Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

Thermodynamic analysis of snowball Earth hysteresis experiment: Efficiency, entropy production and irreversibility

We present an extensive thermodynamic analysis of a hysteresis experiment performed on a simplified yet Earth-like climate model. We slowly vary the solar constant by 20% around the present value and detect that for a large range of values of the solar constant the realization of snowball or of regular climate conditions depends on the history of the system. Using recent results on the global climate thermodynamics, we show that the two regimes feature radically different properties. The efficiency of the climate machine monotonically increases with decreasing solar constant in present climate conditions, whereas the opposite takes place in snowball conditions. Instead, entropy production is monotonically increasing with the solar constant in both branches of climate conditions, and its value is about four times larger in the warm branch than in the corresponding cold state. Finally, the degree of irreversibility of the system, measured as the fraction of excess entropy production due to irreversible heat transport processes, is much higher in the warm climate conditions, with an explosive growth in the upper range of the considered values of solar constants. Whereas in the cold climate regime a dominating role is played by changes in the meridional albedo contrast, in the warm climate regime changes in the intensity of latent heat fluxes are crucial for determining the observed properties. This substantiates the importance of addressing correctly the variations of the hydrological cycle in a changing climate. An interpretation of the climate transitions at the tipping points based upon macro-scale thermodynamic properties is also proposed. Our results support the adoption of a new generation of diagnostic tools based on the second law of thermodynamics for auditing climate models and outline a set of parametrizations to be used in conceptual and intermediate-complexity models or for the reconstruction of the past climate conditions. Copyright © 2010 Royal Meteorological Society

Convergence analysis of stochastic diffusion search

In this paper we present a connectionist searching technique - the Stochastic Diffusion Search (SDS), capable of rapidly locating a specified pattern in a noisy search space. In operation SDS finds the position of the pre-specified pattern or if it does not exist - its best instantiation in the search space. This is achieved via parallel exploration of the whole search space by an ensemble of agents searching in a competitive cooperative manner. We prove mathematically the convergence of stochastic diffusion search. SDS converges to a statistical equilibrium when it locates the best instantiation of the object in the search space. Experiments presented in this paper indicate the high robustness of SDS and show good scalability with problem size. The convergence characteristic of SDS makes it a fully adaptive algorithm and suggests applications in dynamically changing environments.

Computer generation and quantitative morphometric analysis of virtual neurons

An important goal in computational neuroanatomy is the complete and accurate simulation of neuronal morphology. We are developing computational tools to model three-dimensional dendritic structures based on sets of stochastic rules. This paper reports an extensive, quantitative anatomical characterization of simulated motoneurons and Purkinje cells. We used several local and global algorithms implemented in the L-Neuron and ArborVitae programs to generate sets of virtual neurons. Parameters statistics for all algorithms were measured from experimental data, thus providing a compact and consistent description of these morphological classes. We compared the emergent anatomical features of each group of virtual neurons with those of the experimental database in order to gain insights on the plausibility of the model assumptions, potential improvements to the algorithms, and non-trivial relations among morphological parameters. Algorithms mainly based on local constraints (e.g., branch diameter) were successful in reproducing many morphological properties of both motoneurons and Purkinje cells (e.g. total length, asymmetry, number of bifurcations). The addition of global constraints (e.g., trophic factors) improved the angle-dependent emergent characteristics (average Euclidean distance from the soma to the dendritic terminations, dendritic spread). Virtual neurons systematically displayed greater anatomical variability than real cells, suggesting the need for additional constraints in the models. For several emergent anatomical properties, a specific algorithm reproduced the experimental statistics better than the others did. However, relative performances were often reversed for different anatomical properties and/or morphological classes. Thus, combining the strengths of alternative generative models could lead to comprehensive algorithms for the complete and accurate simulation of dendritic morphology.

