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The right time to learn: mechanisms and optimization of spaced learningJun 27 2016For many types of learning, spaced training that involves repeated long inter-trial intervals (ITIs) leads to more robust memory formation than does massed training that involves short or no intervals. Several cognitive theories have been proposed to ... More

Molecular Constraints on Synaptic Tagging and Maintenance of Long-Term Potentiation: A Predictive ModelJun 16 2012Aug 03 2012Protein synthesis-dependent, late long-term potentiation (LTP) and depression (LTD) at glutamatergic hippocampal synapses are well characterized examples of long-term synaptic plasticity. Persistent increased activity of the enzyme protein kinase M (PKM) ... More

How Can Memories Last for Days, Years, or a Lifetime? Proposed Mechanisms for Maintaining Synaptic Potentiation and MemoryMar 13 2019Apr 16 2019With memory encoding reliant on persistent changes in the properties of synapses, a key question is how can memories be maintained from days to months or a lifetime given molecular turnover? It is likely that positive feedback loops are necessary to persistently ... More

Simulations Suggest Pharmacological Methods for Rescuing Long-Term PotentiationAug 08 2014Congenital cognitive dysfunctions are frequently due to deficits in molecular pathways that underlie synaptic plasticity. For example, Rubinstein-Taybi syndrome (RTS) is due to a mutation in cbp, encoding the histone acetyltransferase CREB-binding protein ... More

Bistable MAP Kinase Activity: A Plausible Mechanism Contributing to Maintenance of Late Long-Term PotentiationFeb 18 2008Bistability of MAP kinase (MAPK) activity has been suggested to contribute to several cellular processes, including differentiation and long-term synaptic potentiation. A recent model (48) predicts bistability due to interactions of the kinases and phosphatases ... More

How Can Memories Last for Days, Years, or a Lifetime? Proposed Mechanisms for Maintaining Synaptic Potentiation and MemoryMar 13 2019With memory encoding reliant on persistent changes in the properties of synapses, a key question is how can memories be maintained from days to months or a lifetime given molecular turnover? It is likely that positive feedback loops are necessary to persistently ... More

Paradoxical LTP maintenance with inhibition of protein synthesis and the proteasome suggests a novel protein synthesis requirement for early LTP reversalAug 20 2018The transition from early long-term potentiation (E-LTP) to late LTP (L-LTP) involves protein synthesis and degradation. L-LTP is blocked by inhibiting either protein synthesis or proteasome-dependent degradation prior to and during a tetanic stimulus, ... More

A Model of the Roles of Essential Kinases in the Induction and Expression of Late Long-Term PotentiationJan 03 2006The induction of late long-term potentiation (L-LTP) involves complex interactions among second messenger cascades. To gain insights into these interactions, a mathematical model was developed for L-LTP induction in the CA1 region of the hippocampus. ... More

How Can Memories Last for Days, Years, or a Lifetime? Proposed Mechanisms for Maintaining Synaptic Potentiation and MemoryMar 13 2019Apr 05 2019With memory encoding reliant on persistent changes in the properties of synapses, a key question is how can memories be maintained from days to months or a lifetime given molecular turnover? It is likely that positive feedback loops are necessary to persistently ... More

Interlinked Dual-Time Feedback Loops can Enhance Robustness to Stochasticity and Persistence of MemoryAug 29 2012Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular calcium release. Recent studies with simplified models have identified two advantages of coupling fast and ... More

Simulation of Drosophila Circadian Oscillations, Mutations, and Light Responses by a Model with VRI, PDP-1, and CLKJan 23 2004A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional ... More

Role of Umklapp Processes in Conductivity of Doped Two-Leg LaddersApr 22 2002Recent conductivity measurements performed on the hole-doped two-leg ladder material $\mathrm{Sr_{14-x}Ca_xCu_{24}O_{41}}$ reveal an approximately linear power law regime in the c-axis DC resistivity as a function of temperature for $x=11$. In this work, ... More

