Results for "Inge Li Gørtz"

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Fast Dynamic ArraysNov 01 2017We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of $n$ elements supporting access in time $O(1)$ and insertion and deletion in time $O(n^\epsilon)$ for $\epsilon > 0$ while using $o(n)$ extra ... More
Finger Search in Grammar-Compressed StringsJul 10 2015Nov 16 2016Grammar-based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. Given a grammar, the random access problem is to compactly ... More
From Regular Expression Matching to ParsingApr 09 2018Jan 29 2019Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular expression parsing ... More
Sparse Regular Expression MatchingJul 10 2019We present the first algorithm for regular expression matching that can take advantage of sparsity in the input instance. Our main result is a new algorithm that solves regular expression matching in $O\left(\Delta \log \log \frac{nm}{\Delta} + n + m\right)$ ... More
Space-Efficient Re-Pair CompressionNov 04 2016Re-Pair is an effective grammar-based compression scheme achieving strong compression rates in practice. Let $n$, $\sigma$, and $d$ be the text length, alphabet size, and dictionary size of the final grammar, respectively. In their original paper, the ... More
Approximation Algorithms for the A Priori TravelingRepairmanJan 19 2019We consider the a priori traveling repairman problem, which is a stochastic version of the classic traveling repairman problem (also called the traveling deliveryman or minimum latency problem). Given a metric $(V,d)$ with a root $r\in V$, the traveling ... More
Practical and Effective Re-Pair CompressionApr 27 2017Re-Pair is an efficient grammar compressor that operates by recursively replacing high-frequency character pairs with new grammar symbols. The most space-efficient linear-time algorithm computing Re-Pair uses $(1+\epsilon)n+\sqrt n$ words on top of the ... More
Subsequence Automata with Default TransitionsOct 29 2015Jan 19 2016Let $S$ be a string of length $n$ with characters from an alphabet of size $\sigma$. The \emph{subsequence automaton} of $S$ (often called the \emph{directed acyclic subsequence graph}) is the minimal deterministic finite automaton accepting all subsequences ... More
Distance labeling schemes for treesJul 14 2015We consider distance labeling schemes for trees: given a tree with $n$ nodes, label the nodes with binary strings such that, given the labels of any two nodes, one can determine, by looking only at the labels, the distance in the tree between the two ... More
A Separation Between Run-Length SLPs and LZ77Nov 20 2017In this paper we give an infinite family of strings for which the length of the Lempel-Ziv'77 parse is a factor $\Omega(\log n/\log\log n)$ smaller than the smallest run-length grammar.
Mergeable Dictionaries With ShiftsJan 03 2019We revisit the mergeable dictionaries with shift problem, where the goal is to maintain a family of sets subject to search, split, merge, make-set, and shift operations. The search, split, and make-set operations are the usual well-known textbook operations. ... More
Deterministic Indexing for Packed StringsDec 06 2016Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string indexing problem ... More
Time-Space Trade-Offs for Lempel-Ziv Compressed IndexingJun 30 2017Jan 09 2018Given a string $S$, the \emph{compressed indexing problem} is to preprocess $S$ into a compressed representation that supports fast \emph{substring queries}. The goal is to use little space relative to the compressed size of $S$ while supporting fast ... More
Compressed Communication Complexity of Longest Common PrefixesJun 08 2018We consider the communication complexity of fundamental longest common prefix (Lcp) problems. In the simplest version, two parties, Alice and Bob, each hold a string, $A$ and $B$, and we want to determine the length of their longest common prefix $l=\text{Lcp}(A,B)$ ... More
Sparse Suffix Tree Construction with Small SpaceJul 04 2012We consider the problem of constructing a sparse suffix tree (or suffix array) for $b$ suffixes of a given text $T$ of size $n$, using only $O(b)$ words of space during construction time. Breaking the naive bound of $\Omega(nb)$ time for this problem ... More
Finger Search in Grammar-Compressed StringsJul 10 2015Jun 24 2016Grammar-based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. Given a grammar, the random access problem is to compactly ... More
Longest Common Extensions in Sublinear SpaceApr 10 2015The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions ... More
Dynamic Relative Compression, Dynamic Partial Sums, and Substring ConcatenationApr 29 2015Sep 16 2016Given a static reference string $R$ and a source string $S$, a relative compression of $S$ with respect to $R$ is an encoding of $S$ as a sequence of references to substrings of $R$. Relative compression schemes are a classic model of compression and ... More
Fingerprints in Compressed StringsMay 13 2013May 16 2013The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string $S$ of size $N$ compressed by a context-free ... More
Fast Lempel-Ziv Decompression in Linear SpaceFeb 28 2018We consider the problem of decompressing the Lempel-Ziv 77 representation of a string $S\in[\sigma]^n$ using a working space as close as possible to the size $z$ of the input. The folklore solution for the problem runs in optimal $O(n)$ time but requires ... More
