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Stability of periodic solutions of conservation laws with viscosity: Analysis of the Evans functionMay 16 2002We establish instability of periodic traveling waves arising in conservation laws featuring phase transition. The analysis uses the Evans function framework introduced by R.A. Gardner in the periodic case. The main new tool is a periodic generalization ... More

Dynamic Structures of 2-adic Fibonacci PolynomialsMar 13 2019The dynamic structures of Fibonacci polynomials over the ring of 2-adic integers are described by investigating minimal decompositions which consist of minimal subsystems and attracting basins.

Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensionsOct 22 2008Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp $L^p$ estimates on the linearized solution operator about a multidimensional planar periodic wave of a system ... More

Weighted Norms of Ambiguity Functions and Wigner DistributionsJan 06 2006Jul 07 2006In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in wide-sense stationary ... More

The Critical Value of the Contact Process with Added and Removed EdgesMay 04 2004Nov 19 2004We show that the critical value for the contact process on a vertex-transitive graph G with finitely many edges added and/or removed is the same as the critical value for the contact process on G.

The noisy voter-exclusion processOct 31 2003The symmetric exclusion process and the voter model are two interacting particle systems for which a dual finite particle system allows one to characterize its invariant measures. Adding spontaneous births and deaths to the two processes still allows ... More

On the Szegö-Asymptotics for Doubly-Dispersive Gaussian ChannelsFeb 25 2011Jun 09 2011We consider the time-continuous doubly-dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further ... More

Approximate Eigenstructure of LTV Channels with Compactly Supported SpreadingJan 06 2007Feb 27 2007In this article we obtain estimates on the approximate eigenstructure of channels with a spreading function supported only on a set of finite measure $|U|$.Because in typical application like wireless communication the spreading function is a random process ... More

Thermodynamics using p4-improved staggered fermion action on QCDOCOct 05 2005We present an exploratory study of the thermodynamics of $N_f=3$ QCD with an improved staggered fermions using the QCDOC supercomputer. We use a p4 action with MILC-style smeared links (Fat 7). Some details of the implementation of the p4 action on QCDOC ... More

CCFM prediction on forward jets and $F_2$: parton level predictions and a new hadron level Monte Carlo generator CASCADEAug 28 1999A solution of the CCFM equation for a description of both the structure function $F_2$ and the cross section of forward jet production as measured by the HERA experiments is obtained on the basis of the parton level Monte Carlo program SMALLX. The treatment ... More

The Bootstrap and von Neumann algebras: The Maximal Intersection LemmaSep 19 2016Given a suitably nested family $Z = \langle Z(m,k,\gamma) \rangle_{m,k \in \mathbb N, \gamma >0}$ of Borel subsets of matrices, and associated Borel measures and rate function, $\mu$, an entropy, $\chi^{\mu}(Z)$, is introduced which generalizes the microstates ... More

Velocity Inversion in Nanochannel FlowSep 13 2006Aug 02 2007The nanoscale cylindrical Couette flow is investigated by means of molecular dynamics simulations, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. We find that the tangential velocity of the low is inverted when ... More

Resolving the existence of Higgsinos in the LHC inverse problemApr 10 2014Jun 17 2014The LHC inverse problem is infamously challenging when neutralinos and charginos are heavy and pure and other superparticles are decoupled. This limit is becoming more relevant to particle physics nowadays. Fortunately, in this limit, Higgsinos produce ... More

On The Complexity of Sparse Label PropagationApr 25 2018May 29 2018This paper investigates the computational complexity of sparse label propagation which has been proposed recently for processing network structured data. Sparse label propagation amounts to a convex optimization problem and might be considered as an extension ... More

An RKHS Approach to Estimation with Sparsity ConstraintsNov 22 2013The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest can be represented ... More

Branching ratio measurements and isospin violation in B-meson decaysOct 12 2015Dec 03 2015The approximate symmetry of the strong interactions under isospin transformations is among the most precise tools available to control hadronic matrix elements. It is crucial in extracting fundamental parameters, but also provides avenues for the search ... More

