Results for "Scott Manifold"

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Quantitative analysis of the interaction between a dc SQUID and an integrated micromechanical doubly clamped cantileverFeb 08 2019Based on the superconducting quantum interference device (SQUID) equations described by the resistively- and capacitively-shunted junction model coupled to the equation of motion of a damped harmonic oscillator, we provide simulations to quantitatively ... More
A few of Michel Henon's contributions to dynamical astronomyNov 17 2014Nov 19 2014This article reviews Michel Henon's contributions to a diverse set of problems in astrophysical dynamics, including violent relaxation, Saturn's rings, roundoff error in orbit integrations, and planet formation.
Splitting the Curvature of the Determinant Line BundleDec 21 1998It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from ... More
The Hilbert Schemes of Degree Three Curves are ConnectedMar 14 1996In this paper we show that the Hilbert scheme $H(3,g)$ of locally Cohen-Macaulay curves in $\Pthree$ of degree three and genus $g$ is connected. In contrast to $H(2,g)$, which is irreducible, $H(3,g)$ generally has many irreducible components (roughly ... More
Oracles Are Subtle But Not MaliciousApr 12 2005Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not prevent us from ... More
Quantum Lower Bound for Recursive Fourier SamplingSep 09 2002Dec 18 2004One of the earliest quantum algorithms was discovered by Bernstein and Vazirani, for a problem called Recursive Fourier Sampling. This paper shows that the Bernstein-Vazirani algorithm is not far from optimal. The moral is that the need to "uncompute" ... More
Particle absorption by black holes and the generalized second law of thermodynamicsJul 11 2008Apr 08 2010The change in entropy, /DeltaS, associated with the quasi-static absorption of a particle of energy u by a Schwarzschild black hole (ScBH) is approximately (u/T)-s, where T is the Hawking temperature of the black hole and s is the entropy of the particle. ... More
A New Large-Number Coincidence and a Scaling Law for the Cosmological ConstantNov 12 2006Mar 16 2008An ensemble of pure numbers of order near 10^122 is produced naturally from the fundamental parameters of modern cosmology. This new large-number coincidence problem is resolved by demonstrating implicit physical connections that follow from the standard ... More
The Planck Length Scale and Einstein Mass-Energy Obtained from the Sciama-Mach Large Number RelationshipSep 22 2003Sep 25 2003If a physical significance should be attributed to the cosmological large number relationship obtained from Sciama's formulation of Mach's Principle, then a number of interesting physical conclusions may be drawn. The Planck length is naturally obtained ... More
Cluster Masses Accounting for Structure along the Line of SightSep 09 2003Weak gravitational lensing of background galaxies by foreground clusters offers an excellent opportunity to measure cluster masses directly without using gas as a probe. One source of noise which seems difficult to avoid is large scale structure along ... More
How much can we learn about the physics of inflation?Mar 25 2014Mar 28 2014The recent BICEP2 measurement of B-modes in the polarization of the cosmic microwave background suggests that inflation was driven by a field at an energy scale of $2\times 10^{16}$ GeV. I explore the potential of upcoming CMB polarization experiments ... More
UV Perturbations in Brane Gas CosmologyFeb 02 2004We consider the effect of the ultraviolet (UV) or short wavelength modes on the background of Brane Gas Cosmology. We find that the string matter sources are negligible in the UV and that the evolution is given primarily by the dilaton perturbation. We ... More
Experimental Design : Optimizing Quantities of Interest to Reliably Reduce the Uncertainty in Model Input ParametersJan 25 2016As stakeholders and policy makers increasingly rely upon quantitative predictions from advanced computational models, a problem of fundamental importance is the quantification and reduction of uncertainties in both model inputs and output data. The typical ... More
