State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis.

The rate of nucleation processes such as the freezing of a supercooled liquid or the condensation of supersaturated vapour is mainly determined by the height of the nucleation barrier and the diffusion coefficient for the motion across it. Here, we use a Bayesian inference algorithm for Markovian dynamics to extract simultaneously the free energy profile and the diffusion coefficient in the nucleation barrier region from short molecular dynamics trajectories. The specific example we study is the nucleation of vapour bubbles in liquid water under strongly negative pressures, for which we use the volume of the largest bubble as a reaction coordinate. Particular attention is paid to the effects of discretisation, the implementation of appropriate boundary conditions and the optimal selection of parameters. We find that the diffusivity is a linear function of the bubble volume over wide ranges of volumes and pressures, and is mainly determined by the viscosity of the liquid, as expected from the Rayleigh-Plesset theory for macroscopic bubble dynamics. The method is generally applicable to nucleation processes and yields important quantities for the estimation of nucleation rates in classical nucleation theory

Fast Parallel Fixed-Parameter Algorithms via Color Coding

Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use of the parallel hardware present in modern computers. We show that parallel fixed-parameter algorithms do not only exist for numerous parameterized problems from the literature -- including vertex cover, packing problems, cluster editing, cutting vertices, finding embeddings, or finding matchings -- but that there are parallel algorithms working in \emph{constant} time or at least in time \emph{depending only on the parameter} (and not on the size of the input) for these problems. Phrased in terms of complexity classes, we place numerous natural parameterized problems in parameterized versions of AC$^0$. On a more technical level, we show how the \emph{color coding} method can be implemented in constant time and apply it to embedding problems for graphs of bounded tree-width or tree-depth and to model checking first-order formulas in graphs of bounded degree

LeoPARD --- A Generic Platform for the Implementation of Higher-Order Reasoners

LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s). It combines a sophisticated data structure layer (polymorphically typed {\lambda}-calculus with nameless spine notation, explicit substitutions, and perfect term sharing) with an ambitious multi-agent blackboard architecture (supporting prover parallelism at the term, clause, and search level). Further features of LeoPARD include a parser for all TPTP dialects, a command line interpreter, and generic means for the integration of external reasoners.Comment: 6 pages, to appear in the proceedings of CICM'2015 conferenc

A New Productivity Strategy for Europe. Bertelsmann Stiftung Inclusive Growth for Europe Policy Paper April 2020.

Europe has a productivity problem. In recent years, pro- ductivity growth in many European economies has sys- tematically slowed down and regional differences have widened. The slowdown is connected to decreasing com- petitiveness, fewer prospects for growth and shrinking opportunities for redistribution. Moreover, diverging changes in productivity within the EU endanger the eco- nomic and, ultimately, political stability of the common economic and monetary area. As a result of the current crisis situation, the productivity problem, which up to now has been of subordinate importance in politics, could pose particular challenges for economic policy. Economic policy measures must have a stimulating effect on the business cycle and at the same time always aim to increase productivity. What policies and instruments can reverse the trend and increase long-term productivity in Europe? This paper proposes nine points for a new productivity strategy in Europe. The main pillars of this strategy are: a substan- tially stronger innovation policy, the targeted promotion of technology diffusion and comprehensive, sustainable investments in the future

Approximate Pure Nash Equilibria in Weighted Congestion Games

We study the existence of approximate pure Nash equilibria in weighted congestion games and develop techniques to obtain approximate potential functions that prove the existence of alpha-approximate pure Nash equilibria and the convergence of alpha-improvement steps. Specifically, we show how to obtain upper bounds for approximation factor alpha for a given class of cost functions. For example for concave cost functions the factor is at most 3/2, for quadratic cost functions it is at most 4/3, and for polynomial cost functions of maximal degree d it is at at most d + 1. For games with two players we obtain tight bounds which are as small as for example 1.054 in the case of quadratic cost functions

Sparse Model Soups: A Recipe for Improved Pruning via Model Averaging

Neural networks can be significantly compressed by pruning, leading to sparse models requiring considerably less storage and floating-point operations while maintaining predictive performance. Model soups (Wortsman et al., 2022) improve generalization and out-of-distribution performance by averaging the parameters of multiple models into a single one without increased inference time. However, identifying models in the same loss basin to leverage both sparsity and parameter averaging is challenging, as averaging arbitrary sparse models reduces the overall sparsity due to differing sparse connectivities. In this work, we address these challenges by demonstrating that exploring a single retraining phase of Iterative Magnitude Pruning (IMP) with varying hyperparameter configurations, such as batch ordering or weight decay, produces models that are suitable for averaging and share the same sparse connectivity by design. Averaging these models significantly enhances generalization performance compared to their individual components. Building on this idea, we introduce Sparse Model Soups (SMS), a novel method for merging sparse models by initiating each prune-retrain cycle with the averaged model of the previous phase. SMS maintains sparsity, exploits sparse network benefits being modular and fully parallelizable, and substantially improves IMP's performance. Additionally, we demonstrate that SMS can be adapted to enhance the performance of state-of-the-art pruning during training approaches.Comment: 9 pages, 5 pages references, 7 pages appendi

The perfect crime? : CCSVI not leaving a trace in MS

Background: Multiple sclerosis (MS) is a chronic, inflammatory demyelinating disease of the central nervous system, believed to be triggered by an autoimmune reaction to myelin. Recently, a fundamentally different pathomechanism termed ‘chronic cerebrospinal venous insufficiency’ (CCSVI) was proposed, provoking significant attention in the media and scientific community. Methods: Twenty MS patients (mean age 42.2±13.3 years; median Extended Disability Status Scale 3.0, range 0–6.5) were compared with 20 healthy controls. Extra- and intracranial venous flow direction was assessed by colour-coded duplex sonography, and extracranial venous cross-sectional area (VCSA) of the internal jugular and vertebral veins (IJV/VV) was measured in B-mode to assess the five previously proposed CCSVI criteria. IJV-VCSA≤0.3 cm2 indicated ‘stenosis,’ and IJV-VCSA decrease from supine to upright position ‘reverted postural control.’ The sonographer, data analyser and statistician were blinded to the patient/control status of the participants. Results: No participant showed retrograde flow of cervical or intracranial veins. IJV-VCSA≤0.3 cm2 was found in 13 MS patients versus 16 controls (p=0.48). A decrease in IJV-VCSA from supine to upright position was observed in all participants, but this denotes a physiological finding. No MS patient and one control had undetectable IJV flow despite deep inspiration (p=0.49). Only one healthy control and no MS patients fulfilled at least two criteria for CCSVI. Conclusions: This triple-blinded extra- and transcranial duplex sonographic assessment of cervical and cerebral veins does not provide supportive evidence for the presence of CCSVI in MS patients. The findings cast serious doubt on the concept of CCSVI in MS

Topology counts: force distributions in circular spring networks

Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network.Comment: 5 pages, 4 figures. Missing labels in Fig. 4 added. Reference fixe