A robust limit for the electric dipole moment of the electronJan 08 2013Jan 22 2013Electric dipole moments constitute a competitive method to search for new physics, being particularly sensitive to new CP-violating phases. Given the experimental and theoretical progress in this field and more generally in particle physics, the necessity ... More

A variant of Gromov's problem on Hölder equivalence of Carnot groupsFeb 20 2017Jul 04 2017It is unknown if there exists a locally $\alpha$-H\"older homeomorphism $f:\mathbb{R}^3\to \mathbb{H}^1$ for any $\frac{1}{2}< \alpha\le \frac{2}{3}$, although the identity map $\mathbb{R}^3\to \mathbb{H}^1$ is locally $\frac{1}{2}$-H\"older. More generally, ... More

Fractal entropies and dimensions for microstate spaces, IIDec 11 2003For a selfadjoint element x in a tracial von Neumann algebra and $\alpha = \delta_0(x)$ we compute bounds for $\mathbb H^{\alpha}(x),$ where $\mathbb H^{\alpha}(x)$ is the free Hausdorff $\alpha$-entropy of $x.$ The bounds are in terms of $\int \int_{\mathbb ... More

The Rank Theorem and $L^2$-invariants in Free Entropy: Global Upper BoundsFeb 15 2016Using an analogy with the rank theorem in differential geometry, it is shown that for a finite $n$-tuple $X$ in a tracial von Neumann algebra and any finite $m$-tuple $F$ of $*$-polynomials in $n$ noncommuting indeterminates, \begin{eqnarray*} \delta_0(X) ... More

Levy-Khintchine random matrices and the Poisson weighted infinite skeleton treeFeb 05 2014Feb 13 2016We study a class of Hermitian random matrices which includes and generalizes Wigner matrices, heavy-tailed random matrices, and sparse random matrices such as the adjacency matrices of Erdos-Renyi random graphs with p ~ 1/N. Our NxN random matrices have ... More

BiLipschitz embeddings of spheres into jet space Carnot groups not admitting Lipschitz extensionsDec 15 2017Sep 07 2018For all $k,n\ge 1$, we construct a biLipschitz embedding of $\mathbb{S}^n$ into the jet space Carnot group $J^k(\mathbb{R}^n)$ that does not admit a Lipschitz extension to $\mathbb{B}^{n+1}$. Let $f:\mathbb{B}^n\to \mathbb{R}$ be a smooth, positive function ... More

Pulse Shaping, Localization and the Approximate Eigenstructure of LTV ChannelsDec 15 2009In this article we show the relation between the theory of pulse shaping for WSSUS channels and the notion of approximate eigenstructure for time-varying channels. We consider pulse shaping for a general signaling scheme, called Weyl-Heisenberg signaling, ... More

Status of dynamical ensemble generationJan 06 2010I give an overview of current and future plans of dynamical QCD ensemble generation activities. A comparison of simulation cost between different discretizations is made. Recent developments in techniques and algorithms used in QCD dynamical simulations, ... More

Resolved Photons and BFKL-type Signatures in Deep Inelastic ScatteringSep 23 1997The concept of resolved virtual photons in addition to direct deep inelastic $ep$ scattering is used to simulate the 2+1 jet - rate and the forward jet cross section, which cannot be described by direct LO/NLO processes. With standard DGLAP evolution ... More

Future Diffraction at HERASep 14 1998Future prospects of hard diffraction at HERA a reviewed. A selection of processes which can be calculated in pQCD is given, with emphasis on the separation of soft and hard diffraction. The main focus will be put on the energy dependence of diffractive ... More

Amenability, tubularity, and embeddings into $\mathcal R^ω$Jun 06 2005Dec 02 2006Suppose $M$ is a tracial von Neumann algebra embeddable into $\mathcal R^{\omega}$ (the ultraproduct of the hyperfinite $II_1$-factor) and $X$ is an $n$-tuple of selfadjoint generators for $M$. Denote by $\Gamma(X;m,k,\gamma)$ the microstate space of ... More

Congestion Control and Routing over Challenged NetworksJan 19 2012This dissertation is a study on the design and analysis of novel, optimal routing and rate control algorithms in wireless, mobile communication networks. Congestion control and routing algorithms upto now have been designed and optimized for wired or ... More

