A Theoretical Framework for Lagrangian Descriptors

This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigourous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs. The definition is stated for $n$-dimensional systems with general time dependence, however we rigorously prove that this method reveals the stable and unstable manifolds of hyperbolic points in four particular 2D cases: a hyperbolic saddle point for linear autonomous systems, a hyperbolic saddle point for nonlinear autonomous systems, a hyperbolic saddle point for linear nonautonomous systems and a hyperbolic saddle point for nonlinear nonautonomous systems. We also discuss further rigorous results which show the ability of LDs to highlight additional invariants sets, such as $n$-tori. These results are just a simple extension of the ergodic partition theory which we illustrate by applying this methodology to well-known examples, such as the planar field of the harmonic oscillator and the 3D ABC flow. Finally, we provide a thorough discussion on the requirement of the objectivity (frame-invariance) property for tools designed to reveal phase space structures and their implications for Lagrangian descriptors

Simulating the behavior of the human brain on GPUS

The simulation of the behavior of the Human Brain is one of the most important challenges in computing today. The main problem consists of finding efficient ways to manipulate and compute the huge volume of data that this kind of simulations need, using the current technology. In this sense, this work is focused on one of the main steps of such simulation, which consists of computing the Voltage on neurons’ morphology. This is carried out using the Hines Algorithm and, although this algorithm is the optimum method in terms of number of operations, it is in need of non-trivial modifications to be efficiently parallelized on GPUs. We proposed several optimizations to accelerate this algorithm on GPU-based architectures, exploring the limitations of both, method and architecture, to be able to solve efficiently a high number of Hines systems (neurons). Each of the optimizations are deeply analyzed and described. Two different approaches are studied, one for mono-morphology simulations (batch of neurons with the same shape) and one for multi-morphology simulations (batch of neurons where every neuron has a different shape). In mono-morphology simulations we obtain a good performance using just a single kernel to compute all the neurons. However this turns out to be inefficient on multi-morphology simulations. Unlike the previous scenario, in multi-morphology simulations a much more complex implementation is necessary to obtain a good performance. In this case, we must execute more than one single GPU kernel. In every execution (kernel call) one specific part of the batch of the neurons is solved. These parts can be seen as multiple and independent tridiagonal systems. Although the present paper is focused on the simulation of the behavior of the Human Brain, some of these techniques, in particular those related to the solving of tridiagonal systems, can be also used for multiple oil and gas simulations. Our studies have proven that the optimizations proposed in the present work can achieve high performance on those computations with a high number of neurons, being our GPU implementations about 4× and 8× faster than the OpenMP multicore implementation (16 cores), using one and two NVIDIA K80 GPUs respectively. Also, it is important to highlight that these optimizations can continue scaling, even when dealing with a very high number of neurons.This project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement No. 720270 (HBP SGA1), from the Spanish Ministry of Economy and Competitiveness under the project Computación de Altas Prestaciones VII (TIN2015-65316-P), the Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Programació i Entorns d’Execució Parallels (2014-SGR-1051). We thank the support of NVIDIA through the BSC/UPC NVIDIA GPU Center of Excellence, and the European Union’s Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie Grant Agreement No. 749516.Peer ReviewedPostprint (published version

Aproximación al léxico de la ciencia aplicada en el Renacimiento hispano

In this study we analyze the appearance of technical vocabulary during the spanish Renaissance. Some of the main linguistic characteristics are taken into account from various levels: phonetics, morphology and semantics, with a series of specific examples. Several examples of loanwords are studied from either classic or modern language, chosen from the most prestigious languages of the time.<br><br>En este trabajo se enfoca el surgimiento del vocabulario especializado en el campo de la ciencia aplicada durante el período del renacimiento español. Se analizan algunas de las principales características desde los planos gráfico-fonético, morfológico y semántico, de las que se aportan ejemplos concretos, y se recogen testimonios de préstamos procedentes, tanto de lenguas clásicas, como de otras de prestigio cultural en la época

Aproximación al léxico de la ciencia aplicada en el Renacimiento hispano

In this study we analyze the appearance of technical vocabulary during the spanish Renaissance. Some of the main linguistic characteristics are taken into account from various levels: phonetics, morphology and semantics, with a series of specific examples. Several examples of loanwords are studied from either classic or modern language, chosen from the most prestigious languages of the time.En este trabajo se enfoca el surgimiento del vocabulario especializado en el campo de la ciencia aplicada durante el período del renacimiento español. Se analizan algunas de las principales características desde los planos gráfico-fonético, morfológico y semántico, de las que se aportan ejemplos concretos, y se recogen testimonios de préstamos procedentes, tanto de lenguas clásicas, como de otras de prestigio cultural en la época

Distinguished trajectories in time dependent vector fields

We introduce a new definition of distinguished trajectory that generalises the concepts of fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for identifying distinguished trajectories with hyperbolic and non-hyperbolic types of stability. The definition is implemented numerically and the procedure consist in determining a path of limit coordinates. It has been successfully applied to known examples of distinguished trajectories. In the context of highly aperiodic realistic flows our definition characterises distinguished trajectories in finite time intervals, and states that outside these intervals trajectories are no longer distinguished.Comment: Chaos 19 (2009), 013111-1-013111-1

