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Polynomial-time word problemsAug 23 2006We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these results follow from ... More

Sphere recognition lies in NPJul 05 2004We prove that the three-sphere recognition problem lies in the complexity class NP. Our work relies on Thompson's original proof that the problem is decidable [Math. Res. Let., 1994], Casson's version of her algorithm, and recent results of Agol, Hass, ... More

The compression body graph has infinite diameterMar 16 2018We show that the compression body graph has infinite diameter, and that every subgroup in the Johnson filtration of the mapping class group contains elements which act loxodromically on the compression body graph. Our methods give an alternate proof of ... More

Computing Triangulations of Mapping Tori of Surface HomeomorphismsDec 01 2000Mar 19 2001We present the mathematical background of a software package that computes triangulations of mapping tori of surface homeomorphisms, suitable for Jeff Weeks's program SnapPea. It consists of two programs. jmt computes triangulations and prints them in ... More

Triple gearApr 25 2013A relatively common sight in graphic designs is a planar arrangement of three gears in contact. However, since neighboring gears must rotate in opposite directions, none of the gears can move. We give a non-planar, and non-frozen, arrangement of three ... More

Distance and bridge positionAug 29 2003J. Hempel's definition of the distance of a Heegaard surface generalizes to a complexity for a knot which is in bridge position with respect to a Heegaard surface. Our main result is that the distance of a knot in bridge position is bounded above by twice ... More

Distances of Heegaard splittingsJun 03 2003Dec 25 2004J Hempel [Topology, 2001] showed that the set of distances of the Heegaard splittings (S,V, h^n(V)) is unbounded, as long as the stable and unstable laminations of h avoid the closure of V in PML(S). Here h is a pseudo-Anosov homeomorphism of a surface ... More

The curves not carriedOct 17 2014Sep 21 2015Suppose $\tau$ is a train track on a surface $S$. Let $C(\tau)$ be the set of isotopy classes of simple closed curves carried by $\tau$. Masur and Minsky [2004] prove $C(\tau)$ is quasi-convex inside the curve complex $C(S)$. We prove the complement, ... More

Puzzling the 120-cellOct 14 2013Nov 20 2015We introduce Quintessence: a family of burr puzzles based on the geometry and combinatorics of the 120-cell. We discuss the regular polytopes, their symmetries, the dodecahedron as an important special case, the three-sphere, and the quaternions. We then ... More

On the conjugacy problem in braid groups: Garside theory and subsurfacesJul 04 2018Jul 05 2018Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed ... More

Effective distance between nested Margulis tubesJan 16 2018Aug 16 2018We give sharp, effective bounds on the distance between tori of fixed injectivity radius inside a Margulis tube in a hyperbolic 3-manifold.

Compressed decision problems in hyperbolic groupsAug 21 2018Sep 21 2018We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight line programs defined over a finite ... More

On train track splitting sequencesApr 26 2010We show that the subsurface projection of a train track splitting sequence is an unparameterized quasi-geodesic in the curve complex of the subsurface. For the proof we introduce induced tracks, efficient position, and wide curves. This result is an important ... More

The disjoint curve propertyJan 28 2004A Heegaard splitting of a closed, orientable three-manifold satisfies the disjoint curve property if the splitting surface contains an essential simple closed curve and each handlebody contains an essential disk disjoint from this curve [Thompson, 1999]. ... More

Waldhausen's TheoremApr 01 2009This note is an exposition of Waldhausen's proof of Waldhausen's Theorem: the three-sphere has a single Heegaard splitting, up to isotopy, in every genus. As a necessary step we also give a sketch of the Reidemeister-Singer Theorem.

On the tree-width of knot diagramsSep 06 2018We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We use this to ... More

The end of the curve complexAug 21 2006Suppose that S is a surface of genus two or more, with exactly one boundary component. Then the curve complex of S has one end.

