Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes

Fluorescence in situ hybridization (FISH) is a powerful single-cell technique for studying nuclear structure and organization. Here we report two advances in FISH-based imaging. We first describe the in situ visualization of single-copy regions of the genome using two single-molecule super-resolution methodologies. We then introduce a robust and reliable system that harnesses single-nucleotide polymorphisms (SNPs) to visually distinguish the maternal and paternal homologous chromosomes in mammalian and insect systems. Both of these new technologies are enabled by renewable, bioinformatically designed, oligonucleotide-based Oligopaint probes, which we augment with a strategy that uses secondary oligonucleotides (oligos) to produce and enhance fluorescent signals. These advances should substantially expand the capability to query parent-of-origin-specific chromosome positioning and gene expression on a cell-by-cell basis

Our Deep CNN Face Matchers Have Developed Achromatopsia

Modern deep CNN face matchers are trained on datasets containing color images. We show that such matchers achieve essentially the same accuracy on the grayscale or the color version of a set of test images. We then consider possible causes for deep CNN face matchers ``not seeing color''. Popular web-scraped face datasets actually have 30 to 60\% of their identities with one or more grayscale images. We analyze whether this grayscale element in the training set impacts the accuracy achieved, and conclude that it does not. Further, we show that even with a 100\% grayscale training set, comparable accuracy is achieved on color or grayscale test images. Then we show that the skin region of an individual's images in a web-scraped training set exhibit significant variation in their mapping to color space. This suggests that color, at least for web-scraped, in-the-wild face datasets, carries limited identity-related information for training state-of-the-art matchers. Finally, we verify that comparable accuracy is achieved from training using single-channel grayscale images, implying that a larger dataset can be used within the same memory limit, with a less computationally intensive early layer

P2RX7 Deletion in T Cells Promotes Autoimmune Arthritis by Unleashing the Tfh Cell Response

Rheumatoid arthritis (RA) is an autoimmune disease that affects ~1% of the world's population. B cells and autoantibodies play an important role in the pathogenesis of RA. The P2RX7 receptor is an ATP-gated cation channel and its activation results in the release of pro-inflammatory molecules. Thus, antagonists of P2RX7 have been considered to have potential as novel anti-inflammatory therapies. Although originally identified for its role in innate immunity, P2RX7 has recently been found to negatively control Peyer's patches (PP) T follicular helper cells (Tfh), which specialize in helping B cells, under homeostatic conditions. We have previously demonstrated that PP Tfh cells are required for the augmentation of autoimmune arthritis mediated by gut commensal segmented filamentous bacteria (SFB). Thus, we hypothesized that P2RX7 is required to control autoimmune disease by keeping the Tfh cell response in check. To test our hypothesis, we analyzed the impact of P2RX7 deficiency in vivo using both the original K/BxN autoimmune arthritis model and T cell transfers in the K/BxN system. We also examined the impact of P2RX7 ablation on autoimmune development in the presence of the gut microbiota SFB. Our data illustrate that contrary to exerting an anti-inflammatory effect, P2RX7 deficiency actually enhances autoimmune arthritis. Interestingly, SFB colonization can negate the difference in disease severity between WT and P2RX7-deficient mice. We further demonstrated that P2RX7 ablation in the absence of SFB caused reduced apoptotic Tfh cells and enhanced the Tfh response, leading to an increase in autoantibody production. It has been shown that activation of TIGIT, a well-known T cell exhaustion marker, up-regulates anti-apoptotic molecules and promotes T cell survival. We demonstrated that the reduced apoptotic phenotype of P2rx7−/− Tfh cells is associated with their increased expression of TIGIT. This suggested that while P2RX7 was regulating the Tfh population by promoting cell death, TIGIT may have been opposing P2RX7 by inhibiting cell death. Together, these results demonstrated that systemic administration of general P2RX7 antagonists may have detrimental effects in autoimmune therapies, especially in Tfh cell-dependent autoimmune diseases, and cell-specific targeting of P2RX7 should be considered in order to achieve efficacy for P2RX7-related therapy

Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models

The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.Comment: 10 pages, 4 figure

Direct and indirect control of the initiation of meiotic recombination by DNA damage checkpoint mechanisms in budding yeast

Meiotic recombination plays an essential role in the proper segregation of chromosomes at meiosis I in many sexually reproducing organisms. Meiotic recombination is initiated by the scheduled formation of genome-wide DNA double-strand breaks (DSBs). The timing of DSB formation is strictly controlled because unscheduled DSB formation is detrimental to genome integrity. Here, we investigated the role of DNA damage checkpoint mechanisms in the control of meiotic DSB formation using budding yeast. By using recombination defective mutants in which meiotic DSBs are not repaired, the effect of DNA damage checkpoint mutations on DSB formation was evaluated. The Tel1 (ATM) pathway mainly responds to unresected DSB ends, thus the sae2 mutant background in which DSB ends remain intact was employed. On the other hand, the Mec1 (ATR) pathway is primarily used when DSB ends are resected, thus the rad51 dmc1 double mutant background was employed in which highly resected DSBs accumulate. In order to separate the effect caused by unscheduled cell cycle progression, which is often associated with DNA damage checkpoint defects, we also employed the ndt80 mutation which permanently arrests the meiotic cell cycle at prophase I. In the absence of Tel1, DSB formation was reduced in larger chromosomes (IV, VII, II and XI) whereas no significant reduction was found in smaller chromosomes (III and VI). On the other hand, the absence of Rad17 (a critical component of the ATR pathway) lead to an increase in DSB formation (chromosomes VII and II were tested). We propose that, within prophase I, the Tel1 pathway facilitates DSB formation, especially in bigger chromosomes, while the Mec1 pathway negatively regulates DSB formation. We also identified prophase I exit, which is under the control of the DNA damage checkpoint machinery, to be a critical event associated with down-regulating meiotic DSB formation

Random Tilings: Concepts and Examples

We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile densities. In this context, and under rather mild assumptions, we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble. Explicit examples are obtained through the re-interpretation of several exactly solvable models. This also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum.Comment: 32 pages, 42 eps-figures, Latex2e updated version, minor grammatical change

Irreducible holonomy algebras of Riemannian supermanifolds

Possible irreducible holonomy algebras \g\subset\osp(p,q|2m) of Riemannian supermanifolds under the assumption that \g is a direct sum of simple Lie superalgebras of classical type and possibly of a one-dimensional center are classified. This generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian manifolds.Comment: 27 pages, the final versio

The complex universe: recent observations and theoretical challenges

The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical characterization of these structures shows that galaxy distribution is inhomogeneous in these samples, being characterized by large-amplitude fluctuations of large spatial extension. Over a large range of scales, both the average conditional density and its variance show a nontrivial scaling behavior: at small scales, r<20 Mpc/h, the average (conditional) density scales as 1/r. At larger scales, the density depends only weakly (logarithmically) on the system size and density fluctuations follow the Gumbel distribution of extreme value statistics. These complex behaviors are different from what is expected in a homogeneous distribution with Gaussian fluctuations. The observed density inhomogeneities pose a fundamental challenge to the standard picture of cosmology but it also represent an important opportunity which points to new directions with respect to many cosmological puzzles. Indeed, the fact that matter distribution is not uniform, in the limited range of scales sampled by observations, rises the question of understanding how inhomogeneities affect the large-scale dynamics of the universe. We discuss several attempts which try to model inhomogeneities in cosmology, considering their effects with respect to the role and abundance of dark energy and dark matter.Comment: 30 pages, 10 figure