MPI+OpenMP tasking scalability for the simulation of the human brain

The simulation of the behavior of the Human Brain is one of the most ambitious challenges today with a non-end of important applications. We can find many different initiatives in the USA, Europe and Japan which attempt to achieve such a challenging target. In this work we focus on the most important European initiative (Human Brain Project) and on one of the tools (Arbor). This tool simulates the spikes triggered in a neuronal network by computing the voltage capacitance on the neurons' morphology, being one of the most precise simulators today. In the present work, we have evaluated the use of MPI+OpenMP tasking on top of the Arbor simulator. In this paper, we present the main characteristics of the Arbor tool and how these can be efficiently managed by using MPI+OpenMP tasking. We prove that this approach is able to achieve a good scaling even when computing a relatively low workload (number of neurons) per node using up to 32 nodes. Our target consists of achieving not only a highly scalable implementation based on MPI, but also to develop a tool with a high degree of abstraction without losing control and performance by using MPI+OpenMP tasking.We would like to apreciate the valuable feedback and help provided by Benjamin Cumming and Alexander Peyser. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 720270 (HBP SGA1 and HBP SGA2), from the Spanish Ministry of Economy and Competitiveness under the project Computacion de Altas Prestaciones VII (TIN2015- ´ 65316-P) and the Departament d’Innovacio, Universitats i ´ Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Programacio i Entorns d’Execuci ´ o Paral ´ ·lels (2014-SGR-1051). This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska Curie grand agreement No.749516Peer ReviewedPostprint (author version

Deceleration area and fetal acidemia

Aims: To compare the predictive ability for neonatal acidemia of individual components of intrapartum cardiotocography (CTG) described by National Institute of Child Health and Human Development (NICHD) system and deceleration area. Design: Case-control study. Setting: Spanish tertiary obstetrical hospital. Population: CTG patterns of 102 acidemic fetus (umbilical arterial cord gas pH =7.10, base deficit (BD>48) and 102 nonacidemic controls (umbilical arterial cord gas pH>7.10). Methods: Two reviewers blind to clinical and outcome data analyzed the last thirty minutes before delivery of 204 fetal heart rate (FHR) tracings, extracting those features defined by NICHD and certain measures of FHR decelerations, including deceleration area, not considered by this system. Outcome measures: The primary outcome was the predictive ability of NICHD features and non-NICHD deceleration measures for fetal acidemia. The secondary outcome was the impact of deceleration area in the last 30 min of labor on gasometry components (pH, BD and lactate). Results: Minimal variability (area under the curve (AUC) 0.74), total number of late (AUC: 0.75) and prolonged decelerations (0.77) were the three NICHD features with the greatest predictive ability for fetal acidemia in the last thirty minutes of labor. Total deceleration area demonstrated the highest discrimination power (AUC: 0.83) of all the analyzed elements. For each cm2 the area increases in the last 30 min of labor, pH decreases 0.08 units, BD increases 0.272 mEq/L and lactate 0.183 mEq/L. Conclusions: Total deceleration area showed the greatest predictive ability for fetal acidemia and its measure could help to estimate intrapartum fetal acid-base status

Automating the application data placement in hybrid memory systems

Multi-tiered memory systems, such as those based on Intel® Xeon Phi™processors, are equipped with several memory tiers with different characteristics including, among others, capacity, access latency, bandwidth, energy consumption, and volatility. The proper distribution of the application data objects into the available memory layers is key to shorten the time– to–solution, but the way developers and end-users determine the most appropriate memory tier to place the application data objects has not been properly addressed to date.In this paper we present a novel methodology to build an extensible framework to automatically identify and place the application’s most relevant memory objects into the Intel Xeon Phi fast on-package memory. Our proposal works on top of inproduction binaries by first exploring the application behavior and then substituting the dynamic memory allocations. This makes this proposal valuable even for end-users who do not have the possibility of modifying the application source code. We demonstrate the value of a framework based in our methodology for several relevant HPC applications using different allocation strategies to help end-users improve performance with minimal intervention. The results of our evaluation reveal that our proposal is able to identify the key objects to be promoted into fast on-package memory in order to optimize performance, leading to even surpassing hardware-based solutions.This work has been performed in the Intel-BSC Exascale Lab. Antonio J. Peña is cofinanced by the Spanish Ministry of Economy and Competitiveness under Juan de la Cierva fellowship number IJCI-2015-23266. We would like to thank the Intel’s DCG HEAT team for allowing us to access their computational resources. We also want to acknowledge this team, especially Larry Meadows and Jason Sewall, as well as Pardo Keppel for the productive discussions. We thank Raphaël Léger for allowing us to access the MAXW-DGTD application and its input.Peer ReviewedPostprint (author's final draft

A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics

The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its torsion is totally skew-symmetric. The class of the nearly Kaehler manifolds with respect to the first almost complex structure is of special interest. It is proved that D has a D-parallel torsion and is weak if it is not flat. Some curvature properties of these manifolds are studied.Comment: 18 page