On the approximation of the subgrid scale for systems of equations

Postprint (published version)

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

A non-linear Bayesian approach for upscaling local-scale hydraulic conductivity measurements based on local- and regional-scale geophysical data

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed an upscaling procedure based on a Bayesian sequential simulation approach. This method is then applied to the stochastic integration of low-resolution, regional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this upscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Predicting the physicochemical profile of diastereoisomeric histidine-containing dipeptides by property space analysis.

OBJECTIVES: This study aimed at measuring the lipophilicity and ionization constants of diastereoisomeric dipeptides, interpreting them in terms of conformational behavior, and developing statistical models to predict them. METHODS: A series of 20 dipeptides of general structure NH(2) -L-X-(L or D)-His-OMe was designed and synthetized. Their experimental ionization constants (pK(1) , pK(2) and pK(3) ) and lipophilicity parameters (log P(N) and log D(7.4) ) were measured by potentiometry. Molecular modeling in three media (vacuum, water, and chloroform) was used to explore and sample their conformational space, and for each stored conformer to calculate their radius of gyration, virtual log P (preferably written as log P(MLP) , meaning obtained by the molecular lipophilicity potential (MLP) method) and polar surface area (PSA). Means and ranges were calculated for these properties, as was their sensitivity (i.e., the ratio between property range and number of rotatable bonds). RESULTS: Marked differences between diastereoisomers were seen in their experimental ionization constants and lipophilicity parameters. These differences are explained by molecular flexibility, configuration-dependent differences in intramolecular interactions, and accessibility of functional groups. Multiple linear equations correlated experimental lipophilicity parameters and ionization constants with PSA range and other calculated parameters. CONCLUSION: This study documents the differences in lipophilicity and ionization constants between diastereoisomeric dipeptides. Such configuration-dependent differences are shown to depend markedly on differences in conformational behavior and to be amenable to multiple linear regression. Chirality 24:566-576, 2012. © 2012 Wiley Periodicals, Inc.

Short-term stability of testosterone and epitestosterone conjugates in urine samples: quantification by liquid chromatography-linear ion trap mass spectrometry.

A simple method using liquid chromatography-linear ion trap mass spectrometry for simultaneous determination of testosterone glucuronide (TG), testosterone sulfate (TS), epitestosterone glucuronide (EG) and epitestosterone sulfate (ES) in urine samples was developed. For validation purposes, a urine containing no detectable amount of TG, TS and EG was selected and fortified with steroid conjugate standards. Quantification was performed using deuterated testosterone conjugates to correct for ion suppression/enhancement during ESI. Assay validation was performed in terms of lower limit of detection (1-3ng/mL), recovery (89-101%), intraday precision (2.0-6.8%), interday precision (3.4-9.6%) and accuracy (101-103%). Application of the method to short-term stability testing of urine samples at temperature ranging from 4 to 37 degrees C during a time-storage of a week lead to the conclusion that addition of sodium azide (10mg/mL) is required for preservation of the analytes.

Simulating maize phenology as a function of air temperature with a linear and a nonlinear model

The objective of this study was to adapt a nonlinear model (Wang and Engel - WE) for simulating the phenology of maize (Zea mays L.), and to evaluate this model and a linear one (thermal time), in order to predict developmental stages of a field-grown maize variety. A field experiment, during 2005/2006 and 2006/2007 was conducted in Santa Maria, RS, Brazil, in two growing seasons, with seven sowing dates each. Dates of emergence, silking, and physiological maturity of the maize variety BRS Missões were recorded in six replications in each sowing date. Data collected in 2005/2006 growing season were used to estimate the coefficients of the two models, and data collected in the 2006/2007 growing season were used as independent data set for model evaluations. The nonlinear WE model accurately predicted the date of silking and physiological maturity, and had a lower root mean square error (RMSE) than the linear (thermal time) model. The overall RMSE for silking and physiological maturity was 2.7 and 4.8 days with WE model, and 5.6 and 8.3 days with thermal time model, respectively.

Análise genética de escores de avaliação visual de bovinos com modelos bayesianos de limiar e linear

O objetivo deste trabalho foi comparar as estimativas de parâmetros genéticos obtidas em análises bayesianas uni-característica e bi-característica, em modelo animal linear e de limiar, considerando-se as características categóricas morfológicas de bovinos da raça Nelore. Os dados de musculosidade, estrutura física e conformação foram obtidos entre 2000 e 2005, em 3.864 animais de 13 fazendas participantes do Programa Nelore Brasil. Foram realizadas análises bayesianas uni e bi-características, em modelos de limiar e linear. De modo geral, os modelos de limiar e linear foram eficientes na estimação dos parâmetros genéticos para escores visuais em análises bayesianas uni-características. Nas análises bi-características, observou-se que: com utilização de dados contínuos e categóricos, o modelo de limiar proporcionou estimativas de correlação genética de maior magnitude do que aquelas do modelo linear; e com o uso de dados categóricos, as estimativas de herdabilidade foram semelhantes. A vantagem do modelo linear foi o menor tempo gasto no processamento das análises. Na avaliação genética de animais para escores visuais, o uso do modelo de limiar ou linear não influenciou a classificação dos animais, quanto aos valores genéticos preditos, o que indica que ambos os modelos podem ser utilizados em programas de melhoramento genético.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

GPS to LRM: Integration of Spatial Point Features with Linear Referencing Methods, 2001

Global positioning systems (GPS) offer a cost-effective and efficient method to input and update transportation data. The spatial location of objects provided by GPS is easily integrated into geographic information systems (GIS). The storage, manipulation, and analysis of spatial data are also relatively simple in a GIS. However, many data storage and reporting methods at transportation agencies rely on linear referencing methods (LRMs); consequently, GPS data must be able to link with linear referencing. Unfortunately, the two systems are fundamentally incompatible in the way data are collected, integrated, and manipulated. In order for the spatial data collected using GPS to be integrated into a linear referencing system or shared among LRMs, a number of issues need to be addressed. This report documents and evaluates several of those issues and offers recommendations. In order to evaluate the issues associated with integrating GPS data with a LRM, a pilot study was created. To perform the pilot study, point features, a linear datum, and a spatial representation of a LRM were created for six test roadway segments that were located within the boundaries of the pilot study conducted by the Iowa Department of Transportation linear referencing system project team. Various issues in integrating point features with a LRM or between LRMs are discussed and recommendations provided. The accuracy of the GPS is discussed, including issues such as point features mapping to the wrong segment. Another topic is the loss of spatial information that occurs when a three-dimensional or two-dimensional spatial point feature is converted to a one-dimensional representation on a LRM. Recommendations such as storing point features as spatial objects if necessary or preserving information such as coordinates and elevation are suggested. The lack of spatial accuracy characteristic of most cartography, on which LRM are often based, is another topic discussed. The associated issues include linear and horizontal offset error. The final topic discussed is some of the issues in transferring point feature data between LRMs.

Use of Remote Sensing for Collection of Data Elements for Linear Referencing Systems, 2001

This report evaluates the use of remotely sensed images in implementing the Iowa DOT LRS that is currently in the stages of system architecture. The Iowa Department of Transportation is investing a significant amount of time and resources into creation of a linear referencing system (LRS). A significant portion of the effort in implementing the system will be creation of a datum, which includes geographically locating anchor points and then measuring anchor section distances between those anchor points. Currently, system architecture and evaluation of different data collection methods to establish the LRS datum is being performed for the DOT by an outside consulting team.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

J2 effect and elliptic inclined periodic orbits in the collision three-body problem

The existence of a new class of inclined periodic orbits of the collision restricted three-body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet

Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended