Search NASA⌕ Search

SEARCH · Search NASA

Results for “matching complex”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Model predictive control for robust quantum state preparation

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Regional specialization in prefrontal cortex manifests in the reliability of task progression codes

The brain has the remarkable ability to guide the performance of complex tasks. Distinct prefrontal cortical areas make specific contributions to this ability, with the orbitofrontal cortex (OFC) critical for processing information related to trial outcomes and the dorsomedial prefrontal cortex (dmPFC) critical for sustained effort and selecting the right action at the right time. Yet, in both areas, neural activity represents both outcome- and action-related quantities. How similar neural representations support different functions remains unclear. Here, we compared OFC and dmPFC activity in rats performing a spatial alternation task. We show that, in contrast to other task-related variables, task progression is represented in both areas, but with distinct patterns of across-trial reliability that match each area’s previously documented functional specialization. Our results indicate that the engagement of reliable, task-phase-specific activity patterns differs across prefrontal regions in a manner well suited to engage different computations at different times.

Biological and medical sciences↗
DOE OSTI2022

Illustrating galaxy–halo connection in the DESI era with illustrisTNG

ABSTRACT We employ the hydrodynamical simulation illustrisTNG to inform the galaxy–halo connection of the Luminous Red Galaxy (LRG) and Emission Line Galaxy (ELG) samples of the Dark Energy Spectroscopic Instrument (DESI) survey at redshift z ∼ 0.8. Specifically, we model the galaxy colours of illustrisTNG and apply sliding DESI colour–magnitude cuts, matching the DESI target densities. We study the halo occupation distribution (HOD) model of the selected samples by matching them to their corresponding dark matter haloes in the illustrisTNG dark matter run. We find the HOD of both the LRG and ELG samples to be consistent with their respective baseline models, but also we find important deviations from common assumptions about the satellite distribution, velocity bias, and galaxy secondary biases. We identify strong evidence for concentration-based and environment-based occupational variance in both samples, an effect known as ‘galaxy assembly bias’. The central and satellite galaxies have distinct dependencies on secondary halo properties, showing that centrals and satellites have distinct evolutionary trajectories and should be modelled separately. These results serve to inform the necessary complexities in modelling galaxy–halo connection for DESI analyses and also prepare for building high-fidelity mock galaxies. Finally, we present a shuffling-based clustering analysis that reveals a 10–15 ${{\ \rm per\ cent}}$ excess in the LRG clustering of modest statistical significance due to secondary galaxy biases. We also find a similar excess signature for the ELGs, but with much lower statistical significance. When a larger hydrodynamical simulation volume becomes available, we expect our analysis pipeline to pinpoint the exact sources of such excess clustering signatures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Assimilation of a Coordinated Fleet of Uncrewed Aircraft System Observations in Complex Terrain: Observing System Experiments

Uncrewed aircraft system (UAS) observations from the Lower Atmospheric Profiling Studies at Elevation–A Remotely-Piloted Aircraft Team Experiment (LAPSE-RATE) field campaign were assimilated into a high-resolution configuration of the Weather Research and Forecasting (WRF) Model. The impact of assimilating targeted UAS observations in addition to surface observations was compared to that obtained when assimilating surface observations alone using observing system experiments (OSEs) for a terrain-driven flow case and a convection initiation (CI) case observed within Colorado’s San Luis Valley (SLV). The assimilation of UAS observations in addition to surface observations results in a clear increase in skill for both flow regimes over that obtained when assimilating surface observations alone. For the terrain-driven flow case, the UAS observations improved the representation of thermal stratification across the northern SLV, which produced stronger upvalley flow over the eastern half of the SLV that better matched the observations. For the CI case, the UAS observations improved the representation of the pre-convective environment by reducing dry biases across the SLV and over the surrounding terrain. This led to earlier CI and more organized convection over the foothills that spilled outflows into the SLV, ultimately helping to increase low-level convergence and CI there. In addition, the importance of UAS capturing an outflow that originated over the Sangre de Cristo Mountains and triggered CI is discussed. These outflows and subsequent CI were not well captured in the simulation that assimilated surface observations alone. We report that observations obtained with a fleet of UAS are shown to notably improve high-resolution analyses and short-term predictions of two very different mesogamma-scale weather events.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Unconventional surface state pairs in a high-symmetry lattice with anti-ferromagnetic band-folding

