Ergodic Control and Polyhedral approaches to PageRank Optimization

We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a link, and a discrete one, in which in each page, there are obligatory links, facultative links and forbidden links. We show that the continuous problem, as well as its discrete variant when there are no constraints coupling different pages, can both be modeled by constrained Markov decision processes with ergodic reward, in which the webmaster determines the transition probabilities of websurfers. Although the number of actions turns out to be exponential, we show that an associated polytope of transition measures has a concise representation, from which we deduce that the continuous problem is solvable in polynomial time, and that the same is true for the discrete problem when there are no coupling constraints. We also provide efficient algorithms, adapted to very large networks. Then, we investigate the qualitative features of optimal outlink strategies, and identify in particular assumptions under which there exists a "master" page to which all controlled pages should point. We report numerical results on fragments of the real web graph.Comment: 39 page

Development and analysis of the Soil Water Infiltration Global database

In this paper, we present and analyze a novel global database of soil infiltration measurements, the Soil Water Infiltration Global (SWIG) database. In total, 5023 infiltration curves were collected across all continents in the SWIG database. These data were either provided and quality checked by the scientists who performed the experiments or they were digitized from published articles. Data from 54 different countries were included in the database with major contributions from Iran, China, and the USA. In addition to its extensive geographical coverage, the collected infiltration curves cover research from 1976 to late 2017. Basic information on measurement location and method, soil properties, and land use was gathered along with the infiltration data, making the database valuable for the development of pedotransfer functions (PTFs) for estimating soil hydraulic properties, for the evaluation of infiltration measurement methods, and for developing and validating infiltration models. Soil textural information (clay, silt, and sand content) is available for 3842 out of 5023 infiltration measurements ( ∼ 76%) covering nearly all soil USDA textural classes except for the sandy clay and silt classes. Information on land use is available for 76% of the experimental sites with agricultural land use as the dominant type ( ∼ 40%). We are convinced that the SWIG database will allow for a better parameterization of the infiltration process in land surface models and for testing infiltration models. All collected data and related soil characteristics are provided online in *.xlsx and *.csv formats for reference, and we add a disclaimer that the database is for public domain use only and can be copied freely by referencing it. Supplementary data are available at https://doi.org/10.1594/PANGAEA.885492 (Rahmati et al., 2018). Data quality assessment is strongly advised prior to any use of this database. Finally, we would like to encourage scientists to extend and update the SWIG database by uploading new data to it

Development and analysis of the Soil Water Infiltration Global database.

In this paper, we present and analyze a novel global database of soil infiltration measurements, the Soil Water Infiltration Global (SWIG) database. In total, 5023 infiltration curves were collected across all continents in the SWIG database. These data were either provided and quality checked by the scientists who performed the experiments or they were digitized from published articles. Data from 54 different countries were included in the database with major contributions from Iran, China, and the USA. In addition to its extensive geographical coverage, the collected infiltration curves cover research from 1976 to late 2017. Basic information on measurement location and method, soil properties, and land use was gathered along with the infiltration data, making the database valuable for the development of pedotransfer functions (PTFs) for estimating soil hydraulic properties, for the evaluation of infiltration measurement methods, and for developing and validating infiltration models. Soil textural information (clay, silt, and sand content) is available for 3842 out of 5023 infiltration measurements (~76%) covering nearly all soil USDA textural classes except for the sandy clay and silt classes. Information on land use is available for 76% of the experimental sites with agricultural land use as the dominant type (~40%). We are convinced that the SWIG database will allow for a better parameterization of the infiltration process in land surface models and for testing infiltration models. All collected data and related soil characteristics are provided online in *.xlsx and *.csv formats for reference, and we add a disclaimer that the database is for public domain use only and can be copied freely by referencing it. Supplementary data are available at https://doi.org/10.1594/PANGAEA.885492 (Rahmati et al., 2018). Data quality assessment is strongly advised prior to any use of this database. Finally, we would like to encourage scientists to extend and update the SWIG database by uploading new data to it

Toric Sylvester forms and applications in elimination theory

In this paper, we investigate the structure of the saturation of ideals generated by square systems of sparse homogeneous polynomials over a toric variety $X$ with respect to the irrelevant ideal of $X$. As our main results, we establish a duality property and make it explicit by introducing toric Sylvester forms, under a certain positivity assumption on $X$. In particular, we prove that toric Sylvester forms yield bases of some graded components of $I^{sat}/I$, where $I$ denotes an ideal generated by $n + 1$ generic forms, $n$ is the dimension of $X$ and $I$ sat the saturation of $I$ with respect to the irrelevant ideal of the Cox ring of $X$. Then, to illustrate the relevance of toric Sylvester forms we provide three consequences in elimination theory: (1) we introduce a new family of elimination matrices that can be used to solve sparse polynomial systems by means of linear algebra methods, including overdetermined polynomial systems; (2) by incorporating toric Sylvester forms to the classical Koszul complex associated to a polynomial system, we obtain new expressions of the sparse resultant as a determinant of a complex; (3) we prove a new formula for computing toric residues of the product of two forms.Comment: 25 pages, 1 figur

