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The goal of the present paper is to collect the results related to dynamics of a one-dimensional piecewise linear map widely known as the skew tent map. These results may be useful for the researchers working on theoretical and applied problems in the field of nonsmooth dynamical systems. In particular, we propose the complete description of the bifurcation structure of the parameter space of the skew tent map, providing the related proofs. It is also shown how these results can be used to classify border collision bifurcations in one-dimensional piecewise smooth maps. [ABSTRACT FROM AUTHOR]

In this paper, we study the complex interaction between environmental damage and location in space of firms and entrepreneurial households. We use a New Economic Geography (NEG) framework, suitably extended to account for environmental damage and the two mobility processes. The resulting model is a two-dimensional piecewise smooth map with two constraints for each variable, and we use analytic and numerical tools to explore its long-run dynamics. We pay special attention to the different types of fixed points and the structure of the respective basins of attraction. Their complexity re-enforces a core theme of the NEG: History matters for the long run location in space of economic activity.

This paper contributes to studying the bifurcations of closed invariant curves in piecewise-smooth maps. Specifically, we discuss a border collision bifurcation of a repelling resonant closed invariant curve (a repelling saddle-node connection) colliding with the border by a point of the repelling cycle. As a result, this cycle becomes attracting and the curve is destroyed, while a new repelling closed invariant curve appears (not in a neighborhood of the previously existing invariant curve), being associated with quasiperiodic dynamics. This leads to a global restructuring of the phase portrait since both curves mentioned above belong to basin boundaries of coexisting attractors.

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is, a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to infinity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.

We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.

The aim of the CADASTER project (CAse Studies on the Development and Application of in Silico Techniques for Environmental Hazard and Risk Assessment) was to exemplify REACH-related hazard assessments for four classes of chemical compound, namely, polybrominated diphenylethers, per and polyfluorinated compounds, (benzo)triazoles, and musks and fragrances. The QSPR-THESAURUS website (http: / /qspr-thesaurus.eu) was established as the project's online platform to upload, store, apply, and also create, models within the project. We overview the main features of the website, such as model upload, experimental design and hazard assessment to support risk assessment, and integration with other web tools, all of which are essential parts of the QSPR-THESAURUS., (2014 FRAME.)

The dimethyl sulfoxide (DMSO) solubility data from Enamine and two UCB pharma compound collections were analyzed using 8 different machine learning methods and 12 descriptor sets. The analyzed data sets were highly imbalanced with 1.7-5.8% nonsoluble compounds. The libraries' enrichment by soluble molecules from the set of 10% of the most reliable predictions was used to compare prediction performances of the methods. The highest accuracies were calculated using a C4.5 decision classification tree, random forest, and associative neural networks. The performances of the methods developed were estimated on individual data sets and their combinations. The developed models provided on average a 2-fold decrease of the number of nonsoluble compounds amid all compounds predicted as soluble in DMSO. However, a 4-9-fold enrichment was observed if only 10% of the most reliable predictions were considered. The structural features influencing compounds to be soluble or nonsoluble in DMSO were also determined. The best models developed with the publicly available Enamine data set are freely available online at http://ochem.eu/article/33409 .

The importance of reliable methods for representative sub-sampling in terms of experimental design and risk assessment within the European Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH) system is crucial. We developed experimental design approaches, by utilising predicted properties and the 'distance to model' parameter, to estimate the benefits of certain compounds to the quality of a resulting model. A statistical evaluation of four regression data sets and one classification data set showed that the adaptive concept of iteratively refining the representation of the chemical space contributes to a more efficient and more reliable selection in comparison to traditional approaches. The evaluation of compounds with regard to the uncertainty and the correlation of prediction is beneficial, and in particular, for regression data sets of sufficient size, whereas the use of predicted properties to define the chemical space is beneficial for classification models., (2013 FRAME.)

The article presents a Web-based platform for collecting and storing toxicological structural alerts from literature and for virtual screening of chemical libraries to flag potentially toxic chemicals and compounds that can cause adverse side effects. An alert is uniquely identified by a SMARTS template, a toxicological endpoint, and a publication where the alert was described. Additionally, the system allows storing complementary information such as name, comments, and mechanism of action, as well as other data. Most importantly, the platform can be easily used for fast virtual screening of large chemical datasets, focused libraries, or newly designed compounds against the toxicological alerts, providing a detailed profile of the chemicals grouped by structural alerts and endpoints. Such a facility can be used for decision making regarding whether a compound should be tested experimentally, validated with available QSAR models, or eliminated from consideration altogether. The alert-based screening can also be helpful for an easier interpretation of more complex QSAR models. The system is publicly accessible and tightly integrated with the Online Chemical Modeling Environment (OCHEM, http://ochem.eu). The system is open and expandable: any registered OCHEM user can introduce new alerts, browse, edit alerts introduced by other users, and virtually screen his/her data sets against all or selected alerts. The user sets being passed through the structural alerts can be used at OCHEM for other typical tasks: exporting in a wide variety of formats, development of QSAR models, additional filtering by other criteria, etc. The database already contains almost 600 structural alerts for such endpoints as mutagenicity, carcinogenicity, skin sensitization, compounds that undergo metabolic activation, and compounds that form reactive metabolites and, thus, can cause adverse reactions. The ToxAlerts platform is accessible on the Web at http://ochem.eu/alerts, and it is constantly growing.

