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Accelerated High-Resolution Photoacoustic Tomography via Compressed SensingApr 30 2016Sep 28 2016Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue. ... More

Synthesis and structural characterization of uranium-doped Ca2CuO3, a 1D quantum antiferromagnetFeb 11 2008Apr 30 2008The technological settings of a modified sol-gel method for preparation of highly fine homogeneous powder Ca2CuO3 doped with uranium 238 (x=0-0.05) is presented. The analysis of structure, purity of phases and the justification for the role of uranium ... More

Hypergraph based semi-supervised learning algorithms applied to speech recognition problem: a novel approachOct 28 2018Most network-based speech recognition methods are based on the assumption that the labels of two adjacent speech samples in the network are likely to be the same. However, assuming the pairwise relationship between speech samples is not complete. The ... More

A conductive topological insulator with colossal spin Hall effect for ultra-low power spin-orbit-torque switchingSep 22 2017Sep 25 2017Spin-orbit-torque (SOT) switching using the spin Hall effect (SHE) in heavy metals and topological insulators (TIs) has great potential for ultra-low power magnetoresistive random-access memory (MRAM). To be competitive with conventional spin-transfer-torque ... More

A Genetic Algorithm for Power-Aware Virtual Machine Allocation in Private CloudFeb 19 2013Energy efficiency has become an important measurement of scheduling algorithm for private cloud. The challenge is trade-off between minimizing of energy consumption and satisfying Quality of Service (QoS) (e.g. performance or resource availability on ... More

Construction of hyperbolic hypersurfaces of low degree in $\mathbb{p}^n(\mathbb{c})$Jan 25 2016May 09 2016We construct families of hyperbolic hypersurfaces $X_d\subset\mathbb{P}^{n+1}(\mathbb{C})$ of degree $d\geq {\textstyle{(\frac{n+3}{2})^2}}$.

Examples of hyperbolic hypersurfaces of low degree in projective spacesJul 13 2015Dec 29 2015We construct families of hyperbolic hypersurfaces of degree $2n$ in the projective space $\mathbb{P}^n(\mathbb{C})$ for $3 \leq n \leq 6$.

Spatiotemporal KSVD Dictionary Learning for Online Multi-target TrackingJul 05 2018In this paper, we present a new spatial discriminative KSVD dictionary algorithm (STKSVD) for learning target appearance in online multi-target tracking. Different from other classification/recognition tasks (e.g. face, image recognition), learning target's ... More

The matroid secretary problem for minor-closed classes and random matroidsMar 22 2016Dec 21 2016We prove that for every proper minor-closed class $M$ of matroids representable over a prime field, there exists a constant-competitive matroid secretary algorithm for the matroids in $M$. This result relies on the extremely powerful matroid minor structure ... More

The matroid secretary problem for minor-closed classes and random matroidsMar 22 2016Jul 13 2016We prove that for every proper minor-closed class $M$ of matroids representable over a prime field, there exists a constant-competitive matroid secretary algorithm for the matroids in $M$. This result relies on the extremely powerful matroid minor structure ... More

A Codebook-Based Limited Feedback System for Large-Scale MIMONov 06 2014In this paper, we consider limited feedback systems for FDD large-scale (massive) MIMO. A new codebook-based framework for multiuser (MU) MIMO downlink systems is introduced and then compared with an ideal non-codebook based system. We are particularly ... More

Locally Lipschitz BSDE driven by a continuous martingale: path-derivative approachJun 13 2016Jun 18 2017Using a new notion of path-derivative, we study well-posedness of backward stochastic differential equation driven by a continuous martingale $M$ when $f(s,\gamma,y,z)$ is locally Lipschitz in $(y,z)$: \[Y_{t}=\xi(M_{[0,T]})+\int_{t}^{T}f(s,M_{[0,s]},Y_{s-},Z_{s}m_{s})d{\rm ... More

An Overview of the Square Kilometre ArrayNov 18 2013The Square Kilometre Array (SKA) will be the premier instrument to study radiation at centimetre and metre wavelengths from the cosmos, and in particular hydrogen, the most abundant element in the universe. The SKA will probe the dawn of galaxy formation ... More

Locally solvable subnormal subgroups in division ringsMar 27 2019Mar 28 2019Let $D$ be a division ring with center $F$. If $G$ is a locally solvable subnormal subgroup of $D^*$, then $G$ is contained in $F$. This generalizes the results of Stuth and Huzurbazar which asserted that any weakly nilpotent or solvable subnormal subgroup ... More

