Berlin Mathematical School

Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in "one shot," vast computational effort is invested for simulating these systems in small steps, e.g., using molecular dynamics. Combining deep learning and statistical mechanics, we developed Boltzmann generators, which are shown to generate unbiased one-shot equilibrium samples of representative condensed-matter systems and proteins. Boltzmann generators use neural networks to learn a coordinate transformation of the complex configurational equilibrium distribution to a distribution that can be easily sampled. Accurate computation of free-energy differences and discovery of new configurations are demonstrated, providing a statistical mechanics tool that can avoid rare events during sampling without prior knowledge of reaction coordinates.

We propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, cannot be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equations and establish their relation to the continuous-time random walk theory. We show that the distributed-order time fractional diffusion equation describes the subdiffusion random process that is subordinated to the Wiener process and whose diffusion exponent decreases in time (retarding subdiffusion). This process may lead to superslow diffusion, with the mean square displacement growing logarithmically in time. We also demonstrate that the distributed-order space fractional diffusion equation describes superdiffusion phenomena with the diffusion exponent increasing in time (accelerating superdiffusion).

Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.

In this paper we prove that no packing of unit balls in Euclidean space $\mathbb{R}^8$ has density greater than that of the $E_8$-lattice packing.

Supercapacitors are perfect energy storage devices; they can be charged almost instantly and release energy over a long time.

In this article, the authors explore semantic context effects in speaking. In particular, the authors investigate a marked discrepancy between categorically and associatively induced effects; only categorical relationships have been reported to cause interference in object naming. In Experiments 1 and 2, a variant of the semantic blocking paradigm was used to induce two different types of semantic context effects. Pictures were either named in the context of categorically related objects (e.g., animals: bee, cow, fish) or in the context of associatively related objects from different semantic categories (e.g., apiary: bee, honey, bee keeper). Semantic interference effects were observed in both conditions, relative to an unrelated context. Experiment 3 replicated the classic effects of categorical interference and associative facilitation in a picture-word interference paradigm with the material used in Experiment 2. These findings suggest that associates are active lexical competitors and that the microstructure of lexicalization is highly flexible and adjustable to the semantic context in which the utterance takes place.

Control of human soil-transmitted helminths (STHs) relies on preventive chemotherapy of schoolchildren applying the benzimidazoles (BZ) albendazole or mebendazole. Anthelmintic resistance (AR) is a common problem in nematodes of veterinary importance but for human STHs, information on drug efficacy is limited and routine monitoring is rarely implemented. Herein, the efficacy of single dose albendazole (400 mg) was evaluated in 12 schools in the Huye district of Rwanda where Ascaris is the predominant STH. Ascaris eggs were detected by wet mount microscopy and the Mini-FLOTAC method to assess cure rate (CR) and faecal egg count reduction (FECR). Blood and faecal samples were analysed for co-infections with Plasmodium sp. and Giardia duodenalis, respectively. Ascaris positive samples collected before and after treatment were analysed for putatively BZ-resistance associated β-tubulin gene single nucleotide polymorphisms. The overall CR was 69.9% by Mini-FLOTAC and 88.6% by wet mount microscopy. The FECR was 75.4% and the 95% calculated confidence intervals were 50.4-87.8% using sample variance, 55.4-88.8% by bootstrapping, and 75.0-75.7% applying a Markov Chain Monte Carlo Bayesian approach. FECR varied widely between 0 and 96.8% for individual schools. No putative BZ-resistance associated polymorphisms were found in the four Ascaris β-tubulin isotype genes examined. Since FECRs <95% indicate reduced efficacy, these findings raise the suspicion of BZ resistance. In the absence of respective molecular evidence, heritable AR in the local Ascaris populations cannot be formally proven. However, since FECRs <95% indicate reduced efficacy, BZ resistance may be suspected which would be alarming and calls for further analyses and routine monitoring in preventive chemotherapy programs.

