Results for "M. Alexeev"

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Terahertz optoelectronics of quantum rings and nanohelicesMar 18 2019We outline a range of proposals on using quantum rings and nanohelices for terahertz device implementations. We show that an Aharonov-Bohm quantum ring system and a double-gated quantum ring system both permit control over the polarization properties ... More
Toric degenerations of spherical varietiesMar 23 2004We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by Mirror Symmetry, we give conditions for the limit toric variety to be a Gorenstein ... More
Hultman numbers, polygon gluings and matrix integralsNov 13 2011The Hultman numbers enumerate permutations whose cycle graph has a given number of alternating cycles (they are relevant to the Bafna-Pevzner approach to genome comparison and genome rearrangements). We give two new interpretations of the Hultman numbers: ... More
A rearrangement step with potential uses in priority queuesMar 01 2012Link-based data structures, such as linked lists and binary search trees, have many well-known rearrangement steps allowing for efficient implementations of insertion, deletion, and other operations. We describe a rearrangement primitive designed for ... More
Stable pair compactification of moduli of K3 surfaces of degree 2Mar 23 2019We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs $(X,\epsilon R)$ over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of K3 surfaces ... More
Exciton and trion dynamics in atomically thin MoSe2 and WSe2: effect of localizationAug 13 2016We present a detailed investigation of the exciton and trion dynamics in naturally doped MoSe2 and WSe2 single atomic layers as a function of temperature in the range 10-300K under above band-gap laser excitation. By combining time-integrated and time-resolved ... More
A Computational Method for the Rate Estimation of Evolutionary TranspositionsJan 29 2015Genome rearrangements are evolutionary events that shuffle genomic architectures. Most frequent genome rearrangements are reversals, translocations, fusions, and fissions. While there are some more complex genome rearrangements such as transpositions, ... More
On the asymptotic distribution of the singular values of powers of random matricesDec 13 2010We consider powers of random matrices with independent entries. Let $X_{ij}, i,j\ge 1$, be independent complex random variables with $\E X_{ij}=0$ and $\E |X_{ij}|^2=1$ and let $\mathbf X$ denote an $n\times n$ matrix with $[\mathbf X]_{ij}=X_{ij}$, for ... More
Aharonov-Bohm quantum rings in high-Q microcavitiesFeb 08 2013A single-mode microcavity with an embedded Aharonov-Bohm quantum ring, which is pierced by a magnetic flux and subjected to a lateral electric field, is studied theoretically. It is shown that external electric and magnetic fields provide additional means ... More
All-Dielectric Silicon/Phase-Change Optical Metasurfaces with Independent and Reconfigurable Control of Resonant ModesJan 15 2019All-dielectric metasurfaces consisting of arrays of nanostructured high-refractive-index materials, typically Si, are re-writing what is achievable in terms of the manipulation of light. Such devices support very strong magnetic, as well as electric, ... More
Log canonical singularities and complete moduli of stable pairsAug 17 19961) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space M_{g,n} of pointed stable curves. Each stable pair has semi log canonical singularities. ... More
On lengths of rainbow cyclesJul 22 2005Aug 18 2006We prove several results regarding edge-colored complete graphs and rainbow cycles, cycles with no color appearing on more than one edge. We settle a question posed by Ball, Pultr, and Vojt\v{e}chovsk\'{y} by showing that if such a coloring does not contain ... More
Divisors on Burniat surfacesSep 18 2013Nov 23 2013In this short note, we extend the results of [Alexeev-Orlov, 2012] about Picard groups of Burniat surfaces with $K^2=6$ to the cases of $2\le K^2\le 5$. We also compute the semigroup of effective divisors on Burniat surfaces with $K^2=6$. Finally, we ... More
Weighted grassmannians and stable hyperplane arrangementsJun 05 2008Jun 11 2008We give a common generalization of (1) Hassett's weighted stable curves, and (2) Hacking-Keel-Tevelev's stable hyperplane arrangements.
