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Simultaneous Learning of Trees and Representations for Extreme Classification and Density EstimationOct 14 2016Mar 02 2017We consider multi-class classification where the predictor has a hierarchical structure that allows for a very large number of labels both at train and test time. The predictive power of such models can heavily depend on the structure of the tree, and ... More

Deep learning with Elastic Averaging SGDDec 20 2014Oct 25 2015We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes ... More

Stochastic Bound MajorizationSep 22 2013Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order optimization methods ... More

VisualBackProp: efficient visualization of CNNsNov 16 2016May 19 2017This paper proposes a new method, that we call VisualBackProp, for visualizing which sets of pixels of the input image contribute most to the predictions made by the convolutional neural network (CNN). The method heavily hinges on exploring the intuition ... More

Explaining How a Deep Neural Network Trained with End-to-End Learning Steers a CarApr 25 2017As part of a complete software stack for autonomous driving, NVIDIA has created a neural-network-based system, known as PilotNet, which outputs steering angles given images of the road ahead. PilotNet is trained using road images paired with the steering ... More

Logarithmic Time Online Multiclass predictionJun 06 2014Nov 14 2015We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction approaches for constructing ... More

Binary embeddings with structured hashed projectionsNov 16 2015Jul 01 2016We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are independent ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests have been used to both assess the patient condition and to monitor the patient progress. This ... More

Structured adaptive and random spinners for fast machine learning computationsOct 19 2016Nov 26 2016We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners, which are formed ... More

Entropy-SGD: Biasing Gradient Descent Into Wide ValleysNov 06 2016Apr 21 2017This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues ... More

Notes on using Determinantal Point Processes for Clustering with Applications to Text ClusteringOct 26 2014In this paper, we compare three initialization schemes for the KMEANS clustering algorithm: 1) random initialization (KMEANSRAND), 2) KMEANS++, and 3) KMEANSD++. Both KMEANSRAND and KMEANS++ have a major that the value of k needs to be set by the user ... More

On the boosting ability of top-down decision tree learning algorithm for multiclass classificationMay 17 2016We analyze the performance of the top-down multiclass classification algorithm for decision tree learning called LOMtree, recently proposed in the literature Choromanska and Langford (2014) for solving efficiently classification problems with very large ... More

Entropy-SGD: Biasing Gradient Descent Into Wide ValleysNov 06 2016Dec 05 2016This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape at solutions found by gradient descent. Local extrema with low generalization error have ... More

Semistochastic Quadratic Bound MethodsSep 05 2013Feb 17 2014Partition functions arise in a variety of settings, including conditional random fields, logistic regression, and latent gaussian models. In this paper, we consider semistochastic quadratic bound (SQB) methods for maximum likelihood inference based on ... More

Entropy-SGD: Biasing Gradient Descent Into Wide ValleysNov 06 2016Nov 13 2016This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape at solutions found by gradient descent. Local extrema with low generalization error have ... More

Entropy-SGD: Biasing Gradient Descent Into Wide ValleysNov 06 2016This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape at solutions found by gradient descent. Local extrema with low generalization error have ... More

Differentially- and non-differentially-private random decision treesOct 26 2014Feb 05 2015We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works well in practice despite the simplicity of the setting, but its statistical mechanism is not yet well-understood. ... More

Simultaneous Learning of Trees and Representations for Extreme Classification, with Application to Language ModelingOct 14 2016This paper addresses the problem of multi-class classification with an extremely large number of classes, where the class predictor is learned jointly with the data representation, as is the case in language modeling problems. The predictor admits a hierarchical ... More

The Loss Surfaces of Multilayer NetworksNov 30 2014Jan 21 2015We study the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model under the assumptions of: i) variable independence, ii) redundancy ... More

VisualBackProp: visualizing CNNs for autonomous drivingNov 16 2016This paper proposes a new method, that we call VisualBackProp, for visualizing which sets of pixels of the input image contribute most to the predictions made by the convolutional neural network (CNN). The method heavily hinges on exploring the intuition ... More

Structured adaptive and random spinners for fast machine learning computationsOct 19 2016We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners, which are formed ... More

Structured adaptive and random spinners for fast machine learning computationsOct 19 2016Oct 28 2016We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners, which are formed ... More