Systematic multiscale perturbation theory is utilized to develop self-consistent simplified model equations for the interaction across multiple spatial and/or temporal scales in the Tropics.One of these models involves simplified equations for intraseasonal planetary equatorial synoptic-scale dynamics (IPESD).This model includes the self-consistent quasi-linear interaction of synoptic-scale generalized steady Matsuno-Webster-Gill models with planetary-scale dynamics of equatorial long waves.These new models have the potential for providing self-consistent prognostic and diagnostic models for the intraseasonal tropical oscillation.Other applications of the systematic approach reveal three different balanced weak temperature gradient (WTG) approximations for the Tropics with different regimes of validity in space and time: a synoptic equatorial-scale WTG (SEWTG); a mesoscale equatorial WTG (MEWTG), which reduces to the classical models treated by others; and a new seasonal planetary equatorial WTG (SPEWTG).Both the SPEWTG and MEWTG model equations have solutions with general vertical structure, yet have the linearized dispersion relation of barotropic Rossby waves; thus, these models can play an important role in theories for midlatitude connections with the Tropics.The models are derived both from the equatorial shallow water equations in a simplified context and also as distinguished limits from the compressible primitive equations in general.

The aims of this book are threefold: We start with a naive description of a Markov chain as a memoryless random walk on a finite set. This is complemented by a rigorous definition in the framework of

Abstract We consider the approximate solution of self‐adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non‐uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. As the performance of hierarchical bases preconditioners deteriorates in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real‐life problem arising from hyperthermia, a recent clinical method for cancer therapy.

INTRODUCTION: Additional biomarkers in sepsis are needed to tackle the challenges of determining prognosis and optimizing selection of high-risk patients for application of therapy. In the present study, conducted in a cohort of medical intensive care unit patients, our aim was to compare the prognostic value of mid-regional pro-atrial natriuretic peptide (ANP) levels with those of other biomarkers and physiological scores. METHODS: Blood samples obtained in a prospective observational study conducted in 101 consecutive critically ill patients admitted to the intensive care unit were analyzed. The prognostic value of pro-ANP levels was compared with that of the Acute Physiology and Chronic Health Evaluation (APACHE) II score and with those of various biomarkers (i.e. C-reactive protein, IL-6 and procalcitonin). Mid-regional pro-ANP was detected in EDTA plasma from all patients using a new sandwich immunoassay. RESULTS: On admission, 53 patients had sepsis, severe sepsis, or septic shock, and 68 had systemic inflammatory response syndrome. The median pro-ANP value in the survivors was 194 pmol/l (range 20-2000 pmol/l), which was significantly lower than in the nonsurvivors (median 853.0 pmol/l, range 100-2000 pmol/l; P < 0.001). On the day of admission, pro-ANP levels, but not levels of other biomarkers, were significantly higher in non-surviving [corrected] than in surviving [corrected] sepsis patients (P = 0.001). In a receiver operating characteristic curve analysis for the survival of patients with sepsis, the area under the curve (AUC) for pro-ANP was 0.88, which was significantly greater than the AUCs for procalcitonin and C-reactive protein, and similar to the AUC for the APACHE II score. CONCLUSION: Pro-ANP appears to be a valuable tool for individual risk assessment in sepsis patients and for stratification of high-risk patients in future intervention trials. Further studies are needed to validate our results.

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.

BACKGROUND/AIMS: Lanthanum carbonate (LC, FOSRENOL) is an effective phosphate binder for which tolerability and a safety profile have been reported in haemodialysis patients. Patients from previous studies entered a 2-year extension, enabling assessment of efficacy and safety for up to 6 years of LC monotherapy. METHODS: Patients from four previous trials entered this study. RESULTS: Ninety-three patients started the extension, with 22 entering a sixth year of LC treatment. Two-thirds of all patients received LC doses of 2,250 or 3,000 mg/day. Reductions in serum phosphate and calcium x phosphate product were maintained for up to 6 years. There were no new or unexpected adverse events (AEs), and no increase in the incidence of events with increasing treatment exposure. Over the complete duration of therapy, treatment-related AEs occurred in 25.8% of patients and were primarily gastrointestinal in nature. No clinically relevant changes in liver function tests were observed and there was no evidence of adverse effects on the liver, bone or the central nervous system. CONCLUSIONS: LC monotherapy was effective and well tolerated for up to 6 years with no evidence of safety concerns or increased frequency of AEs.

We present a combination of force field and ab initio molecular dynamics simulations together with neutron scattering experiments with isotopic substitution that aim at characterizing ion hydration and pairing in aqueous calcium chloride and formate/acetate solutions. Benchmarking against neutron scattering data on concentrated solutions together with ion pairing free energy profiles from ab initio molecular dynamics allows us to develop an accurate calcium force field which accounts in a mean-field way for electronic polarization effects via charge rescaling. This refined calcium parameterization is directly usable for standard molecular dynamics simulations of processes involving this key biological signaling ion.

in 5 M KOH electrolyte for carbon nanospheres synthesized at 800, 700 and 500 °C, respectively. These are on a par with those of prior electrodes made of biologically derived carbon nanospheres but the cycle lives were remarkably higher than those of any previous efforts. The electrodes showed 94% capacitance retention even after 5200 charge/discharge cycles entailing excellent recycling durability. In addition, the practical symmetrical supercapacitor showed good electrochemical behaviour under a potential window up to 1.7 V. This brings us one step closer to fabricating a commercial green electrode which exhibits high performance for supercapacitors. This is also a waste to wealth approach based carbon material for cost effective supercapacitors with high performance for power storage devices.

In this paper we study the maximum value of the largest eigenvalue for simple bipartite graphs, where the number of edges is given and the number of vertices on each side of the bipartition is given. We state a conjectured solution, which is an analog of the Brualdi-Hoffman conjecture for general graphs, and prove the conjecture in some special cases.

In this article we introduce a black box type algorithm for the approximation of tensors A in high dimension d. The algorithm adaptively determines the positions of entries of the tensor that have to be computed or read, and using these (few) entries it constructs a low rank tensor approximation X that minimizes the ℓ 2-distance between A and X at the chosen positions. The full tensor A is not required, only the evaluation of A at a few positions. The minimization problem is solved by Newton’s method, which requires the computation and evaluation of the Hessian. For efficiency reasons the positions are located on fiber-crosses of the tensor so that the Hessian can be assembled and evaluated in a data-sparse form requiring a complexity of $\mathcal{O}(Pd)$ , where P is the number of fiber-crosses and d the order of the tensor.

BACKGROUND: Flux coupling analysis (FCA) has become a useful tool in the constraint-based analysis of genome-scale metabolic networks. FCA allows detecting dependencies between reaction fluxes of metabolic networks at steady-state. On the one hand, this can help in the curation of reconstructed metabolic networks by verifying whether the coupling between reactions is in agreement with the experimental findings. On the other hand, FCA can aid in defining intervention strategies to knock out target reactions. RESULTS: We present a new method F2C2 for FCA, which is orders of magnitude faster than previous approaches. As a consequence, FCA of genome-scale metabolic networks can now be performed in a routine manner. CONCLUSIONS: We propose F2C2 as a fast tool for the computation of flux coupling in genome-scale metabolic networks. F2C2 is freely available for non-commercial use at https://sourceforge.net/projects/f2c2/files/.

The distribution of functional groups in polymer chains produced in radical copolymerization by starved‐feed semibatch operation is simulated using three different methodologies. Even under perfect control of the overall copolymer composition, a significant fraction of the polymer chains produced contain no functionality. A deterministic model is formulated to separately track the homopolymer chains that are produced without the desired functionality, a Monte Carlo (MC) model is written to represent the system, and a hybrid deterministic/MC approach is taken using new capabilities within the software package PREDICI. The advantages and disadvantages of each approach are discussed.

We introduce hexagonal global parameterization, a new type of surface parameterization in which parameter lines respect sixfold rotational symmetries (6-RoSy). Such parameterizations enable the tiling of surfaces with nearly regular hexagonal or triangular patterns, and can be used for triangular remeshing. Our framework to construct a hexagonal parameterization, referred to as HEXCOVER, extends the QUADCOVER algorithm and formulates necessary conditions for hexagonal parameterization. We also provide an algorithm to automatically generate a 6-RoSy field that respects directional and singularity features in the surface. We demonstrate the usefulness of our geometry-aware global parameterization with applications such as surface tiling with nearly regular textures and geometry patterns, as well as triangular and hexagonal remeshing.