Complete moduli in the presence of semiabelian group actionMay 18 1999Sep 15 2004I prove the existence, and describe the structure, of moduli space of pairs $(p,\Theta)$ consisting of a projective variety $P$ with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every connected component ... More
Two Two-dimensional TerminationsJun 12 1992Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the interesting sets, associated with these varieties have ... More
Higher-dimensional analogues of stable curvesJul 26 2006The Minimal Model Program offers natural higher-dimensional analogues of stable $n$-pointed curves and maps: stable pairs consisting of a projective variety $X$ of dimension $\ge2$ and a divisor $B$, that should satisfy a few simple conditions, and stable ... More
Compactified jacobiansAug 17 1996Aug 19 1996Let J be the jacobian of a reduced projective curve C with nodes only. 1) We give a simple and natural definition for its many compactifications and show the connection with various other definitions appearing in the literature. 2) Among all compactifications ... More
Minimal DFAs for Testing DivisibilitySep 29 2003We present and prove a theorem answering the question "how many states does a minimal deterministic finite automaton (DFA) that recognizes the set of base-b numbers divisible by k have?"
On extra components in the functorial compactification of A_gMay 22 1999A short note that contains some Cliff's notes of the general theory (see math.AG/9905103) but concentrates on one of the stranger aspects of it - existence of other irreducible components.
Moduli spaces $M_{g,n}(W)$ for surfacesOct 05 1994We construct and prove the projectiveness of the moduli spaces which are natural generalizations to the case of surfaces of the following: 1) $M_{g,n}$, the moduli space of $n$-marked stable curves, 2) $M_{g,n}(W)$, the moduli space of $n$-marked stable ... More
Limits of stable pairsJul 26 2006Nov 05 2007Let (X_0,B_0) be the canonical limit of a one-parameter family of stable pairs, provided by the log Minimal Model Program. We prove that X_0 is S2 and that [B_0] is S_1, as an application of a general local statement: if (X,B+\epsilon D) is log canonical ... More
Boundedness and $K^2$ for log surfacesFeb 09 1994Apr 13 1994Stronger results. Easier to read. Typos fixed. (If you get this replacement more than one time, blame it on the publications.math.duke.edu computer, please).
Synchronised Swimming of Two FishOct 13 2016We study the fluid dynamics of two fish-like bodies with synchronised swimming patterns. Our studies are based on two-dimensional simulations of viscous incompressible flows. We distinguish between motion patterns that are externally imposed on the swimmers ... More
Status of COMPASS RICH-1 Upgrade with MPGD-based Photon DetectorsOct 25 2017A Set of new MPGD-based Photon Detectors is being built for the upgrade of COMPASS RICH-1. The detectors cover a total active area of 1.4 m$^2$ and are based on a hybrid architecture consisting of two THGEM layers and a Micromegas. A CsI film on one THGEM ... More
Problems of antimatter after Big Bang, dark energy and dark matter. Solutions in the frame of non-local physicsDec 22 2010Quantum solitons are discovered with the help of generalized quantum hydrodynamics. The solitons have the character of the stable quantum objects in the self consistent electric field. The delivered theory demonstrates the great possibilities of the generalized ... More
Solution of the Dark Matter Problem in the Frame of the Non-Local PhysicsJul 16 2010Mar 10 2012The unified generalized non-local quantum kinetic and hydrodynamic theory is applied for mathematical modeling of objects in the giant scale diapason from the galaxy and Universe scale to atom structures. The principle of universal antigravitation is ... More
On the Log Discrepancies in Toric Mori ContractionsAug 16 2012Feb 07 2013It was conjectured by McKernan and Shokurov that for all Mori contractions from X to Y of given dimensions, for any positive epsilon there is a positive delta, such that if X is epsilon-log terminal, then Y is delta-log terminal. We prove this conjecture ... More
Open surfaces of small volumeDec 29 2016Jan 31 2017We construct a surface with log terminal singularities and ample canonical class that has $K_X^2=1/48 983$ and a log canonical pair $(X,B)$ with a nonempty reduced divisor $B$ and ample $K_X+B$ that has $(K_X+B)^2 = 1/462$. Both examples significantly ... More
ADE surfaces and their moduliDec 21 2017Jan 12 2018We define a class of surfaces and surface pairs corresponding to the ADE root lattices and construct compactifications of their moduli spaces, generalizing Losev-Manin spaces of curves.