Top Tree Compression of TriesFeb 06 2019We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to preprocess ... More
Locating Depots for Capacitated Vehicle RoutingMar 04 2011We study a location-routing problem in the context of capacitated vehicle routing. The input is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each vehicle, and compute ... More
Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed TextsSep 15 2006May 03 2007We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms ... More
Minimum Makespan Multi-vehicle Dial-a-RideFeb 26 2011Dial a ride problems consist of a metric space (denoting travel time between vertices) and a set of m objects represented as source-destination pairs, where each object requires to be moved from its source to destination vertex. We consider the multi-vehicle ... More
Stochastic Vehicle Routing with RecourseFeb 26 2012Mar 01 2012We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only ... More
Capacitated Vehicle Routing with Non-Uniform SpeedsDec 08 2010The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple vehicles having ... More
Tree Compression with Top TreesApr 21 2013May 11 2014We introduce a new compression scheme for labeled trees based on top trees. Our compression scheme is the first to simultaneously take advantage of internal repeats in the tree (as opposed to the classical DAG compression that only exploits rooted subtree ... More
Time-Space Trade-Offs for Longest Common ExtensionsNov 01 2012Apr 22 2013We revisit the longest common extension (LCE) problem, that is, preprocess a string $T$ into a compact data structure that supports fast LCE queries. An LCE query takes a pair $(i,j)$ of indices in $T$ and returns the length of the longest common prefix ... More
Longest Common Extensions in TreesDec 03 2014Jul 09 2015The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE queries. In ... More
The initial meadowsJun 13 2008A \emph{meadow} is a commutative ring with an inverse operator satisfying $0^{-1}=0$. We determine the initial algebra of the meadows of characteristic 0 and show that its word problem is decidable.
Extended statistical modeling under symmetry; the link toward quantum mechanicsMar 29 2005Jul 07 2012We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the cartesian ... More
Some properties of finite meadowsDec 06 2007The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary, we obtain a unique representation of minimal meadows ... More
An epistemic interpretation and foundation of quantum theoryMay 16 2019The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical inference theory. ... More
Symmetry in a space of conceptual variablesMay 16 2019A conceptual variable is any variable defined by a person or by a group of persons. Such variables may be inaccessible, meaning that they cannot be measured with arbitrary accuracy on the physical system under consideration at any given time. An example ... More
A Comparative Analysis of Feature Selection Methods for Biomarker Discovery in Study of Toxicant-treated Atlantic Cod (Gadus morhua) LiverMay 20 2019Univariate and multivariate feature selection methods can be used for biomarker discovery in analysis of toxicant exposure. Among the univariate methods, differential expression analysis (DEA) is often applied for its simplicity and interpretability. ... More
EFSIS: Ensemble Feature Selection Integrating StabilityNov 19 2018Ensemble learning that can be used to combine the predictions from multiple learners has been widely applied in pattern recognition, and has been reported to be more robust and accurate than the individual learners. This ensemble logic has recently also ... More
Prediction of multivariate responses with a select number of principal componentsJul 25 2008This paper proposes a new method and algorithm for predicting multivariate responses in a regression setting. Research into classification of High Dimension Low Sample Size (HDLSS) data, in particular microarray data, has made considerable advances, but ... More
Straight-line instruction sequence completeness for total calculation on cancellation meadowsMay 28 2009May 29 2009A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the instruction set $\{x \Leftarrow 0, x \Leftarrow 1, x\Leftarrow ... More
A negative result on algebraic specifications of the meadow of rational numbersJul 02 2015Jan 22 2016$\mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0$. In this note, we prove that $\mathbb{Q}_0$ cannot be specified by the ... More
On the contribution of backward jumps to instruction sequence expressivenessMay 31 2010We investigate the expressiveness of backward jumps in a framework of formalized sequential programming called program algebra. We show that - if expressiveness is measured in terms of the computability of partial Boolean functions - then backward jumps ... More
Subvarieties of the variety of meadowsOct 14 2015Apr 19 2016Meadows - commutative rings equipped with a total inversion operation - can be axiomatized by purely equational means. We study subvarieties of the variety of meadows obtained by extending the equational theory and expanding the signature.
