Chaos decomposition and gap renormalization of brownian self-intersection local times

We study the chaos decomposition of self-intersection local times and their regularization, with a particular view towards Varadhan's renormalization for the planar Edwards model.

A class of domain decomposition preconditioners for hp-discontinuous Galerkin finite element methods

In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results confirming the theoretical estimates are also presented.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Thermogravimetric and kinetic analysis of the decomposition of solid recovered fuel from municipal solid waste

The thermal decomposition of a solid recovered fuel has been studied using thermogravimetry, in order to get information about the main steps in the decomposition of such material. The study comprises two different atmospheres: inert and oxidative. The kinetics of decomposition is determined at three different heating rates using the same kinetic constants and model for both atmospheres at all the heating rates simultaneously. A good correlation of the TG data is obtained using three nth-order parallel reactions.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

The Processing of Aluminum Gasarites via Thermal Decomposition of Interstitial Hydrides

Gasarite structures are a unique type of metallic foam containing tubular pores. The original methods for their production limited them to laboratory study despite appealing foam properties. Thermal decomposition processing of gasarites holds the potential to increase the application of gasarite foams in engineering design by removing several barriers to their industrial scale production. The following study characterized thermal decomposition gasarite processing both experimentally and theoretically. It was found that significant variation was inherent to this process therefore several modifications were necessary to produce gasarites using this method. Conventional means to increase porosity and enhance pore morphology were studied. Pore morphology was determined to be more easily replicated if pores were stabilized by alumina additions and powders were dispersed evenly. In order to better characterize processing, high temperature and high ramp rate thermal decomposition data were gathered. It was found that the high ramp rate thermal decomposition behavior of several hydrides was more rapid than hydride kinetics at low ramp rates. This data was then used to estimate the contribution of several pore formation mechanisms to the development of pore structure. It was found that gas-metal eutectic growth can only be a viable pore formation mode if non-equilibrium conditions persist. Bubble capture cannot be a dominant pore growth mode due to high bubble terminal velocities. Direct gas evolution appears to be the most likely pore formation mode due to high gas evolution rate from the decomposing particulate and microstructural pore growth trends. The overall process was evaluated for its economic viability. It was found that thermal decomposition has potential for industrialization, but further refinements are necessary in order for the process to be viable.

INTERACTIVE EFFECTS OF CLIMATE CHANGE AND FUNGAL COMMUNITIES ON THE DECOMPOSITION OF WOOD-DERIVED CARBON IN FOREST SOILS

Soils are the largest sinks of carbon in terrestrial ecosystems. Soil organic carbon is important for ecosystem balance as it supplies plants with nutrients, maintains soil structure, and helps control the exchange of CO2 with the atmosphere. The processes in which wood carbon is stabilized and destabilized in forest soils is still not understood completely. This study attempts to measure early wood decomposition by different fungal communities (inoculation with pure colonies of brown or white rot, or the original microbial community) under various interacting treatments: wood quality (wood from +CO2, +CO2+O3, or ambient atmosphere Aspen-FACE treatments from Rhinelander, WI), temperature (ambient or warmed), soil texture (loamy or sandy textured soil), and wood location (plot surface or buried 15cm below surface). Control plots with no wood chips added were also monitored throughout the study. By using isotopically-labelled wood chips from the Aspen-FACE experiment, we are able to track wood-derived carbon losses as soil CO2 efflux and as leached dissolved organic carbon (DOC). We analyzed soil water for chemical characteristics such as, total phenolics, SUVA254, humification, and molecular size. Wood chip samples were also analyzed for their proportion of lignin:carbohydrates using FTIR analysis at three time intervals throughout 12 months of decomposition. After two years of measurements, the average total soil CO2 efflux rates were significantly different depending on wood location, temperature, and wood quality. The wood-derived portion soil CO2 efflux also varied significantly by wood location, temperature, and wood quality. The average total DOC and the wood-derived portion of DOC differed between inoculation treatments, wood location, and temperature. Soil water chemical characteristics varied significantly by inoculation treatments, temperature, and wood quality. After 12 months of decomposition the proportion of lignin:carbohydrates varied significantly by inoculation treatment, with white rot having the only average proportional decrease in lignin:carbohydrates. Both soil CO2 efflux and DOC losses indicate that wood location is important. Carbon losses were greater from surface wood chips compared with buried wood chips, implying the importance of buried wood for total ecosystem carbon stabilization. Treatments associated with climate change also had an effect on the level of decomposition. DOC losses, soil water characteristics, and FTIR data demonstrate the importance of fungal community on the degree of decomposition and the resulting byproducts found throughout the soil.