Explicit compactifications of moduli spaces of Campedelli and Burniat surfacesJan 28 2009We describe the compactifications obtained by adding slc surfaces X with ample K_X, for two connected components in the moduli space of surfaces of general type: Campedelli surfaces with \pi_1(X)=\bZ_2^3, and Burniat surfaces with K_X^2=6.
Mathematical Modeling of Soliton's Evolution in Generalized Quantum HydrodynamicsApr 22 2008May 24 2008This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of unified theory ... More
On the complexity of Mumford-Shah type regularization, viewed as a relaxed sparsity constraintJan 18 2010We show that inverse problems with a truncated quadratic regularization are NP-hard in general to solve, or even approximate up to an additive error. This stands in contrast to the case corresponding to a finite-dimensional approximation to the Mumford-Shah ... More
Comment on Sound Dispersion in Single-Component SystemApr 30 2009This paper was initiated by publication of Ref. [1] and can be considered as Comments on Ref. [1]. Authors of Ref. [1] investigate analytically the propagation of sound waves in one component monatomic gas (especially for the intermediate Knudses number ... More
Generalized Quantum Hydrodynamics and Principles of non-Local PhysicsSep 01 2007Jul 31 2008This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of unified theory ... More
Singular Values Distribution of Squares of Elliptic Random Matrices and Type B Narayana PolynomialsJan 19 2015Apr 08 2016We consider Gaussian elliptic random matrices $X$ of a size $N \times N$ with parameter $\rho$, i.e., matrices whose pairs of entries $(X_{ij}, X_{ji})$ are mutually independent Gaussian vectors, $E X_{ij} = 0$, $E X^2_{ij} = 1$ and $E X_{ij} X_{ji} = ... More
On the existence of ramified abelian coversOct 23 2012Jan 22 2013Given a normal complete variety $Y$, distinct effective Weil divisors $D_1,... D_n$ of $Y$ and positive integers $d_1,... d_n$, we spell out the conditions for the existence of an abelian cover of $Y$ branched with order $d_i$ on $D_i$. As an application, ... More
Stable reductive varieties I: Affine varietiesJul 29 2002Sep 15 2003The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected reductive ... More
Stable reductive varieties II: Projective caseJul 29 2002Sep 15 2003We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stable n-pointed curves and generalize to the non-commutative case a functorial ... More
Complete moduli spaces of branchvarietiesFeb 27 2006Aug 06 2006The space of subvarieties of P^n with a fixed Hilbert polynomial is not complete. Grothendieck defined a completion by relaxing "variety" to "scheme", giving the complete_Hilbert scheme_ of subschemes of P^n with fixed Hilbert polynomial. We instead relax ... More
Extending Torelli map to toroidal compactifications of Siegel spaceFeb 16 2011Oct 10 2011It has been known since the 1970s that the Torelli map $M_g \to A_g$, associating to a smooth curve its jacobian, extends to a regular map from the Deligne-Mumford compactification $\bar{M}_g$ to the 2nd Voronoi compactification $\bar{A}_g^{vor}$. We ... More
Nef divisors on $\bar{M}_{0,n}$ from GITDec 03 2008Jan 27 2011We introduce and study the GIT CONE of $\bar{M}_{0,n}$, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients $(\mathbb P^1)^n//SL(2)$. We give an explicit formula for these line bundles and prove a number of basic ... More
Generalized Theory of Landau DampingJul 31 2008Collisionless damping of electrical waves in plasma is investigated in the frame of the classical formulation of the problem. The new principle of regularization of the singular integral is used. The exact solution of the corresponding dispersion equation ... More
On Mumford's construction of degenerating abelian varietiesAug 17 1996May 18 1999We prove that a 1-dimnl family of abelian varieties with an ample sheaf defining principal polarization can be canonically compactified (after a finite base change) to a projective family with an ample sheaf. We show that the central fiber (P,L), which ... More
