Mathematics and Statistics

Unmanned Aerial Vehicles (UAVs) are already broadly employed for 3D modeling of large objects such as trees and monuments via photogrammetry. The usual workflow includes two distinct steps: image acquisition with UAV and computationally demanding post-flight image processing. Insufficient feature overlaps across images is a common shortcoming in post-flight image processing resulting in the failure of 3D reconstruction. Here we propose a real-time control system that overcomes this limitation by targeting specific spatial locations for image acquisition thereby providing sufficient feature overlap. We initially benchmark several implementations of the Scale-Invariant Feature Transform (SIFT) feature identification algorithm to determine whether they allow real-time execution on the low-cost processing hardware embedded on the UAV. We then experimentally test our UAV platform in virtual and real-life environments. The presented architecture consistently decreases failures and improves the overall quality of 3D reconstructions.

Forest dynamics are highly dimensional phenomena that are not fully understood theoretically. Forest inventory datasets offer unprecedented opportunities to model these dynamics, but they are analytically challenging due to high dimensionality and sampling irregularities across years. We develop a data-intensive methodology for predicting forest stand dynamics using such datasets. Our methodology involves the following steps: 1) computing stand level characteristics from individual tree measurements, 2) reducing the characteristic dimensionality through analyses of their correlations, 3) parameterizing transition matrices for each uncorrelated dimension using Gibbs sampling, and 4) deriving predictions of forest developments at different timescales. Applying our methodology to a forest inventory database from Quebec, Canada, we discovered that four uncorrelated dimensions were required to describe the stand structure: the biomass, biodiversity, shade tolerance index and stand age. We were able to successfully estimate transition matrices for each of these dimensions. The model predicted substantial short-term increases in biomass and longer-term increases in the average age of trees, biodiversity, and shade intolerant species. Using highly dimensional and irregularly sampled forest inventory data, our original data-intensive methodology provides both descriptions of the short-term dynamics as well as predictions of forest development on a longer timescale. This method can be applied in other contexts such as conservation and silviculture, and can be delivered as an efficient tool for sustainable forest management.

Tungsten is a widely used transition metal that has not been thoroughly investigated with regards to its ecotoxicological effects. Tungsten anions polymerize in environmental systems as well as under physiological conditions in living organisms. These polymerization/condensation reactions result in the development of several types of stable polyoxoanions. Certain chemical properties (in particular redox and acidic properties) differentiate these polyanions from monotungstates. However, our current state of knowledge on tungsten toxicology, biological and environmental effects is based entirely on experiments where monotungstates were used and assumed by the authors to be the form of tungsten that was present and that produced the observed effect. Recent discoveries indicate that tungsten speciation may be important to ecotoxicology. New results obtained by different research groups demonstrate that polytungstates develop and persist in environmental systems, and that polyox-otungstates are much more toxic than monotungstates. This paper reviews the available toxicological information from the standpoint of tungsten speciation and identifies knowledge gaps and pertinent future research directions.

Tungsten is a widely used transition metal for which very limited information on environmental and toxicological effects is available. Of particular interest is the lack of information linking tungsten speciation and environmental effects. Tungsten anions may polymerize (depending upon concentration, pH, and aquatic geochemistry) in aquatic and soil systems. However, to this date, of all soluble tungstate species only monotungstates have been scrutinized to a fair extent in toxicological studies. The objective of this work is a comparative assessment of the acute toxicity of monotungstates (sodium tungstate, Na 2 WO 4) and polytungstates (sodium metatungstate, 3Na 2 WO 4 Á 9WO 3) to Poecilia reticulate. The experiments have been performed according to the OEDC protocols 203 and 204. LD50 values for 1– 14 days show that sodium metatungstate is significantly more toxic to fish than sodium tungstate. Based on LD50 (0.86–3.88 g L À 1 or 4.67–21.1 Â10 À 3 mol Na 2 WO 4 L À 1), sodium tungstate may be classified as a chemical of low toxicity to fish. Sodium metatungstate caused similar fish mortality to sodium tungstate when it was introduced in 55–80 times lower concentrations (in terms of mol L À 1) than sodium tungstate. LD50 values for sodium metatungstate range from 0.13 to 0.85 g W L À 1 or 5.69 to 38.71 Â10 À 5 mol 3Na 2 WO 4 Á 9WO 3 L À 1. Based on these values sodium metatungstate can be classified as a moderate toxic agent to fish.