Many complex magnetic structures in a high-symmetry lattice can arise from a superposition of well-defined magnetic wave vectors. These “multi-q” structures have garnered much attention because of interesting real-space spin textures such as skyrmions. However, the role multi-q structures play in the topology of electronic bands in momentum space has remained rather elusive. Here we show that the type-I anti-ferromagnetic 1q, 2q and 3q structures in an face-centered cubic sublattice with band inversion, such as NdBi, can induce unconventional surface state pairs inside the band-folding hybridization bulk gap. Our density functional theory calculations match well with the recent experimental observation of unconventional surface states with hole Fermi arc-like features and electron pockets below the Neel temperature. We further show that these multi-q structures have Dirac and Weyl nodes. Our work reveals the special role that band-folding from anti-ferromagnetism and multi-q structures can play in developing new types of surface states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A contactless in situ EFISH method for measuring electrostatic potential profile of semiconductor/electrolyte junctions

In photoelectrochemical cells, promising devices for directly converting solar energy into storable chemical fuels, the spatial variation of the electrostatic potential across the semiconductor–electrolyte junction is the key parameter that determines the cell performance. In principle, electric field induced second harmonic generation (EFISH) provides a contactless in situ spectroscopic tool to measure the spatial variation of electrostatic potential. However, the total second harmonic generation (SHG) signal contains the contributions of the EFISH signals of semiconductor space charge layer and the electric double layer, in addition to the SHG signal of the electrode surface. The interference of these complex quantities hinders their analysis. In this work, to understand and deconvolute their contributions to the total SHG signals, bias-dependent SHG measurements are performed on the rutile TiO2(100)–electrolyte junction as a function of light polarization and crystal azimuthal angle (angle of the incident plane relative to the crystal [001] axis). A quadratic response between SHG intensity and the applied potential is observed in both the accumulation and depletion regions of TiO2. The relative phase difference and amplitude ratio are extracted at selected azimuthal angles and light polarizations. At 0° azimuthal angle and s-in–p-out polarization, the SHG intensity minimum has the best match with the TiO2 flatband potential due to the orthogonal relative phase difference between bias-dependent and bias-independent SHG terms. We further measure the pH-dependent flatband potential and probe the photovoltage under open circuit conditions using the EFISH technique, demonstrating the capability of this contactless method for measuring electrostatic potential at semiconductor–electrolyte junctions.

Chemistry↗
DOE OSTI2021

Distributed Acoustic Sensing Based on Coherent Microwave Photonics Interferometry

A microwave photonics method has been developed for measuring distributed acoustic signals. This method uses microwave-modulated low coherence light as a probe to interrogate distributed in-fiber interferometers, which are used to measure acoustic-induced strain. By sweeping the microwave frequency at a constant rate, the acoustic signals are encoded into the complex microwave spectrum. The microwave spectrum is transformed into the joint time–frequency domain and further processed to obtain the distributed acoustic signals. The method is first evaluated using an intrinsic Fabry Perot interferometer (IFPI). Acoustic signals of frequency up to 15.6 kHz were detected. The method was further demonstrated using an array of in-fiber weak reflectors and an external Michelson interferometer. Two piezoceramic cylinders (PCCs) driven at frequencies of 1700 Hz and 3430 Hz were used as acoustic sources. The experiment results show that the sensing system can locate multiple acoustic sources. The system resolves 20 nε when the spatial resolution is 5 cm. The recovered acoustic signals match the excitation signals in frequency, amplitude, and phase, indicating an excellent potential for distributed acoustic sensing (DAS).

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Characteristics of thermospheric infrasound predicted using ray tracing and weakly non-linear waveform analyses

Infrasonic signals refracted by thermal gradients in the rarefied upper atmosphere are modeled using a combination of ray tracing and weak shock theory to develop an understanding of thermospheric infrasound signals produced by energetic, transient sources. Canonical arrival structures in the form of u-wave signatures are identified for returns refracted at lower altitudes within the thermosphere, and possible multi-pathing produced by effective sound speed inflections are investigated to elucidate more complex arrival structures, which are found to be spatially localized. Furthermore, variability in the source characteristics is investigated and it is found that whereas some waveform phase information is lost due to finite amplitude effects, arrival characteristics are strongly dependent on the peak overpressure near the source. Variability in the propagation path is considered using archived atmospheric specifications and implies that despite uncertainties related to the dynamic and sparsely sampled nature of the atmosphere, thermospheric signatures might be useful in estimating the yield for explosive sources. Last, thermospheric arrivals from a failed rocket launch, as well as those from several large chemical explosions, are analyzed and it is found that qualitative trends match those predicted, and analyses here provide additional insight into such signatures.

