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This dataset contains high-frequency vertical velocity recorded by fixed-point vertical scans done by the Lawrence Livermore National Laboratory Halo Streamline scanning lidar at Tree Tops. The quality control is performed according to the algorithm of Goring & Nikora (2002).
The periods of the theorem for the algebraic multigrid projection (MGP) for eigenvalue problems, and of the multigrid fixed point theorem for multigrid cycles combining MGP with backrotations, are presented. The MGP and the backrotations are central eigenvector separation techniques for multigrid eigenvalue algorithms. They allow computation on coarse levels of eigenvalues of a given eigenvalue problem, and are efficient tools in the computation of eigenvectors.
Asymptotic fixed point theorems and periodic systems of functional-differential equations
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
We present strong numerical evidence for the existence of an infrared fixed point in the renormalization group flow of the SU(3) gauge-fermion system with twelve massless fermions in the fundamental representation. Our numerical simulations using nHYP-smeared staggered fermions with Pauli-Villars improvement do not exhibit any first-order bulk phase transition in the investigated parameter region. We utilize an infinite volume renormalization scheme based on the gradient flow transformation to determine the renormalization group β function. The gradient flow β function exhibits a zero at g GF ⋆ 2 = 6.60 ( 62 ) , implying that the system is infrared conformal. We calculate the leading irrelevant critical exponent γ g ⋆ = 0.199 ( 32 ) . Our prediction for γ g ⋆ is consistent with available literature at the 1 − 2 σ level. Published by the American Physical Society 2024
The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real-space renormalization group (RG) scheme. Numerically approximate fixed-point (FP) tensors are widely used to extract the conformal data of the underlying conformal field theory (CFT) describing critical phenomena. In this paper, we present an explicit analytical construction of the FP tensor for 2D rational CFT. We define it as a correlation function between the “boundary-changing operators” (BCO) on triangles. Our construction fully captures all the real-space RG conditions. We also provide concrete examples, such as Ising, Yang-Lee, and tricritical Ising models, to compute the scaling dimensions explicitly based on the corresponding FP tensor. The BCO descendants turn out to be an optimal basis such that truncation in bond dimensions naturally produces comparable accuracies with the leading existing FP algorithms. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door toward understanding CFT in higher dimensions. Published by the American Physical Society 2025
Results are presented from temporally dense measurements of crustal deformation associated with the convergence of the Eurasian (EUR), Pacific, North American, and Philippine Sea (PHS) plates, carried out in April 1988 by a 10-station GPS fixed-point network established in central Japan. Using regional orbit relaxation methods, the analysis of the first 17-month data revealed significant horizontal deformation across the Suruga trough. Namely, it was found that a site in the northern tip of PHS plate moved nearly westward with a velocity of 28 +/-5 mm per year, and a site at the southeastern tip of EUR plate moved south-southwestward with a velocity of 18 +/-5 mm per year. A significant vertical uplift with a velocity of 20 mm/yr was detected at a site inland of the Tokai district located in the Akaishi uplift zone and at a site on the Hatsushima Island in Sagami Bay.
Grover's algorithm provides a quadratic speedup for searching unstructured databases and is traditionally implemented with qubits in Hilbert spaces whose dimensions are powers of two. With the advent of quantum platforms utilizing qudits---quantum systems with more than two levels---there is a need to generalize Grover search to these architectures, including heterogeneous systems with qudits of varying dimensions. Here, we present a unified framework for qudit-based Grover search, detailing the construction of oracles and diffusion operators with and without ancilla qubits and generalizing deterministic and fixed-point search variants that ensure exact or bounded success probabilities. We analyze phase-matching techniques and provide explicit circuit decompositions suitable for diverse hardware platforms. We also compare the corresponding trajectories on the Bloch sphere to provide an intuitive visualization of how the different phase choices amplify the target state. These results facilitate flexible, hardware-oriented protocols for implementing Grover search on qudit processors, potentially reducing circuit depth and enhancing success probabilities, thereby offering a practical toolkit for quantum computation and sensing applications leveraging multilevel quantum systems.
Forces and torques acting on satellites and dynamical equations for describing satellite attitude
Neutral functional differential equation solution operator properties
Monte Carlo simulation of autonomous orbit determination has validated the use of an 18-bit NASA Standard Spacecraft Computer (NSSC) for the extended Kalman filter. Dimensionally consistent scales are chosen for all variables in the algorithm, such that nearly all of the onboard computation can be performed in single precision without matrix square root formulations. Allowable simplifications in algorithm implementation and practical means of ensuring convergence are verified for accuracies of a few km provided by star/vertical observations
In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H).