SU(3) Ghosts with SpinJun 15 2007A new Lorentz-covariant gauge is presented for SU(3). In this gauge, both the ghosts and the gauge fields in the (4, 5, 6, 7) gauge directions acquire half-integral spin. As a result, the ghosts in these directions have the correct relationship between ... More
Symmetry Breaking in BRST Quantization of SU(3)Jan 21 2007New BRST-invariant states for SU(3) gauge field theory are presented. The states have finite norms and unlike the states that are usually used to derive path integrals, they break SU(3) symmetry by choosing preferred gauge directions. This symmetry breaking ... More
New Ghost States in SU(3) Gauge Field TheoryDec 26 2006The ghost sector of SU(3) gauge field theory is studied, and new BRST-invariant states are presented that do not have any analog in other SU(N) field theories. The new states come in either ghost doublets or triplets, and they appear exclusively in SU(3) ... More
PT-Invariance and Indefinite MetricOct 27 2009A new proof is given for why the non-Hermitian, PT-Invariant cubic oscillator with imaginary coupling has real eigenvalues. The proof consists of two steps. In the first step, it is shown that for many PT-Invariant Hamiltonians, one can define corresponding ... More
Viscosity at RHIC: Theory and PracticeSep 01 2008Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics. An explanation of Israel-Stewart hydrodynamics is presented here, with an emphasis on the tangible benefits compared ... More
Formulating Viscous Hydrodynamics for Large Velocity GradientsNov 25 2007Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity g radients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, ... More
Alternative Contributions to the Angular Correlations Observed at RHIC Associated with Parity FluctuationsFeb 09 2010Recent measurements at RHIC of angular correlations of same-sign vs. opposite sign pairs have been interpreted as evidence for large-scale fluctuations of parity-odd fields. In this paper, we provide alternative explanations of the same phenomena based ... More
The Long Slow Death of the HBT PuzzleDec 26 2008Femtoscopic measurements at RHIC have been hailed as a source of insight into the bulk properties of QCD matter. However, hydrodynamic models, which have been successful in reproducing other observables have failed to satisfactorily explain femtoscopic ... More
Correlations and Fluctuations, A Summary of Quark Matter 2002Aug 06 2003Results for correlations and fluctuations presented at Quark Matter 2002 are summarized. These results include Hanbury-Brown Twiss interferometry of a wide variety of species, large scale fluctuations and correlations in $p_t$ and multiplicity, and charge ... More
A family of critically finite maps with symmetryJul 03 2003May 17 2005The symmetric group S_n acts as a reflection group on CP^{n-2} (for $n\geq 3$) . Associated with each of the $\binom{n}{2}$ transpositions in S_n is an involution on CP^{n-2} that pointwise fixes a hyperplane--the mirrors of the action. For each such ... More
A selective version of Lin's TheoremAug 14 2018Aug 24 2018We prove a selective version of Lin's Theorem for nearly commuting operators. This is accomplished by establishing the tracial stability of a certain class of graph products of $C^*$-algebras. This result involves the development of the "pincushion class" ... More
The Whitney Extension Theorem for $C^1$, horizontal curves in the Heisenberg groupJul 08 2015Nov 04 2016For a real valued function defined on a compact set $K \subset \mathbb{R}^m$, the classical Whitney Extension Theorem from 1934 gives necessary and sufficient conditions for the existence of a $C^k$ extension to $\mathbb{R}^m$. In this paper, we prove ... More
Computing and Sampling Restricted Vertex Degree Subgraphs and Hamiltonian CyclesAug 31 2000Feb 27 2001Let $G=(V,E)$ be a bipartite graph embedded in a plane (or $n$-holed torus). Two subgraphs of $G$ differ by a {\it $Z$-transformation} if their symmetric difference consists of the boundary edges of a single face---and if each subgraph contains an alternating ... More
Rank of Submatrices of the Pascal MatrixFeb 10 2017In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem. In this paper, ... More
Kergin Approximation in Banach SpacesOct 01 2008We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges.
