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Microwave-to-optical transduction using coupled piezoelectric and optomechanical resonatorsJul 10 2019The successes of superconducting quantum circuits at local manipulation of quantum information and photonics technology at long-distance transmission of the same have spurred interest in the development of quantum transducers for efficient, low-noise, ... More

Figures of merit for quantum transducersOct 04 2016Dec 09 2017Recent technical advances have sparked renewed interest in physical systems that couple simultaneously to different parts of the electromagnetic spectrum, thus enabling transduction of signals between vastly different frequencies at the level of single ... More

Three-dimensional theory of quantum memories based on Lambda-type atomic ensemblesMay 13 2011Oct 31 2011We develop a three-dimensional theory for quantum memories based on light storage in ensembles of Lambda-type atoms, where two long-lived atomic ground states are employed. We consider light storage in an ensemble of finite spatial extent and we show ... More

Engineering asymmetric steady-state Einstein-Podolsky-Rosen steering in macroscopic hybrid systemsJan 14 2019Generation of quantum correlations between separate objects is of significance both in fundamental physics and in quantum networks. One important challenge is to create the directional "spooky action-at-a-distance" effects that Schr\"odinger called "steering" ... More

Figures of merit for quantum transducersOct 04 2016Recent technical advances have sparked renewed interest in physical systems that couple simultaneously to different parts of the electromagnetic spectrum, thus enabling transduction of signals between vastly different frequencies at the level of single ... More

Quantum Feedback Cooling of a Mechanical Oscillator Using Variational Measurements:Tweaking Heisenberg's MicroscopeApr 18 2016Jun 03 2016We revisit the problem of preparing a mechanical oscillator in the vicinity of its quantum-mechanical ground state by means of feedback cooling based on continuous optical detection of the oscillator position. In the parameter regime relevant to ground ... More

High capacity spatial multimode quantum memories based on atomic ensemblesOct 31 2011Dec 04 2012We study spatial multimode quantum memories based on light storage in extended ensembles of Lambda-type atoms. We show that such quantum light-matter interfaces allow for highly efficient storage of many spatial modes. In particular, forward operating ... More

Electro-optomechanical equivalent circuits for quantum transductionOct 27 2017Jun 14 2018Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals ... More

Unconditional steady-state entanglement in macroscopic hybrid systems by coherent noise cancellationJan 08 2018Generation of entanglement between disparate physical objects is a key ingredient in the field of quantum technologies, since they can have different functionalities in a quantum network. Here we propose and analyze a generic approach to steady-state ... More

Unconditional steady-state entanglement in macroscopic hybrid systems by coherent noise cancellationJan 08 2018Sep 18 2018The generation of entanglement between disparate physical objects is a key ingredient in the field of quantum technologies, since they can have different functionalities in a quantum network. Here we propose and analyze a generic approach to steady-state ... More

Correlated photon dynamics in dissipative Rydberg mediaAug 22 2016Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging ... More

Correlated photon dynamics in dissipative Rydberg mediaAug 22 2016Jun 14 2018Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging ... More

Spacelike Singularities and String TheoryDec 08 1994Dec 21 1994An interpretation of spacelike singularities in string theory uses target space duality to relate the collapsing Schwarzschild geometry near the singularity to an inflationary cosmology in dual variables. An appealing picture thus results whereby gravitational ... More

Multiply quantized vortices in trapped Bose-Einstein condensatesMar 13 2001Oct 05 2001Vortex configurations in rotating Bose-Einstein condensed gases trapped in power-law and anharmonic potentials are studied. When the confining potential is steeper than harmonic in the plane perpendicular to the axis of rotation, vortices with quantum ... More

A Computational Non-Commutative Geometry Program for Disordered Topological InsulatorsNov 29 2016A computational program based on the principles of non-commutative geometry is presented. This includes the general algebraic principles, the algorithms themselves, the error estimates and the applications. The latter are mainly on the integer quantum ... More

Vector orthogonal polynomials with Bochner's propertySep 20 2016Classical orthogonal polynomial systems of Jacobi, Hermite, Laguerre and Bessel have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a classical theorem by Bochner they ... More