Data-Driven Constraint Handling in Multi-Objective Inductor Design

This paper analyses the multi-objective design of an inductor for a DC-DC buck converter. The core volume and total losses are the two competing objectives, which should be minimised while satisfying the design constraints on the required differential inductance profile and the maximum overheating. The multi-objective optimisation problem is solved by means of a population-based metaheuristic algorithm based on Artificial Immune Systems (AIS). Despite its effectiveness in finding the Pareto front, the algorithm requires the evaluation of many candidate solutions before converging. In the case of the inductor design problem, the evaluation of a configuration is time-consuming. In fact, a non-linear iterative technique (fixed point) is needed to obtain the differential inductance profile of the configuration, as it may operate in conditions of partial saturation. However, many configurations evaluated during an optimisation do not comply with the design constraint, resulting in expensive and unnecessary calculations. Therefore, this paper proposes the adoption of a data-driven surrogate model in a pre-selection phase of the optimisation. The adopted model should classify newly generated configurations as compliant or not with the design constraint. Configurations classified as unfeasible are disregarded, thus avoiding the computational burden of their complete evaluation. Interesting results have been obtained, both in terms of avoided configuration evaluations and the quality of the Pareto front found by the optimisation procedure

Stability analysis of an earth embankment subjected to rainfall infiltration - Analisi di stabilità di un rilevato in terra soggetto ad infiltrazione di acque di pioggia

In the present thesis, an attempt was made to study, with a numerical software, how the rainfall infiltration influences the stresses and the behavior of a soil embankment according to different hydraulic permeability values and rainfall intensities. In particular the analyses performed can be distinguished in four main types: an infiltration analysis, a stress-deformation analysis, a slope stability analysis and a parametric stud

Assessing and Improving Pollution Prevention by Swales

Roadside swales are drainage ditches that also treat runoff to improve water quality, including infiltration of water to reduce pollutant load. In the infiltration study, a quick and simple device, the Modified Philip Dunne (MPD) infiltrometer, was utilized to measure an important infiltration parameter (saturated hydraulic conductivity, Ksat) at multiple locations in a number of swales. The study showed that the spatial variability in the swale infiltration rate was substantial, requiring 20 or more measurements along the highway to get a good estimate of the mean swale infiltration rate. This study also developed a ditch check filtration system that can be installed in swales to provide significant treatment of dissolved heavy metals and dissolved phosphorous in stormwater runoff. The results were utilized to develop design guidelines and recommendations, including sizing and treatment criteria for optimal performance of the full-scale design of these filters. Finally, the best available knowledge on swale maintenance was combined with information obtained from new surveys conducted to develop recommendations for swale maintenance schedules and effort. The recommendations aim toward optimizing the cost-effectiveness of roadside swales and thus provide useful information to managers and practitioners of roadways. The research results and information obtained from this study can thus be used to design swale systems for use along linear roadway projects that will receive pollution prevention credits for infiltration. This will enable the utilization of drainage ditches to their full pollution prevention potential, before building other more expensive stormwater treatment practices throughout Minnesota and the United States

Geocellular railway drainage systems: physical and numerical modelling

The importance of resilient railway infrastructure is paramount when considering the increased likelihood of extreme weather and flash flood events in coming years. One of the main causes of instability of railway tracks is excess water in the trackbed, particularly when it is at or above the interface of the ballast and subgrade. Conventional drainage systems are susceptible to clogging and deterioration. Resilient track drainage systems should therefore have sufficient capacity to allow water to dissipate quickly, but they should also be designed to ensure long-term operation with minimal or easily performed maintenance. This paper presents results from an investigation of a potential new railway drainage system using geocellular components. In the paper, the development of a large scale physical model is described which represents a full scale unit cell of a sleeper-to-sleeper track substructure. The physical model includes ballast and subgrade layers, under-track and lateral drainage systems, rainfall simulation, and instrumentation. Results demonstrate the relative hydraulic response of the drainage system with and without the geocellular components. The paper also describes the development of a numerical model of the track subgrade and drainage system, which was first calibrated and verified using experimental data from the physical model, then extended to study the effect of certain parameters on the hydraulic response of the railway track. Results indicate that the under-track geocellular drainage system offers potential benefits in terms of maintaining a lower water table level within the subgrade as well as in aiding the migration of fines out of the ballast

Complexity Theory

Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness and randomness extraction. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes