Young-Capelli bitableaux, Capelli immanants in U(gl(n)) and the Okounkov quantum immanants

We propose a new approach to a unified study of determinants, permanents, immanants, (determinantal) bitableaux and symmetrized bitableaux in the polynomial algebra $C[M_{n, n}]$ as well as of their Lie analogues in the enveloping algebra $U(gl(n))$. This leads to new relevant classes of elements in $U(gl(n))$: Capelli bitableaux, right Young-Capelli bitableaux and Capelli immanants. The set of standard Capelli bitableaux and the set of standard right Young-Capelli bitableaux are bases of $U(gl(n))$, whose action on the Gordan-Capelli basis of $C[M_{n, n}]$ have remarkable properties. Capelli immanants can be efficiently computed and provide a system of generators of $U(gl(n))$. The Okounkov quantum immanants are proved to be simple linear combinations of Capelli immanants. Several examples are provided throughout the paper.Comment: arXiv admin note: text overlap with arXiv:1608.0678

Parameter Estimation from Time-Series Data with Correlated Errors: A Wavelet-Based Method and its Application to Transit Light Curves

We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as $1/f^\gamma$. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the midtransit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for midtransit times and truer estimates of their uncertainties.Comment: Accepted in ApJ. Illustrative code may be found at http://www.mit.edu/~carterja/code/ . 17 page

Water formation at low temperatures by surface O2 hydrogenation I: characterization of ice penetration

Water is the main component of interstellar ice mantles, is abundant in the solar system and is a crucial ingredient for life. The formation of this molecule in the interstellar medium cannot be explained by gas-phase chemistry only and its surface hydrogenation formation routes at low temperatures (O, O2, O3 channels) are still unclear and most likely incomplete. In a previous paper we discussed an unexpected zeroth-order H2O production behavior in O2 ice hydrogenation experiments compared to the first-order H2CO and CH3OH production behavior found in former studies on hydrogenation of CO ice. In this paper we experimentally investigate in detail how the structure of O2 ice leads to this rare behavior in reaction order and production yield. In our experiments H atoms are added to a thick O2 ice under fully controlled conditions, while the changes are followed by means of reflection absorption infrared spectroscopy (RAIRS). The H-atom penetration mechanism is systematically studied by varying the temperature, thickness and structure of the O2 ice. We conclude that the competition between reaction and diffusion of the H atoms into the O2 ice explains the unexpected H2O and H2O2 formation behavior. In addition, we show that the proposed O2 hydrogenation scheme is incomplete, suggesting that additional surface reactions should be considered. Indeed, the detection of newly formed O3 in the ice upon H-atom exposure proves that the O2 channel is not an isolated route. Furthermore, the addition of H2 molecules is found not to have a measurable effect on the O2 reaction channel.Comment: 1 page, 1 figur

Quantification of segregation dynamics in ice mixtures

(Abridged) The observed presence of pure CO2 ice in protostellar envelopes is attributed to thermally induced ice segregation, but a lack of quantitative experimental data has prevented its use as a temperature probe. Quantitative segregation studies are also needed to characterize diffusion in ices, which underpins all ice dynamics and ice chemistry. This study aims to quantify the segregation mechanism and barriers in different H2O:CO2 and H2O:CO ice mixtures covering a range of astrophysically relevant ice thicknesses and mixture ratios. The ices are deposited at 16-50 K under (ultra-)high vacuum conditions. Segregation is then monitored at 23-70 K as a function of time, through infrared spectroscopy. Thin (8-37 ML) H2O:CO2/CO ice mixtures segregate sequentially through surface processes, followed by an order of magnitude slower bulk diffusion. Thicker ices (>100 ML) segregate through a fast bulk process. The thick ices must therefore be either more porous or segregate through a different mechanism, e.g. a phase transition. The segregation dynamics of thin ices are reproduced qualitatively in Monte Carlo simulations of surface hopping and pair swapping. The experimentally determined surface-segregation rates for all mixture ratios follow the Ahrrenius law with a barrier of 1080[190] K for H2O:CO2 and 300[100] K for H2O:CO mixtures. During low-mass star formation H2O:CO2 segregation will be important already at 30[5] K. Both surface and bulk segregation is proposed to be a general feature of ice mixtures when the average bond strengths of the mixture constituents in pure ice exceeds the average bond strength in the ice mixture.Comment: Accepted for publication in A&A. 25 pages, including 13 figure