Maximally informative ensembles for SIC-POVMs in dimension 3Apr 30 2014Nov 16 2014In order to find out for which initial states of the system the uncertainty of the measurement outcomes will be minimal, one can look for the minimizers of the Shannon entropy of the measurement. In case of group covariant measurements this question becomes ... More

Strong electroweak symmetry breaking (or, if no SM Higgs, then what?)Jun 08 2012While the LHC takes on the challenge of experimentally exploring the electroweak symmetry breaking sector, it is not only interesting but also crucial to explore alternatives to the Standard Model scenario with an elementary scalar Higgs boson. The idea ... More

Detection techniques for the H.E.S.S. II telescope, data modeling of gravitational lensing and emission of blazars in HE-VHE astronomyJul 15 2013This thesis presents the study of four aspects of high energy astronomy. The first part of the thesis is dedicated to an aspect of instrument development for imaging atmospheric Cherenkov telescopes, namely the Level 2 trigger system of the High Energy ... More

Two-weight norm inequalities for potential type and maximal operators in a metric spaceMay 13 2011Dec 31 2012We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group structure or non-empty ... More

Stochastic Volterra equations of nonscalar type in Hilbert spaceSep 01 2005Dec 02 2005In the paper stochastic Volterra equations of nonscalar type in Hilbert space are studied. The aim of the paper is to provide some results on stochastic convolution and mild solutions to those Volterra equations. The motivation of the paper comes from ... More

Gauss diagrams of 3-manifoldsAug 06 2003We present a simple combinatorial method to encode 3-dimensional manifolds, based on their Heegaard diagrams. The notion of a Gauss diagram of a 3-manifold is introduced. We check the conditions for a Gauss diagram to represent a closed manifold and a ... More

A counterpart of the Verlinde algebra for the small quantum groupJul 19 2001May 07 2002Let $\bar{Pr}$ denote the ideal spanned by the characters of projective modules in the Grothendieck ring of the category of finite dimensional modules over the small quantum group $u_l$. We show that $\bar{Pr}$ admits a description completely parallel ... More

Asymptotic expansions for trace functionalsDec 30 2013We obtain Taylor approximations for functionals $V\mapsto Tr(f(H_0+V))$ defined on the bounded self-adjoint operators, where $H_0$ is a self-adjoint operator with compact resolvent and $f$ is a sufficiently nice scalar function, relaxing assumptions on ... More

B-orbits of nilpotent order 2 and link patternsMar 13 2007Sep 03 2008In this paper we describe geometry of orbits of upper triangular matrices of nilpotent order 2 under conjugation by the group of upper triangular invertible matrices in terms of link patterns. Further we apply this description to the computations of the ... More

Description of B-orbit closures of order 2 in upper-triangular matricesDec 15 2003Nov 10 2005Let n_n(C) be the algebra of strictly upper-triangular n x n matrices over the field of complex numbers and X_2 the subset of matrices of nilpotent order 2. Let B_n(C) be the group of invertible upper-triangular matrices acting on n_n(C) by conjugation. ... More

Generalized channels: channels for convex subsets of the state spaceMay 10 2011Mar 12 2012Let $K$ be a convex subset of the state space of a finite dimensional $C^*$-algebra. We study the properties of channels on $K$, which are defined as affine maps from $K$ into the state space of another algebra, extending to completely positive maps on ... More

Geodesic distances on density matricesDec 17 2003We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.

Flat connections and Wigner-Yanase-Dyson metricsJul 28 2003On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using the $\alpha$-embeddings and finding the duals with ... More

Extremality conditions for generalized channelsApr 12 2012A generalized channel is a completely positive map that preserves trace on a given subspace. We find conditions under which a generalized channel with respect to a positively generated subspace J is an extreme point in the set of all such generalized ... More

Resolutions of p-stratifolds with isolated singularitiesNov 18 2003Recently M. Kreck introduced a class of stratified spaces called p-stratifolds [M. Kreck, Stratifolds, Preprint]. He defined and investigated resolutions of p-stratifolds analogously to resolutions of algebraic varieties. In this note we study a very ... More

