2D String Theory as Normal Matrix Model

We show that the $c=1$ bosonic string theory at finite temperature has two matrix-model realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics in the inverted oscillator potential. The second realization, which we derive here, is given by the normal matrix model. Both matrix models exhibit the Toda integrable structure and are associated with two dual cycles (a compact and a non-compact one) of a complex curve with the topology of a sphere with two punctures. The equivalence of the two matrix models holds for an arbitrary tachyon perturbation and in all orders in the string coupling constant.Comment: lanlmac, 21 page

Parametric Modeling as a Technology of Rapid Prototyping in Light Industry

The paper deals with the parametric modeling method of virtual mannequins for the purposes of design automation in clothing industry. The described approach includes the steps of generation of the basic model on the ground of the initial one (obtained in 3D-scanning process), its parameterization and deformation. The complex surfaces are presented by the wireframe model. The modeling results are evaluated with the set of similarity factors. Deformed models are compared with their virtual prototypes. The results of modeling are estimated by the standard deviation factor

Integrable flows in c=1 string theory

In these notes we review the method to construct integrable deformations of the compactified c=1 bosonic string theory by primary fields (momentum or winding modes), developed recently in collaboration with S. Alexandrov and V. Kazakov. The method is based on the formulation of the string theory as a matrix model. The flows generated by either momentum or winding modes (but not both) are integrable and satisfy the Toda lattice hierarchy.Comment: sect.1 extended and typos correcte

Time-dependent backgrounds of 2D string theory

We study possible backgrounds of 2D string theory using its equivalence with a system of fermions in upside-down harmonic potential. Each background corresponds to a certain profile of the Fermi sea, which can be considered as a deformation of the hyperbolic profile characterizing the linear dilaton background. Such a perturbation is generated by a set of commuting flows, which form a Toda Lattice integrable structure. The flows are associated with all possible left and right moving tachyon states, which in the compactified theory have discrete spectrum. The simplest nontrivial background describes the Sine-Liouville string theory. Our methods can be also applied to the study of 2D droplets of electrons in a strong magnetic field.Comment: 28 pages, 2 figures, lanlma

Shapes of polyhedra, mixed volumes and hyperbolic geometry

We generalize to higher dimensions the Bavard–Ghys construction of the hyperbolic metric on the space of polygons with fixed directions of edges. The space of convex d -dimensional polyhedra with fixed directions of facet normals has a decomposition into type cones that correspond to different combinatorial types of polyhedra. This decomposition is a subfan of the secondary fan of a vector configuration and can be analyzed with the help of Gale diagrams. We construct a family of quadratic forms on each of the type cones using the theory of mixed volumes. The Alexandrov–Fenchel inequalities ensure that these forms have exactly one positive eigenvalue. This introduces a piecewise hyperbolic structure on the space of similarity classes of polyhedra with fixed directions of facet normals. We show that some of the dihedral angles on the boundary of the resulting cone-manifold are equal to π/2

Molecular and Microbial Microenvironments in Chronically Diseased Lungs Associated with Cystic Fibrosis.

To visualize the personalized distributions of pathogens and chemical environments, including microbial metabolites, pharmaceuticals, and their metabolic products, within and between human lungs afflicted with cystic fibrosis (CF), we generated three-dimensional (3D) microbiome and metabolome maps of six explanted lungs from three cystic fibrosis patients. These 3D spatial maps revealed that the chemical environments differ between patients and within the lungs of each patient. Although the microbial ecosystems of the patients were defined by the dominant pathogen, their chemical diversity was not. Additionally, the chemical diversity between locales in the lungs of the same individual sometimes exceeded interindividual variation. Thus, the chemistry and microbiome of the explanted lungs appear to be not only personalized but also regiospecific. Previously undescribed analogs of microbial quinolones and antibiotic metabolites were also detected. Furthermore, mapping the chemical and microbial distributions allowed visualization of microbial community interactions, such as increased production of quorum sensing quinolones in locations where Pseudomonas was in contact with Staphylococcus and Granulicatella, consistent with in vitro observations of bacteria isolated from these patients. Visualization of microbe-metabolite associations within a host organ in early-stage CF disease in animal models will help elucidate the complex interplay between the presence of a given microbial structure, antibiotics, metabolism of antibiotics, microbial virulence factors, and host responses.IMPORTANCE Microbial infections are now recognized to be polymicrobial and personalized in nature. Comprehensive analysis and understanding of the factors underlying the polymicrobial and personalized nature of infections remain limited, especially in the context of the host. By visualizing microbiomes and metabolomes of diseased human lungs, we reveal how different the chemical environments are between hosts that are dominated by the same pathogen and how community interactions shape the chemical environment or vice versa. We highlight that three-dimensional organ mapping methods represent hypothesis-building tools that allow us to design mechanistic studies aimed at addressing microbial responses to other microbes, the host, and pharmaceutical drugs