Discrete Mathematics

The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way} (see, e.g. \cite{KY}). The themes are organized into a suitable sequence that allows us to derive any result from the preceding ones by elementary processes. Definitions of \textit{combinatorial coefficients} are just by their \textit{combinatorial meaning}. The derivation techniques of formulae/results are founded upon constructions and two general and elementary principles/methods: - The \textit{bad element} method (for \textit{recursive} formulae). As the reader should recognize, the bad element method might be regarded as a combinatorial companion of the idea of \textit{conditional probability}. - The \textit{overcounting} principle (for \textit{close form} formulae). Therefore, \textit{no computation} is required in \textit{proofs}: \textit{computation formulae are byproducts of combinatorial constructions}. We tried to provide a self-contained presentation: the only prerequisite is standard high school mathematics. We limited ourselves to the \textit{combinatorial point of view}: we invite the reader to draw the (obvious) \textit{probabilistic interpretations}

Quantum immanants, double Young-Capelli bitableaux and Schur shifted symmetric functions

We propose a new method for a unified study of some of the main features of the theory of the center $\boldsymbol{\zeta}(n)$ of the enveloping algebra U(gl(n)) and of the algebra $\Lambda^*(n)$ of shifted symmetric polynomials, that allows the whole theory to be developed, in a transparent and concise way, from the representation-theoretic point of view, that is entirely in the center of U(gl(n)). Our methodological innovation is the systematic use of the superalgebraic method of virtual variables for gl(n), which is, in turn, an extension of Capelli's method of ``variabili ausiliarie''. The passage $n \rightarrow \infty$ for the algebras $\boldsymbol{\zeta}(n)$ and $\Lambda^*(n)$ is here obtained both as direct and inverse limit in the category of filtered algebras. The present approach leads to proofs that are almost direct consequences of the definitions and constructions: they often reduce to a few lines computation

Capelli-Deruyts bitableaux and the classical Capelli generators of the center of the enveloping algebra U(gl(n))U(gl(n))

In this paper, we consider a special class of Capelli bitableaux, namely the Capelli-Deruyts bitableaux. The main results we prove are the hook coefficient lemma and the expansion theorem. Capelli-Deruyts bitableaux of rectangular shape are of particular interest since they are central elements in the enveloping algebra. The expansion theorem implies that these central element is explicitely described as a polynomial in the classical Capelli central elements. The hook coefficient lemma implies that the Capelli-Deruyts bitableaux are (canonically) expressed as the products of column determinants.Comment: arXiv admin note: text overlap with arXiv:2107.1020

Compaction of microporous amorphous solid water by ion irradiation

We have studied the compaction of vapor-deposited amorphous solid water by energetic ions at 40 K. The porosity was characterized by ultraviolet-visible spectroscopy, infrared spectroscopy, and methane adsorption/desorption. These three techniques provide different and complementary views of the structural changes in ice resulting from irradiation. We find that the decrease in internal surface area of the pores, signaled by infrared absorption by dangling bonds, precedes the decrease in the pore volume during irradiation. Our results imply that impacts from cosmic rays can cause compaction in the icy mantles of the interstellar grains, which can explain the absence of dangling bond features in the infrared spectrum of molecular clouds.Fil: Raut, U.. University of Virginia; Estados UnidosFil: Teolis, B. D.. University of Virginia; Estados UnidosFil: Loeffler, M. J.. University of Virginia; Estados UnidosFil: Vidal, Ricardo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Famá, M.. University of Virginia; Estados UnidosFil: Baragiola, R. A.. University of Virginia; Estados Unido