Gauge Transformations and Inverse Quantum Scattering with Medium-Range Magnetic FieldsDec 30 2004Jul 14 2005The time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are considered. The electrostatic ... More

Recent results from CCFM evolutionDec 04 2003Recent developments of the small $x$ CCFM evolution are described, including improvements of the splitting function. The resulting unintegrated gluon densities are used for predictions of hadronic final state measurements like jet production at HERA and ... More

Vector meson cross sections at HERAJan 13 2008Inelastic and elastic (exclusive) cross section measurements of vector meson production at HERA are discussed.

Learning the Conditional Independence Structure of Stationary Time Series: A Multitask Learning ApproachApr 04 2014Jan 11 2015We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a parametric process ... More

Quadratic matings and ray connectionsJul 03 2017A topological mating is a map defined by gluing together the filled Julia sets of two quadratic polynomials. The identifications are visualized and understood by pinching ray-equivalence classes of the formal mating. For postcritically finite polynomials ... More

The Thurston Algorithm for quadratic matingsJun 13 2017Mating is an operation to construct a rational map f from two polynomials, which are not in conjugate limbs of the Mandelbrot set. When the Thurston Algorithm for the unmodified formal mating is iterated in the case of postcritical identifications, it ... More

Bounds on new physics from electric dipole momentsSep 16 2015Electric dipole moments are extremely sensitive probes for additional sources of CP violation in new physics models. The multi-scale problem of relating the high-precision measurements with neutrons, atoms and molecules to fundamental parameters can be ... More

A propagation property of free entropy dimensionNov 17 2006Nov 29 2006Let M be a tracial von Neumann algebra and A be a weakly dense unital C*-subalgebra of M. We say that a set X is a W*-generating set for M if the von Neumann algebra generated by X is M and that X is a C*-generating set for A if the unital C*-algebra ... More

Some free entropy dimension inequalities for subfactorsOct 28 2004Suppose $N \subset M$ is an inclusion of $II_1$-factors of finite index. If $N$ can be generated by a finite set of elements, then there exist finite generating sets $X$ for $N$ and $Y$ for $M$ such that $\delta_0(X) \geq \delta_0(Y)$, where $\delta_0$ ... More

Monopole-antimonopole condensation in the interpolating Georgi-Glashow modelDec 22 1997We study the three dimensional Georgi-Glashow model (which interpolates smoothly between pure U(1) and SU(2) limits) using a constrained cooling which preserves 't Hooft-Polyakov monopoles. We find that the monopole-antimonopole condensation gives an ... More

Unintegrated parton densities applied to heavy quark production in the CCFM approachSep 17 2001Nov 25 2001The application of k_t - factorization supplemented with the CCFM small-x evolution equation to heavy quark production is discussed. The b-b_bar production cross sections at the TEVATRON can be consistently described using the k_t-factorization formalism ... More

Heavy quark production at HERA in k_t factorization supplemented with CCFM evolutionOct 26 2001The application of k_t - factorization, supplemented with the CCFM small-x evolution equation, to heavy quark production is discussed. Differential cross sections of b-b_bar production and also inelastic J/psi production as measured at HERA are compared ... More

Un-integrated PDFs in CCFMNov 22 2004The un-integrated parton distribution functions (uPDFs) obtained from a CCFM evolution are studied in terms of the intrinsic transverse momentum distribution at low scales. The uPDFs are studied for variations of the renormalization and factorization ... More

Simulations of a model for the Northern Spotted OwlFeb 19 2014In this paper, a branching process model of the Northern Spotted Owl is simulated. We focus on the time until extinction. It is shown how an approximation of the model with a multivariate autoregressive process works well near the equilibrium, but does ... More

A hyperfinite inequality for free entropy dimensionAug 28 2003Nov 25 2003If $X, Y,$ and $Z$ are finite sets of selfadjoint elements in a tracial von Neumann algebra and $X$ generates a hyperfinite von Neumann algebra, then $\delta_0(X \cup Y \cup Z) \leq \delta_0(X \cup Y) + \delta_0(X \cup Z) - \delta_0(X).$ We draw several ... More