42 ENGINEERING↗
DOE OSTI2021

The agglomeration and dispersion dichotomy of human settlements on Earth

Human settlements on Earth are scattered in a multitude of shapes, sizes and spatial arrangements. These patterns are often not random but a result of complex geographical, cultural, economic and historical processes that have profound human and ecological impacts. However, little is known about the global distribution of these patterns and the spatial forces that creates them. This study analyses human settlements from high-resolution satellite imagery and provides a global classification of spatial patterns. We find two emerging classes, namely agglomeration and dispersion. In the former, settlements are fewer than expected based on the predictions of scaling theory, while an unexpectedly high number of settlements characterizes the latter. To explain the observed spatial patterns, we propose a model that combines two agglomeration forces and simulates human settlements’ historical growth. Our results show that our model accurately matches the observed global classification (F1: 0.73), helps to understand and estimate the growth of human settlements and, in turn, the distribution and physical dynamics of all human settlements on Earth, from small villages to cities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Entanglement rearrangement in self-consistent nuclear structure calculations

Background: Entanglement plays a central role in a diverse array of increasingly important research areas, including quantum computation, simulation, measurement, sensing, and communication. Extensive suites of investigations have been performed to better understand entanglement in atomic and molecular quantum many-body systems, while the exploration of entanglement in the structure of nuclei and their reactions is presently in its infancy. Purpose: The goal of this work is to begin investigating the entanglement properties of nuclei from first-principles nuclear many-body calculations. We attempt to identify common features and emergent structures of entanglement that could ultimately lead to new and natural many-body schemes. With an eye toward quantum accelerators in future hybrid-supercomputers, criteria for partitioning nuclear many-body calculations into quantum and classical components may provide advantages in future large-scale computations. Along the way we look for explanations of the relative success of phenomenological models such as the nuclear shell model, and for better ways to match to low-energy nuclear effective field theories and lattice QCD calculations to nuclear many-body techniques that are based upon entanglement. Method: We explore the entanglement between single-particle states in 4 He and 6 He. The patterns of entanglement emerging from different single-particle bases are compared, and possible links with the convergence of observables are explored, in particular, ground-state energies. The nuclear wave functions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases exhibiting different degrees of complexity are determined, in particular, harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases. Specifically, single-orbital entanglement entropy, two-orbital mutual information, and negativity are studied. Results: The entanglement structures in 4 He and 6 He are found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters we have worked with. In particular a core-valence structure clearly emerges from the full no-core calculation of 6 He. Here, the two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces. Conclusions: Measures of one- and two-nucleon entanglement are found to be useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Optimizing metaproteomics database construction: lessons from a study of the vaginal microbiome

Metaproteomics, a method for untargeted, high-throughput identification of proteins in complex samples, provides functional information about microbial communities and can tie functions to specific taxa. Metaproteomics often generates less data than other omics techniques, but analytical workflows can be improved to increase usable data in metaproteomic outputs. Identification of peptides in the metaproteomic analysis is performed by comparing mass spectra of sample peptides to a reference database of protein sequences. Although these protein databases are an integral part of the metaproteomic analysis, few studies have explored how database composition impacts peptide identification. Here, we used cervicovaginal lavage (CVL) samples from a study of bacterial vaginosis (BV) to compare the performance of databases built using six different strategies. We evaluated broad versus sample-matched databases, as well as databases populated with proteins translated from metagenomic sequencing of the same samples versus sequences from public repositories. Smaller sample-matched databases performed significantly better, driven by the statistical constraints on large databases. Additionally, large databases attributed up to 34% of significant bacterial hits to taxa absent from the sample, as determined orthogonally by 16S rRNA gene sequencing. We also tested a set of hybrid databases which included bacterial proteins from NCBI RefSeq and translated bacterial genes from the samples. These hybrid databases had the best overall performance, identifying 1,068 unique human and 1,418 unique bacterial proteins, ~30% more than a database populated with proteins from typical vaginal bacteria and fungi. Our findings can help guide the optimal identification of proteins while maintaining statistical power for reaching biological conclusions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Local rare-earth dopant structure in a complex-oxide/semiconductor heterojunction: Molecular beam epitaxy grown Yb-doped SrTiO3 on Si(001)