Estimation and experimental design in a non-linear regression model that is used in microbiology are studied. The Monod model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, water research, pharmacokinetics and plant physiology. It is proved that least squares estimates are asymptotically unbiased and normally distributed. The asymptotic covariance matrix of the estimator is the basis for the construction of efficient designs of experiments. In particular locally D-, E-and c-optimal designs are determined and their properties are studied theoretically and by simulation. If certain intervals for the non-linear parameters can be specified, locally optimal designs can be constructed which are robust with respect to a misspecification of the initial parameters and which allow efficient parameter estimation. Parameter variances can be decreased by a factor of 2 by simply sampling at optimal times during the experiment.

In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D-and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.

Individual-based forest simulators, such as TASS and SORTIE, are spatial stochastic processes that predict properties of populations and communities by simulating the fate of every plant throughout its life cycle. Although they are used for forest management and are able to predict dynamics of real forests, they are also analytically intractable, which limits their usefulness to basic scientists. We have developed a new spatial individual-based forest model that includes a perfect plasticity formulation for crown shape. Its structure allows us to derive an accurate approximation for the individual-based model that predicts mean densities and size structures using the same parameter values and functional forms, and also it is analytically tractable. The approximation is represented by a system of von Foerster partial differential equations coupled with an integral equation that we call the perfect plasticity approximation (PPA). We have derived a series of analytical results including equilibrium abundances for trees of different crown shapes, stability conditions, transient behaviors, such as the constant yield law and self-thinning exponents, and two species coexistence conditions.

Imitation is one of the central processes underlying learning. Although the mechanisms of imitation at the individual level have received considerable attention, the population effects of imitative behavior have scarcely been investigated. In this paper I address the problem of self-organization at the population level emerging from imitative behavior between individuals. The model considered is a modification of that developed by Durrett and Levin [Durrett, R., Levin, S.A., 2005. Can stable social groups be maintained by homophilous imitation alone? J. Econ. Behav. Organ. 57, 267–286] in investigation of the coexistence of social groups. I modified the previous model in order to approach it in describing not only human societies but also animal populations with simpler cultures. In contrast with the other studies, I do not assume any payoffs related to imitation behavior and the existence of social rank. Individuals are assumed to be of equal rank and to accept opinions of others in proportion to their similarity (homophilous imitation). The symmetrical structure of interactions induces random drift and development of stable self-organized social groups in both homogeneous and spatially distributed societies. This type of self-organization may be widely distributed in natural systems, where imitative behavior takes place. In particular, it can be involved in origins of dialects and ring species.

Increasing occurrence of droughts is a major environmental concern, however its consequences on forested ecosystems are not fully understood at the landscape level. Here we link the forest shade tolerance index to soil moisture in the North America using the U.S. and Quebec forest inventories. We report a significant decrease of shade tolerance index along the hydric–mesic–xeric soil transition in most of the area considered except three subtropical/tropical ecoregions of the Southeastern U.S. We conclude that droughts may alter forest succession, and in particular decrease the role of forest gap dynamics and dominance of the shade-tolerant species in mature forests.