Tail gas catalyzed N2O decomposition over Fe-beta zeolite. On the promoting role of framework connected AlO6 sites in the vicinity of Fe by controlled dealumination during exchange

A novel route to prepare highly active and stable N2O decomposition catalysts is presented, based on Fe-exchanged beta zeolite. The procedure consists of liquid phase Fe(III) exchange at low pH. By varying the pH systematically from 3.5 to 0, using nitric acid during each Fe(III)-exchange procedure, the degree of dealumination was controlled, verified by ICP and NMR. Dealumination changes the presence of neighbouring octahedral Al sites of the Fe sites, improving the performance for this reaction. The so-obtained catalysts exhibit a remarkable enhancement in activity, for an optimal pH of 1. Further optimization by increasing the Fe content is possible. The optimal formulation showed good conversion levels, comparable to a benchmark Fe-ferrierite catalyst. The catalyst stability under tail gas conditions containing NO, O2 and H2O was excellent, without any appreciable activity decay during 70 h time on stream. Based on characterisation and data analysis from ICP, single pulse excitation NMR, MQ MAS NMR, N2 physisorption, TPR(H2) analysis and apparent activation energies, the improved catalytic performance is attributed to an increased concentration of active sites. Temperature programmed reduction experiments reveal significant changes in the Fe(III) reducibility pattern with the presence of two reduction peaks; tentatively attributed to the interaction of the Fe-oxo species with electron withdrawing extraframework AlO6 species, causing a delayed reduction. A low-temperature peak is attributed to Fe-species exchanged on zeolitic AlO4 sites, which are partially charged by the presence of the neighbouring extraframework AlO6 sites. Improved mass transport phenomena due to acid leaching is ruled out. The increased activity is rationalized by an active site model, whose concentration increases by selectively washing out the distorted extraframework AlO6 species under acidic (optimal) conditions, liberating active Fe species.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

An investigation of the relationship between the components of tumour microenvironment, signal transduction pathways and outcome in breast cancer

