On orthogonal systems of functions
Extension of Hilbert method of linear functional equations to orthogonal systems of functions
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Extension of Hilbert method of linear functional equations to orthogonal systems of functions
The paper proposes the use of the orthogonal arrays for neural network learning. Learning can be seen as a search for the neural weights that give an optimal network performance.
Empirical orthogonal function modeling is explained and applied to identify compact discrete-time nonlinear unsteady aerodynamic models from data generated by an unsteady three-dimensional compressible Navier-Stokes flow solver for an airfoil undergoing various pitching motions. Model structures, model parameter estimates, and model parameter uncertainty estimates for nondimensional lift, drag, and pitching moment coefficient models were determined autonomously and directly from the data. Prediction tests using data that were not used in the modeling process showed that the identified models exhibited excellent prediction capability, which is a strong indicator of an accurate model.
A novel method for three-dimensional flowfield reconstruction is presented that utilizes spectral proper orthogonal decomposition (SPOD). The time-resolved PIV data are acquired in multiple two-dimensional spanwise planes, with adequate streamwise spacing to resolve the out-of-plane wavelength. Knowledge of the out-of-plane phase speed is also required, and for the present case this value was obtained using instantaneous hot-wire measurements. The method is validated by comparing phase-averaged results acquired with a forcing signal to the SPOD reconstructed results using the same data. The method is also applied to data with no forcing applied, and the results are shown to be similar to the forced case. This method is particularly useful for cases in which there are multiple frequencies of interest, or cases in which the phenomena occur over a broad range of frequencies. This method allows reconstruction of the frequencies of interest without the need for a forcing signal, so the flow can be studied in its natural (undisturbed) state.
This presentation discusses Spectral Proper Orthogonal Decomposition (SPOD) of Unsteady Pressure-Sensitive Paint (uPSP) measurements in the Space Launch System (SLS) Ascent Transient Aerodynamics Test (ATAT) and its application in the structural dynamics analysis.
This paper discusses Spectral Proper Orthogonal Decomposition (SPOD) of the Unsteady Pressure-Sensitive Paint (uPSP) measurements in recent NASA Ames wind tunnel test. The uPSP measurements were collected using Innovative Scientific Solutions, Inc. (ISSI) Porous, Fast-Response Pressure-Sensitive Paint (FP-XXX), 40 ISSI four-inch air-cooled Light-Emitting Diodes (LEDs), and 8 Phantom v2512 high-speed cameras at 10,000 frames per second in the Launch Vehicle Demo Test (LVDT) of the Space Launch System (SLS) Block 1B crew vehicle in the 11-by 11-foot transonic test section of the Unitary Plan Wind Tunnel (UPWT) at NASA Ames Research Center in April 2024. Fig. 1 shows the scale model of the SLS launch vehicle installed in the wind tunnel during the test.
Controlling the spectral and polarization response of two-dimensional (2D) crystals is vital for developing ultrathin platforms for compact optoelectronic devices. However, independently tuning optical anisotropy and spectral response remains challenging in conventional semiconductors due to the intertwined nature of their lattice and electronic structures. Here, we report spectra-orthogonal optical anisotropy─where polarization anisotropy is tuned independently of spectral response─in wafer-scale, one-atom-thick 2D molecular crystal (2DMC) monolayers synthesized on monolayer transition-metal dichalcogenide (TMD) crystals. Utilizing the concomitant spectral consistency and structural tunability of perylene derivatives, we demonstrate tunable optical polarization anisotropy in 2DMCs with similar spectral profiles, as confirmed by room-temperature scanning tunneling microscopy and cross-polarized reflectance microscopy. Additional angle-dependent analysis of the single-crystal and polycrystalline molecular domains reveals an epitaxial relationship between the 2DMC and TMD. In conclusion, our results establish a scalable, molecule-based 2D crystalline platform for unique and tunable functionalities unattainable in covalent 2D solids.