A note on Cauchy integrabilitySep 23 2014We show that for any bounded function $f:[a,b]\rightarrow{\mathbb R}$ and $\epsilon>0$ there is a partition $P$ of $[a,b]$ with respect to which the Riemann sum of $f$ using right endpoints is within $\epsilon$ of the upper Darboux sum of $f$. This leads ... More
CP-odd Phases in Slepton Pair ProductionMar 23 1998Mar 27 1998The effects of CP-odd supersymmetric phases on slepton pair production are considered. It is shown that CP-even observables in $e^+ e^-$ and $e^- e^-$ collisions, such as the total selectron cross section, can depend on CP-odd supersymmetric phases through ... More
The braid group surjects onto $G_2$ tensor spaceJul 01 2009Let V be the 7-dimensional irreducible representation of the quantum group U_q(g_2). For each n, there is a map from the braid group B_n to the endomorphism algebra of the n-th tensor power of V, given by R-matrices. We can extend this linearly to a map ... More
Quasi-arithmeticity of lattices in PO(n,1)Dec 16 2014Jun 17 2015We show that the non-arithmetic lattices in PO(n,1) of Belolipetsky and Thomson (2011), obtained as fundamental groups of closed hyperbolic manifolds with short systole, are quasi-arithmetic in the sense of Vinberg, and, by contrast, the well-known non-arithmetic ... More
The irreducible unipotent modules of the finite general linear groups via tableauxFeb 23 2015Jul 29 2015We construct the irreducible unipotent modules of the finite general linear groups using tableaux. Our construction is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction exists. Our ... More
A Cohomology Theory for Planar Trivalent Graphs with Perfect MatchingsOct 16 2018Dec 28 2018In this paper, we prove a new cohomology theory that is an invariant of a planar trivalent graph with a given perfect matching. This bigraded cohomology theory appears to be very powerful: the graded Euler characteristic of the cohomology is a one variable ... More
The hole probability for Gaussian random SU(2) polynomialsOct 23 2006We show that for Gaussian random SU(2)polynomials of a large degree $N$ the probability that there are no zeros in the disk of radius $r$ is less than $e^{-c_{1,r} N^2}$, and is also greater than $e^{-c_{2,r} N^2}$. Enroute to this result, we also derive ... More
Encoding Data for HTM SystemsFeb 18 2016Hierarchical Temporal Memory (HTM) is a biologically inspired machine intelligence technology that mimics the architecture and processes of the neocortex. In this white paper we describe how to encode data as Sparse Distributed Representations (SDRs) ... More
The evolution of galaxy formationDec 01 2011Our history of understanding galaxy formation could be traced through the development of individual ideas. A cynic might be tempted to suggest that new catchphrases are developed at a faster rate than genuine progress is made.
CMB ANISOTROPIES: AN OVERVIEWFeb 02 1995A brief outline of the current status of CMB anisotropies and what they might mean, heavily biased towards the perspective of Berkeley theorists. Based on a talk presented at the 17th Texas Symposium on Relativistic Astrophysics held in Munich, December ... More
Dynamics of a soccer ballApr 11 2014Exploiting the symmetry of the regular icosahedron, Peter Doyle and Curt McMullen constructed a solution to the quintic equation. Their algorithm relied on the dynamics of a certain icosahedral equivariant map for which the icosahedron's twenty face-centers--one ... More
Solving the quintic by iteration in three dimensionsMar 09 1999Oct 06 1999The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S_5. Induced by its five-dimensional linear permutation representation is a three-dimensional projective action. ... More
Relative Zeta Determinants and the Quillen MetricOct 27 1999We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary ... More
The statistical mechanics of planet orbitsApr 05 2015Jun 10 2015The final "giant-impact" phase of terrestrial planet formation is believed to begin with a large number of planetary "embryos" on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits ... More
Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry PropertyApr 12 2016We investigate the sign-linear embeddings of 1-bit compressed sensing given by Gaussian measurements. One can give short arguments concerning a Restricted Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse hemispheres. This approach ... More
The Whitney Extension Theorem for $C^1$, horizontal curves in $\mathbb{H}^n$Jul 08 2015Jul 16 2015For a real valued function defined on a compact set $K \subset \mathbb{R}^m$, the classical Whitney Extension Theorem from 1934 gives necessary and sufficient conditions for the existence of a $C^k$ extension to $\mathbb{R}^m$. In this paper, we prove ... More
The Complexity of AgreementJun 30 2004A celebrated 1976 theorem of Aumann asserts that honest, rational Bayesian agents with common priors will never "agree to disagree": if their opinions about any topic are common knowledge, then those opinions must be equal. Economists have written numerous ... More
Quantum Lower Bound for the Collision ProblemNov 20 2001The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Theta(n^{1/5}) on the number of queries needed by a quantum computer to solve this problem ... More
The Equivalence of Sampling and SearchingSep 26 2010In a sampling problem, we are given an input x, and asked to sample approximately from a probability distribution D_x. In a search problem, we are given an input x, and asked to find a member of a nonempty set A_x with high probability. (An example is ... More
Quantum Computing and Hidden Variables II: The Complexity of Sampling HistoriesAug 19 2004This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory satisfying a reasonable ... More
Book Review: 'A New Kind of Science'Jun 13 2002Jul 30 2002This is a critical review of the book 'A New Kind of Science' by Stephen Wolfram. We do not attempt a chapter-by-chapter evaluation, but instead focus on two areas: computational complexity and fundamental physics. In complexity, we address some of the ... More
A Fundamental Scale for Acceleration from the Holographic PrincipleMay 25 2005Jun 26 2005From the Eddington-Weinberg relationship, which may be explained by the holographic principle and the cosmic coincidence in a flat Universe, it follows that the characteristic gravitational acceleration aN associated with the nucleon and its Compton wavelength ... More
The Large Number Coincidence, The Cosmic Coincidence and the Critical AccelerationFeb 09 2005May 19 2006The coincidence problem among the pure numbers of order near 10^{40} is resolved with the Raychaudhuri and Friedmann-Robertson-Lemaitre-Walker equations and a trivial relationship involving the fine structure constant. The fact that the large number coincidence ... More
An Inertial Reaction to Cosmological AccelerationsSep 01 2003May 17 2005Mach's "fixed stars" are actually not fixed at all. The distant clusters of galaxies are not only receding from each observer but they are also accelerating since the rate of cosmological expansion is not constant. If the distant cosmic masses in someway ... More
Stars and the holographic upper bound on gravitational actionApr 14 2007Dec 22 2008The holographic upper bound on entropy is applied to the gravitational action associated with the non-relativistic contraction of a nebula. A critical radius is identified, as a function of the initial radius and mass, for which the number of bits associated ... More
A Cosmological Modification to Energy from Mach-Hamilton ConsistencyMar 24 2004If Mach's Principle explains the Newtonian inertial reaction to acceleration then the role of the 'fixed stars' should also be manifest through Hamilton's formulation of mechanics. This consistency may be achieved if the expression for relativistic energy ... More
The Real Problem with MONDDec 06 2011Gravitational potentials in the cosmos are deeper than expected from observed visible objects, a phenomenon usually attributed to dark matter, presumably in the form of a new fundamental particle. Until such a particle is observed, the jury remains out ... More
Cross-Correlating Probes of Primordial Gravitational WavesJan 27 2010One of the most promising ways of detecting primordial gravitational waves generated during inflation is to observe B-modes of polarization, generated by Thomson scattering after reionization, in the cosmic microwave background (CMB). Large scale foregrounds ... More
A geometric invariant for the study of planar curves and its application to spiral tip meanderFeb 25 2016Planar curves with periodically varying curvature arise in the natural sciences as the result of a wide variety of periodic processes. The total curvature of a periodic arc in such curves constrains their symmetry. It is shown how the total curvature ... More
Moduli Stabilization with the String Higgs EffectApr 23 2004May 02 2004We review the notion of the Higgs effect in the context of string theory. We find that by including this effect in time dependent backgrounds, one is led to a natural mechanism for stabilizing moduli at points of enhanced gauge symmetry. We consider this ... More
An Exposition on Inflationary CosmologyApr 29 2000May 27 2000This paper is intended to offer a pedagogical treatment of cosmological modeling and inflationary cosmology. In recent years, inflation has become accepted as a standard scenario making predictions that are testable by observations of the cosmic background. ... More
Szemerédi's Regularity Lemma for matrices and sparse graphsOct 04 2010Nov 08 2010Szemer\'edi's Regularity Lemma is an important tool for analyzing the structure of dense graphs. There are versions of the Regularity Lemma for sparse graphs, but these only apply when the graph satisfies some local density condition. In this paper, we ... More
General Charge Balance Functions, A Tool for Studying the Chemical Evolution of the Quark-Gluon PlasmaSep 16 2011Jan 13 2012In the canonical picture of the evolution of the quark-gluon plasma during a high-energy heavy-ion collision, quarks are produced in two waves. The first is during the first fm/c of the collision, when gluons thermalize into the QGP. After a roughly isentropic ... More
Universal Flow in the Early Stages at RHICMar 09 2009Pre-thermal flow plays an important role in the final state evolution of heavy ion collisions at RHIC. We show that flow has universal features for a wide range of models. This significantly reduces the uncertainty in initializing hydrodynamic models ... More
Refractive Distortions of Two-Particle CorrelationsNov 02 2005Using optical model calculations it has recently been shown that refractive phenomena from the collective mean field can significantly alter the sizes inferred from two-pion correlations. We demonstrate that such effects can be accounted for in classical ... More
Canonical and Microcanonical Distributions for Fermi SystemsMay 26 1999Oct 14 1999Recursion relations are presented that allow exact calculation of canonical and microcanonical partition functions of degenerate Fermi systems, assuming no explicit two-body interactions. Calculations of the level density, sorted by angular momentum, ... More
Searches for Particle Dark Matter: An IntroductionOct 12 2011The identity of dark matter is one of the key outstanding problems in both particle and astrophysics. In this thesis, I describe a number of complementary searches for particle dark matter. I discuss how the impact of dark matter on stars can constrain ... More
Supercharacter theories constructed by the method of little groupsMay 21 2014May 22 2014The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of semidirect ... More
Classifying Spinor StructuresJun 10 2001I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The central result ... More
Reciprocity and rationality for the greedy normal form of a Coxeter groupSep 12 2008We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of ... More
Vogan Duality for ~Spin(p,q)Aug 13 2009The main purpose of this paper is to describe a symmetry in the set genuine parameters for even rank nonlinear Spin groups in type B at certain half-integral infinitesimal characters. This symmetry is used to establish a duality of the corresponding generalized ... More
One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized UnitarityAug 01 2011Dec 06 2011We combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a new formalism for computing one-loop amplitudes in dimensionally regularized QCD. With this procedure, we simultaneously obtain ... More
Pricing for Large Positions in Contingent ClaimsFeb 17 2012Dec 11 2013Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches ... More
On graph products of multipliers and the Haagerup property for $C^*$-dynamical systemsMar 05 2018We consider the notion of the graph product of actions of groups $\left\{G_v\right\}$ on a $C^*$-algebra $\mathcal{A}$ and show that under suitable commutativity conditions the graph product action $\bigstar_\Gamma \alpha_v: \bigstar_\Gamma G_v \curvearrowright ... More
Supersymmetry in the Very Early UniverseJun 16 1995Jun 24 1995Supersymmetric flat directions can have a number of important consequences in the very early universe. Depending on the form of the SUSY breaking potential arising from the finite energy density at early times, coherent production of scalar condensates ... More
Baryons and Dark Matter from the Late Decay of a Supersymmetric CondensateJun 09 1995The possibility that both the baryon asymmetry and dark matter arise from the late decay of a population of supersymmetric particles is considered. If the decay takes place below the LSP freeze out temperature, a nonthermal distribution of LSPs results. ... More
Electromagnetic Contributions to the Schiff MomentFeb 07 1994The Schiff moment, $\smij$, is a parity and time reversal violating fermion-fermion coupling. The nucleus-electron Schiff moment generically gives the most important contribution to the electric dipole moments of atoms and molecules with zero net intrinsic ... More
Elementary treatment of $p^a \pm p^b + 1 = x^2$Aug 31 2006We give a shorter simpler proof of a result of Szalay on the equation $2^a + 2^b + 1 = x^2$. We give an elementary proof of a result of Luca on the equation of the title for prime $p > 2$. The elementary treatment is made possible by a lemma which is ... More
Augmented Homotopical Algebraic GeometryNov 07 2017We develop the framework for augmented homotopical algebraic geometry. This is an extension of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. To do so, we define the notion of augmentation categories, ... More
Torus Invariant CurvesApr 13 2013Jul 30 2013Using the language of T-varieties, we study torus invariant curves on a complete normal variety $X$ with an effective codimension-one torus action. In the same way that the $T$-invariant Weil divisors on $X$ are sums of "vertical" divisors and "horizontal" ... More
51 constructions of the Moonshine moduleJul 10 2017Jul 18 2017We show using Borcherds products that for any fixed-point free automorphism of the Leech lattice satisfying a "no massless states" condition, the corresponding cyclic orbifold of the Leech lattice vertex operator algebra is isomorphic to the Monster vertex ... More
Generalized Moonshine IV: Monstrous Lie algebrasAug 30 2012Aug 20 2016For each element of the Fischer-Griess Monster sporadic simple group, we construct an infinite dimensional Lie algebra equipped with a projective action of the centralizer of that element. Our construction is given by a string-theoretic "add a spacetime ... More
