Classical Mapping Methods Research Articles

Simulation of quantum shortcuts to adiabaticity by classical oscillators

It is known that the dynamics and geometric phase of a quantum system can be simulated by classical coupled oscillators using the quantum−classical mapping method without loss of physics. In this work, we show that this method can also be used to simulate the schemes of quantum shortcuts to adiabaticity, which can quickly achieve the adiabatic effect through a non-adiabatic process. By mapping quantum systems by classical oscillators, two schemes, Berry’s “transitionless quantum driving” and the Lewis−Riesenfeld invariant method, are simulated by a corresponding transitionless classical driving method, which keeps adiabatic phase trajectories and acquires Hannay’s angle and the classical Lewis−Riesenfeld invariant method by manipulating the configurations of classical coupled oscillators. The classical shortcuts to adiabaticity for the two coupled classical oscillators, which is the classical version of a spin-1/2 in a magnetic field, is employed to illustrate our results and compared with quantum shortcuts-to-adiabaticity methods.

Refining the glacial lake coverage of the southern Laurentide ice margin using Lidar-DEM based reconstructions: The case of Lake Obedjiwan in south-central Quebec, Canada

The existence of former glacial lakes remains poorly documented in the remote regions of the Canadian Shield where the dense forest cover and poor access complicate classical mapping methods. Here we use a high-resolution Digital Elevation Model (DEM; 1 m/pixel) based on LiDAR data to map Quaternary deposits and landforms in the vicinity of the Gouin reservoir in the Laurentian Highlands of Quebec (Canada). A total of 598 raised shorelines were identified, providing new evidence for the presence of a large proglacial lake – Lake Obedjiwan – that formed in front of the northward retreating Laurentide ice sheet margin during the last deglaciation, a few kilometers east of the larger Lake Ojibway that covered extensive areas in northern Ontario and Quebec. The elevation of shorelines outlines a tilted water plane that depicts the influence of the glacio-isostatic adjustment across the basin, with shorelines ranging from 409 m in the south to 439 m in the north. The calculated uplift gradient of 0.78 m/km indicates that the lake developed during the early stages of the deglaciation. Our reconstruction constrains the full areal extent and maximum elevation of the lake, which covered an area of 1800 km2 and reached an elevation of 450 m. It also indicates that Lake Obedjiwan developed independently from Lake Ojibway. The lake-surface elevation was controlled by an outlet located in the southeastern part of the basin where a topographic depression lying at an elevation of 390 m routed meltwater overflow southward through the Saint-Maurice River and into the St. Lawrence River. Another important outlet is located in the northernmost part of the basin and ice retreat beyond this topographic depression (427 m) caused the drawdown of the Lake Obedjiwan, which drained westward into Lake Ojibway. This discharge added around 19 km3 of meltwater, an event that likely impacted the hydrological budget and sedimentology of Lake Ojibway. The results suggest that other glacial lakes probably developed along the southern LIS ice margin and that the approach developed in this study may contribute to the refinement of their areal coverage and improve paleogeographic reconstructions.

Mapping rainfall hazard based on rain gauge data: an objective cross-validation framework for model selection

Abstract. We propose an objective framework for selecting rainfall hazard mapping models in a region starting from rain gauge data. Our methodology is based on the evaluation of several goodness-of-fit scores at regional scale in a cross-validation framework, allowing us to assess the goodness-of-fit of the rainfall cumulative distribution functions within the region but with a particular focus on their tail. Cross-validation is applied both to select the most appropriate statistical distribution at station locations and to validate the mapping of these distributions. To illustrate the framework, we consider daily rainfall in the Ardèche catchment in the south of France, a 2260 km2 catchment with strong inhomogeneity in rainfall distribution. We compare several classical marginal distributions that are possibly mixed over seasons and weather patterns to account for the variety of climatological processes triggering precipitation, and several classical mapping methods. Among those tested, results show a preference for a mixture of Gamma distribution over seasons and weather patterns, with parameters interpolated with thin plate spline across the region.

