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The Takeoff Towards Optimal Sorting NetworksFeb 16 2015Mar 12 2015A complete set of filters $F_n$ for the optimal-depth $n$-input sorting network problem is such that if there exists an $n$-input sorting network of depth $d$ then there exists one of the form $C \oplus C'$ for some $C \in F_n$. Previous work on the topic ... More

Vectorization of Multibyte Floating Point Data FormatsJan 26 2016Jul 22 2016We propose a scheme for reduced-precision representation of floating point data on a continuum between IEEE-754 floating point types. Our scheme enables the use of lower precision formats for a reduction in storage space requirements and data transfer ... More

Practical Algorithms for Finding Extremal SetsAug 07 2015The minimal sets within a collection of sets are defined as the ones which do not have a proper subset within the collection, and the maximal sets are the ones which do not have a proper superset within the collection. Identifying extremal sets is a fundamental ... More

Sorting Networks: The Final CountdownFeb 20 2015In this paper we extend the knowledge on the problem of empirically searching for sorting networks of minimal depth. We present new search space pruning techniques for the last four levels of a candidate sorting network by considering only the output ... More

On the GI-Completeness of a Sorting Networks IsomorphismJul 21 2015Jan 19 2016The subitemset isomorphism problem is really important and there are excellent practical solutions described in the literature. However, the computational complexity analysis and classification of the BZ (Bundala and Zavodny) subitemset isomorphism problem ... More

Mutual Inclusivity of the Critical Path and its Partial Schedule on Heterogeneous SystemsJan 30 2017The critical path of a group of tasks is an important measure that is commonly used to guide task allocation and scheduling on parallel computers. The critical path is the longest chain of dependencies in an acyclic task dependence graph. A problem arises ... More

Winograd Convolution for DNNs: Beyond linear polinomialsMay 13 2019We investigated a wider range of Winograd family convolution algorithms for Deep Neural Network. We presented the explicit Winograd convolution algorithm in general case (used the polynomials of the degrees higher than one). It allows us to construct ... More

Low Complexity Multiply Accumulate Unit for Weight-Sharing Convolutional Neural NetworksAug 30 2016Convolutional Neural Networks (CNNs) are one of the most successful deep machine learning technologies for processing image, voice and video data. Implementations of CNNs require very large amounts of processing capacity and data, which is problematic ... More

Scalar Arithmetic Multiple Data: Customizable Precision for Deep Neural NetworksSep 27 2018Quantization of weights and activations in Deep Neural Networks (DNNs) is a powerful technique for network compression, and has enjoyed significant attention and success. However, much of the inference-time benefit of quantization is accessible only through ... More

Customizable Precision of Floating-Point Arithmetic with Bitslice Vector TypesFeb 15 2016Customizing the precision of data can provide attractive trade-offs between accuracy and hardware resources. We propose a novel form of vector computing aimed at arrays of custom-precision floating point data. We represent these vectors in bitslice format. ... More

Matrix formulae and skein relations for cluster algebras from surfacesAug 17 2011This paper concerns cluster algebras with principal coefficients A(S,M) associated to bordered surfaces (S,M), and is a companion to a concurrent work of the authors with Schiffler [MSW2]. Given any (generalized) arc or loop in the surface -- with or ... More

Paths to Understanding Birational Rowmotion on Products of Two ChainsJan 11 2018Aug 09 2018Birational rowmotion is an action on the space of assignments of rational functions to the elements of a finite partially-ordered set (poset). It is lifted from the well-studied rowmotion map on order ideals (equivariantly on antichains) of a poset $P$, ... More

A construction of generalized Harish-Chandra modules for locally reductive Lie algebrasApr 30 2007We study cohomological induction for a pair $(\frak g,\frak k)$, $\frak g$ being an infinite dimensional locally reductive Lie algebra and $\frak k \subset\frak g$ being of the form $\frak k_0 + C_\gg(\frak k_0)$, where $\frak k_0\subset\frak g$ is a ... More

Quasiinvariants of $S_3$Mar 20 2006Let $s_{ij}$ represent a tranposition in $S_n$. A polynomial $P$ in $\mathbb{Q}[X_n]$ is said to be $m$-quasiinvariant with respect to $S_n$ if $(x_i-x_j)^{2m+1}$ divides $(1-s_{ij})P$ for all $1 \leq i, j \leq n$. We call the ring $m$-quasiinvariants ... More

