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NASA NTRS2007

Distributed Saturation

The Saturation algorithm for symbolic state-space generation, has been a recent break-through in the exhaustive veri cation of complex systems, in particular globally-asyn- chronous/locally-synchronous systems. The algorithm uses a very compact Multiway Decision Diagram (MDD) encoding for states and the fastest symbolic exploration algo- rithm to date. The distributed version of Saturation uses the overall memory available on a network of workstations (NOW) to efficiently spread the memory load during the highly irregular exploration. A crucial factor in limiting the memory consumption during the symbolic state-space generation is the ability to perform garbage collection to free up the memory occupied by dead nodes. However, garbage collection over a NOW requires a nontrivial communication overhead. In addition, operation cache policies become critical while analyzing large-scale systems using the symbolic approach. In this technical report, we develop a garbage collection scheme and several operation cache policies to help on solving extremely complex systems. Experiments show that our schemes improve the performance of the original distributed implementation, SmArTNow, in terms of time and memory efficiency.

Chung, Ming-Ying↗

NASA NTRS1993

Programmable noise bandwidth reduction by means of digital averaging

Predetection noise bandwidth reduction is effected by a pre-averager capable of digitally averaging the samples of an input data signal over two or more symbols, the averaging interval being defined by the input sampling rate divided by the output sampling rate. As the averaged sample is clocked to a suitable detector at a much slower rate than the input signal sampling rate the noise bandwidth at the input to the detector is reduced, the input to the detector having an improved signal to noise ratio as a result of the averaging process, and the rate at which such subsequent processing must operate is correspondingly reduced. The pre-averager forms a data filter having an output sampling rate of one sample per symbol of received data. More specifically, selected ones of a plurality of samples accumulated over two or more symbol intervals are output in response to clock signals at a rate of one sample per symbol interval. The pre-averager includes circuitry for weighting digitized signal samples using stored finite impulse response (FIR) filter coefficients. A method according to the present invention is also disclosed.

Poklemba, John J.↗

NASA NTRS2010

Universal Decoder for PPM of any Order

A recently developed algorithm for demodulation and decoding of a pulse-position- modulation (PPM) signal is suitable as a basis for designing a single hardware decoding apparatus to be capable of handling any PPM order. Hence, this algorithm offers advantages of greater flexibility and lower cost, in comparison with prior such algorithms, which necessitate the use of a distinct hardware implementation for each PPM order. In addition, in comparison with the prior algorithms, the present algorithm entails less complexity in decoding at large orders. An unavoidably lengthy presentation of background information, including definitions of terms, is prerequisite to a meaningful summary of this development. As an aid to understanding, the figure illustrates the relevant processes of coding, modulation, propagation, demodulation, and decoding. An M-ary PPM signal has M time slots per symbol period. A pulse (signifying 1) is transmitted during one of the time slots; no pulse (signifying 0) is transmitted during the other time slots. The information intended to be conveyed from the transmitting end to the receiving end of a radio or optical communication channel is a K-bit vector u. This vector is encoded by an (N,K) binary error-correcting code, producing an N-bit vector a. In turn, the vector a is subdivided into blocks of m = log2(M) bits and each such block is mapped to an M-ary PPM symbol. The resultant coding/modulation scheme can be regarded as equivalent to a nonlinear binary code. The binary vector of PPM symbols, x is transmitted over a Poisson channel, such that there is obtained, at the receiver, a Poisson-distributed photon count characterized by a mean background count nb during no-pulse time slots and a mean signal-plus-background count of ns+nb during a pulse time slot. In the receiver, demodulation of the signal is effected in an iterative soft decoding process that involves consideration of relationships among photon counts and conditional likelihoods of m-bit vectors of coded bits. Inasmuch as the likelihoods of all the m-bit vectors of coded bits mapping to the same PPM symbol are correlated, the best performance is obtained when the joint mbit conditional likelihoods are utilized. Unfortunately, the complexity of decoding, measured in the number of operations per bit, grows exponentially with m, and can thus become prohibitively expensive for large PPM orders. For a system required to handle multiple PPM orders, the cost is even higher because it is necessary to have separate decoding hardware for each order. This concludes the prerequisite background information. In the present algorithm, the decoding process as described above is modified by, among other things, introduction of an lbit marginalizer sub-algorithm. The term "l-bit marginalizer" signifies that instead of m-bit conditional likelihoods, the decoder computes l-bit conditional likelihoods, where l is fixed. Fixing l, regardless of the value of m, makes it possible to use a single hardware implementation for any PPM order. One could minimize the decoding complexity and obtain an especially simple design by fixing l at 1, but this would entail some loss of performance. An intermediate solution is to fix l at some value, greater than 1, that may be less than or greater than m. This solution makes it possible to obtain the desired flexibility to handle any PPM order while compromising between complexity and loss of performance.

