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At least 73 records · Page 4

Orbit Clustering Based on Transfer Cost

We propose using cluster analysis to perform quick screening for combinatorial global optimization problems. The key missing component currently preventing cluster analysis from use in this context is the lack of a useable metric function that defines the cost to transfer between two orbits. We study several proposed metrics and clustering algorithms, including k-means and the expectation maximization algorithm. We also show that proven heuristic methods such as the Q-law can be modified to work with cluster analysis.

combinatorial optimization↗

ACES M and S: Unmitigated Factorial Encounter Study on DAA/TCAS Interoperability

Realization of the expected proliferation of Unmanned Aircraft System (UAS) operations in the National Airspace System (NAS) depends on the development and validation of standards for UAS Detect and Avoid (DAA) Systems. The RTCA Special Committee 228 is charged with leading the development of draft Minimum Operational Performance Standards (MOPS) for UAS DAA Systems. NASA, as a participating member of RTCA SC-228 is committed to supporting the development and validation of draft requirements for DAA alerting and guidance systems. This presentation contains the results of two combinatorial encounter analysis studies using NASA's SAA Control fast-time simulation capability for this purpose. In these studies, encounters between two aircraft were simulated one at a time for the full factorial combination of encounter geometries (e.g., encounter angle, CPA offset) and aircraft performance (e.g., ownership and intruder ground speeds and vertical rates). The first study analyzes the relationships (e.g., timeline) between the different alerting-safety regions in the SC-228 MOPS (in order of increasing severity): 1) DAA warning alert, 2) well clear recovery (WCR) guidance, 3) DAA-Collision Avoidance (CA), and 4) TCAS RA. This study will focus primarily on encounter situations in which TCAS RA occurs prior to any of the other alerting-safety boundaries. In particular, this study will investigate whether using vertical distance or vertical distance at closest point of approach (i.e., vertical miss distance or VMD) is more appropriate for the definition of the DAA-CA region. In addition, cases where transitions between different regions skip an intermediate region will be analyzed. The second study in this presentation explores a proposal to use an altitude rate error threshold to determine if vertical maneuvers are acceptable for DAA WCR guidance against non-cooperative intruders. This study incorporates the radar from the Honeywell sensor model and examines a series of pairwise encounters between a non-cooperative intruder and a UAS ownship, with different combinations of intruder states and ownship performance levels. The study uses SAA Control as a simulation platform and pilot model, and Omnibands to provide DWC recovery guidance. Two simulation sets, one that allows vertical DWC recovery guidance and one that does not, are compared to determine if encounters with altitude rate errors above 250 feet-per-minute are more likely to have more severe losses of well clear, as determined by the Loss of Well-Clear Severity metric.

SaaControl↗

SEAL /Subnetwork Enumeration And Listing/

SEAL /Subnetwork Enumeration And Listing/ computer program uses combinatorial techniques to generate all of the nonredundant subnetwork configurations derivable from an asymmetrical network or device. This is accomplished by a systematic shorting and opening of accessible terminals to obtain the desired allowable configurations.

Happ, W. W.↗

Communications system research

Coding, synchronization, combinatorial, multiple access, propagation, and permutation studies for telecommunications systems

Source record↗

Methodologies for optimal resource allocation to the national space program and new space utilizations. Volume 1: Technical description

The optimal allocation of resources to the national space program over an extended time period requires the solution of a large combinatorial problem in which the program elements are interdependent. The computer model uses an accelerated search technique to solve this problem. The model contains a large number of options selectable by the user to provide flexible input and a broad range of output for use in sensitivity analyses of all entering elements. Examples of these options are budget smoothing under varied appropriation levels, entry of inflation and discount effects, and probabilistic output which provides quantified degrees of certainty that program costs will remain within planned budget. Criteria and related analytic procedures were established for identifying potential new space program directions. Used in combination with the optimal resource allocation model, new space applications can be analyzed in realistic perspective, including the advantage gain from existing space program plant and on-going programs such as the space transportation system.

Source record↗

Aspects of job scheduling

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Communications Complex, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germane to scheduling are presented.

Phillips, K.↗

Sin(x)**2 + cos(x)**2 = 1

Attempts to achieve tasteful automatic employment of the identities sin sq x + cos sq x = 1 and cos sq h x -sin sq h x = 1 in a manner which truly minimizes the complexity of the resulting expression are described. The disappointments of trigonometric reduction, trigonometric expansion, pattern matching, Poisson series, and Demoivre's theorem are related. The advantages of using the method of comparative combinatorial substitutions are illustrated.

Stoutemyer, D. R.↗

Behavior of queues at signalized intersections in heavy traffic

This paper derives the asymptotic behavior of traffic queues at signalized intersections when the excess of departure capacity over arrivals approaches zero from above. The most interesting result is that the distribution of queue length approaches a negative exponential, with fewer restrictive assumptions than hitherto known. The main improvement results from more precise use of a combinatorial lemma of Spitzer, giving the maximum of the partial sums of a sequence of independent identically distributed random variables, plus some specific constructive probability calculations, many of them involving the Fourier transform. New results are presented on the probability that the queue be below a fixed bound and/or on the probability that the queue be empty. Applications to on-line estimators for real-time traffic control are suggested.

Posner, E. C.↗

On the existence of binary simplex codes

Using a simple combinatorial construction, the existence of a binary simplex code with m codewords for all m is greater than or equal to 1 is proved. The problem of the shortest possible length is left open.

Taylor, H.↗

The Lovasz bound and some generalizations

The zero error capacity of a discrete memoryless channel is defined as the largest rate at which information can be transmitted over the channel with zero error probability. One channel with five inputs and outputs whose zero capacity remained unsolved until very recently is considered. An extremely powerful and general technique phased in terms of graph theory, for studying combinatorial packing problems is presented. In particular, Delsarte's linear programming bound for cliques in association schemes appears as a special case of the Lovasz bound.

Mceliece, R. J.↗

An upper bound for codes in a two-access binary erasure channel

A method for determining an upper bound for the size of a code for a two-access binary erasure channel is presented. For uniquely decodable codes, this bound gives a combinatorial proof of a result by Liao. Examples of the bound are given for codes with minimum distance 4.

Van Tilborg, H. C. A.↗