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We present a general union-Chernoff bound on the bit error probability for coded communication systems and apply it to examples of antijam systems. The key feature of this bound is the decoupling of the coding aspects of the system from the remaining part of the communication system which includes jamming, suboptimum detectors, and arbitrary decoding metrics which may or may not use jammer state knowledge
An improved finite difference procedure based upon second order central differences is developed. Several difficulties encountered in earlier works with fictitious stations that arise in using second order central differences, are eliminated by developing certain recursive relations. The need for forward or backward differences at the beam boundaries or other similar procedures is eliminated in the present theory. By using this improved theory, the vibration characteristics of pretwisted and tapered blades are calculated. Results of the second order theory are compared with published theoretical and experimental results and are found to be in good agreement. The present method generally produces close lower bound solutions and shows fast convergence. Thus, extrapolation procedures that are customary with first order finite-difference methods are unnecessary. Furthermore, the computational time and effort needed for this improved method are almost the same as required for the conventional first order finite-difference approach.
Random access signaling, which allows slotted packets to spill over into adjacent slots, is investigated. It is shown that sloppy-slotted ALOHA can always provide higher throughput than conventional slotted ALOHA. The degree of improvement depends on the timing error distribution. Throughput performance is presented for Gaussian timing error distributions, modified to include timing error corrections. A general channel capacity lower bound, independent of the specific timing error distribution, is also presented.
A bidirectional horizontal-path optical link was demonstrated between Strawberry Peak (SP), Lake Arrowhead, California, and the JPL Table Mountain Facility (TMF), Wrightwood, California, during June and November of 1998. The 0.6-m telescope at TMF was used to broadcast a 4-beam 780-nm beacon to SP. The JPL-patented Optical Communications Demonstrator (OCD) at SP received the beacon, performed ne tracking to compensate for the atmosphere-induced beacon motion and retransmitted a 844-nm communications laser beam modulated at 40 to 500 Mb/s back to TMF. Characteristics of the horizontal-path atmospheric channel as well as performance of the optical communications link were evaluated. The normalized variance of the irradiance fluctuations or scintillation index delta2/I at either end was determined. At TMF where a single 844-nm beam was received by a 0.6-m aperture, the measured delta2/I covered a wide range from 0.07 to 1.08. A single 780-nm beam delta2/I measured at SP using a 0.09-m aperture yielded values ranging from 0.66 to 1.03, while a combination of four beams reduced the scintillation index due to incoherent averaging to 0.22 to 0.40. This reduction reduced the dynamic range of the fluctuations from 17 to 21 dB to 13 to 14 dB as compared with the OCD tracking sensor dynamic range of 10 dB. Predictions of these values also were made based on existing theories and are compared. Generally speaking, the theoretical bounds were reasonable. Discussions on the probability density function (PDF) of the intensity fluctuations are presented and compared with the measurements made. The lognormal PDF was found to agree for the weak scintillation regime as expected. The present measurements support evidence presented by earlier measurements made using the same horizontal path, which suggests that the aperture averaging effect is better than theoretically predicted.
An important step in system identification of aircraft is the estimation of stability and control derivatives from flight data along with an assessment of parameter accuracy. When the maximum likelihood estimation technique is used, parameter accuracy is commonly assessed by the Cramer-Rao lower bound. It is known, however, that in some cases the lower bound can be substantially different from the parameter variance. Under these circumstances the Cramer-Rao bounds may be misleading as an accuracy measure. This paper discusses the confidence interval estimation problem based on likelihood ratios, which offers a more general estimate of the error bounds. Four approaches are considered for computing confidence intervals of maximum likelihood parameter estimates. Each approach is applied to real flight data and compared.
Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.
Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.
This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector (n, b) in terms of linear matrix inequalities in its state-space realization matrices, which represents a generalization of similar conditions for bounded H(sub infinity)-norm systems. Further, a weaker definition of LTI systems strictly inside closed sector (a, b) is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems.
The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.
The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.
Two classes of nonparametric density estimators, the histogram and the kernel estimator, both require a choice of smoothing parameter, or 'window width'. The optimum choice of this parameter is in general very difficult. An upper bound to the choices that depends only on the standard deviation of the distribution is described.
We consider the problem of triangulating a d-dimensional uniform grid of d-cubes that is cut by a k-dimensional affine subspace. The goal is to obtain a triangulation with bounded aspect ratio. To achieve this goal, we allow some of the box faces near the affine subspace to be displaced. This problem has applications to finite element mesh generation. For general d and k, the bound on aspect ratio that we attain is double-exponential in d. For the important special case of d = 3, the aspect ratio bound is small enough that the technique is useful in practice.
