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

A short proof of the phase transition for the vacant set of random interlacementsJul 31 2014Jan 22 2015The vacant set of random interlacements at level $u>0$, introduced in arXiv:0704.2560, is a percolation model on $\mathbb{Z}^d$, $d \geq 3$ which arises as the set of sites avoided by a Poissonian cloud of doubly infinite trajectories, where $u$ is a ... More

Percolation on the stationary distributions of the voter modelFeb 04 2015Feb 18 2016The voter model on $\mathbb{Z}^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \geq 3$, the set of (extremal) stationary ... More

Field-theoretical study of the Bose polaronAug 15 2013Dec 16 2013We study the properties of the Bose polaron, an impurity strongly interacting with a Bose-Einstein condensate, using a field-theoretic approach and make predictions for the spectral function and various quasiparticle properties that can be tested in experiment. ... More

Weak Minimal Area In Entanglement EntropyJun 21 2014Mar 26 2015We re-visit the minimal area condition of Ryu-Takayanagi in the holographic calculation of the entanglement entropy. In particular, the Legendre test and the Jacobi test. The necessary condition for the weak minimality is checked via Legendre test and ... More

A number field extension of a question of MilnorJan 10 2016Milnor formulated a conjecture about rational linear independence of some special Hurwitz zeta values. The second and third authors along with Ram Murty studied this conjecture and suggested an extension of Milnor's conjecture. In this note, we investigate ... More

On chemical distances and shape theorems in percolation models with long-range correlationsDec 12 2012Oct 02 2014In this paper we provide general conditions on a one parameter family of random infinite subsets of Z^d to contain a unique infinite connected component for which the chemical distances are comparable to the Euclidean distances, focusing primarily on ... More

Efimov physics beyond universalityJan 20 2012Dec 17 2012We provide an exact solution of the Efimov spectrum in ultracold gases within the standard two-channel model for Feshbach resonances. It is shown that the finite range in the Feshbach coupling makes the introduction of an adjustable three-body parameter ... More

Feller property of the multiplicative coalescent with linear deletionSep 30 2016We modify the definition of Aldous' multiplicative coalescent process and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with ... More

Time evolution of dense multigraph limits under edge-conservative preferential attachment dynamicsDec 19 2009Apr 26 2012We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge reconnecting ... More

Non-local order in Mott insulators, Duality and Wilson LoopsFeb 04 2013May 02 2013It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local 'parity order parameter' which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose ... More

On decoupling inequalities and percolation of excursion sets of the Gaussian free fieldJul 10 2013Feb 04 2015We prove decoupling inequalities for the Gaussian free field on $\mathbb{Z}^d$, $d\geq 3$. As an application, we obtain exponential decay (with logarithmic correction for $d=3$) of the connectivity function of excursion sets for large values of the threshold. ... More

Structural modification in Au/Si(100) system: Role of surface oxide and vacuum levelApr 24 2012To understand surface structural modifications for Au/Si (100) system, a thin gold film of ~2.0 nm was deposited under ultra high vacuum (UHV) condition on reconstructed Si surfaces using molecular beam epitaxy (MBE). Post annealing was done at 500{\deg}C ... More

Diophantine properties of continued fractions on the Heisenberg groupSep 20 2013Aug 11 2014We provide several results on the diophantine properties of continued fractions on the Heisenberg group, many of which are analogous to classical results for real continued fractions. In particular, we show an analog of Khinchin's theorem and that convergents ... More

Authentication Based Solutions to Counterfeiting of Manufactured GoodsNov 27 2015May 21 2016Counterfeiting of manufactured goods is presented as the theft of intellectual property, patents, copyright etc. accompanied by identity theft. The purpose of the identity theft is to facilitate the intellectual property theft. Without it the intellectual ... More

The Game of PhishingNov 12 2015Aug 04 2016Phishing attacks occur because of a failure of computer users to authenticate Bob. The computer user's role, her job, is to authenticate Bob. Nobody else can carry out this task. I researched the ability of browsers to counterfeit the behaviour of installed ... More

