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We prove new boundary Harnack inequalities in Lipschitz domains for equations with a right hand side. Our main result applies to non-divergence form operators with bounded measurable coefficients and to divergence form operators with continuous coefficients, whereas the right hand side is in L q with q > n . Our approach is based on the scaling and comparison arguments of [13] , and we show that all our assumptions are sharp. As a consequence of our results, we deduce the C 1 , α regularity of the free boundary in the fully nonlinear obstacle problem and the fully nonlinear thin obstacle problem.

Geological and geophysical studies in complex valley troughs provide a key record for the reconstruction of paleoenvironmental conditions during the Quaternary. Here we present a study of the sedimentary infill of the El Cervunal kame complex or El Cervunal trough (Sierra de Gredos, Iberian Central System) by means of a combined interpretation of near-surface geophysical techniques supported by geomorphological and borehole data. A set of 1D and 2D near-surface geophysical methods, including electrical (Vertical Electrical Sounding and 2D Electrical Resistivity Tomography), seismic (2D Seismic Tomography and 1D Refraction Microtremor) and Magnetic Resonance Sounding techniques, were used to test their applicability in providing better insight on the infill nature and geometry. Because of greater sensitivity and higher resolution and coverage achieved with resistivity methods, the electrical resistivity has proven to be the most informative physical parameter, while seismic and magnetic resonance methods were complementary. The sedimentary infill was classified into three geophysical units and five sub-units with their geological interpretation. Unit 1 consists of a postglacial sedimentary sequence and includes alluvial-plain and alluvial-fan deposits. Units 2 and 3 below the postglacial unit were interpreted as glacial sequences including kame (glacigenetic and fluvio-glacial) and morainic deposits, respectively. Subsoil information combined with the geomorphological data enabled the partial reconstruction of the map-view geometry of the morainic bodies at the El Cervunal trough. The results suggest a complex evolution of the study area where erosive-sedimentary processes dominate, but also structural factors should be considered. At least five well-differentiated stages can be established to explain the occurrence of the trough infill: pre-glacial, maximum glacial extension, trough obturation, glacial retreat and periglacial-postglacial., This work was mainly supported by the Spanish Ministry of Science and Innovation (Spanish initials: MINECO; project CGL2016-78380-P) and UCLM Research Groups (Project 2020-GRIN-28992). The authors acknowledge the help received from the Sierra de Gredos Regional Park and the Consejería de Medio Ambiente of the Junta de Castilla y León (JCyL). Additional support comes from the Program I+D CARESOIL (S2018/EMT-4317) of the Comunidad Autónoma of Madrid

A new record from a long sediment core (S3) in Navamuño (1505 m asl, western Iberian Central System) provides the reconstruction of the vegetation history and environmental changes in the region between 15.6 and 10.6 ka cal BP, namely during the Late Glacial and the early Holocene, using a multiproxy analysis (pollen-based vegetation and climate reconstruction, sedimentary macrocharcoals, loss-on-ignition, magnetic susceptibility and X-ray fluorescence (XRF) measurements). The results are then compared with other sequences from the Iberian Central System and the whole Iberian Peninsula in order to better understand the past dynamics of the main forest constituents. The pollen record shows a shift from open pine forests ∼15.6–14.7 ka cal BP (Oldest Dryas) to mixed open pine-birch woodlands ∼14.7–14.0 ka cal BP (Bølling). Woodlands were succeeded by a steppe-like landscape until ∼13.4 ka cal BP (Older Dryas), which was replaced again by high-mountain pine forests and riparian woodlands ∼13.4–12.6 ka cal BP (Allerød). A great development of cold steppe grasslands linked to the decline of birch woodlands is documented ∼12.6–11.7 ka cal BP (Younger Dryas). The early Holocene (11.7–10.6 ka cal BP) was characterized by a progressive reforestation of the study area by pine and birch forests in the highlands and oak woods in the lowlands. Temperate tree taxa (Carpinus betulus, Castanea sativa, Corylus avellana, Fraxinus, Juglans, Tilia, and Ulmus) were also common but likely at lower elevations. Pollen of Fagus sylvatica was already recorded during the Late Glacial and the early Holocene. The marked increasing local fire activity during the warmer and wetter Allerød oscillation could be related to a rise in tree cover, supporting the climatically driven character of these fires. Nevertheless, the strong increase in fire activity during the Younger Dryas would probably be related to growing tree and shrub mortality, as well as to the wet/dry biphasic structure of this stadial. The standard “Modern Analogue Technique” has been also applied to the Navamuño sequence to provide quantitative climate estimations for the Late Glacial and the early Holocene periods. This record is one of the few continental archives that show the climatic trend between the Late Glacial and the early Holocene in central Iberia, agreeing with many other regional records from the Western Mediterranean.

