Enumeration of 3-letter patterns in compositions

Let A be any set of positive integers and n a positive integer. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. We derive generating functions for the number of compositions of n with m parts in A that have r occurrences of 3-letter patterns formed by two (adjacent) instances of levels, rises and drops. We also derive asymptotics for the number of compositions of n that avoid a given pattern. Finally, we obtain the generating function for the number of k-ary words of length m which contain a prescribed number of occurrences of a given pattern as a special case of our results.Comment: 20 pages, 1 figure; accepted for the Proceedings of the 2005 Integer Conferenc

Supplementary publications presented by Mr J. M. Stagg for the degree of D.Sc.

Volume 01 | BRITISH POLAR YEAR EXPEDITION FORT RAE, N.W. CANADA 1932-33 VOLUME I | DISCUSSION OF RESULTSVolume 02 | BRITISH POLAR YEAR EXPEDITION FORT RAE, N.W. CANADA 1932-33 VOLUME II | TABLESVolume 03 | 01. Some General Characteristics of Aurora at Fort Rae N.W. Canada 1932-33 | 02. NUMERICAL CHARACTER FIGURES OF MAGNETIC DISTURBANCE IN RELATION TO GEOMAGNETIC LATITUDE | 03. .Aspects of the Current System Producing Magnetic Disturbance | 04. The Diurnal Variation of Magnetic Disturbance in High Latitudes | 05. On the Variability of the Quiet -Day Diurnal Magnetic Variation at Eskdalemuir and Greenwich. By S. CHAPMAN, F.R.S., AND J. M. STAGG. | 06. On the Variability of the Quiet -Day Diurnal Magnetic Variation. Part II. BY S. CHAPMAN, F.R.S., AND J. M. STAGG. | 07. On the Variability of the Quiet -Day Diurnal Magnetic Variation. Part II. BY S. CHAPMAN, F.R.S., AND J. M. STAGG. | 08. Hourly Character Figures of Magnetic Disturbance at Kew Observatory, Richmond 1913-23 | 09. The Time Interval BETWEEN Magnetic Disturbance AND Associated Sunspot Changes | 10. THE ABSOLUTE DAILY RANGE OF MAGNETIC DECLINATION AT KEW OBSERVATORY, RICHMOND, 1901 to 1910 | 11. On Magnetic Fluctuations and Sunspot Frequency: A Discussion based primarily on the daily ranges of Declination as recorded at Kew Observatory, Richmond, during the 67 years 1858-1924 | 12. The 27-Day Recurrence Interval in Magnetic Disturbance: An Examination made with the aid of hourly Character Figures

Numerical modeling of dielectrophoretic effect for manipulation of bio-particles

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This text describes different aspects of the design of a Doctor-on-a-Chip device. Doctor-on-a-Chip is a DNA analysis system integrated on a single chip, which should provide all of the advantages that stem from the system integration, such as small sample volume, fast and accurate analysis, and low cost. The text describes all of the steps of the on-chip sample analysis, including DNA extraction from the sample, purification, PCR amplification, novel dielectrophoretic sorting of the DNA molecules, and finally detection. The overview is given of the technologies which are available to make the integration on a single chip possible. The microfluidic technologies that are used to manipulate the sample and other chemical reagents are already known and in this text they are analyzed in terms of their feasibility in the on-chip system integration. These microfluidic technologies include, but are not limited to, microvalves, micromixers, micropumps, and chambers for PCR amplification. The novelty in the DNA analysis brought by Doctor-on-a-Chip is the way in which the different DNA molecules in the sample (for example, human and virus DNA) are sorted into different populations. This is done by means of dielectrophoresis – the force experienced by dielectric particles (such as DNA molecules) when subject to a non-uniform electric field. Different DNA molecules within a sample experience different dielectrophoretic forces within the same electric field, which makes their separation, and therefore detection, possible. In this text, the emphasis is put on numerical modelling of the dielectrophoretic effect on biological particles. The importance of numerical modelling lies in the fact that with the accurate model it is easier to design systems of microelectrodes for dielectrophoretic separation, and tune their sub-micrometre features to achieve the maximum separation efficacy. The numerical model described in this text is also experimentally verified with the novel microelectrodes design for dielectrophoretic separation, which is successfully used to separate the mixture of different particles in the micron and sub-micron range

Specification and Model-driven Trace Checking of Complex Temporal Properties

Offline trace checking is a procedure used to evaluate requirement properties over a trace of recorded events. System properties verified in the context of trace checking can be specified using different specification languages and formalisms; in this thesis, we consider two classes of complex temporal properties: 1) properties defined using aggregation operators; 2) signal-based temporal properties from the Cyber Physical System (CPS) domain. The overall goal of this dissertation is to develop methods and tools for the specification and trace checking of the aforementioned classes of temporal properties, focusing on the development of scalable trace checking procedures for such properties. The main contributions of this thesis are: i) the TEMPSY-CHECK-AG model-driven approach for trace checking of temporal properties with aggregation operators, defined in the TemPsy-AG language; ii) a taxonomy covering the most common types of Signal-based Temporal Properties (SBTPs) in the CPS domain; iii) SB-TemPsy, a trace-checking approach for SBTPs that strikes a good balance in industrial contexts in terms of efficiency of the trace checking procedure and coverage of the most important types of properties in CPS domains. SB-TemPsy includes: 1) SB-TemPsy-DSL, a DSL that allows the specification of the types of SBTPs identified in the aforementioned taxonomy, and 2) an efficient trace-checking procedure, implemented in a prototype tool called SB-TemPsy-Check; iv) TD-SB-TemPsy-Report, a model-driven trace diagnostics approach for SBTPs expressed in SB-TemPsy-DSL. TD-SB-TemPsy-Report relies on a set of diagnostics patterns, i.e., undesired signal behaviors that might lead to property violations. To provide relevant and detailed information about the cause of a property violation, TD-SB-TemPsy-Report determines the diagnostics information specific to each type of diagnostics pattern. Our technological contributions rely on model-driven approaches for trace checking and trace diagnostics. Such approaches consist in reducing the problem of checking (respectively, determining the diagnostics information of) a property over an execution trace to the problem of evaluating an OCL (Object Constraint Language) constraint (semantically equivalent to ) on an instance (equivalent to ) of a meta-model of the trace. The results — in terms of efficiency of our model-driven tools—presented in this thesis are in line with those presented in previous work, and confirm that model-driven technologies can lead to the development of tools that exhibit good performance from a practical standpoint, also when applied in industrial contexts