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In this paper, an analytical method for comparing the performance of an ideal forecasting algorithm to the best statistical methods in terms of average data return is derived.
Recently, the problem of compiling general quantum algorithms for implementation on near-term quantum processors has been introduced to the AI community. Previous work demonstrated that temporal planning is an attractive approach for part of this compilation task, specifically, the routing of circuits that implement the Quantum Alternating Operator Ansatz (QAOA) applied to theMaxCut problem on a quantum processor architecture. In this paper, we extend the earlier work to route circuits that implement QAOAfor Graph Coloring problems. QAOA for coloring requires execution of more, and more complex, operations on the chip, which makes routing a more challenging problem. We evaluate the approach on state-of-the-art hardware architectures from leading quantum computing companies. Additionally, we investigate applying the planning approach to qubit initialization as well as routing. Our empirical evaluation shows that temporal planning compares well to reasonable analytic upper bounds [20], and that solving qubit initialization with a classical planner generally helps temporal planners in finding shorter-makespan compilations for QAOA for Graph Coloring.These advances suggest that temporal planning can be an effective approach for more complex quantum computing algorithms and architectures.
Given a system which can fail in 1 or n different ways, a fault detection and isolation (FDI) algorithm uses sensor data in order to determine which fault is the most likely to have occurred. The effectiveness of an FDI algorithm can be quantified by a confusion matrix, which i ndicates the probability that each fault is isolated given that each fault has occurred. Confusion matrices are often generated with simulation data, particularly for complex systems. In this paper we perform FDI using sums of squares of sensor residuals (SSRs). We assume that the sensor residuals are Gaussian, which gives the SSRs a chi-squared distribution. We then generate analytic lower and upper bounds on the confusion matrix elements. This allows for the generation of optimal sensor sets without numerical simulations. The confusion matrix bound s are verified with simulated aircraft engine data.
Using an exhaustive computation, the unequal error protection capabilities of all binary cyclic codes of odd length up to 65 that have minimum distances at least 3 are found. For those codes that can only have upper bounds on their unequal error protection capabilities computed, an analytic method developed by Dynkin and Togonidze (1976) is used to show that the upper bounds meet the exact unequal error protection capabilities.
This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.
In the past few years, the mixed H(sub 2)/H-infinity control problem has been the object of much research interest since it allows the incorporation of robust stability into the LQG framework. The general mixed H(sub 2)/H-infinity design problem has yet to be solved analytically. Numerous schemes have considered upper bounds for the H(sub 2)-performance criterion and/or imposed restrictive constraints on the class of systems under investigation. Furthermore, many modern control applications rely on dynamic models obtained from finite-element analysis and thus involve high-order plant models. Hence the capability to design low-order (fixed-order) controllers is of great importance. In this research a new design method was developed that optimizes the exact H(sub 2)-norm of a certain subsystem subject to robust stability in terms of H-infinity constraints and a minimal number of system assumptions. The derived algorithm is based on a differentiable scalar time-domain penalty function to represent the H-infinity constraints in the overall optimization. The scheme is capable of handling multiple plant conditions and hence multiple performance criteria and H-infinity constraints and incorporates additional constraints such as fixed-order and/or fixed structure controllers. The defined penalty function is applicable to any constraint that is expressible in form of a real symmetric matrix-inequity.
The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.
The resonance diffusion of electrons in velocity space caused by the excited EM wave fields is considered to be the dominant saturation process of cyclotron maser instability that is driven by an electron loss-cone distribution. An upper bound of the saturation level is derived analytically. Since the resulting saturation level is low, the resonance diffusion is indeed responsible for the saturation of the cyclotron maser instability.
The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.
