An extension of set partitioning with application to scheduling problems

The well known problems of set covering, set partitioning and set packing are defined and their interrelationship is considered. A natural generalisation called the extended set partitioning model is presented and the three standard models are shown to be special cases of this generalisation. In addition, the extended model includes another type of set problem which can be of greater use in certain applications. The model forms the basis of a computer assisted bus crew scheduling system developed by the authors. The system is in regular use by Dublin City Services in the Republic of Ireland. Finally, the equivalence between a special case of the set partitioning problem and the shortest route problem is considered and it is shown that this equivalence also applies to the extended model

On the construction of a digital transfer function from its real part on unit circle

It is shown in this correspondence that the system function H(z) of a linear time invariant (LTI) causal digital filter with real impulse response coefficients can be obtained from the real part of its frequency response HR(ejω) given in the form of a rational trigonomentric function, using algebraic methods rather than complex contour integration techniques

Polyphase networks, block digital filtering, LPTV systems, and alias-free QMF banks: a unified approach based on pseudocirculants

The relationship between block digital filtering and quadrature mirror filter (QMF) banks is explored. Necessary and sufficient conditions for alias cancellation in QMF banks are expressed in terms of an associated matrix, derived from the polyphase components of the analysis and synthesis filters. These conditions, called the pseudocirculant conditions, make it possible to unite QMF banks with the framework of block digital filtering directly. Absence of amplitude distortion in an alias-free QMF bank translates into the 'losslessness' property of the pseudocirculant matrix involved

Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures

The concepts of losslessness and maximum available power are basic to the low-sensitivity properties of doubly terminated lossless networks of the continuous-time domain. Based on similar concepts, we develop a new theory for low-sensitivity discrete-time filter structures. The mathematical setup for the development is the bounded-real property of transfer functions and matrices. Starting from this property, we derive procedures for the synthesis of any stable digital filter transfer function by means of a low-sensitivity structure. Most of the structures generated by this approach are interconnections of a basic building block called digital "two-pair," and each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The theory and synthesis procedures also cover special cases such as wave digital filters, which are derived from continuous-time networks, and digital lattice structures, which are closely related to unit elements of distributed network theory

T invariance of Higgs interactions in the standard model

In the standard model, the Cabibbo-Kobayashi-Maskawa matrix, which incorporates the time-reversal violation shown by the charged current weak interactions, originates from the Higgs-quark interactions. The Yukawa interactions of quarks with the physical Higgs particle can contain further complex phase factors, but nevertheless conserve T, as shown by constructing the fermion T transformation and the invariant euclidean fermion measure.Comment: LaTeX, 4 pages; presented at PASCOS'0

Very low sensitivity FIR filter implementation using 'structural passivity' concept

The concept of "structurally bounded" or "structurally passive" FIR filter implementation is introduced, as a means of achieving very low passband sensitivities. The resulting filter structures, called FIRBR structures, can easily be transformed into very low-sensitivity "passive" two-dimensional FIR filter structures. From a layout point of view, the new structures are not any more complicated than the well-known cascade form. The FIRBR structures do not depend, for synthesis, upon continuous-time filter circuits

A Volume Clearing Algorithm for Muon Tomography

The primary objective is to enhance muon-tomographic image reconstruction capability by providing distinctive information in terms of deciding on the properties of regions or voxels within a probed volume "V" during any point of scanning: threat type, non-threat type, or not-sufficient data. An algorithm (MTclear) is being developed to ray-trace muon tracks and count how many straight tracks are passing through a voxel. If a voxel "v" has sufficient number of straight tracks (t), then "v" is a non-threat type voxel, unless there are sufficient number of scattering points (p) in "v" that will make it a threat-type voxel. The algorithm also keeps track of voxels for which not enough information is known: where p and v both fall below their respective threshold parameters. We present preliminary results showing how the algorithm works on data collected with a Muon Tomography station based on gas electron multipliers operated by our group. The MTclear algorithm provides more comprehensive information to a human operator or to a decision algorithm than that provided by conventional muon-tomographic reconstruction algorithms, in terms of qualitatively determining the threat possibility from a probed volume. This is quite important because only low numbers of cosmic ray source muons are typically available in nature for tomography, while a quick determination of threats is essential.Comment: 3 pages, 3 figures, submitted to conf. record of 2014 IEEE Nucl. Sci. Symposium, Seattl