One of the main problems when introducing beneficial microbes to the plant rhizosphere is that the plant growth promoting rhizobacteria (PGPR) do not survive or do not execute their specific function. The goal of our research was to evaluate microbial inoculant survival in rhizospheres, using mathematical modeling and computer-based simulations. We tested several abiotic factors effects on PGPR survival: the availability of soluble organic compounds and molecular oxygen, and the concentration of mineral nitrogen in soil. The principal biotic factors considered were the direct and indirect interactions between PGPR and resident microorganisms, protozoan predation, and bacterial parasitism. A model system of four non-linear ordinary differential equations was developed to simulate the growth of PGPR populations in the rhizosphere. Simulation results indicated that the competition for limiting resources between the introduced population and the resident microorganisms was the most important factor determining PGPR survival. The most effective PGPR inoculation was expected in organic and mineral poor soils or stressed soils, when development of the resident microflora was inhibited. Another important factor for PGPR survival was compatibility between the composition of the host plant root exudates, and ability of the PGPR to utilize those compounds.

The acute toxicity of four different nanosized particulate materials (titanium dioxide, boron nanoparticles, and two types of aluminum nanoparticles (ALEX and L-ALEX)) were evaluated using two tests: the Microtox toxicity test and the acute toxicity test with Daphnia magna. The results were analyzed in order to calculate LD 50 at 24 and 48 h. It was found that titanium dioxide nanoparticles show a low level of toxicity, and LD 50 values cannot be calculated. Conversely, boron nanoparticles with EC 50 ranging from 56 to 66 mg L À1 , depending upon the age of the solution, can be classified as ''harmful'' to aquatic microorganisms (EC 50 in the range 10–100 mg L À1). We have also discussed possible mechanisms of nanoparticle toxicity and potential problems in ecotoxicological testing of nanomaterials. The studied nanomaterials can be ranked in the following order according to their Daphnia acute toxicity: boron nanoparticles>ALEX>L-ALEX> TiO 2 .

Understanding forest complexity and self-organization across multiple scales is essential for both ecology and natural resource management. In this paper, we develop a Markov chain approach for the modelling of forest stand dynamics. The aim of this work is to generalize the recently developed Perfect Plasticity Approximation (PPA) model for scaling of vegetation dynamics from individual level to the landscape level through the ecosystem hierarchical structure. Our basic assumption is that the forested ecosystem and disturbance regimes can be modelled on 3 hierarchical scales (levels): individual trees, forest stand (or patch, defined as a spatial unit about 0.5e1 ha of the same forest at one successional stage.) and landscape (collection of forest patches of different forest/soil types at different successional stages) levels. In our modelling approach the PPA model is an intermediate step for scaling from the individual level to the forest stand level (or patch level). In this paper we develop a Markov chain model for stage-structured dynamics of forest stands (patches). In order to determine the structure of the Markov chain model and estimate parameters, we analyze the patch-mosaic patterns of forest stands of the Lake States (MI, WI, and MN) recorded in the USDA FIA database as well as data for other US states and Canada. The distribution of macroscopic characteristics of a large collection of forest patches is considered as an estimate of the stationary distribution of the underlying Markov chain. The data demonstrates that this distribution is unimodal and skewed to the right. We identify the simplest Markov chain that produces such a distribution and estimate the upper bound of the probability of disaster for this Markov chain.

The Monod model is a classical microbiological model often used in environmental sciences, for example to evaluate biodegradation processes. The model describes microbial growth kinetics in batch culture experiments using three parameters: the maximal specific growth rate, the saturation constant and the yield coefficient. However, identification of these parameter values from experimental data is a challenging problem. Recently, it was demonstrated theoretically that the application of optimal design theory in this model is an efficient method for both parameter value identification and economic use of experimental resources [Dette, H., Melas, V.B., Pepelyshev, A., Strigul, N., 2003. Efficient design of experiments in the Monod model. J. R. Stat. Soc. B 65 (Part 3), 725–742]. The purpose of this paper is to provide this method as a computational ''tool'' such that it can be used by practitioners without a strong mathematical and statistical background for the efficient design of experiments in the Monod model. The paper presents careful explanations of the principal theoretical concepts, and a simple algorithm for practical optimal design calculations.