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A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.
Investigating the structural evolution and phase transformation of iron oxides is crucial for gaining a deeper understanding of geological changes on diverse planets and preparing oxide materials suitable for industrial applications. In this study, we employed in-situ heating techniques in conjunction with transmission electron microscopy (TEM) observations and ex-situ characterization to thoroughly analyze the thermal solid-phase transformation of akaganéite one-dimensional (1D) nanostructures with varying diameters. Our findings offer compelling evidence for a size-dependent morphology evolution in akaganéite 1D nanostructures, which can be attributed to the transformation from akaganéite to maghemite (?-Fe2O3) and subsequent crystal growth. Specifically, we observed that akaganéite nanorods with a diameter of around 50 nm transformed into hollow polycrystalline maghemite nanorods, which demonstrated remarkable stability without arresting crystal growth under continuous heating. In contrast, smaller akaganéite nanoneedles or nanowires with a diameter ranging from 20 to 8 nm displayed a propensity for forming single-crystal nanoneedles or nanowires through phase transformation and densification. By manipulating the size of the precursors, we have developed a straightforward method for the synthesis of single-crystal and polycrystalline maghemite nanowires through solid-phase transformation. These significant findings provide new insights into the size-dependent structural evolution and phase transformation of iron oxides at the nanoscale.
Vision Transformers have emerged as state-of-the-art image recognition tools, but may still exhibit incorrect behavior. Incorrect image recognition can have disastrous consequences in safety-critical real-world applications such as self-driving automobiles. In this paper, we present Provable Repair of Vision Transformers (PRoViT), a provable repair approach that guarantees the correct classification of images in a repair set for a given Vision Transformer without modifying its architecture. PRoViT avoids negatively affecting correctly classified images (drawdown) by minimizing the changes made to the Vision Transformer’s parameters and original output. Here, we observe that for Vision Transformers, unlike for other architectures such as ResNet or VGG, editing just the parameters in the last layer achieves correctness guarantees and very low drawdown. We introduce a novel method for editing these last-layer parameters that enables PRoViT to efficiently repair state-of-the-art Vision Transformers for thousands of images, far exceeding the capabilities of prior provable repair approaches.
Miscanthus × giganteus ( M × g ) is a high-yielding perennial C4 bioenergy crop, but genetic improvement by breeding is constrained by triploid sterility and clonal propagation. Improving genetic transformation methods for M × g would provide opportunities for advantageous trait introgression. Use of an easy to phenotype reporter gene is a promising strategy to improve transformation processes and efficiency. This study presents an efficient novel method for biolistic transformation of inflorescence-derived callus in M × g and demonstrates its efficacy using RUBY, a betalain-based noninvasive reporter that is visible throughout the transformation process. RUBY expression ( Zea mays codon optimized) was visible from callus stage through plantlet development into maturity. RUBY expressing independently transformed plants were confirmed by hygromycin phosphotransferase ELISA and by genomic PCR demonstrating that the RUBY phenotype is sufficient for screening transformants. The Zea mays codon optimized hygromycin selection marker was driven by previously established promoters for Miscanthus, ZmUBI and 2×35S, while the RUBY gene expression was controlled by a known Zea mays C4 promoter, Brachypodium UBI10, newly employed in Miscanthus. The construct containing the 2×35S promoter for hygromycin had a 15.1% transformation efficiency while the ZmUBI promoter had a 20.5% transformation efficiency. This study provides a novel, highly efficient protocol for successful biolistic transformation of M × g for stable expression. This study also demonstrates that RUBY expression can be used as a convenient and powerful monitor of transformation in ongoing and future work to engineer M × g into an improved bioproduct feedstock.
Miscanthus × giganteus ( M × g ) is a high- yielding perennial C4 bioenergy crop, but genetic improvement by breeding is constrained by triploid sterility and clonal propagation. Improving genetic transformation methods for M × g would provide opportunities for advantageous trait introgression. Use of an easy to phenotype reporter gene is a promising strategy to improve transformation processes and efficiency. This study presents an efficient novel method for biolistic transformation of inflorescence- derived callus in M × g and demonstrates its efficacy using RUBY, a betalain-based noninvasive reporter that is visible throughout the transformation process. RUBY expression ( Zea mays codon optimized) was visible from callus stage through plantlet development into maturity. RUBY expressing independently transformed plants were confirmed by hygromycin phosphotransferase ELISA and by genomic PCR demonstrating that the RUBY phenotype is sufficient for screening transformants. The Zea mays codon optimized hygromycin selection marker was driven by previously established promoters for Miscanthus, ZmUBI and 2×35S, while the RUBY gene expression was controlled by a known Zea mays C4 promoter, Brachypodium UBI10, newly employed in Miscanthus. The construct containing the 2×35S promoter for hygromycin had a 15.1% transformation efficiency while the ZmUBI promoter had a 20.5% transformation efficiency. This study provides a novel, highly efficient protocol for successful biolistic transformation of M × g for stable expression. This study also demonstrates that RUBY expression can be used as a convenient and powerful monitor of transformation in ongoing and future work to engineer M × g into an improved bioproduct feedstock. **NOTE: in "TableS2_ProtocolComparison.csv", the data from row 665 to 971 should be removed.