Cluster expansion formulas and perfect matchingsOct 20 2008We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain ... More

A Taxonomy of Channel Pruning Signals in CNNsJun 11 2019Convolutional neural networks (CNNs) are widely used for classification problems. However, they often require large amounts of computation and memory which are not readily available in resource constrained systems. Pruning unimportant parameters from ... More

Parallel Multi Channel Convolution using General Matrix MultiplicationApr 06 2017Jul 03 2017Convolutional neural networks (CNNs) have emerged as one of the most successful machine learning technologies for image and video processing. The most computationally intensive parts of CNNs are the convolutional layers, which convolve multi-channel images ... More

Beam me up, Spotty: Toward a new understanding of the physics of massive star photospheresJul 31 2014For 30 years, cyclical wind variability in OB stars has puzzled the astronomical community. Phenomenological models involving co-rotating bright spots provide a potential explanation for the observed variations, but the underlying physics remains unknown. ... More

Spectral Convolution NetworksNov 16 2016Previous research has shown that computation of convolution in the frequency domain provides a significant speedup versus traditional convolution network implementations. However, this performance increase comes at the expense of repeatedly computing ... More

Error Analysis and Improving the Accuracy of Winograd Convolution for Deep Neural NetworksMar 29 2018Sep 22 2018Modern deep neural networks (DNNs) spend a large amount of their execution time computing convolutions. Winograd's minimal algorithm for small convolutions can greatly reduce the number of arithmetic operations. However, a large reduction in floating ... More

Coherent State Quantum Key Distribution with Entanglement WitnessingMay 17 2013Sep 16 2013An entanglement witness approach to quantum coherent state key distribution and a system for its practical implementation are described. In this approach, eavesdropping can be detected by a change in sign of either of two witness functions, an entanglement ... More

An investigation of the Eigenvalue Calibration Method (ECM) using GASP for non-imaging and imaging detectorsSep 17 2015Polarised light from astronomical targets can yield a wealth of information about their source radiation mechanisms, and about the geometry of the scattered light regions. Optical observations, of both the linear and circular polarisation components, ... More

An efficient approach to approximating the pair distribution function of the inhomogeneous hard-sphere fluidMar 26 2014Sep 24 2014We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact which has been shown to accurately reproduce ... More

Error Analysis and Improving the Accuracy of Winograd Convolution for Deep Neural NetworksMar 29 2018May 01 2019Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software frameworks. However, ... More

Low-memory GEMM-based convolution algorithms for deep neural networksSep 08 2017Deep neural networks (DNNs) require very large amounts of computation both for training and for inference when deployed in the field. A common approach to implementing DNNs is to recast the most computationally expensive operations as general matrix multiplication ... More

Discovery of electron cyclotron MASER emission from the magnetic Bp star HD 133880 with the Giant Metrewave Radio TelescopeNov 27 2017Nov 29 2017We report the discovery of coherent radio emission from the young, rapidly-rotating magnetic Bp star HD 133880 at a frequency of 610 MHz with the Giant Metrewave Radio Telescope (GMRT). This is only the second magnetic star in which coherent radio emission ... More

Detection of coherent emission from the Bp star HD 142990 at uGMRT frequenciesApr 17 2019HD 142990 is a Bp-type star with a nearly dipolar surface magnetic field of kG strength. Recently Lenc et al. (2018) reported the tentative discovery of Electron Cyclotron Maser Emission (ECME) from this star at 200 MHz. This type of emission has been ... More

Combinatorial Aspects of Elliptic CurvesJul 23 2007Given an elliptic curve C, we study here $N_k = #C(F_{q^k})$, the number of points of C over the finite field F_{q^k}. This sequence of numbers, as k runs over positive integers, has numerous remarkable properties of a combinatorial flavor in addition ... More

Disentangling microlensing and differential extinction in the double QSO HE0512-3329Apr 24 2003We present the first separate spectra of both components of the small-separation double QSO HE0512-3329 obtained with HST/STIS in the optical and near UV. The similarities especially of the emission line profiles and redshifts strongly suggest that this ... More