Spatial Point Pattern and Urban Morphology: Perspectives from Entropy, Complexity and NetworksApr 22 2019Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding various aspects ... More

Synthetic Aperture Sonar Imaging via One-Way Wave EquationsJul 13 2009We develop an efficient algorithm for Synthetic Aperture Sonar imaging based on the one-way wave equations. The algorithm utilizes the operator-splitting method to integrate the one-way wave equations. The well-posedness of the one-way wave equations ... More

Path-differentiability of BSDE driven by a continuous martingaleJun 13 2016Jun 25 2016We study existence, uniqueness, and path-differentiability of solution for backward stochastic differential equation (BSDE) driven by a continuous martingale $M$ with $[M,M]_{t}=\int_{0}^{t}m_{s}m_{s}^{*}d{\rm tr}[M,M]_{s}$: \[ Y_{t}=\xi(M_{[0,T]})+\int_{t}^{T}f(s,M_{[0,s]},Y_{s-},Z_{s}m_{s})d{\rm ... More

Hypoelliptic diffusions with singular driftsJun 26 2018Oct 05 2018We establish the well-posedness of stochastic differential equations possessing degenerate diffusions and singular drifts. We prove that SDEs defined on the homogeneous Carnot group, whose hypoelliptic diffusion part is given by the horizontal Brownian ... More

HOD in natural models of AD^+Jan 30 2012Sep 01 2013This paper analyzes full HOD of natural models of AD^+ under a certain smallness assumption of the models. This assumption is made to utilize Sargsyan's work on the theory of hod mice. We show that HOD is a fine-structural model and in particular satisfies ... More

Capacity Bounds for the $K$-User Gaussian Interference ChannelJun 10 2015Jul 17 2015The capacity region of the $K$-user Gaussian interference channel (GIC) is a long-standing open problem and even capacity outer bounds are little known in general. A significant progress on degrees-of-freedom (DoF) analysis, a first-order capacity approximation, ... More

Stochastic Differential Equations with Critical DriftsJan 31 2018Oct 05 2018We establish the well-posedness of SDE with the additive noise when a singular drift belongs to the critical spaces. We prove that if the drift belongs to the Orlicz-critical space $L^{q,1}([0,T],L^p_x)$ for $p,q\in (1,\infty)$ satisfying $\frac{2}{q}+\frac{d}{p} ... More

Large deviations and localization of the microcanonical ensembles given by multiple constraintsSep 11 2018Jan 22 2019We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple constraints case. ... More

Casimir Force in Compact Noncommutative Extra Dimensions and Radius StabilizationAug 09 2000We compute the one loop Casimir energy of an interacting scalar field in a compact noncommutative space of $R^{1,d}\times T^2_\theta$, where we have ordinary flat $1+d$ dimensional Minkowski space and two dimensional noncommuative torus. We find that ... More

Approximate k-space models and Deep Learning for fast photoacoustic reconstructionJul 09 2018We present a framework for accelerated iterative reconstructions using a fast and approximate forward model that is based on k-space methods for photoacoustic tomography. The approximate model introduces aliasing artefacts in the gradient information ... More

Model based learning for accelerated, limited-view 3D photoacoustic tomographyAug 31 2017Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide ... More

Enhancing Compressed Sensing Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ... More

Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018Jun 15 2018A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ... More

Intertwining connectivities for representable matroidsApr 24 2013Let M be a representable matroid, and Q, R, S, T subsets of the ground set. We prove that, if M is sufficiently large, then there is an element e such that deleting or contracting e preserves both the Q-R and the S-T connectivities. For matroids representable ... More

Ekeland's inverse function theorem in graded Fr{é}chet spaces revisited for multifunctionsOct 27 2016In this paper, we present some implicit function theorems for set-valued mappings between Fr{\'e}chet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions ... More

Generalized W-type and H-type algebrasDec 30 1997It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra. We also generalize the Hamiltonian Lie algebra using exponential ... More

Cutoff for the Swendsen-Wang dynamics on the latticeMay 11 2018We study the Swendsen-Wang dynamics for the $q$-state Potts model on the lattice. Introduced as an alternative algorithm of the classical single-site Glauber dynamics, the Swendsen-Wang dynamics is a non-local Markov chain that recolors many vertices ... More

Calabi-Yau coverings over some singular varieties and new Calabi-Yau 3-folds with Picard number oneOct 02 2006Jan 14 2008This note is a report on the observation that some singular varieties admit Calabi--Yau coverings. As an application, we construct 18 new Calabi--Yau 3-folds with Picard number one that have some interesting properties.