OD matrices that describe mobility patterns provide major input to most transport analysis models. Since OD matrices are not yet directly observable, they are usually estimated indirectly. Data from new sources such as mobile phone records and GPS traces from mobile apps are emerging alternatives that allow for cheaper and timely estimates. However, they are still hindered by weaknesses that must be studied for use as input to transportation models. This paper presents a case study using mobility data from mobile phone records, with the goal of establishing a methodology for validating the obtained OD matrices and generating the appropriate input for traffic assignment models. Spatial and temporal consistency of OD data elaborated from mobile records has been proved to be useful for transportation modelling needs.

While optimization models play a key role in transportation analysis, the objective function to be optimized, however, cannot always be defined analytically. It is therefore necessary to resort to non-differentiable optimization methods that usually pivot on evaluating the objective function. Special cases of particular interest are those in Dynamic OD Estimation, which cannot evaluate the objective analytically and thus the formulation falls within the computational framework of Simulation-Optimization. SPSA is not limited to the inputs from conventional traffic counts and can be easily extended to account for the measurements of traffic variables supplied by emerging sensors exploiting Information and Communication Technologies (ICT). Numerical experiments have been conducted with a real network, and the results have been analyzed from two different perspectives: performance and solution quality. This allows understanding the behavior of the SPSA algorithm and new variants, which altogether contribute to the aim of adding ICT measures in the future. Their sensitivity to the initial values, the effect of bounding the variables and scaling techniques are going to be analyzed. This paper will report on the results of the numerical experiments, their analyses, conclusions and further research.

The Navamuño peatbog (Sierra de Béjar, western Spain) is a ∼14 ha pseudo-endorheic depression with boundaries defined by a lateral moraine of the Cuerpo de Hombre paleoglacier and fault-line scarps on granite bedrock. The stratigraphy of the Navamuño peatbog system is characterized here using borehole data to a depth of 20 m. An integrated interpretation from direct-push coring, dynamic probing boreholes and handheld auger drillings advances our knowledge of the Navamuño polygenetic infill. Correlating this data with those obtained in other studies of the chronology and evolutionary sequence of the Cuerpo de Hombre paleoglacier has enabled us to establish the sequence of the hydrological system in the Navamuño depression. During the Late Pleistocene (MIS2), the depression was dammed by the Cuerpo de Hombre glacier and fed by its lateral meltwaters, and was filled with glaciolacustrine deposits. The onset of the Holocene in Navamuño is linked to a flat, fluviotorrential plain with episodes of local shallow pond/peat bog sedimentation. This evolutionary sequence is congruent with the age model obtained from available radiocarbon dating, obtaining 19 ages from ∼800 cal yr BP (at depth 1.11 m) to ∼16800 cal yr BP (at depth 15.90–16.0 m). Finally, the sedimentary record enabled interpretation of the environmental changes occurring in this zone during the late glacial (from the Older Dryas to the Younger Dryas) and postglacial (Holocene) stages, placing them within the paleoclimatic context of the Iberian Peninsula and Mediterranean regions., This work was supported by the Spanish Ministry of Economy and Competitiveness (Projects CGL2013-44076-P and CGL2016-78380-P). The authors also wish to acknowledge the help and assistance of the Regional Environment Department (JCyL) and the Local Authority in the village of Candelario. Valenti Turu acknowledges grant ATC013 -and- 2015/2016 from the Government of Andorra.

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Mathematical and simulation models of systems lay at the core of many decision support systems, and their role becomes more critical when the system is more complex. The decision process usually involves optimizing some utility function that evaluates the performance indicators measuring the impacts of the decisions. The complexity of the system directly increases the difficulty when the associated function to be optimized is a non-analytical, non-differentiable, non-linear function that can only be evaluated by simulation. Simulation-optimization techniques are especially suited to these cases, and its use is becoming increasingly used with traffic models, which represent an archetypal case of complex, dynamic systems that exhibit highly stochastic characteristics. In this approach, simulation is used to evaluate the objective function, and it is combined with a non-differentiable optimization technique for solving the associated optimization problem. Of these techniques, one of the most commonly used is Stochastic Perturbation Stochastic Approximation (SPSA). This paper analyses, discusses and presents the computational results from applying this technique in the calibration of traffic simulation models. This study uses variants of the SPSA by replacing the usual gradient approach with a combination of projected gradient and trust region methods. A special approach has also been analyzed for parameter calibration cases in which each variable has a different magnitude.

In this Note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semilinear problems with supercritical nonlinearities in star-shaped domains.