Equations resolving a conjecture of Rado on partition regularityDec 08 2008Jan 25 2009A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive integer k, there exists a linear equation that is (k-1)-regular but not k-regular. ... More
Moduli of affine schemes with reductive group actionJan 24 2003Sep 15 2003For a connected reductive group G and a finite-dimensional G-module V, we study the invariant Hilbert scheme that parameterizes closed G-stable subschemes of V affording a fixed, multiplicity-finite representation of G in their coordinate ring. We construct ... More
Boundedness of spherical Fano varietiesJan 19 2003We prove that for any e>0, there exists only finitely many e-log terminal spherical Fano varieties of fixed dimension. We also introduce an invariant of a spherical subgroup H in a reductive group G which measures how nice an equivariant Fano compactification ... More
An analysis of a war-like card gameJan 07 2010In his book "Mathematical Mind-Benders", Peter Winkler poses the following open problem, originally due to the first author: "[In the game Peer Pressure,] two players are dealt some number of cards, initially face up, each card carrying a different integer. ... More
Log surfaces of Picard rank one from four lines in the planeJan 31 2019We derive simple formulas for the basic numerical invariants of a singular surface with Picard number one obtained by blowups and contractions of the four-line configuration in the plane. As an application, we establish the smallest positive volume and ... More
On accumulation points of volumes of log surfacesMar 26 2018Let $\mathcal C\subset(0,1]$ be a set satisfying the descending chain condition. We show that any accumulation point of volumes of log canonical surfaces $(X, B)$ with coefficients in $\mathcal C$ can be realized as the volume of a log canonical surface ... More
See Project for Testing Gravity in Space: Current Status and New EstimatesFeb 25 2000We describe some new estimates concerning the recently proposed SEE (Satellite Energy Exchange) experiment for measuring the gravitational interaction parameters in space. The experiment entails precision tracking of the relative motion of two test bodies ... More
On Possible Measurement of Gravitational Interaction Parameters on Board a SatelliteMar 29 1994Mar 31 1994The recently suggested SEE (Satellite Energy Exchange) method of measuring the gravitational constant $G$, possible equivalence principle violation (measured by the E\"{o}tv\"{o}s parameter $\eta$) and the hypothetic 5th force parameters $\alpha$ and ... More
Resonantly excited exciton dynamics in two-dimensional MoSe$_2$ monolayersApr 17 2017We report on the exciton and trion density dynamics in a single layer of MoSe$_2$, resonantly excited and probed using three-pulse four-wave mixing (FWM), at temperatures from 300K to 77K . A multi-exponential third-order response function for amplitude ... More
Derived categories of Burniat surfaces and exceptional collectionsAug 21 2012Aug 28 2012We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this ... More
Application of Generalized Quantum Hydrodynamics In the Theory of Quantum Soliton's Evolution, Atom Structure and Lightning BallJul 29 2008Quantum solitons are discovered with the help of generalized quantum hydrodynamics (GQH). The solitons have the character of the stable quantum objects in the self consistent electric field. These effects can be considered as explanation of the existence ... More
To the Non-Local Theory of the High Temperature SuperconductivityJan 30 2012The possibility of the non local physics application in the theory of superconductivity is investigated. It is shown that by the superconducting conditions the relay ("estafette") motion of the soliton' system ("attice ion - electron") is realizing by ... More
Antigravitation, Dark Energy, Dark Matter - Alternative SolutionAug 15 2009Sep 04 2009Collisional damping of gravitational waves in the Newtonian matter is investigated. The generalized theory of Landau damping is applied to the gravitational physical systems in the context of the plasma gravitational analogy.