Phase transition for accessibility percolation on hypercubesFeb 26 2015In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d.\ uniform random variables on vertices of a hypercube, and study whether there is a path (possibly with back steps) connecting two vertices such that the values of ... More
Note on paraconsistency and reasoning about fractionsOct 31 2014Mar 06 2015We apply a paraconsistent logic to reason about fractions.
Hyperscaling Violating Solutions in Generalised EMD TheoryAug 10 2016Sep 01 2016This short note is devoted to deriving scaling but hyperscaling violating solutions in a generalised Einstein-Maxwell-Dilaton theory with an arbitrary number of scalars and vectors. We obtain analytic solutions in some special case and discuss the physical ... More
Phase transition for accessibility percolation on hypercubesFeb 26 2015Jun 02 2017In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d. uniform [0,1] random variables on vertices of a hypercube, and study whether there is a path connecting two vertices such that the values of these random variables ... More
Numerical Methods as an Integrated Part of Physics EducationMay 17 2005During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on mainframe machines ... More
Extremely high conductivity observed in the triple point topological metal MoPMar 10 2017Jun 11 2019Weyl and Dirac fermions have created much attention in condensed matter physics and materials science. Recently, several additional distinct types of fermions have been predicted. Here, we report ultra-high electrical conductivity in MoP at low temperature, ... More
A process algebra based framework for promise theoryJul 05 2007We present a process algebra based approach to formalize the interactions of computing devices such as the representation of policies and the resolution of conflicts. As an example we specify how promises may be used in coming to an agreement regarding ... More
Equations for formally real meadowsOct 18 2013Jan 13 2015We consider the signatures $\Sigma_m=(0,1,-,+, \cdot, \ ^{-1})$ of meadows and $(\Sigma_m, {\mathbf s})$ of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first ... More
Cancellation Meadows: a Generic Basis Theorem and Some ApplicationsMar 27 2008May 22 2013Let Q_0 denote the rational numbers expanded to a "meadow", that is, after taking its zero-totalized form (0^{-1}=0) as the preferred interpretation. In this paper we consider "cancellation meadows", i.e., meadows without proper zero divisors, such as ... More
Ratchet effects for paramagnetic beads above striped ferrite-garnet filmsSep 29 2011We calculate the motion of a small paramagnetic bead which is manipulated by the stripe domain pattern of a ferrite-garnet film. A model for the bead's motion in a liquid above the film is developed and used to look for ratchet solutions, where the bead ... More
TaintAssembly: Taint-Based Information Flow Control Tracking for WebAssemblyFeb 04 2018WebAssembly (wasm) has recently emerged as a promisingly portable, size-efficient, fast, and safe binary format for the web. As WebAssembly can interact freely with JavaScript libraries, this gives rise to a potential for undesirable behavior to occur. ... More
Multiscale socio-ecological networks in the age of informationMay 02 2018Nov 02 2018Interactions between people and ecological systems, through leisure or tourism activities, form a complex socio-ecological spatial network. The analysis of the benefits people derive from their interactions with nature -- also referred to as cultural ... More
The structure of finite meadowsMar 06 2009A meadow is a commutative ring with a total inverse operator satisfying 0^{-1}=0. We show that the class of finite meadows is the closure of the class of Galois fields under finite products. As a corollary, we obtain a unique representation of minimal ... More
Fully Homomorphic Image ProcessingOct 08 2018Fully homomorphic encryption has allowed devices to outsource computation to third parties while preserving the secrecy of the data being computed on. Many images contain sensitive information and are commonly sent to cloud services to encode images for ... More
Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classificationAug 11 2013We develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local operations and classical ... More
Implicit Asymptotic Preserving Method for Linear Transport EquationsFeb 01 2016The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the speed of light, ... More
