Search NASA⌕ Search

SEARCH · Search NASA

Results for “Generalization Bounds”

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 217 records · Page 12

A multiloop generalization of the circle stability criterion

A frequency-domain stability criterion is presented, generalizing the well-known circle stability criterion to multiloop feedback systems having bounded nonlinearity, parameter variations, and/or frequency-dependent ignorance of component dynamics. Unlike previous generalizations, the theory is not restricted to weakly-coupled, diagonally dominant or nearly normal systems. Potential applications include the analysis of feedback system integrity and multiloop feedback system stability margins.

Safonov, M. G.↗

Information models of software productivity - Limits on productivity growth

Research into generalized information-metric models of software process productivity establishes quantifiable behavior and theoretical bounds. The models establish a fundamental mathematical relationship between software productivity and the human capacity for information traffic, the software product yield (system size), information efficiency, and tool and process efficiencies. An upper bound is derived that quantifies average software productivity and the maximum rate at which it may grow. This bound reveals that ultimately, when tools, methodologies, and automated assistants have reached their maximum effective state, further improvement in productivity can only be achieved through increasing software reuse. The reuse advantage is shown not to increase faster than logarithmically in the number of reusable features available. The reuse bound is further shown to be somewhat dependent on the reuse policy: a general 'reuse everything' policy can lead to a somewhat slower productivity growth than a specialized reuse policy.

Tausworthe, Robert C.↗

UT-GOM2-2 Preliminary Report: Terrebonne Basin Northern Gulf of Mexico, 30 July-28 September 2023

In the summer and fall of 2023, the Gulf of Mexico Deepwater Hydrate Coring Expedition (UT-GOM2-2) drilled, cored, made downhole measurements, and analyzed samples from the seafloor to the base of the gas hydrate stability zone in one location (Site H, WR313) in the Terrebonne basin, deepwater Gulf of Mexico. Analyses of data and samples from the expedition will inform biological, geochemical, and geomechanical models to constrain the role of gas hydrates in the carbon cycle and the potential for gas hydrates as an energy resource. Pressure and conventional cores were collected continuously to a depth of 155.1 meters below the seafloor (mbsf). At deeper depths, cores were taken periodically from hydrate-bearing sands and their bounding muds to a total depth of 861.3 mbsf. 162.6 m of conventional core and 54.8 m of pressure core were obtained. Twelve temperature measurements were made between 27.1 and 144.5 mbsf to determine the geothermal gradient. At the seafloor, more than 4 m of sandy silt of unknown origin was encountered. Beneath this sand, to a depth of ~200 mbsf, the section was composed of interbedded mud and biogenic carbonate ooze. The biogenic ooze correlated to low density and high porosity intervals observed in the previously acquired logging while drilling (LWD) data and as measured. Calcareous nannofossil biostratigraphy constrains the entire record to the Pleistocene (< 0.91 million years) with a pronounced increase in sedimentation rate with depth. Beneath 200 mbsf, the section was predominantly composed of mud with two thicker, hydrate-bearing coarse-grained intervals, which are commonly known as the Blue and Orange sands. The dissolved gas concentration was quantified from pressure cores. In the shallow section, dissolved methane concentration increased below the sulfate-methane transition zone (SMTZ) and reaches saturation (the limit of solubility for methane) at 147 mbsf. Gas expansion was very common in conventional and depressurized pressure (conventionalized) cores below the SMTZ. At deeper depths, the methane concentration within muds bounding the Blue and Orange reservoirs was generally found to be less than saturation. The dissolved and hydrate gas composition is consistent with a microbial source, containing greater than 99.99% methane and only trace concentrations of ethane, propane, and butane. The methane to ethane ratio (C 1 /C 2 ) and the methane to ethane plus propane (C 1 /(C 2 +C 3 )) decrease with depth down to at least 678 mbsf, mainly driven by the increase in ethane with depth. It is unclear if this trend continues through the Orange sand interval. The δ 13 C isotopic signature of methane ranges between -69.9 and -78.5 ‰ Vienna Pee Dee Belemnite (VPDB). Pressure core recovery of all sandy intervals was poor. However, pressure core logs of the Orange sand show intervals of low density and high velocity, which are indicative of high hydrate saturation. One core from within the Orange sand was composed of interbedded graded sandy silt and mud. The sandy silts from this core are composed of mainly quartz and feldspar with some lithics. Most of the recovered pressure core samples are maintained at near in-situ pressure and temperature (within the hydrate stability field) at the University of Texas Pressure Core Center awaiting analysis. In the shallow section, samples will be used to determine the flux of organic carbon through the basin system, find the rate at which that carbon was consumed, and understand the microbial population responsible for these processes. In the deeper section, samples from in and around the hydrate reservoirs will be used to determine the petrophysical properties of the reservoir and bounding seals in these systems.

