A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding

Brown representability for space-valued functors

In this paper we prove two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify small contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we show that every small contravariant functor from spaces to spaces which takes coproducts to products up to homotopy and takes homotopy pushouts to homotopy pullbacks is naturally weekly equivalent to a representable functor. The second representability theorem states: every contravariant continuous functor from the category of finite simplicial sets to simplicial sets taking homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a representable functor. This theorem may be considered as a contravariant analog of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of Mathematic

Self-similar solutions for the LSW model with encounters

The LSW model with encounters has been suggested by Lifshitz and Slyozov as a regularization of their classical mean-field model for domain coarsening to obtain universal self-similar long-time behavior. We rigorously establish that an exponentially decaying self-similar solution to this model exist, and show that this solutions is isolated in a certain function space. Our proof relies on setting up a suitable fixed-point problem in an appropriate function space and careful asymptotic estimates of the solution to a corresponding homogeneous problem.Comment: 22 page

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

Systematic comparison of monoclonal versus polyclonal antibodies for mapping histone modifications by ChIP-seq.

BackgroundThe robustness of ChIP-seq datasets is highly dependent upon the antibodies used. Currently, polyclonal antibodies are the standard despite several limitations: They are non-renewable, vary in performance between lots and need to be validated with each new lot. In contrast, monoclonal antibody lots are renewable and provide consistent performance. To increase ChIP-seq standardization, we investigated whether monoclonal antibodies could replace polyclonal antibodies. We compared monoclonal antibodies that target five key histone modifications (H3K4me1, H3K4me3, H3K9me3, H3K27ac and H3K27me3) to their polyclonal counterparts in both human and mouse cells.ResultsOverall performance was highly similar for four monoclonal/polyclonal pairs, including when we used two distinct lots of the same monoclonal antibody. In contrast, the binding patterns for H3K27ac differed substantially between polyclonal and monoclonal antibodies. However, this was most likely due to the distinct immunogen used rather than the clonality of the antibody.ConclusionsAltogether, we found that monoclonal antibodies as a class perform equivalently to polyclonal antibodies for the detection of histone post-translational modifications in both human and mouse. Accordingly, we recommend the use of monoclonal antibodies in ChIP-seq experiments

On realizing diagrams of Pi-algebras

Given a diagram of Pi-algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized Pi-algebras. This extends a program begun in [J. Pure Appl. Alg. 103 (1995) 167-188] and [Topology 43 (2004) 857-892] to study the realization of a single Pi-algebra. In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations.Comment: This is the version published by Algebraic & Geometric Topology on 21 June 200

Numerably Contractible Spaces

Numerably contractible spaces play an important role in the theory of homotopy pushouts and pullbacks. The corresponding results imply that a number of well known weak homotopy equivalences are genuine ones if numerably contractible spaces are involved. In this paper we give a first systematic investigation of numerably contractible spaces. We list the elementary properties of the category of these spaces. We then study simplicial objects in this category. In particular, we show that the topological realization functor preserves fibration sequences if the base is path-connected and numerably contractible in each dimension. Consequently, the loop space functor commutes with realization up to homotopy. We give simple conditions which assure that free algebras over a topological operad are numerably contractible.Comment: 24 page

The effect of LRRK2 loss-of-function variants in humans

Analysis of large genomic datasets, including gnomAD, reveals that partial LRRK2 loss of function is not strongly associated with diseases, serving as an example of how human genetics can be leveraged for target validation in drug discovery. Human genetic variants predicted to cause loss-of-function of protein-coding genes (pLoF variants) provide natural in vivo models of human gene inactivation and can be valuable indicators of gene function and the potential toxicity of therapeutic inhibitors targeting these genes(1,2). Gain-of-kinase-function variants in LRRK2 are known to significantly increase the risk of Parkinson's disease(3,4), suggesting that inhibition of LRRK2 kinase activity is a promising therapeutic strategy. While preclinical studies in model organisms have raised some on-target toxicity concerns(5-8), the biological consequences of LRRK2 inhibition have not been well characterized in humans. Here, we systematically analyze pLoF variants in LRRK2 observed across 141,456 individuals sequenced in the Genome Aggregation Database (gnomAD)(9), 49,960 exome-sequenced individuals from the UK Biobank and over 4 million participants in the 23andMe genotyped dataset. After stringent variant curation, we identify 1,455 individuals with high-confidence pLoF variants in LRRK2. Experimental validation of three variants, combined with previous work(10), confirmed reduced protein levels in 82.5% of our cohort. We show that heterozygous pLoF variants in LRRK2 reduce LRRK2 protein levels but that these are not strongly associated with any specific phenotype or disease state. Our results demonstrate the value of large-scale genomic databases and phenotyping of human loss-of-function carriers for target validation in drug discovery.Peer reviewe

Systems Perspectives on the Interaction Between Human and Technological Resources

Peer reviewe

Colloquium: Statistical mechanics of money, wealth, and income

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.Comment: 24 pages, 13 figures; v.2 - minor stylistic changes and updates of references corresponding to the published versio