Strongly irreducible surface automorphismsAug 14 2002A surface automorphism is strongly irreducible if every essential simple closed curve in the surface has nontrivial geometric intersection with its image. We show that a three-manifold admits only finitely many inequivalent surface bundle structures with ... More

The Pants Complex Has Only One EndDec 19 2003The authors prove that for a closed surface of genus at least 3, the graph of pants decompositions has only one end.

Canonical triangulations of Dehn fillingsMay 09 2008Every cusped, finite-volume hyperbolic three-manifold has a canonical decomposition into ideal polyhedra. We study the canonical decomposition of the hyperbolic manifold obtained by filling some (but not all) of the cusps with solid tori: in a broad range ... More

Sculptures in S^3Apr 23 2012May 17 2012We construct a number of sculptures, each based on a geometric design native to the three-dimensional sphere. Using stereographic projection we transfer the design from the three-sphere to ordinary Euclidean space. All of the sculptures are then fabricated ... More

Dehn twists have rootsOct 28 2008We construct nontrivial roots of Dehn twists about nonseparating curves.

Cusp geometry of fibered 3-manifoldsAug 29 2011Apr 17 2013Let F be a surface and suppose that \phi: F -> F is a pseudo-Anosov homeomorphism fixing a puncture p of F. The mapping torus M = M_\phi is hyperbolic and contains a maximal cusp C about the puncture p. We show that the area (and height) of the cusp torus ... More

Squares that Look Round: Transforming Spherical ImagesMay 04 2016We propose M\"obius transformations as the natural rotation and scaling tools for editing spherical images. As an application we produce spherical Droste images. We obtain other self-similar visual effects using rational functions, elliptic functions, ... More

The geometry of the disk complexOct 15 2010We give a distance estimate for the metric on the disk complex and show that it is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting, up to an error depending only ... More

Covers and the curve complexJan 25 2007Jun 28 2007We provide the first non-trivial examples of quasi-isometric embeddings between curve complexes. These are induced either by puncturing a closed surface or via orbifold coverings. As a corollary, we give new quasi-isometric embeddings between mapping ... More

Thin Position for TanglesMar 15 2002If a tangle, K, in the 3-ball has no planar, meridional, essential surfaces in its exterior then thin position for K has no thin levels.

Automorphisms of the disk complexOct 11 2009We show that the automorphism group of the disk complex is isomorphic to the handlebody group. Using this, we prove that the outer automorphism group of the handlebody group is trivial.

Essential loops in taut ideal triangulationsFeb 08 2019In this note we combinatorialise a technique of Novikov. We use this to prove that, in a three-manifold equipped with a taut ideal triangulation, any vertical or normal loop is essential in the fundamental group.

Surface bundles versus Heegaard splittingsDec 06 2002This paper studies Heegaard splittings of surface bundles via the curve complex of the fibre. The translation distance of the monodromy is the smallest distance it moves any vertex of the curve complex. We prove that the translation distance is bounded ... More

Curve complexes are rigidOct 19 2007May 12 2010Any quasi-isometry of the complex of curves is bounded distance from a simplicial automorphism. As a consequence, the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.

Slow north-south dynamics on $\mathcal{PML}$Dec 02 2015May 11 2016We consider the action of a pseudo-Anosov mapping class on $\mathcal{PML}(S)$. This action has north-south dynamics and so, under iteration, laminations converge exponentially to the stable lamination. We study the rate of this convergence and give examples ... More

Connectivity of the space of ending laminationsJan 20 2008May 09 2009We prove that for any closed surface of genus at least four, and any punctured surface of genus at least two, the space of ending laminations is connected. A theorem of E. Klarreich implies that this space is homeomorphic to the Gromov boundary of the ... More

Hyperbolic spaces in Teichmüller spacesOct 29 2011Feb 05 2013We prove, for any n, that there is a closed connected orientable surface S so that the hyperbolic space H^n almost-isometrically embeds into the Teichm\"uller space of S, with quasi-convex image lying in the thick part. As a consequence, H^n quasi-isometrically ... More