03 NATURAL GAS↗

Expedition UT-GOM2-2 Site H

Pressure and conventional cores were collected at Site H of the Walker Ridge Protracted Area Block 313 in the Terrebonne Basin, deepwater Gulf of America (Gulf of Mexico) during the University of Texas (UT) Deepwater Hydrate Coring Expedition (UT-GOM2-2). Pressure and conventional cores were collected continuously to a depth of 155.1 meters below the seafloor (mbsf). At deeper depths, cores were taken periodically from hydrate-bearing sands and their bounding muds to a total depth of 861.3 mbsf. 162.6 m of conventional core and 54.8 m of pressure core were recovered. Twelve temperature measurements were made between 27.1 and 144.5 mbsf to determine the geothermal gradient. At the seafloor, more than 4 m of sandy silt of unknown origin was encountered. Beneath this sand, to a depth of about 200 mbsf, the section was composed of interbedded mud and biogenic carbonate ooze. The ooze correlated to low density and high porosity intervals observed in the previously acquired logging while drilling (LWD) data and as measured. These ooze intervals also correspond to lighter sediment color, increased Ca content based on X-ray florescence (XRF) core scanning, and increased calcareous nannofossil abundance. Calcareous nannofossil biostratigraphy constrains the entire record to the Pleistocene (< 0.91 million years), with a pronounced increase in sedimentation rate with depth. Below 200 mbsf, the section was predominantly composed of mud with two thicker, hydrate-bearing coarse-grained intervals, which are commonly known as the Blue and Orange sands. The dissolved gas concentration was quantified from pressure cores. In the shallow section, dissolved methane concentration increased below the sulfate-methane transition zone (SMTZ) and reaches saturation (the limit of solubility for methane) at 147 mbsf. Gas expansion was very common in conventional and depressurized pressure (conventionalized) cores below the SMTZ. At deeper depths, the methane concentration within muds bounding the Blue and Orange reservoirs was generally found to be less than saturation. The dissolved and hydrate gas composition is consistent with a microbial source, containing greater than 99.99% methane and only trace concentrations of ethane, propane, and butane. The methane to ethane ratio (C1 /C2 ) and the methane to ethane plus propane (C1 /(C2 +C3 )) decrease with depth down to at least 678 mbsf, mainly driven by the increase in ethane with depth. It is unclear if this trend continues through the Orange sand interval. The δ13C isotopic signature of methane ranges between -69.9 and -78.5 ‰ relative to the Vienna Pee Dee Belemnite (VPDB) standard. Pressure core recovery in sandy intervals was poor. However, pressure core logs of the Orange sand show intervals of low density and high velocity, which are indicative of high hydrate saturation. One pressure core was degassed and the average hydrate saturation in the core was determined to be 24%. One core from within the Orange sand was composed of interbedded graded sandy silt and mud. The sandy silts from this core are composed of mainly quartz and feldspar with some lithics. Most of the recovered pressure core samples are maintained at near in-situ pressure and temperature (within the hydrate stability field) at the University of Texas Pressure Core Center awaiting analysis. In the shallow section, samples will be used to determine the flux of organic carbon through the basin system, find the rate at which that carbon was consumed, and understand the microbial population responsible for these processes. In the deeper section, samples from in and around the hydrate reservoirs will be used to determine the petrophysical properties of the reservoir and bounding seals in these systems.

03 NATURAL GAS↗

Quadrature solution for the general relativistic motion of a satellite or a planet.

