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Ab initio vibrational free energies including anharmonicity for multicomponent alloysFeb 28 2019A density-functional-theory based approach to efficiently compute numerically exact vibrational free energies - including anharmonicity - for chemically complex multicomponent alloys is developed. It is based on a combination of thermodynamic integration ... More

Crosscap slides and the level 2 mapping class group of a nonorientable surfaceJun 28 2010Aug 19 2011Crosscap slide is a homeomorphism of a nonorientable surface of genus at least 2, which was introduced under the name Y-homeomorphism by Lickorish as an example of an element of the mapping class group which cannot be expressed as a product of Dehn twists. ... More

Low dimensional linear representations of the mapping class group of a nonorientable surfaceMar 08 2013Suppose that $f$ is a homomorphism from the mapping class group $\mathcal{M}(N_{g,n})$ of a nonorientable surface of genus $g$ with $n$ boundary components, to $\mathrm{GL}(m,\mathbb{C})$. We prove that if $g\ge 5$, $n\le 1$ and $m\le g-2$, then $f$ factors ... More

A finite generating set for the level 2 mapping class group of a nonorientable surfaceAug 19 2011We obtain a finite set of generators for the level 2 mapping class group of a closed nonorientable surface of genus $g\ge 3$. This set consists of isotopy classes of Lickorish's Y-homeomorphisms also called crosscap slides.

Particle Gibbs algorithms for Markov jump processesMay 06 2015In the present paper we propose a new MCMC algorithm for sampling from the posterior distribution of hidden trajectory of a Markov jump process. Our algorithm is based on the idea of exploiting virtual jumps, introduced by Rao and Teh (2013). The main ... More

Classical R-matrix theory of dispersionless systems: II. (2+1)-dimension theoryNov 13 2002A systematic way of construction of (2+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the so-called central extension procedure and classical R-matrix applied to the Poisson algebras of formal Laurent ... More

On deformations of standard R-matrices for integrable infinite-dimensional systemsJan 24 2005Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are presented as ... More

Classical R-matrix theory for bi-Hamiltonian field systemsFeb 09 2009The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The theory is developed ... More

Dispersionful analogue of the Whitham hierarchyJul 07 2007The dispersionful analogue, by means of Lax formalism, of the zero-genus universal Whitham hierarchy together with its algebraic orbit finite-field reductions is considered. The theory is illustrated by several significant examples.

Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systemsOct 26 2005Rational Lax hierarchies introduced by Krichever are generalized. A systematic construction of infinite multi-Hamiltonian hierarchies and related conserved quantities is presented. The method is based on the classical R-matrix approach applied to Poisson ... More

A note on the longest common Abelian factor problemMar 03 2015Mar 11 2015Abelian string matching problems are becoming an object of considerable interest in last years. Very recently, Alatabbi et al. \cite{AILR2015} presented the first solution for the longest common Abelian factor problem for a pair of strings, reaching $O(\sigma ... More

BracketsJan 02 2013Mar 26 2013We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as the supergeometric setting. The review is supplemented by a few new concepts ... More

Quasi-derivations and QD-algebroidsJan 21 2003Mar 14 2003Axioms of Lie algebroid are discussed in order to review some known aspects for non-experts. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the Functions(M)-module F of sections of a vector bundle E over a manifold M ... More

Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theoryNov 06 2002A systematic way of construction of (1+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the classical R-matrix on Poisson algebras of formal Laurent series. Results are illustrated with the known and new ... More

A note on the longest common substring with $k$-mismatches problemSep 25 2014Oct 14 2014The recently introduced longest common substring with $k$-mismatches ($k$-LCF) problem is to find, given two sequences $S_1$ and $S_2$ of length $n$ each, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ ... More

On Turing dynamical systems and the Atiyah problemApr 12 2010Dec 12 2014Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti ... More

Structural stability and thermodynamics of CrN magnetic phases from ab initio and experimentAug 14 2014The dynamical and thermodynamic phase stabilities of the stoichiometric compound CrN including different structural and magnetic configurations are comprehensively investigated using a first-principles density-functional-theory (DFT) plus U approach in ... More

Basal Slip in Laves Phases: the Synchroshear DislocationFeb 05 2019Two different mechanisms have been reported in previous ab initio studies to describe basal slip in complex intermetallic Laves phases: synchroshear and undulating slip. To date, no clear answer has been given on which is the energetically favourable ... More

Computational engineering of sublattice ordering in a hexagonal AlHfScTiZr high entropy alloyFeb 14 2017Multi-principle element alloys have enormous potential, but their exploration suffers from the tremendously large range of configurations. In the last decade such alloys have been designed with a focus on random solid solutions. Here we apply an experimentally ... More