On supercompactness of $ω_1$Apr 03 2019This paper studies structural consequences of supercompactness of $\omega_1$ under $\sf{ZF}$. We show that the Axiom of Dependent Choice $(\sf{DC})$ follows from "$\omega_1$ is supercompact". "$\omega_1$ is supercompact" also implies that $\sf{AD}^+$, ... More

Calabi-Yau double coverings of Fano-Enriques threefoldsMar 08 2017This note is a report on the observation that the Enriques-Fano threefolds with terminal cyclic quotient singularities admit Calabi-Yau threefolds as their double coverings. We calculate the invariants of those Calabi-Yau threefolds when the Picard number ... More

Creative Community Demystified: A Statistical Overview of BehanceMar 02 2017Online communities are changing the ways that creative professionals such as artists and designers share ideas, receive feedback, and find inspiration. While they became increasingly popular, there have been few studies so far. In this paper, we investigate ... More

Hyers-Ulam stability of loxodromic Möbius difference equationAug 28 2018Hyers-Ulam of the sequence $ \{z_n\}_{n \in \mathbb{N}} $ satisfying the difference equation $ z_{i+1} = g(z_i) $ where $ g(z) = \frac{az + b}{cz + d} $ with complex numbers $ a $, $ b $, $ c $ and $ d $ is defined. Let $ g $ be loxodromic M\"obius map, ... More

Invariant space under Hénon renormalization : Intrinsic geometry of Cantor attractorAug 20 2014Jun 23 2015Three dimensional H\'non-like map $$ F(x,y,z) = (f(x) - \epsilon (x,y,z),\ x,\ \delta (x,y,z)) $$ is defined on the cubic box $ B $. An invariant space under renormalization would appear only in higher dimension. Consider renormalizable maps each of which ... More

Locally self-avoiding eulerian toursNov 22 2016H\"aggkvist and Kriesell independently conjectured that, given a positive integer $\ell$, every simple eulerian graph with high minimum degree (depending on $\ell$) admits an eulerian tour such that every walk of length $\ell$ along the tour is a path. ... More

Critique of optical transition theories based on projection and population criteriaJul 23 2014Some many-body theories of optical transitions in solids were examined from projection and population criteria. The results showed that state-independent projection methods cannot be applied to electron systems with non-uniform energy spectra. Moreover, ... More

Some Consequences of the Hypothesis of Minimal LengthsMay 07 2004Talk presented at the 3rd International Symposium on Quantum Theory and Symmetries, September 13, 2003, University of Cincinnati, OH. Dedicated to the memory of Freydoon Mansouri.

The recoverability limit for superresolution via sparsityFeb 04 2015We consider the problem of robustly recovering a $k$-sparse coefficient vector from the Fourier series that it generates, restricted to the interval $[- \Omega, \Omega]$. The difficulty of this problem is linked to the superresolution factor SRF, equal ... More

Singular Abreu equations and minimizers of convex functionals with a convexity constraintNov 06 2018Apr 30 2019We study the solvability of second boundary value problems of fourth order equations of Abreu type arising from approximation of convex functionals whose Lagrangians depend on the gradient variable, subject to a convexity constraint. These functionals ... More

The second boundary value problem of the prescribed affine mean curvature equation and related linearized Monge-Ampère equationFeb 27 2017Apr 11 2017These lecture notes are concerned with the solvability of the second boundary value problem of the prescribed affine mean curvature equation and related regularity theory of the Monge-Amp\`ere and linearized Monge-Amp\`ere equations. The prescribed affine ... More

On optimal Hölder regularity of solutions to the equation $Δ u+b\cdot\nabla u=0$ in two dimensionsNov 21 2016We show that for an $L^2$ drift $b$ in two dimensions, if the Hardy norm of $\text{div }b$ is small, then the weak solutions to $\Delta u+b\cdot\nabla u=0$ have the same optimal H\"older regularity as in the case of divergence-free drift, that is, $u\in ... More