Cluster expansion and the boxdot conjectureAug 05 2013The boxdot conjecture asserts that every normal modal logic that faithfully interprets T by the well-known boxdot translation is in fact included in T. We confirm that the conjecture is true. More generally, we present a simple semantic condition on modal ... More

Rules with parameters in modal logic IMay 21 2013Apr 03 2015We study admissibility of inference rules and unification with parameters in transitive modal logics (extensions of K4), in particular we generalize various results on parameter-free admissibility and unification to the setting with parameters. Specifically, ... More

Blending margins: The modal logic K has nullary unification typeAug 31 2011Oct 11 2013We investigate properties of the formula $p \to \Box p$ in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins $\phi \to \Box\phi / \phi, \neg\phi$, and as a consequence, we obtain various negative results ... More

Intrinsic Differential Geometry and the Existence of Quasimeromorphic MappingsDec 31 2008We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.

The Data Singular and the Data Isotropic Loci for Affine ConesJul 10 2015The generic number of critical points of the Euclidean distance function from a data point to a variety is called the Euclidean distance degree. The two special loci of the data points where the number of critical points is smaller then the ED degree ... More

Recursive functions and existentially closed structuresOct 26 2017The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$ does not interpret ... More

Metric Ricci curvature for $PL$ manifoldsMar 07 2012We introduce a metric notion of Ricci curvature for $PL$ manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers Theorem, for surfaces as well as for a large class of higher dimensional manifolds.

A note on the substructural hierarchyJul 02 2015Oct 19 2015We prove that all axiomatic extensions of the full Lambek calculus with exchange can be axiomatized by formulas on the $\mathcal N_3$ level of the substructural hierarchy.

Rules with parameters in modal logic IIMay 30 2019We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers. We completely classify the complexity ... More

On the properties of the combinatorial Ricci flow for surfacesApr 11 2011Jun 07 2011We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for the combinatorial ... More

On a construction of Burago and ZalgallerSep 29 2010The purpose of this note is to scrutinize the proof of Burago and Zalgaller regarding the existence of $PL$ isometric embeddings of $PL$ compact surfaces into $\mathbb{R}^3$. We conclude that their proof does not admit a direct extension to higher dimensions. ... More

Fat Triangulations and Differential GeometryAug 17 2011We study the differential geometric consequences of our previous result on the existence of fat triangulations, in conjunction with a result of Cheeger, M\"{u}ller and Schrader, regarding the convergence of Lipschitz-Killing curvatures of piecewise-flat ... More

Curvature based triangulation of metric measure spacesJan 29 2010We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower ... More

Generalized Gould-Hopper polynomialsSep 20 2016Classical orthogonal polynomial systems of Jacobi, Hermite, Laguerre and Bessel have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are ... More

Induction rules in bounded arithmeticSep 27 2018We study variants of Buss's theories of bounded arithmetic axiomatized by induction schemes disallowing the use of parameters, and closely related induction inference rules. We put particular emphasis on $\hat\Pi^b_i$ induction schemes, which were so ... More

The minimal resolution of a cointerval edge ideal is multiplicativeSep 23 2016We show that the minimal resolution of the quotient of the polynomial algebra over a field by a cointerval edge ideal can be given the structure of a DG-algebra.

Resolutions of modules with initially linear syzygiesJun 09 2011Dec 16 2011We introduce the class of modules with initially linear syzygies, which includes ideals with linear quotients, and study their minimal resolutions. Using a contracting homotopy for the resolutions, we see that the minimal resolution of a matroidal monomial ... More

The Existence of Quasimeromorphic MappingsApr 30 2004We prove that a Kleinian group $G$ acting upon $\mathbb{H}^{n}$ admits a non-constant $G$-automorphic function, even if it has torsion elements, provided that the orders of the elliptic (torsion) elements are uniformly bounded. This is accomplished by ... More

The complexity of admissible rules of Łukasiewicz logicAug 31 2011Feb 28 2012We investigate the computational complexity of admissibility of inference rules in infinite-valued {\L}ukasiewicz propositional logic (\L). It was shown in [13] that admissibility in {\L} is checkable in PSPACE. We establish that this result is optimal, ... More

Existence of Weak Solutions for the Incompressible Euler EquationsFeb 17 2011Using a recent result of C. De Lellis and L. Sz\'{e}kelyhidi Jr. we show that, in the case of periodic boundary conditions and for dimension greater or equal 2, there exist infinitely many global weak solutions to the incompressible Euler equations with ... More