We have investigated the structural and electronic properties of Yb-doped SrTiO3/Si(001) grown by molecular beam epitaxy. Other rare-earth donor dopants that result in n-type conductivity typically substitute for Sr at the A-sites in the perovskite lattice. In contrast, Yb has been found to substitute predominantly for Ti at the perovskite B-sites based on data from atomically resolved scanning transmission electron microscopy and spectroscopy, as well as extended x-ray absorption fine structure. Yb exhibits two distinct charge states as determined by x-ray absorption spectroscopy and associated modeling, +2.7 and +2.1. These aliovalent substitutional dopants are compensated by donor electrons from oxygen vacancies that form during epitaxial film growth. An atom beam flux mismatch was present during film depositions because it was assumed that Yb would occupy A-sites, leading to a flux matching formula given by Yb + Sr = Ti. However, the formation of YbTi rather than YbSr results in Sr vacancies and extraneous (i.e. non-lattice) Ti atoms in the films, or on the film surfaces. The presence of these defects, together with oxygen vacancies, leads to deep-level electron traps that were detected by resonant photoemission and much higher sheet resistance than that associated with, for instance, La-doped films.

Chambers, Scott A. (ORCID:000000025415043X)↗
DOE OSTI2024

Establishing performance metrics for quantitative non-targeted analysis: a demonstration using per- and polyfluoroalkyl substances

Abstract Non-targeted analysis (NTA) is an increasingly popular technique for characterizing undefined chemical analytes. Generating quantitative NTA (qNTA) concentration estimates requires the use of training data from calibration “surrogates,” which can yield diminished predictive performance relative to targeted analysis. To evaluate performance differences between targeted and qNTA approaches, we defined new metrics that convey predictive accuracy, uncertainty (using 95% inverse confidence intervals), and reliability (the extent to which confidence intervals contain true values). We calculated and examined these newly defined metrics across five quantitative approaches applied to a mixture of 29 per- and polyfluoroalkyl substances (PFAS). The quantitative approaches spanned a traditional targeted design using chemical-specific calibration curves to a generalizable qNTA design using bootstrap-sampled calibration values from “global” chemical surrogates. As expected, the targeted approaches performed best, with major benefits realized from matched calibration curves and internal standard correction. In comparison to the benchmark targeted approach, the most generalizable qNTA approach (using “global” surrogates) showed a decrease in accuracy by a factor of ~4, an increase in uncertainty by a factor of ~1000, and a decrease in reliability by ~5%, on average. Using “expert-selected” surrogates ( n = 3) instead of “global” surrogates ( n = 25) for qNTA yielded improvements in predictive accuracy (by ~1.5×) and uncertainty (by ~70×) but at the cost of further-reduced reliability (by ~5%). Overall, our results illustrate the utility of qNTA approaches for a subclass of emerging contaminants and present a framework on which to develop new approaches for more complex use cases. Graphical Abstract

Pu, Shirley (ORCID:0000000201223797)↗
DOE OSTI2023

Ultrahigh performance LC/FT-MS non-targeted screening for biomass burning organic aerosol with MZmine2 and MFAssignR

In recent years, ultrahigh performance liquid chromatography Fourier transform mass spectrometry (LC/FT-MS) based non-targeted screening (NTS) methods have become increasingly popular for comprehensive analysis of complex organic mixtures. However, applying these methods for environmental complex mixture analysis is challenging due to the extreme complexity of natural samples and a lack of standard samples or surrogates for environmental complex mixtures. Furthermore, limited molecular markers in the databases and insufficient data processing software workflows make the application of these methods more challenging for environmental complex mixtures. In this work, we implement a new NTS data processing workflow to process data collected from ultrahigh performance liquid chromatography and Fourier transform Orbitrap Elite Mass Spectrometry (LC/FT-MS) by combining MZmine2 and MFAssignR, two opensource data processing tools and commercial Mesquite liquid smoke as a surrogate for biomass burning organic aerosol. MZmine2.53 data extraction followed MFAssignR molecular formula assignment offered noise free and highly accurate 1733 individual molecular formulas presented in liquid smoke with 4906 molecular species, including isomers. The results of this new approach were consistent with the results of direct infusion FT-MS analysis confirming its reliability. Over 90% of the molecular formulas presented in mesquite liquid smoke were matched with the molecular formulas of ambient biomass burning organic aerosol. This suggests the potential use of commercial liquid smoke as a surrogate for biomass burning organic aerosol research. Furthermore, the presented method significantly improves the identification of the molecular composition of biomass burning organic aerosol by successfully addressing some of the limitations related to the data analysis and giving a semi quantitative insight into the analysis.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote—and, in some cases, may be necessary for—the self-assembly of a binary cocrystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of nearly hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Formal Experimentation and Analysis of Handheld RFID Readers as a Tool for Nuclear Material Accounting

