Parabolic Anderson model with a finite number of moving catalysts

We consider the parabolic Anderson model (PAM) which is given by the equation $\partial u/\partial t = \kappa\Delta u + \xi u$ with $u\colon\, \Z^d\times [0,\infty)\to \R$, where $\kappa \in [0,\infty)$ is the diffusion constant, $\Delta$ is the discrete Laplacian, and $\xi\colon\,\Z^d\times [0,\infty)\to\R$ is a space-time random environment that drives the equation. The solution of this equation describes the evolution of a "reactant" $u$ under the influence of a "catalyst" $\xi$. In the present paper we focus on the case where $\xi$ is a system of $n$ independent simple random walks each with step rate $2d\rho$ and starting from the origin. We study the \emph{annealed} Lyapunov exponents, i.e., the exponential growth rates of the successive moments of $u$ w.r.t.\ $\xi$ and show that these exponents, as a function of the diffusion constant $\kappa$ and the rate constant $\rho$, behave differently depending on the dimension $d$. In particular, we give a description of the intermittent behavior of the system in terms of the annealed Lyapunov exponents, depicting how the total mass of $u$ concentrates as $t\to\infty$. Our results are both a generalization and an extension of the work of G\"artner and Heydenreich 2006, where only the case $n=1$ was investigated.Comment: In honour of J\"urgen G\"artner on the occasion of his 60th birthday, 25 pages. Updated version following the referee's comment

Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

Space-efficient Feature Maps for String Alignment Kernels

String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, which limits large-scale applications in practice. We address this need by presenting the first approximation for string alignment kernels, which we call space-efficient feature maps for edit distance with moves (SFMEDM), by leveraging a metric embedding named edit sensitive parsing (ESP) and feature maps (FMs) of random Fourier features (RFFs) for large-scale string analyses. The original FMs for RFFs consume a huge amount of memory proportional to the dimension d of input vectors and the dimension D of output vectors, which prohibits its large-scale applications. We present novel space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds. We experimentally test SFMEDM on its ability to learn SVM for large-scale string classifications with various massive string data, and we demonstrate the superior performance of SFMEDM with respect to prediction accuracy, scalability and computation efficiency.Comment: Full version for ICDM'19 pape

Inductive queries for a drug designing robot scientist

It is increasingly clear that machine learning algorithms need to be integrated in an iterative scientific discovery loop, in which data is queried repeatedly by means of inductive queries and where the computer provides guidance to the experiments that are being performed. In this chapter, we summarise several key challenges in achieving this integration of machine learning and data mining algorithms in methods for the discovery of Quantitative Structure Activity Relationships (QSARs). We introduce the concept of a robot scientist, in which all steps of the discovery process are automated; we discuss the representation of molecular data such that knowledge discovery tools can analyse it, and we discuss the adaptation of machine learning and data mining algorithms to guide QSAR experiments

Particle Compression Test: A Key Step towards Tailoring of Feedstock Powder for Cold Spraying

Copyright © 2020 by the authors. Cold spray is on the way to becoming a mainstream technology for coating and additive manufacturing processes. While there have been many advances in various aspects of this technology, the question of tailoring the ‘ideal’ feedstock powder for cold spraying has remained open. In particular, the mechanical strength and its dependence on the particle size, which are amongst the most relevant properties of the feedstock powder for cold spraying, are rarely covered when reporting powder specifications. This is mainly because of the lack of standardised methods of characterisation for these specific properties. In the present case study, we demonstrate how compression tests of single Inconel 718 particles by using a modified nanoindenter can address this central question. Data analyses are supported by finite element modelling of particle compression for a range of plastic behaviours. The results of simulation are then stored in the form of a surrogate model for subsequent comparison with the experimental data. Thus, the ultimate tensile strength and the size of the examined particles are calculated directly from the measured force-displacement data. The paper will also discuss how this information can be used to optimise cold spraying, and so, unveils a key step towards the design and manufacturing of cold-spray-specific feedstock powder

Micrometer-sized Water Ice Particles for Planetary Science Experiments: Influence of Surface Structure on Collisional Properties

Models and observations suggest that ice-particle aggregation at and beyond the snowline dominates the earliest stages of planet formation, which therefore is subject to many laboratory studies. However, the pressure–temperature gradients in protoplanetary disks mean that the ices are constantly processed, undergoing phase changes between different solid phases and the gas phase. Open questions remain as to whether the properties of the icy particles themselves dictate collision outcomes and therefore how effectively collision experiments reproduce conditions in protoplanetary environments. Previous experiments often yielded apparently contradictory results on collision outcomes, only agreeing in a temperature dependence setting in above ≈210 K. By exploiting the unique capabilities of the NIMROD neutron scattering instrument, we characterized the bulk and surface structure of icy particles used in collision experiments, and studied how these structures alter as a function of temperature at a constant pressure of around 30 mbar. Our icy grains, formed under liquid nitrogen, undergo changes in the crystalline ice-phase, sublimation, sintering and surface pre-melting as they are heated from 103 to 247 K. An increase in the thickness of the diffuse surface layer from ≈10 to ≈30 Å (≈2.5 to 12 bilayers) proves increased molecular mobility at temperatures above ≈210 K. Because none of the other changes tie-in with the temperature trends in collisional outcomes, we conclude that the surface pre-melting phenomenon plays a key role in collision experiments at these temperatures. Consequently, the pressure–temperature environment, may have a larger influence on collision outcomes than previously thought

The long noncoding RNA neuroLNC regulates presynaptic activity by interacting with the neurodegeneration-associated protein TDP-43

The cellular and the molecular mechanisms by which long noncoding RNAs (lncRNAs) may regulate presynaptic function and neuronal activity are largely unexplored. Here, we established an integrated screening strategy to discover lncRNAs implicated in neurotransmitter and synaptic vesicle release. With this approach, we identified neuroLNC, a neuron-specific nuclear lncRNA conserved from rodents to humans. NeuroLNC is tuned by synaptic activity and influences several other essential aspects of neuronal development including calcium influx, neuritogenesis, and neuronal migration in vivo. We defined the molecular interactors of neuroLNC in detail using chromatin isolation by RNA purification, RNA interactome analysis, and protein mass spectrometry. We found that the effects of neuroLNC on synaptic vesicle release require interaction with the RNA-binding protein TDP-43 (TAR DNA binding protein-43) and the selective stabilization of mRNAs encoding for presynaptic proteins. These results provide the first proof of an lncRNA that orchestrates neuronal excitability by influencing presynaptic function