Two-weight commutator estimates: general multi-parameter frameworkJun 26 2019We provide an explicit technical framework for proving very general two-weight commutator estimates in arbitrary parameters. The aim is to both clarify existing literature, which often explicitly focuses on two parameters only, and to extend very recent ... More

M-theory and N=2 StringsOct 15 1997N=2 heterotic strings may provide a window into the physics of M-theory radically different than that found via the other supersymmetric string theories. In addition to their supersymmetric structure, these strings carry a four-dimensional self-dual structure, ... More

Scalar Gravitational Waves in the Effective Theory of GravityJun 29 2016As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective ... More

Functional Integration Over GeometriesFeb 17 1995The geometric construction of the functional integral over coset spaces ${\cal M}/{\cal G}$ is reviewed. The inner product on the cotangent space of infinitesimal deformations of $\cal M$ defines an invariant distance and volume form, or functional integration ... More

The homology of Heisenberg Lie algebras over fields of characteristic twoDec 05 2003The generating function of the Betti numbers of the Heisenberg Lie algebra over a field of characteristic 2 is calculated using discrete Morse theory.

Note on a Theorem of MunkresMar 02 2004Mar 14 2004We prove that given a $\mathcal{C^\infty}$ Riemannian manifold with boundary, any fat triangulation of the boundary can be extended to the whole manifold. We also show that this result holds extends to $\mathcal{C}^1$ manifolds, and that in dimensions ... More

Computational Many-Body Physics via $\mathcal M_{2^q}$ AlgebraJun 17 2019The many-body Hamiltonians and other fermionic physical observables are expressed in terms of fermionic creation and annihilation operators, which form the algebra of canonical anti-commutation relations (CAR). In this work we use a canonical isomorphism ... More

Isometric Embeddings in Imaging and Vision: Facts and FictionApr 29 2010May 11 2010We explore the practicability of Nash's Embedding Theorem in vision and imaging sciences. In particular, we investigate the relevance of a result of Burago and Zalgaller regarding the existence of isometric embeddings of polyhedral surfaces in $\mathbb{R}^3$ ... More

The Two-Dimensional Quantum Galilei GroupsApr 09 1998The Poisson structures on two-dimensional Galilei group, classified in the author previous paper are quantized. The dual quantum Galilei Lie algebras are found.

Lie Bialgebra Structures on Twodimensional Galilei Algebra and their Lie-Poisson CounterpartsApr 10 1997All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie-Poisson structures on Galilei group are found.

Geometrical Structures of M-TheoryAug 03 1996N=(2,1) heterotic string theory provides clues about hidden structure in M-theory related to string duality; in effect it geometrizes some aspects of duality. The program whereby one may deduce this hidden structure is outlined, together with the results ... More

Estimating Global Errors in Time SteppingMar 17 2015Apr 13 2016This study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical solution much like solving for the correction or Zadunaisky's procedure; however, the proposed approach ... More

d-orthogonal polynomials, Toda Lattice and Virasoro symmetriesApr 17 2019The subject of this paper is a connection between d-orthogonal polynomials and the Toda lattice hierarchy. In more details we consider some polynomial systems similar to Hermite polynomials, but satisfying $d+2$-term recurrence relation, $d >1$. Any such ... More

Galois connection for multiple-output operationsDec 13 2016Jul 29 2017It is a classical result from universal algebra that the notions of polymorphisms and invariants provide a Galois connection between suitably closed classes (clones) of finitary operations $f\colon B^n\to B$, and classes (coclones) of relations $r\subseteq ... More

Rigid models of Presburger arithmeticMar 15 2018Nov 08 2018We present a description of rigid models of Presburger arithmetic (i.e., Z-groups). In particular, we show that Presburger arithmetic has rigid models of all infinite cardinalities up to the continuum, but no larger.