A general class of even/odd transforms is presented that includes the Karhunen-Loeve transform, the discrete cosine transform, the Walsh-Hadamard transform, and other familiar transforms. The more complex even/odd transforms can be computed by combining a simpler even/odd transform with a sparse matrix multiplication. A theoretical performance measure is computed for some even/odd transforms, and two image compression experiments are reported.
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for nonnormal matrices. Here, we propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation method [D. An, J.-P. Liu, and L. Lin, Phys. Rev. Lett., 131 (2023), 150603; D. An, A. M. Childs, and L. Lin, Commun. Math. Phys. 407, 19 (2026)] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, 𝐴 −𝑘 , and the exponential of the matrix inverse, 𝑒 −𝐴 −1 . The latter can be interpreted as the solution of a mass-matrix differential equation of the form form 𝐴𝑢′(𝑡) =−𝑢(𝑡). We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting 𝐴, thereby reducing the computational complexity.
Rural, isolated power systems in the mainland U.S. and in states like Alaska and Hawaii are powered by assets like diesel generators. These rural, isolated power systems also cannot operate at the higher band of medium voltage (like 69kV). They are primarily in the 12 to 14 kV range to keep the cost of the distribution investments lower. Because of this mid-band medium voltage range, the line losses and distribution transformers losses consume significant diesel consumption (almost 10 percent of the peak load). This work considers one such power system powering an isolated system and presents key findings online losses, and transformer losses. Understanding and documenting the impacts is critical for these communities operating their power systems and take actions to reduce expensive diesel consumption. In this paper, we will present one such typical grid and model it in electromagnetic transients (EMT) domain. We used the tower structure, under ground cabling installation to develop high fidelity models of lines. We also used high fidelity models of distribution transformers to present the no-load losses and full load loses. We will also present technical solutions available commercially off-the-shelf to reduce these losses and reduce diesel consumption. This work will be a primer for communities to understand the technical challenges and to understand the possible solution available to solve such challenges for rural, isolated power system operators.
This study investigates the structural evolution of LiMn0.5Ni0.5O2 cathode materials for Li-ion batteries as a function of synthesis temperature and its effect on electrochemical performance. It is demonstrated that, as the synthesis temperature increases from 400 to 900 ?C, a gradual topotactic transformation occurs between a lithiated spinel structure, denoted herein as “lithium-excess spinel” LxS-LiMn0.5Ni0.5O2 (or LxS-LMNO), and the well-known layered LiMn0.5Ni0.5O2 structure prepared at high temperature, HT-LiMn0.5Ni0.5O2 (HT-LMNO). The electrochemical capacity of the LiMn0.5Ni0.5O2 electrodes follows a parabolic trend with increasing synthesis temperature, which is attributed primarily to the gradual transformation of 3-dimensional (3-D) to 2-dimensional (2-D) diffusion pathways for the Li ions. When synthesized at 400 °C, LxS-LiMn0.5Ni0.5O2 electrodes perform well, benefitting from the 3-D network of channels within the LxS structure. By contrast, when prepared at 500-700 °C, LiMn0.5Ni0.5O2 electrodes operate poorly, which is attributed to the formation of locally disordered structural arrangements that impede Li-ion diffusion. Such an increase in local disorder in the mid-temperature synthesis range is attributed to the structural frustration between the lithium-excess spinal and layered end-members. The transformation from the locally disordered to more ordered layered components between 700 °C and 900 °C enhances electrochemical performance. The study opens new avenues for designing next-generation Mn-rich cathode materials by fine-tuning the synthesis conditions as well as the composition and structure of LxS-LMNO electrodes.
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
In this study, we use dilatometry to construct an extended Continuous Cooling Transformation (CCT) diagram for 410 stainless steel, capturing both δ → γ and γ → αʹ transformations specifically for directed energy deposition (DED) additive manufacturing (AM) applications. To ensure that the findings are representative of AM specific microstructures and compositions, dilatometry coupons were extracted from a wire arc DED wall, thereby preserving the inherent microstructural and compositional variability within the material. The on-heating phase transformations, including A c1 , A c3 , and γ → δ, were found to be essentially location independent, despite the typical heterogeneity associated with AM. Conversely, increasing cooling rates were observed to shift the start and finish temperatures of both δ → γ and γ → αʹ transformations to lower values. The resulting extended CCT diagram offers a more complete depiction of phase transformation behavior in the system, enabling accurate microstructure evolution modeling and residual stress predictions specifically for directed energy deposition additive manufacturing applications.
The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Delta(omega) = pi/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter, m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally spaced samples of the inverse Laplace transform function can be obtained by (m/2) + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations.