Moision, Bruce E.↗

NASA NTRS2005

Coupled Receiver/Decoders for Low-Rate Turbo Codes

been proposed for receiving weak single- channel phase-modulated radio signals bearing low-rate-turbo-coded binary data. Originally intended for use in receiving telemetry signals from distant spacecraft, the proposed receiver/ decoders may also provide enhanced reception in mobile radiotelephone systems. A radio signal of the type to which the proposal applies comprises a residual carrier signal and a phase-modulated data signal. The residual carrier signal is needed as a phase reference for demodulation as a prerequisite to decoding. Low-rate turbo codes afford high coding gains and thereby enable the extraction of data from arriving radio signals that might otherwise be too weak. In the case of a conventional receiver, if the signal-to-noise ratio (specifically, the symbol energy to one-sided noise power spectral density) of the arriving signal is below approximately 0 dB, then there may not be enough energy per symbol to enable the receiver to recover properly the carrier phase. One could solve the problem at the transmitter by diverting some power from the data signal to the residual carrier. A better solution . a coupled receiver/decoder according to the proposal . could reduce the needed amount of residual carrier power. In all that follows, it is to be understood that all processing would be digital and the incoming signals to be processed would be, more precisely, outputs of analog-to-digital converters that preprocess the residual carrier and data signals at a rate of multiple samples per symbol. The upper part of the figure depicts a conventional receiving system, in which the receiver and decoder are uncoupled, and which is also called a non-data-aided system because output data from the decoder are not used in the receiver to aid in recovering the carrier phase. The receiver tracks the carrier phase from the residual carrier signal and uses the carrier phase to wipe phase noise off the data signal. The receiver typically includes a phase-locked loop (PLL) or Costas loop that requires no delay or perhaps a single sample delay. The lower part of the figure depicts a basic coupled receiver/decoder . a data-aided system that would implement an iterative receiving/decoding process. The receiver would include a PLL or a Wiener filter that, to the extent possible, would track the residual carrier signal, wipe phase noise off the data signal, then send the result to the turbo decoder. Recovery of timing could be effected by, for example, a digital transition tracking loop (DTTL) or other, similar loop. The first iteration of turbo decoding would yield soft data symbols, which would be sent back to the receiver for use in softly wiping off the data signal in an effort to recover the residual carrier signal. The wiped signal would contain a relatively large carrier-phase component that could be tracked by use of a second Wiener filter.

Hamkins, Jon↗

NASA NTRSDate not supplied

Application of Variable Data Rate (VDR) Towards Channel Optimization

Recognizing the vagaries of channel impediments, one way to optimize aggregate channel information throughput is to maintain a constant symbol rate but vary the modulation scheme and/or the codec rate. The CCSDS VCM and ACM standards promulgation relies upon this kind of an approach. We offer a considerably simpler alternative for spacecraft that are not parked in geo-stationary orbit, one that can rely upon conventional spacecraft housekeeping schedules to change spacecraft and ground operations and will minimize the possibility of requiring any spacecraft hardware accommodations to incorporate. We suggest the use of varying the physical symbol rate within the channel to both initiate acquisition earlier in a pass and retain the link longer as the pass tends toward loss of signal. There is nothing new in what we propose, just a recognition of what has been successful in the past and employed in multiple missions. Integrating over the periodicity of orbit repetition, we shall show that any link that is dependent primarily on a varying range from spacecraft to ground only requires a maximum of five symbol rate transitions in order to optimize total information throughput. By applying these symbol rate transitions using almost rigid rules, we anticipate doubling the information throughput for conventional LEO sun-synchronous orbits. We provide other examples as well.

variable data rate↗

NASA NTRSDate not supplied

Application of Variable Data Rate (VDR) Towards Channel Optimization

Variable Data Rate↗

DOE OSTI2024

Modeling plasticity-mediated void growth at the single crystal scale: A physics-informed machine learning approach

Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. Here, this present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.