Current-carrying molecules: a real space pictureJun 30 2005An approach is presented to calculate characteristic current vs voltage curves for isolated molecules without explicit description of leads. The Hamiltonian for current-carrying molecules is defined by making resort to Lagrange multipliers, while the ... More

The Fokker-Planck equation for bistable potential in the optimized expansionNov 21 2001The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential is shown to ... More

A new structural approach to isoparametric hypersurfaces in spheresOct 22 2014The classification of isoparametric hypersurfaces in spheres with four or six different principal curvatures is still not complete. In this paper we develop a structural approach that may be helpful for a classification. Instead of working with the isoparametric ... More

Stellar Archaeology: New Science with Old StarsDec 06 2010The abundance patterns of metal-poor stars provide us a wealth of chemical information about various stages of cosmic chemical evolution. In particular, these stars allow us to study the formation and evolution of the elements, and the involved nucleosynthesis ... More

Average optimality for risk-sensitive control with general state spaceApr 03 2007This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing ... More

Supersymmetric Seesaw without Singlet Neutrinos: Neutrino Masses and Lepton-Flavour ViolationJul 01 2002Jul 08 2002We consider the supersymmetric seesaw mechanism induced by the exchange of heavy SU(2)_W triplet states, rather than `right-handed' neutrino singlets, to generate neutrino masses. We show that in this scenario the neutrino flavour structure tested at ... More

On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner MatricesJan 14 2012We continue investigations of our previous papers, in which there were proved central limit theorems (CLT) for linear eigenvalue statistics Tr f(M_n) and there were found the limiting probability laws for the normalised matrix elements of differential ... More

On a new transformation for generalised porous medium equations: from weak solutions to classicalOct 24 2014Nov 07 2015It is well-known that solutions for generalised porous medium equations are, in general, only H\"older continuous. In this note, we propose a new variable substitution for such equations which transforms weak solutions into classical.

Traces in Complex Hyperbolic Triangle GroupsFeb 10 2004Jun 21 2004We present several formulas for the traces of elements in complex hyperbolic triangle groups generated by complex reflections. The space of such groups of fixed signature is of real dimension one. We parameterise this space by a real invariant alpha of ... More

On the convex structure of process POVMsAug 03 2015Measurements on quantum channels are described by so-called process operator valued measures, or process POVMs. We study implementing schemes of extremal process POVMs. As it turns out, the corresponding measurement must satisfy certain extremality property, ... More

Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravityJun 24 2015Aug 17 2015The ultraviolet divergences of amplitude diagrams in maximal supergravity are characterised by a first possible divergence at seven loops for the 4-point amplitude (logarithmic) and, in its absence, at eight loops. We revisit the pure spinor superfield ... More

Self-similarity of Jankins-Neumann zigguratMar 10 2015Primarily having emerged from a topological question, Jankins-Neumann ziggurat also appears in the theory of dynamical systems on the circle. It describes an answer to the following question: given the rotation numbers of two orientation-preserving circle ... More

A Characterization of almost universal ternary inhomogeneous quadratic polynomials with conductor 2Jan 07 2015An integral quadratic polynomial (with positive definite quadratic part) is called almost universal if it represents all but finitely many positive integers. In this paper, we provide a characterization of almost universal ternary quadratic polynomials ... More

Ultraviolet divergences in maximal supergravity from a pure spinor point of viewDec 18 2014Aug 17 2015The ultraviolet divergences of amplitude diagrams in maximal supergravity are investigated using the pure spinor superfield formalism in maximal supergravity, with maximally supersymmetric Yang-Mills theory for reference. We comment on the effects of ... More

Rigorous enclosures of rotation numbers by interval methodsSep 24 2015We apply set-valued numerical methods to compute an accurate enclosure of the rotation number. The described algorithm is supplemented with a method of proving the existence of periodic points, which is used to check the rationality of the rotation number. ... More

Almost invariance of distributions for random walks on groupsMar 04 2016Apr 28 2016We study the neighborhoods of a typical point $Z_n$ visited at $n$-th step of a random walk, determined by the condition that the transition probabilities stay close to $\mu^{*n}(Z_n)$. If such neighborhood contains a ball of radius $C \sqrt{n}$, we say ... More