Turbulence damping as a measure of the flow dimensionalityDec 07 2010The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads to increased ... More

Robust inverse energy cascade and turbulence structure in three-dimensional layers of fluidSep 13 2011Here we report the first evidence of the inverse energy cascade in a flow dominated by 3D motions. Experiments are performed in thick fluid layers where turbulence is driven electromagnetically. It is shown that if the free surface of the layer is not ... More

Tensor Representation of Rank-Metric CodesApr 10 2019We present the theory of rank-metric codes with respect to the 3-tensors that generate them. We define the generator tensor and the parity check tensor of a matrix code, and describe the properties of a code through these objects. We define the tensor ... More

Recursion Rules for the Hypergeometric Zeta FunctionsMay 08 2013The hypergeometric zeta function is defined in terms of the zeros of the Kummer function M(a, a + b; z). It is established that this function is an entire function of order 1. The classical factorization theorem of Hadamard gives an expression as an infinite ... More

Acoustic Supercoupling in a Zero-Compressibility WaveguideDec 18 2018Funneling acoustic waves through largely mismatched channels is of fundamental importance to tailor and transmit sound for a variety of applications. In electromagnetics, zero-permittivity metamaterials have been used to enhance the coupling of energy ... More

Conditions for large non-Gaussianity in two-field slow-roll inflationJul 07 2008Oct 06 2008We study the level of primordial non-Gaussianity in slow-roll two-field inflation. Using an analytic formula for the nonlinear parameter f_nl in the case of a sum or product separable potential, we find that it is possible to generate significant non-Gaussianity ... More

Large non-Gaussianity from two-component hybrid inflationDec 04 2008Feb 12 2009We study the generation of non-Gaussianity in models of hybrid inflation with two inflaton fields, (2-brid inflation). We analyse the region in the parameter and the initial condition space where a large non-Gaussianity may be generated during slow-roll ... More

Encoding Reality: Prediction-Assisted Cortical Learning Algorithm in Hierarchical Temporal MemorySep 28 2015Oct 08 2015In the decade since Jeff Hawkins proposed Hierarchical Temporal Memory (HTM) as a model of neocortical computation, the theory and the algorithms have evolved dramatically. This paper presents a detailed description of HTM's Cortical Learning Algorithm ... More

The Cause of GravityFeb 18 1999Feb 25 1999Einstein said that gravity is an acceleration like any other acceleration. But gravity causes relativistic effects at non-relativistic speeds; so gravity could have relativistic origins. And since the strong force is thought to cause most of mass, and ... More

A Survey of Miss-Ratio Curve Construction TechniquesApr 05 2018Miss-ratio curve (MRC), or equivalently hit-ratio curve (HRC), construction techniques have recently gathered the attention of many researchers. Recent advancements have allowed for approximating these curves in constant time, allowing for online working-set-size ... More

Symphony from Synapses: Neocortex as a Universal Dynamical Systems Modeller using Hierarchical Temporal MemoryDec 16 2015Reverse engineering the brain is proving difficult, perhaps impossible. While many believe that this is just a matter of time and effort, a different approach might help. Here, we describe a very simple idea which explains the power of the brain as well ... More

Universal Extra Dimensions and Charged LKPsNov 12 2003We consider the possibility of charged stable Kaluza-Klein leptons in orbifold models in which all the Standard Model fields propagate (UED models). At tree level the masses of the 1st mode states are nearly identical and kinematics can prevent the decays ... More

Quantum GravityApr 29 2000Gravitons should have momentum just as photons do; and since graviton momentum would cause compression rather than elongation of spacetime outside of matter; it does not appear that gravitons are compatible with Swartzchild's spacetime curvature. Also, ... More

On the Weight Distribution of Codes over Finite RingsJan 07 2011Let R > S be finite Frobenius rings for which there exists a trace map T from R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is an S-linear subring-subcode of a left linear code over R. We consider functions f for which the ... More