The Evolutionary Origin of Man Can Be Traced in the Layers of Defunct Ancestral Alpha Satellites Flanking the Active Centromeres of Human Chromosomes

Alpha satellite domains that currently function as centromeres of human chromosomes are flanked by layers of older alpha satellite, thought to contain dead centromeres of primate progenitors, which lost their function and the ability to homogenize satellite repeats, upon appearance of a new centromere. Using cladistic analysis of alpha satellite monomers, we elucidated complete layer patterns on chromosomes 8, 17, and X and related them to each other and to primate alpha satellites. We show that discrete and chronologically ordered alpha satellite layers are partially symmetrical around an active centromere and their succession is partially shared in non-homologous chromosomes. The layer structure forms a visual representation of the human evolutionary lineage with layers corresponding to ancestors of living primates and to entirely fossil taxa. Surprisingly, phylogenetic comparisons suggest that alpha satellite arrays went through periods of unusual hypermutability after they became “dead” centromeres. The layer structure supports a model of centromere evolution where new variants of a satellite repeat expanded periodically in the genome by rounds of inter-chromosomal transfer/amplification. Each wave of expansion covered all or many chromosomes and corresponded to a new primate taxon. Complete elucidation of the alpha satellite phylogenetic record would give a unique opportunity to number and locate the positions of major extinct taxa in relation to human ancestors shared with extant primates. If applicable to other satellites in non-primate taxa, analysis of centromeric layers could become an invaluable tool for phylogenetic studies

Creating a 3D microbial and chemical snapshot of a human habitat

Kapono CA, Morton JT, Bouslimani A, et al. Creating a 3D microbial and chemical snapshot of a human habitat. Scientific Reports. 2018;8(1): 3669

Large Tandem, Higher Order Repeats and Regularly Dispersed Repeat Units Contribute Substantially to Divergence Between Human and Chimpanzee Y Chromosomes

Comparison of human and chimpanzee genomes has received much attention, because of paramount role for understanding evolutionary step distinguishing us from our closest living relative. In order to contribute to insight into Y chromosome evolutionary history, we study and compare tandems, higher order repeats (HORs), and regularly dispersed repeats in human and chimpanzee Y chromosome contigs, using robust Global Repeat Map algorithm. We find a new type of long-range acceleration, human-accelerated HOR regions. In peripheral domains of 35mer human alphoid HORs, we find riddled features with ten additional repeat monomers. In chimpanzee, we identify 30mer alphoid HOR. We construct alphoid HOR schemes showing significant human-chimpanzee difference, revealing rapid evolution after human-chimpanzee separation. We identify and analyze over 20 large repeat units, most of them reported here for the first time as: chimpanzee and human ~1.6 kb 3mer secondary repeat unit (SRU) and ~23.5 kb tertiary repeat unit (~0.55 kb primary repeat unit, PRU); human 10848, 15775, 20309, 60910, and 72140 bp PRUs; human 3mer SRU (~2.4 kb PRU); 715mer and 1123mer SRUs (5mer PRU); chimpanzee 5096, 10762, 10853, 60523 bp PRUs; and chimpanzee 64624 bp SRU (10853 bp PRU). We show that substantial human-chimpanzee differences are concentrated in large repeat structures, at the level of as much as ~70% divergence, sizably exceeding previous numerical estimates for some selected noncoding sequences. Smeared over the whole sequenced assembly (25 Mb) this gives ~14% human--chimpanzee divergence. This is significantly higher estimate of divergence between human and chimpanzee than previous estimates.Comment: 22 pages, 7 figures, 12 tables. Published in Journal of Molecular Evolutio