Multidimensional quadratic and subquadratic BSDEs with special structureSep 26 2013Jan 29 2015We study multidimensional BSDEs of the form $$ Y_t = \xi + \int_t^T f(s,Y_s,Z_s)ds - \int_t^T Z_s dW_s $$ with bounded terminal conditions $\xi$ and drivers $f$ that grow at most quadratically in $Z_s$. We consider three different cases. In the first ... More

Neuronal micro-culture engineering by microchannel devices of cellular scale dimensionsFeb 05 2015Purpose: The purpose of the current study was to investigate the effect of microchannel geometry on neuronal cultures and to maintain these cultures for long period of time (over several weeks) inside the closed microchannels of cellular scale dimensions. ... More

Correlated time-changed Lévy ProcessesAug 06 2018Time-changed L\'evy processes, which consist of a L\'evy process runs on a stochastic time, can effectively capture main empirical regularities of asset returns such as jumps, stochastic volatility, and leverage. However, neither their transitional density ... More

Model based learning for accelerated, limited-view 3D photoacoustic tomographyAug 31 2017Mar 26 2018Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide ... More

A Characterization of Gorenstein Planar graphsMar 01 2016Mar 02 2016We prove that a planar graph is Gorenstein if and only if its independence complex is Eulerian.

The Fermat-Torricelli Problem in the Light of Convex AnalysisFeb 21 2013Nov 06 2013In the early 17th century, Pierre de Fermat proposed the following problem: given three points in the plane, find a point such that the sum of its Euclidean distances to the three given points is minimal. This problem was solved by Evangelista Torricelli ... More

Multi-Level and Multi-Scale Feature Aggregation Using Sample-level Deep Convolutional Neural Networks for Music ClassificationJun 21 2017Music tag words that describe music audio by text have different levels of abstraction. Taking this issue into account, we propose a music classification approach that aggregates multi-level and multi-scale features using pre-trained feature extractors. ... More

Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefoldsAug 07 2017We present a new construction of mirror pairs of Calabi-Yau manifolds by smoothing normal crossing varieties, consisting of two quasi-Fano manifolds. We introduce a notion of mirror pairs of quasi-Fano manifolds with anticanonical Calabi-Yau fibrations ... More

Vector-current correlation and charge separation via chiral-magnetic effectApr 20 2010We investigate the vector-current correlation Pi_{mu nu} (VCC) in the presence of a strong external magnetic field (B_0 in the z direction) at low temperature (T<T^chi_c) with C- and CP-violations, indicated by the nonzero chiral-chemical potential (mu_chi>0), ... More

Chiral magnetic effect at low temperatureNov 03 2009We investigate the chiral magnetic effect (CME) under a strong magnetic field B = B_0 x_3 at low temperature T < T^chi_c. For this purpose, we employ the instanton vacuum configuration with the finite instanton-number fluctuation Delta, which relates ... More

An effective thermodynamic potential from the instanton with Polyakov-loop contributionsMay 22 2009Feb 05 2010We derive an effective thermodynamic potential (Omega_eff) at finite temperature (T>0) and zero quark-chemical potential (mu_R=0), using the singular-gauge instanton solution and Matsubara formula for N_c=3 and N_f=2 in the chiral limit. The momentum-dependent ... More

B\bar{B} Mixing and CP Violation in SU(2)_L \times SU(2)_R \times U(1) ModelsJun 04 2002Jun 17 2002We reexamine the mass mixing and CP violation in the B\bar{B} system in general SU(2)_L \times SU(2)_R \times U(1) models related to the recent measurements. The right-handed contributions can be sizable in B\bar{B} mixing and CP asymmetry in B decays ... More

Learning Multi-Domain Convolutional Neural Networks for Visual TrackingOct 27 2015Jan 06 2016We propose a novel visual tracking algorithm based on the representations from a discriminatively trained Convolutional Neural Network (CNN). Our algorithm pretrains a CNN using a large set of videos with tracking ground-truths to obtain a generic target ... More

The determinantal ideals of extended Hankel matricesAug 23 2010Mar 01 2011In this paper, we use the tools of Gr\"{o}bner bases and combinatorial secant varieties to study the determinantal ideals $I_t$ of the extended Hankel matrices. Denote by $c$-chain a sequence $a_1,\...,a_k$ with $a_i+c<a_{i+1}$ for all $i=1,\...,k-1$. ... More