Spatial GravityApr 25 2000Hubble's correlation of red-shift with distance reveals that the universe is expanding, and that spacetime curvature has increased over time. And since time and space have equal status as dimensions, an object moving through time experiences increasing ... More

Induced Weights on Quotient Modules and an Application to Error Correction in Coherent NetworksNov 29 2016Oct 18 2017We consider distance functions on a quotient module $M/K$ induced by distance functions on a module $M$. We define error-correction for codes in $M/K$ with respect to induced distance functions. For the case that the metric is induced by a homogeneous ... More

Computational modeling of protein interactions and phosphoform kinetics in the KaiABC cyanobacterial circadian clockMay 14 2014The KaiABC circadian clock from cyanobacteria is the only known three-protein oscillatory system which can be reconstituted outside the cell and which displays sustained periodic dynamics in various molecular state variables. Despite many recent experimental ... More

Devil's crevasse and macroscopic entanglement in two-component Bose-Einstein condensatesMay 22 2013Spin coherent states are the matter equivalent of optical coherent states, where a large number of two component particles form a macroscopic state displaying quantum coherence. Here we give a detailed study of entanglement generated between two spin-1/2 ... More

The Duality of Nature: Why N Equals 10Jan 05 1999Negative solutions are possible for Einstein's Special Relativity equation, as well as Dirac's, Maxwell's, and Schrodinger's equations; and Schrodinger's equation utilizes antitime to calculate quantum probabilities. Also, since no ground state seems ... More

Bounds on Network Codes for the Homogeneous WeightNov 29 2016We give upper bounds on the size of a code whose fundamental parameters are determined by a a directed acyclic graph. These are extensions of Plotkin and Elias bounds of classical coding theory.

Empirical AUC for evaluating probabilistic forecastsAug 22 2015Scoring functions are used to evaluate and compare partially probabilistic forecasts. We investigate the use of rank-sum functions such as empirical Area Under the Curve (AUC), a widely-used measure of classification performance, as a scoring function ... More

A Technical Review of Penning Trap based Investigations in Neutron DecayJul 11 2014This review is concerned with a detailed analysis of some of the technical problems which arise in the application of the Penning trap method to the experimental study of neutron $\beta $ -decay,a technique which was first successfully tested on the low-flux ... More

Maximizing General Set Functions by Submodular DecompositionMay 30 2009We present a branch and bound method for maximizing an arbitrary set function h mapping 2^V to R. By decomposing h as f-g, where f is a submodular function and g is the cut function of a (simple, undirected) graph G with vertex set V, our original problem ... More

Persistent Currents in the Heisenberg chain with a weak linkMay 08 2002May 14 2002The Heisenberg chain with a weak link is studied, as a simple example of a quantum ring with a constriction or defect. The Heisenberg chain is equivalent to a spinless electron gas under a Jordan-Wigner transformation. Using density matrix renormalization ... More

Models, measurement and inference in epithelial tissue dynamicsJun 16 2015The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that have been used ... More

Age patterns in a sample of nearby spiral galaxiesMar 21 2011We present the burst ages for young stellar populations in a sample of six nearby (< 10 Mpc) spiral galaxies using a differential pixel-based analysis of the ionized gas emission. We explore this as an alternative approach for connecting large-scale dynamical ... More

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case StudyFeb 06 2015Jul 30 2015The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical ... More

Widespread Excess Ice in Arcadia Planitia, MarsSep 10 2015The distribution of subsurface water ice on Mars is a key constraint on past climate, while the volumetric concentration of buried ice (pore-filling versus excess) provides information about the process that led to its deposition. We investigate the subsurface ... More

Mapping the aberrations of a wide-field spectrograph using a photonic combApr 27 2017We demonstrate a new approach to calibrating the spectral-spatial response of a wide-field spectrograph using a fibre etalon comb. Conventional wide-field instruments employed on front-line telescopes are mapped with a grid of diffraction-limited holes ... More