Empirical orthogonal functions (EOFs) applied to gridded Earth system data enables users to diagnose modes of variability with relative ease. Yet, many challenges to interpretation exist such that they must be used with awareness and intention when applied to gridded climate data, especially with large ensembles. Utilizing data from two different Earth system modelling large ensemble frameworks, the Energy Exoscale Earth System Model and the Community Earth System Model, as well as reanalysis data, common EOF pitfalls are summarized and discussed. Challenges include erroneous mode swapping, sign flipping, and the temporal variability of the centers of action. For modes of variability with similar contribution to variance, mode swapping is not uncommon. Sign flipping can occur with almost any mode where the pattern is correct, but the sign is arbitrary. Although the variability of the center of action is not necessarily problematic, it potentially complicates interpretation over multi-century timescales. A wide variety of alternative methods to EOFs exist, but fitness-for-purpose must be evaluated. Additionally, illustrations of alternative methods and examples of proper use are provided. Alternative methods fit into three categories: EOF variants, linear methods, and multilinear methods.
Abstract The in vivo continuous evolution system OrthoRep (orthogonal replication) is a powerful strategy for rapid enzyme evolution inSaccharomyces cerevisiaethat diversifies genes at a rate exceeding the endogenous genome mutagenesis rate by several orders of magnitude. However, it is difficult to neofunctionalize genes using OrthoRep partly because of the way selection pressures are applied. Here we combine OrthoRep with optogenetics in a selection strategy we call OptoRep, which allows fine-tuning of selection pressure with light. With this capability, we evolved a truncated form of the endogenous monocarboxylate transporterJEN1 (JEN1t)into a de novo mevalonate importer. We demonstrate the functionality of the evolvedJEN1t(JEN1t Y180C/G ) in the production of farnesene, a renewable aviation biofuel, from mevalonate fed to fermentation media or produced by microbial consortia. This study shows that the light-induced complementation of OptoRep may improve the ability to evolve functions not currently accessible for selection, while its fine tunability of selection pressure may allow the continuous evolution of genes whose desired function has a restrictive range between providing effective selection and cellular viability.
The second-order optical susceptibility of semiconductors $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ finds application in metrology, spectroscopy, telecommunications, material characterization, and quantum information. Pioneering calculations of $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ utilized non-orthogonal Gaussian orbitals centered at atoms. That formulation transitioned into plane-wave-based algorithms as time went by. As of late, nevertheless, multiple tools for calculating optical susceptibilities have recast the problem using Wannier (i.e. localized) orbitals, making a comeback onto frameworks based on localized basis sets. Here, in this work, we present an approach for calculating $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ reliant on numerical pseudo-atomic orbitals (PAOs) within perturbation theory in the velocity gauge. Its salient feature is a calculation of ‘Slater–Koster-like’ two-center integrals of the momentum operator in between PAOs identified by symmetry. The approach was successfully tested on paradigmatic cubic silicon carbide (3C-SiC) and gallium arsenide, for which linear responses are contributed as well.
Operator spreading under stroboscopic time evolution under a unitary is studied. An operator Krylov space is constructed and mapped to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parametrizing the ITFIM. The relations between the OPUC and spectral functions are summarized and several applications are presented. These include derivation of analytic expressions for the OPUC under persistent m-periodic dynamics, and the numerical construction of the OPUC for autocorrelations of the homogeneous Floquet-Ising model as well as the Z 3 clock model. The numerically obtained Krylov angles of the Z 3 clock model with long-lived period tripled autocorrelations show a spatial periodicity of six, and this observation is used to develop an analytically solvable model for the ITFIM that mimics this behavior.
One can improve predictability in the unknown domain by combining forecasts of imperfect complex computational models using a Bayesian statistical machine learning framework. In many cases, however, the models used in the mixing process are similar. In addition to contaminating the model space, the existence of such similar, or even redundant, models during the multimodeling process can result in misinterpretation of results and deterioration of predictive performance. In this paper we describe a method based on the principal component analysis that eliminates model redundancy. We show that by adding model orthogonalization to the proposed Bayesian model combination framework, one can arrive at better prediction accuracy and reach excellent uncertainty quantification performance.
