Robust estimation of stationary continuous-time ARMA models via indirect inference

In this paper we present a robust estimator for the parameters of a continuous-time ARMA(p,q) (CARMA(p,q)) process sampled equidistantly which is not necessarily Gaussian. Therefore, an indirect estimation procedure is used. It is an indirect estimation because we first estimate the parameters of the auxiliary AR(r) representation ($r\geq 2p-1$) of the sampled CARMA process using a generalized M- (GM-)estimator. Since the map which maps the parameters of the auxiliary AR(r) representation to the parameters of the CARMA process is not given explicitly, a separate simulation part is necessary where the parameters of the AR(r) representation are estimated from simulated CARMA processes. Then, the parameter which takes the minimum distance between the estimated AR parameters and the simulated AR parameters gives an estimator for the CARMA parameters. First, we show that under some standard assumptions the GM-estimator for the AR(r) parameters is consistent and asymptotically normally distributed. Next, we prove that the indirect estimator is consistent and asymptotically normally distributed as well using in the simulation part the asymptotically normally distributed LS-estimator. The indirect estimator satisfies several important robustness properties such as weak resistance, $\pi_{d_n}$-robustness and it has a bounded influence functional. The practical applicability of our method is demonstrated through a simulation study with replacement outliers and compared to the non-robust quasi-maximum-likelihood estimation method

Visualization of Data by Method of Elastic Maps and Its Applications in Genomics, Economics and Sociology

Technology of data visualization and data modeling is suggested. The basic of the technology is original idea of elastic net and methods of its construction and application. A short review of relevant methods has been made. The methods proposed are illustrated by applying them to the real economical, sociological and biological datasets and to some model data distributions. The basic of the technology is original idea of elastic net - regular point approximation of some manifold that is put into the multidimensional space and has in a certain sense minimal energy. This manifold is an analogue of principal surface and serves as non-linear screen on what multidimensional data are projected. Remarkable feature of the technology is its ability to work with and to fill gaps in data tables. Gaps are unknown or unreliable values of some features. It gives a possibility to predict plausibly values of unknown features by values of other ones. So it provides technology of constructing different prognosis systems and non-linear regressions. The technology can be used by specialists in different fields. There are several examples of applying the method presented in the end of this paper

Seven clusters in genomic triplet distributions

Motivation: In several recent papers new algorithms were proposed for detecting coding regions without requiring learning dataset of already known genes. In this paper we studied cluster structure of several genomes in the space of codon usage. This allowed to interpret some of the results obtained in other studies and propose a simpler method, which is, nevertheless, fully functional. Results: Several complete genomic sequences were analyzed, using visualization of tables of triplet counts in a sliding window. The distribution of 64-dimensional vectors of triplet frequencies displays a well-detectable cluster structure. The structure was found to consist of seven clusters, corresponding to protein-coding information in three possible phases in one of the two complementary strands and in the non-coding regions. Awareness of the existence of this structure allows development of methods for the segmentation of sequences into regions with the same coding phase and non-coding regions. This method may be completely unsupervised or use some external information. Since the method does not need extraction of ORFs, it can be applied even for unassembled genomes. Accuracy calculated on the base-pair level (both sensitivity and specificity) exceeds 90%. This is not worse as compared to such methods as HMM, however, has the advantage to be much simpler and clear

Influence of convection and biomass burning outflow on tropospheric chemistry over the tropical Pacific

Observations over the tropics from the Pacific Exploratory Mission-Tropics A Experiment are analyzed using a one-dimensional model with an explicit formulation for convective transport. Adopting tropical convective mass fluxes from a general circulation model (GCM) yields a large discrepancy between observed and simulated CH3I concentrations. Observations of CH3I imply the convective mass outflux to be more evenly distributed with altitude over the tropical ocean than suggested by the GCM. We find that using a uniform convective turnover lifetime of 20 days in the upper and middle troposphere enables the model to reproduce CH3I observations. The model reproduces observed concentrations of H2O2 and CH3OOH. Convective transport of CH3OOH from the lower troposphere is estimated to account for 40-80% of CH3OOH concentrations in the upper troposphere. Photolysis of CH3OOH transported by convection more than doubles the primary HOx source and increases OH concentrations and O3 production by 10-50% and 0.4 ppbv d-1, respectively, above 11 km. Its effect on the OH concentration and O3 production integrated over the tropospheric column is, however, small. The effects of pollutant import from biomass burning regions are much more dominant. Using C2H2 as a tracer, we estimate that biomass burning outflow enhances O3 concentrations, O3 production, and concentrations of NOx and OH by 60%, 45%, 75%, and 7%, respectively. The model overestimates HNO3 concentrations by about a factor of 2 above 4 km for the upper one-third quantile of C2H2 data while it generally reproduces HNO3 concentrations for the lower and middle one-third quantiles of C2H2 data. Copyright 2000 by the American Geophysical Union