Division by zeroApr 25 2016Sep 24 2016For any sufficiently strong theory of arithmetic, the set of Diophantine equations provably unsolvable in the theory is algorithmically undecidable, as a consequence of the MRDP theorem. In contrast, we show decidability of Diophantine equations provably ... More

Estimating Global Errors in Time SteppingMar 17 2015May 10 2017This study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical solution much like solving for the correction or Zadunaisky's procedure; however, the proposed approach ... More

Ramsey properties of randomly perturbed dense graphsFeb 06 2019We investigate Ramsey properties of a random graph model in which random edges are added to a given dense graph. Specifically, we determine lower and upper bounds on the function $p=p(n)$ that ensures that for any dense graph $G_n$ a.a.s. every 2-colouring ... More

Algebraic Morse theory and homological perturbation theoryNov 22 2013We show that the main result of algebraic Morse theory can be obtained as a consequence of the perturbation lemma of Brown and Gugenheim.

The ubiquity of conservative translationsAug 31 2011Jul 31 2012We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas ... More

Compilation as a Typed EDSL-to-EDSL TransformationMar 29 2016Apr 19 2018This article is about an implementation and compilation technique that is used in RAW-Feldspar which is a complete rewrite of the Feldspar embedded domain-specific language (EDSL) (Axelsson et al. 2010). Feldspar is high-level functional language that ... More

Vector orthogonal polynomials with Bochner's propertySep 20 2016Oct 01 2017Classical orthogonal polynomial systems of Jacobi, Hermite, Laguerre and Bessel have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a classical theorem by Bochner they ... More

A Simple Sampling Method for Metric Measure SpacesMar 20 2011We introduce a new, simple metric method of sampling metric measure spaces, based on a well-known "snowflakeing operator" and we show that, as a consequence of a classical result of Assouad, the sampling of doubling metric spaces is bilipschitz equivalent ... More

Back action evading quantum measurement of motion in a negative mass reference frameAug 11 2016Quantum mechanics dictates that a measurement without perturbation is not possible. A textbook example is the observation of the position of an object, which imposes a random back action perturbation on the momentum. This randomness translates with time ... More

Quantum back action evading measurement of motion in a negative mass reference frameAug 11 2016Apr 12 2017Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random back action perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty ... More

Photon propagation through dissipative Rydberg media at large input ratesJul 19 2018Aug 01 2018We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency (EIT). Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions ... More

Compilation as a Typed EDSL-to-EDSL TransformationMar 29 2016Apr 05 2016This article is about an implementation and compilation technique that is used in RAW-Feldspar which is a complete rewrite of the Feldspar embedded domain-specific language (EDSL) (Axelsson et al. 2010). Feldspar is high-level functional language that ... More

Two weight $L^{p}$-inequalities for dyadic shifts and the dyadic square functionApr 22 2015We consider two weight $L^{p}\to L^{q}$-inequalities for dyadic shifts and the dyadic square function with general exponents $1<p,q<\infty$. It is shown that if a so-called quadratic $\mathscr{A}_{p,q}$-condition related to the measures holds, then a ... More

The Light Cone in String TheoryApr 08 1993Apr 12 1993The causal boundary of string propagation -- defined as the hypersurface in loop space bordering the timelike(spacelike) domains in which two successive measurements of the string field do(do not) interfere with one another -- is argued to be $0=\int ... More

An Introduction to 2d Gravity and Solvable String ModelsDec 09 1991Continuum and discrete approaches to 2d gravity coupled to $c<1$ matter are reviewed.

Reproducible Research: Best Practices and Potential MisuseMay 02 2019The scientific world is becoming more open to the public and fellow researchers. Open access publishing is becoming accepted, even if some publishers are resisting. The next step is the open code and data paradigm, which was briefly discussed in the "From ... More

The uniform distribution of sequences generated by iterated polynomialsSep 20 2017Assume that $m,s\in\mathbb N$, $m>1$, while $f$ is a polynomial with integer coefficients, $\text{deg}~f>1$, $f^{(i)}$ is the $i$th iteration of the polynomial $f$, $\kappa_n$ has a discrete uniform distribution on the set $\{0,1,\ldots,m^n - 1\}$. We ... More

Dust clouds and plasmoids in Saturn's Magnetosphere as seen with four Cassini instrumentsFeb 06 2017We revisit the evidence for a "dust cloud" observed by the Cassini spacecraft at Saturn in 2006. The data of four instruments are simultaneously compared to interpret the signatures of a coherent swarm of dust that would have remained near the equatorial ... More