Sweepouts of amalgamated 3-manifoldsJul 25 2005Feb 26 2009We show that if two 3-manifolds with toroidal boundary are glued via a `sufficiently complicated' map then every Heegaard splitting of the resulting 3-manifold is weakly reducible. Additionally, if Z is a manifold obtained by gluing X and Y, two connected ... More

Geodesic ideal triangulations exist virtuallyJan 16 2007It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover ... More

The universal Cannon--Thurston maps and the boundary of the curve complexAug 26 2008Feb 17 2009In genus two and higher, the fundamental group of a closed surface acts naturally on the curve complex of the surface with one puncture. Combining ideas from previous work of Kent--Leininger--Schleimer and Mitra, we construct a universal Cannon--Thurston ... More

Uniform hyperbolicity of the curve graph via surgery sequencesFeb 22 2013We prove that the curve graph $\calC^{(1)}(S)$ is Gromov-hyperbolic with a constant of hyperbolicity independent of the surface $S$. The proof is based on the proof of hyperbolicity of the free splitting complex by Handel and Mosher, as interpreted by ... More

High distance knotsJul 11 2006Aug 15 2007We construct knots in S^3 with Heegaard splittings of arbitrarily high distance, in any genus. As an application, for any positive integers t and b we find a tunnel number t knot in the three-sphere which has no (t,b)-decomposition.

Heegaard splittings of the form H + nKJul 30 2004Suppose that a three-manifold M contains infinitely many distinct strongly irreducible Heegaard splittings H + nK, obtained by Haken summing the surface H with n copies of the surface K. We show that K is incompressible. All known examples, of manifolds ... More

Trees and mapping class groupsNov 08 2006Sep 10 2007There is a forgetful map from the mapping class group of a punctured surface to that of the surface with one fewer puncture. We prove that finitely generated purely pseudo-Anosov subgroups of the kernel of this map are convex cocompact in the sense of ... More

Spin Waves as Metric in a Kinetic Space-TimeApr 17 2003Nov 29 20041) A wave equation is derived from the kinetic equations governing media with rotational as well as translational degrees of freedom. In this wave the fluctuating quantity is a vector, the bulk spin. The transmission is similar to compressive waves but ... More

Is Complex Probability Theory Consistent with Bell's Theorem?Jun 28 1994Sep 15 1995Bayesian complex probability theory is shown to be consistent with Bell's theorem and with other recent limitations on local realistic theories which agree with the predictions of quantum mechanics.

Minimising the time to reach a target and returnJul 11 2012Jan 09 2013Motivated by a problem in simulated tempering (a form of Markov chain Monte Carlo), we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to 1 and then return. ... More

Qualitative changes in spike-based neural coding and synchronization at the saddle-node loop bifurcationJun 23 2016Nov 12 2016Information processing in the brain crucially depends on encoding properties of single neurons, with particular relevance of the spike-generation mechanism. The latter hinges upon the bifurcation type at the transition point between resting state and ... More

Markov chains conditioned never to wait too long at the originJun 21 2009Motivated by Feller's coin-tossing problem, we consider the problem of conditioning an irreducible Markov chain never to wait too long at 0. Denoting by $\tau$ the first time that the chain, $X$, waits for at least one unit of time at the origin, we consider ... More

Physics with exotic probability theoryOct 29 2001Dec 06 2001Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities. These copies, ... More

Quantum Mechanics as an Exotic Probability TheorySep 11 1995Recent results suggest that quantum mechanical phenomena may be interpreted as a failure of standard probability theory and may be described by a Bayesian complex probability theory.

