Towards Tight Lower Bounds for Range Reporting on the RAM

In the orthogonal range reporting problem, we are to preprocess a set of $n$ points with integer coordinates on a $U \times U$ grid. The goal is to support reporting all $k$ points inside an axis-aligned query rectangle. This is one of the most fundamental data structure problems in databases and computational geometry. Despite the importance of the problem its complexity remains unresolved in the word-RAM. On the upper bound side, three best tradeoffs exists: (1.) Query time $O(\lg \lg n + k)$ with $O(nlg^{\varepsilon}n)$ words of space for any constant $\varepsilon>0$. (2.) Query time $O((1 + k) \lg \lg n)$ with $O(n \lg \lg n)$ words of space. (3.) Query time $O((1+k)\lg^{\varepsilon} n)$ with optimal $O(n)$ words of space. However, the only known query time lower bound is $\Omega(\log \log n +k)$, even for linear space data structures. All three current best upper bound tradeoffs are derived by reducing range reporting to a ball-inheritance problem. Ball-inheritance is a problem that essentially encapsulates all previous attempts at solving range reporting in the word-RAM. In this paper we make progress towards closing the gap between the upper and lower bounds for range reporting by proving cell probe lower bounds for ball-inheritance. Our lower bounds are tight for a large range of parameters, excluding any further progress for range reporting using the ball-inheritance reduction

Developing Guidelines for Two-Dimensional Model Review and Acceptance

Two independent modelers ran two hydraulic models, SRH-2D and HEC-RAS 2D. The models were applied to the Lakina River (MP 44 McCarthy Road) and to Quartz Creek (MP 0.7 Quartz Creek Road), which approximately represent straight and bend flow conditions, respectively. We compared the results, including water depth, depth averaged velocity, and bed shear stress, from the two models for both modelers. We found that the extent and density of survey data were insufficient for Quartz Creek. Neither model was calibrated due to the lack of basic field data (i.e., discharge, water surface elevation, and sediment characteristics). Consequently, we were unable to draw any conclusion about the accuracy of the models. Concerning the time step and the equations used (simplified or full) to solve the momentum equation in the HEC-RAS 2D model, we found that the minimum time step allowed by the model must be used if the diffusion wave equation is used in the simulations. A greater time step can be used if the full momentum equation is used in the simulations. We developed a set of guidelines for reviewing model results, and developed and provided a two-day training workshop on the two models for ADOT&PF hydraulic engineers

Global optimization in systems biology: stochastic methods and their applications

Mathematical optimization is at the core of many problems in systems biology: (1) as the underlying hypothesis for model development, (2) in model identification, or (3) in the computation of optimal stimulation procedures to synthetically achieve a desired biological behavior. These problems are usually formulated as nonlinear programing problems (NLPs) with dynamic and algebraic constraints. However the nonlinear and highly constrained nature of systems biology models, together with the usually large number of decision variables, can make their solution a daunting task, therefore calling for efficient and robust optimization techniques. Here, we present novel global optimization methods and software tools such as cooperative enhanced scatter search (eSS), AMIGO, or DOTcvpSB, and illustrate their possibilities in the context of modeling including model identification and stimulation design in systems biology.This work was supported by the Spanish MICINN project ”MultiSysBio” (ref. DPI2008-06880-C03-02), and by CSIC intramural project ”BioREDES” (ref. PIE-201170E018).Peer reviewe

On the role of pre and post-processing in environmental data mining

The quality of discovered knowledge is highly depending on data quality. Unfortunately real data use to contain noise, uncertainty, errors, redundancies or even irrelevant information. The more complex is the reality to be analyzed, the higher the risk of getting low quality data. Knowledge Discovery from Databases (KDD) offers a global framework to prepare data in the right form to perform correct analyses. On the other hand, the quality of decisions taken upon KDD results, depend not only on the quality of the results themselves, but on the capacity of the system to communicate those results in an understandable form. Environmental systems are particularly complex and environmental users particularly require clarity in their results. In this paper some details about how this can be achieved are provided. The role of the pre and post processing in the whole process of Knowledge Discovery in environmental systems is discussed

Towards Tight Lower Bounds for Range Reporting on the RAM

In the orthogonal range reporting problem, we are to preprocess a set of n points with integer coordinates on a UxU grid. The goal is to support reporting all k points inside an axis-aligned query rectangle. This is one of the most fundamental data structure problems in databases and computational geometry. Despite the importance of the problem its complexity remains unresolved in the word-RAM. On the upper bound side, three best tradeoffs exist, all derived by reducing range reporting to a ball-inheritance problem. Ball-inheritance is a problem that essentially encapsulates all previous attempts at solving range reporting in the word-RAM. In this paper we make progress towards closing the gap between the upper and lower bounds for range reporting by proving cell probe lower bounds for ball-inheritance. Our lower bounds are tight for a large range of parameters, excluding any further progress for range reporting using the ball-inheritance reduction

The interaction of labor markets and inflation: analysis of micro data from the International Wage Flexibility Project

Inflation can “grease” the wheels of economic adjustment in the labor market by relieving the constraint imposed by downward nominal wage rigidity, but not if there is also substantial downward real wage rigidity. At the same time, inflation can throw “sand” in the wheels of economic adjustment by degrading the value of price signals. A number of recent studies suggest that wage rigidity is much more important for business cycles and monetary policy than previously believed (see Erceg, Henderson and Levin, 2000, Smets and Wouters, 2003, and Hall, 2005). Thus, our results on how wage rigidity and other labor market imperfections vary between countries and how they are affected by the rate of inflation should be of considerable value in formulating monetary policy and conducting related research.

Spatial characteristics of thunderstorm rainfall fields and their relation to runoff

The main aim of this study was to assess the ability of simple geometric measures of thunderstorm rainfall in explaining the runoff response from the watershed. For calculation of storm geometric properties (e.g. areal coverage of storm, areal coverage of the high-intensity portion of the storm, position of storm centroid and the movement of storm centroid in time), spatial information of rainfall is needed. However, generally the rainfall data consists of rainfall depth values over an unevenly spaced network of raingauges. For this study, rainfall depth values were available for 91 raingauges in a watershed of about 148 km2. There was a question about which interpolation method should be used for obtaining uniformly gridded data. Therefore, a small study was undertaken to compare cross-validation statistics and computed geometric parameters using two interpolation methods (kriging and multiquadric). These interpolation methods were used to estimate precipitation over a uniform 100 m × 100 m grid. The cross-validation results from the two methods were generally similar and neither method consistently performed better than the other did. In view of these results we decided to use multiquadric interpolation method for the rest of the study. Several geometric measures were then computed from interpolated surfaces for about 300 storm events occurring in a 17-year period. The correlation of these computed measures with basin runoff were then observed in an attempt to assess their relative importance in basin runoff response. It was observed that the majority of the storms (observed in the study) covered the entire watershed. Therefore, it was concluded that the areal coverage of storm was not a good indicator of the amount of runoff produced. The areal coverage of the storm core (10-min intensity greater than 25 mm/h), however, was found to be a much better predictor of runoff volume and peak rate. The most important variable in runoff production was found to be the volume of the storm core. It was also observed that the position of the storm core relative to the watershed outlet becomes more important as the catchment size increases, with storms positioned in the central portion of the watershed producing more runoff than those positioned near the outlet or near the head of the watershed. This observation indicates the importance of interaction of catchment size and shape with the spatial storm structure in runoff generation. Antecedent channel wetness was found to be of some importance in explaining runoff for the largest of the three watersheds studied but antecedent watershed wetness did not appreciably contributed to runoff explanation. © 2002 Elsevier Science B.V. All rights reserved