Scalar Gravitational Waves in the Effective Theory of GravityJun 29 2016Oct 03 2018As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective ... More

Mott insulator dynamicsMay 06 2011Jun 13 2011The hydrodynamics of a lattice Bose gas in a time-dependent external potential is studied in a mean-field approximation. The conditions under which a Mott insulating region can melt, and the local density adjust to the new potential, are determined. In ... More

Ueber die Geometrie der alten AegypterJun 05 2008Lecture given before the Royal Academy Vienna that summarizes the state of knowledge about the mathematics of the ancient Egyptians, up to 1884. Contains all relevant references to classical Greek texts, and the 'latest' archeology results. Later published ... More

Process Description of COM Object Life CycleDec 20 2009The objective of this article is to provide for the reader a basic description of all the steps involved in the COM object life-cycle process. COM is a software technology and process performer. The first section briefly introduces the Component Object ... More

The edge spectrum of Chern insulators with rough boundariesSep 15 2008Feb 04 2009Chern insulators are periodic band insulators with the property that their projector onto the occupied bands have non-zero Chern number. Chern insulator with a homogeneous boundary display continuum spectrum that fills the entire insulating gap. The local ... More

On the Dipole Swing and the Search for Frame Independence in the Dipole ModelSep 10 2007Nov 06 2007Small-x evolution in QCD is conveniently described by Mueller's dipole model which, however, does not include saturation effects in a way consistent with boost invariance. In this paper we first show that the recently studied zero and one dimensional ... More

Saturation In Deep Inelastic ScatteringJun 14 2004The solution to the BFKL equation grows like a power of center of mass energy, s, violating unitarity conditions at high energies. The growth of the cross section can be tamed by taking into account multiple pomeron exchanges. This is known as saturation ... More

Period-doubled breathing in trapped Bose-Einstein condensatesMay 14 2004The response of a trapped Bose-Einstein condensed gas to a periodic driving force is studied theoretically in the framework of the nonlinear Gross-Pitaevskii equation. The monopole mode is driven by periodical modulation of the frequency of the isotropic ... More

Strictly nilpotent elements and bispectral operators in the Weyl algebraJun 18 2002In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of ... More

The Non-Commutative Geometry of the Complex Classes of Topological InsulatorsFeb 28 2014Jun 13 2014Alain Connes' Non-Commutative Geometry program [Connes 1994] has been recently carried out [Prodan, Leung, Bellissard 2013, Prodan, Schulz-Baldes 2014] for the entire A- and AIII-symmetry classes of topological insulators, in the regime of strong disorder ... More

General Belief MeasuresFeb 27 2013Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of firstorder ... More

In Love With a Robot: the Dawn of Machine-To-Machine MarketingFeb 18 2013Aug 03 2016The article looks at mass market artificial intelligence tools in the context of their ever-growing sophistication, availability and market penetration. The subject is especially relevant today for these exact reasons - if a few years ago AI was the subject ... More

The Existence of Quasimeromorphic Mappings in Dimension 3Nov 16 2003Mar 03 2004We prove that a Kleinian group $G$ acting upon $\mathbb{H}^{3}$ admits a non-constant $G$-automorphic function, even if it has torsion elements, provided that the orders of the elliptic (i.e torsion) elements are uniformly bounded. This is accomplished ... More

L^{p}(μ)-L^{q}(ν) characterization for well localized operatorsDec 05 2014Jan 26 2016We consider a two weight $L^{p}(\mu) \to L^{q}(\nu)$-inequality for well localized operators as defined and studied by F. Nazarov, S. Treil and A. Volberg when $p=q=2$. A counterexample of F. Nazarov shows that the direct analogue of these results fails ... More

Open induction in a bounded arithmetic for TC^0Apr 29 2014May 28 2014The elementary arithmetic operations $+,\cdot,\le$ on integers are well-known to be computable in the weak complexity class $\mathrm{TC}^0$, and it is a basic question what properties of these operations can be proved using only $\mathrm{TC}^0$-computable ... More

Sequence encoding without inductionJan 27 2012We show that the universally axiomatized, induction-free theory PA^- is a sequential theory in the sense of Pudl\'ak [5], in contrast to the closely related Robinson's arithmetic.