Modular classes of skew algebroid relationsAug 11 2011Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is a homogeneous ... More

Courant-Nijenhuis tensors and generalized geometriesJan 31 2006Nijenhuis tensors $N$ on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form $N+N^*=aI$ for irreducible Courant algebroids, in particular for the extended tangent bundles $TM\oplus T^*M$. ... More

Anomalous phonon lifetime shortening in paramagnetic CrN caused by magneto-lattice coupling: A combined spin and ab initio molecular dynamics studyFeb 08 2018We study the mutual coupling of spin fluctuations and lattice vibrations in paramagnetic CrN by combining atomistic spin dynamics and ab initio molecular dynamics. The two degrees of freedom are dynamically coupled leading to non-adiabatic effects. Those ... More

New tabulation and sparse dynamic programming based techniques for sequence similarity problemsDec 08 2013May 21 2014Calculating the length of a longest common subsequence (LCS) of two strings $A$ and $B$ of length $n$ and $m$ is a classic research topic, with many worst-case oriented results known. We present two algorithms for LCS length calculation with respectively ... More

Local Lie algebra determines base manifoldJun 28 2005Aug 26 2006It is proven that a local Lie algebra in the sense of A. A. Kirillov determines the base manifold up to a diffeomorphism provided the anchor map is nowhere-vanishing. In particular, the Lie algebras of nowhere-vanishing Poisson or Jacobi brackets determine ... More

Graded contact manifolds and contact Courant algebroidsDec 04 2011Feb 06 2013We develop a systematic approach to contact and Jacobi structures on graded supermanifolds. In this framework, contact structures are interpreted as symplectic principal GL(1,R)-bundles. Gradings compatible with the GL(1,R)-action lead to the concept ... More

An introduction to loopoidsOct 12 2015We discuss a concept of loopoid as a non-associative generalization of (Brandt) groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework ... More

Isomorphisms of algebras of smooth functions revisitedOct 18 2003Nov 27 2004It is proved that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms. It is not required that manifolds are second countable nor paracompact. This solves a problem stated by A. Wienstein. ... More

Modular classes revisitedNov 15 2013Aug 29 2014We present a graded-geometric approach to modular classes of Lie algebroids and their generalizations, introducing in this setting an idea of relative modular class of a Dirac structure for a certain type of Courant algebroids, called projectable. This ... More

Adaptive parallel tempering algorithmMay 04 2012Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler depend strongly ... More

R-matrix approach to integrable systems on time scalesMar 10 2008A general unifying framework for integrable soliton-like systems on time scales is introduced. The $R$-matrix formalism is applied to the algebra of $\delta$-differential operators in terms of which one can construct infinite hierarchy of commuting vector ... More

Bi-Hamiltonian structures for integrable systems on regular time scalesOct 04 2008A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is introduced. The linear ... More

Novikov algebras and a classification of multicomponent Camassa-Holm equationsSep 12 2013Jan 30 2014A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by Bai and Meng. ... More

Construction and separability of nonlinear soliton integrable couplingsFeb 13 2012A very natural construction of integrable extensions of soliton systems is presented. The extension is made on the level of evolution equations by a modification of the algebra of dynamical fields. The paper is motivated by recent works of Wen-Xiu Ma ... More

Computational modeling of collective human behavior: Example of financial marketsDec 14 2008We discuss how minimal financial market models can be constructed by bridging the gap between two existing, but incomplete, market models: a model in which a population of virtual traders make decisions based on common global information but lack local ... More

A practical index for approximate dictionary matching with few mismatchesJan 20 2015Feb 12 2016Approximate dictionary matching is a classic string matching problem (checking if a query string occurs in a collection of strings) with applications in, e.g., spellchecking, online catalogs, geolocation, and web searchers. We present a surprisingly simple ... More

Two simple full-text indexes based on the suffix arrayMay 22 2014May 23 2016We propose two suffix array inspired full-text indexes. One, called SA-hash, augments the suffix array with a hash table to speed up pattern searches due to significantly narrowed search interval before the binary search phase. The other, called FBCSA, ... More

On Lie induction and the exceptional seriesSep 20 2004May 10 2005Lie bialgebras occur as the principal objects in the infinitesimalisation of the theory of quantum groups - the semi-classical theory. Their relationship with the quantum theory has made available some new tools that we can apply to classical questions. ... More