Performance analysis of data transmissions in MPLS and non-MPLS networks

Basic Network transactions specifies that datagram from source to destination is routed through numerous routers and paths depending on the available free and uncongested paths which results in the transmission route being too long, thus incurring greater delay, jitter, congestion and reduced throughput. One of the major problems of packet switched networks is the cell delay variation or jitter. This cell delay variation is due to the queuing delay depending on the applied loading conditions. The effect of delay, jitter accumulation due to the number of nodes along transmission routes and dropped packets adds further complexity to multimedia traffic because there is no guarantee that each traffic stream will be delivered according to its own jitter constraints therefore there is the need to analyze the effects of jitter. IP routers enable a single path for the transmission of all packets. On the other hand, Multi-Protocol Label Switching (MPLS) allows separation of packet forwarding and routing characteristics to enable packets to use the appropriate routes and also optimize and control the behavior of transmission paths. Thus correcting some of the shortfalls associated with IP routing. Therefore MPLS has been utilized in the analysis for effective transmission through the various networks. This paper analyzes the effect of delay, congestion, interference, jitter and packet loss in the transmission of signals from source to destination. In effect the impact of link failures, repair paths in the various physical topologies namely bus, star, mesh and hybrid topologies are all analyzed based on standard network conditions.

Time complexity analysis of the stochastic diffusion search

The Stochastic Diffusion Search algorithm -an integral part of Stochastic Search Networks is investigated. Stochastic Diffusion Search is an alternative solution for invariant pattern recognition and focus of attention. It has been shown that the algorithm can be modelled as an ergodic, finite state Markov Chain under some non-restrictive assumptions. Sub-linear time complexity for some settings of parameters has been formulated and proved. Some properties of the algorithm are then characterised and numerical examples illustrating some features of the algorithm are presented.

Sequence and phylogenetic analysis of viper venom serine proteases

Snakebites are a major neglected tropical disease responsible for as many as 95000 deaths every year worldwide. Viper venom serine proteases disrupt haemostasis of prey and victims by affecting various stages of the blood coagulation system. A better understanding of their sequence, structure, function and phylogenetic relationships will improve the knowledge on the pathological conditions and aid in the development of novel therapeutics for treating snakebites. A large dataset for all available viper venom serine proteases was developed and analysed to study various features of these enzymes. Despite the large number of venom serine protease sequences available, only a small proportion of these have been functionally characterised. Although, they share some of the common features such as a C-terminal extension, GWG motif and disulphide linkages, they vary widely between each other in features such as isoelectric points, potential N-glycosylation sites and functional characteristics. Some of the serine proteases contain substitutions for one or more of the critical residues in catalytic triad or primary specificity pockets. Phylogenetic analysis clustered all the sequences in three major groups. The sequences with substitutions in catalytic triad or specificity pocket clustered together in separate groups. Our study provides the most complete information on viper venom serine proteases to date and improves the current knowledge on the sequence, structure, function and phylogenetic relationships of these enzymes. This collective analysis of venom serine proteases will help in understanding the complexity of envenomation and potential therapeutic avenues.

System identification algorithms for the analysis of dielectric responses from broadband spectroscopies

We discuss the modeling of dielectric responses for an electromagnetically excited network of capacitors and resistors using a systems identification framework. Standard models that assume integral order dynamics are augmented to incorporate fractional order dynamics. This enables us to relate more faithfully the modeled responses to those reported in the Dielectrics literature.

Empirical test of an agricultural landscape model: the importance of farmer preference for risk aversion and crop complexity

Developing models to predict the effects of social and economic change on agricultural landscapes is an important challenge. Model development often involves making decisions about which aspects of the system require detailed description and which are reasonably insensitive to the assumptions. However, important components of the system are often left out because parameter estimates are unavailable. In particular, measurements of the relative influence of different objectives, such as risk, environmental management, on farmer decision making, have proven difficult to quantify. We describe a model that can make predictions of land use on the basis of profit alone or with the inclusion of explicit additional objectives. Importantly, our model is specifically designed to use parameter estimates for additional objectives obtained via farmer interviews. By statistically comparing the outputs of this model with a large farm-level land-use data set, we show that cropping patterns in the United Kingdom contain a significant contribution from farmer’s preference for objectives other than profit. In particular, we found that risk aversion had an effect on the accuracy of model predictions, whereas preference for a particular number of crops grown was less important. While nonprofit objectives have frequently been identified as factors in farmers’ decision making, our results take this analysis further by demonstrating the relationship between these preferences and actual cropping patterns.