Two weight $L^{p}$-inequalities for dyadic shifts and the dyadic square functionApr 22 2015Jan 24 2017We consider two weight $L^{p}\to L^{q}$-inequalities for dyadic shifts and the dyadic square function with general exponents $1<p,q<\infty$. It is shown that if a so-called quadratic $\mathscr{A}_{p,q}$-condition related to the measures holds, then a ... More

$d$-Orthogonal Analogs of Classical Orthogonal PolynomialsSep 20 2016Jun 26 2018Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are the only ... More

N=2 Supersymmetric Integrable Hierarchies: Additional Symmetries and Darboux-Backlund SolutionsMar 29 2001Aug 06 2001We study additional non-isospectral symmetries of constrained (reduced) N=2 supersymmetric KP hierarchies of integrable ``soliton''-like evolution equations. These symmetries are shown to form an infinite-dimensional non-Abelian superloop superalgebra. ... More

Hydrodynamic Approach to Vortex Lifetime in Trapped Bose CondensatesOct 15 1999Jan 04 2000We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schroedinger Lagrangian, we obtain the effective potential ... More

$\bf W_\infty$ Gravity - a Geometric ApproachJul 14 1992A brief review is given of an adaptation of the coadjoint orbit method appropriate for study of models with infinite-dimensional symmetry groups. It is illustrated on several examples, including derivation of the WZNW action of induced $D=2\,$ $(N,0)\,$ ... More

Probing Matrix Black HolesJan 12 1998Black holes in matrix theory may consist of interacting clusters (correlated domains) which saturate the uncertainty principle. We show that this assumption qualitatively accounts for the thermodynamic properties of both charged and neutral black holes, ... More

Renormalization of active scalar equationsMay 15 2018We consider transport equations with an incompressible transporting vector field. Whereas smooth solutions of such equations conserve every $L^p$ norm simply by the chain rule, the question arises how regular a weak solution needs to be to guarantee this ... More

A New Look at Cell-Free Massive MIMO: Making It Practical With Dynamic CooperationJun 26 2019This paper takes a new look at Cell-free Massive MIMO (multiple-input multiple-output) through the lens of the dynamic cooperation cluster framework from the Network MIMO literature. The purpose is to identify and address scalability issues that appear ... More

Aspects of the $L^{2}$-Sobolev theory of the $\bar{\partial}$-Neumann problemJan 06 2006The $\bar{\partial}$-Neumann problem is the fundamental boundary value problem in several complex variables. It features an elliptic operator coupled with non-coercive boundary conditions. The problem is globally regular on many, but not all, pseudoconvex ... More

Geometric conditions which imply compactness of the $\bar{\partial}$-Neumann operatorSep 11 2003For smooth bounded pseudoconvex domains in $mathbb{C}^{2}$, we provide geometric conditions on (the points of infinite type in) the boundary which imply compactness of the $\bar{\partial}$-Neumann operator. It is noteworthy that the proof of compactness ... More

Emergent interactions in conditioned processes: a route to smart matter?Jul 02 2019We propose a method to derive `smart' active-matter interactions, such as collision avoidance, from first principles. Begin from a system with naive interactions, for example hardcore exclusion, and identify the natural fluctuations which by serendipity ... More

U(1) Charges and Moduli in the D1-D5 SystemMay 10 1999Jun 18 1999The decoupling limit of the D1-D5 system compactified on T^4\times S^1 has a rich spectrum of U(1) charged excitations. Even though these states are not BPS in the limit, BPS considerations determine the mass and the semiclassical entropy for a given ... More

The existence of thick triangulations -- an "elementary" proofDec 02 2008We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary differential ... More

Top dense hyperbolic ball packings and coverings for complete Coxeter orthoscheme groupsDec 14 2016In $n$-dimensional hyperbolic space $\mathbf{H}^n$ $(n\ge2)$ there are $3$-types of spheres (balls): the sphere, horosphere and hypersphere. If $n=2,3$ we know an universal upper bound of the ball packing densities, where each ball volume is related to ... More

Towards the Theory of Non--Abelian Tensor Fields IIJun 03 2005We go on with the definition of the theory of the non--Abelian two--tensor fields and find the gauge transformation rules and curvature tensor for them. To define the theory we use the surface {\it exponent} proposed in hep--th/0503234. We derive the ... More