36 MATERIALS SCIENCE↗

NASA NTRS2003

Bimanual cross-talk during reaching movements is primarily related to response selection, not the specification of motor parameters

Simultaneous reaching movements made with the two hands can show a considerable increase in reaction time (RT) when they differ in terms of direction or extent, compared to when the movements involve the same direction and extent. This cost has been attributed to cross-talk in the specification of the motor parameters for the two hands. However, a recent study [Diedrichsen, Hazeltine, Kennerley, & Ivry, (2001). Psychological Science, 12, 493-498] indicates that when reaching movements are cued by the onset of the target endpoint, no compatibility effects are observed. To determine why directly cued movements are immune from interference, we varied the stimulus onset asynchrony for the two movements and used different combinations of directly cued and symbolically cued movements. In two experiments, compatibility effects were only observed when both movements were symbolically cued. No difference was found between compatible and incompatible movements when both movements were directly cued or when one was directly cued and the other was symbolically cued. These results indicate that interference is not related to the specification of movement parameters but instead emerges from processes associated with response selection. Moreover, the data suggest that cross-talk, when present, primarily shortens the RT of the second movement on compatible trials rather than lengthening this RT on incompatible trials.

Randomized Controlled Trial↗

DOE OSTI2013

Leading singularities and off-shell conformal integrals

The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Hexagon functions and the three-loop remainder function

We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar NN = 4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann ζ valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.

extended supersymmetry↗

DOE OSTI2014

Distinguishing between evidence and its explanations in the steering of atomic clocks

Quantum theory reflects within itself a separation of evidence from explanations. This separation leads to a known proof that: (1) no wave function can be determined uniquely by evidence, and (2) any chosen wave function requires a guess reaching beyond logic to things unforeseeable. Chosen wave functions are encoded into computer-mediated feedback essential to atomic clocks, including clocks that step computers through their phases of computation and clocks in space vehicles that supply evidence of signal propagation explained by hypotheses of spacetimes with metric tensor fields. The propagation of logical symbols from one computer to another requires a shared rhythm—like a bucket brigade. Here we show how hypothesized metric tensors, dependent on guesswork, take part in the logical synchronization by which clocks are steered in rate and position toward aiming points that satisfy phase constraints, thereby linking the physics of signal propagation with the sharing of logical symbols among computers. Recognizing the dependence of the phasing of symbol arrivals on guesses about signal propagation transports logical synchronization from the engineering of digital communications to a discipline essential to physics. Within this discipline we begin to explore questions invisible under any concept of time that fails to acknowledge unforeseeable events. In particular, variation of spacetime curvature is shown to limit the bit rate of logical communication. - Highlights: • Atomic clocks are steered in frequency toward an aiming point. • The aiming point depends on a chosen wave function. • No evidence alone can determine the wave function. • The unknowability of the wave function has implications for spacetime curvature. • Variability in spacetime curvature limits the bit rate of communications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Structures of ordered tungsten- or molybdenum-containing quaternary perovskite oxides