Non-normal abelian coversFeb 21 2011Oct 10 2011An abelian cover is a finite morphism $X\to Y$ of varieties which is the quotient map for a generically faithful action of a finite abelian group $G$. Abelian covers with $Y$ smooth and $X$ normal were studied in \cite{Pardini_AbelianCovers}. Here we ... More
On K-Stability of Reductive VarietiesNov 26 2003Jan 13 2004G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [Don02] Donaldson partially confirmed it in the case of projective toric varieties. ... More
Stable spherical varieties and their moduliMay 31 2005We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group $G$ and their flat equivariant degenerations. Given any projective space $\bP$ where $G$ acts linearly, we construct a moduli space for stable ... More
A fast and parametric digitization for triple-GEM detectorsApr 12 2019Triple-GEM detectors are a well known technology in high energy physics. In order to have a complete understanding of their behavior, in parallel with on beam testing, a Monte Carlo code has to be developed to simulate their response to the passage of ... More
Measurement of the gravitational constant $G$ in space (Project SEE): sensitivity to orbital parameters and space charge effectApr 20 2001We describe some new estimates concerning the recently proposed SEE (Satellite Energy Exchange) experiment for measuring the gravitational interaction parameters in space. The experiment entails precision tracking of the relative motion of two test bodies ... More
Estimation of the True Evolutionary Distance under the Fragile Breakage ModelOct 27 2015The ability to estimate the evolutionary distance between extant genomes plays a crucial role in many phylogenomic studies. Often such estimation is based on the parsimony assumption, implying that the distance between two genomes can be estimated as ... More
An impossibility theorem for gerrymanderingOct 11 2017Oct 26 2017The U.S. Supreme Court is currently deliberating over whether a proposed mathematical formula should be used to detect unconstitutional partisan gerrymandering. We show that in some cases, this formula will only flag bizarrely shaped districts as potentially ... More
Classification of log del Pezzo surfaces of index $\le 2$Jun 25 2004Jun 10 2006This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all exceptional curves ... More
Extended Torelli map to the Igusa blowup in genus 6, 7, and 8May 23 2011Oct 10 2011It was conjectured in \cite{Namikawa_ExtendedTorelli} that the Torelli map $M_g\to A_g$ associating to a curve its jacobian extends to a regular map from the Deligne-Mumford moduli space of stable curves $\bar{M}_g$ to the (normalization of the) Igusa ... More
TAU-4 installation intended for long-term monitoring of a half-life value of the $^{212}$PoDec 12 2018Description of the TAU-4 installation intended for long-term monitoring of the half-life value $T_{1/2}$ of the $^{212}$Po is presented. Natural thorium used as a source of the mother's chain. The methods of measurement and data processing are described. ... More
Combinatorial Scoring of Phylogenetic NetworksFeb 09 2016Aug 08 2016Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for tree/network ... More
Estimation of the True Evolutionary Distance under the Fragile Breakage ModelOct 27 2015May 25 2017The ability to estimate the evolutionary distance between extant genomes plays a crucial role in many phylogenomic studies. Often such estimation is based on the parsimony assumption, implying that the distance between two genomes can be estimated as ... More
Partisan gerrymandering with geographically compact districtsDec 14 2017Bizarrely shaped voting districts are frequently lambasted as likely instances of gerrymandering. In order to systematically identify such instances, researchers have devised several tests for so-called geographic compactness (i.e., shape niceness). We ... More
Non-rational centers of log canonical singularitiesSep 19 2011Jun 28 2012We show that if $(X,B)$ is a log canonical pair with $\dim X\geq d+2$, whose non-klt centers have dimension $\geq d$, then $X$ is has depth $\ge d+2$ at every closed point.