Towards Label Imbalance in Multi-label Classification with Many LabelsApr 05 2016In multi-label classification, an instance may be associated with a set of labels simultaneously. Recently, the research on multi-label classification has largely shifted its focus to the other end of the spectrum where the number of labels is assumed ... More
Network analysis of the state space of chaotic map in digital domainOct 28 2014Nov 04 2014Complex dynamics of chaotic maps under an infinite-precision mathematical framework have been well known. The case in a finite-precision computer remains to be further explored. Previous work treated a digital chaotic map as a black box and gave different ... More
Novel Algorithm for Sparse Solutions to Linear Inverse Problems with Multiple MeasurementsMay 20 2009In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly sparse recovery ... More
Beat the Rayleigh limit: OAM based super-resolution diffraction tomographyJun 27 2013This letter is the first to report that a super-resolution imaging beyond the Rayleigh limit can be achieved by using classical diffraction tomography (DT) extended with orbital angular momentum (OAM), termed as OAM based diffraction tomography (OAM-DT). ... More
The neighbor-scattering number can be computed in polynomial time for interval graphsMar 17 2006Neighbor-scattering number is a useful measure for graph vulnerability. For some special kinds of graphs, explicit formulas are given for this number. However, for general graphs it is shown that to compute this number is NP-complete. In this paper, we ... More
Effects of alpha particles on the angular momentum loss from the SunJun 07 2006The classic Weber-Davis model of the solar wind is reconsidered by incorporating alpha particles and by allowing the solar wind to flow out of the equatorial plane in an axisymmetrical configuration. In the ion momentum equations of the solar wind, the ... More
Chemical distances for percolation of planar Gaussian free fields and critical random walk loop soupsMay 14 2016Aug 29 2016We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical ... More
A New Unified Theory of Electromagnetic and Gravitational InteractionsNov 04 2015Mar 30 2016In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations ... More
Variational Neural Networks: Every Layer and Neuron Can Be UniqueOct 14 2018The choice of activation function can significantly influence the performance of neural networks. The lack of guiding principles for the selection of activation function is lamentable. We try to address this issue by introducing our variational neural ... More
Characters and patterns of communities in networksJan 14 2013In this paper, we propose some new notions to characterize and analyze the communities. The new notions are general characters of the communities or local structures of networks. At first, we introduce the notions of internal dominating set and external ... More
Global existence of weak solutions for quantum MHD equationsMay 07 2018In this paper, we consider the quantum MHD equations with both the viscosity coefficient and the magnetic diffusion coefficient are depend on the density. we prove the global existence of weak solutions and perform the lower planck limit in a 3-dimensional ... More
Optimal Deployment of Drone Base Stations for Cellular Communication by Network-based LocalizationSep 19 2018Drone base stations can assist cellular networks in a variety of scenarios. To serve the maximum number of users in an area without apriori user distribution information, we proposed a two-stage algorithm to find the optimal deployment of drone base stations. ... More
Quantum Criticality and DBI Magneto-resistanceAug 08 2016Sep 01 2016We use the DBI action from string theory and holography to study the magneto-resistance at quantum criticality with hyperscaling violation. We find and analyze a rich class of scaling behaviors for the magneto-resistance. A special case describes the ... More
Radioactive $γ$-Ray Emissions from Neutron Star MergersAug 29 2018Jan 20 2019Gravitational waves and electromagnetic radiations from a neutron star merger were discovered on 17 August 2017. Multiband observations of the optical transient have identified brightness and spectrum features broadly consistent with theoretical predictions. ... More
Towards extremely high-resolution broad-band flat-field spectrometer in 'water window'Aug 19 2018The optical design of a novel spectrometer is present, combining a cylindrically convex pre-mirror with a cylindrically concave VLS grating (both in meridional) to deliver a resolving power of 100,000-200,000 in 'water window' (2-5nm). More remarkably, ... More
Two-sample Test of Community Memberships of Weighted Stochastic Block ModelsNov 30 2018Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two networks are the ... More
