Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions

Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting problems, however, are among the hardest problems to access computationally. Here, we suggest a novel method to access a benchmark counting problem, finding chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern matching algorithm that exploits the equivalence between the chromatic polynomial and the zero-temperature partition function of the Potts antiferromagnet on the same graph. Implementing this bottom-up algorithm using appropriate computer algebra, the new method outperforms standard top-down methods by several orders of magnitude, already for moderately sized graphs. As a first application, we compute chromatic polynomials of samples of the simple cubic lattice, for the first time computationally accessing three-dimensional lattices of physical relevance. The method offers straightforward generalizations to several other counting problems.Comment: 7 pages, 4 figure

The Extended Dawid-Skene Model:Fusing Information from Multiple Data Schemas

While label fusion from multiple noisy annotations is a well understood concept in data wrangling (tackled for example by the Dawid-Skene (DS) model), we consider the extended problem of carrying out learning when the labels themselves are not consistently annotated with the same schema. We show that even if annotators use disparate, albeit related, label-sets, we can still draw inferences for the underlying full label-set. We propose the Inter-Schema AdapteR (ISAR) to translate the fully-specified label-set to the one used by each annotator, enabling learning under such heterogeneous schemas, without the need to re-annotate the data. We apply our method to a mouse behavioural dataset, achieving significant gains (compared with DS) in out-of-sample log-likelihood (-3.40 to -2.39) and F1-score (0.785 to 0.864).Comment: Updated with Author-Preprint version following Publication in P. Cellier and K. Driessens (Eds.): ECML PKDD 2019 Workshops, CCIS 1167, pp. 121 - 136, 202

Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem

In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability p_{n,k} to find exactly k real eigenvalues in the spectrum of an nxn real asymmetric matrix drawn at random from Ginibre's Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof of the Pfaffian integration theorem, the key ingredient of our analysis of the statistics of real eigenvalues in the GinOE. We also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a GinOE matrix restricted to have exactly k real eigenvalues. In the particular case of k=0, all correlation functions of complex eigenvalues are determined

Broad Phylogenomic Sampling and the Sister Lineage of Land Plants

The tremendous diversity of land plants all descended from a single charophyte green alga that colonized the land somewhere between 430 and 470 million years ago. Six orders of charophyte green algae, in addition to embryophytes, comprise the Streptophyta s.l. Previous studies have focused on reconstructing the phylogeny of organisms tied to this key colonization event, but wildly conflicting results have sparked a contentious debate over which lineage gave rise to land plants. The dominant view has been that ‘stoneworts,’ or Charales, are the sister lineage, but an alternative hypothesis supports the Zygnematales (often referred to as “pond scum”) as the sister lineage. In this paper, we provide a well-supported, 160-nuclear-gene phylogenomic analysis supporting the Zygnematales as the closest living relative to land plants. Our study makes two key contributions to the field: 1) the use of an unbiased method to collect a large set of orthologs from deeply diverging species and 2) the use of these data in determining the sister lineage to land plants. We anticipate this updated phylogeny not only will hugely impact lesson plans in introductory biology courses, but also will provide a solid phylogenetic tree for future green-lineage research, whether it be related to plants or green algae

Small-molecule dual PLK1 and BRD4 inhibitors are active against preclinical models of pediatric solid tumors

Simultaneous inhibition of multiple molecular targets is an established strategy to improve the continuance of clinical response to therapy. Here, we screened 49 molecules with dual nanomolar inhibitory activity against BRD4 and PLK1, best classified as dual kinase-bromodomain inhibitors, in pediatric tumor cell lines for their antitumor activity. We identified two candidate dual kinase-bromodomain inhibitors with strong and tumor-specific activity against neuroblastoma, medulloblastoma, and rhabdomyosarcoma tumor cells. Dual PLK1 and BRD4 inhibitor treatment suppressed proliferation and induced apoptosis in pediatric tumor cell lines at low nanomolar concentrations. This was associated with reduced MYCN-driven gene expression as assessed by RNA sequencing. Treatment of patient-derived xenografts with dual inhibitor UMB103 led to significant tumor regression. We demonstrate that concurrent inhibition of two central regulators of MYC protein family of protooncogenes, BRD4, and PLK1, with single small molecules has strong and specific antitumor effects in preclinical pediatric cancer models

Correlations in spiking neuronal networks with distance dependent connections

Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs. We also demonstrate the crucial role of the weight distribution, most notably the compliance with Dales principle, for the activity dynamics in recurrent networks of different types

A genome-wide association scan implicates <i>DCHS2, RUNX2, GLI3, PAX1</i> and <i>EDAR</i> in human facial variation

We report a genome-wide association scan for facial features in ∼6,000 Latin Americans. We evaluated 14 traits on an ordinal scale and found significant association (P values−8) at single-nucleotide polymorphisms (SNPs) in four genomic regions for three nose-related traits: columella inclination (4q31), nose bridge breadth (6p21) and nose wing breadth (7p13 and 20p11). In a subsample of ∼3,000 individuals we obtained quantitative traits related to 9 of the ordinal phenotypes and, also, a measure of nasion position. Quantitative analyses confirmed the ordinal-based associations, identified SNPs in 2q12 associated to chin protrusion, and replicated the reported association of nasion position with SNPs in PAX3. Strongest association in 2q12, 4q31, 6p21 and 7p13 was observed for SNPs in the EDAR, DCHS2, RUNX2 and GLI3 genes, respectively. Associated SNPs in 20p11 extend to PAX1. Consistent with the effect of EDAR on chin protrusion, we documented alterations of mandible length in mice with modified Edar function