Breast cancer, the most commonly diagnosed type of cancer in women, is a major cause of morbidity and mortality in the western world. Well-established risk factors of breast cancer are mostly related to women’s reproductive history, such as early menarche, late first pregnancy and late menopause. Survival rates have improved due to a combination of factors, including better health education, early detection with large-scale use of screening mammogram, improved surgical techniques, as well as widespread use of adjuvant therapy. At initial presentation, clinicopathological features of breast cancer such as age, nodal status, tumour size, tumour grade, and hormonal receptor status are considered to be the standard prognostic and predictive markers of patient survival, and are used to guide appropriate treatment strategies. Lymphovascular invasion (LBVI), including lymphatic (LVI) and blood (BVI) vessel invasion, has been reported to be prognostic and merit accurate evaluation, particularly in patients with node negative tumours who might benefit from adjuvant chemotherapy. There is a lack of standard assessment and agreement on distinguishing LVI from BVI despite the major challenges in the field. A systematic review of the literatures, examining methods of detection and the prognostic significance of LBVI, LVI and BVI, was carried out. The majority of studies used haematoxylin and eosin (H&E) and classical histochemistry to identify LVI and BVI. Only few recent studies used immunohistochemistry (IHC) staining of the endothelium lining lymphatic and blood vessels, and were able to show clear differences between LVI and BVI. The prognostic significance of LBVI and LVI was well-documented and strongly associated with aggressive features of breast tumours, while the prognostic value and the optimal detection method of BVI were unclear. Assessment and prognostic value of LBVI on H&E sections (LBVIH&E) was examined and compared to that of LVI and BVI detected using IHC with D2-40 for LVI (LVID2–40) and Factor VIII for BVI (BVIFVIII) in patients with breast cancer including node negative and triple negative patients (n=360). LBVIH&E, LVID2–40 and BVIFVIII were present in 102 (28%), 127 (35%) and 59 (16%) patients respectively. In node negative patients (206), LBVIH&E, LVID2–40 and BVIFVIII were present in 41 (20%), 53 (26%) and 21 (10%) respectively. In triple negative patients (102), LBVIH&E, LVID2–40 and BVIFVIII were present in 35 (29%), 36 (35%) and 14 (14%) respectively. LBVIH&E, LVID2–40 and BVIFVIII were all significantly associated with tumour recurrence in all cohorts. On multivariate survival analysis, only LVID2–40 and BVIFVIII were independent predictors of cancer specific survival (CSS) in the whole cohort (P=0.022 and P<0.001 respectively), node negative (P=0.008 and P=0.001 respectively) and triple negative patients (P=0.014 and P<0.001 respectively). Assessment of LVI and BVI by IHC, using D2-40 and Factor VIII, improves prediction of outcome in patients with node negative and triple negative breast cancer and was superior to the conventional detection method. Breast cancer is recognised as a complex molecular disease and histologically identical tumours may have highly variable outcomes, including different responses to therapy. Therefore, there is a compelling need for new prognostic and predictive markers helpful of selecting patients at risk and patients with aggressive diseases who might benefit from adjuvant and targeted therapy. It is increasingly recognised that the development and progression of human breast cancer is not only determined by genetically abnormal cells, but also dependent on complex interactions between malignant cells and the surrounding microenvironment. This has led to reconsider the features of tumour microenvironment as potential predictive and prognostic markers. Among these markers, tumour stroma percentage (TSP) and tumour budding, as well as local tumour inflammatory infiltrate have received recent attention. In particular, the local environment of cytokines, proteases, angiogenic and growth factors secreted by inflammatory cells and stromal fibroblasts has identified crucial roles in facilitating tumour growth, and metastasis of cancer cells through lymphatic and/or blood vessel invasion. This might help understand the underlying process promoting tumour invasion into these vessels. An increase in the proportion of tumour stroma and an increase in the dissociation of tumour cells have been associated with poorer survival in a number of solid tumours, including breast cancer. However, the interrelationship between these variables and other features of the tumour microenvironment in different subgroups of breast cancer are not clear. Also, whether their prognostic values are independent of other components of the tumour microenvironment have yet to be identified. Therefore, the relationship between TSP, clinicopathological characteristics and outcome in patients with invasive ductal breast cancer, in particular node negative and triple negative disease was examined in patients with invasive ductal breast cancer (n=361). The TSP was assessed on the haematoxylin and eosin-stained tissue sections. With a cut-off value of 50% TSP, patients with ≤50% stroma were classified as the low-TSP group and those with >50% stroma were classified as the high-TSP group. A total of 109 (30%) patients had high TSP. Patients with high TSP were old age (P=0.035), had involved lymph node (P=0.049), Her-2 positive tumours (P=0.029), low-grade peri-tumoural inflammatory infiltrate (P=0.034), low CD68+ macrophage infiltrate (P<0.001), low CD4+ (P=0.023) and low CD8+ T-lymphocytes infiltrate (P=0.017), tumour recurrence (P=0.015) and shorter CSS (P<0.001). In node negative patients (n=207), high TSP was associated with low CD68+ macrophage infiltrate (P=0.001), low CD4+ (P=0.040) and low CD8+ T-lymphocytes infiltrate (P=0.016) and shorter CSS (P=0.005). In triple negative patients (n=103), high TSP was associated with increased tumour size (P=0.017) high tumour grade (P=0.014), low CD8+ T-lymphocytes infiltrate (P=0.048) and shorter CSS (P=0.041). The 15-year cancer specific survival rate was 79% vs 21% in the low-TSP group vs high-TSP group. On multivariate survival analysis, a high TSP was associated with reduced CSS in the whole cohort (P=0.007), node negative patients (P=0.005) and those who received systemic adjuvant therapy (P=0.016), independent of other pathological characteristics including local host inflammatory responses. Therefore, a high TSP in invasive ductal breast cancer was associated with recurrence and poorer long-term survival. The inverse relation with the tumour inflammatory infiltrate highlights the importance of the amount of tumour stroma on immunological response in patients with invasive ductal breast cancer. Implementing this simple and reproducible parameter in routine pathological examination may help optimise risk stratification in patients with breast cancer. Similarly, the relationship between tumour budding, clinicopathological characteristics and outcome was examined in patients with invasive ductal breast cancer (n=474), using routine pathological sections. Tumour budding was associated with several adverse pathological characteristics, including positive lymph node (P=0.009), presence of LVI (P<0.001), and high TSP (P=0.001) and low-grade general peri-tumural inflammatory infiltrative (P=0.002). In node negative patients, a high tumour budding was associated with presence of LVI (P<0.001) and low-grade general peri-tumural inflammatory infiltrative (P=0.038). On multivariate survival analysis, tumour budding was associated with reduced CSS (P=0.001), independent of nodal status, tumour necrosis, CD8+ and CD138+ inflammatory cells infiltrate, LVI, BVI and TSP. Furthermore, tumour budding was independently associated with reduced CSS in node negative patients (P=0.004) and in those who have low TSP (P=0.003) and high-grade peri-tumoural inflammatory infiltrative (P=0.012). A high tumour budding was significantly associated with shorter CSS in luminal B and triple negative breast cancer subtypes (all P<0.001). Therefore, tumour budding was a significant predictor of poor survival in patients with invasive ductal breast cancer, independent of adverse pathological characteristics and components of tumour microenvironment. These results suggest that tumour budding may promote disease progression through a direct effect on local and distant invasion into lymph nodes and lymphatic vessels. Therefore, detection of tumour buds at the stroma invasive front might therefore represent a morphologic link between tumour progression, lymphatic invasion, spread of tumour cells to regional lymph nodes, and the establishment of metastatic dissemination. Given the potential importance of the tumour microenvironment, the characterisation of intracellular signalling pathways is important in the tumour microenvironment and is of considerable interest. One plausible signalling molecule that links tumour stroma, inflammatory cell infiltrate and tumour budding is the signal transducer and activator of transcription (STAT). The relationship between total and phosphorylated STAT1 (ph-STAT1), and total and ph-STAT3 tumour cell expression, components of tumour microenvironment and survival in patients with invasive ductal breast cancer was examined. IHC of total and ph-STAT1/STAT3 was performed on tissue microarray of 384 breast cancer specimens. Cellular STAT1 and cellular STAT3 expression at both cytoplasmic and nuclear locations were combined and identified as STAT1/STAT3 tumour cell expression. These results were then related to CSS and phenotypic features of the tumour and host. A high ph-STAT1 and a high ph-STAT3 tumour cell expression was associated with increased ER (P=0.001 and P<0.001 respectively) and PR (all P<0.05), reduced tumour grade (P=0.015 and P<0.001 respectively) and necrosis (all P=0.001). Ph-STAT1 was associated with increased general peri-tumoural inflammatory infiltrate (P=0.007) and ph-STAT3 was associated with lower CD4+ T-lymphocyte infiltrate (P=0.024). On multivariate survival analysis, including both ph-STAT1 and ph-STAT3 tumour cell expression, only high ph-STAT3 tumour cell expression was significantly associated with improved CSS (P=0.010) independent of other tumour and host-based factors. In patients with high necrosis grade, high ph-STAT3 tumour cell expression was independent predictor of improved CSS (P=0.021). Ph-STAT1 and ph-STAT3 were also significantly associated with improved cancer specific survival in luminal A and B subtypes. STAT1 and STAT3 tumour cell expression appeared to be an important determinant of favourable outcome in patients with invasive ductal breast cancer. The present results suggest that STATs may affect disease outcome through direct impact on tumour cells, and the surrounding microenvironment. The above observations of the present thesis point to the importance of the tumour microenvironment in promoting tumour budding, LVI and BVI. The observations from STATs work may suggest that an important driving mechanism for the above associations is the presence of tumour necrosis, probably secondary to hypoxia. Further work is needed to examine the interaction of other molecular pathways involved in the tumour microenvironment, such as HIF and NFkB in patients with invasive ductal breast cancer.