The FTMap family of web servers for determining and characterizing ligand-binding hot spots of proteins

FTMap is a computational mapping server that identifies binding hot spots of macromolecules-i.e., regions of the surface with major contributions to the ligand-binding free energy. To use FTMap, users submit a protein, DNA or RNA structure in PDB (Protein Data Bank) format. FTMap samples billions of positions of small organic molecules used as probes, and it scores the probe poses using a detailed energy expression. Regions that bind clusters of multiple probe types identify the binding hot spots in good agreement with experimental data. FTMap serves as the basis for other servers, namely FTSite, which is used to predict ligand-binding sites, FTFlex, which is used to account for side chain flexibility, FTMap/param, used to parameterize additional probes and FTDyn, for mapping ensembles of protein structures. Applications include determining the druggability of proteins, identifying ligand moieties that are most important for binding, finding the most bound-like conformation in ensembles of unliganded protein structures and providing input for fragment-based drug design. FTMap is more accurate than classical mapping methods such as GRID and MCSS, and it is much faster than the more-recent approaches to protein mapping based on mixed molecular dynamics. By using 16 probe molecules, the FTMap server finds the hot spots of an average-size protein in <1 h. As FTFlex performs mapping for all low-energy conformers of side chains in the binding site, its completion time is proportionately longer.

An improved classical mapping method for homogeneous electron gases at finite temperature.

We introduce a modified classical mapping method to predict the exchange-correlation free energy and the structure of homogeneous electron gases (HEG) at finite temperature. With the classical map temperature parameterized on the basis of the quantum Monte Carlo simulation data for the correlation energy and exact results at high and low temperature limits, the new theoretical procedure greatly improves the classical mapping method for correlating the energetic properties HEG over a broad range of thermodynamic conditions. Improvement can also be identified in predicting the long-range components of the spin-averaged pair correlation functions.

A bridge-functional-based classical mapping method for predicting the correlation functions of uniform electron gases at finite temperature

Efficient and accurate prediction of the correlation functions of uniform electron gases is of great importance for both practical and theoretical applications. This paper presents a bridge-functional-based classical mapping method for calculating the correlation functions of uniform spin-unpolarized electron gases at finite temperature. The bridge functional is formulated by following Rosenfeld's universality ansatz in combination with the modified fundamental measure theory. The theoretical predictions are in good agreement with recent quantum Monte Carlo results but with negligible computational cost, and the accuracy is better than a previous attempt based on the hypernetted-chain approximation. We find that the classical mapping method is most accurate if the effective mass of electrons increases as the density falls.

A new exchange–correlation functional free of delocalization and static correlation errors

Predicting the correct binding curves of H2(+) and H2 systems presents a great challenge in current applications of electronic density functional theory. Here we report a new functional for the exchange-correlation energy based on the weighted density approximation and the classical mapping method. With the exact sum rule for the exchange-correlation hole and accurate correlation functions of uniform electrons as the input, the new functional is free of delocalization and static correlation errors. It yields the exact results for any one-electron systems and the correct asymptotic limit of the binding energy between hydrogen atoms.

Virtual circle mapping for master–slave hand systems

The classical mapping methods were developed based on anthropomorphic robot hands. Normally, they are not applicable or cannot provide satisfactory performance if the robot hand is non-anthropomorphic. This paper presents a virtual circle mapping method dealing with the three-fingered non-anthropomorphic robot hand. The basic idea is to express the operator's motion by a virtual circle determined by the three fingertips. Four sets of parameters are used to describe the circle: circle radius, central angles, circle center and circle orientation. By transforming the four sets of parameters from the human frame to the robot frame, the information of relative positions between the fingertips is delivered. The robot fingertip positions are then computed according to the transformed parameters. The concept is introduced and implemented on a specific three-fingered non-anthropomorphic robot hand. The simulation results and the experiments have shown that the proposed method is able to obtain better workspace matching and, thus, the operator can tele-control the robot hand more intuitively.

Determining and representing width of soil boundaries using electrical conductivity and MultiGrid

In classical soil mapping, map unit boundaries are considered crisp even though all experienced survey personnel are aware of the fact, that soil boundaries really are transition zones of varying width. However, classification of transition zone width on site is difficult in a practical survey. The objective of this study is to present a method for determining soil boundary width and a way of representing continuous soil boundaries in GIS. A survey was performed using the non-contact conductivity meter EM38 from Geonics Inc., which measures the bulk Soil Electromagnetic Conductivity (SEC). The EM38 provides an opportunity to classify the width of transition zones in an unbiased manner. By calculating the spatial rate of change in the interpolated EM38 map across the crisp map unit delineations from a classical soil mapping, a measure of transition zone width can be extracted. The map unit delineations are represented as transition zones in a GIS through a concept of multiple grid layers, a MultiGrid. Each layer corresponds to a soil type and the values in a layer represent the percentage of that soil type in each cell. As a test, the subsoil texture was mapped at the Vindum field in Denmark using both the classical mapping method with crisp representation of the boundaries and the new map with MultiGrid and continuous boundaries. These maps were then compared to an independent reference map of subsoil texture. The improvement of the prediction of subsoil texture, using continuous boundaries instead of crisp, was in the case of the Vindum field, 15%.