P. Roman

P. Roman
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Mathematics - Classical Analysis and ODEs (14)
 
Mathematics - Representation Theory (7)
 
Solar and Stellar Astrophysics (6)
 
Earth and Planetary Astrophysics (6)
 
Mathematics - Mathematical Physics (5)
 
Mathematical Physics (5)
 
Mathematics - Probability (3)
 
Mathematics - Quantum Algebra (2)
 
Mathematics - Complex Variables (2)
 
Astrophysics of Galaxies (1)
 
Astrophysics (1)
 
Computer Science - Computer Vision and Pattern Recognition (1)
 
Computer Science - Distributed; Parallel; and Cluster Computing (1)
 
Instrumentation and Methods for Astrophysics (1)

Publications Authored By P. Roman

The maximum entropy method (MEM) is a well known deconvolution technique in radio-interferometry. This method solves a non-linear optimization problem with an entropy regularization term. Other heuristics such as CLEAN are faster but highly user dependent. Read More

We present an approach to sums of random Hermitian matrices via the theory of spherical functions for the Gelfand pair $(\mathrm{U}(n) \ltimes \mathrm{Herm}(n), \mathrm{U}(n))$. It is inspired by a similar approach of Kieburg and K\"osters for products of random matrices. The spherical functions have determinantal expressions because of the Harish-Chandra/Itzykson-Zuber integral formula. Read More

The aim of this paper is to study some continuous-time bivariate Markov processes arising from group representation theory. The first component (level) can be either discrete (quasi-birth-and-death processes) or continuous (switching diffusion processes), while the second component (phase) will always be discrete and finite. The infinitesimal operators of these processes will be now matrix-valued (either a block tridiagonal matrix or a matrix-valued second-order differential operator). Read More

In this paper we present a method to obtain deformations of families of matrix-valued orthogonal polynomials that are associated to the representation theory of compact Gelfand pairs. These polynomials have the Sturm-Liouville property in the sense that they are simultaneous eigenfunctions of a symmetric second order differential operator and we deform this operator accordingly so that the deformed families also have the Sturm-Liouville property. Our strategy is to deform the system of spherical functions that is related to the matrix-valued orthogonal polynomials and then check that the polynomial structure is respected by the deformation. Read More

The problem of object recognition in natural scenes has been recently successfully addressed with Deep Convolutional Neuronal Networks giving a significant break-through in recognition scores. The computational efficiency of Deep CNNs as a function of their depth, allows for their use in real-time applications. One of the key issues here is to reduce the number of windows selected from images to be submitted to a Deep CNN. Read More

We consider the quantum symmetric pair $(\mathcal{U}_q(\mathfrak{su}(3)), \mathcal{B})$ where $\mathcal{B}$ is a right coideal subalgebra. We prove that all finite-dimensional irreducible representations of $\mathcal{B}$ are weight representations and are characterised by their highest weight and dimension. We show that the restriction of a finite-dimensional irreducible representation of $\mathcal{U}_q(\mathfrak{su}(3))$ to $\mathcal{B}$ decomposes multiplicity free into irreducible representations of $\mathcal{B}$. Read More

A matrix-valued measure $\Theta$ reduces to measures of smaller size if there exists a constant invertible matrix $M$ such that $M\Theta M^*$ is block diagonal. Equivalently, the real vector space ${\mathscr A}$ of all matrices $T$ such that $T\Theta(X)=\Theta(X) T^*$ for any Borel set $X$ is non-trivial. If the subspace $A_h$ of self-adjoints elements in the commutant algebra $A$ of $\Theta$ is non-trivial, then $\Theta$ is reducible via a unitary matrix. Read More

Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of $(SU(2) \times SU(2), \text{diag})$ are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised universal enveloping algebra with a coideal subalgebra. The matrix-valued spherical functions give rise to matrix-valued orthogonal polynomials, which are matrix-valued analogues of a subfamily of Askey-Wilson polynomials. Read More

The finding of residual gas in the large central cavity of the HD142527 disk motivates questions on the origin of its non-Keplerian kinematics, and possible connections with planet formation. We aim to understand the physical structure that underlies the intra-cavity gaseous flows, guided by new molecular-line data in CO(6-5) with unprecedented angular resolutions. Given the warped structure inferred from the identification of scattered-light shadows cast on the outer disk, the kinematics are consistent, to first order, with axisymmetric accretion onto the inner disk occurring at all azimuth. Read More

A pathway to the formation of planetesimals, and eventually giant planets, may occur in concentrations of dust grains trapped in pressure maxima. Dramatic crescent-shaped dust concentrations have been seen in recent radio images at sub-mm wavelengths. These disk asymmetries could represent the initial phases of planet formation in the dust trap scenario, provided that grain sizes are spatially segregated. Read More

The identification of on-going planet formation requires the finest angular resolutions and deepest sensitivities in observations inspired by state-of-the-art numerical simulations. Hydrodynamic simulations of planet-disk interactions predict the formation of circumplanetary disks (CPDs) around accreting planetary cores. These CPDs have eluded unequivocal detection -their identification requires predictions in CPD tracers. Read More

The formation of planetesimals requires that primordial dust grains grow from micron- to km-sized bodies. Dust traps caused by gas pressure maxima have been proposed as regions where grains can concentrate and grow fast enough to form planetesimals, before radially migrating onto the star. We report new VLA Ka & Ku observations of the protoplanetary disk around the Herbig Ae/Be star MWC 758. Read More