The room temperature crystal structures of six A{sub 2}MMoO{sub 6} and A{sub 2}MWO{sub 6} ordered double perovskites were determined from X-ray and neutron powder diffraction data. Ba{sub 2}MgWO{sub 6} and Ba{sub 2}CaMoO{sub 6} both adopt cubic symmetry (space group Fm3-bar m, tilt system a{sup 0}a{sup 0}a{sup 0}). Ba{sub 2}CaWO{sub 6} has nearly the same tolerance factor (t=0.972) as Ba{sub 2}CaMoO{sub 6} (t=0.974), yet it surprisingly crystallizes with I4/m symmetry indicative of out-of-phase rotations of the MO{sub 6} octahedra about the c-axis (a{sup 0}a{sup 0}c{sup -}). Sr{sub 2}ZnMoO{sub 6} (t=0.979) also adopts I4/m symmetry; whereas, Sr{sub 2}ZnWO{sub 6} (t=0.976) crystallizes with monoclinic symmetry (P2{sub 1}/n) with out-of-phase octahedral tilting distortions about the a- and b-axes, and in-phase tilting about the c-axis (a{sup -}a{sup -}c{sup +}). Ca{sub 2}CaWO{sub 6} (t=0.867) also has P2{sub 1}/n symmetry with large tilting distortions about all three crystallographic axes and distorted CaO{sub 6} octahedra. Analysis of 93 double perovskites and their crystal structures showed that while the type and magnitude of the octahedral tilting distortions are controlled primarily by the tolerance factor, the identity of the A-cation acts as the secondary structure directing factor. When A=Ba{sup 2+} the boundary between cubic and tetragonal symmetries falls near t=0.97, whereas when A=Sr{sup 2+} this boundary falls somewhere between t=1.018 and t=0.992. - Graphical abstract: A survey of the tolerance factor of 41 Mo/W- and 52 Nb/Ta-containing quaternary perovskites plotted as a function of the difference between the two six-coordinate M-cation ionic radii. Compounds with cubic symmetry are represented by diamonds, those with tetragonal symmetry are represented by squares, those with I2/m monoclinic symmetry are represented by Multiplication-Sign , and those with P2{sub 1}/n monoclinic symmetry are represented by triangles. White symbols represent compositions where A=Ba{sup 2+}, gray symbols represent compositions where A=Sr{sup 2+}, and black symbols represent where A=Ca{sup 2+}. The filled circle represents rhombohedral Ba{sub 2}BiTaO{sub 6} (t=0.961; space group-R3-bar ; tilt system-a{sup -}a{sup -}a{sup -}). References for the compounds included in this figure are listed in the Supporting Information File. Black-Small-Square Highlights: Black-Right-Pointing-Pointer Reports the structures of six double perovskites containing either Mo{sup 6+} or W{sup 6+}. Black-Right-Pointing-Pointer Compounds with similar tolerance factors (t) exhibited different symmetries. Black-Right-Pointing-Pointer This effect was observed in Sr{sub 2}ZnMO{sub 6} and Ba{sub 2}CaMO{sub 6} (M=Mo or W). Black-Right-Pointing-Pointer Contains a structural survey of 93 double perovskites. Black-Right-Pointing-Pointer Octahedral tilting distortions are controlled by t and the nature of the A-cation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Rare-earth metal gallium silicides via the gallium self-flux method. Synthesis, crystal structures, and magnetic properties of RE(Ga 1–x Si x )₂ (RE=Y, La–Nd, Sm, Gd–Yb, Lu)

Fifteen ternary rare-earth metal gallium silicides have been synthesized using molten Ga as a molten flux. They have been structurally characterized by single-crystal and powder X-ray diffraction to form with three different structures—the early to mid-late rare-earth metals RE=La–Nd, Sm, Gd–Ho, Yb and Y form compounds with empirical formulae RE(Ga x Si 1–x )₂ (0.38≤x≤0.63), which crystallize with the tetragonal α-ThSi₂ structure type (space group I4₁/amd, No. 141; Pearson symbol tI12). The compounds of the late rare-earth crystallize with the orthorhombic α-GdSi₂ structure type (space group Imma, No. 74; Pearson symbol oI12), with refined empirical formula REGa x Si 2–x–y (RE=Ho, Er, Tm; 0.33≤x≤0.40, 0.10≤y≤0.18). LuGa₀.₃₂₍₁₎Si₁.₄₃₍₁₎ crystallizes with the orthorhombic YbMn₀.₁₇Si₁.₈₃ structure type (space group Cmcm, No. 63; Pearson symbol oC24). Structural trends are reviewed and analyzed; the magnetic susceptibilities of the grown single-crystals are presented. - Graphical abstract: This article details the exploration of the RE–Ga–Si ternary system with the aim to systematically investigate the structural “boundaries” between the α-ThSi₂ and α-GdSi₂-type structures, and studies of the magnetic properties of the newly synthesized single-crystalline materials. Highlights: • Light rare-earth gallium silicides crystallize in α-ThSi₂ structure type. • Heavy rare-earth gallium silicides crystallize in α-GdSi₂ structure type. • LuGaSi crystallizes in a defect variant of the YbMn₀.₁₇Si₁.₈₃ structure type.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