Commercial, off-the-shelf Radio Frequency Identification (RFID) systems have been successfully deployed for inventory tracking in numerous industries, but their viability in the tracking of complex environments containing nuclear material is less understood. Of primary interest in this setting is a RFID tracking system for nuclear material accounting which can reliably identify as many tags as possible with high accuracy, while also reducing an operator’s exposure to radiation. In this work, we develop a formal statistical approach to identify relevant handheld RFID reader settings which optimize tagging performance. To achieve this goal, we design a full factorial split-plot experiment for a static shelf configuration scene with 50 randomly placed nuclear material containers affixed with RFID tags. We use Bayesian inference to fit a second-order response surface model which expresses the probability of a successful match for each container as a function of the experimental factors. Such effects are allowed to vary across individual containers and the containers’ population in its entirety to estimate overall effects. Uncertainties of estimates and predictions are quantified via their corresponding posterior distributions. Following extensive model checking and validation, the fitted model is used to identify experimental factors which maximize matching probabilities at both the container-level and for the full shelf configuration scene. We also analyze sensitivity of performance to relevant factors.

25 ENERGY STORAGE↗
DOE OSTI2026

Thermally Stable Co@C3N4 Single-Atom Catalysts for CO Oxidation: Atomic-Level Insights into Structure and Activity

Single Co atoms supported on C3N4 (Co@C3N4) have demonstrated high activity and selectivity in photocatalysis. However, the investigation of structure–function relationships and reaction mechanisms under photocatalytic conditions is very challenging due to the complex conditions of light absorption, charge transfer, and catalysis. In this study, we employed thermal CO oxidation as a prototypical probe reaction to benchmark the intrinsic catalytic performance and track the active-site evolution of Co@C3N4. Single Co atoms were identified and shown to be the catalytically active sites for CO oxidation based on control experiments and isotope-labeling experiments. The Co sites remained atomically dispersed before, during, and after the reaction with temperatures up to 400 °C, as established by in situ X-ray absorption fine structure (XAFS) combined with density functional theory (DFT), FDMNES simulations, and dynamic-time-warping (DTW)-assisted X-ray absorption near edge structure (XANES) matching. Together with theoretical calculations, the integrated analysis reveals a stable coordination environment under reaction conditions, which correlates with sustained activity, establishing Co@C3N4 single-atom catalysts as thermally stable CO oxidation catalysts. Beyond these findings, the current study provides a workflow for unambiguously assigning active sites in Co@C3N4 for thermal CO oxidation. This workflow will aid the understanding of their behavior in photocatalysis in the future, where light-driven dynamics obscure direct structure–function links. Notably, this study provides fundamental insights for the rational design of robust single-atom catalysts and a foundation for the broader application of Co@C3N4 catalysts in oxidation reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Information Processing Capacity of Spintronic Oscillator

Physical reservoir computing is a framework that enables energy‐efficient information processing by using physical systems. Nonlinear dynamics in physical systems provide a computational capability that is unique to reservoirs. It is, however, difficult to find an appropriate task for a reservoir because of the complexity of nonlinear information processing. The information processing capacity has recently been used to clarify systematically the tasks that are solved by reservoirs; it quantifies the memory capacity of reservoirs in accordance with the order of nonlinearity. Herein, an experimental evaluation of the information processing capacity of a spintronic oscillator consisting of nanostructured ferromagnets is reported. The spintronic reservoir state is electrically manipulated by adding a delayed‐feedback circuit. The total capacity reaches a maximum of 5.6 at the edge of the echo state property. A trade‐off between the linear and nonlinear components of the capacity is also found. The result can be used to better understand the nonlinear information processing in reservoirs and to find good matches between reservoirs and tasks. As an example, a function‐approximation task is performed and it is found that it can be efficiently solved when the reservoir state is appropriately tuned so that its information processing capacity matches that of the task.

97 MATHEMATICS AND COMPUTING↗