Prediction of CYP450 inhibition activity of small molecules poses an important task due to high risk of drug-drug interactions. CYP1A2 is an important member of CYP450 superfamily and accounts for 15% of total CYP450 presence in human liver. This article compares 80 in-silico QSAR models that were created by following the same procedure with different combinations of descriptors and machine learning methods. The training and test sets consist of 3745 and 3741 inhibitors and noninhibitors from PubChem BioAssay database. A heterogeneous external test set of 160 inhibitors was collected from literature. The studied descriptor sets involve E-state, Dragon and ISIDA SMF descriptors. Machine learning methods involve Associative Neural Networks (ASNN), K Nearest Neighbors (kNN), Random Tree (RT), C4.5 Tree (J48), and Support Vector Machines (SVM). The influence of descriptor selection on model accuracy was studied. The benefits of "bagging" modeling approach were shown. Applicability domain approach was successfully applied in this study and ways of increasing model accuracy through use of applicability domain measures were demonstrated as well as fragment-based model interpretation was performed. The most accurate models in this study achieved values of 83% and 68% correctly classified instances on the internal and external test sets, respectively. The applicability domain approach allowed increasing the prediction accuracy to 90% for 78% of the internal and 17% of the external test sets, respectively. The most accurate models are available online at http://ochem.eu/models/Q5747 .

The estimation of accuracy and applicability of QSAR and QSPR models for biological and physicochemical properties represents a critical problem. The developed parameter of "distance to model" (DM) is defined as a metric of similarity between the training and test set compounds that have been subjected to QSAR/QSPR modeling. In our previous work, we demonstrated the utility and optimal performance of DM metrics that have been based on the standard deviation within an ensemble of QSAR models. The current study applies such analysis to 30 QSAR models for the Ames mutagenicity data set that were previously reported within the 2009 QSAR challenge. We demonstrate that the DMs based on an ensemble (consensus) model provide systematically better performance than other DMs. The presented approach identifies 30-60% of compounds having an accuracy of prediction similar to the interlaboratory accuracy of the Ames test, which is estimated to be 90%. Thus, the in silico predictions can be used to halve the cost of experimental measurements by providing a similar prediction accuracy. The developed model has been made publicly available at http://ochem.eu/models/1 .

Metzlers inventory model may produce dampened fluctuations in economic activity, thus contributing to our understanding of business cycle dynamics. For some parameter combinations, however, the model generates oscillations with increasing amplitude, implying that the inventory stock of firms eventually turns negative. Taking this observation into account, we reformulate Metzlers model by simply putting a floor to the inventory level. Within the new piecewise linear model, endogenous business cycle dynamics may now be triggered via a center bifurcation, i.e. for certain parameter combinations production changes are (quasi-)periodic.

The estimation of the accuracy of predictions is a critical problem in QSAR modeling. The "distance to model" can be defined as a metric that defines the similarity between the training set molecules and the test set compound for the given property in the context of a specific model. It could be expressed in many different ways, e.g., using Tanimoto coefficient, leverage, correlation in space of models, etc. In this paper we have used mixtures of Gaussian distributions as well as statistical tests to evaluate six types of distances to models with respect to their ability to discriminate compounds with small and large prediction errors. The analysis was performed for twelve QSAR models of aqueous toxicity against T. pyriformis obtained with different machine-learning methods and various types of descriptors. The distances to model based on standard deviation of predicted toxicity calculated from the ensemble of models afforded the best results. This distance also successfully discriminated molecules with low and large prediction errors for a mechanism-based model developed using log P and the Maximum Acceptor Superdelocalizability descriptors. Thus, the distance to model metric could also be used to augment mechanistic QSAR models by estimating their prediction errors. Moreover, the accuracy of prediction is mainly determined by the training set data distribution in the chemistry and activity spaces but not by QSAR approaches used to develop the models. We have shown that incorrect validation of a model may result in the wrong estimation of its performance and suggested how this problem could be circumvented. The toxicity of 3182 and 48774 molecules from the EPA High Production Volume (HPV) Challenge Program and EINECS (European chemical Substances Information System), respectively, was predicted, and the accuracy of prediction was estimated. The developed models are available online at http://www.qspr.org site.

We study the influence of quasiperiodic forcing on synchronization and desynchronization using two coupled quasiperiodically forced logistic maps as a paradigm. We show that due to the forcing the synchronization region in parameter space shrinks. The loss of transverse stability of the synchronized attractors leads to desynchronization. Two types of such blowout bifurcations are described, namely, the blowout bifurcations of synchronized quasiperiodic motion on invariant curves and synchronized strange nonchaotic attractors, both yielding desynchronized chaotic attractors.

Spatial distribution and component structure of movement-related brain potentials (MRBP) were studied in 6-7-years-old children. The structure of Bereitschaftspotentials was found to be complex and heterogeneous the latency of P200 component being shorter than that in adults. MRBP recorded contained specific for children late negative wave that had been called postaction negativity, or PAN. The amplitudes of almost all MRBP components in children under study was the highest in the frontal areas. The results obtained may reflect neurophysiological changes associated with motor development.