The RELi{sub x}Sn{sub 2} (RE=La–Nd, Sm, and Gd; 0≤x<1) series revisited. Synthesis, crystal chemistry, and magnetic susceptibilities

This study is concerned with the ternary compounds RELi{sub x}Sn{sub 2} (RE=La–Nd, Sm, and Gd; 0≤x<1), which have been previously thought to be the stoichiometric RELiSn{sub 2} phases. These materials crystallize with the base-centered orthorhombic space group Cmcm (No. 63), and can be formally assigned with the CeNiSi{sub 2} structure type (Pearson symbol oC16). Our systematic single-crystal X-ray diffraction studies revealed substantial Li-deficiencies in all cases, with SmSn{sub 2} (space group Cmmm, ZrGa{sub 2} structure type, Pearson symbol oC12) and GdSn{sub 2} (space group Cmcm, ZrSi{sub 2} structure type, Pearson symbol oC12) being completely lithium-free. The structure refinements also uncovered positional disorder on the Sn site neighboring the vacancies. The Sn-disorder and the Li-deficiency correlate, and vary monotonically with the decreased size of the rare-earth atoms in the order RE=La–Nd. The SmSn{sub 2} and GdSn{sub 2} structures are devoid of any disorder. Temperature-dependent studies of the magnetic response of the title compounds are also presented and discussed. -- Graphical abstract: RELi{sub x}Sn{sub 2} (RE=La–Nd, 0≤x<1) crystallize in a defect variants of the CeNiSi{sub 2} structure type (a). The Sn-disorder and the Li-deficiency correlate, and vary monotonically with the decreased size of the rare-earth atoms in the order RE=La–Nd. The SmSn{sub 2} (b) and GdSn{sub 2} (c) structures are devoid of any disorder. Highlights: • The crystal structures of the RELi{sub x}Sn{sub 2} (RE=La–Nd, 0≤x<1) compounds are revised using single-crystal X-ray diffraction data. • The structure is a filled derivative of the ZrSi{sub 2} structure type or defect variant of the CeNiSi{sub 2} structure type. • SmSn{sub 2} is isotypic with the ZrGa{sub 2} structure, while RESn{sub 2} (RE=Gd–Lu) are isotypic with the ZrSi{sub 2} structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗

DOE OSTI2025

Baseflow Identification via Explainable AI With Kolmogorov‐Arnold Networks

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decrease the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance

baseflow↗

DOE OSTI2026

Secure Wireless Communication Using Distributed Coherent Transmission and Spatial Signal Decomposition

We present a new approach to secure wireless communications using coherent distributed transmission of signals that are spatially decomposed between a two-element distributed antenna array. High-accuracy distributed coordination of microwave wireless systems supports the ability to transmit different parts of a signal from separate transmitters such that they combine coherently at a designated destination. In this article, we explore this concept using a two-element coherent distributed phased array where each of the two transmitters sends a separate component of a communication signal, where each symbol is decomposed into a sum of two pseudorandom signal vectors, the coherent summation of which yields the intended symbol. By directing the transmission to an intended receiver using distributed beamforming, the summation of the two vector components is largely confined to a spatial region at the destination receiver. We implement the technique in a $50−λ$ array operating at 3 GHz. We evaluate the symbol error rate (SER) in 2-D space through simulation and measurement, showing that the approach yields a spatially confined secure region where the information is recoverable (i.e., the received signal has low SER), and outside of which the information is unrecoverable (high SER). The proposed system is also compared against a traditional beamforming system where each node sends the same data. We validate experimentally that our approach achieves a low SER of 0.0082 at broadside and an SER above 0.25 at all other locations compared to a traditional beamforming approach that achieves a SER of 0 at all locations measured.

Engineering - Electronic and electrical engineerin↗