Penguin contributions to B to J/Psi P DecaysDec 19 2012The high precision to which the standard model has been confirmed implies that new physics effects have to be small in the observed processes. Together with the outstanding precision expected from present and future collider experiments this renders the ... More

Dimension results for mappings of jet space Carnot groupsApr 24 2018We propose analogues of horizontal and vertical projections for model filiform jet space Carnot groups. Every pair consisting of the jet of a smooth function on $\mathbb{R}$ and a vertical hyperplane with first coordinate fixed provides a splitting of ... More

On the existence of open and bi-continuing codesOct 25 2008Feb 27 2009Given an irreducible sofic shift X, we show that an an irreducible SFT Y of lower entropy is a factor of X if and only if it is a factor of X by an open bi-continuing code. If these equivalent conditions hold and Y is mixing, then any code from a proper ... More

Relating U(1) monopole configurations to SU(2) saddle-point configurationsOct 17 1996We have studied field configurations of the 3-dimensional Georgi-Glashow model which interpolate between the $U(1)$ and the $SU(2)$ limits. In the intermediate region, these configurations contain 't-Hooft--Polyakov monopoles. We use cooling and extremization ... More

Analysis of saddle-point configurations in 3-dimensional SU(2) gauge theoryOct 31 1995We discuss the properties of a class of saddle point solutions in SU(2) in three dimensions (SU$(2)_3$), exhibiting localized peaks in the action. These configurations are generated by deterministic cooling and extremizing algorithms from analytic configurations. ... More

Investigation of next-to-leading effects in CCFMJul 19 2002Jul 24 2002The effect of formally next-to-leading contributions to the CCFM evolution equation are discussed.

Heavy Quark production at the TEVATRON and HERA using k_t-factorization with CCFM evolutionOct 02 2001Nov 25 2001The application of k_t-factorization supplemented with the CCFM small-x evolution equation to heavy quark production at the TEVATRON and at HERA is discussed. The bb_bar production cross sections at the TEVATRON can be consistently described using the ... More

Continuum directions for supervised dimension reductionJun 20 2016We consider dimension reduction of multivariate data under the existence of various types of auxiliary information. We propose a criterion that provides a series of orthogonal directional vectors, that form a basis for dimension reduction. The proposed ... More

Inference on subspheres model for directional dataJun 13 2016Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis, and assume that ... More

Pointwise asymptotic behavior of modulated periodic reaction-diffusion wavesDec 03 2011By working with the periodic resolvent kernel and Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction diffusion equations.With ... More

Theory of electric dipole moments and lepton flavour violationAug 12 2016Electric dipole moments and charged-lepton flavour-violating processes are extremely sensitive probes for new physics, complementary to direct searches as well as flavour-changing processes in the quark sector. Beyond the "smoking-gun" feature of a potential ... More

Random-time isotropic fractional stable fieldsDec 20 2011Jun 27 2012Generalizing both Substable FSMs and Indicator FSMs, we introduce alpha-stabilized subordination, a procedure which produces new FSMs (H-sssi symmetric stable processes) from old ones. We extend these processes to isotropic stable fields which have stationary ... More

On the Approximate Eigenstructure of Time-Varying ChannelsMar 05 2008Jul 10 2008In this article we consider the approximate description of doubly--dispersive channels by its symbol. We focus on channel operators with compactly supported spreading, which are widely used to represent fast fading multipath communication channels. The ... More

Precoding for 2x2 Doubly-Dispersive WSSUS ChannelsOct 20 2005Jan 16 2006Optimal link adaption to the scattering function of wide sense stationary uncorrelated scattering (WSSUS) mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission ... More

Extremal Reversible Measures for the Exclusion ProcessSep 14 2003We give a characterization of the invariant measures for the exclusion process on the integers with certain reversible transition kernels. Some examples include all nearest-neighbor kernels with asymptotic mean zero. One tool used is a necessary and sufficient ... More

Exit times for multivariate autoregressive processesNov 09 2012We study exit times from a set for a family of multivariate autoregressive processes with normally distributed noise. By using the large deviation principle, and other methods, we show that the asymptotic behavior of the exit time depends only on the ... More