Comparison of quantum channels and statistical experimentsJan 24 2016Apr 24 2016For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two ensembles obtained ... More

MCRG study of 12 fundamental flavors with mixed fundamental-adjoint gauge actionDec 28 2011I discuss the infrared behavior of the SU(3) gauge model with 12 fundamental fermions. Using a Monte Carlo renormalization group technique I investigate the fixed point structure in the chiral limit and show that this system has an infrared fixed point ... More

Infrared fixed point of the 12-fermion SU(3) gauge model based on 2-lattice MCRG matchingJun 27 2011I investigate an SU(3) gauge model with 12 fundamental fermions. The physically interesting region of this strongly coupled system can be influenced by an ultraviolet fixed point due to lattice artifacts. I suggest to use a gauge action with an additional ... More

Scaling properties of many-fermion systems from MCRG studiesNov 03 2009Monte Carlo renormalization group methods were designed to study the phase structure and critical behavior of statistical systems. They are well suited to determine the running coupling and to investigate the properties of fixed points of gauge-fermion ... More

Transversals in completely reducible multiary quasigroups and in multiary quasigroups of order 4Dec 06 2016An $n$-ary quasigroup $f$ of order $q$ is an $n$-ary operation over a set of cardinality $q$ such that the Cayley table of the operation is an $n$-dimensional latin hypercube of order $q$. A transversal in a quasigroup $f$ (or in the corresponding latin ... More

Fundamental Domains in Lorentzian GeometryAug 28 2003Nov 02 2004We consider discrete subgroups Gamma of the simply connected Lie group SU~(1,1), the universal cover of SU(1,1), of finite level, i.e. the subgroup intersects the centre of SU~(1,1) in a subgroup of finite index, this index is called the level of the ... More

Rényi relative entropies and noncommutative $L_p$-spaces IIJun 30 2017We show the relation between two versions of sandwiched R\'enyi relative entropies for von Neumann algebras, introduced recently in [M. Berta et al, arXiv:1608.05317] and [A. Jen\v{c}ov\'a, arXiv:1609.08462]. It is also proved that equality in data processing ... More

Sturmian numeration systems and decompositions to palindromesOct 31 2017Nov 02 2017We extend the classical Ostrowski numeration systems, closely related to Sturmian words, by allowing a wider range of coefficients, so that possible representations of a number $n$ better reflect the structure of the associated Sturmian word. In particular, ... More

What made discy galaxies giant?Oct 03 2017I studied giant discy galaxies with optical radii more than 30 kpc. The comparison of these systems with discy galaxies of moderate sizes revealed that they tend to have higher rotation velocities, B-band luminosities, HI masses and dark-to-luminous mass ... More

Heritability estimation of diseases in case-control studiesNov 09 2016In the field of genetics, the concept of heritability refers to the proportion of variations of a biological trait or disease that can be explained by genetic factors. Quantifying the heritability of a disease is a fundamental challenge in human genetics, ... More

Spin-structures on real Bott manifolds with Kähler structuresMar 24 2017Let M be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization we give necessary and sufficient condition for the existence of the Spin-structure on M. In proof we use the technic developed in Popko, Szczepa\'{n}ski "Cohomological ... More

Ecology of galaxy stellar populations from optical spectroscopic surveysOct 12 2009The age and chemical composition of the stars in present-day galaxies carry important clues about their star formation processes. The latest generation of population synthesis models have allowed to derive age and stellar metallicity estimates for large ... More

Refined invariants and TQFT's from Homfly skein theoryJun 17 1998Jul 03 1998We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants. ... More

On the equivalence of two expected average cost criteria for semi- Markov control processesSep 19 2013The two expected average costs used in the theory of semi-Markov control processes with a Borel state space are considered. Under some stochastic stability conditions, we prove that the two criteria are equivalent in the sense that they lead to the same ... More

Rook numbers and the normal ordering problemFeb 23 2004Jul 15 2004For an element $w$ in the Weyl algebra generated by $D$ and $U$ with relation $DU=UD+1$, the normally ordered form is $w=\sum c_{i,j}U^iD^j$. We demonstrate that the normal order coefficients $c_{i,j}$ of a word $w$ are rook numbers on a Ferrers board. ... More

Stochastic Integral with respect to Cylindrical Wiener ProcessNov 21 2005This paper is devoted to a construction of the stochastic It\^o integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the ... More

Multiple operator integrals and spectral shiftJul 02 2009Mar 06 2011Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.