The apparent tidal disruption of Periodic Comet Shoemaker-Levy 9 (1993e) during a close encounter within approximately 1.62 planetary radii of Jupiter can be used along with theoretical models of tidal disruption to place an upper bound on the density of the predisruption body. Depending on the theoretical model used, these upper bounds range from rho(sub c) less than 0.702 +/- 0.080 g/cu cm for a simple analytical model calibrated by numerical smoothed particle hydrodynamics (SPH) simulations to rho(sub c) less than 1.50 +/- 0.17 g/cu cm for a detailed semianalytical model. The quoted uncertainties stem from an assumed uncertainty in the perijove radius. However, the uncertainty introduced by the different theoretical models is the major source of error; this uncertainty could be eliminated by future SPH simulations specialized to cometary disruptions, including the effects of initially prolate, spinning comets. If the SPH-based upper bound turns out to be most appropriate, it would be consistent with the predisruption body being a comet with a relatively low density and porous structure, as has been asserted previously based on observations of cometary outgassing. Regardless of which upper bound is preferable, the models all agree that the predisruption body could not have been a relatively high-density body, such as an asteroid with rho approximately = 2 g/cu cm.
A three-dimensional numerical model for current collection in a magnetized plasma is reported. The model is based on an electrostatic particle-in-cell code. The model yields self-consistent sheath structure including distributions of plasma and the electric potential around the body and the collection of electrons. The analytical theory of current collection by a body in a magnetized plasma yields an upper bound for the collected current determined by the conservation of energy and canonical angular momentum. The theory shows that the collected charged particles come from a cylindrical volume aligned with the magnetic shadow of the body; the maximum radius r(sub o) of this volume is determined by the body size, body potential, and the ambient magnetic field. This theory does not deal with the sheath structure around the body. The condition for the actual current to approach the upper-bound value has been a matter of debate. Our simulations reveal when and why the collected current becomes equal to its upper-bound value. Sheath size in the radial direction perpendicular to the axial ambient magnetic field is determined by the current-limiting radius r(sub o). Our simulation yields time-average current in good agreement with its upper bound. This feature of the current collection is explained as follows: Once electrons enter the sheath, some of them are freely accelerated perpendicular to the magnetic field because they are demagnetized by the large gradients in the perpendicular electric fields. Simulations show a large perpendicular acceleration, producing perpendicular energy as large as that determined by the potential on the body, especially in the region where perpendicular electric fields (E perpendicular) are the strongest. An analysis shows that the demagnetization of electrons occurs above a threshold potential on the body. This threshold condition follows from the breakdown of the adiabaticity of the electron dynamics inside the sheath.
The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.
The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.
Based on moving total Lagrangian coordinates, a so-called traveling Hughes type contact strategy is developed. Employing the modified contact scheme in conjunction with a traveling finite element strategy, an overall solution methodology is developed to handle transient and steady viscoelastic rolling contact. To verify the scheme, the results of both experimental and analytical benchmarking is presented. The experimental benchmarking includes the handling of rolling tires up to their upper bound behavior, namely the standing wave response.
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.
The magnetic determination of the depth of the core-mantle boundary using MAGSAT data is discussed. Refinements to the approach of using the pole-strength of Earth to evaluate the radius of the Earth's core-mantle boundary are reported. The downward extrapolation through the electrically conducting mantle was reviewed. Estimates of an upper bound for the time required for Earth's liquid core to overturn completely are presented. High order analytic approximations to the unsigned magnetic flux crossing the Earth's surface are also presented.
The effects of programmer experience level, different program usage distributions, and programming languages are explored. All these factors affect performance, and some tentative relational hypotheses are presented. An analytic framework for replicated and non-replicated (traditional) software experiments is presented. A method of obtaining an upper bound on the error rate of the next error is proposed. The method was validated empirically by comparing forecasts with actual data. In all 14 cases the bound exceeded the observed parameter, albeit somewhat conservatively. Two other forecasting methods are proposed and compared to observed results. Although demonstrated relative to this framework that stages are neither independent nor exponentially distributed, empirical estimates show that the exponential assumption is nearly valid for all but the extreme tails of the distribution. Except for the dependence in the stage probabilities, Cox's model approximates to a degree what is being observed.
The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occurs. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub e (u) for the (255, 223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.