Bounding the optimal rate of the ICSI and ICCSI problemApr 20 2016In this work we study both the index coding with side information (ICSI) problem and the more general problem of index coding with coded side information (ICCSI), as introduced by Shum et al in 2012. We investigate the optimal rate of an instance of the ... More

An Assmus-Mattson Theorem for Rank Metric CodesJun 01 2018Jun 06 2018A $t$-$(n,d,\lambda)$ design over ${\mathbb F}_q$, or a subspace design, is a collection of $d$-dimensional subspaces of ${\mathbb F}_q^n$, called blocks, with the property that every $t$-dimensional subspace of ${\mathbb F}_q^n$ is contained in the same ... More

Bitcoin and quantum computingNov 12 2017Jan 09 2018Bitcoin is a digital currency and payment system based on classical cryptographic technologies which works without a central administrator such as in traditional currencies. It has long been questioned what the impact of quantum computing would be on ... More

Generalized framework for applying the Kelly criterion to stock marketsJun 13 2018We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by ... More

Adaptive Detection of Structured Signals in Low-Rank InterferenceAug 16 2018Feb 15 2019In this paper, we consider the problem of detecting the presence (or absence) of an unknown but structured signal from the space-time outputs of an array under strong, non-white interference. Our motivation is the detection of a communication signal in ... More

Quadratic Binomial APN Functions and Absolutely Irreducible PolynomialsOct 24 2008We show that many quadratic binomial functions on a finite field of characteristic 2 are not APN infinitely often. This is of interest in the light of recent discoveries of new families of quadratic binomial APN functions. The proof uses the Weil bound ... More

Vortex Dynamics in Cerebral AneurysmsSep 30 2013We use an autonomous three-dimensional dynamical system to study embedded vortex structures that are observed to form in computational fluid dynamic simulations of patient-specific cerebral aneurysm geometries. These structures, described by a vortex ... More

Quantum feedback control of atomic ensembles and spinor Bose-Einstein condensatesAug 29 2016Sep 01 2016Cold atomic ensembles and spinor Bose-Einstein condensates (BECs) are potential candidates for quantum memories as they have long coherence times and can be coherently controlled. Unlike most candidates for quantum memories which are genuine or effective ... More

Next generation neural mass modelsJul 21 2016Neural mass models have been actively used since the 1970s to model the coarse grained activity of large populations of neurons and synapses. They have proven especially useful in understanding brain rhythms. However, although motivated by neurobiological ... More

Next generation neural mass modelsJul 21 2016Nov 07 2016Neural mass models have been actively used since the 1970s to model the coarse grained activity of large populations of neurons and synapses. They have proven especially useful in understanding brain rhythms. However, although motivated by neurobiological ... More

Investigating the Kinematics of Coronal Mass Ejections with the Automated CORIMP CatalogJun 12 2015Studying coronal mass ejections (CMEs) in coronagraph data can be challenging due to their diffuse structure and transient nature, compounded by the variations in their dynamics, morphology, and frequency of occurrence. The large amounts of data available ... More

Quantum teleportation of spin coherent states: beyond continuous variables teleportationMay 11 2013Jul 29 2014We introduce a quantum teleportation scheme that can transfer a macroscopic spin coherent state between two locations. In the scheme a large number of copies of a qubit, such as realized in a coherent two-component Bose-Einstein condensate, is teleported ... More

Unfolding and Shrinking Neural Machine Translation EnsemblesApr 11 2017Jul 21 2017Ensembling is a well-known technique in neural machine translation (NMT) to improve system performance. Instead of a single neural net, multiple neural nets with the same topology are trained separately, and the decoder generates predictions by averaging ... More

Covering Radius of Matrix Codes Endowed with the Rank MetricAug 31 2016In this paper we study properties and invariants of matrix codes endowed with the rank metric, and relate them to the covering radius. We introduce new tools for the analysis of rank-metric codes, such as puncturing and shortening constructions. We give ... More