Triple-point cell contrains about 300 g of high-purity succinontrile. Experiments show that lower 4 cm of thermometer well are virtually isothermal, making placement of thermometer not very critical. Bulb at bottom of well helps to prevent solid succinontrile mantel from slipping.
Fixed points of diffeomorphism class of Smale and exponential function
A polyphase fast Fourier transform (FFT) spectrum analyzer being designed for NASA's Search for Extraterrestrial Intelligence (SETI) Sky Survey at the Jet Propulsion Laboratory is described. By replacing the time domain multiplicative window preprocessing with polyphase filter processing, much of the processing loss of windowed FFTs can be eliminated. Polyphase coefficient memory costs are minimized by effective use of run length compression. Finite word length effects are analyzed, producing a balanced system with 8 bit inputs, 16 bit fixed point polyphase arithmetic, and 24 bit fixed point FFT arithmetic. Fixed point renormalization midway through the computation is seen to be naturally accommodated by the matrix FFT algorithm proposed. Simulation results validate the finite word length arithmetic analysis and the renormalization technique.
Coinduction is a powerful technique for reasoning about unfounded sets, unbounded structures, infinite automata, and interactive computations [6]. Where induction corresponds to least fixed point's semantics, coinduction corresponds to greatest fixed point semantics. Recently coinduction has been incorporated into logic programming and an elegant operational semantics developed for it [11, 12]. This operational semantics is the greatest fix point counterpart of SLD resolution (SLD resolution imparts operational semantics to least fix point based computations) and is termed co- SLD resolution. In co-SLD resolution, a predicate goal p( t) succeeds if it unifies with one of its ancestor calls. In addition, rational infinite terms are allowed as arguments of predicates. Infinite terms are represented as solutions to unification equations and the occurs check is omitted during the unification process. Coinductive Logic Programming (Co-LP) and Co-SLD resolution can be used to elegantly perform model checking and planning. A combined SLD and Co-SLD resolution based LP system forms the common basis for planning, scheduling, verification, model checking, and constraint solving [9, 4]. This is achieved by amalgamating SLD resolution, co-SLD resolution, and constraint logic programming [13] in a single logic programming system. Given that parallelism in logic programs can be implicitly exploited [8], complex, compute-intensive applications (planning, scheduling, model checking, etc.) can be executed in parallel on multi-core machines. Parallel execution can result in speed-ups as well as in larger instances of the problems being solved. In the remainder we elaborate on (i) how planning can be elegantly and efficiently performed under real-time constraints, (ii) how real-time systems can be elegantly and efficiently model- checked, as well as (iii) how hybrid systems can be verified in a combined system with both co-SLD and SLD resolution. Implementations of co-SLD resolution as well as preliminary implementations of the planning and verification applications have been developed [4]. Co-LP and Model Checking: The vast majority of properties that are to be verified can be classified into safety properties and liveness properties. It is well known within model checking that safety properties can be verified by reachability analysis, i.e, if a counter-example to the property exists, it can be finitely determined by enumerating all the reachable states of the Kripke structure.
This paper presents the correctness proof of Saturation, an algorithm for generating state spaces of concurrent systems, implemented in the SMART tool. Unlike the Breadth First Search exploration algorithm, which is easy to understand and formalise, Saturation is a complex algorithm, employing a mutually-recursive pair of procedures that compute a series of non-trivial, nested local fixed points, corresponding to a chaotic fixed point strategy. A pencil-and-paper proof of Saturation exists, but a machine checked proof had never been attempted. The key element of the proof is the characterisation theorem of saturated nodes in decision diagrams, stating that a saturated node represents a set of states encoding a local fixed-point with respect to firing all events affecting only the node s level and levels below. For our purpose, we have employed the Prototype Verification System (PVS) for formalising the Saturation algorithm, its data structures, and for conducting the proofs.
In this paper, we propose a proof-carrying code framework for program-generators. The enabling technique is abstract parsing, a static string analysis technique, which is used as a component for generating and validating certificates. Our framework provides an efficient solution for certifying program-generators whose safety properties are expressed in terms of the grammar representing the generated program. The fixed-point solution of the analysis is generated and attached with the program-generator on the code producer side. The consumer receives the code with a fixed-point solution and validates that the received fixed point is indeed a fixed point of the received code. This validation can be done in a single pass.