The general relativistic motion of a particle in a bounded orbit around a central mass M is derived with the aid of the Schwarzschild field of M. A quadrature gives the central angle as a quasi-periodic function of an effective true anomaly. The mean rate of advance of the pericenter is investigated. Classical and general relativistic orbiters with the same initial conditions are compared, taking into account the treatment of the general relativistic effect by means of a differential correction. General relativistic variations are discussed, giving attention to the variation of the eccentric anomaly and the variation of the central angle.

Vinti, J. P.↗

Upper bounds on sequential decoding performance parameters

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.

Jelinek, F.↗

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

Cheyney, H., III↗

Jensen–Shannon divergence based novel loss functions for Bayesian neural networks

Bayesian neural networks (BNNs) are state-of-the-art machine learning methods that can naturally regularize and systematically quantify uncertainties using their stochastic parameters. Kullback–Leibler (KL) divergence-based variational inference used in BNNs suffer from unstable optimization and challenges in approximating light-tailed posteriors due to the unbounded nature of the KL divergence. To resolve these issues, we formulate a novel loss function for BNNs based on a new modification to the generalized Jensen–Shannon (JS) divergence, which is bounded. In addition, we propose a Geometric JS divergence-based loss, which is computationally efficient since it can be evaluated analytically. We found that the JS divergence-based variational inference is intractable, and hence employed a constrained optimization framework to formulate these losses. Our theoretical analysis and empirical experiments on multiple regression and classification data sets suggest that the proposed losses perform better than the KL divergence-based loss, especially when the data sets are noisy or biased. Specifically, there are approximately 5% and 8% improvements in accuracy for a noise-added CIFAR-10 dataset and a regression dataset, respectively. There is about 13% reduction in false negative predictions of a biased histopathology dataset. Additionally, we quantify and compare the uncertainty metrics for the regression and classification tasks.

97 MATHEMATICS AND COMPUTING↗

One-shot holography

Following the work of [J. High Energy Phys. 04, 062 (2021)], we define a generally covariant max-entanglement wedge of a boundary region B, which we conjecture to be the bulk region reconstructible from B. We similarly define a covariant min-entanglement wedge, which we conjecture to be the bulk region that can influence the state on B. We prove that the min- and max-entanglement wedges obey various properties necessary for this conjecture, such as nesting, inclusion of the causal wedge, and a reduction to the usual quantum extremal surface prescription in the appropriate special cases. These proofs rely on one-shot versions of the (restricted) quantum focusing conjecture (QFC) that we conjecture to hold. We argue that these QFCs imply a one-shot generalized second law (GSL) and quantum Bousso bound. Moreover, in a particular semiclassical limit we prove this one-shot GSL directly using algebraic techniques. Finally, in order to derive our results, we extend both the frameworks of one-shot quantum Shannon theory and state-specific reconstruction to finite-dimensional von Neumann algebras, allowing nontrivial centers.

Akers, Chris (ORCID:0000000227929827)↗

A critical examination of the validity of simplified models for radiant heat transfer analysis.

Examination of the directional effects of the simplified models by comparing the experimental data with the predictions based on simple and more detailed models for the radiation characteristics of surfaces. Analytical results indicate that the constant property diffuse and specular models do not yield the upper and lower bounds on local radiant heat flux. In general, the constant property specular analysis yields higher values of irradiation than the constant property diffuse analysis. A diffuse surface in the enclosure appears to destroy the effect of specularity of the other surfaces. Semigray and gray analyses predict the irradiation reasonably well provided that the directional properties and the specularity of the surfaces are taken into account. The uniform and nonuniform radiosity diffuse models are in satisfactory agreement with each other.

Toor, J. S.↗

On optimal soft-decision demodulation

A necessary condition is derived for optimal J-ary coherent demodulation of M-ary (M greater than 2) signals. Optimality is defined as maximality of the symmetric cutoff rate of the resulting discrete memoryless channel. Using a counterexample, it is shown that the condition derived is generally not sufficient for optimality. This condition is employed as the basis for an iterative optimization method to find the optimal demodulator decision regions from an initial 'good guess'. In general, these regions are found to be bounded by hyperplanes in likelihood space; the corresponding regions in signal space are found to have hyperplane asymptotes for the important case of additive white Gaussian noise. Some examples are presented, showing that the regions in signal space bounded by these asymptotic hyperplanes define demodulator decision regions that are virtually optimal.