The Maximum Length of Circuit Codes With Long Bit Runs and a New Characterization TheoremSep 22 2018Oct 30 2018We study circuit codes with long bit runs (sequences of distinct transitions) and derive a formula for the maximum length for an infinite class of symmetric circuit codes with long bit runs. This formula also results in an improved lower bound on the ... More

Discussion of "Geodesic Monte Carlo on Embedded Manifolds"Nov 05 2013Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)

A Non-Degenerate Perturbation of the Assignment Polytope and its Application to Graph MatchingDec 08 2014We consider maximizing a continuous convex function over the assignment polytope. Such problems arise in Graph Matching (the optimization version of Graph Isomorphism) and Quadratic Assignment problems. In the typical case of maximizing a convex function ... More

Constraints on generating the primordial curvature perturbation and non-Gaussianity from instant preheatingOct 22 2008Dec 03 2008We analyse models of inflation in which isocurvature perturbations present during inflation are converted into the primordial curvature perturbation during instant preheating. This can be due to an asymmetry between the fields present either during inflation ... More

Simulating lattice gauge theories on a quantum computerOct 04 2005We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators ... More

Bounding the optimal rate of the ICSI and ICCSI problemApr 20 2016Dec 12 2016In this work we study both the index coding with side information (ICSI) problem introduced by Birk and Kol in 1998 and the more general problem of index coding with coded side information (ICCSI), described by Shum et al in 2012. We estimate the optimal ... More

Post-common envelope binary stars: Radiative Levitation and Blue Large- Amplitude PulsatorsNov 27 2018Following the recent discovery of a new class of pulsating star, the blue large-amplitude pulsators (BLAPs), pulsation stability analysis was carried out on evolutionary models of post-common envelope (CE) ejection stars of 0.3 and 0.46 solar masses. ... More

Time dynamics of Bethe ansatz solvable modelsMay 09 2019We develop a method for finding the time evolution of exactly solvable models by Bethe ansatz. The dynamical Bethe wavefunction takes the same form as the stationary Bethe wavefunction except for time varying Bethe parameters and a complex phase prefactor. ... More

An Assmus-Mattson Theorem for Rank Metric CodesJun 01 2018Mar 15 2019A $t$-$(n,d,\lambda)$ design over ${\mathbb F}_q$, or a subspace design, is a collection of $d$-dimensional subspaces of ${\mathbb F}_q^n$, called blocks, with the property that every $t$-dimensional subspace of ${\mathbb F}_q^n$ is contained in the same ... More

Investigating the relationship between biodiversity and ecosystem multifunctionality: Challenges and solutionsMay 09 2013Extensive research shows that more species-rich assemblages are generally more productive and efficient in resource use than comparable assemblages with fewer species. But the question of how diversity simultaneously affects the wide variety of ecological ... More

Design of Optically Path Length Matched, Three-Dimensional Photonic Circuits Comprising Uniquely Routed WaveguidesSep 24 2012A method for designing physically path length matched, three-dimensional photonic circuits is described. We focus specifically on the case where all the waveguides are uniquely routed from the input to output; a problem which has not been addressed to ... More

Error Correction for Index Coding With Coded Side InformationJun 02 2015Jul 18 2016Index coding is a source coding problem in which a broadcaster seeks to meet the different demands of several users, each of whom is assumed to have some prior information on the data held by the sender. If the sender knows its clients' requests and their ... More

Implementing the Deutsch-Jozsa algorithm with macroscopic ensemblesApr 29 2016Quantum computing implementations under consideration today typically deal with systems with microscopic degrees of freedom such as photons, ions, cold atoms, and superconducting circuits. The quantum information is stored typically in low-dimensional ... More

Lecture notes on non-GaussianityNov 25 2014We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. ... More

Radiative forcings for 28 potential Archean greenhouse gasesSep 05 2014Despite reduced insolation in the late Archean, evidence suggests a warm climate which was likely sustained by a stronger greenhouse effect, the so-called Faint Young Sun Problem (FYSP). CO2 and CH4 are generally thought to be the mainstays of this enhanced ... More