The normality of digits in almost constant additive functionsJun 06 2012We consider numbers formed by concatenating some of the base b digits from additive functions f(n) that closely resemble the prime counting function \Omega(n). If we concatenate the last \lceil y \frac{\log \log \log n}{\log b} \rceil digits of each f(n) ... More

On multiplicativity of Fourier coefficients at cusps other than infinityFeb 11 2011This paper treats the problem of determining conditions for the Fourier coefficients of a Maass-Hecke newform at cusps other than infinity to be multiplicative. To be precise, the Fourier coefficients are defined using a choice of matrix in SL(2, Z) which ... More

On On_pAug 03 2011Feb 17 2015Generalizing John Conway's construction of the Field On_2, we give the "minimal" definitions of addition and multiplication that turn the ordinals into a Field of characteristic p, for any prime p. We then analyze the structure of the resulting Field, ... More

Cover times and generic chainingJul 04 2012Jul 10 2012A recent result of Ding, Lee and Peres expresses the cover time of the random walk on a graph in terms of generic chaining for the commute distance. Their proof is very involved and the purpose of this article is to present a simpler approach to this ... More

Generically large nongaussianity in small multifield inflationFeb 09 2015Jul 14 2015If forthcoming measurements of cosmic photon polarization restrict the primordial tensor-to-scalar ratio to $r < 0.01$, small field inflation will be a principal candidate for the origin of the universe. Here we show that small multifield inflation, without ... More

A preparation theorem for the kashiwara $b(\infty)$ crystalOct 21 2015The Kashiwara $B(\infty)$ crystal pertains to a Verma module for a Kac- Moody Lie algebra. Ostensibly it provides only a parametrisation of the global/canonical basis for the latter. Yet it is much more having a rich combinatorial structure from which ... More

Particle phenomenology on noncommutative spacetimeNov 24 2008May 12 2009We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spcetime noncommutativity is constrained from the CPT violation measurements in $K^{0}-\bar{K}^{0}$ system and $g-2$ difference ... More

Blackbody Friction: Analytic expressions for velocity and positionNov 08 2012The equations of motion are solved analytically for speed and position for the case of blackbody friction on objects traveling at relativistic speeds with respect to observers fixed in the frame of the blackbody radiation. Two model cases are considered, ... More

Intersections via resolutionsApr 08 2014We investigate the viability of defining an intersection product on algebraic cycles on a singular algebraic variety by pushing forward intersection products formed on a resolution of singularities. For varieties with resolutions having a certain structure ... More

The $R_{\mathrm{h}}=ct$ universe and quintessenceJan 20 2016Over the last few years the $R_{\mathrm{h}}=ct$ universe has received a lot of attention, particularly when observational evidence seems to favor this over the standard $\Lambda$ cold dark matter ($\Lambda CDM$) universe. Like the $\Lambda CDM$, the $R_{\mathrm{h}}=ct$ ... More

Dileptons and Photons from Coarse-Grained Microscopic Dynamics and Hydrodynamics Compared to Experimental DataOct 09 2002We compute the radiation of dileptons and photons using relativistic hydrodynamics and a coarse-grained version of the microscopic event generator UrQMD, both of which provide a good description of the hadron spectra. The currently most accurate dilepton ... More

Variable Selection in High Dimensions with Random Designs and Orthogonal Matching PursuitSep 04 2011The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the design matrix, ... More

Midy's Theorem for Periodic DecimalsMay 07 2006The decimal expansion of 1/7 is 0.142857142857..., the block 142857 repeating forever. We call 142857 the period and its length is 6 = 2x3. If the period is broken into 2 pieces each of length 3 which are then added, the result is 142 + 857 = 999; similarly ... More

Wave approach for the resonances of rectangular and triangular membranesJun 09 2011This study develops a ray technique for determining the resonance frequencies of triangular membranes. The technique is demonstrated for homogenous rectangular and triangular membranes with fixed boundaries. Where possible, the results are compared with ... More

Relativity and Aether Theory, a Crucial DistinctionOct 10 2006Dec 14 2008We study the case of two rockets which meet at a point O of an inertial co-ordinate system S, and are scheduled to move at constant speed, in opposite directions, toward two targets placed at equal distances from point O. At the instant they meet, the ... More

On Multiplicative Functions with Bounded Partial SumsAug 06 2011Consider a multiplicative function f(n) taking values on the unit circle. Is it possible that the partial sums of this function are bounded? We show that if we weaken the notion of multiplicativity so that f(pn)=f(p)f(n) for all primes p in some finite ... More

On diagonal lower bound of Markov kernel from $L^2$ analyticityAug 10 2015Let $\Gamma$ be a graph and $P$ be a reversible random walk on $\Gamma$. From the $L^2$ analyticity of the Markov operator $P$, we deduce an on-diagonal lower bound of an iterate of odd number of $P$. The proof does not require the doubling property on ... More

Riesz transform on graphs under subgaussian estimatesMay 26 2015Jan 14 2016Let $\Gamma$ be a doubling graph satisfying some pointwise subgaussian estimates of the Markov kernel. We introduce a space $H^1(\Gamma)$ of functions and a space $H^1(T_\Gamma)$ of 1-forms and give various characterizations of them. We prove the $H^1$-boundedness ... More

Cosmic ConundrumsApr 10 2014What do we do when cosmology raises questions it cannot answer? These include the existence of a multiverse and the universality of the laws of physics. We cannot settle any of these issues by experiment, and this is where philosophers enter the debate. ... More

Feedback in Galaxy FormationFeb 01 2011I review the outstanding problems in galaxy formation theory, and the role of feedback in resolving them. I address the efficiency of star formation, the galactic star formation rate, and the roles of supernovae and supermassive black holes.

Failure of the parametric h-principle for maps with prescribed jacobianDec 06 2005Let M and N be closed n-dimensional manifolds, and equip N with a volume form \sigma. Let \mu be an exact n-form on M. Arnold then asked the question: When can one find a map f:;N such that f*\sigma=\mu. In 1973 Eliashberg and Gromov showed that this ... More

Symplectomorphism groups and isotropic skeletonsApr 27 2004Jun 17 2005The symplectomorphism group of a 2-dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition of the symplectic ... More

Derived autoequivalences from periodic algebrasJun 14 2011Feb 18 2013We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalises autoequivalences previously constructed by Rouquier-Zimmermann and ... More

Random Heegaard splittingsSep 29 2008Nov 16 2010A random Heegaard splitting is a 3-manifold obtained by using a random walk of length n on the mapping class group as the gluing map between two handlebodies. We show that the joint distribution of random walks of length n and their inverses is asymptotically ... More

Regularization in $L_1$ for the Ornstein--Uhlenbeck semigroupMay 15 2015Let $\gamma_n$ be the standard Gaussian measure on $\mathbb R^n$ and let $(Q_t)$ be the Ornstein--Ulhenbeck semigroup. Eldan and Lee recently established that for every non--negative function $f$ of integral $1$ and any time $t$ the following tail inequality ... More

Functional calculus and joint torsion of pairs of almost commuting operatorsSep 22 2014This paper investigates the transformation of determinants of pairs of Fredholm operators with trace class commutators. We study the extent to which the functional calculus commutes, modulo operator ideals, with projections in a finitely summable Fredholm ... More

Stacks in Representation Theory. What is a continuous representation of an algebraic group ?Oct 02 2014May 12 2016In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group $G$ as a sheaf on some geometric object (a stack). This point of view necessarily ... More

Prequantization of logsymplectic structuresJan 12 2010In this paper, we study quatization condition of logsymplectic struc- ture using integrality of such structue on the complement of associated divisor D.