Sobolev extensions of Lipschitz mappings into metric spacesAug 02 2016Aug 02 2017Wenger and Young proved that the pair $(\mathbb{R}^m,\mathbb{H}^n)$ has the Lipschitz extension property for $m \leq n$ where $\mathbb{H}^n$ is the sub-Riemannian Heisenberg group. That is, for some $C>0$, any $L$-Lipschitz map from a subset of $\mathbb{R}^m$ ... More
Supercharacters of unipotent groups defined by involutionsNov 07 2013Dec 15 2014We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters of algebra ... More
The odd couple: quasars and black holesJul 23 2014Quasars emit more energy than any other objects in the universe, yet are not much bigger than the solar system. We are almost certain that quasars are powered by giant black holes of up to $10^{10}$ times the mass of the Sun, and that black holes of between ... More
On the origin of irregular structure in Saturn's ringsNov 07 2002We suggest that the irregular structure in Saturn's B ring arises from the formation of shear-free ring-particle assemblies of up to ~100 km in radial extent. The characteristic scale of the irregular structure is set by the competition between tidal ... More
A Counterexample to the Generalized Linial-Nisan ConjectureOct 27 2011In earlier work, we gave an oracle separating the relational versions of BQP and the polynomial hierarchy, and showed that an oracle separating the decision versions would follow from what we called the Generalized Linial-Nisan (GLN) Conjecture: that ... More
Why Philosophers Should Care About Computational ComplexityAug 08 2011Aug 14 2011One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue ... More
QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum ProtocolsOct 31 2005Apr 02 2006This paper introduces a new technique for removing existential quantifiers over quantum states. Using this technique, we show that there is no way to pack an exponential number of bits into a polynomial-size quantum state, in such a way that the value ... More
Are Quantum States Exponentially Long Vectors?Jul 26 2005I'm grateful to Oded Goldreich for inviting me to the 2005 Oberwolfach Meeting on Complexity Theory. In this extended abstract, which is based on a talk that I gave there, I demonstrate that gratitude by explaining why Goldreich's views about quantum ... More
Limits on Efficient Computation in the Physical WorldDec 20 2004Feb 15 2005More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the ... More
Limitations of Quantum Advice and One-Way CommunicationFeb 15 2004Oct 01 2004Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only limited advantages ... More
Is Quantum Mechanics An Island In Theoryspace?Jan 12 2004Mar 17 2004This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2-norm by some other p-norm, then there are no nontrivial norm-preserving linear maps. Second, ... More
The Ghost in the Quantum Turing MachineJun 02 2013Jun 07 2013In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will. I focus relatively narrowly on a notion that I call "Knightian freedom": a certain ... More
Lower Bounds for Local Search by Quantum ArgumentsJul 21 2003Feb 05 2004The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1}^n, we show a lower bound of Omega(2^{n/4}/n) on the number of ... More
Quantum Computing and Dynamical Quantum ModelsMay 11 2002A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum state. We study ... More
Three Discrete Models of Planar Lie Group Equivariant PresheavesAug 25 2016We utilise the theory of crossed simplicial groups to introduce a collection of Quillen model structures on the category of simplicial presheaves with a compact planar Lie group action on a small Grothendieck site.
Action in a fractal universe and the holographic upper boundFeb 28 2008Aug 13 2008The basic scaling laws for structures in a fractal universe require that the characteristic quantity of action associated with astronomical bodies should be of order near the maximum possible action allowed by the holographic upper bound. That conclusion ... More
A fundamental scale of mass for black holes from the cosmological constantJan 24 2007Dec 22 2008The existence of a positive cosmological constant leads naturally to two fundamental scales of length, being the De Sitter horizon and the radius of the cell associated with a holographic degree of freedom. Associated with each of those scales of length ... More
Scaling Law for the Cosmological Constant from Quantum Cosmology with Seven Extra DimensionsOct 09 2006Mar 16 2008According to a model of quantum cosmology the maximum number of degrees of freedom allowed in our three dimensions was determined by the size of seven extra dimensions in an initial excited state before inflation. The size of the extra dimensions can ... More
The fundamental scales of structures from first principlesApr 15 2008May 29 2008Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe, clusters, galaxies, ... More
Coherent Phase Argument for InflationSep 05 2003Cosmologists have developed a phenomenally successful picture of structure in the universe based on the idea that the universe expanded exponentially in its earliest moments. There are three pieces of evidence for this exponential expansion -- {\it inflation} ... More