Bell Gems: the Bell basis generalizedJul 29 2004A class of self-similar sets of entangled quantum states is introduced, for which a recursive definition is provided. These sets, the "Bell gems," are defined by the subsystem exchange symmetry characteristic of the Bell states. Each Bell gem is shown ... More

In Appreciation of Abner ShimonyDec 10 2015Dec 16 2015Abner Shimony was an exceptional human being and a remarkably lucid and penetrating thinker whose work centered on some of the most significant physical and philosophical questions of his era at their nexus. He approached these questions with an open, ... More

Investigating the origin of cyclical spectral variations in hot, massive starsOct 12 2013OB stars are known to exhibit various types of wind variability, as detected in their ultraviolet spectra, amongst which are the ubiquitous discrete absorption components (DACs). These features have been associated with large-scale azimuthal structures ... More

A Phase Variable Approach for Improved Volitional and Rhythmic Control of a Powered Knee-Ankle ProsthesisNov 13 2018Although there has been recent progress in control of multi-joint prosthetic legs for periodic tasks such as walking, volitional control of these systems for non-periodic maneuvers is still an open problem. In this paper, we develop a new controller that ... More

The FIRST-2MASS Red Quasar SurveyJun 21 2007Combining radio observations with optical and infrared color selection -- demonstrated in our pilot study to be an efficient selection algorithm for finding red quasars -- we have obtained optical and infrared spectroscopy for 120 objects in a complete ... More

The First FIRST Gravitationally Lensed Quasar: FBQ 0951+2635Oct 13 1997The V=16.9 quasar FBQ 0951+2635 at redshift z=1.24 appears double on CCD exposures taken in subarcsecond seeing. The two objects are separated by 1.1" and differ in brightness by 0.9 mag. VLA observations show the radio source to be double with the same ... More

Book Review: Bohmian Mechanics and Quantum Theory: An AppraisalJun 25 1999Jun 29 1999A review of "Bohmian Mechanics and Quantum Theory: An Appraisal" (James Cushing, Arthur Fine and Sheldon Goldstein, Eds.), an extensive collection of articles on Bohmian mechanics. In addition to broad, critical overviews of Bohmian mechanics, the reviewed ... More

Invariants, Kronecker Products, and Combinatorics of Some Remarkable Diophantine Systems (Extended Version)Oct 01 2008This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single formal power series ... More

Aztec Castles and the dP3 QuiverAug 19 2013Aug 25 2014Bipartite, periodic, planar graphs known as brane tilings can be associated to a large class of quivers. This paper will explore new algebraic properties of the well-studied del Pezzo 3 quiver and geometric properties of its corresponding brane tiling. ... More

First Empirical Constraints on the Low H$α$ Mass-Loss Rates of Magnetic O-StarsNov 01 2018A small subset of Galactic O-stars possess surface magnetic fields that alter the outflowing stellar wind by magnetically confining it. Key to the magnetic confinement is that it induces rotational modulation of spectral lines over the full EM domain; ... More

FIRST-2MASS Sources Below the APM Detection Threshold: A Population of Highly Reddened QuasarsFeb 16 2004We have constructed a sample of bright near-infrared sources which are detected at radio wavelengths but undetected on the POSS I plates in order to search for a population of dust-obscured quasars. Optical and infrared spectroscopic followup of the sample ... More

Rotationally modulated photometric variations in B supergiants?Nov 22 2017In this contribution, we present BRITE observations of the early-B supergiants $\epsilon$ Ori and $\kappa$ Ori. We perform a preliminary analysis of the data acquired over the first two Orion observing runs. We evaluate whether they are compatible with ... More

Discovery of a High-Redshift (z=0.96) Cluster of Galaxies Using a FIRST Wide-Angle Tailed Radio SourceDec 18 2002Using a combination of near-infrared and optical photometry, along with multi-object spectroscopy, we have confirmed the existence of a high-redshift cluster of galxies at z = 0.96. The cluster was found using a wide-angle tailed radio source selected ... More

X-ray emission from magnetic massive starsSep 05 2014Mar 08 2016Magnetically confined winds of early-type stars are expected to be sources of bright and hard X-rays. To clarify the systematics of the observed X-ray properties, we have analyzed a large series of Chandra and XMM observations, corresponding to all available ... More

The Strongest Magnetic Fields on the Coolest Brown DwarfsAug 07 2018We have used NSF's Karl G. Jansky Very Large Array (VLA) to observe a sample of five known radio-emitting late L and T dwarfs ranging in age from ~0.2 - 3.4Gyr. We observed each target for seven hours, extending to higher frequencies than previously attempted ... More

Fractal states in quantum information processingAug 01 2007The fractal character of some quantum properties has been shown for systems described by continuous variables. Here, a definition of quantum fractal states is given that suits the discrete systems used in quantum information processing, including quantum ... More

Combinatorial Aspects of Elliptic Curves II: Relationship between Elliptic Curves and Chip-Firing Games on GraphsOct 02 2007Let q be a power of a prime and E be an elliptic curve defined over F_q. In "Combinatorial aspects of elliptic curves" [17], the present author examined a sequence of polynomials which express the N_k's, the number of points on E over the field extensions ... More

A graph theoretic expansion formula for cluster algebras of classical typeOct 18 2007Nov 05 2007In this paper we give a graph theoretic combinatorial interpretation for the cluster variables that arise in most cluster algebras of finite type. In particular, we provide a family of graphs such that a weighted enumeration of their perfect matchings ... More

Magnetic Cataclysmic Variables Discovered in the Palomar Transient FactoryApr 16 2013The Palomar Transient Factory proves to be a prolific source of Magnetic Cataclysmic Variables, selected by their distinctive photometric variability, and followed up spectroscopically. Here, we present six new candidate systems, together with preliminary ... More

Magnetic Fields of Slowly Pulsating B Stars and β Cep Variables: Comparing Results from FORS1/2 and ESPaDOnSSep 26 2011Oct 12 2011Recently announced magnetic models for four SPB and {\beta} Cep stars, along with magnetic detections for two additional stars, have potentially doubled the number of known magnetic SPB and \beta Cep stars (see Grunhut et al., these proceedings). We have ... More

Systematic detection of magnetic fields in massive, late-type supergiantsJun 30 2010Jul 01 2010We report the systematic detection of magnetic fields in massive (M > 5 M$_\odot$) late-type supergiants, using spectropolarimetric observations obtained with ESPaDOnS at the Canada-France-Hawaii Telescope. Our observations reveal detectable Stokes V ... More

Auroral radio emission from late L and T dwarfs: A new constraint on dynamo theory in the substellar regimeNov 11 2015We have observed 6 late-L and T dwarfs with the Karl G. Jansky Very Large Array (VLA) to investigate the presence of highly circularly polarized radio emission, associated with large-scale auroral currents. Previous surveys encompassing ~60 L6 or later ... More

A Phase Variable Approach for Improved Rhythmic and Non-Rhythmic Control of a Powered Knee-Ankle ProsthesisNov 13 2018Apr 12 2019Although there has been recent progress in control of multi-joint prosthetic legs for rhythmic tasks such as walking, control of these systems for non-rhythmic motions and general real-world maneuvers is still an open problem. In this article, we develop ... More

An I-Band-Selected Sample of Radio-Emitting Quasars: Evidence for a Large Population of Red QuasarsApr 01 2003We present a new sample of 35 quasars selected from the FIRST radio survey and the Deeprange I-band survey (Postman et al. 1998, 2002). A comparison with the FIRST Bright Quasar survey samples reveals that this I-band selected sample is redder by 0.25-0.5 ... More

The FIRST Bright QSO SurveyApr 24 1996The FIRST Radio Survey provides a new resource for constructing a large quasar sample. With source positions accurate to better than 1\arcsec\ and a point source sensitivity limit of 1 mJy, it reaches 50 times deeper than previous radio catalogs. We report ... More

Manipulating Ferroelectric Domains in Nanostructures Under Electron BeamsOct 30 2013Freestanding BaTiO3 nanodots exhibit domain structures characterized by distinct quadrants of ferroelastic 90{\deg} domains in transmission electron microscopy (TEM) observations. These differ significantly from flux-closure domain patterns in the same ... More