Moduli of weighted stable maps and their gravitational descendantsJul 26 2006Nov 13 2007We study the intersection theory on the moduli spaces of maps of $n$-pointed curves $f:(C,s_1,... s_n)\to V$ which are stable with respect to a weight data $(a_1,..., a_n)$, $0\le a_i\le 1$. After describing the structure of these moduli spaces, we prove ... More
Extreme thermodynamics with polymer gel tori: harnessing thermodynamic instabilities to induce large-scale deformationsJun 28 2018When a swollen, thermoresponsive polymer gel is heated in a solvent bath, it expels solvent and deswells. When this heating is slow, deswelling proceeds homogeneously, as observed in a toroid-shaped gel that changes volume whilst maintaining its toroidal ... More
Investigation of scaling properties of a thin current sheet by means of particle trajectories studyJun 17 2015A thin current sheet (TCS), with the width of an order of thermal proton gyroradius, appears a fundamental physical object which plays an important role in structuring of major magnetospheric current systems (magnetotail, magnetodisk, etc.). The TCSs ... More
Invariance properties of thematic factorizations of matrix functionsJan 22 2001Jan 26 2001We study the problem of invariance of indices of thematic factorizations. Such factorizations were introduced in [PY1] for studying superoptimal approximation by bounded analytic matrix functions. As shown in [PY1], the indices may depend on the choice ... More
On minimal colorings without monochromatic solutions to a linear equationSep 21 2010For a ring R and system L of linear homogeneous equations, we call a coloring of the nonzero elements of R minimal for L if there are no monochromatic solutions to L and the coloring uses as few colors as possible. For a rational number q and positive ... More
Partially Ionized Plasmas in AstrophysicsJul 25 2017Jul 26 2017Partially ionized plasmas are found across the Universe in many different astrophysical environments. They constitute an essential ingredient of the solar atmosphere, molecular clouds, planetary ionospheres and protoplanetary disks, among other environments, ... More
The ultrafast dynamics and conductivity of photoexcited graphene at different Fermi energiesDec 07 2017For many of the envisioned optoelectronic applications of graphene it is crucial to understand the sub-picosecond carrier dynamics immediately following photoexcitation, as well as the effect on the electrical conductivity - the photoconductivity. Whereas ... More
Verification of Monte Carlo transport codes against measured small angle p-, d-, and t-emission in carbon fragmentation at 600 MeV/nucleonFeb 05 2015Momentum spectra of hydrogen isotopes have been measured at 3.5 deg from C12 fragmentation on a Be target. Momentum spectra cover both the region of fragmentation maximum and the cumulative region. Differential cross sections span five orders of magnitude. ... More
Microfluidic pumping using artificial magnetic ciliaJul 18 2018One of the vital functions of naturally occurring cilia is fluid transport. Biological cilia use spatially asymmetric strokes to generate a net fluid flow that can be utilized for feeding, swimming, and other functions. Biomimetic synthetic cilia with ... More
Full Spark FramesOct 17 2011Apr 09 2012Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic constructions of frames ... More
Conformal blocks divisors on $\bar{M}_{0,n}$ from $sl_2$Nov 30 2010We study a family of semiample divisors on $\bar{M}_{0,n}$ defined using conformal blocks and analyze their associated morphisms.