The eigenvalue problem for the Monge-Ampère operator on general bounded convex domainsJan 18 2017Jun 19 2017In this paper, we study the eigenvalue problem for the Monge-Amp\`ere operator on general bounded convex domains. We prove the existence, uniqueness and variational characterization of the Monge-Amp\`ere eigenvalue. The convex Monge-Amp\`ere eigenfunctions ... More

Boundary Harnack inequality for the linearized Monge-Ampère equations and applicationsNov 04 2015Feb 21 2016In this paper, we obtain boundary Harnack estimates and comparison theorem for nonnegative solutions to the linearized Monge-Amp\`ere equations under natural assumptions on the domain, Monge-Amp\`ere measures and boundary data. Our results are boundary ... More

On the second inner variation of the Allen-Cahn Functional and its applicationsSep 28 2010In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only approximates well the area functional up to the first ... More

On the Harnack inequality for degenerate and singular elliptic equations with unbounded lower order terms via sliding paraboloidsMar 15 2016Jul 05 2016We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized Monge-Amp\`ere ... More

Remarks on the Green's function of the linearized Monge-Ampère operatorJun 04 2015Jul 21 2015In this note, we obtain sharp bounds for the Green's function of the linearized Monge-Amp\`ere operators associated to convex functions with either Hessian determinant bounded away from zero and infinity or Monge-Amp\`ere measure satisfying a doubling ... More

BSE's, BSDE's and fixed point problemsOct 06 2014Mar 26 2017In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be translated into ... More

Hyers-Ulam stability of elliptic Möbius difference equationMar 03 2017The linear fractional map $ f(z) = \frac{az+ b}{cz + d} $ on the Riemann sphere with complex coefficients $ ad-bc \neq 0 $ is called M\"obius map. If $ f $ satisfies $ ad-bc=1 $ and $ -2<a+d<2 $, then $ f $ is called $\textit{elliptic}$ M\"obius map. ... More

Renormalization of three dimensional Hénon map I : Reduction of ambient spaceAug 19 2014Three dimensional analytic H\'enon-like map $$ F(x,y,z) = (f(x) - \epsilon(x,y,z),\, x,\, \delta(x,y,z)) $$ and its {\em period doubling} renormalization is defined. If $ F $ is infinitely renormalizable map, Jacobian determinant of $ n^{th} $ renormalized ... More

Hyers-Ulam stability of parabolic Möbius difference equationAug 29 2017Mar 31 2019The linear fractional map $ g(z) = \frac{az+ b}{cz + d} $ on the Riemann sphere with complex coefficients $ ad-bc = 1 $ is and $ a+d = \pm 2 $, then $ g $ is called {\em parabolic} M\"obius map. Let $ \{ b_n \}_{n \in \mathbb{N}_0} $ be the solution of ... More

Hénon renormalization in arbitrary dimension : Invariant space under renormalization operatorJun 24 2015Infinitely renormalizable H\'enon-like map in arbitrary finite dimension is considered. The set, $\mathcal N$ of infinitely renormalizable H\'enon-like maps satisfying the certain condition is invariant under renormalization operator. The Cantor attractor ... More

Subdifferential Formulas for a Class of Nonconvex Infimal ConvolutionsDec 30 2013In this paper, we provide a number of subdifferential formulas for a class of nonconvex infimal convolutions in normed spaces. The formulas obtained unify several results on subdifferentials of the distance function and the minimal time function. In particular, ... More

Formal local homologyJul 19 2016We introduce a concept of formal local homology modules which is in some sense dual to P. Schenzel's concept of formal local cohomology modules. The dual theorem and the non-vanishing theorem of formal local homology modules will be shown. We also give ... More

On the number of electrons that a nucleus can bindSep 17 2012Dec 07 2012We review some results on the ionization conjecture, which says that a neutral atom can bind at most one or two extra electrons.