The Reddest QuasarsJul 23 2001In a survey of quasar candidates selected by matching the FIRST and 2MASS catalogs, we have found two extraordinarily red quasars. FIRST J013435.7-093102 is a 1 Jy source at z=2.216 and has B-K > 10, while FIRST J073820.1+275045 is a 2.5 mJy source at ... More

The FIRST Radio-Loud Broad Absorption Line QSO and Evidence for a Hidden Population of QuasarsJan 31 1997We have discovered two low-ionization broad absorption line quasars in programs to obtain optical spectra for radio-selected quasar candidates from the VLA FIRST Survey (Becker, White, & Helfand 1995). Both belong to the extremely rare class of BAL QSOs ... More

Disentanglement and decoherence in two-spin and three-spin systems under dephasingMar 23 2007We compare disentanglement and decoherence rates within two-spin and three-spin entangled systems subjected to all possible combinations of local and collective pure dephasing noise combinations. In all cases, the bipartite entanglement decay rate is ... More

Generalized Harish-Chandra modules with generic minimal $\frak k$-typeSep 16 2004We make a first step towards a classification of simple generalized Harish-Chandra modules which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary algebraic reductive pair of complex Lie algebras $(\g,\k)$, we construct, ... More

Neutron diffraction strain tomography: 2D axisymmetric sample geometryJun 17 2019We consider a method for neutron residual strain/stress analysis combining features of transmission strain tomography (e.g. through Braggs edge imaging) and neutron diffraction techniques. Analogous to transmission strain tomography, our approach observes ... More

Beyond Aztec Castles: Toric Cascades in the $dP_3$ QuiverDec 01 2015Jul 13 2016Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can associate a corresponding toric variety (which is a Calabi-Yau 3-fold) as well as an associated combinatorial model known as a brane tiling. In combinatorial ... More

Local-dephasing-induced entanglement sudden death in two-component finite-dimensional systemsSep 20 2007Entanglement sudden death (ESD), the complete loss of entanglement in finite time, is demonstrated to occur in a class of bipartite states of qu-d-it pairs of any finite dimension d > 2, when prepared in so-called `isotropic states' and subject to multi-local ... More

Entanglement sudden death in qubit-qutrit systemsJul 30 2007We demonstrate the existence of entanglement sudden death (ESD), the complete loss of entanglement in finite time, in qubit-qutrit systems. In particular, ESD is shown to occur in such systems initially prepared in a one-parameter class of entangled mixed ... More

Dungeons and Dragons: Combinatorics for the $dP_3$ QuiverMay 23 2018Jul 27 2018In this paper, we utilize the machinery of cluster algebras, quiver mutations, and brane tilings to study a variety of historical enumerative combinatorics questions all under one roof. Previous work by the second author and REU students [Zha, LMNT14], ... More

A new characterization for the m-quasiinvariants of S_n and explicit basis for two row hook shapesJul 21 2007Jul 23 2007In 2002, Feigin and Veselov defined the space of m-quasiinvariants for any Coxeter group, building on earlier work of Chalykh and Veselov. While many properties of those spaces were proven from this definition, an explicit computation of a basis was only ... More

On the existence of infinite-dimensional generalized harish-chandra modulesJul 05 2018We prove a general existence result for infinite-dimensional admissible (g;k)-modules, where g is a reductive finite-dimensional complex Lie algebra and k is a reductive in g algebraic subalgebra.

T-Path Formula and Atomic Bases for Cluster Algebras of Type DSep 11 2014Jul 28 2015We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type D.

The cyclotomic polynomial topologicallyDec 08 2010Apr 16 2012We interpret the coefficients of the cyclotomic polynomial in terms of simplicial homology.