Self-Organized Criticality on Quasiperiodic GraphsApr 16 1999Jul 26 1999Self-organized critical models are used to describe the 1/f-spectra of rather different physical situations like snow avalanches, noise of electric currents, luminosities of stars or topologies of landscapes. The prototype of the SOC-models is the sandpile ... More

Chaos in the black hole S-matrixMay 29 2015Jun 01 2015Recent work by Shenker, Stanford, and Kitaev has related the black hole horizon geometry to chaotic behavior. We extend this from eternal black holes to black holes that form and then evaporate. This leads to an identity for the change in the black hole ... More

The Cosmological Constant and the String LandscapeMar 31 2006Apr 21 2006Theories of the cosmological constant fall into two classes, those in which the vacuum energy is fixed by the fundamental theory and those in which it is adjustable in some way. For each class we discuss key challenges. The string theory landscape is ... More

S-Matrices from AdS SpacetimeJan 18 1999In the large-N limit of d=4, N=4 gauge theory, the dual AdS spacetime becomes flat. We identify a gauge theory correlator whose large-N limit is the flat spacetime S-matrix.

Recent Results in String DualityNov 22 1995Nov 22 1995This is a talk given at YKIS '95, primarily to non-string theorists. I review the evidence for string duality, the principle that any string theory at strong coupling looks like another string theory at weak coupling. A postscript summarizes developments ... More

Low Energy Dynamics of the Spinon-Gauge SystemMar 21 1993The normal phase of the high-$T_c$ cuprates is apparently not described by Fermi liquid theory. It has been proposed that a dynamically generated gauge field must appear in the effective field theory. Even a simple spinon-gauge system is complicated, ... More

General bound of overfitting for MLP regression modelsJan 03 2012Multilayer perceptrons (MLP) with one hidden layer have been used for a long time to deal with non-linear regression. However, in some task, MLP's are too powerful models and a small mean square error (MSE) may be more due to overfitting than to actual ... More

Testing the number of parameters with multidimensional MLPFeb 21 2008This work concerns testing the number of parameters in one hidden layer multilayer perceptron (MLP). For this purpose we assume that we have identifiable models, up to a finite group of transformations on the weights, this is for example the case when ... More

Pénalisations of Walsh's Brownian motionJun 16 2005In this paper, we construct a family of probability measures, by penalizations of a Walsh's Brownian motion with a weight dependent on its value and its local time at a time t. We prove that this family converges to a probability measure as t tends to ... More

Containment in (s,t)-core PartitionsSep 12 2008We introduce the idea of (s,t)-closure and delta-sets and show that (s,t)-closed beta-sets which are contained set-wise in (s,t)-closed delta-sets are also contained partition-wise. This implies the maximal (s,t)-core partition theorem of Olsson and Stanton. ... More

On the Yao-Yao partition theoremNov 09 2010The Yao-Yao partition theorem states that given a probability measure on an affine space of dimension n having a density which is continuous and bounded away from 0, it is possible to partition the space into 2^n regions of equal measure in such a way ... More

Period three actions on lens spacesNov 02 2003Feb 04 2008We show that a free period three action on a lens space is standard, i.e. the quotient is homeomorphic to a lens space. This is an extension of the result for period three actions on the three-sphere, arXiv:math.GT/0204077, by the author and J. Hyam Rubinstein. ... More

Practical scheme for a light-induced gauge field in an atomic Bose gasNov 24 2008Feb 03 2009We propose a scheme to generate an Abelian gauge field in an atomic gas using two crossed laser beams. If the internal atomic state follows adiabatically the eigenstates of the atom-laser interaction, Berry's phase gives rise to a vector potential that ... More

Multigraph limit of the dense configuration model and the preferential attachment graphJun 10 2011Apr 10 2012The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special form of limit objects of convergent sequences of configuration models. ... More

Multigraph limits and exchangeabilityOct 03 2009Jun 11 2010The theory of limits of dense graph sequences was initiated by Lovasz and Szegedy. We give a possible generalization of this theory to multigraphs. Our proofs are based on the correspondence between dense graph limits and countable, exchangeable arrays ... More

