Effect of Knotting on the Shape of Polymers

Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots.

Probability of achieving optimal molecular response to imatinib in chronic myeloid leukemia (CML) patients: Pharmacokinetic/Pharmacodynamic (PK/PD) relationships observed under field-conditions

Objectives: Imatinib has been increasingly proposed for therapeutic drug monitoring (TDM), as trough concentrations (Cmin) correlate with response rates in CML patients. This analysis aimed to evaluate the impact of imatinib exposure on optimal molecular response rates in a large European cohort of patients followed by centralized TDM.¦Methods: Sequential PK/PD analysis was performed in NONMEM 7 on 2230 plasma (PK) samples obtained along with molecular response (PD) data from 1299 CML patients. Model-based individual Bayesian estimates of exposure, parameterized as to initial dose adjusted and log-normalized Cmin (log-Cmin) or clearance (CL), were investigated as potential predictors of optimal molecular response, while accounting for time under treatment (stratified at 3 years), gender, CML phase, age, potentially interacting comedication, and TDM frequency. PK/PD analysis used mixed-effect logistic regression (iterative two-stage method) to account for intra-patient correlation.¦Results: In univariate analyses, CL, log-Cmin, time under treatment, TDM frequency, gender (all p<0.01) and CML phase (p=0.02) were significant predictors of the outcome. In multivariate analyses, all but log-Cmin remained significant (p<0.05). Our model estimates a 54.1% probability of optimal molecular response in a female patient with a median CL of 14.4 L/h, increasing by 4.7% with a 35% decrease in CL (percentile 10 of CL distribution), and decreasing by 6% with a 45% increased CL (percentile 90), respectively. Male patients were less likely than female to be in optimal response (odds ratio: 0.62, p<0.001), with an estimated probability of 42.3%.¦Conclusions: Beyond CML phase and time on treatment, expectedly correlated to the outcome, an effect of initial imatinib exposure on the probability of achieving optimal molecular response was confirmed in field-conditions by this multivariate analysis. Interestingly, male patients had a higher risk of suboptimal response, which might not exclusively derive from their 18.5% higher CL, but also from reported lower adherence to the treatment. A prospective longitudinal study would be desirable to confirm the clinical importance of identified covariates and to exclude biases possibly affecting this observational survey.

Double adjunctions

We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg-Moore objects in double categories. We improve upon an earlier result of Fiore-Gambino-Kock in [7] to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category horizontally and vertically, and also in its vertical 2-category. We also prove that a double category admits Eilenberg-Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double Yoneda Lemma.

Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers

Recent technological advances in remote sensing have enabled investigation of the morphodynamics and hydrodynamics of large rivers. However, measuring topography and flow in these very large rivers is time consuming and thus often constrains the spatial resolution and reach-length scales that can be monitored. Similar constraints exist for computational fluid dynamics (CFD) studies of large rivers, requiring maximization of mesh-or grid-cell dimensions and implying a reduction in the representation of bedform-roughness elements that are of the order of a model grid cell or less, even if they are represented in available topographic data. These ``subgrid'' elements must be parameterized, and this paper applies and considers the impact of roughness-length treatments that include the effect of bed roughness due to ``unmeasured'' topography. CFD predictions were found to be sensitive to the roughness-length specification. Model optimization was based on acoustic Doppler current profiler measurements and estimates of the water surface slope for a variety of roughness lengths. This proved difficult as the metrics used to assess optimal model performance diverged due to the effects of large bedforms that are not well parameterized in roughness-length treatments. However, the general spatial flow patterns are effectively predicted by the model. Changes in roughness length were shown to have a major impact upon flow routing at the channel scale. The results also indicate an absence of secondary flow circulation cells in the reached studied, and suggest simpler two-dimensional models may have great utility in the investigation of flow within large rivers. Citation: Sandbach, S. D. et al. (2012), Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers, Water Resour. Res., 48, W12501, doi: 10.1029/2011WR011284.

Nonpersistence of resonant caustics in perturbed elliptic billiards

Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard table is an ellipse, any nonsingular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics —the ones whose tangent trajectories are closed polygons— are destroyed under generic perturbations of the billiard table. We prove that none of the resonant elliptical caustics persists under a large class of explicit perturbations of the original ellipse. This result follows from a standard Melnikov argument and the analysis of the complex singularities of certain elliptic functions.

Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

Automatització d'enquestes

La realització d'aquest projecte genererà un aplicatiu que permetrà la realització d'enquestes telefòniques a usuaris predefinits, automatització la execució de qüestionaris parametritzats amb XML, i gravant aquestes respostes en local i en una base de dades remota.

Análisis y diseño de antenas dipolo y parche para aplicaciones implantadas en el cuerpo humano

En els darrers anys, els sistemes de telemetria per a aplicacions mèdiques han crescut significativament en el diagnòstic i en la monitorització de, per exemple, la glucosa, la pressió de la sang, la temperatura, el ritme cardíac... Els dispositius implantats amplien les aplicacions en medicina i incorpora una millora de qualitat de vida per a l’usuari. Per aquest motiu, en aquest projecte s’estudien dues de les antenes més comuns, com son l’antena dipol i el patch, aquesta última és especialment utilitzada en aplicacions implantades. En l’anàlisi d’aquestes antenes s’han parametritzat característiques relacionades amb l’entorn de l’aplicació, així com també de la pròpia antena, explicant el comportament que, a diferencia amb l’espai lliure, les antenes presenten a canvis d’aquests paràmetres. Al mateix temps, s’ha implementat una configuració per a la mesura d’antenes implantades basat en el model del cos humà d’una capa. Comparant amb els resultats de les simulacions realitzades mitjançant el software FEKO, s’ha obtingut gran correspondència en la mesura empírica d’adaptació i de guany de les antenes microstrip. Gràcies a l’anàlisi paramètric, aquest projecte també presenta diversos dissenys de les antenes optimitzant el guany realitzable amb l’objectiu d’aconseguir la millor comunicació possible amb el dispositiu extern o estació base.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Implementing interactive computing in an object-oriented environment

Statistical computing when input/output is driven by a Graphical User Interface is considered. A proposal is made for automatic control ofcomputational flow to ensure that only strictly required computationsare actually carried on. The computational flow is modeled by a directed graph for implementation in any object-oriented programming language with symbolic manipulation capabilities. A complete implementation example is presented to compute and display frequency based piecewise linear density estimators such as histograms or frequency polygons.

Optimal taxation without state-contingent debt

To recover a version of Barro's (1979) `random walk'tax smoothing outcome, we modify Lucas and Stokey's (1983) economyto permit only risk--free debt. This imparts near unit root like behaviorto government debt, independently of the government expenditureprocess, a realistic outcome in the spirit of Barro's. We showhow the risk--free--debt--only economy confronts the Ramsey plannerwith additional constraints on equilibrium allocations thattake the form of a sequence of measurability conditions.We solve the Ramsey problem by formulating it in terms of a Lagrangian,and applying a Parameterized Expectations Algorithm tothe associated first--order conditions. The first--order conditions andnumerical impulse response functions partially affirmBarro's random walk outcome. Though the behaviors oftax rates, government surpluses, and government debts differ, allocationsare very close for computed Ramsey policies across incomplete and completemarkets economies.

A low dimensional Kalman filter for systems with lagged observables

This note describes how the Kalman filter can be modified to allow for thevector of observables to be a function of lagged variables without increasing the dimensionof the state vector in the filter. This is useful in applications where it is desirable to keepthe dimension of the state vector low. The modified filter and accompanying code (whichnests the standard filter) can be used to compute (i) the steady state Kalman filter (ii) thelog likelihood of a parameterized state space model conditional on a history of observables(iii) a smoothed estimate of latent state variables and (iv) a draw from the distribution oflatent states conditional on a history of observables.

Total curvature and total torsion of knotted polymers

Previous work on radius of gyration and average crossing number has demonstrated that polymers with fixed topology show a different scaling behavior with respect to these characteristics than polymers with unrestricted topology. Using numerical simulations, we show here that the difference in the scaling behavior between polymers with restricted and unrestricted topology also applies to the total curvature and total torsion. For each knot type, the equilibrium length with respect to a given spatial characteristic is the number of edges at which the value of the characteristic is the same as the average for all polygons. This number appears to be correlated to physical properties of macromolecules, for example gel mobility as measured by the separation between distinct knot types. We also find that, on average, closed polymers require slightly more total curvature and slightly less total torsion than open polymers with the corresponding number of monomers.

Physiologically based pharmacokinetic modeling of arsenic in the mouse

A remarkable feature of the carcinogenicity of inorganic arsenic is that while human exposures to high concentrations of inorganic arsenic in drinking water are associated with increases in skin, lung, and bladder cancer, inorganic arsenic has not typically caused tumors in standard laboratory animal test protocols. Inorganic arsenic administered for periods of up to 2 yr to various strains of laboratory mice, including the Swiss CD-1, Swiss CR:NIH(S), C57Bl/6p53(+/-), and C57Bl/6p53(+/+), has not resulted in significant increases in tumor incidence. However, Ng et al. (1999) have reported a 40% tumor incidence in C57Bl/6J mice exposed to arsenic in their drinking water throughout their lifetime, with no tumors reported in controls. In order to investigate the potential role of tissue dosimetry in differential susceptibility to arsenic carcinogenicity, a physiologically based pharmacokinetic (PBPK) model for inorganic arsenic in the rat, hamster, monkey, and human (Mann et al., 1996a, 1996b) was extended to describe the kinetics in the mouse. The PBPK model was parameterized in the mouse using published data from acute exposures of B6C3F1 mice to arsenate, arsenite, monomethylarsonic acid (MMA), and dimethylarsinic acid (DMA) and validated using data from acute exposures of C57Black mice. Predictions of the acute model were then compared with data from chronic exposures. There was no evidence of changes in the apparent volume of distribution or in the tissue-plasma concentration ratios between acute and chronic exposure that might support the possibility of inducible arsenite efflux. The PBPK model was also used to project tissue dosimetry in the C57Bl/6J study, in comparison with tissue levels in studies having shorter duration but higher arsenic treatment concentrations. The model evaluation indicates that pharmacokinetic factors do not provide an explanation for the difference in outcomes across the various mouse bioassays. Other possible explanations may relate to strain-specific differences, or to the different durations of dosing in each of the mouse studies, given the evidence that inorganic arsenic is likely to be active in the later stages of the carcinogenic process. [Authors]

Surface topography and mixed-pixel effects on the simulated L-band brightness temperatures.

The impact of topography and mixed pixels on L-band radiometric observations over land needs to be quantified to improve the accuracy of soil moisture retrievals. For this purpose, a series of simulations has been performed with an improved version of the soil moisture and ocean salinity (SMOS) end-to-end performance simulator (SEPS). The brightness temperature generator of SEPS has been modified to include a 100-m-resolution land cover map and a 30-m-resolution digital elevation map of Catalonia (northeast of Spain). This high-resolution generator allows the assessment of the errors in soil moisture retrieval algorithms due to limited spatial resolution and provides a basis for the development of pixel disaggregation techniques. Variation of the local incidence angle, shadowing, and atmospheric effects (up- and downwelling radiation) due to surface topography has been analyzed. Results are compared to brightness temperatures that are computed under the assumption of an ellipsoidal Earth.