In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.
Lunar mare basalts are depleted in F and Cl by approximately an order of magnitude relative to mid-ocean ridge basalts and contain two Cl-bearing components with elevated isotopic compositions relative to the bulk-Earth value of ∼0‰. The first is a watersoluble chloride constituting 65 ± 10% of total Cl with δ37Cl values averaging 3.0 ± 4.3‰. The second is structurally bound chloride with δ37Cl values averaging 7.3 ± 3.5‰. These high and distinctly different isotopic values are inconsistent with equilibrium fractionation processes and instead suggest early and extensive degassing of an isotopically light vapor. No relationship is observed between F/Cl ratios and δ37Cl values, which suggests that lunar halogen depletion largely resulted from the Moon-forming Giant Impact. The δ37Cl values of apatite are generally higher than the structurally bound Cl, and ubiquitously higher than the calculated bulk δ37Cl values of 4.1 ± 4.0‰. The apatite grains are not representative of the bulk rock, and instead record localized degassing during the final stages of lunar magma ocean (LMO) or later melt crystallization. The large variability in the δ37Cl values of apatite within individual thin sections further supports this conclusion. While urKREEP (primeval KREEP [potassium/rare-earth elements/phosphorus]) has been proposed to be the source of the Moon’s high Cl isotope values, the ferroan anorthosites (FANs) have the highest δ37Cl values and have a positive correlation with Cl content, and yet do not contain apatite, nor evidence of a KREEP component. The high δ37Cl values in this lithology are explained by the incorporation of a >30‰ HCl vapor from a highly evolved LMO.
We study future DUNE sensitivity to various electromagnetic couplings of neutrinos, including magnetic moments, milli-charges, and charge radii. The DUNE PRISM capabilities play a crucial role in constraining the electron flavored couplings. We find that DUNE will be able to place the strongest beam based constraint on the muon-neutrino magnetic moment by improving on LSND’s bounds by roughly a factor of two, although Borexino’s constraint from solar neutrinos will be stronger. For the muon neutrino millicharge DUNE can place the leading beam based bound, with two orders of magnitude improvement compared to the existing COHERENT constraint, suggesting that DUNE can be useful for light mediators more generally. Despite this strength, the millicharge bounds are not competitive with strong bounds from stellar cooling, beta-decay, and matter stability. Finally, DUNE may be able to test the SM prediction for the muon neutrino charge radius, by placing a constraint two times better than CHARM-II and CCFR experiments.
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.
The first general research objective was to address control design challenges of the Spacecraft Control Laboratory Experiment (SCOLE) via the two stage approach: (1) slew the whole as if it were a rigid body about one Space Shuttle body axis each time using the onboard Reaction Control System (RCS) thrusters; and (2) damp out excited vibrations. The second objective was to examine the feasibility of applying the approach to shuttle-attached flexible space structures. The following was accomplished: (1) a standard bang-bang control technique was adapted; (2) a slew rate limit was imposed in the design; and (3) slew acceleration deviation was defined as the index of slew performance degradation.
Lactones are prevalent in biological and industrial settings, yet there is a lack of information regarding enzymes used to metabolize these compounds. One compound, γ-valerolactone (GVL), is used as a solvent to dissolve plant cell walls into sugars and aromatic molecules for subsequent microbial conversion to fuels and chemicals. Despite the promise of GVL as a renewable solvent for biomass deconstruction, residual GVL can be toxic to microbial fermentation. Here, we identified a Ca 2+ -dependent enzyme from Rhodopseudomonas palustris (Rpa3624) and showed that it can hydrolyze aliphatic and aromatic lactones and esters, including GVL. Maximum-likelihood phylogenetic analysis of other related lactonases with experimentally determined substrate preferences shows that Rpa3624 separates by sequence motifs into a subclade with preference for hydrophobic substrates. Additionally, we solved crystal structures of this β-propeller enzyme separately with either phosphate, an inhibitor, or a mixture of GVL and products to define an active site where calcium-bound water and calcium-bound aspartic and glutamic acid residues make close contact with substrate and product. Our kinetic characterization of WT and mutant enzymes combined with structural insights inform a reaction mechanism that centers around activation of a calcium-bound water molecule promoted by general base catalysis and close contacts with substrate and a potential intermediate. Similarity of Rpa3624 with other β-propeller lactonases suggests this mechanism may be relevant for other members of this emerging class of versatile catalysts.