HD 35502: a hierarchical triple system with a magnetic B5IVpe primaryMay 04 2016We present our analysis of HD~35502 based on high- and medium-resolution spectropolarimetric observations. Our results indicate that the magnetic B5IVsnp star is the primary component of a spectroscopic triple system and that it has an effective temperature ... More

Resolving the Stellar Population of the Standard Elliptical Galaxy NGC3379Dec 05 2003Using the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) on board the Hubble Space Telescope, we have obtained F110W (J-band) and F160W (H-band) images of three fields in NGC3379, a nearby normal giant elliptical galaxy. These images resolve ... More

Local basis-dependent noise-induced Bell-nonlocality sudden death in tripartite systemsDec 31 2007We demonstrate that multipartite Bell-inequality violations can be fully destroyed in finite time in three-qubit systems subject only to the mechanism of local external asymptotic dephasing noise. This broadens the study of local-noise-induced sudden ... More

Ultra-Wideband Detection of 22 Coherent Radio Bursts on M DwarfsOct 01 2018Coherent radio bursts detected from M dwarfs have some analogy with solar radio bursts, but reach orders of magnitude higher luminosities. These events trace particle acceleration, powered by magnetic reconnection, shock fronts (such as formed by coronal ... More

Generalized Harish-Chandra Modules: A New DirectionOct 09 2003Let $\frak g$ be a reductive Lie algebra over $\bold C$. We say that a $\frak g$-module $M$ is a generalized Harish-Chandra module if, for some subalgebra $\frak k \subset\frak g$, $M$ is locally $\frak k$-finite and has finite $\frak k$-multiplicities. ... More

Higher Cluster Categories and QFT DualitiesNov 03 2017We present a unified mathematical framework that elegantly describes minimally SUSY gauge theories in even dimension, ranging from $6d$ to $0d$, and their dualities. This approach combines recent developments on graded quiver with potentials, higher Ginzburg ... More

Dungeons and Dragons: Combinatorics for the $dP_3$ QuiverMay 23 2018Apr 30 2019In this paper, we utilize the machinery of cluster algebras, quiver mutations, and brane tilings to study a variety of historical enumerative combinatorics questions all under one roof. Previous work [Zha, LMNT14], which arose during the second author's ... More

Beyond Aztec Castles: Toric Cascades in the $dP_3$ QuiverDec 01 2015Aug 03 2017Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can associate a corresponding toric variety (which is a Calabi-Yau 3-fold) as well as an associated combinatorial model known as a brane tiling. In combinatorial ... More

Algebraic methods in the theory of generalized Harish-Chandra modulesOct 30 2013This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of $(\mathfrak{g},\mathfrak{k})-$modules, ... More

The Infrared Diameter -- Velocity Dispersion Relation for Elliptical GalaxiesJun 28 1995Using single channel infrared photometry from the literature, a provisional K-band diameter--velocity dispersion relation for elliptical galaxies in the Coma and Virgo clusters is derived. The Coma cluster relation has \~1.5 times lower scatter at K than ... More

A Construction of Generalized Harish-Chandra Modules with Arbitrary Minimal k-TypeMar 15 2006Let g be a semisimple complex Lie algebra and k in g be any algebraic subalgebra reductive in g. For any simple finite dimensional k-module V, we construct simple (g; k)-modules M with finite dimensional k-isotypic components such that V is a k-submodule ... More

Disentanglement and decoherence in a pair of qutrits under dephasing noiseSep 17 2007Nov 04 2009We relate disentanglement and decoherence rates in a pair of three-level atoms subjected to multi-local and collective pure dephasing noise acting in a preferred basis. The bipartite entanglement decay rate, as bounded from above by the negativity, is ... More

On C*-Extreme Maps and *-Homomorphisms of a Commutative C*-AlgebraFeb 09 2009Feb 12 2009The generalized state space of a commutative C*-algebra, denoted S_H(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative analogs of convexity ... More

The greedy basis equals the theta basisAug 06 2015Aug 07 2015We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.

A compendium on the cluster algebra and quiver package in sageFeb 23 2011Mar 29 2011This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by gathering data, ... More

The Coma - Leo I Distance Ratio and the Hubble ConstantMar 05 1997The diameter - velocity dispersion relation in B, V, and K for three early-type galaxies in the Leo I (M96) group is derived from published photometry and kinematic data. The relations in all three colors have slopes which agree well with those for the ... More

Paths to Understanding Birational Rowmotion on Products of Two ChainsJan 11 2018Birational rowmotion is an action on the space of assignments of rational functions to the elements of a finite partially-ordered set (poset). It is lifted from the well-studied rowmotion map on order ideals (equivariantly on antichains) of a poset $P$ ... More

