Publications  Mathematics, Statistics, and Computer Science
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Arithmetic Properties of the Frobenius Traces Defined by a Rational Abelian Variety (with two appendices by JP. Serre)
(Oxford University Press, 201706)Let A be an abelian variety over Q of dimension g such that the image of its associated absolute Galois representation rho(A) is open in GSp(2g)((Z) over cap). We investigate the arithmetic of the traces a(1,p) of the ... 
Nuclear norm of higherorder tensors
(American Mathematical Society, 201611)We establish several mathematical and computational properties of the nuclear norm for higherorder tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field  the value of the ... 
NUMERICAL SIMULATION OF GRATING STRUCTURES INCORPORATING TWODIMENSIONAL MATERIALS: A HIGHORDER PERTURBATION OF SURFACES FRAMEWORK
(Society for Industrial and Applied Mathematics, 20180102)The plasmonics of twodimensional materials, such as graphene, has become an important field of study for devices operating in the terahertz to midinfrared regime where such phenomena are supported. The semimetallic character ... 
AVERAGING OF NONLINEAR SCHRODINGER EQUATIONS ¨ WITH STRONG MAGNETIC CONFINEMENT
(International Press, 201611)We consider the dynamics of nonlinear Schrödinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement, based on the spectral properties of the ... 
Nonparametric Independence Screening via Favored Smoothing Bandwidth
(Elsevier, 20171123)We propose a flexible nonparametric regression method for ultrahighdimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. ... 
Functional envelope for modelfree sufficient dimension reduction
(Elsevier, 201710)In this article, we introduce the functional envelope for sufficient dimension reduction and regression with functional and longitudinal data. Functional sufficient dimension reduction methods, especially the inverse ... 
The tensor rank of tensor product of two threequbit W states is eight
(Elsevier, 201708)We show that the tensor rank of tensor product of two threequbit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor ... 
Large portfolio allocation using highfrequency financial data
(International Press, 201801)Asset allocation strategy involves dividing an investment portfolio among different assets according to their risk levels. In recent decades, estimating volatilities of asset returns based on highfrequency data has emerged ... 
Generalized Conditional Gradient for Sparse Estimation
(Journal of Machine Learning Research, 201701)Sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate ... 
DOPTIMAL DESIGNS WITH ORDERED CATEGORICAL DATA
(STATISTICA SINICA, 201710)Cumulative link models have been widely used for ordered categorical responses. Uniform allocation of experimental units is commonly used in practice, but often suffers from a lack of efficiency. We consider Doptimal ... 
Comparison of Fair and Optimum Ridesharing Plans
(20170628)Services like "Uber" and "Lyft" have become widespread in large cities for everyday mobility. This is due to the ease of requesting a ride (you can simply download the mobile app and request a driver on the fly from where ... 
Optimal designs for 2k factorial experiments with binary response
(Academia Sinica, Institute of Statistical Science, 2016)We consider the problem of obtaining Doptimal designs for factorial experiments with a binary response and k qualitative factors each at two levels. We obtain a characterization of locally Doptimal designs. We then ... 
A pathology of asymptotic multiplicity in the relative setting
(International Press, 20150210)We point out an example of a projective family π : X → S, a πpseudoeffective divisor D on X, and a subvariety V ⊂ X for which the asymptotic multiplicity σV (D; X/S) is infinite. This shows that the divisorial Zariski ... 
Ulrich Schur Bundles on Flag Varieties
(Academic Press Inc., 20170315)In this paper, we study equivariant vector bundles on partial flag varieties arising from Schur functors. We show that a partial flag variety with three or more steps does not admit an Ulrich bundle of this form with ... 
Effective Cones of Cycles on Blowups of Projective Space
(Mathematical Sciences Publishers, 20160315)In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blowups of projective space. We determine bounds on the number of points for which these cones are generated by the classes of ... 
On the evolution of scattering data under perturbations of the Toda lattice
(Elsevier, 201609)We present the results of an analytical and numerical study of the longtime behavior for certain FermiPastaUlam (FPU) lattices viewed as perturbations of the completely integrable Toda lattice. Our main tools are the ... 
Constructing many atomic models in ℵ1
(Association for Symbolic Logic, 201609)We introduce the notion of pseudoalgebraicity to study atomic models of first order theories (equivalently models of a complete sentence of Lω1,ω). Theorem: Let T be any complete firstorder theory in a countable language ... 
Decoupling Of Deficiency Indices And Applications To SchrodingerType Operators With Possibly Strongly Singular Potentisld.
(Elsevier Inc., 201610)We investigate closed, symmetric L2 (Rn)realizations H of Schr¨odingertype operators (−∆ + V ) C∞0 (Rn\Σ) whose potential coefficient V has a countable number of wellseparated singularities on compact sets Σj , j ... 
Inertia of Loewner matrices.
(Indiana University Mathematics Journal, 2016)Given positive numbers p_1 < p_2 < ... < p_n, and a real number r let L_r be the n by n matrix with its (i,j) entry equal to (p_i^rp_j^r)/(p_ip_j). A wellknown theorem of C. Loewner says that L_r is positive definite ... 
Turán problems and shadows III: Expansions of graphs
(Society for Industrial and Applied Mathematics, 2015)The expansion G+ of a graph G is the 3uniform hypergraph obtained from G by enlarging each edge of G with a new vertex disjoint from V (G) such that distinct edges are enlarged by distinct vertices. Let ex3(n, F) denote ...