Analysis of Pancreas Histological Images for Glucose Intolerance Identification using Wavelet Decomposition

Subtle structural differencescan be observed in the islets of Langer-hans region of microscopic image of pancreas cell of the rats having normal glucose tolerance and the rats having pre-diabetic(glucose intolerant)situa-tions. This paper proposes a way to automatically segment the islets of Langer-hans region fromthe histological image of rat's pancreas cell and on the basis of some morphological feature extracted from the segmented region the images are classified as normal and pre-diabetic.The experiment is done on a set of 134 images of which 56 are of normal type and the rests 78 are of pre-diabetictype. The work has two stages: primarily,segmentationof theregion of interest (roi)i.e. islets of Langerhansfrom the pancreatic cell and secondly, the extrac-tion of the morphological featuresfrom the region of interest for classification. Wavelet analysis and connected component analysis method have been used for automatic segmentationof the images. A few classifiers like OneRule, Naïve Bayes, MLP, J48 Tree, SVM etc.are used for evaluation among which MLP performed the best.

Decomposition of organic matter in the presence of the herbicide clomazone.

Clomazone (2-(2-chlorophenyl) methyl-4.4-dimethyl-3-isoxazolidinone) is a post emergence herbicide widely used in rice fields in Rio Grande do Sul (Brazil) with high activity against Gramineae at the recommended application rate of 700 g/ha. The presence of this chemical in the water may affect microorganisms responsible for the decomposition of organic matter. Thus, a disturbe in the trophic chain sustained by the decompositors could happen. In the present work the decomposition rate of organic matter (Typha latifolia) exposed to several concentrations of a clomazone formulation: 0 (control), 25.0, 62.0, 156.0, 390.0 and 976.0mg/L on the basis of the active ingredient was evaluated. Five litter bags containing about 3.0g of pieces of T. latifolia leaves wereplaced in aquariums with 15 of reconstituted water. In cach aquarium were added 500g of sediment from the same place of the plant collection, as a source of decompositors microorganisms. The results relative tothe control, showed that the decomposition rate in the highest and lowest dose was reduced in 50.05 and 1,28%, respectively, after 80 days.

Microenvironment and prognostic factors in bone tumors: IDH mutations in chondrosarcoma

Microenvironment in bone tumors is a dynamic entity composed of cells from different origins (immune cells, stromal cells, mesenchymal stem cells, endothelial cells, pericytes) and vascular structures surrounded by a matrix of different nature (bone, cartilage, myxoid). Interactions between cancer cells and tumor microenvironment (TME) are complex and can change as tumor progress, but are also crucial in determining response to cancer therapies. Chondrosarcoma is the second most frequent bone cancer in adult age, but its treatment still represents a challenge, for the intrinsic resistance to conventional chemotherapy and radiation therapy. This resistance is mainly due to pathological features, as dense matrix, scarce mitoses and poor vascularization, sustained by biological mechanisms only partially delucidated. Somatic mutation in the Krebs cycle enzyme isocytrate dehydrogenase (IDH) have been described in gliomas, acute myeloid leukemia, cholangiocarcinoma, melanoma, colorectal, prostate cancer, thyroid carcinoma and other cancers. In mesenchymal tumors IDH mutations are present in about 50% of central chondrosarcoma. IDH mutations are an early event in chondrosarcoma-genesis, and contribute to the acquisition of malignancy through the block of cellular differentiation, hypoxia induction through HIF stabilization, DNA methylation and alteration of cellular red-ox balance. While in gliomas IDH mutations confers a good prognosis, in chondrosarcoma IDH prognostic role is controversial in different reported series. First aim of this project is to define the prevalence and the prognostic role of IDH mutation in high grade central conventional chondrosarcoma patients treated at Istituto Ortopedico Rizzoli. Second aim is the critical revision of scientific literature to understand better how a genomic event in cancer cell can trigger alteration in the TME, through immune infiltrate reshaping, angiogenesis induction, metabolic and methylation rewiring. Third aim is to screen other sarcoma histotypes for the presence of IDH mutation.

Tensor-Train decomposition for image classification problems

In these last years a great effort has been put in the development of new techniques for automatic object classification, also due to the consequences in many applications such as medical imaging or driverless cars. To this end, several mathematical models have been developed from logistic regression to neural networks. A crucial aspect of these so called classification algorithms is the use of algebraic tools to represent and approximate the input data. In this thesis, we examine two different models for image classification based on a particular tensor decomposition named Tensor-Train (TT) decomposition. The use of tensor approaches preserves the multidimensional structure of the data and the neighboring relations among pixels. Furthermore the Tensor-Train, differently from other tensor decompositions, does not suffer from the curse of dimensionality making it an extremely powerful strategy when dealing with high-dimensional data. It also allows data compression when combined with truncation strategies that reduce memory requirements without spoiling classification performance. The first model we propose is based on a direct decomposition of the database by means of the TT decomposition to find basis vectors used to classify a new object. The second model is a tensor dictionary learning model, based on the TT decomposition where the terms of the decomposition are estimated using a proximal alternating linearized minimization algorithm with a spectral stepsize.