Uncertainties and shortcomings of ground surface temperature histories derived from inversion of temperature logsJun 14 2008Analysing borehole temperature data in terms of ground surface history can add useful information to reconstructions of past climates. Therefore, a rigorous assessment of uncertainties and error sources is a necessary prerequisite for the meaningful interpretation ... More

Gold assisted molecular beam epitaxy of Ge nanostructures on Ge(100) SurfaceAug 01 2012We report on the gold assisted epitaxial growth of Ge nanostructures under ultra high vacuum (UHV) conditions (\approx3\times 10-10 mbar) on clean Ge (100) surfaces. For this study, \approx2.0 nm thick Au samples were grown on the substrate surface by ... More

Temperature-dependent electron microscopy study of Au thin films on Si (100) with and without native oxide layer as barrier at the interfaceFeb 03 2012Real time electron microscopy observation on morphological changes in gold nano structures deposited on Si (100) surfaces as a function of annealing temperatures has been reported. Two types of interfaces with the substrate silicon were used prior to ... More

The Specification of SugarscapeMay 22 2015Jul 01 2016Sugarscape is a well known and influential Agent Based Social Simulation (ABSS). Various parts of Sugarscape are supplied as examples in almost all Agent Based Model (ABM) toolkits. It has been used for demonstrating the applicability of different approaches ... More

Category of fuzzy hyper BCK-algebrasJan 13 2011In this paper we ?rst de?ne the category of fuzzy hyper BCK- algebras. After that we show that the category of hyper BCK-algebras has equalizers, coequalizers, products. It is a consequence that this category is complete and hence has pullbacks.

Siegel zeros of Eisenstein seriesDec 05 2005If E(z,s) is the nonholomorphic Eisenstein series on the upper half plane, then for all y sufficiently large, E(z,s) has a "Siegel zero." That is E(z,\beta)=0 for a real number \beta just to the left of one. We give a generalization of this result to ... More

Tropical analytic geometry, Newton polygons, and tropical intersectionsJul 15 2010In this paper we use the connections between tropical algebraic geometry and rigid analytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: ... More

The Case for Massive, Evolving Winds in Black Hole X-ray BinariesApr 22 2013In the last decade, high-resolution X-ray spectroscopy has revolutionized our understanding of the role of accretion disk winds in black hole X-ray binaries. Here I present a brief review of the state of wind studies in black hole X-ray binaries, focusing ... More

An Ansatz for Hyperkähler $8$-Manifolds with two Commuting Rotating Killing FieldsSep 27 2014We consider a hyperk\"{a}hler $8$-manifold admitting either a $U(1) \times \mathbb{R}$, or a $U(1) \times U(1)$ action, where the first factor preserves $g$ and $I$, and acts on $\omega_2+i\omega_3$ by multiplying it by itself, while the second factor ... More

New normality constructions for continued fraction expansionsJul 01 2015Adler, Keane, and Smorodinsky showed that if one concatenates the finite continued fraction expansions of the sequence of rationals \[ \frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{1}{5}, \cdots \] into an infinite ... More

Dark matter ignition of type Ia supernovaeMay 27 2015Sep 25 2015Recent studies of low redshift type Ia supernovae (SNIa) indicate that half explode from less than Chandrasekhar mass white dwarfs, implying ignition must proceed from something besides the canonical criticality of Chandrasekhar mass SNIa progenitors. ... More

Borell's formula for a Riemannian manifold and applicationsDec 18 2015Borell's formula is a stochastic variational formula for the log-Laplace transform of a function of a Gaussian vector. We establish an extension of this to the Riemannian setting and give a couple of applications, including a new proof of a convolution ... More

The class number formula for imaginary quadratic fieldsFeb 17 2015It is shown that the class number for negative discriminant $D$ can be expressed in terms of the base $B$ expansions of reduced fractions $\frac{x}{|D|}$, where $B$ is an integer prime to $D$. This result is then formulated to obtain information about ... More