New bounds on the maximum ionization of atomsSep 13 2010Nov 26 2011We prove that the maximum number $N_c$ of non-relativistic electrons that a nucleus of charge $Z$ can bind is less than $1.22Z+3Z^{1/3}$. This improves Lieb's upper bound $N_c<2Z+1$ [{\it Phys. Rev. A} {\bf 29}, 3018-3028 (1984)] when $Z\ge 6$. Our method ... More

On Learning Vector Representations in Hierarchical Label SpacesDec 22 2014Apr 16 2015An important problem in multi-label classification is to capture label patterns or underlying structures that have an impact on such patterns. This paper addresses one such problem, namely how to exploit hierarchical structures over labels. We present ... More

BSEs, BSDEs and fixed point problemsOct 06 2014Aug 14 2015In this paper we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be translated into a ... More

Simple Lie algebras which generalize Witt algebrasDec 30 1997We introduce a new class of simple Lie algebras $W(n,m)$ that generalize the Witt algebra by using "exponential" functions, and also a subalgebra $W^*(n,m)$ thereof; and we show each derivation of $W^*(1,0)$ can be written as a sum of an inner derivation ... More

Solving the De Prony's Problem of Separation of the Overlapping Exponents in DLTSJan 27 2007This paper presents the solution to the De Prony's problem of separation of the overlapping exponents using the binomial coefficient as the weighting factors. The algebraic structure of the signal classes is discussed and the applicability of method is ... More

Deterministic Compressed Sensing Matrices from Additive Character SequencesSep 30 2010Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive character sequences. ... More

Reed-Muller Codes for Peak Power Control in Multicarrier CDMAOct 01 2010Reed-Muller codes are studied for peak power control in multicarrier code-division multiple access (MC-CDMA) communication systems. In a coded MC-CDMA system, the information data multiplexed from users is encoded by a Reed-Muller subcode and the codeword ... More

Deterministic Construction of Partial Fourier Compressed Sensing Matrices Via Cyclic Difference SetsAug 04 2010Dec 28 2010Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a $K \times N$ partial Fourier measurement matrix for compressed sensing which is deterministically constructed via cyclic ... More

On a class of maximality principlesAug 19 2016Apr 16 2017We study various classes of maximality principles, $\rm{MP}(\kappa,\Gamma)$, introduced by J.D. Hamkins, where $\Gamma$ defines a class of forcing posets and $\kappa$ is a cardinal. We explore the consistency strength and the relationship of $\textsf{MP}(\kappa,\Gamma)$ ... More

BSDEs with terminal conditions that have bounded Malliavin derivativeNov 06 2012Nov 09 2013We show existence and uniqueness of solutions to BSDEs of the form $$ Y_t = \xi + \int_t^T f(s,Y_s,Z_s)ds - \int_t^T Z_s dW_s$$ in the case where the terminal condition $\xi$ has bounded Malliavin derivative. The driver $f(s,y,z)$ is assumed to be Lipschitz ... More

Low cost quantum circuits for classically intractable instances of the Hamiltonian dynamics simulation problemMay 12 2018Jul 03 2018We develop circuit implementations for digital-level quantum Hamiltonian dynamics simulation algorithms suitable for implementation on a reconfigurable quantum computer, such as the trapped ions. Our focus is on the co-design of a problem, its solution, ... More

Renormalization of Hénon map in arbitrary dimension I : Universality and reduction of ambient spaceJun 07 2015Jun 23 2015Period doubling H\'enon renormalization of strongly dissipative maps is generalized in arbitrary finite dimension. In particular, a small perturbation of toy model maps with dominated splitting has invariant $C^r$ surfaces embedded in higher dimension ... More

Acoustic Wave Field Reconstruction from Compressed Measurements with Application in Photoacoustic TomographySep 09 2016We present a method for the recovery of compressively sensed acoustic fields using patterned, instead of point-by-point, detection. From a limited number of such compressed measurements, we propose to reconstruct the field on the sensor plane in each ... More

Stability of Depths of Powers of Edge IdealsJan 12 2016Let $G$ be a graph and let $I := I (G)$ be its edge ideal. In this paper, we provide an upper bound of $n$ from which $\depth R/ I(G)^n$ is stationary, and compute this limit explicitly. This bound is always achieved if $G$ has no cycles of length $4$ ... More

Indistinguishability and Energy Sensitivity of Asymptotically Gaussian Compressed EncryptionSep 18 2017The principle of compressed sensing (CS) can be applied in a cryptosystem by providing the notion of security. In information-theoretic sense, it is known that a CS-based cryptosystem can be perfectly secure if it employs a random Gaussian sensing matrix ... More

Deterministic Compressed Sensing Matrices from Multiplicative Character SequencesNov 11 2010Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative character sequences. ... More