Tangent Lifts of Poisson and Related StructuresJan 02 2007The derivation $d_T$ on the exterior algebra of forms on a manifold $M$ with values in the exterior algebra of forms on the tangent bundle $TM$ is extended to multivector fields. These tangent lifts are studied with applications to the theory of Poisson ... More

Graded bundles and homogeneity structuresFeb 01 2011Sep 25 2011We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms. Graded bundles ... More

Graded cluster algebrasSep 24 2013Jun 18 2015In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We transfer a definition ... More

Algebroids - general differential calculi on vector bundlesSep 29 1999A notion of an algebroid - a generalization of a Lie algebroid structure is introduced. We show that many objects of the differential calculus on a manifold M associated with the canonical Lie algebroid structure on T^M can be obtained in the framework ... More

A triple construction for Lie bialgebrasDec 30 2003Jan 21 2005We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the algebraic structure of the triple, analogous to ... More

Generalized n-Poisson brackets on a symplectic manifoldFeb 23 1999On a symplectic manifold a family of generalized Poisson brackets associated with powers of the symplectic form is studied. The extreme cases are related to the Hamiltonian and Liouville dynamics. It is shown that the Dirac brackets can be obtained in ... More

On computing homology gradients over finite fieldsOct 07 2014Jun 06 2016Recently the so-called Atiyah conjecture about l^2-Betti numbers has been disproved. The counterexamples were found using a specific method of computing the spectral measure of a matrix over a complex group ring. We show that in many situations the same ... More

A bloated FM-index reducing the number of cache misses during the searchDec 07 2015The FM-index is a well-known compressed full-text index, based on the Burrows-Wheeler transform (BWT). During a pattern search, the BWT sequence is accessed at "random" locations, which is cache-unfriendly. In this paper, we are interested in speeding ... More

Numerical Coding of Nominal DataJan 08 2016In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other properties previously ... More

Binary operations in classical and quantum mechanicsJan 10 2002Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply the properties which usually are additionally required. ... More

Braided-Lie bialgebras associated to Kac-Moody algebrasAug 30 2007Dec 19 2007Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each inclusion of ... More

Dirac Algebroids in Lagrangian and Hamiltonian MechanicsJan 13 2011We present a unified approach to constrained implicit Lagrangian and Hamiltonian systems based on the introduced concept of Dirac algebroid. The latter is a certain almost Dirac structure associated with the Courant algebroid on the dual $E^\ast$ to a ... More

Jacobi structures revisitedNov 13 2001Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie algebroids in the ... More

Influence of temporal aspects and age-correlations on the process of opinion formation based on Polish contact surveyJul 09 2016On the basis of the experimental data concerning interactions between humans the process of Ising-based model of opinion formation in a social network was investigated. In the paper the data concerning human social activity, i.e. frequency and duration ... More

On Duplication in Mathematical RepositoriesMay 06 2010Building a repository of proof-checked mathematical knowledge is without any doubt a lot of work, and besides the actual formalization process there also is the task of maintaining the repository. Thus it seems obvious to keep a repsoitory as small as ... More

A lattice of Magneto-Optical and Magnetic traps for cold atomsAug 30 2002Mar 13 2003We describe basic periodic trapping configurations for ultracold atoms above surfaces. The approach is based on a simple wire grid and can be scaled to provide large arrays of periodically arranged magnetic or magneto-optical traps. The unit cells of ... More

Efficient algorithms for the longest common subsequence in $k$-length substringsNov 18 2013Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences $A$ and $B$ ... More

New algorithms for binary jumbled pattern matchingOct 23 2012May 01 2013Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a string to ... More

Remarks on Nambu-Poisson and Nambu-Jacobi bracketsFeb 23 1999Apr 15 1999It is shown that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: a n-bracket, n>2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get a (n-1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we ... More

Tangent and cotangent lifts and graded Lie algebras associated with Lie algebroidsOct 14 1997Generalized Schouten, Froelicher-Nijenhuis and Froelicher-Richardson brackets are defined for an arbitrary Lie algebroid. Tangent and cotangent lifts of Lie algebroids are introduced and discussed and the behaviour of the related graded Lie brackets under ... More

Rank and select: Another lesson learnedMay 05 2016May 12 2016Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet in 1980s, these ... More

Lie algebraic characterization of manifoldsOct 14 2003Feb 03 2005Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized ... More

Examples of quantum cluster algebras associated to partial flag varietiesJul 28 2009Jul 27 2010We give several explicit examples of quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky, on quantized coordinate rings of partial flag varieties and their associated unipotent radicals. These structures are shown to be quantizations ... More

Tulczyjew triples: from statics to field theoryJun 12 2013Jan 18 2014We propose a geometric approach to dynamical equations of physics, based on the idea of the Tulczyjew triple. We show the evolution of these concepts, starting with the roots lying in the variational calculus for statics, through Lagrangian and Hamiltonian ... More

Remarks on generalized Lie algebroids and related conceptsJan 25 2017We prove that "generalized Lie algebroid", a geometric object which appeared recently in the literature, is a misconception.