Sparse Label PropagationDec 05 2016We consider massive heterogeneous datasets with intrinsic network structure, i.e., big data over networks. These datasets can be modelled by graph signals, which are defined over large-scale irregular graphs representing complex networks. We show that ... More

A Fixed-Point of View on Gradient Methods for Big DataJun 29 2017Aug 15 2017Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in machine learning ... More

Bounding the number of nodal domains of eigenfunctions without singular points on the squareDec 26 2017Aug 30 2018We prove Polterovich's conjecture concerning the growth of the number of nodal domains for eigenfunctions on a unit square domain, under the assumption that the eigenfunctions do not have any singular points.

Theory of electric dipole moments and lepton flavour violationAug 12 2016Nov 02 2016Electric dipole moments and charged-lepton flavour-violating processes are extremely sensitive probes for new physics, complementary to direct searches as well as flavour-changing processes in the quark sector. Beyond the "smoking-gun" feature of a potential ... More

Flavour Physics in two-Higgs-doublet modelsDec 29 2010Despite the tremendous success of the Standard Model, the arguments for the necessity of an extension are compelling. An attractive option is provided by Two-Higgs-Doublet models, due to their simplicity and them being the low-energy limit of some more ... More

Is there a non-standard-model contribution in non-leptonic b to s decays?Oct 08 2009The data on high-precision flavour observables reveal certain puzzles when compared to Standard Model expectations based on a global fit of the CKM unitarity triangle and general theoretical estimates. The discussion of these tensions in the channels ... More

A Free Entropy Dimension LemmaJul 17 2002Dec 24 2002Suppose M is a von Neumann algebra with normal, tracial state phi and {a_1,...,a_n} is a set of self-adjoint elements in M. We provide an alternative uniform packing description of delta_0(a_1,...,a_n), the modified free entropy dimension of {a_1,...,a_n}. ... More

Dimension and Entropy Computations for $L(F_r)$Feb 15 2003We show that certain generating sets of Dykema and Radulescu for $L(F_r)$ have free Hausdorff dimension r and nondegenerate free Hausdorff r-entropy

Fractal entropies and dimensions for microstate spacesDec 01 2002Sep 10 2003Using Voiculescu's notion of a matricial microstate we introduce fractal dimensions and entropies for finite sets of selfadjoint operators in a tracial von Neumann algebra. We show that they possess properties similar to their classical predecessors. ... More

Quantitative quantum ergodicity and the nodal domains of Maass-Hecke cusp formsJan 26 2013May 08 2016We prove a quantitative statement of the quantum ergodicity for Hecke--Maass cusp forms on the modular surface. As an application of our result, along a density $1$ subsequence of even Hecke--Maass cusp forms, we obtain a sharp lower bound for the $L^2$-norm ... More

On sparsity of positive-definite automorphic forms within a familyJan 02 2012It is known due to Baker and Montgomery that almost all Fekete polynomials under certain ordering have at least one zero on the interval (0, 1). In terms of the positive-definiteness, Fekete polynomial has no zero on the interval (0, 1) if and only if ... More

Open maps between shift spacesOct 25 2008Given a code from a shift space to an irreducible sofic shift, any two of the following three conditions -- open, constant-to-one, (right or left) closing -- imply the third. If the range is not sofic, then the same result holds when bi-closingness replaces ... More

Indicator fractional stable motionsOct 15 2010Mar 05 2011Using the framework of random walks in random scenery, Cohen and Samorodnitsky (2006) introduced a family of symmetric $\alpha$-stable motions called local time fractional stable motions. When $\alpha=2$, these processes are precisely fractional Brownian ... More

Perturbations of the Symmetric Exclusion ProcessSep 15 2003Feb 27 2004For the exclusion process with symmetric kernel p(x,y)=p(y,x), the set of invariant measures has been completely studied. This paper gives results concerning the invariant measures for exclusion processes where p(x,y)=p(y,x) except for finitely many (x,y). ... More