Lee, L.-N.↗

On the error probability of general trellis codes with applications to sequential decoding

An upper bound on the average probability of error for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n with distinction between memory length and tail length is given. It is shown that the bound is independent of the length L of the information sequence if the memory length exceeds the tail length by a specified amount that depends on L. Sequential decoding simulations using the stack algorithm were conducted to test the dependence of the undetected error probability on tail length and memory length, and the results corroborated the theory.

Johannesson, R.↗

Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization

The problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case. The minimum value of the objective function can be obtained by solving a semiinfinite linear programming problem, and an iterative procedure for obtaining approximate solutions is introduced. Application of the l1-optimal problem to robustness is discussed. A mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations.

Dahleh, Munther A.↗

Harmonic oscillator representation in the theory of scattering and nuclear reactions

The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.

Smirnov, Yuri F.↗

Automorphic spectra and the conformal bootstrap

We describe a new method for constraining Laplacian spectra of hyperbolic surfaces and 2-orbifolds. The main ingredient is consistency of the spectral decomposition of integrals of products of four automorphic forms. Using a combination of representation theory of PSL 2 (R) and semidefinite programming, the method yields rigorous upper bounds on the Laplacian spectral gap. In several examples, the bound is nearly sharp. For instance, our bound on all genus-2 surfaces is λ 1 ≤ 3.8388976481, while the Bolza surface has λ 1 ≈ 3.838887258. The bounds also allow us to determine the set of spectral gaps attained by all hyperbolic 2-orbifolds. Our methods can be generalized to higher-dimensional hyperbolic manifolds and to yield stronger bounds in the two-dimensional case. The ideas were closely inspired by modern conformal bootstrap.

Kravchuk, Petr↗

The Cauchy Problem for Boltzmann Bi-linear Systems: The Mixing of Monatomic and Polyatomic Gases

Abstract From a unified vision of vector valued solutions in weighted Banach spaces, this paper establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex gas dynamical structures. This broader vision is directly applied to dilute multi-component gas mixtures composed of both monatomic and polyatomic gases. Such models can be viewed as extensions of scalar Boltzmann binary elastic flows, as much as monatomic gas mixtures with disparate masses and single polyatomic gases, providing a unified approach for vector valued solutions in weighted Banach spaces. Novel aspects of this work include developing the extension of a general ODE theory in vector valued weighted Banach spaces, precise lower bounds for the collision frequency in terms of the weighted Banach norm, energy identities, angular or compact manifold averaging lemmas which provide coerciveness resulting into global in time stability, a new combinatorics estimate for p -binomial forms producing sharper estimates for the k -moments of bi-linear collisional forms. These techniques enable the Cauchy problem improvement that resolves the model with initial data corresponding to strictly positive and bounded initial vector valued mass and total energy, in addition to only a $$2^+$$ 2 + moment determined by the hard potential rates discrepancy, a result comparable in generality to the classical Cauchy theory of the scalar homogeneous Boltzmann equation.

Physics↗

Radiative Electronic Bound States in the Continuum from Defects in Semiconductors

Continuum-buried defect states in semiconductors are generally expected to be optically inactive because of their strong coupling to continuum bands. Here, we show that such defects can instead host radiative electronic bound states in the continuum (BICs) using the silicon G center as a prototypical example. Hybrid functional first-principles calculations with a Hubbard U correction reveal that a localized defect state, initially buried below the valence band maximum (VBM) in the ground state, undergoes exchange-driven energy-level reordering under optical excitation and shifts above the VBM. This exchange-induced transition suppresses nonradiative decay and enables a robust radiative emission. By computing temperature-dependent nonradiative lifetimes and comparing them to experimental photoluminescence (PL) lifetimes, we quantitatively reproduce the observed temperature dependence of the emission. These results uncover a stabilization mechanism for continuum-embedded defect states and establish electronic BICs as a general paradigm for designing defect-based optical systems, including quantum emitters and qubits.

Hong, SeongYun↗