Braided Rota-Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebrasJan 09 2019Rota-Baxter algebras and the closely related dendriform algebras have important physics applications, especially to renormalization of quantum field theory. Braided structures provide effective ways of quantization such as for quantum groups. Continuing ... More
Uniqueness of positive bound states to Schrodinger systems with critical exponentsAug 02 2007We prove the uniqueness for the positive solutions of the following elliptic systems: \begin{eqnarray*} \left\{\begin{array}{ll} - \lap (u(x)) = u(x)^{\alpha}v(x)^{\beta} - \lap (v(x)) = u(x)^{\beta} v(x)^{\alpha} \end{array} \right. \end{eqnarray*} Here ... More
The Politics of AttentionOct 26 2018Jan 20 2019We develop an equilibrium theory of attention and politics. In a spatial model of electoral competition where candidates have varying policy preferences, we examine what kinds of political behaviors capture voters' limited attention and how this concern ... More
Gradient Estimates for Parabolic Systems from Composite MaterialMay 07 2011Jul 05 2012In this paper we derive $W^{1,\infty}$ and piecewise $C^{1,\alpha}$ estimates for solutions, and their $t-$derivatives, of divergence form parabolic systems with coefficients piecewise H\"older continuous in space variables $x$ and smooth in $t$. This ... More
MB-tensors and MB0-tensorsNov 24 2014Dec 01 2014The class of MB(MB0)-tensors, which is a generation of B(B0)-tensors and quasi-double B(B0)-tensors, is proposed. And we prove that an even order symmetric MB(MB0)-tensor is positive (semi-)definite. This provides a positive answer for the conjecture ... More
Double B-tensor and quasi-double B-tensorAug 11 2014In this paper, we propose two new classes of tensors: double B-tensors and quasi-double B-tensors, give some properties of double B-tensors and quasi-double B-tensors, discuss their relationships with B-tensors and positive definite tensors and show that ... More
A Novel Feature-based Bayesian Model for Query Focused Multi-document SummarizationDec 10 2012Dec 27 2013Both supervised learning methods and LDA based topic model have been successfully applied in the field of query focused multi-document summarization. In this paper, we propose a novel supervised approach that can incorporate rich sentence features into ... More
Angular momentum transport in a multicomponent solar wind with differentially flowing, thermally anisotropic ionsDec 09 2008The Helios measurements of the angular momentum flux $L$ for the fast solar wind show that the individual ion contributions, $L_p$ and $L_\alpha$, tend to be negative (i.e., in the sense of counter-rotation with the Sun). However, the opposite holds for ... More
Unconditionally Secure Quantum Bit Commitment Protocols Based on Correlation Immune Boolean FunctionJul 14 2006Aug 10 2006A class of quantum protocols of bit commitment is constructed based on the nonorthogonal states coding and the correlation immunity of some Boolean functions. The binding condition of these protocols is guaranteed mainly by the law of causality and the ... More
One-way information reconciliation schemes of quantum key distributionJan 05 2012May 14 2012Information reconciliation(IR) is a basic step of quantum key distribution (QKD). Classical message interaction is necessary in a practical IR scheme, and the communication complexity has become a bottleneck of QKD's development. Here we propose a concatenated ... More
Probing equilibration with respect to isospin degree of freedom in intermediate energy heavy ion collisionsSep 26 2001We have studied equilibration with respect to isospin degree of freedom in four 96 mass systems $^{96}Ru+^{96}Ru$, $^{96}Ru+^{96}Zr$, $^{96}Zr+^{96}Ru$, $^{96}Zr+^{96}Zr$ at 100 AMeV and 400 AMeV with isospin dependent QMD. We propose that the neutron-proton ... More
Engineering two-mode squeezed states of cold atomic clouds with a superconducting stripline resonatorSep 16 2010A scheme is proposed for engineering two-mode squeezed states of two separated cold atomic clouds positioned near the surface of a superconducting stripline resonator. Based on the coherent magnetic coupling between the atomic spins and a stripline resonator ... More
Lawson homology, morphic cohomology and Chow motivesNov 04 2007In this paper, the Lawson homology and morphic cohomology are defined on the Chow motives. We also define the rational coefficient Lawson homology and morphic cohomology of the Chow motives of finite quotient projective varieties. As a consequence, we ... More