The CRISPR (Clustered, Regularly Interspaced, Short Palindromic Repeats)/Cas9 system has revolutionized genome editing by providing unprecedented DNA-targeting specificity. Here we demonstrate that this system can be also applied in vitro to fundamental cloning steps to facilitate efficient plasmid selection for transformation and selective gene insertion into plasmid vectors by cleaving unwanted plasmid byproducts with a single-guide RNA (sgRNA)-Cas9 nuclease complex. Using fluorescent and chromogenic proteins as reporters, we demonstrate that CRISPR/Cas9 cleavage excludes multiple plasmids as well as unwanted ligation byproducts resulting in an unprecedented increase in the transformation success rate from approximately 20% to nearly 100%. Thus, this CRISPR/Cas9-Assisted Transformation-Efficient Reaction (CRATER) protocol is a novel, inexpensive, and convenient application to conventional molecular cloning to achieve near-perfect selective transformation.
The NOvA Transformer Energy Estimator (Transformer_EE) is a universal machine learning tool currently used to infer the incoming beam neutrino energy and the outgoing lepton energy in both near andfar detectors. It uses a unique, highly flexible framework for simultaneous multivariate prediction that supports many possible loss functions. A spectral reweighting and flattening scheme lessens training bias. A feature noising subroutine enables adversarial-like training, mitigating sensitivities to certain systematic effects at marginal resolution loss at inference time. The state of the Transformer_EE will be reviewed, and its robustness with respect to several NOvA Near and Far Detector systematics highlighted.
The Transformational Concept of Operations (CONOPS) provides a long-term, sustainable vision for future U.S. space transportation infrastructure and operations. This vision presents an interagency concept, developed cooperatively by the Department of Defense (DoD), the Federal Aviation Administration (FAA), and the National Aeronautics and Space Administration (NASA) for the upgrade, integration, and improved operation of major infrastructure elements of the nation s space access systems. The interagency vision described in the Transformational CONOPS would transform today s space launch infrastructure into a shared system that supports worldwide operations for a variety of users. The system concept is sufficiently flexible and adaptable to support new types of missions for exploration, commercial enterprise, and national security, as well as to endure further into the future when space transportation technology may be sufficiently advanced to enable routine public space travel as part of the global transportation system. The vision for future space transportation operations is based on a system-of-systems architecture that integrates the major elements of the future space transportation system - transportation nodes (spaceports), flight vehicles and payloads, tracking and communications assets, and flight traffic coordination centers - into a transportation network that concurrently accommodates multiple types of mission operators, payloads, and vehicle fleets. This system concept also establishes a common framework for defining a detailed CONOPS for the major elements of the future space transportation system. The resulting set of four CONOPS (see Figure 1 below) describes the common vision for a shared future space transportation system (FSTS) infrastructure from a variety of perspectives.
Abstract We pursue the use of deep learning methods to improve state-of-the-art computations in theoretical high-energy physics. Planar N = 4 Super Yang-Mills theory is a close cousin to the theory that describes Higgs boson production at the Large Hadron Collider; its scattering amplitudes are large mathematical expressions containing integer coefficients. In this paper, we apply Transformers to predict these coefficients. The problem can be formulated in a language-like representation amenable to standard cross-entropy training objectives. We design two related experiments and show that the model achieves high accuracy (> 98%) on both tasks. Our work shows that Transformers can be applied successfully to problems in theoretical physics that require exact solutions.
Here, we present a simulation-based cosmological analysis using a combination of Gaussian and non-Gaussian statistics of the weak lensing mass (convergence) maps from the first three years of the Dark Energy Survey. We implement the following: (1) second and third moments; (2) wavelet phase harmonics; (3) the scattering transform. Our analysis is fully based on simulations, spans a space of seven 𝑤 Cold Dark Matter (𝑤 CDM) cosmological parameters, and forward models the most relevant sources of systematics inherent in the data: masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration. We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a simulation-based inference approach. Including and combining different non-Gaussian statistics is a powerful tool that strongly improves constraints over Gaussian statistics (in our case, the second moments); in particular, the figure of merit (𝑆 8 , Ω m ) is improved by 70% (Λ CDM) and 90% (𝑤 CDM). When all the summary statistics are combined, we achieve a 2% constraint on the amplitude of fluctuations parameter 𝑆 8 ≡ 𝜎 8 (Ω m /0.3) 0.5 , obtaining 𝑆 8 = 0.794 ±0.017 (Λ CDM) and 𝑆 8 = 0.817 ±0.021 (𝑤 CDM), and a ∼10% constraint on Ω m , obtaining Ω m =0.259 ±0.025 (Λ CDM) and Ω m = 0.273 ±0.029 (𝑤 CDM). In the context of the 𝑤 CDM scenario, these statistics also strengthen the constraints on the parameter 𝑤, obtaining 𝑤 <−0.72. The constraints from different statistics are shown to be internally consistent (with a 𝑝-value>0.1 for all combinations of statistics examined). We compare our results to other weak lensing results from the first three years of the Dark Energy Survey data, finding good consistency; we also compare with results from external datasets, such as planck constraints from the cosmic microwave background, finding statistical agreement, with discrepancies no greater than <2.2𝜎.
Gauge transformations of third kind and operator gauge transformations of first and second kinds, relating electron and photon propagators to quantum electrodynamical vertex function