Higher order spectral shift, II. Unbounded caseJan 16 2009Jul 01 2009We construct higher order spectral shift functions, which represent the remainders of Taylor-type approximations for the value of a function at a perturbed self-adjoint operator by derivatives of the function at an initial unbounded operator. In the particular ... More

On partitions of the unit interval generated by Brocot sequencesDec 27 2005Dec 15 2007Let $ p_{i, n}, i=1,..., N(n)=2^{n-1} $ be the lengths of intervals between the neighboring fractions of Brocot sequence $ F_n $. We obtain an asymptotic formula for $\sigma_{\beta}(F_n)=\sum_{i=1}^{N(n)} p_{i, n}^{\beta} $,which improves known estimates. ... More

On orbital variety closures in sl(n). II. Descendants of a Richardson orbital varietyNov 26 2003For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g*. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sl(n) orbital ... More

Comparison of quantum binary experimentsOct 21 2011Jun 21 2012A quantum binary experiment consists of a pair of density operators on a finite dimensional Hilbert space. An experiment E is called \epsilon-deficient with respect to another experiment F if, up to \epsilon, its risk functions are not worse than the ... More

Affine connections, duality and divergences for a von Neumann algebraNov 05 2003On the predual of a von Neumann algebra, we define a differentiable manifold structure and affine connections by embeddings into non-commutative L_p-spaces. Using the geometry of uniformly convex Banach spaces and duality of the L_p and L_q spaces for ... More

Base norms and discrimination of generalized quantum channelsAug 19 2013We introduce and study norms in the space of hermitian operators, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels ... More

Trace formulas for tuples of commuting contractionsSep 18 2013Sep 22 2013This paper extends the trace formulas of [5] with perturbations in normed ideals of $B(H)$ to multivariate functions of commuting contractions admitting a dilation to commuting normal contractions.

Rarefaction waves in nonlocal convection-diffusion equationsMar 29 2013Apr 16 2013We consider the "convection-diffussion" equation $u_t=J*u-u-uu_x,$ where $J$ is a probability density. We supplement this equation with step-like initial conditions and prove a convergence of corresponding solution towards a rarefaction wave, i.e. a unique ... More

Generating the Ideals Defining Unions of Schubert VarietiesMay 12 2014This note computes a Gr\"obner basis for the ideal defining a union of Schubert varieties. More precisely, it computes a Gr\"obner basis for unions of schemes given by northwest rank conditions on the space of all matrices of a fixed size. Schemes given ... More

Stellar Archaeology -- Exploring the Universe with Metal-Poor StarsJun 11 2010The abundance patterns of the most metal-poor stars in the Galactic halo and small dwarf galaxies provide us with a wealth of information about the early Universe. In particular, these old survivors allow us to study the nature of the first stars and ... More

Levi-Civita connections of flag manifoldsDec 05 2005For any flag manifold G/T we obtain an explicit expression of its Levi-Civita connection with respect to any invariant Riemannian metric.

The Effective Action for Local Composite Operators $Φ^2(x)$ and $Φ^4(x)$Jun 13 1996The generating functionals for the local composite operators, $\Phi^2(x)$ and $\Phi^4(x)$, are used to study excitations in the scalar quantum field theory with $\lambda \Phi^4$ interaction. The effective action for the composite operators is obtained ... More

Dynamical Simulations with Smeared Link Staggered FermionsNov 04 2002One of the most serious problems of the staggered fermion lattice action is flavor symmetry violation. Smeared link staggered fermions can improve flavor symmetry by an order of magnitude relative to the standard thin link action. Over the last few years ... More

Topological Susceptibility on Dynamical Staggered Fermion ConfigurationsApr 30 2001The topological susceptibility is one of the few physical quantities that directly measure the properties of the QCD vacuum. Chiral perturbation theory predicts that in the small quark mass limit the topological susceptibility depends quadratically on ... More