Optical conductivity of a superfluid density waveJan 04 2002We present a calculation of the low frequency optical conductivity of a superconductor in the presence of quenched inhomogeneity in both the superfluid and normal fluid densities. We find that inhomogeneity in the superfluid density displaces spectral ... More

Kondo lattice on the edge of a two-dimensional topological insulatorMar 30 2012Jun 13 2012We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling ... More

Algebra properties for Besov spaces on unimodular Lie groupsMay 26 2015We consider the Besov space $B^{p,q}_\alpha(G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $\Delta$. Using estimates of the heat kernel associated with $\Delta$, we give several characterizations of Besov spaces, and show an algebra property ... More

Relative decidability and definability in henselian valued fieldsOct 14 2009Let K be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. Two applications ... More

Albedo heterogeneity on the surface of (1943) AnterosDec 28 2009We have investigated the effect of rotation on the polarization of scattered light for the near-Earth asteroid (1943) Anteros using the Dual Beam Imaging Polarimeter on the University of Hawaii's 2.2 m telescope. Anteros is an L-type asteroid that has ... More

Wave propagation on microstate geometriesSep 06 2016Supersymmetric microstate geometries were recently conjectured to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, ... More

5D Maximally Supersymmetric Yang-Mills on the LatticeOct 11 2016We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation is interesting ... More

A Euclidean Lattice Formulation of D=5 Maximally Supersymmetric Yang-Mills TheoryApr 10 2016Jun 13 2016We construct lattice action for five-dimensional maximally supersymmetric Yang-Mills theory. This supersymmetric lattice formulation can be used to explore the non-perturbative regime of the continuum target theory, which has a known gravitational dual. ... More

Distances and Absolute Magnitudes of Dwarf Novae: Murmurs of Period BounceMar 05 2009Oct 23 2010We redetermine the relationship between absolute magnitude and orbital period for dwarf novae, based on 46 stars with good distance estimates. This improves upon Warner's previous relation, building upon today's improved estimates of distance and binary ... More

Accelerators Beyond The Tevatron?Jun 30 2010Following the successful operation of the Fermilab superconducting accelerator three new higher energy accelerators were planned. They were the UNK in the Soviet Union, the LHC in Europe, and the SSC in the United States. All were expected to start producing ... More

The Hilbert-Chow morphism and the incidence divisorSep 29 2010For a smooth projective variety $P$, we construct a Cartier divisor supported on the incidence locus in $\mathscr{C}_a (P) \times \mathscr{C}_{\dim(P)-a-1}(P)$. There is a natural definition of the corresponding line bundle on a product of Hilbert schemes, ... More

Indicators of Bismash Products from Exact Symmetric Group FactorizationsDec 15 2014Jul 22 2015We prove that all irreducible representations of the bismash product $H = \mathbb{k} ^G \# \mathbb{k} S_{n-k}$ have Frobenius-Schur indicators +1 or 0 where $\mathbb{k}$ is an algebraically closed field and $S_n = S_{n-k}\cdot G$ is an exact factorization. ... More

On Bass' question for finitely generated algebras over large fieldsMar 11 2008Aug 25 2008Recently Cortinas-Haesemayer-Walker-Weibel gave affirmative answer to Bass' 1972 question on NK-groups for algebras of essentially finite type over large fields of characteristic 0. Here we give an alternative short proof of this result for algebras of ... More

Explicit filtering for large eddy simulation as use of a spectral bufferOct 06 2016The explicit filtering method for large eddy simulation (LES,) which comprises integration of the governing equations without any added terms for sub-grid-scale modeling and the application of a low-pass filter to transported fields, is discussed. The ... More

Is the aether entrained by the motion of celestial bodies? What do the experiments tell us?Mar 20 2012Dec 17 2013Even though the concept has evolved and if the designation as aether is improperly regarded as outdated, nobody today considers that the vacuum is empty. However, the nature and the properties of the substratum, which permeates the entire universe, remain ... More