Finite-time destruction of entanglement and non-locality by environmental influencesFeb 27 2009Entanglement and non-locality are non-classical global characteristics of quantum states important to the foundations of quantum mechanics. Recent investigations have shown that environmental noise, even when it is entirely local in influence, can destroy ... More

Generic tripartite Bell nonlocality sudden death under local phase noiseOct 01 2008Oct 02 2008We definitively show, using an explicit and broadly applicable model, that local phase noise that is capable of eliminating state coherence only in the infinite-time limit is capable of eliminating nonlocality in finite time in three two-level systems ... More

Unsharp Quantum RealityMay 04 2010Aug 06 2010The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion ... More

Combinatorial interpretations for rank-two cluster algebras of affine typeFeb 19 2006May 17 2007Fomin and Zelevinsky show that a certain two-parameter family of rational recurrence relations, here called the (b,c) family, possesses the Laurentness property: for all b,c, each term of the (b,c) sequence can be expressed as a Laurent polynomial in ... More

On Maximal Green Sequences For Type A QuiversMar 24 2014May 18 2016Given a framed quiver, i.e. one with a frozen vertex associated to each mutable vertex, there is a concept of green mutation, as introduced by Keller. Maximal sequences of such mutations, known as maximal green sequences, are important in representation ... More

Counting Arithmetical Structures on Paths and CyclesJan 23 2017Jul 23 2018Let $G$ be a finite, simple, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(\mathrm{diag}(\mathbf{d})-A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate ... More

An upper-limit on the linear polarization fraction of the GW170817 radio continuumJun 08 2018We present late-time radio observations of GW170817, the first binary neutron star merger discovered through gravitational waves by the advanced LIGO and Virgo detectors. Our observations, carried out with the Karl G. Jansky Very Large Array, were optimized ... More

Long-term Optical Variability of Radio-Selected Quasars from the FIRST SurveyDec 20 2000We have obtained single-epoch optical photometry for 201 quasars, taken from the FIRST Bright Quasar Survey, which span a wide range in radio loudness. Comparison with the magnitudes of these objects on the POSS-I plates provides by far the largest sample ... More

A turnover in the radio light curve of GW170817Mar 19 2018Apr 29 2018We present 2-9 GHz radio observations of GW170817 covering the period 125-200 days post-merger, taken with the Australia Telescope Compact Array and the Karl G. Jansky Very Large Array. Our observations demonstrate that the radio afterglow peaked at $149\pm2$ ... More

Magnetism in the Brown Dwarf RegimeMar 27 2019A suite of discoveries in the last two decades demonstrate that we are now at a point where incorporating magnetic behavior is key for advancing our ability to characterize substellar and planetary systems. The next decade heralds the exciting maturation ... More

Reverberation Mapping of the Kepler-Field AGN KA1858+4850Aug 29 2014KA1858+4850 is a narrow-line Seyfert 1 galaxy at redshift 0.078 and is among the brightest active galaxies monitored by the Kepler mission. We have carried out a reverberation mapping campaign designed to measure the broad-line region size and estimate ... More

Continuous wave magnonic fractals in dynamic artificial crystalFeb 11 2019We report on the first observation of an exact fractal pattern in the time-domain arising spontaneously from an all-magnon process in a passive, unlithographed magnetic waveguide. A spatiotemporally periodic potential created by a standing spin wave of ... More

On Modified Dispersion Relations and the Chandrasekhar Mass LimitJun 23 2008Jun 21 2010Modified dispersion relations from effective field theory are shown to alter the Chandrasekhar mass limit. At exceptionally high densities, the modifications affect the pressure of a degenerate electron gas and can increase or decrease the mass limit, ... More

Force networks and the dynamic approach to jamming in sheared granular mediaDec 28 2006Diverging correlation lengths on either side of the jamming transition are used to formulate a rheological model of granular shear flow, based on the propagation of stress through force chain networks. The model predicts three distinct flow regimes, characterized ... More

Small semisimple subalgebras of semisimple Lie algebrasAug 23 2004The main goal of this paper is to prove the following theorem: Let $\frak k$ be an $\frak {sl}_2$-subalgebra of a semisimple Lie algebra $\frak g$, none of whose simple factors is of type $A1$. Then there exists a positive integer $b(\frak k, \frak g)$, ... More