Homeomorphisms of the Mandelbrot SetDec 14 2003On subsets E of the Mandelbrot set M, homeomorphisms are constructed by quasi-conformal surgery. When the dynamics of quadratic polynomials is changed piecewise by a combinatorial construction, a general theorem yields the corresponding homeomorphism ... More

The CCFM Monte Carlo generator CASCADESep 12 2001CASCADE is a full hadron level Monte Carlo event generator for e-p, gamma-p and p-p_bar processes, which uses the CCFM evolution equation for the initial state cascade in a backward evolution approach supplemented with off-shell matrix elements for the ... More

Photon structure at HERAJun 09 2000Jun 13 2000The structure of the virtual photon and its contribution to small x processes in deep inelastic scattering at HERA is discussed.

CCFM prediction for F_2 and forward jets at HERAMay 31 1999Jun 03 1999Predictions of the CCFM evolution equation for F_2 and forward jets at HERA energies are obtained from a modified version of the Monte Carlo program SMALLX. The treatment of the non-Sudakov form factor $\Delta_{ns}$ is discussed as well as the effect ... More

Monte Carlo Implementations of Diffraction at HERASep 14 1998The Monte Carlo implementation of different approaches for diffractive scattering in $e - p$ collisions (resolved $\PO$, pQCD, soft color interactions) is described, with emphasis on the construction of the hadronic final state. Simple models for proton ... More

Pointwise stability estimates for periodic traveling wave solutions of systems of viscous conservation lawsOct 12 2012Oct 21 2012In the previous paper \cite{J1}, we established pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves $\bar u$ of a system of reaction diffusion equations, and also obtained pointwise nonlinear ... More

kt - factorization and CCFM - the solution for describing the hadronic final states - everywhere ?Nov 20 2003Nov 25 2003The basic ideas of kt-factorization and CCFM parton evolution is discussed. The unintegrated gluon densities, obtained from CCFM fits to the proton structure function data at HERA are used to predict hadronic final state cross sections like jet production ... More

Machine Learning: Basic PrinciplesMay 14 2018Jan 28 2019This tutorial is based on the lecture notes for, and the plentiful student feedback received from, the courses "Machine Learning: Basic Principles" and "Artificial Intelligence", which I have co-taught since 2015 at Aalto University. The aim is to provide ... More

Graphs of functions and vanishing free entropyJul 10 2007Suppose X is an n-tuple of selfadjoint elements in a tracial von Neumann algebra M. If z is a selfadjoint element in M and for some selfadjoint element y in the von Neumann algebra generated by X $\delta_0(y, z) < \delta_0(y) + \delta_0(z)$, then $\chi(X ... More

Strongly 1-bounded von Neumann algebrasOct 26 2005Oct 31 2005Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M. For $\alpha >0$, F is $\alpha$-bounded if the free packing $\alpha$-entropy of F is bounded from above. We say that M is strongly 1-bounded if M has a 1-bounded finite ... More

Universality of Composition Operators and Applications to Holomorphic DynamicsMar 03 2016By investigating which level of universality composition operators $C_f$ can have, where the symbol $f$ is given by the restriction of a transcendental entire function to suitable parts of the Fatou set of $f$, this work combines the theory of dynamics ... More

The free entropy dimension of hyperfinite von Neumann algebrasDec 04 2001Sep 13 2003Suppose M is a hyperfinite von Neumann algebra with a tracial state $\phi$ and $\{a_1,...,a_n\}$ is a set of selfadjoint generators for M. We calculate $\delta_0(a_1,...,a_n)$, the modified free entropy dimension of $\{a_1,...,a_n\}$. Moreover we show ... More

Iterated trilinear Fourier integrals with arbitrary symbolsNov 07 2013Aug 24 2015We prove $L^p$ estimates for trilinear multiplier operators with singular symbols. These operators arise in the study of iterated trilinear Fourier integrals, which are trilinear variants of the bilinear Hilbert transform. Specifically, we consider trilinear ... More

Sharp bounds for the intersection of nodal lines with certain curvesAug 11 2011May 29 2016Let $Y$ be a hyperbolic surface and let $\phi$ be a Laplacian eigenfunction having eigenvalue $-1/4-\tau^2$ with $\tau>0$. Let $N(\phi)$ be the set of nodal lines of $\phi$. For a fixed analytic curve $\gamma$ of finite length, we study the number of ... More