Genetically engineered microbes have the potential to increase efficiency in the bioeconomy by overcoming growth-limiting production stress. Screens of gene perturbation libraries against production stressors can identify high-value engineering targets, but follow-up experiments needed to guard against false positives are slow and resource-intensive. In principle, the use of orthogonal gene perturbation approaches could increase recovery of true positives over false positives because the strengths of one technique compensate for the weaknesses of the other, but, in practice, two parallel screens are rarely performed at the genome scale. Here, we screen genome-scale CRISPRi (CRISPR interference) knockdown and transposon insertion libraries of the bioenergy-relevant Alphaproteobacterium, Zymomonas mobilis, against growth inhibitors commonly found in deconstructed plant material. Integrating data from the two gene perturbation techniques, we established an approach for defining engineering targets with high specificity. This allowed us to identify all known genes in the cytochrome bc1 and cytochrome c synthesis pathway as potential targets for engineering resistance to phenolic acids under anaerobic conditions, a subset of which we validated using precise gene deletions. Strikingly, this finding is specific to the cytochrome bc1 and cytochrome c pathway and does not extend to other branches of the electron transport chain. We further show that exposure of Z. mobilis to ferulic acid causes substantial remodeling of the cell envelope proteome, as well as the downregulation of TonB-dependent transporters. Our work provides a generalizable strategy for identifying high-value engineering targets from gene perturbation screens that is broadly applicable.
Classifies model Empirical Orthogonal Functions (EOFs) of sea-level pressure as East Atlantic (EA) or Scandinavian (SCA) patterns using subspace projection, correlation, and k-means methods.
A colinear Second-Harmonic Orthogonal Polarized (SHOP) interferometer diagnostic capable of making electron areal density measurements of plasmas formed in Magnetically Insulated Transmission Lines (MITLs) has been developed.
Photosystems are incredible biological machines that use sunlight to drive the conversion of carbon dioxide to sugar. The amount of sunlight available for photosynthesis sometimes exceeds the amount of energy plants can use. This excess energy has to be safely dissipated through non-productive biological processes. The ultimate goal of this project is to understand whether we can utilize that otherwise unused excess energy. In our previous work, we showed that, in principle, it is possible to attach a catalyst to photosystem I and generate H2 using light. Our current strategy is to genetically fuse parts of the photosystem I complex with a recently discovered oxygen-tolerant [FeFe] hydrogenase. Our rationale is that such chimeric proteins may potentially result in the natural incorporation of the photosystem I-hydrogenase link using the inherent genetic machinery of the cell. In this project, we aim to verify that light-driven hydrogen production in this construction is possible. Throughout the project, we designed nanoconstructs that showcase the plausibility of this technology, at least in vitro. We take advantage of these constructs to investigate details of the coupling between photosystem I and a H2-producing enzyme called [FeFe] hydrogenase. This part of the project reveals details of the electron transfer between photosystem I and the attached hydrogenase, providing information that can lead to new strategies for improved biological photocatalysis. We also researched efficient and robust tethering of the [FeFe] hydrogenase to photosystem I in cyanobacteria. This work will highlight successful design strategies to guide the future development of photosynthetic biohybrids. Uncovering the principles governing the utilization of otherwise unusable energy significantly further our understanding of cyanobacterial photosynthesis. The work proposed establishes the feasibility of diverting excess energy under high light conditions to orthogonal enzymatic pathways and set design rules for efficient utilization of such a strategy for scientific and industrial applications in biosensing, renewable energy, and high-value chemicals production. The work addresses the DOE-BES Photosynthetic Systems program goal to develop a multidimensional understanding of photosystems that would provide specific metrics that instruct strategies for improving biological photosynthesis and for guiding the future development of bioreactors and biomimetic energy systems.
Arbitrary quasi-orthogonals for calculating flow distribution in meridional plane of turbomachine
Turbomachine blade surface flow distribution analysis by arbitrary quasi-orthogonals - radial inflow turbine Fortran computer program