Computational diagnosis and risk evaluation for canine lymphoma

The canine lymphoma blood test detects the levels of two biomarkers, the acute phase proteins (C-Reactive Protein and Haptoglobin). This test can be used for diagnostics, for screening, and for remission monitoring as well. We analyze clinical data, test various machine learning methods and select the best approach to these problems. Three family of methods, decision trees, kNN (including advanced and adaptive kNN) and probability density evaluation with radial basis functions, are used for classification and risk estimation. Several pre-processing approaches were implemented and compared. The best of them are used to create the diagnostic system. For the differential diagnosis the best solution gives the sensitivity and specificity of 83.5% and 77%, respectively (using three input features, CRP, Haptoglobin and standard clinical symptom). For the screening task, the decision tree method provides the best result, with sensitivity and specificity of 81.4% and >99%, respectively (using the same input features). If the clinical symptoms (Lymphadenopathy) are considered as unknown then a decision tree with CRP and Hapt only provides sensitivity 69% and specificity 83.5%. The lymphoma risk evaluation problem is formulated and solved. The best models are selected as the system for computational lymphoma diagnosis and evaluation the risk of lymphoma as well. These methods are implemented into a special web-accessed software and are applied to problem of monitoring dogs with lymphoma after treatment. It detects recurrence of lymphoma up to two months prior to the appearance of clinical signs. The risk map visualisation provides a friendly tool for explanatory data analysis.

Geometrical complexity of data approximators

There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types of principal curves and principal trees, and so on. For each type of approximators the measure of the approximator complexity was developed too. These measures are necessary to find the balance between accuracy and complexity and to define the optimal approximations of a given type. We propose a measure of complexity (geometrical complexity) which is applicable to approximators of several types and which allows comparing data approximations of different types.

Initialization of Self-Organizing Maps: Principal Components Versus Random Initialization. A Case Study

The performance of the Self-Organizing Map (SOM) algorithm is dependent on the initial weights of the map. The different initialization methods can broadly be classified into random and data analysis based initialization approach. In this paper, the performance of random initialization (RI) approach is compared to that of principal component initialization (PCI) in which the initial map weights are chosen from the space of the principal component. Performance is evaluated by the fraction of variance unexplained (FVU). Datasets were classified into quasi-linear and non-linear and it was observed that RI performed better for non-linear datasets; however the performance of PCI approach remains inconclusive for quasi-linear datasets.

Thermodynamics in the Limit of Irreversible Reactions

For many real physico-chemical complex systems detailed mechanism includes both reversible and irreversible reactions. Such systems are typical in homogeneous combustion and heterogeneous catalytic oxidation. Most complex enzyme reactions include irreversible steps. The classical thermodynamics has no limit for irreversible reactions whereas the kinetic equations may have such a limit. We represent the systems with irreversible reactions as the limits of the fully reversible systems when some of the equilibrium concentrations tend to zero. The structure of the limit reaction system crucially depends on the relative rates of this tendency to zero. We study the dynamics of the limit system and describe its limit behavior as $t to infty$. If the reversible systems obey the principle of detailed balance then the limit system with some irreversible reactions must satisfy the {em extended principle of detailed balance}. It is formulated and proven in the form of two conditions: (i) the reversible part satisfies the principle of detailed balance and (ii) the convex hull of the stoichiometric vectors of the irreversible reactions does not intersect the linear span of the stoichiometric vectors of the reversible reactions. These conditions imply the existence of the global Lyapunov functionals and alow an algebraic description of the limit behavior. The thermodynamic theory of the irreversible limit of reversible reactions is illustrated by the analysis of hydrogen combustion.