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Discovery of new stable and high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019In conventional Ti-Ta shape memory alloys (SMAs), high (>100{\deg}C) transformation temperatures cannot be achieved without compromising the stability of the shape memory effect. A solution to this problem is the addition of other elements to form Ti-Ta-X ... More

The construction problem for Hodge numbers modulo an integerMar 13 2019For any integer $m\ge2$ and any dimension $n\ge1$, we show that any $n$-dimensional Hodge diamond with values in $\mathbb Z/m\mathbb Z$ is attained by the Hodge numbers of an $n$-dimensional smooth complex projective variety. As a corollary, there are ... More

A law of large numbers for limit order booksJan 05 2015We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps the expected ... More

Complexity and capacity bounds for quantum channelsOct 17 2017We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum channel requires ... More

Unusual composition dependence of transformation temperatures in Ti-Ta-X shape memory alloysApr 12 2018Ti-Ta-X (X = Al, Sn, Zr) compounds are emerging candidates as high-temperature shape memory alloys (HTSMAs). The stability of the one-way shape memory effect (1WE), the exploitable pseudoelastic (PE) strain intervals as well as the transformation temperature ... More

Ruin models with investment incomeJun 25 2008Dec 18 2008This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integro-differential equations, exact and numerical solutions, ... More

On the rationality of quadric surface bundlesNov 13 2018Dec 05 2018For any standard quadric surface bundle over $\mathbb P^2$, we show that the locus of rational fibres is dense in the moduli space.

A Dynamical Systems Approach to the Kadison-Singer ProblemJun 18 2007Nov 15 2007In these notes we develop a link between the Kadison-Singer problem and questions about certain dynamical systems. We conjecture that whether or not a given state has a unique extension is related to certain dynamical properties of the state. We prove ... More

Vector spaces with an order unitDec 17 2007Jun 10 2009We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple extensions to ... More

Equivariant Maps and Bimodule ProjectionsOct 28 2005We construct a contractive, idempotent, MASA bimodule map on B(H), whose range is not a ternary subalgebra of B(H). Our method uses a crossed-product to reduce the existence of such an idempotent map to an analogous problem about the ranges of idempotent ... More

Weak Expectations and the Injective EnvelopeJul 18 2008Given a unital C*-subalgebra of B(H), we study the set of all possible images of its injective envelope that are contained in B(H) and their position relative to the double commutant of the algebra in order to obtain more information about the existence ... More

Noise Fit, Estimation Error and a Sharpe Information Criterion: Linear CaseFeb 19 2016Sep 08 2017We derive (1) an unbiased estimator for the out-of-sample Sharpe ratio when the in-sample Sharpe ratio is obtained by optimizing over a $k$-dimensional parameter space. The estimator corrects the in-sample Sharpe ratio for both: noise fit and estimation ... More

Diagonals in Tensor Products of Operator AlgebrasJul 10 2001In this paper we give a short, direct proof, using only properties of the Haagerup tensor product, that if an operator algebra A possesses a diagonal in the Haagerup tensor product of A with itself, then A must be isomorphic to a finite dimensional $C^*$-algebra. ... More

Wrapping liquids, solids, and gases in thin sheetsApr 20 2018Jul 02 2018Many objects in nature and industry are wrapped in a thin sheet to enhance their chemical, mechanical, or optical properties. There are similarly a variety of methods for wrapping, from pressing a film onto a hard substrate, to using capillary forces ... More

Syndetic Sets, Paving, and the Feichtinger ConjectureJan 25 2010We prove that if a Bessel sequence in a Hilbert space, that is indexed by a countably infinite group in an invariant manner, can be partitioned into finitely many Riesz basic sequences, then each of the sets in the partition can be chosen to be syndetic. ... More

On non-trivial barrier solutions of the dividend problem for a diffusion under constant and proportional transaction costsMar 23 2012In Bai and Paulsen (SIAM J. Control optim. 48, 2010) the optimal dividend problem under transaction costs was analyzed for a rather general class of diffusion processes. It was divided into several subclasses, and for the majority of subclasses the optimal ... More

Lie Ideals in Operator AlgebrasNov 21 2002Let $\mathcal A$ be a Banach algebra for which the group of invertible elements is connected. A subspace $\mathcal L \subseteq \mathcal A$ is a Lie ideal in $\mathcal A$ if, and only if, it is invariant under inner automorphisms. This applies, in particular, ... More

Noise Fit, Estimation Error and a Sharpe Information Criterion: Linear CaseFeb 19 2016May 28 2019When the in-sample Sharpe ratio is obtained by optimizing over a k-dimensional parameter space, it is a biased estimator for what can be expected on unseen data (out-of-sample). We derive (1) an unbiased estimator adjusting for both sources of bias: noise ... More

Noise Fit, Estimation Error and a Sharpe Information CriterionFeb 19 2016When optimizing the Sharpe ratio over a k-dimensional parameter space the thus obtained in-sample Sharpe ratio tends to be higher than what will be captured out-of-sample. For two reasons: the estimated parameter will be skewed towards the noise in the ... More

Approach and Coalescence of Liquid Drops in AirAug 26 2013Jan 09 2014The coalescence of liquid drops has conventionally been thought to have just two regimes when the drops are brought together slowly in vacuum or air: a viscous regime corresponding to the Stokes-flow limit and a later inertially-dominated regime. Recent ... More

Operator Algebras of FunctionsJul 29 2009We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar multipliers of a ... More

Construction of normal numbers with respect to Generalized Lüroth Series from equidistributed sequencesSep 28 2015Generalized L\"uroth series generalize $b$-adic representations as well as L\"uroth series. Almost all real numbers are normal, but it is not easy to construct one. In this paper, a new construction of normal numbers with respect to Generalized L\"uroth ... More

Synchronous correlation matrices and Connes' embedding conjectureMar 24 2015In a recent paper, the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain C*-algebras. In particular, synchronous correlation matrices arose in their study of various versions of ... More

Enumeration of concave integer partitionsSep 04 2003Jan 19 2004An integer partition \lambda of n corresponds, via its Ferrers diagram, to an artinian monomial ideal I of colength n in the polynomial ring on two variables. If the partition \lambda corresponds to an integrally closed ideal we call \lambda concave. ... More

Syndetic Sets and AmenabilityFeb 17 2010Feb 02 2011We prove that if an infinite, discrete semigroup has the property that every right syndetic set is left syndetic, then the semigroup has a left invariant mean. We prove that the weak*-closed convex hull of the two-sided translates of every bounded function ... More

Tensor Products of the Operator System Generated by the Cuntz IsometriesJul 24 2015We study tensor products and nuclearity-related properties of the operator system $\mathcal S_n$ generated by the Cuntz isometries. By using the nuclearity of the Cuntz algebra, we can show that $\mathcal{S}_n$ is $C^*$-nuclear, and this implies a dual ... More

The Feichtinger Conjecture and Reproducing Kernel Hilbert SpacesApr 08 2010Dec 05 2010We prove two new equivalences of the Feichtinger conjecture that involve reproducing kernel Hilbert spaces. We prove that if for every Hilbert space, contractively contained in the Hardy space, each Bessel sequence of normalized kernel functions can be ... More

On the ranges of bimodule projectionsJan 25 2003Oct 27 2005We develop a symbol calculus for normal bimodule maps over a masa that is the natural analogue of the Schur product theory. Using this calculus we are able to easily give a complete description of the ranges of contractive normal bimodule idempotents ... More

Quasimultipliers of Operator SpacesDec 30 2003We use the injective envelope to study quasimultipliers of operator spaces. We prove that all representable operator algebra products that an operator space can be endowed with are induced by quasimultipliers. We obtain generalizations of the Banach-Stone ... More

Representations of logmodular algebrasJun 02 2008Mar 23 2010We study the question of whether or not contractive representations of logmodular algebras are completely contractive. We prove that a 2-contractive representation of a logmodular algebra extends to a positive map on the enveloping C*-algebra, which we ... More

Injective and projective Hilbert C*-modules, and C*-algebras of compact operatorsNov 12 2006Feb 18 2008We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded (bi-)module morphisms, ... More

Complete positivity of the map from a basis to its dual basisDec 19 2012The dual of a matrix ordered space has a natural matrix ordering that makes the dual space matrix ordered as well. The purpose of these notes is to give a condition that describes when the linear map taking a basis of the n by n matrices to its dual basis ... More

Edge Ideals of Weighted GraphsMay 16 2012Jun 10 2012We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the ... More

Characterizations of essential ideals as operator modules over C*-algebrasFeb 16 2001In this paper we give characterizations of essential left ideals of a C*-algebra $A$ in terms of their properties as operator $A$-modules. Conversely, we seek C*-algebraic characterizations of those ideals $J$ in $A$ such that $A$ is an essential extension ... More

Operator system quotients of matrix algebras and their tensor productsJan 04 2011Jul 22 2011An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered. Some applications ... More