Source contributions to ambient VOCs and CO at a rural site in eastern China

Ambient data on volatile organic compounds (VOCs) and carbon monoxide (CO) obtained at a rural site in eastern China are analyzed to investigate the nature of emission sources and their relative contributions to ambient concentrations. A principal component analysis (PCA) showed that vehicle emissions and biofuel burning, biomass burning and industrial emissions were the major sources of VOCs and CO at the rural site. The source apportionments were then evaluated using an absolute principal component scores (APCS) technique combined with multiple linear regressions. The results indicated that 71%±5% (average±standard error) of the total VOC emissions were attributed to a combination of vehicle emissions and biofuel burning, and 7%±3% to gasoline evaporation and solvent emissions. Both biomass burning and industrial emissions contributed to 11%±1% and 11%±0.03% of the total VOC emissions, respectively. In addition, vehicle emissions and biomass and biofuel burning accounted for 96%±6% of the total CO emissions at the rural site, of which the biomass burning was responsible for 18%±3%. The results based on PCA/APCS are generally consistent with those from the emission inventory, although a larger relative contribution to CO from biomass burning is indicated from our analysis. © 2004 Elsevier Ltd. All rights reserved

Emission characteristics of CO, NOx, SO2 and indications of biomass burning observed at a rural site in eastern China

Atmospheric O3, CO, SO2, and NO* y (NO* y ≈ NO + NO2 + PAN + organic nitrates + HNO3 + N2O5 + ⋯) were measured in 1999-2000 at a rural/agricultural site in the Yangtze Delta of China. In this paper we analyze the measurement results to show the emission characteristics of the measured gases and to infer relevant emission ratios. Positive correlations were found between CO and NO* y with a slope (Δ[CO]/Δ[NO* y]) of 36 (ppbv/ppbv) for the winter and nighttime measurements. The ratio is considerably larger than that (≈10 ppbv/ppbv) observed in the industrialized countries. The highest CO/NO* y ratio (30-40 ppbv/ppbv) occurred in September-December 1999 and June 2000. The good correlation between CO and the biomass burning tracer CH3Cl and the lack of correlation with the industrial tracer C2Cl4 suggests that the burning of biofuels and crop residues is a major source for the elevated CO and possibly for other trace gases as well. The average SO2 to NO* y ratio was 1.37 ppbv/ppbv, resulting from the use of relatively high-sulfur coals in China. The measured SO2/NO* y and ΔCO/ΔNO* y were compared with the respective ratios from the current emission inventories for the study region, which indicated a comparable SO2/NOx emission ratio but a large discrepancy for CO/NOx. The observed CO to NO* y ratio was more than 3 times the emission ratio derived from the inventories, indicating the need for further improvement of emission estimates for the rural/agricultural regions in China. Additional research will be needed to study the implications of rural emissions to atmospheric chemistry and climate on both regional and global scales.Department of Civil and Environmental Engineerin

Two novel glycyl radical decarboxylase systems from Clostridium scatologenes and Tannerella forsythensis

