Manin matrices and Talalaev's formula

We study special class of matrices with noncommutative entries and demonstrate their various applications in integrable systems theory. They appeared in Yu. Manin's works in 87-92 as linear homomorphisms between polynomial rings; more explicitly they read: 1) elements in the same column commute; 2) commutators of the cross terms are equal: $[M_{ij}, M_{kl}]=[M_{kj}, M_{il}]$ (e.g. $[M_{11}, M_{22}]=[M_{21}, M_{12}]$). We claim that such matrices behave almost as well as matrices with commutative elements. Namely theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) holds true for them. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation "RTT=TTR" and the so--called Cartier-Foata matrices. Also, they enter Talalaev's hep-th/0404153 remarkable formulas: $det(\partial_z-L_{Gaudin}(z))$, det(1-e^{-\p}T_{Yangian}(z)) for the "quantum spectral curve", etc. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g in the construction of new generators in $Z(U(\hat{gl_n}))$ (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We also discuss applications to the separation of variables problem, new Capelli identities and the Langlands correspondence.Comment: 40 pages, V2: exposition reorganized, some proofs added, misprints e.g. in Newton id-s fixed, normal ordering convention turned to standard one, refs. adde

Search Method Based on Figurative Indexation of Folksonomic Features of Graphic Files

In this paper the search method based on usage of figurative indexation of folksonomic characteristics of graphical files is described. The method takes into account extralinguistic information, is based on using a model of figurative thinking of humans. The paper displays the creation of a method of searching image files based on their formal, including folksonomical clues

Positioning of Chromosomes in Human Spermatozoa Is Determined by Ordered Centromere Arrangement

<div><p>The intranuclear positioning of chromosomes (CHRs) is a well-documented fact; however, mechanisms directing such ordering remain unclear. Unlike somatic cells, human spermatozoa contain distinct spatial markers and have asymmetric nuclei which make them a unique model for localizing CHR territories and matching peri-centromere domains. In this study, we established statistically preferential longitudinal and lateral positioning for eight CHRs. Both parameters demonstrated a correlation with the CHR gene densities but not with their sizes. Intranuclear non-random positioning of the CHRs was found to be driven by a specific linear order of centromeres physically interconnected in continuous arrays. In diploid spermatozoa, linear order of peri-centromeres was identical in two genome sets and essentially matched the arrangement established for haploid cells. We propose that the non-random longitudinal order of CHRs in human spermatozoa is generated during meiotic stages of spermatogenesis. The specific arrangement of sperm CHRs may serve as an epigenetic basis for differential transcription/replication and direct spatial CHR organization during early embryogenesis.</p> </div

Localization of chromosome territories in human spermatozoa.

<p>(A) A typical image of chromosome territories in spermatozoa obtained using FISH with WCP probes. HSA18 paint – red, HSA3 – green, total DNA stained with DAPI – blue. (B) The scheme explaining the determination of CT center coordinates following FISH. The apical end of the ellipsoid sperm cell is on the left (<b><i>x</i></b> = 0), the tail (green) attachment point - on the right. (C) Examples of the statistical evaluation of chromosome positioning. Position of each CT was determined in ≥80 cells. Left - contour plots showing the probability to find the CT center within the given area of the nucleus (red – the most probable localization). The color-coded bar at the bottom of the figure represents the p-value, with the red indicating p≤0.125 (the most probable localization) and the navy 0.875≤p≤1.000. The central and the right panels – frequency distribution plots for the longitudinal (along the long nuclear axis) and the lateral (along the short nuclear axis) positioning, respectively. Scale bar – 5 µm.</p

Relation between chromosome properties and their intranuclear localization in spermatozoa.

<p>(A) Examples of the CHR longitudinal coordinate determination using the Gaussian approximation (red line) of the frequency distribution data (black line). Numerical values of longitudinal (B) and lateral (D) coordinates of the CT centers. Correlations between the longitudinal (C) or the lateral (E) chromosome positioning and densities of coding sequences (left panels) or the chromosome size (right panels). <b><i>x</i></b> – the distance from the apical end of the sperm nuclei, <b><i>h</i></b> – the distance between the CT center and the long nuclear axis as described in the scheme <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052944#pone-0052944-g001" target="_blank">Fig. 1,B</a>.</p

In human spermatozoa, nonhomologous centromeres are arranged in arrays with the fixed chromosome-specific linear order.

<p>(A) Visualization of CEN arrays using FISH with pan-CEN DNA probe. Nucleus borders, determined by DAPI staining are shown by a blue dashed line. (B) The outline of the sequential FISH procedure. First, cells were hybridized with pan-CEN probe (a, green). Cells that demonstrated unfolded CEN strings were subjected to sequential FISH with chromosome-specific peri-CEN probes (b–e). (f) - Artificial colors were assigned to the peri-CEN signals and images were merged. (g) - Schematic representation of the chromosome-specific peri-CEN localization. (C) Examples of CEN localization along sperm chromocenter arrays. (D) The cumulative scheme. (E) The order of CENs is preserved in diploid sperm nuclei. (a) Diploid sperm cells revealed using FISH with chromosome-specific peri-CEN probes; merged images after sequential FISH. (b) - Schematic representation of chromosome-specific peri-CEN localization. (c) - Cumulative scheme. Noteworthy, two sets of chromosomes have the same linear order matching with the arrangement established in haploid sperm nuclei (D). Scale bars in A–E – 5 µm.</p

Model of chromosome organization in human spermatozoa.

<p>Compact CTs (filled contours) have overall hairpin conformations (chromosome paths indicated by dashed lines) with the <i>p</i> and <i>q</i> telomere/sub-telomere domains (orange circles) forming dimers at nuclear periphery. Gene-rich CHRs – rosy, gene-poor – indigo. CTs are connected via centromeres/peri-centromeres (green circles and lines) into arrays and have a fixed linear order which determines the longitudinal positioning of chromosomes.</p

Localization of chromosome-specific peri-centromeric sequences in human spermatozoa.

<p>(A) Typical patterns of FISH with HSA18 peri-CEN probe. Scale bar – 5 µm. (B) The contour plot showing the preferential intranuclear localization of HSA18 (n≥80). (C) Sample frequency distribution plots for HSA 1, 17 and Y show that longitudinal localization of CTs (black lines) matches with the localization of corresponding CENs (red lines). (D) The correlation between the longitudinal positioning of CT and peri-CEN.</p

Development of oral cancer tissue-mimicking phantom based on polyvinyl chloride plastisol and graphite for terahertz frequencies

SIGNIFICANCE: A new concept of a biotissue phantom for terahertz (THz) biomedical applications is needed for reliable and long-term usage. AIM: We aimed to develop a new type of biotissue phantom without water content and with controllable THz optical properties by applying graphite powders into a polyvinyl chloride plastisol (PVCP) matrix and to give a numerical description to the THz optical properties of the phantoms using the Bruggeman model (BM) of the effective medium theory (EMT). APPROACH: The THz optical properties of graphite and the PVCP matrix were measured using THz time-domain spectroscopy, which works in the frequency range from 0.1 to 1 THz. Two phantoms with 10% and 12.5% graphite were fabricated to evaluate the feasibility of describing phantoms using the EMT. The EMT then was used to determine the concentration of graphite required to mimic the THz optical properties of human cancerous and healthy oral tissue. RESULTS: The phantom with 16.7% of graphite has the similar THz optical properties as human cancerous oral tissue in the frequency range of 0.2 to 0.7 THz. The THz optical properties of the phantom with 21.9% of graphite are close to those of human healthy oral tissue in the bandwidth from 0.6 to 0.8 THz. Both the refractive index and absorption coefficient of the samples increase with an increase of graphite concentration. The BM of the EMT was used as the numerical model to describe the THz optical properties of the phantoms. The relative error of the BM for the refractive index estimation and the absorption coefficient is up to 4% and 8%, respectively. CONCLUSIONS: A water-free biotissue phantom that mimics the THz optical properties of human cancerous oral tissue was developed. With 21.9% of graphite, the phantom also mimics human healthy oral tissue in a narrow frequency range. The BM proved to be a suitable numerical model of the phantom

Carboranyl-Chlorin e6 as a Potent Antimicrobial Photosensitizer.

Antimicrobial photodynamic inactivation is currently being widely considered as alternative to antibiotic chemotherapy of infective diseases, attracting much attention to design of novel effective photosensitizers. Carboranyl-chlorin-e6 (the conjugate of chlorin e6 with carborane), applied here for the first time for antimicrobial photodynamic inactivation, appeared to be much stronger than chlorin e6 against Gram-positive bacteria, such as Bacillus subtilis, Staphyllococcus aureus and Mycobacterium sp. Confocal fluorescence spectroscopy and membrane leakage experiments indicated that bacteria cell death upon photodynamic treatment with carboranyl-chlorin-e6 is caused by loss of cell membrane integrity. The enhanced photobactericidal activity was attributed to the increased accumulation of the conjugate by bacterial cells, as evaluated both by centrifugation and fluorescence correlation spectroscopy. Gram-negative bacteria were rather resistant to antimicrobial photodynamic inactivation mediated by carboranyl-chlorin-e6. Unlike chlorin e6, the conjugate showed higher (compared to the wild-type strain) dark toxicity with Escherichia coli ΔtolC mutant, deficient in TolC-requiring multidrug efflux transporters