciently, online and in record time. Automatic identi cation tools has never been tried out on Unobserved Components models (UC). This chapter shows how information criteria, such as Akaike's or Schwarz's, are rather useful for model selection within the UC family. The di culty lies, however, on choosing an appropriate and as general as possible set of models to search in. A set too narrow would render poor forecast accuracy, while a set too wide would be highly time consuming. The forecasting results suggest that UC models are powerful potential forecasting competitors to other well-known methods. Though there are several pieces of software available for UC modeling, this is the rst implementation of an automatic algorithm for this class of models, to the best of the authors knowledge

Forecasting: theory and practice

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases

Integrated Ugi-Based Assembly of Functionally, Skeletally, and Stereochemically Diverse 1,4-Benzodiazepin-2-ones

A practical, integrated and versatile U-4CR-based assembly of 1,4-benzodiazepin-2-ones exhibiting functionally, skeletally, and stereochemically diverse substitution patterns is described. By virtue of its convergence, atom economy, and bond-forming efficiency, the methodology documented herein exemplifies the reconciliation of structural complexity and experimental simplicity in the context of medicinal chemistry projects.This work was financially supported by the Galician Government (Spain), Projects: 09CSA016234PR and GPC-2014-PG037. J.A. thanks FUNDAYACUCHO (Venezuela) for a predoctoral grant and Deputación da Coruña (Spain) for a postdoctoral research grant. A.N.-V. thanks the Spanish government for a Ramón y Cajal research contract