Stable pair compactification of moduli of K3 surfaces of degree 2Mar 23 2019Apr 16 2019We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs $(X,\epsilon R)$ over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of K3 surfaces ... More
Heterogeneous epidemic model for assessing data dissemination in opportunistic networksMar 23 2014Mar 27 2014In this paper we investigate a susceptible-infected-susceptible (SIS) epidemic model describing data dissemination in opportunistic networks with heterogeneous setting of transmission parameters. We obtained the estimation of the final epidemic size assuming ... More
Generalized Hultman Numbers and Cycle Structures of Breakpoint GraphsMar 18 2015Feb 09 2016Genome rearrangements can be modeled by $k$-breaks, which break a genome at $k$ positions and glue the resulting fragments in a new order. In particular, reversals, translocations, fusions, and fissions are modeled as $2$-breaks, and transpositions are ... More
On the asymptotic distribution of singular values of products of large rectangular random matricesDec 12 2010Apr 26 2011We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is described by its ... More
Asymptotic distribution of singular values of powers of random matricesFeb 24 2010Let $x$ be a complex random variable such that ${\E {x}=0}$, ${\E |x|^2=1}$, ${\E |x|^{4} < \infty}$. Let $x_{ij}$, $i,j \in \{1,2,...\}$ be independet copies of $x$. Let ${\Xb=(N^{-1/2}x_{ij})}$, $1\leq i,j \leq N$ be a random matrix. Writing $\Xb^*$ ... More
Degenerations of Prym varietiesJan 29 2001Jan 08 2002Let $(C,\iota)$ be a stable curve with an involution. Following a classical construction one can define its Prym variety $P$, which in this case turns out to be a semiabelian group variety and usually not complete. In this paper we study the question ... More
Termination of (many) 4-dimensional log flipsMay 04 2006May 16 2006We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(K+D) is numerically equivalent to an effective divisor, terminates. This implies termination of flips that begin with a log Fano pair and termination of ... More
Photo-induced doping and strain in exfoliated grapheneOct 03 2013The modification of single layer graphene due to intense, picoseconds near-infrared laser pulses is investigated. We monitor the stable changes introduced to graphene upon photoexcitation using Raman spectroscopy. We find that photoexcitation leads to ... More
Forbidden induced subgraphs of double-split graphsDec 16 2010In the course of proving the strong perfect graph theorem, Chudnovsky, Robertson, Seymour, and Thomas showed that every perfect graph either belongs to one of five basic classes or admits one of several decompositions. Four of the basic classes are closed ... More
Experiments on the generation of long wavelength edge radiation along directions nearly coincident with the axis of a straight section of the "Pakhra" synchrotronMay 22 2000May 23 2000Generation of long wavelength edge radiation along directions nearly coincident with the axes of straight sections of storage rings and synchrotrons is discussed. The removal of destructive interference from the superimposed edge radiation patterns of ... More
Tensor Rank: Some Lower and Upper BoundsFeb 01 2011The results of Strassen and Raz show that good enough tensor rank lower bounds have implications for algebraic circuit/formula lower bounds. We explore tensor rank lower and upper bounds, focusing on explicit tensors. For odd d, we construct field-independent ... More
Badly approximable matrix functions and canonical factorizationsJan 26 2001We continue studying the problem of analytic approximation of matrix functions. We introduce the notion of a partial canonical factorization of a badly approximable matrix function $\Phi$ and the notion of a canonical factorization of a very badly approximable ... More
Unitary interpolants and factorization indices of matrix functionsJan 26 2001For an $n\times n$ bounded matrix function $\Phi$ we study unitary interpolants $U$, i.e., unitary-valued functions $U$ such that $\hat U(j)=\hat\Phi(j)$, $j<0$. We are looking for unitary interpolants $U$ for which the Toeplitz operator $T_U$ is Fredholm. ... More
Application of Non-local Quantum Hydrodynamics to the Description of the Charged Density Waves in the Graphen Crystal LatticeNov 24 2012The motion of the charged particles in graphen in the frame of the quantum non-local hydrodynamic description is considered. It is shown as results of the mathematical modeling that the mentioned motion is realizing in the soliton forms. The dependence ... More
Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperatureApr 10 2017Strong-coupling of monolayer metal dichalcogenide semiconductors with light offers encouraging prospects for realistic exciton devices at room temperature. However, the nature of this coupling depends extremely sensitively on the optical confinement and ... More
Imaging of interlayer coupling in van der Waals heterostructures using a bright-field optical microscopeDec 23 2016May 01 2017Vertically stacked atomic layers from different layered crystals can be held together by van der Waals forces, which can be used for building novel heterostructures, offering a platform for developing a new generation of atomically thin, transparent and ... More
The uniformization of the moduli space of principally polarized abelian 6-foldsJul 21 2015Mar 15 2018Starting from a beautiful idea of Kanev, we construct a uniformization of the moduli space A_6 of principally polarized abelian 6-folds in terms of curves and monodromy data. We show that the general ppav of dimension 6 is a Prym-Tyurin variety corresponding ... More