Multilayer optical calculationsMar 06 2016Nov 05 2018When light hits a multilayer planar stack, it is reflected, refracted, and absorbed in a way that can be derived from the Fresnel equations. The analysis is treated in many textbooks, and implemented in many software programs, but certain aspects of it ... More

The Kinematics and Morphology of Solar Coronal Mass EjectionsFeb 17 2012Solar coronal mass ejections (CMEs) are large-scale eruptions of plasma and magnetic field from the Sun into the corona and interplanetary space. They are the most significant drivers of adverse space weather at Earth and other locations in the heliosphere, ... More

Photorefractive second-harmonic detection for ultrasound-modulated optical tomographyApr 18 2018Ultrasound-modulated optical tomography enables sharp 3D optical imaging of tissues and other turbid media, but the light modulation signals are hard to sensitively measure. A common solution, involving photorefractive crystals, enables the measurement ... More

Variables effecting photomosaic reconstruction and ortho-rectification from aerial survey datasetsNov 10 2016Unmanned aerial vehicles now make it possible to obtain high quality aerial imagery at a low cost, but processing those images into a single, useful entity is neither simple nor seamless. Specifically, there are factors that must be addressed when merging ... More

Light mediated non-Gaussian atomic ensemble entanglementMar 23 2017We analyze a similar scheme for producing light-mediated entanglement between atomic ensembles, as first realized by Julsgaard, Kozhekin and Polzik [Nature {\bf 413}, 400 (2001)]. In the standard approach to modeling the scheme, a Holstein-Primakoff approximation ... More

Multilayer optical calculationsMar 06 2016Aug 28 2016When light hits a multilayer planar stack, it is reflected, refracted, and absorbed in a way that can be derived from the Fresnel equations. The analysis is treated in many textbooks, and implemented in many software programs, but certain aspects of it ... More

A Graph Theoretical Analysis of Low-Power Coding Schemes for One-Hop NetworksJun 03 2016Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In this paper, coding ... More

Sparse Multinomial Logistic Regression via Approximate Message PassingSep 15 2015Jun 14 2016For the problem of multi-class linear classification and feature selection, we propose approximate message passing approaches to sparse multinomial logistic regression (MLR). First, we propose two algorithms based on the Hybrid Generalized Approximate ... More

Geodesic Monte Carlo on Embedded ManifoldsJan 25 2013Jun 25 2013Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows ... More

Quintessence and Varying αfrom Shape ModuliFeb 09 2004In extra-dimensional models which are compactified on an n-torus (n>1) there exist moduli associated with the torus volume (which sets the fundamental Planck scale), the ratios of the torus radii, and the angle(s) of periodicity. We consider a model with ... More

A New Method for Constructing Circuit CodesApr 10 2016Circuit codes are constructed from induced cycles in the graph of the $n$ dimensional hypercube. They are both theoretically and practically important, as circuit codes can be used as error correcting codes. When constructing circuit codes, the length ... More

The skyrmion quantum spin Hall effectMay 04 2019The quantum spin Hall effect is conventionally thought to require a strong spin-orbit coupling, producing an effective spin-dependent magnetic field. However, spin currents can also be present without transport of spins, for example in spin-waves or skyrmions. ... More

Partition-Balanced Families of Codes and Asymptotic Enumeration in Coding TheoryMay 05 2018Dec 12 2018We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise asymptotic ... More

First Light: A Brief ReviewJan 23 2012Jun 19 2012The first stars in the universe are thought to be massive, forming in dark matter halos with masses around 10^6 solar masses. Recent simulations suggest that these metal-free (Population III) stars may form in binary or multiple systems. Because of their ... More

A Novel Visualization of the Geometry of Special RelativityOct 29 2015Apr 05 2016The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR that may, by complementing ... More

