Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.

Influence of agricultural biomass burning on aerosol size distribution and dry deposition in southeastern Brazil

The size distributed composition of ambient aerosols is used to explore seasonal differences in particle chemistry and to show that dry deposition fluxes of soluble species, including important plant nutrients, increase during periods of biomass (sugar cane trash) burning in São Paulo State, Brazil. Measurements were made at a single site centrally located in the State's sugar cane growing region but away from the immediate vicinity of burns, so that the air sampled was representative of the regional background. Calculation of ion equivalent balances showed that during burning periods smaller particles (Aitken and accumulation modes) were more acidic, containing higher concentrations of SO(4)(2-), oxalate, NO(3)(-), HCOO(-), CH(3)COO(-), and Cl(-), but insufficient NH(4)(+) and K(+) to achieve neutrality. Larger particles showed an anion deficit due to the presence of unmeasured ions and comprised resuspended dusts modified by accumulation of nitrate, chloride, and organic anions. Increases of resuspended particles during the burning season were attributed to release of earlier deposits from the surfaces of burning vegetation as well as increased vehicle movement on unsurfaced roads. During winter months the relative contribution of combined emissions from road transport and industry diminished due to increased emissions from biomass combustion and other activities specifically associated with the harvest period. Positive increments in annual particulate dry deposition fluxes due to higher fluxes during the sugar cane harvest were 44.3% (NH(4)(+)), 42.1 % (K(+)), 31.8% (Mg(2+)), 30.4% (HCOO(-)), 12.8% (Cl(-)), 6.6% (CH(3)COO(-)), 5.2% (Ca(2+)), 3.8% (SO(4)(2-)), and 2.3% (NO(3)(-)). Na(+) and oxalate fluxes were seasonally invariant. Annual aerosol dry deposition fluxes (kg ha(-1)) were 0.5 (Na(+)), 0.25 (NH(4)(+)), 0.39 (K(+)), 0.51 (Mg(2+)), 3.19 (Ca(2+)), 1.34 (Cl(-)), 4.47 (NO(3)(-)), 3.59 (SO(4)(2-)), 0.58 (oxalate), 0.71 (HCOO(-)), and 1.38 (CH(3)COO(-)). Contributions of this mechanism to combined aerosol dry deposition and precipitation scavenging (inorganic species, excluding gaseous dry deposition) were 31% (Na(+)), 8% (NH(4)(+)), 26% (K(+)), 63% (Mg(2+)), 66% (Ca(2+)), 32% (Cl(-)), 33% (NO(3)(-)), and 36% (SO(4)(2-)).

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half-century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential-power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity-dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

(Table 1) n-alkane distribution, and stable carbon and deuterium isotope ratios of DSDP Hole 10-94

Hydrology, source region, and timing of precipitation are important controls on the climate of the Great Plains of North America and the composition of terrestrial ecosystems. Moisture delivered to the Great Plains varies seasonally and predominately derives from the Gulf of Mexico/Atlantic Ocean with minor contributions from the Pacific Ocean and Arctic region. For this work, we evaluate long-term relationships for the past ~ 35 million years between North American hydrology, climate, and floral change, using isotopic records and average carbon chain lengths of higher plant n-alkanes from Gulf of Mexico sediments (DSDP Site 94). We find that carbon isotope values (d13C) of n-alkanes, corrected for variations in the d13C value of atmospheric CO2, provide minor evidence for contributions of C4 plants prior to the Middle Miocene. A sharp spike in C4 input is identified during the Middle Miocene Climatic Optimum, and the influence of C4 plants steadily increased during the Late Miocene into the Pleistocene - consistent with other North American records. Chain-length distributions of n-alkanes, indicative of the composition of higher plant communities, remained remarkably constant from 33 to 4 Ma. However, a trend toward longer chain lengths occurred during the past 4 million years, concurrent with an increase in d13C values, indicating increased C4 plant influence and potentially aridity. The hydrogen isotope values (dD) of n-alkanes are relatively invariant between 33 and 9 Ma, and then become substantially more negative (75 per mil) from 9 to 2 Ma. Changes in the plant community and temperature of precipitation can solely account for the observed variations in dD from 33 to 5 Ma, but cannot account for Plio-Pleistocene dD variations and imply substantial changes in the source region of precipitation and seasonality of moisture delivery. We posit that hydrological changes were linked to tectonic and oceanographic processes including the shoaling and closure of the Panamanian Seaway, amplification of North Atlantic Deep Water Production and an associated increase of meridional winds. The southerly movement of the Intertropical Convergence Zone near 4 Ma allowed for the development of a near-modern pressure/storm track system, driving increased aridity and changes in seasonality within the North American interior.