Metropolis-type algorithms for Continuous Time Bayesian NetworksMar 17 2014We present a Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm for detecting hidden variables in a continuous time Bayesian network (CTBN), which uses reversible jumps in the sense defined by (Green 1995). In common with several Monte Carlo ... More

The dynamics of co- and counter rotating coupled spherical pendulumsMar 05 2014The dynamics of co- and counter-rotating coupled spherical pendulums (two lower pendulums are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. Starting from linear modes allow we ... More

Relating the microscopic rules in coalescence-fragmentation models to the macroscopic cluster size distributions which emergeJul 31 2008Oct 08 2009Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used for coalescence ... More

Integrable quantum Stäckel systemsMay 24 2013Aug 02 2013The St\"ackel separability of a Hamiltonian system is well known to ensure existence of a complete set of Poisson commuting integrals of motion quadratic in the momenta. In the present paper we consider a class of St\"ackel separable systems where the ... More

Asymptotics of Monte Carlo maximum likelihood estimatorsDec 19 2014We describe Monte Carlo approximation to the maximum likelihood estimator in models with intractable norming constants and explanatory variables. We consider both sources of randomness (due to the initial sample and to Monte Carlo simulations) and prove ... More

Characterization of Null Geodesics on Kerr SpacetimesNov 17 2016We consider null geodesics in the domain of outer communication of a sub-extremal Kerr spacetime. We show, that most fundamental properties of null geodesics can be represented in one plot. In particular one can see immediately that the ergoregion and ... More

Crosscap slides and the level 2 mapping class group of a nonorientable surfaceJun 28 2010Feb 08 2017Crosscap slide is a homeomorphism of a nonorientable surface of genus at least 2, which was introduced under the name Y-homeomorphism by Lickorish as an example of an element of the mapping class group which cannot be expressed as a product of Dehn twists. ... More

On the commutator length of a Dehn twistJul 01 2010Jul 05 2010We show that on a nonorientable surface of genus at least 7 any power of a Dehn twist is equal to a single commutator in the mapping class group and the same is true, under additional assumptions, for the twist subgroup, and also for the extended mapping ... More

Tight and simple Web graph compressionJun 04 2010Sep 06 2011Analysing Web graphs has applications in determining page ranks, fighting Web spam, detecting communities and mirror sites, and more. This study is however hampered by the necessity of storing a major part of huge graphs in the external memory, which ... More

On Filippov algebroids and multiplicative Nambu-Poisson structuresFeb 23 1999We discuss relations between linear Nambu-Poisson structures and Filippov algebras and define Filippov algebroids which are n-ary generalizations of Lie algebroids. We also prove results describing multiplicative Nambu- Poisson structures on Lie groups. ... More

Sampling the suffix array with minimizersJun 09 2014Dec 03 2014Sampling (evenly) the suffixes from the suffix array is an old idea trading the pattern search time for reduced index space. A few years ago Claude et al. showed an alphabet sampling scheme allowing for more efficient pattern searches compared to the ... More

Derivations of the Lie Algebras of Differential OperatorsDec 08 2003Jan 17 2005This paper encloses a complete and explicit description of the derivations of the Lie algebra D(M) of all linear differential operators of a smooth manifold M, of its Lie subalgebra D^1(M) of all linear first-order differential operators of M, and of ... More

Pontryagin Maximum Principle - a generalizationMay 17 2009Dec 01 2011The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields, in particular, ... More

Non-antisymmetric versions of Nambu-Poisson and Lie algebroidsApr 11 2001We show that one can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be ... More

The Lie algebra of a Lie algebroidMar 06 2002Results describing Lie ideals and maximal finite-codimensional Lie subalgebras of the Lie algebras associated with Lie algebroids with non-singular anchor maps are presented. It is also proved that every isomorphism of such Lie algebras induces a diffeomorphism ... More

On n-tuple principal bundlesJul 30 2018We develop the concept of a double (more generally n-tuple) principal bundle departing from a compatibility condition for a principal action of a Lie group on a groupoid.