Non-Discrete Complex Hyperbolic Triangle Groups of Type (m,m,infinity)Apr 30 2010In this note we prove that a complex hyperbolic triangle group of type (m,m,infinity), i.e. a group of isometries of the complex hyperbolic plane, generated by complex reflections in three complex geodesics meeting at angles Pi/m, Pi/m and 0, is not discrete ... More

Spectral Stieltjes-Type Integration and Some ApplicationsNov 25 2005Mar 06 2011This paper presents Stieltjes-type integration for operator-valued functions with respect to spectral families. The relation between Riemann-Stieltjes integrals associated with some classes of spectral families including, in particular, those that arise ... More

Almost Kähler 4-dimensional Lie groups with $J$-invariant Ricci tensorAug 03 2003The aim of this paper is to determine left-invariant strictly almost K\"ahler structures on 4-dimensional Lie groups $(g, J, \Omega)$ such that the Ricci tensor is $J$-invariant.

The culmination of an inverse cascade: mean flow and fluctuationsOct 25 2017Feb 01 2018Two dimensional turbulence has a remarkable tendency to self-organize into large, coherent structures, forming a mean flow. The purpose of this paper is to elucidate how these structures are sustained, and what determines them and the fluctuations around ... More

Development of novel plastic scintillators based on polyvinyltoluene for the hybrid J-PET/MR tomographOct 23 2017A novel plastic scintillator, referred to as J-PET scintillator, has been developed for the application in the digital positron emission tomography (PET). The novelty of the concept lies in application of the 2-(4-styrylphenyl)benzoxazole as a wavelength ... More

Non-classical features in general probabilistic theoriesMay 22 2017Jan 23 2018We study incompatibility of measurements and its relation to steering and nonlocality in finite dimensional general probabilistic theories (GPT). The basic idea is to represent finite collections of measurements as affine maps of a state space into a ... More

CoVaR-based portfolio selectionMar 04 2017We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions are given ... More

Transversals in completely reducible multiary quasigroups and in multiary quasigroups of order 4Dec 06 2016Sep 11 2017An $n$-ary quasigroup $f$ of order $q$ is an $n$-ary operation over a set of cardinality $q$ such that the Cayley table of the operation is an $n$-dimensional latin hypercube of order $q$. A transversal in a quasigroup $f$ (or in the corresponding latin ... More

Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutionsOct 16 2017Jan 27 2018In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions ... More

Recent results from the ARIANNA neutrino experimentSep 23 2016The ARIANNA experiment is currently taking data in its pilot-phase on the Ross ice-shelf. Fully autonomous stations measure radio signals in the frequency range from 100 MHz to 1 GHz. The seven station HRA was completed in December 2014, and augmented ... More

The Malliavin derivative and compactness: application to a degenerate PDE-SDE couplingSep 06 2016Jun 29 2017Compactness is one of the most versatile tools in the analysis of nonlinear PDEs and systems. Usually, compactness is established by means of some embedding theorem between functional spaces. Such theorems, in turn, rely on appropriate estimates for a ... More

Rational surgery formula for Habiro-Le invariants of rational homology 3-spheresApr 12 2006Apr 13 2006The results become part of an upcoming paper.

Negational Fragment of Intuitionistic Control LogicAug 09 2014We investigate properties of monadic purely negational fragment of Intuitionistic Control Logic (ICL). This logic arises from Intuitionistic Propositional Logic (IPL) by extending language of IPL by additional new constant for falsum. Having two different ... More

Ambiguity of converting phase-averaged flux into luminosity for millisecond pulsars in gamma raysMay 16 2008Oct 15 2008We study a magnitude of possible over/underestimation of the actual gamma-ray luminosity L_{actual} of a millisecond pulsar when using so-called pseudo luminosity L_{pseudo} which is inferred from a phase-averaged flux. Both, L_{actual} and L_{pseudo} ... More

On orbital variety closures in sl(n). I. Induced Duflo orderNov 26 2003For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g*. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sl(n) orbital ... More

Composite or elementary? Probing the nature of the HiggsMay 23 2013I discuss consequences of electroweak symmetry breaking by strong dynamics, assuming the existence of a light composite scalar appearing as a pseudo-Goldstone boson of some global symmetry of the new strongly interacting sector. In such a scenario, the ... More