This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure: \[ \frac{1}{x-c}x^{\alpha }e^{-x}dx+N\delta (x-c), \] for $x\in[0,\infty)$, $\alpha>-1$, a free parameter $N\in \mathbb{R}_{+}$ and a shift $c<0$. We analyze the asymptotic behavior (both strong and relative to classical Laguerre polynomials) of these orthogonal polynomials as $n$ tends to infinity. Read More

We present ALMA (Cycle 0) band-6 and band-3 observations of the transition disk Sz\,91. The disk inclination and position angle are determined to be $i=49.5\degr\pm3. Read More

Inner cavities and annular gaps in circumstellar disks are possible signposts of giant planet formation. The young star HD 142527 hosts a massive protoplanetary disk with a large cavity that extends up to 140 au from the central star, as seen in continuum images at infrared and millimeter wavelengths. Estimates of the survival of gas inside disk cavities are needed to discriminate between clearing scenarios. Read More

We consider polynomials $P_n$ orthogonal with respect to the weight $J_{\nu}$ on $[0,\infty)$, where $J_{\nu}$ is the Bessel function of order $\nu$. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for oscillatory integrals. They observed that the zeros are complex and accumulate as $n \to \infty$ near the vertical line $\textrm{Re}\, z = \frac{\nu \pi}{2}$. Read More

We introduce matrix-valued weight functions of arbitrary size, which are analogues of the weight function for the Gegenbauer or ultraspherical polynomials for the parameter $\nu>0$. The LDU-decomposition of the weight is explicitly given in terms of Gegenbauer polynomials. We establish a matrix-valued Pearson equation for these matrix weights leading to explicit shift operators relating the weights for parameter $\nu$ and $\nu+1$. Read More

We present a method to obtain infinitely many examples of pairs $(W,D)$ consisting of a matrix weight $W$ in one variable and a symmetric second-order differential operator $D$. The method is based on a uniform construction of matrix valued polynomials starting from compact Gelfand pairs $(G,K)$ of rank one and a suitable irreducible $K$-representation. The heart of the construction is the existence of a suitable base change $\Psi_{0}$. Read More

2013May
Affiliations: 11. Departamento de Astronomia, Universidad de Chile 2. Joint ALMA Observatory 3. European Southern Observatory 4. National Radio Astronomy Observatory, USA 5. Observatoire de Geneve 6. Departamento de Astronomia, Pontificia Universidad Catolica de Chile 7. UMI-FCA, CNRS / INSU France, 21. Departamento de Astronomia, Universidad de Chile 2. Joint ALMA Observatory 3. European Southern Observatory 4. National Radio Astronomy Observatory, USA 5. Observatoire de Geneve 6. Departamento de Astronomia, Pontificia Universidad Catolica de Chile 7. UMI-FCA, CNRS / INSU France, 31. Departamento de Astronomia, Universidad de Chile 2. Joint ALMA Observatory 3. European Southern Observatory 4. National Radio Astronomy Observatory, USA 5. Observatoire de Geneve 6. Departamento de Astronomia, Pontificia Universidad Catolica de Chile 7. UMI-FCA, CNRS / INSU France

Gaseous giant planet formation is thought to occur in the first few million years following stellar birth. Models predict that giant planet formation carves a deep gap in the dust component (shallower in the gas). Infrared observations of the disk around the young star HD142527, at ~140pc, found an inner disk ~10AU in radius, surrounded by a particularly large gap, with a disrupted outer disk beyond 140AU, indicative of a perturbing planetary-mass body at ~90 AU. Read More

In a previous paper we have introduced matrix-valued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2)\times SU(2). In particular the matrix-size of the polynomials is arbitrarily large. The matrix-valued orthogonal polynomials and the corresponding weight function are studied. Read More

We consider a model of $n$ non-intersecting squared Bessel processes with one starting point $a>0$ at time t=0 and one ending point $b>0$ at time $t=T$. After proper scaling, the paths fill out a region in the $tx$-plane. Depending on the value of the product $ab$ the region may come to the hard edge at 0, or not. Read More

The matrix-valued spherical functions for the pair (K x K, K), K=SU(2), are studied. By restriction to the subgroup A the matrix-valued spherical functions are diagonal. For suitable set of representations we take these diagonals into a matrix-valued function, which are the full spherical functions. Read More

We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). Based on the four-term recurrence relation, it is shown that, after proper scaling, the sequence of normalized zero counting measures converges weakly to the first component of a vector of two measures which satisfies a vector equilibrium problem with two external fields. We also give the explicit formula for the equilibrium vector in terms of solutions of an algebraic equation. Read More

In this paper we consider the model of $n$ non-intersecting squared Bessel processes with parameter $\alpha$, in the confluent case where all particles start, at time $t=0$, at the same positive value $x=a$, remain positive, and end, at time $T=t$, at the position $x=0$. The positions of the paths have a limiting mean density as $n\to\infty$ which is characterized by a vector equilibrium problem. We show how to obtain this equilibrium problem from different considerations involving the recurrence relations for multiple orthogonal polynomials associated with the modified Bessel functions. Read More

The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in \cite{T2}. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. Read More

The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {P_n}_n, with respect to a weight W, that are eigenfunctions of a second order differential operator D. The weight W and the differential operator D were found in [12], using some aspects of the theory of the spherical functions associated to the complex projective spaces. We also find other second order differential operator E symmetric with respect to W and we describe the algebra generated by D and E. Read More

We describe the calibration, measurements and data reduction, of the dark current of the ISOCAM/LW detector. We point-out the existence of two significant drifts of the LW dark-current, one throughout the ISO mission, on a timescale of days, another within each single revolution, on a timescale of hours. We also show the existence of a dependence of the dark current on the temperature of the ISOCAM detector. Read More