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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

On finite index subgroups of the mapping class group of a nonorientable surfaceJan 15 2014Let $M(N_{h,n})$ denote the mapping class group of a compact nonorientable surface of genus $h\ge 7$ and $n\le 1$ boundary components, and let $T(N_{h,n})$ be the subgroup of $M(N_{h,n})$ generated by all Dehn twists. It is known that $T(N_{h,n})$ is ... 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

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

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

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.

Heuristic for Network Coverage Optimization Applied in Finding Organizational Change AgentsNov 29 2014Authors compare different ways of selecting change agents within network analysis paradigm and propose a new algorithm of doing so. All methods are evaluated against network coverage measure that calculates how many network members can be directly reached ... More

Model for simulating mechanisms responsible of similarities between people connected in networks of social relationsNov 28 2014It the literature have been identified three social mechanisms explaining the similarity between people connected in the network of social relations homophily, confounding and social contagion. The article proposes a simple model for simulating mechanisms ... More

A presentation for the mapping class group of a nonorientable surfaceAug 27 2013Let $N_{g,n}$ denote the nonorientable surface of genus $g$ with $n$ boundary components and $M(N_{g,n})$ its mapping class group. We obtain an explicit finite presentation of $M(N_{g,n})$ for $n=0,1$ and all $g$ such that $g+n>3$.

Beyond Complex Langevin Equations: a Progress ReportOct 26 2018After a short review of one of proposals to avoid complex stochastic processes in Complex Langevin studies, the recent progress in the former is reported. In particular, the new developments allow now to construct positive and normalizable representations ... More

Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other IdentitiesDec 17 2015Feb 27 2016The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear operators are introduced, which must satisfy some integrability conditions, ... More

Target Space Duality: The Dilaton FieldDec 31 2007Classical target space duality transformations are studied for the non-linear sigma model with a dilaton field. Working within the framework of the Hamiltonian formalism we require the duality transformation to be a property only of the target spaces. ... More

Classical $r$-matrix like approach to Frobenius manifolds, WDVV equations and flat metricsApr 07 2013Jun 11 2015A general scheme for construction of flat pencils of contravariant metrics and Frobenius manifolds as well as related solutions to WDVV associativity equations is formulated. The advantage is taken from the Rota-Baxter identity and some relation being ... 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

Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systemsJul 08 2008Sep 23 2008We introduce the cotangent universal hierarchy that extends the so-called universal hierarchy (as for the latter, see e.g. arXiv:nlin/0202008, arXiv:nlin/0312043 and arXiv:nlin/0310036). Then we construct a (2+1)-dimensional double central extension of ... More

A fast anharmonic free energy method with an application to vacancies in ZrCApr 04 2019We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a $\times10$ speed-up on ... 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

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

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

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

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

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

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

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

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

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

Basal Slip in Laves Phases: the Synchroshear DislocationFeb 05 2019Mar 12 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

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

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

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

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

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

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

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

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

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

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

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

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

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

Faster batched range minimum queriesJun 21 2017Jul 10 2017Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time queries, there ... 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

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

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.

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

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

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

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

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 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

Solvable Lie algebras of vector fields and a Lie's conjectureJul 05 2019We present a local constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional analytical solvable ... More

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

Lightweight Fingerprints for Fast Approximate Keyword Matching Using Bitwise OperationsNov 22 2017We aim to speed up approximate keyword matching by storing a lightweight, fixed-size block of data for each string, called a fingerprint. These work in a similar way to hash values; however, they can be also used for matching with errors. They store information ... 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

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

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

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

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

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

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

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

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

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

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

copMEM: Finding maximal exact matches via sampling both genomesMay 22 2018Genome-to-genome comparisons require designating anchor points, which are given by Maximum Exact Matches (MEMs) between their sequences. For large genomes this is a challenging problem and the performance of existing solutions, even in parallel regimes, ... More

Lie algebroids and Poisson-Nijenhuis structuresOct 07 1997Poisson-NIjenhuis structures for an arbitrary Lie agebroid are defined and studied by means of tangent lifts of tensor fields.

Faster range minimum queriesNov 28 2017Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time queries, practical ... 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

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

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

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

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

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

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.

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

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

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

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

Handel: Practical Multi-Signature Aggregation for Large Byzantine CommitteesJun 12 2019We present Handel, a Byzantine fault tolerant aggregation protocol that allows for the quick aggregation of cryptographic signatures over a WAN. Handel has logarithmic time and polylogarithmic network complexity and needs minimal computing resources. ... 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

Characterization of Null Geodesics on Kerr SpacetimesNov 17 2016Oct 18 2017We 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

Low temperature features in the heat capacity of unary metals and intermetallics for the example of bulk aluminum and Al$_3$ScJan 24 2017We explore the competition and coupling of vibrational and electronic contributions to the heat capacity of Al and Al$_3$Sc at temperatures below 50 K combining experimental calorimetry with highly converged finite temperature density functional theory ... More

Adaptive Monte Carlo Maximum LikelihoodDec 19 2014We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We examine asymptotics ... 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

Non-asymptotic Analysis of Biased Stochastic Approximation SchemeFeb 02 2019Mar 31 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

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