Saddle-node loop bifurcations ubiquitously occur in conductance-based model neurons and promote spike-based coding and synchronizationJun 23 2016Information processing in the brain crucially depends on coding properties of single neurons shaped by their intrinsic dynamics. Our theoretical study shows that neuronal excitability, spike-based coding, and synchronization change drastically around ... More

QCD, Symmetry Breaking and the Random LatticeFeb 15 2006According to the Nielsen-Ninomiya No-Go theorem, the doubling of fermions on the lattice cannot be suppressed in a chiral theory. Whereas Wilson and staggered fermions suppress doublers with explicit breaking of chiral symmetry, the random lattice does ... More

The Formation of Very Narrow Waist Bipolar Planetary NebulaeNov 09 1999We discuss the interaction of the slow wind blown by an asymptotic giant branch (AGB) star with a collimated fast wind (CFW) blown by its main sequence or white dwarf companion, at orbital separations in the range of several AU to about 200 AU. The CFW ... More

Broken Symmetry and Nonequilibrium Superfluid 3HeOct 18 1999Oct 26 1999These lecture notes provide an introduction to non-equilibrium superfluid 3He, with applications to high-frequency excitations, including aspects of symmetry breaking in 3He and its effects on collective mode dynamics. In 1957 Landau predicted that liquid ... More

An asymptotic decrease of (m_p/m_e) with cosmological time, from a decreasing, small effective vacuum expectation value moving from a potential maximum in the early universeJun 09 2006Sep 21 2006The empirical, possible small variation downward by about 10^-5, of the ratio of the proton mass to the electron mass, over a characteristic time interval estimated here to be about a billion years, is related to the decrease with time of a small, effective ... More

Very high-energy neutrinos from slowly decaying, massive dark matter, as a source of explosive energy for gamma-ray burstsJun 19 2002We consider a speculative model for gamma-ray bursts (GRB), which predicts that the total kinetic energy in the ejected matter is less than the total energy in the gamma rays. There is also secondary energy in X-rays, which are emitted contemporaneously ... More

Effects of a dynamical role for exchanged quarks and nuclear gluons in nuclei: multinucleon correlations in deep-inelastic lepton scatteringFeb 23 2000Jun 14 2000It is shown that new data from the HERMES collaboration, as well as all of the earlier improved data from experiments concerning the EMC effect and shadowing in deep-inelastic scattering of leptons from nuclei, provide strong evidence for an explicit ... More

Aggregate and mixed-order Markov models for statistical language processingJun 09 1997We consider the use of language models whose size and accuracy are intermediate between different order n-gram models. Two types of models are studied in particular. Aggregate Markov models are class-based bigram models in which the mapping from words ... More

Unusual behavior in pbar-p and l-p collisions involving high energy and momenum transfer: Z0(W+-) and scalar jetsMay 13 1997May 21 1997We show that the axial-vector coupling of Z0(W+-) to quarks, when acting together with the emission of a hypothetical spin-zero jet-generating quantum coupled to quarks results in an unusual behavior in certain processes, at high energy and momentum transfer. ... More

On representing claims for coherent risk measuresAug 03 2007We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined by Delbaen. In a similar way ... More

A vertex-structure model for new direct CP-violating effects in Bbar^0(B^0) -> phi K_S and in B^-+ -> pi^-+ eta' (eta)May 08 2006Jul 03 2006We consider effective Lagrangian models of CP-violating vertex structure in which a $b -> uW$ vertex, proportional to $s_{13}e^{-i\delta_{13}}$ with $s_{13}$ very small (milliweak interaction) and $\delta_{13}$ large, is dynamically generated. A consequent, ... More

Cyclonic spectra, cyclotomic spectra, and a conjecture of KaledinFeb 05 2016With an explicit, algebraic indexing $(2,1)$-category, we develop an efficient homotopy theory of cyclonic objects: circle-equivariant objects relative to the family of finite subgroups. We construct an $\infty$-category of cyclotomic spectra as the homotopy ... More

On the informational structure in optimal dynamic stochastic controlMar 09 2015Sep 20 2016We formulate a very general framework for optimal dynamic stochastic control problems which allows for a control-dependent informational structure. The issue of informational consistency is investigated. Bellman's principle is formulated and proved. In ... More

The Kerr MetricOct 08 2014Jan 15 2015This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness ... More