WARP: Wavelets with adaptive recursive partitioning for multi-dimensional dataNov 02 2017Jul 10 2018Traditional statistical wavelet analysis carries out modeling and inference under a given, predetermined wavelet transform. This approach can quickly lose efficiency for multi-dimensional data (e.g., observations measured on a multi-dimensional grid), ... More
Membrane paradigm of the static black bottleOct 02 2017In the membrane paradigm of black holes, it is usually assumed that the normal vector of the stretched horizon has a vanishing acceleration. This assumption breaks down for black bottles, a class of solutions discovered recently in the asymptotically ... More
Dirichlet problems of a quasi-linear elliptic systemNov 20 2003We discuss the Dirichlet problem of the quasi-linear elliptic system \begin{eqnarray*} -e^{-f(U)}div(e^{f(U)}\bigtriangledown U)+&{1/2}f'(U)|\bigtriangledown U|^2&=0, {in $\Omega$}, & U|_{\partial\Omega}&=\phi. \end{eqnarray*} Here $\Omega$ a smooth bounded ... More
A Fast Anderson-Chebyshev Mixing Method for Nonlinear OptimizationSep 07 2018Apr 01 2019Anderson mixing (or Anderson acceleration) is an efficient acceleration method for fixed point iterations $x_{t+1}=G(x_t)$, e.g., gradient descent can be viewed as iteratively applying the operation $G(x) = x-\alpha\nabla f(x)$. It is known that Anderson ... More
Notes on a minimal set of generators for the radical ideal defining the diagonal locus of $(\C^2)^n$Jan 09 2009Sep 09 2009We develop several techniques for the study of the radical ideal $I$ defining the diagonal locus of $(\C^2)^n$. Using these techniques, we give combinatorial construction of generators for $I$ of certain bi-degrees.
A/D Converter Architectures for Energy-Efficient Vision ProcessorMar 05 2017Mar 21 2017AI applications have emerged in current world. Among AI applications, computer-vision (CV) related applications have attracted high interest. Hardware implementation of CV processors necessitates a high performance but low-power image detector. The key ... More
Edge-grafting theorems on permanents of the Laplacian matrices of graphs and their applicationsJun 20 2012The trees, respectively unicyclic graphs, on $n$ vertices with the smallest Laplacian permanent are studied. In this paper, by edge-grafting transformations, the $n$-vertex trees of given bipartition having the second and third smallest Laplacian permanent ... More
Note on the complexity of deciding the rainbow connectedness for bipartite graphsSep 26 2011Sep 27 2011A path in an edge-colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge-colored graph is (strongly) rainbow connected if there exists a rainbow (geodesic) path between every pair of vertices. The (strong) ... More
Monochromatic disconnection of graphsJan 05 2019Jan 26 2019For an edge-colored graph $G$, we call an edge-cut $R$ of $G$ monochromatic if the edges of $R$ are colored with a same color. The graph $G$ is called monochromatically disconnected if any two distinct vertices of $G$ are separated by a monochromatic ... More
Develop a perfect spectrometer in water windowOct 12 2017We report a novelly universal scheme for design of a grazing incidence spectrometer, which creates an excellent meridional flat field in its detector domain to deliver the desired spectral resolution throughout the full designated spectral range, while ... More
WARP: Wavelets with adaptive recursive partitioning for multi-dimensional dataNov 02 2017Apr 29 2019Effective identification of asymmetric and local features in images and other data observed on multi-dimensional grids plays a critical role in a wide range of applications including biomedical and natural image processing. Moreover, the ever increasing ... More
Global existence and boundedness of weak solutions to a chemotaxis-stokes system with rotational flux termMar 14 2018In this paper, the three-dimensional chemotaxis-stokes system \begin{eqnarray*} \left\{\begin{array}{lll} \medskip n_{t}+u\cdot\nabla n=\Delta n^m-\nabla\cdot(n S(x,n,c)\cdot\nabla c),&x\in\Omega,\ \ t>0, \medskip c_t+u\cdot\nabla c=\Delta c-nf(c),&x\in\Omega,\ ... More
Optomechanical photon shuttling between photonic cavitiesSep 03 2014Mechanical motion of photonic devices driven by optical forces provides a profound means of coupling between optical fields. The current focus of these optomechanical effects has been on cavity optomechanics systems in which co-localized optical and mechanical ... More
On the exterior Dirichlet problem for Hessian quotient equationsSep 14 2017In this paper, we establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for Hessian quotient equations with prescribed asymptotic behavior at infinity. This extends the previous related results on the Monge-Amp\`{e}re ... More