Hyers-Ulam stability of parabolic Möbius difference equationAug 29 2017The linear fractional map $ g(z) = \frac{az+ b}{cz + d} $ on the Riemann sphere with complex coefficients $ ad-bc = 1 $ is and $ a+d = \pm 2 $, then $ g $ is called {\em parabolic} M\"obius map. Let $ \{ b_n \}_{n \in \mathbb{N}_0} $ be the solution of ... More

Calculation of the Electron Spin Relaxation Times in InSb and InAs by the Projection-Reduction MethodJul 22 2014The electron spin relaxation times in a system of electrons interacting with piezoelectric phonons mediated through spin-orbit interactions were calculated using the formula derived from the projection-reduction method. The results showed that the temperature ... More

Electron Spin Relaxation in Two Polymorphic Structures of GaNAug 04 2014The relaxation process of electron spin in systems of electrons interacting with piezoelectric deformation phonons that are mediated through spin-orbit interactions was interpreted from a microscopic point of view using the formula for the electron spin ... More

A compact manifold with holonomy Spin(7) from Beauville's Calabi-Yau fourfoldAug 10 2014We give a new example of a compact manifold with holonomy Spin(7) from a Beauville's Calabi-Yau fourfold. Its construction is very concrete, starting with products of elliptic curves with complex multiplications --- so probably more accessible to physicists. ... More

The fine structure of operator miceMar 31 2016Apr 07 2016We develop the theory of abstract fine structural operators and operator-premice. We identify properties, which we require of operator-premice and operators, which ensure that certain basic facts about standard premice generalize. We define fine condensation ... More

An effective thermodynamic potential from the instanton vacuum with the Polyakov loopFeb 28 2011In this talk, we report our recent studies on an effective thermodynamic potential (Omega_eff) at finite temperature (T>0) and zero quark-chemical potential (mu_R=0), using the singular-gauge instanton solution and Matsubara formula for N_c=3 and N_f=2 ... More

Entropy spectra of black holes from resonance modes in scattering by the black holesFeb 17 2011Since the Bekenstein's proposal that a black hole has equally spaced area spectrum, the quasinormal modes as the characteristic modes of a black hole have been used in obtaining the horizon area spectrum of the black hole. However, the area spectrum of ... More

N=2 Supersymmetric SO(N)/Sp(N) Gauge Theories from Matrix ModelJan 25 2003Mar 26 2003We use the matrix model to describe the N=2 SO(N)/Sp(N) supersymmetric gauge theories with massive hypermultiplets in the fundamental representation. By taking the tree level superpotential perturbation made of a polynomial of a scalar chiral multiplet, ... More

CP asymmetries in penguin-induced B decays in general left-right modelsAug 15 2003We study CP asymmetries in penguin-induced b -> s\bar{s}s decays in general left-right models without imposing manifest or pseudomanifest left-right symmetry. Using the effective Hamiltonian approach, we evaluate CP asymmetries in B^\pm -> \phi K^{(\ast)\pm} ... More

Integrable structure in supersymmetric gauge theories with massive hypermultipletsMar 06 1996We study the quantum moduli space of vacua of $N=2$ supersymmetric $SU(N_c)$ gauge theories coupled to $N_f$ flavors of quarks in the fundamental representation. We identify the moduli space of the $N_c = 3$ and $N_f=2$ massless case with the full spectral ... More

Calabi-Yau construction by smoothing normal crossing varietiesApr 27 2006May 14 2007We investigate a method of construction of Calabi--Yau manifolds, that is, by smoothing normal crossing varieties. We develop some theories for calculating the Picard groups of the Calabi--Yau manifolds obtained in this method. Some applications are included, ... More

Global Hölder estimates for 2D linearized Monge-Ampère equations with right-hand side in divergence formFeb 21 2019We establish global H\"older estimates for solutions to inhomogeneous linearized Monge-Amp\`ere equations in two dimensions with the right hand side being the divergence of a bounded vector field. These equations arise in the semi-geostrophic equations ... More

Biases in differential expression analysis of RNA-seq data: A matter of replicate typeAug 15 2015In differential expression (DE) analysis of RNA-seq count data, it is known that genes with a larger read number are more likely to be differentially expressed. This bias has a profound effect on the subsequent Gene Ontology (GO) analysis by perturbing ... More