Evolution of chlorophyll and bacteriochlorophyll: the problem of invariant sites in sequence analysis.

Competing hypotheses seek to explain the evolution of oxygenic and anoxygenic processes of photosynthesis. Since chlorophyll is less reduced and precedes bacteriochlorophyll on the modern biosynthetic pathway, it has been proposed that chlorophyll preceded bacteriochlorophyll in its evolution. However, recent analyses of nucleotide sequences that encode chlorophyll and bacteriochlorophyll biosynthetic enzymes appear to provide support for an alternative hypothesis. This is that the evolution of bacteriochlorophyll occurred earlier than the evolution of chlorophyll. Here we demonstrate that the presence of invariant sites in sequence datasets leads to inconsistency in tree building (including maximum-likelihood methods). Homologous sequences with different biological functions often share invariant sites at the same nucleotide positions. However, different constraints can also result in additional invariant sites unique to the genes, which have specific and different biological functions. Consequently, the distribution of these sites can be uneven between the different types of homologous genes. The presence of invariant sites, shared by related biosynthetic genes as well as those unique to only some of these genes, has misled the recent evolutionary analysis of oxygenic and anoxygenic photosynthetic pigments. We evaluate an alternative scheme for the evolution of chlorophyll and bacteriochlorophyll.

Bayesian invariant measurements of generalisation for discrete distributions

Neural network learning rules can be viewed as statistical estimators. They should be studied in Bayesian framework even if they are not Bayesian estimators. Generalisation should be measured by the divergence between the true distribution and the estimated distribution. Information divergences are invariant measurements of the divergence between two distributions. The posterior average information divergence is used to measure the generalisation ability of a network. The optimal estimators for multinomial distributions with Dirichlet priors are studied in detail. This confirms that the definition is compatible with intuition. The results also show that many commonly used methods can be put under this unified framework, by assume special priors and special divergences.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Photoelastic Analysis Of Fixed Partial Prosthesis Crown Height And Implant Length On Distribution Of Stress In Two Dental Implant Systems.

The aim of this study was to evaluate by photoelastic analysis stress distribution on short and long implants of two dental implant systems with 2-unit implant-supported fixed partial prostheses of 8 mm and 13 mm heights. Sixteen photoelastic models were divided into 4 groups: I: long implant (5 × 11 mm) (Neodent), II: long implant (5 × 11 mm) (Bicon), III: short implant (5 × 6 mm) (Neodent), and IV: short implants (5 × 6 mm) (Bicon). The models were positioned in a circular polariscope associated with a cell load and static axial (0.5 Kgf) and nonaxial load (15°, 0.5 Kgf) were applied to each group for both prosthetic crown heights. Three-way ANOVA was used to compare the factors implant length, crown height, and implant system (α = 0.05). The results showed that implant length was a statistically significant factor for both axial and nonaxial loading. The 13 mm prosthetic crown did not result in statistically significant differences in stress distribution between the implant systems and implant lengths studied, regardless of load type (P > 0.05). It can be concluded that short implants showed higher stress levels than long implants. Implant system and length was not relevant factors when prosthetic crown height were increased.

Geographical Distribution Of The Association Between El Niño South Oscillation And Dengue Fever In The Americas: A Continental Analysis Using Geographical Information System-based Techniques.

El Niño South Oscillation (ENSO) is one climatic phenomenon related to the inter-annual variability of global meteorological patterns influencing sea surface temperature and rainfall variability. It influences human health indirectly through extreme temperature and moisture conditions that may accelerate the spread of some vector-borne viral diseases, like dengue fever (DF). This work examines the spatial distribution of association between ENSO and DF in the countries of the Americas during 1995-2004, which includes the 1997-1998 El Niño, one of the most important climatic events of 20(th) century. Data regarding the South Oscillation index (SOI), indicating El Niño-La Niña activity, were obtained from Australian Bureau of Meteorology. The annual DF incidence (AIy) by country was computed using Pan-American Health Association data. SOI and AIy values were standardised as deviations from the mean and plotted in bars-line graphics. The regression coefficient values between SOI and AIy (rSOI,AI) were calculated and spatially interpolated by an inverse distance weighted algorithm. The results indicate that among the five years registering high number of cases (1998, 2002, 2001, 2003 and 1997), four had El Niño activity. In the southern hemisphere, the annual spatial weighted mean centre of epidemics moved southward, from 6° 31' S in 1995 to 21° 12' S in 1999 and the rSOI,AI values were negative in Cuba, Belize, Guyana and Costa Rica, indicating a synchrony between higher DF incidence rates and a higher El Niño activity. The rSOI,AI map allows visualisation of a graded surface with higher values of ENSO-DF associations for Mexico, Central America, northern Caribbean islands and the extreme north-northwest of South America.