Non-local exchange effects in zigzag edge magnetism of neutral graphene nanoribbonsJan 28 2011We study the role of non-locality of exchange in a neutral zigzag graphene nanoribbon within the $\pi$-orbital unrestricted Hartree-Fock approximation. Within this theory we find that the magnetic features are further stabilized for both the intra-edge ... More

On the growth of the number of totally geodesic surfaces in some hyperbolic $3$-manifoldsJan 03 2018Let $d$ be a positive square-free integer $\equiv 3 \pmod{4}$ such that there is no invariant of the ideal class group $\mathbb{Q}\lbrack \sqrt{-d}\rbrack$ which is divisible by $4$. We prove an asymptotic formula for the number of immersed totally geodesic ... More

Core entropy and biaccessibility of quadratic polynomialsJan 20 2014For complex quadratic polynomials, the topology of the Julia set and the dynamics are understood from another perspective by considering the Hausdorff dimension of biaccessing angles and the core entropy: the topological entropy on the Hubbard tree. These ... More

Chiral spin states in the pyrochlore Heisenberg magnet: Fermionic mean-field theory and variational Monte Carlo calculationsJul 13 2008Nov 15 2008Fermionic mean-field theory and variational Monte Carlo calculations are employed to shed light on the possible uniform ground states of the Heisenberg model on the pyrochlore lattice. Among the various flux configurations, we find the chiral spin states ... More

Liouville type theorems for transversally harmonic and biharmonic mapsJul 13 2013Jun 29 2016We study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds

Critical Tunneling Currents in Quantum Hall Superfluids: Pseudospin-Transfer Torque TheoryJan 18 2010At total filling factor $\nu=1$ quantum Hall bilayers can have an ordered ground state with spontaneous interlayer phase coherence. The ordered state is signaled experimentally by dramatically enhanced interlayer tunnel conductances at low bias voltages; ... More

Coupling of phonons and spin waves in triangular antiferromagnetApr 26 2007Jul 02 2007We investigate the influence of the spin-phonon coupling in the triangular antiferromagnet where the coupling is of the exchange-striction type. The magnon dispersion is shown to be modified significantly at wave vector (2pi,0) and its symmetry-related ... More

On transversally harmonic maps of foliated Riemannian manifoldsSep 19 2011We study the transversally harmonic maps between foliated Riemannian manifolds. In particular, we prove that under some curvature conditions, any transversally harmonic map is transversally totally geodesic.

Spatially-indirect Exciton Condensate Phases in Double Bilayer GrapheneNov 19 2016We present a theory of spatially indirect exciton condensate states in systems composed of a pair of electrically isolated Bernal graphene bilayers. The ground state phase diagram in a two-dimensional displacement-field/inter-bilayer-bias space includes ... More

How to make a bilayer exciton condensate flowJan 24 2008Bose condensation is responsible for many of the most spectacular effects in physics because it can promote quantum behavior from the microscopic to the macroscopic world. Bose condensates can be distinguished by the condensing object; electron-electron ... More

On Time-Variant Distortions in Multicarrier Transmission with Application to Frequency Offsets and Phase NoiseSep 28 2005Phase noise and frequency offsets are due to their time-variant behavior one of the most limiting disturbances in practical OFDM designs and therefore intensively studied by many authors. In this paper we present a generalized framework for the prediction ... More

Two Phase Transitions for the Contact Process on Small WorldsJan 27 2005Jul 14 2005In our version of Watts and Strogatz's small world model, space is a d-dimensional torus in which each individual has in addition exactly one long-range neighbor chosen at random from the grid. This modification is natural if one thinks of a town where ... More

On reconstruction of dynamic permeability and tortuosity from data at distinct frequenciesNov 13 2013May 28 2014This article focuses on the mathematical problem of reconstructing dynamic permeability $K(\omega)$ of two-phase composites from data at different frequencies, utilizing the analytic structure of the Stieltjes function representation of $K(\omega)$ derived ... More