The energy-cycle analysis of the interactions between shallow and deep atmospheric convection

Interactions between different convection modes can be investigated using an energy–cycle description under a framework of mass–flux parameterization. The present paper systematically investigates this system by taking a limit of two modes: shallow and deep convection. Shallow convection destabilizes itself as well as the other convective modes by moistening and cooling the environment, whereas deep convection stabilizes itself as well as the other modes by drying and warming the environment. As a result, shallow convection leads to a runaway growth process in its stand–alone mode, whereas deep convection simply damps out. Interaction between these two convective modes becomes a rich problem, even when it is limited to the case with no large–scale forcing, because of these opposing tendencies. Only if the two modes are coupled at a proper level can a self–sustaining system arise, exhibiting a periodic cycle. The present study establishes the conditions for self–sustaining periodic solutions. It carefully documents the behaviour of the two mode system in order to facilitate the interpretation of global model behaviours when this energy–cycle is implemented as a closure into a convection parameterization in future.

Multi-site evaluation of an urban land-surface model: intra-urban heterogeneity, seasonality and parameter complexity requirements

An extensive off-line evaluation of the Noah/Single Layer Urban Canopy Model (Noah/SLUCM) urban land-surface model is presented using data from 15 sites to assess (1) the ability of the scheme to reproduce the surface energy balance observed in a range of urban environments, including seasonal changes, and (2) the impact of increasing complexity of input parameter information. Model performance is found to be most dependent on representation of vegetated surface area cover; refinement of other parameter values leads to smaller improvements. Model biases in net all-wave radiation and trade-offs between turbulent heat fluxes are highlighted using an optimization algorithm. Here we use the Urban Zones to characterize Energy partitioning (UZE) as the basis to assign default SLUCM parameter values. A methodology (FRAISE) to assign sites (or areas) to one of these categories based on surface characteristics is evaluated. Using three urban sites from the Basel Urban Boundary Layer Experiment (BUBBLE) dataset, an independent evaluation of the model performance with the parameter values representative of each class is performed. The scheme copes well with both seasonal changes in the surface characteristics and intra-urban heterogeneities in energy flux partitioning, with RMSE performance comparable to similar state-of-the-art models for all fluxes, sites and seasons. The potential of the methodology for high-resolution atmospheric modelling application using the Weather Research and Forecasting (WRF) model is highlighted. This analysis supports the recommendations that (1) three classes are appropriate to characterize the urban environment, and (2) that the parameter values identified should be adopted as default values in WRF.

Generation and analysis of the 2005 land cover map for Mexico using 250m MODIS data

Land cover plays a key role in global to regional monitoring and modeling because it affects and is being affected by climate change and thus became one of the essential variables for climate change studies. National and international organizations require timely and accurate land cover information for reporting and management actions. The North American Land Change Monitoring System (NALCMS) is an international cooperation of organizations and entities of Canada, the United States, and Mexico to map land cover change of North America's changing environment. This paper presents the methodology to derive the land cover map of Mexico for the year 2005 which was integrated in the NALCMS continental map. Based on a time series of 250 m Moderate Resolution Imaging Spectroradiometer (MODIS) data and an extensive sample data base the complexity of the Mexican landscape required a specific approach to reflect land cover heterogeneity. To estimate the proportion of each land cover class for every pixel several decision tree classifications were combined to obtain class membership maps which were finally converted to a discrete map accompanied by a confidence estimate. The map yielded an overall accuracy of 82.5% (Kappa of 0.79) for pixels with at least 50% map confidence (71.3% of the data). An additional assessment with 780 randomly stratified samples and primary and alternative calls in the reference data to account for ambiguity indicated 83.4% overall accuracy (Kappa of 0.80). A high agreement of 83.6% for all pixels and 92.6% for pixels with a map confidence of more than 50% was found for the comparison between the land cover maps of 2005 and 2006. Further wall-to-wall comparisons to related land cover maps resulted in 56.6% agreement with the MODIS land cover product and a congruence of 49.5 with Globcover.