Irrotational Binary Neutron Stars in Quasiequilibrium in General RelativityMar 25 1998May 04 1998Neutron stars in binary orbit emit gravitational waves and spiral slowly together. During this inspiral, they are expected to have very little vorticity. It is in fact a good approximation to treat the system as having zero vorticity, i.e., as irrotational. ... More

The Dynamic Space of General Relativity in Second AtomizationMay 26 2004Aug 09 2005The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping manifests itself ... More

Aberration of the Cosmic Microwave BackgroundJan 24 2006The motion of the solar system barycenter with respect to the cosmic microwave background (CMB) induces a very large apparent dipole component into the CMB brightness map at the 3 mK level. In this Letter we discuss another kinematic effect of our motion ... More

Bondi-Hoyle-Lyttleton Accretion Model for Low-luminosity X-ray Sources in Globular ClustersSep 13 2000Nov 23 2000We present a new model for low-luminosity X-ray sources in globular clusters, with L_x < 10^34 erg/s. The model we propose is that of a single neutron star accreting from cluster gas that has accumulated as a natural product of stellar evolution. An analytic ... More

X-rays from the Globular Cluster G1: Intermediate Mass Black Hole or Low Mass X-ray Binary?May 02 2006The globular cluster G1 (Mayall II) in M31 is the most massive (~10^7 M_sun) stellar cluster in the Local Group, and it has the highest central velocity dispersion (~28 km/s). It has been claimed to host a central ~20,000 M_sun black hole, but these claims ... More

X-ray and Optical Eclipses in ULXs as Possible Indicators of Black Hole MassSep 20 2005Ultraluminous X-ray sources (ULXs) with 10^39 < L_x < 10^41 erg/s have been discovered in great numbers in external galaxies with ROSAT, Chandra, and XMM-Newton. The central question regarding this important class of sources is whether they represent ... More

Departure from Axisymmetry in Planetary NebulaeFeb 12 2001Many planetary nebulae (PNe) exhibit distinctly non-axisymmetric structure in either (i) the shape of the nebula, or (ii) in the off-centered position of the illuminating star. By examining a large number of well resolved images of PNe we estimate that ... More

Preliminary Study of B_K on 2+1 flavor DWF lattices from QCDOCFeb 15 2006I present some preliminary calculations of B_K on 2+1 flavor domain-wall fermion lattices from the QCDOC, including a set of 16^3x32x8 lattices with a^{-1} near 1.6 GeV. Although a final result awaits the production of a much longer run, I will compare ... More

Bayesian estimate of the effect of B^0B^0bar mixing measurements on the CKM matrix elementsJul 30 1996A method employing Bayesian statistics is used to incorporate recent experimental results on BdBdbar and BsBsbar mixing into a measurement of the Cabibbo-Kobayashi-Maskawa matrix elements. The neutral B meson mixing results yield a slight improvement ... More

Random orderings of the integers and card shufflingAug 19 2005In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders ... More

Source Separation and Clustering of Phase-Locked Subspaces: Derivations and ProofsJun 13 2011Due to space limitations, our submission "Source Separation and Clustering of Phase-Locked Subspaces", accepted for publication on the IEEE Transactions on Neural Networks in 2011, presented some results without proof. Those proofs are provided in this ... More

Surface States, Edge Currents and the Angular Momentum of Chiral p-wave SuperfluidsSep 25 2012The spectra of fermionic excitations, pairing correlations and edge currents confined near the boundary of a chiral p-wave superfluid are calculated to leading order in $\hbar/p_f\xi$. Results for the energy- and momentum-resolved spectral functions, ... More

On the density of properly maximal claims in financial markets with transaction costsFeb 26 2006May 02 2007We consider trading in a financial market with proportional transaction costs. In the frictionless case, claims are maximal if and only if they are priced by a consistent price process--the equivalent of an equivalent martingale measure. This result fails ... More

Sound Propagation and Transport Properties of Liquid $^3$He in AerogelOct 01 1997Superfluid $^3$He confined in aerogel offers a unique chance to study the effects of a short mean free path on the properties of a well defined superfluid Fermi liquid with anisotropic pairing. Transport coefficients and collective excitations, e.g. longitudinal ... More

Dynamics of spin transport in voltage-biased Josephson junctionsMar 23 2006Jun 15 2007We investigate spin transport in voltage-biased spin-active Josephson junctions. The interplay of spin filtering, spin mixing, and multiple Andreev reflection leads to nonlinear voltage dependence of the dc and ac spin current. We compute the voltage ... More

Active Switching: Packet Steering Flow AnnotationsMar 27 2014Our previous experience building systems for middlebox chain composition and scaling in software-defined networks has revealed that existing mechanisms of flow annotation commonly do not survive middlebox-traversals, or suffer from extreme identifier ... More

Theory of Heat Transport of Normal Liquid 3He in AerogelMar 08 2010The introduction of liquid 3He into silica aerogel provides us a with model system in which to study the effects of disorder on the properties of a strongly correlated Fermi liquid. The transport of heat, mass and spin exhibits cross-over behavior from ... More

Thermal Conductivity of Superfluid $^3$He in AerogelDec 10 2002We report theoretical calculations of the thermal conductivity of $^3$He impregnated into high-porosity aerogel and compare these results with available experimental data.

Magnetic Susceptibility of the Balian-Werthamer Phase of 3He in AerogelJul 21 2001The equilibrium superfluid phase of 3He impregnated into high-porosity silica aerogels appears to be a non-equal-spin-pairing state in zero field at all pressures, which is generally assumed to be the Balian-Werthamer (BW) phase modified by the depairing ... More

Majorana Excitations, Spin- and Mass Currents on the Surface of Topological Superfluid $^3$He-BAug 20 2013Nov 17 2013The B-phase of superfluid $^3$He is a 3D time-reversal invariant (TRI) topological superfluid with an isotropic energy gap separating the ground-state and bulk continuum states. We report calculations of surface spectrum, spin- and mass current densities ... More

Coupling and tracking of regime-switching martingalesSep 02 2012Apr 06 2015This paper describes two explicit couplings of standard Brownian motions $B$ and $V$, which naturally extend the mirror coupling and the synchronous coupling and respectively maximise and minimise (uniformly over all time horizons) the coupling time and ... More

Spectrum of third sound cavity modes on superfluid $^3$He filmsSep 26 2003We report theoretical calculations of the spectrum of third sound modes for a cylindrically symmetric film of superfluid $^3$He, and compare these results with experimental data for the mode frequencies and amplitude spectrum of surface waves of superfluid ... More

Theory of Nonequilibrium Spin Transport and Spin Transfer Torque in Superconducting-Ferromagnetic NanostructuresFeb 15 2007Sep 05 2008Spin transport currents and the spin-transfer torques in voltage-biased superconducting-ferromagnetic nanopillars (SFNFS point contacts) are computed. We develop and implement an algorithm based on the Ricatti formulation of the quasiclassical theory ... More

Game-theoretic approach to risk-sensitive benchmarked asset managementMar 05 2015In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who ... More

The NMSSM and String TheoryDec 02 2009Dec 11 2009We study the possibility of constructing the NMSSM from the heterotic string. String derived NMSSMs are much more rare than MSSMs due to the extra requirement that there exist a light singlet which couples to the Higgs pairs. They share the common feature ... More

A Search for Radio Transients in VLA Archival Images of the 3C 286 FieldDec 30 2010We present a search for radio transients in the field of the bright radio source 3C 286 using archival observations from the Very Large Array. These observations span 23 years and include 1852 epochs at 1.4 GHz in the C and D configurations. We find no ... More

Electron Bubbles in Superfluid $^3$He-A: Exploring the Quasiparticle-Ion InteractionAug 04 2016When an electron is forced into liquid $^3$He it forms an "electron bubble", a heavy ion with radius, $R\simeq 1.5$ nm, and mass, $M\simeq 100\,m_3$, where $m_3$ is the mass of a $^3$He atom. These negative ions have proven to be powerful local probes ... More

Reply to ``Comment on `Magnetic field effects on neutron diffraction in the antiferromagnetic phase of $UPt_3$'''Feb 27 2002Fak, van Dijk and Wills (FDW) question our interpretation of elastic neutron-scattering experiments in the antiferromagnetic phase of UPt_3. They state that our analysis is incorrect because we average over magnetic structures that are disallowed by symmetry. ... More

Formation and maintenance of nitrogen fixing cell patterns in filamentous cyanobacteriaOct 07 2016Cyanobacteria forming one-dimensional filaments are paradigmatic model organisms of the transition between unicellular and multicellular living forms. Under nitrogen limiting conditions, in filaments of the genus Anabaena, some cells differentiate into ... More

Impurity Effects on the A_1-A_2 Splitting of Superfluid 3He in AerogelJun 04 2003When liquid 3He is impregnated into silica aerogel a solid-like layer of 3He atoms coats the silica structure. The surface 3He is in fast exchange with the liquid on NMR timescales. The exchange coupling of liquid 3He quasiparticles with the localized ... More

Theoretical Considerations on the Properties of Accreting Millisecond PulsarsApr 22 2003We examine a number of evolutionary scenarios for the recently discovered class of accretion-powered millisecond X-ray pulsars in ultracompact binaries, including XTE J0929-314 and XTE J1751-305, with orbital periods of 43.6 and 42.4 minutes, respectively. ... More

Unconventional Pairing in Heavy Fermion MetalsOct 05 1996The Fermi-liquid theory of superconductivity is applicable to a broad range of systems that are candidates for unconventional pairing. Fundamental differences between unconventional and conventional anisotropic superconductors are illustrated by the unique ... More

Magnetic Field Effects on Neutron Diffraction in the Antiferromagnetic Phase of $UPt_3$Apr 14 2000We discuss possible magnetic structures in UPt$_3$ based on our analysis of elastic neutron-scattering experiments in high magnetic fields at temperatures $T<T_N$. The existing experimental data can be explained by a single-{\bf q} antiferromagnetic structure ... More

Nonequilibrium spin-transfer torque in SFNFS junctionsJul 19 2005Sep 06 2006We report theoretical results for the nonequilibrium spin current and spin-transfer torque in voltage-biased SFNFS Josephson structures. The subharmonic gap structures and high voltage asymptotic behaviors of the dc and ac components of the spin current ... More

The most massive objects in the UniverseApr 29 2010May 07 2010We calculate the most massive object in the Universe, finding it to be a cluster of galaxies with total mass M_200=3.8e15 Msun at z=0.22, with the 1 sigma marginalized regions being 3.3e15 Msun<M<4.4e15 Msun and 0.12<z<0.36. We restrict ourselves to self-gravitating ... More

Riemann surfaces defined over the realsAug 12 2015The known (explicit) examples of Riemann surfaces not definable over their field of moduli are not real whose field of moduli is a subfield of the reals. In this paper we provide explicit examples of real Riemann surfaces which cannot be defined over ... More

Connectivity of the branch locus of moduli space of rational mapsFeb 10 2015Jun 09 2015Milnor proved that the moduli space ${\rm M}_{d}$ of rational maps of degree $d \geq 2$ has a complex orbifold structure of dimension $2(d-1)$. Let us denote by ${\mathcal S}_{d}$ the singular locus of ${\rm M}_{d}$ and by ${\mathcal B}_{d}$ the branch ... More

Pseudo-Real Rational Maps and their automorphismsFeb 18 2015A rational maps is called real if it is definable over the reals, equivalently, if it admits a reflection as an anticonformal automorphism. A rational map is called pseudo-real if it admits antiholomorphic automorphisms but it is not real. Real and pseudo-real ... More