Some new equivalences of Anderson's paving conjecturesJun 18 2007Nov 15 2007Anderson's paving conjectures are known to be equivalent to the Kadison-Singer problem. We prove some new equivalences of Anderson's conjectures that require the paving of smaller sets of matrices. We prove that if the strictly upper triangular operatorss ... More

Injective Envelopes of $C^*$-algebras as Operator ModulesJun 15 2001In this paper we give some characterizations of M. Hamana's injective envelope I(A) of a C*-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results ... More

Schur multipliers and operator-valued Foguel-Hankel operatorsJan 11 2005We show that some matrices are Schur multipliers and this is applied to obtain classes of operator-valued Foguel-Hankel operators similar to contractions. This provides partial answers to a problem of K. Davidson and the second author concerning CAR-valued ... More

Density Functional Theory Calculations for Spin Crossover ComplexesJun 11 2012Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT methods are compared ... More

Injectivity and Projectivity in Analysis and TopologyJun 20 2007We give new proofs for many injectivity results in analysis that make more careful use of the duality between unital abelian C*-algebras and compact Hausdorff spaces. We then extend many of these results to incorporate group actions. Our approach uses ... More

Tin-DNA Complexes Investigated by Nuclear Inelastic Scattering of Synchrotron RadiationJun 13 2012Nuclear inelastic scattering (NIS) of synchrotron radiation has been used to investigate the dynamics of tin ions chelated by DNA. Theoretical NIS spectra have been simulated with the help of density functional theory (DFT) calculations using 12 models ... More

Extensions of the Inequalities of Hardy and HilbertFeb 20 2015In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the generalizations are non-trivial. ... More

Perfect Embezzlement of EntanglementJun 16 2016Van Dam and Hayden introduced a concept commonly referred to as embezzlement, where, for any entangled quantum state $\phi$, there is an entangled catalyst state $\psi$, from which a high fidelity approximation of $\phi \otimes \psi$ can be produced using ... More

Stably isomorphic dual operator algebrasMay 21 2007Oct 01 2007We prove that two unital dual operator algebras A, B are stably isomorphic if and only if they are Delta-equivalent, if and only if they have completely isometric normal representations a, b on Hilbert spaces H, K respectively and there exists a ternary ... More

Quantum Graph Homomorphisms via Operator SystemsMay 03 2015Feb 20 2016We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define and study a ... More

A Spectral Characterization of $\mathcal{AN}$ OperatorsJan 23 2015May 19 2016We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless, we prove that ... More

Approximately stretched-exponential relaxation in sheared non-Brownian suspensionsNov 22 2016Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A \exp [-(t/\tau)^{\beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Cort\'e et al. [Nature Phys. 4, 420 (2008)] ... More

Minimal descriptions of cyclic memoriesSep 25 2018Dec 13 2018Many materials that are out of equilibrium can "learn" one or more inputs that are repeatedly applied. Yet, a common framework for understanding such memories is lacking. Here we construct minimal representations of cyclic memory behaviors as directed ... More

Reverse Cholesky factorization and tensor products of nest algebrasApr 14 2017We prove that every positive semidefinite matrix over the natural numbers that is eventually 0 in each row and column can be factored as the product of an upper triangular matrix times a lower triangular matrix. We also extend some known results about ... More

Non-closure of the set of quantum correlations via graphsSep 15 2017Apr 19 2018We prove that the set of quantum correlations for a bipartite system of 5 inputs and 2 outputs is not closed. Our proof relies on computing the correlation functions of a graph, which is a concept that we introduce.

An operator algebraic proof of Agler's factorization theoremJun 16 2008We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional information about ... More

Quantum chromatic numbers via operator systemsNov 26 2013We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the literature and ... More

Multipliers of operator spaces, and the injective envelopeSep 07 1999Jan 26 2000We study the injective envelope I(X) of an operator space X, showing amongst other things that it is a self-dual C$^*-$module. We describe the diagonal corners of the injective envelope of the canonical operator system associated with X. We prove that ... More

A model for approximately stretched-exponential relaxation with continuously varying stretching exponentsNov 22 2016Jan 31 2017Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A \exp [-(t/\tau)^{\beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Cort\'e et al. [Nature Phys. 4, 420 (2008)] ... More

String center of mass operator and its effect on BRST cohomologyNov 15 1995We consider the theory of bosonic closed strings on the flat background R(25,1). We show how the BRST complex can be extended to a complex where the string center of mass operator, x^mu_0, is well defined. We investigate the cohomology of the extended ... More