Die chemisch schwierige Decarboxylierung von 4-Hydroxyphenylacetat zu p-Kresol wird durch das Enzym 4-Hydroxyphenylacetat-Decarboxylase (4-Hpd) katalysiert. Dieses Enzym wurde gereinigt und als Prototyp einer neuen Gruppe innerhalb der Glycylradikalfamilie (GREs) charakterisiert. Frühere Studien haben gezeigt, dass dieses System in C. difficile Eigenschaften aufweist, die es von den gut untersuchten Systemen Pyruvat Format Lyase (Pfl) und anaerobe Ribonucleotid Reduktase (Nrd) unterscheiden. In dieser Arbeit wurden ähnliche Gene aus Clostridium scatologenes (Csd) und Tannerella forsythensis (Tfd) kloniert und in Escherichia coli exprimiert. Die rekombinanten Enzyme wurden gereinigt und vorläufig charakterisiert. Die rekombinanten Decarboxylasen konnten als Hetereokotamere (HpdBC und CsdBC) oder Heterotetramerer (TfdBC) gereinigt werden, waren aus großen (B) und kleinen (C) Untereinheiten in äquimolaren Mengen zusammen gesetzt, und enthielten im Gegensatz zu Pfl und Nrd vier Eisen- und vier Schwefel-Atome pro Heterodimer. Während das Csd System 4-Hydroxyphenylacetat-Decarboxylase Aktivität zeigte und sowohl von CsdA als auch von HpdA aktiviert wurde, war das Tfd System unter allen getesteten Versuchsbedingungen inaktiv, zeigte aber eine teilweise Aktivierung zur Glycyl-Radikal-Form. Wurden die große Untereinheiten der einzelnen Decarboxylasen genetisch mit den kleinen Untereinheiten kombiniert, konnten in einigen Fällen lösliche Proteine gereinigt werden. Auch hier betrug das molare Verhältnis der beiden Untereinheiten 1:1 und es konnten Eisen und Schwefel nachgewiesen werden. Allerdings waren die nativen Komplexe dieser Proteine deutlich kleiner und konnten nicht in die Glycyl-Radikal-Form überführt werden. Die rekombinanten Aktivatoren (CsdA bzw. TfdA) waren Monomere und enthielten 7-8 Eisen- und 6-7 Schwefel-Atome pro Monomer, das auf einen zweiten, zusätzlich zu dem aus Pfl und Nrd bekannten, [4Fe-4S]-Kluster schließen ließ. Der im EPR detektierte, katalytisch entscheidende [4Fe-4S]+ Kluster wurde in CsdA und HpdA nachgewiesen, unterschied sich aber von den Signalen des Pfl- Activator sowie des Nrd- Activator; im Gegensatz zu letzteren beeinflusste die Substratbindung das EPR-Signal nicht signifikant. Der Aktivierungsprozess von CsdBC sowie HpdBC mit den jeweiligen Aktivatoren war transient; einem steilen Anstieg an spezifischer Aktivität in etwa 10 Minuten folgte ein langsamerer Inaktivierungsprozess mit einer Halbwertszeit von etwa 30 Minuten. Das hierbei das Glycylradikal verschwindet, konnte durch sauerstoff-induzierte Spaltung den aktiven Decarboxylase mittels SDS-PAGE sowie in EPR Messungen gezeigt werden. Ob diese Inaktivierung durch ein Elektron aus dem zusätzlichen [4Fe-4S]-Kluster des Aktivators verursacht wird oder durch den [4Fe4S]-Kluster der Decarboxylasen vermittelt wird, bleibt Gegenstand aktueller Untersuchunge

Constructive Methods of Invariant Manifolds for Kinetic Problems

We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in a most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space (the invariance equation). The equation of motion for immersed manifolds is obtained (the film extension of the dynamics). Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability. A collection of methods for construction of slow invariant manifolds is presented, in particular, the Newton method subject to incomplete linearization is the analogue of KAM methods for dissipative systems. The systematic use of thermodynamics structures and of the quasi--chemical representation allow to construct approximations which are in concordance with physical restrictions. We systematically consider a discrete analogue of the slow (stable) positively invariant manifolds for dissipative systems, invariant grids. Dynamic and static postprocessing procedures give us the opportunity to estimate the accuracy of obtained approximations, and to improve this accuracy significantly. The following examples of applications are presented: Nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for Knudsen numbers Kn~1; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of list of variables) to gain more accuracy in description of highly nonequilibrium flows; determination of molecules dimension (as diameters of equivalent hard spheres) from experimental viscosity data; invariant grids for a two-dimensional catalytic reaction and a four-dimensional oxidation reaction (six species, two balances); universal continuous media description of dilute polymeric solution; the limits of macroscopic description for polymer molecules, etc