Distribution Of Lutzomyia Longipalpis Chemotype Populations In São Paulo State, Brazil.

American visceral leishmaniasis (AVL) is an emerging disease in the state of São Paulo, Brazil. Its geographical expansion and the increase in the number of human cases has been linked to dispersion of Lutzomyia longipalpis into urban areas. To produce more accurate risk maps we investigated the geographic distribution and routes of expansion of the disease as well as chemotype populations of the vector. A database, containing the annual records of municipalities which had notified human and canine AVL cases as well as the presence of the vector, was compiled. The chemotypes of L. longipalpis populations from municipalities in different regions of São Paulo State were determined by Coupled Gas Chromatography - Mass Spectrometry. From 1997 to June 2014, L. longipalpis has been reported in 166 municipalities, 148 of them in the Western region. A total of 106 municipalities were identified with transmission and 99 were located in the Western region, where all 2,204 autochthonous human cases occurred. Both the vector and the occurrence of human cases have expanded in a South-easterly direction, from the Western to central region, and from there, a further expansion to the North and the South. The (S)-9-methylgermacrene-B population of L. longipalpis is widely distributed in the Western region and the cembrene-1 population is restricted to the Eastern region. The maps in the present study show that there are two distinct epidemiological patterns of AVL in São Paulo State and that the expansion of human and canine AVL cases through the Western region has followed the same dispersion route of only one of the two species of the L. longipalpis complex, (S)-9-methylgermacrene-B. Entomological vigilance based on the routes of dispersion and identification of the chemotype population could be used to identify at-risk areas and consequently define the priorities for control measures.

Microbial distribution in the root canal system after periapical lesion induction using different methods

The aim of this study was to evaluate the microbial distribution in the root canal system after periapical lesion induction in dogs' teeth using different methods. Fifty-two root canals were assigned to 4 groups (n=13). Groups I and II: root canals were exposed to the oral cavity for 180 days; groups III and IV: root canals were exposed for 7 days and then the coronal openings were sealed for 53 days. The root apices of groups I and III were perforated, while those of groups II and IV remained intact. After the experimental periods, the animals were euthanized and the anatomic pieces containing the roots were processed and stained with the Brown & Brenn method to assess the presence and distribution of microorganisms. The incidence of microorganisms at different sites of the roots and periapical lesions was analyzed statistically by the chi-square test at 5% significance level. All groups presented microorganisms in the entire root canal system. A larger number of microorganisms was observed on the root canal walls, apical delta and dentinal tubules (p<0.05), followed by cementum and cemental resorption areas. In spite of the different periods of exposure to the oral environment, the methods used for induction of periapical periodontitis yielded similar distribution of microorganisms in the root canal system.

Distribution of biotypes and leukotoxic activity of Aggregatibacter actinomycetemcomitans isolated from Brazilian patients with chronic periodontitis

Aggregatibacter actinomycetemcomitans is an important etiologic agent of the periodontitis and is associated with extra-oral infections. In this study, the detection of the ltxA gene as well as the ltx promoter region from leukotoxic A. actinomycetemcomitans isolated from 50 Brazilian patients with periodontitis and 50 healthy subjects was performed. The leukotoxic activity on HL-60 cells was also evaluated. Leukotoxic activity was determined using a trypan blue exclusion method. The 530 bp deletion in the promoter region was evaluated by PCR using a PRO primer pair. A. actinomycetemcomitans was detected by culture and directly from crude subgingival biofilm by PCR using specific primers. By culture, A. actinomycetemcomitans was detected in nine (18%) of the periodontal patients and one (2%) healthy subject. However, by PCR, this organism was detected in 44% of the periodontal patients and in 16% of the healthy subjects. It was verified a great discrepancy between PCR detection of the ltx operon promoter directly from crude subgingival biofilm and from bacterial DNA. Only one periodontal sample harbored highly leukotoxic A. actinomycetemcomitans. Moreover, biotype II was the most prevalent and no correlation between biotypes and leukotoxic activity was observed. The diversity of leukotoxin expression by A. actinomycetemcomitans suggests a role of this toxin in the pathogenesis of periodontal disease and other infectious diseases.