Homological projective duality for quadricsFeb 26 2019Mar 01 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019Mar 01 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

Approximation of discrete functions and size of spectrumApr 02 2013Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$, then measure($S$)$\geq ... More

An ICT-Based Real-Time Surveillance System for Controlling Dengue in Sri LankaMay 16 2014Dengue is a notifiable communicable disease in Sri Lanka since 1996. Dengue fever spread rapidly among people living in most of the districts of Sri Lanka. The present notification system of dengue communicable diseases which is enforced by law is a passive ... More

Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formulaOct 01 1998In this paper we investigate the representations of reductive groups over a finite field, introduced in 1987 by D.Kazhdan and G.Laumon. We show that generically these representations are irreducible and that their character is equal to the function obtained ... More

Discrete Translates in $L^2(R)$Dec 02 2016A set $\Lambda\subset R$ is called $p$-spectral, if there is a function $\varphi\in L^p(R)$ whose $\Lambda$-translates $\{\varphi(t-\lambda),\lambda\in\Lambda\}$ span $L^p(R)$. We prove that exponentially small non-zero perturbations of the integers are ... More

$L^2-$interpolation with error and size of spectraJun 18 2008Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$ through the density ... More

Homological projective duality for quadricsFeb 26 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

Categorical joinsMar 31 2018Feb 26 2019We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. ... More

Scattering theory and Banach space valued singular integralsNov 28 2012We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on estimates for the Cauchy ... More

Moments of random sums and Robbins' problem of optimal stoppingJul 17 2011Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal in the sense ... More

Diagonalization of the Finite Hilbert Transform on two adjacent intervalsNov 06 2015We study the interior problem of tomography. The starting point is the Gelfand-Graev formula, which converts the tomographic data into the finite Hilbert transform (FHT) of an unknown function $f$ along a collection of lines. Pick one such line, call ... More

Subtle Characteristic ClassesJan 26 2014We construct new subtle Stiefel--Whitney classes of quadratic forms. These classes are much more informative than the ones introduced by Milnor. In particular, they see all the powers of the fundamental ideal of the Witt ring, contain the Arason invariant ... More

Governing Singularities of Schubert VarietiesMar 12 2006Jun 29 2006We present a combinatorial and computational commutative algebra methodology for studying singularities of Schubert varieties of flag manifolds. We define the combinatorial notion of *interval pattern avoidance*. For "reasonable" invariants P of singularities, ... More

Lovász theta type norms and Operator SystemsDec 22 2014To each graph on $n$ vertices there is an associated subspace of the $n \times n$ matrices called the operator system of the graph. We prove that two graphs are isomorphic if and only if their corresponding operator systems are unitally completely order ... More

Eventually Entanglement Breaking MapsJan 17 2018We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor ... More

Unitary Correlation SetsDec 08 2016The unitary correlation sets defined by the first author in conjunction with tensor products of $\mathcal{U}_{nc}(n)$ are further studied. We show that Connes' embedding problem is equivalent to deciding whether or not two smaller versions of the unitary ... More

Minimal descriptions of cyclic memoriesSep 25 2018Apr 23 2019Many materials that are out of equilibrium can "learn" one or more inputs that are repeatedly applied. Yet, a common framework for understanding such memories is lacking. Here we construct minimal representations of cyclic memory behaviors as directed ... More

Weak Cayley table groups of some crystallographic groupsMar 11 2016For a group $G$, a weak Cayley isomorphism is a bijection $f:G \to G$ such that $f(g_1g_2)$ is conjugate to $ f(g_1)f(g_2)$ for all $g_1,g_2 \in G$. They form a group $\mathcal W(G)$ that is the group of symmetries of the weak Cayley table of $G$. We ... More

CANAL: A Cache Timing Analysis Framework via LLVM TransformationJul 09 2018A unified modeling framework for non-functional properties of a program is essential for research in software analysis and verification, since it reduces burdens on individual researchers to implement new approaches and compare existing approaches. We ... More

Frames, Graphs and ErasuresJun 08 2004Mar 11 2005Two-uniform frames and their use for the coding of vectors are the main subject of this paper. These frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest possible error when up to two frame coefficients ... More

Interpolation and Balls in C^kApr 23 2006We compare and classify various types of Banach algebra norms on mathbb{C}^k through geometric properties of their unit balls. This study is motivated by various open problems in interpolation theory and in the isometric characterization of operator algebra ... More

Unitary Correlation SetsDec 08 2016Jan 10 2018The unitary correlation sets defined by the first author in conjunction with tensor products of $\mathcal{U}_{nc}(n)$ are further studied. We show that Connes' embedding problem is equivalent to deciding whether or not two smaller versions of the unitary ... More

Answer to the comment of Chudnovsky: On the square-root time relaxation in molecular nanomagnetsApr 22 2000Answer to the comment of E. Chudnovsky concerning the following papers: (1) N.V. Prokof'ev, P.C.E. Stamp, Phys. Rev. Lett.80, 5794 (1998). (2) W. Wernsdorfer, T. Ohm, C. Sangregorio, R. Sessoli, D. Mailly, C. Paulsen, Phys. Rev. Lett. 82, 3903 (1999). ... More

Relaxation in the 3D ordered CoTAC spin chain by quantum nucleation of 0D domain wallsApr 20 2009We have shown that resonant quantum tunnelling of the magnetisation (QTM), until now observed only in 0D cluster systems (SMMs), occurs in the molecular Ising spin chain, CoTAC ([(CH_3)_3NH]CoCl_3 - 2H_2O) which orders as a canted 3D-antiferromagnet at ... More

Resonant quantum tunneling of spin chains in a three-dimensionnal magnetically ordered stateDec 02 2005Aug 30 2006We show that resonant quantum tunneling of the magnetization, until now observed only in zero-dimensional (0D) cluster systems, occurs in the molecular Ising spin chain $[(CH_3)_3NH]CoCl_3\cdot 2H_2O$, which orders as a canted 3D-antiferromagnet at $T_C=4.15 ... More

Eventually Entanglement Breaking MapsJan 17 2018Jun 11 2018We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor ... More

An approximation theorem for nuclear operator systemsSep 14 2010May 05 2011We prove that an operator system $\mathcal S$ is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps $\phi_\lambda : \cl S \to M_{n_\lambda}$ and $\psi_\lambda : M_{n_\lambda} \to \cl S$ such ... More

Operator system structures on ordered spacesApr 24 2009Dec 17 2009Given an Archimedean order unit space (V,V^+,e), we construct a minimal operator system OMIN(V) and a maximal operator system OMAX(V), which are the analogues of the minimal and maximal operator spaces of a normed space. We develop some of the key properties ... More

The SOH Operator SystemMay 01 2015Jun 15 2015In this paper we examine a natural operator system structure on Pisier's self-dual operator space. We prove that this operator system is completely order isomorphic to its dual with the cb-condition number of this isomorphism as small as possible. We ... More

Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)Oct 13 2009We construct full exceptional collections of vector bundles on the Lagrangian Grassmannians LG(4,8) and LG(5,10).

Cauchy independent measures and super-additivity of analytic capacityNov 12 2012We show that, given a family of discs centered at a nice curve, the analytic capacities of arbitrary subsets of these discs add up. However we need that the discs in question would be slightly separated, and it is not clear whether the separation condition ... More

Random "dyadic" lattice in geometrically doubling metric space and $A_2$ conjectureMar 27 2011Apr 21 2011Recently three proofs of the $A_2$-conjecture were obtained. All of them are "glued" to euclidian space and a special choice of one random dyadic lattice. We build a random "dyadic" lattice in any doubling metric space which have properties that are enough ... More

Reachability in Higher-Order-CountersJun 05 2013Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those ... More

Paramagnetic tunneling state concept of the low-temperature magnetic anomalies of multicomponent insulating glassesMar 17 2006A generalized tunneling model of multicomponent insulating glasses is formulated, considering tunneling states to be paramagnetic centers of the electronic hole type. The expression for magnetic field dependent contribution into the free energy is obtained. ... More

Exceptional collections on isotropic GrassmanniansOct 25 2011Sep 13 2015We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the ... More

On multi-dimensional sampling and interpolationApr 02 2013The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from above (from ... More

A Gröbner basis for Kazhdan-Lusztig idealsSep 03 2009Nov 11 2011Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A flag variety. ... More

Neutrino energy quantization in rotating mediumSep 30 2008Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle ... More

General Conditions for Lepton Flavour Violation at Tree- and 1-Loop LevelSep 20 2007In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, ... More

Discrete Uniqueness Sets for Functions with Spectral GapsSep 15 2016It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev spaces ... More

Spectral perturbation theory and the two weights problemJun 08 2013The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis' theorem of 1980 gives a way to construct a certain class of pairs ... More

Categorical joinsMar 31 2018Mar 01 2019We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016Oct 25 2017We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More