Statistical Mechanics of Amplifying ApparatusFeb 08 2005We implement Feynman's suggestion that the only missing notion needed for the puzzle of Quantum Measurement is the statistical mechanics of amplifying apparatus. We define a thermodynamic limit of quantum amplifiers which is a classically describable ... More

Partitions and functional Santalo inequalitiesNov 09 2010We give a direct proof of a functional Santalo inequality due to Fradelizi and Meyer. This provides a new proof of the Blaschke-Santalo inequality. The argument combines a logarithmic form of the Prekopa-Leindler inequality and a partition theorem of ... More

Higher-level canonical subgroups for p-divisible groupsOct 17 2009Mar 16 2011Let R be a complete rank-1 valuation ring of mixed characteristic (0,p), and let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group G of level n over R is said to have a level-n canonical subgroup if there is a K-subgroup of G\tensor_R ... More

Feedback and the Initial Mass functionOct 04 2004I describe a turbulence-inspired model for the stellar initial mass function which includes feedback and self-regulation via protostellar outflows. A new aspect of the model provides predictions of the star formation rate in molecular clouds and gas complexes. ... More

Supermassive Black Holes and Galaxy FormationSep 19 2001The formation of supermassive black holes (SMBH) is intimately related to galaxy formation, although precisely how remains a mystery. I speculate that formation of, and feedback from, SMBH may alleviate problems that have arisen in our understanding of ... More

Maps with symplectic graphsJul 13 2004Oct 22 2004We consider the homotopy type of maps between symplectic surface whose graphs form symplectic submanifolds of the product. We give a purely topological model for this space in terms of maps with constrained numbers of pre-images. We use this to show that ... More

String theory to the rescueDec 08 2015Dec 16 2015The search for a theory of quantum gravity faces two great challenges: the incredibly small scales of the Planck length and time, and the possibility that the observed constants of nature are in part the result of random processes. A priori, one might ... More

Comment on [arXiv:1106.1417] "Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?"Jun 30 2011Sep 02 2011A recent paper by Gambini, Rastgoo and Pullin [arXiv:1106.1417 investigates the important issue of constraints from Lorentz invariance on Planck scale physics, arguing that the classic analysis of Collins, Perez, Sudarsky, Urrutia and Vucetich \cite{cpsuv} ... More

Cosmic Superstrings RevisitedOct 08 2004Dec 21 2004It is possible that superstrings, as well as other one-dimensional branes, could have been produced in the early universe and then expanded to cosmic size today. I discuss the conditions under which this will occur, and the signatures of these strings. ... More

Brane/antibrane dynamics and KKLT stabilitySep 18 2015Sep 25 2015String theory has few or no stable nonsupersymmetric or de Sitter vacua, only metastable ones. Antibranes are a simple source of supersymmetry breaking, as in the KKLT model, but various arguments have been given that these fail to produce the desired ... More

What is String Theory?Nov 04 1994The first part is an introduction to conformal field theory and string perturbation theory. The second part deals with the search for a deeper answer to the question posed in the title. Contents: 1. Conformal Field Theory 2. String Theory 3. Vacua and ... More

The Specification of SugarscapeMay 22 2015Nov 07 2016Sugarscape is a well known and influential Agent Based Social Simulation (ABSS). Various parts of Sugarscape are supplied as examples in almost all Agent Based Model (ABM) toolkits. It has been used for demonstrating the applicability of different approaches ... More

On the Atiyah problem on hyperbolic configurations of four pointsFeb 04 2015Aug 06 2015Given a configuration $\mathbf{x}$ of $n$ distinct points in hyperbolic $3$-space $H^3$, Michael Atiyah associated $n$ polynomials $p_1,\ldots,p_n$ of a variable $t \in \mathbb{C}P^1$, of degree $n-1$, and conjectured that they are linearly independent ... More