On quantum and classical Poisson algebrasOct 03 2005Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular somehow unexpected fact that the ... More

The graded Jacobi algebras and (co)homologyJul 02 2002Nov 18 2002Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such ... More

Engineering Relative Compression of GenomesMar 11 2011Technology progress in DNA sequencing boosts the genomic database growth at faster and faster rate. Compression, accompanied with random access capabilities, is the key to maintain those huge amounts of data. In this paper we present an LZ77-style compression ... More

Variational calculus with constraints on general algebroidsDec 17 2007Mar 06 2008Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the geometrical ... More

On characterization of Poisson and Jacobi structuresOct 23 2002We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and ... More

Higher vector bundles and multi-graded symplectic manifoldsFeb 26 2007Jul 08 2009A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is used in showing ... More

Braided enveloping algebras associated to quantum parabolic subalgebrasJun 04 2007Jul 27 2010Associated to each subset $J$ of the nodes $I$ of a Dynkin diagram is a triangular decomposition of the corresponding Lie algebra $\mathfrak{g}$ into three subalgebras $\widetilde{\mathfrak{g}_{J}}$ (generated by $e_{j}$, $f_{j}$ for $j\in J$ and $h_{i}$ ... More

Automorphisms of quantum and classical Poisson algebrasNov 11 2002We prove Pursell-Shanks type results for the Lie algebra D(M) of all linear differential operators of a smooth manifold M, for its Lie subalgebra D^1(M) of all linear first-order differential operators of M, and for the Poisson algebra S(M)=Pol(T*M) of ... More

Studying Diffusion of Viral Content at Dyadic LevelNov 28 2014Diffusion of information and viral content, social contagion and influence are still topics of broad evaluation. As theory explaining the role of influentials moves slightly to reduce their importance in the propagation of viral content, authors of the ... More

Integrable discrete systems on R and related dispersionless systemsJul 07 2007The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter groups of diffeomorphisms, ... More

Non-asymptotic Analysis of Biased Stochastic Approximation SchemeFeb 02 2019Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions such as unbiased ... More

Quantum Integrals of Motion for the Heisenberg Spin ChainMar 24 1994An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg $s=1/2$ spin chain is presented. The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables. This construction is direct ... More

Quantum chains with a Catalan tree pattern of conserved charges: the $Δ= -1$ XXZ model and the isotropic octonionic chainFeb 07 1995A class of quantum chains possessing a family of local conserved charges with a Catalan tree pattern is studied. Recently, we have identified such a structure in the integrable $SU(N)$-invariant chains. In the present work we find sufficient conditions ... More

Quantum critical benchmark for density functional theoryAug 09 2014Two electrons at the threshold of ionization represent a severe test case for electronic structure theory. A pseudospectral method yields a very accurate density of the two-electron ion with nuclear charge close to the critical value. Highly accurate ... More

Remarks on superdifferential equationsOct 07 2018We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is justified on physical and mathematical grounds that a subclass of them, the ... More

Automorphism groupoids in noncommutative projective geometryJul 17 2018Jul 31 2018We address a natural question in noncommutative geometry, namely the rigidity observed in many examples, whereby noncommutative spaces (or equivalently their coordinate algebras) have very few automorphisms by comparison with their commutative counterparts. ... More

Integrability Test for Spin ChainsDec 05 1994We examine a simple heuristic test of integrability for quantum chains. This test is applied to a variety of systems, including a generic isotropic spin-1 model with nearest-neighbor interactions and a multiparameter family of spin-1/2 models generalizing ... More

On Quantizing Nilpotent and Solvable Basic AlgebrasFeb 08 1999Mar 14 1999We prove an algebraic ``no-go theorem'' to the effect that a nontrivial Poisson algebra cannot be realized as an associative algebra with the commutator bracket. Using this, we show that there is an obstruction to quantizing the Poisson algebra of polynomials ... More

AV-differential geometry: Euler-Lagrange equationsApr 06 2006A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and unifies various ... More

Graded Frobenius cluster categoriesSep 30 2016Recently the first author studied multi-gradings for generalised cluster categories, these being 2-Calabi-Yau triangulated categories with a choice of cluster-tilting object. The grading on the category corresponds to a grading on the cluster algebra ... More

Mixed superposition rules and the Riccati hierarchyMar 01 2012Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The main achievement ... More

The Schroedinger operator in Newtonian space-timeNov 18 2006The Schroedinger operator on the Newtonian space-time is defined in a way which is independent on the class of inertial observers. In this picture the Schroedinger operator acts not on functions on the space-time but on sections of certain one-dimensional ... More