Galaxy rotation curves with log-normal density distributionFeb 10 2015The log-normal distribution represents the probability of finding randomly distributed particles in a micro canonical ensemble with high entropy. To a first approximation, a modified form of this distribution with a truncated termination may represent ... More

Indefinite quadratic forms and the invariance of the interval in Special RelativityApr 24 2009Aug 03 2009A simple theorem on proportionality of indefinite real quadratic forms is proved, and is used to clarify the proof of the invariance of the interval in Special Relativity from Einstein's postulate on the universality of the speed of light; students are ... More

Theoretical Models of Sunspot Structure and DynamicsMar 24 2009Recent progress in theoretical modeling of a sunspot is reviewed. The observed properties of umbral dots are well reproduced by realistic simulations of magnetoconvection in a vertical, monolithic magnetic field. To understand the penumbra, it is useful ... More

Quillen stratification for the Steenrod algebraMar 01 1999Let A be the mod 2 Steenrod algebra, and let Q denote the category of exterior sub-Hopf algebras of A, where the morphisms are given by inclusions. The restriction maps Ext_A (Z/2,Z/2) --> Ext_E (Z/2,Z/2), for E in Q, can be assembled into a map i:Ext_A ... More

The Early Years of String Theory: A Personal PerspectiveAug 14 2007Apr 03 2009This article surveys some of the highlights in the development of string theory through the first superstring revolution in 1984. The emphasis is on topics in which the author was involved, especially the observation that critical string theories provide ... More

Highly Effective ActionsNov 01 2013Nov 22 2013It is conjectured that the world-volume action of a probe D3-brane in an $AdS_5 \times S^5$ background of type IIB superstring theory, with one unit of flux, can be reinterpreted as the exact effective action (or highly effective action) for U(2), ${\cal ... More

The Generalized Stieltjes Transform and Its InverseMay 18 2004The generalized Stieltjes transform (GST) is an integral transform that depends on a parameter $\rho > 0$. In previous work a convenient form of the inverse transformation was derived for the case $\rho = 3/2$. This paper generalizes that result to all ... More

Does Superstring Theory Have a Conformally Invariant Limit?Aug 01 2000This talk describes a proposal, due to Hull, for a conformally invariant limit of superstring theory in six dimensions.

TASI Lectures on Non-BPS D-Brane SystemsAug 20 1999Sep 14 1999In this set of lectures various properties of D-branes are discussed. After reviewing the basics, we discuss unstable D-brane/anti-D-brane systems, a subject pioneered by Sen. Following him, we discuss the construction of the non-BPS D0-brane in type ... More

M Theory Extensions of T DualityJan 15 1996T duality expresses the equivalence of a superstring theory compactified on a manifold K to another (possibly the same) superstring theory compactified on a dual manifold K'. The volumes of K and K' are inversely proportional. In this talk we consider ... More

Superstring Compactification and Target Space DualityAug 26 1991This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces, with completely ... More

Recent Progress in Superstring TheoryJul 17 2000Jul 18 2000Superstring theory has continued to develop at a rapid clip in the past few years. Following a quick review of some of the major discoveries prior to 1998, this talk focuses on a few of the more recent developments. The topics I have chosen to present ... More

Introduction to M Theory and AdS/CFT DualityDec 04 1998Dec 11 1998An introductory survey of some of the developments that have taken place in superstring theory in the past few years is presented. The main focus is on three particular dualities. The first one is the appearance of an 11th dimension in the strong coupling ... More

The M Theory Five-Brane and the Heterotic StringMay 13 1997Brane actions with chiral bosons present special challenges. Recent progress in the description of the two main examples -- the M theory five-brane and the heterotic string -- is described. Also, double dimensional reduction of the M theory five-brane ... More

The Second Superstring RevolutionJul 08 1996Recent developments in superstring theory have led to major advances in understanding. After reviewing where things stood earlier, we sketch the impact of recently identified dualities and D-branes, as well as a hidden eleventh dimension.