Human-Computer Interaction (HCI) in tradition is narrow defined the communication of information between human and machines. Because the limited of the HCI's speed and the natural level, it needs to use the medium form such as symbol instructions and buttons to express the intent of human. In recent year, the trend of HCI development will be focused on human, with directly computing, determining, and displaying technologies progress, and constantly innovation. Somatosensory equipment not only breaks through the limit of HCI but also the mode of interaction of traditional equipment. Somatosensory equipment can retrieve images through the infrared projector or visible camera, capture the human motion and action, and increase its interaction for natural and intuition. But unfortunately, most of systems are limited to a unique application for special areas, and only detected specific sequences of actions. Once changing the interaction of applications then users have to rewrite the action sequences recognition program to satisfy the somatosensory demands. System cannot be defined human action sequences flexible according the applications request of users, the production process is complex and the scope of application is narrow. This thesis presents an Authoring Tool of Vision-based Somatosensory Action (ATVISA) to improve the drawback. Users can define the human action sequences by the graphical interface, customize the visual detection quickly and recognize correspond to the Somatosensory Action. Till the Somatosensory equipment detects the defined action sequences, triggering the correspond event and dealing with the event request. This thesis employs ATVISA applied to the action sequences and three rehabilitation projects, that with the flexibility and diversification. Users also can compile human action sequences with professional expertise to application to area of education, game, rehabilitation, and so on.

The longest common subsequence (LCS) problem is a famous and classical problem in computer science and molecular biology. The common subsequence of multiple sequences shows the identical and similar parts in these sequences. This dissertation pays attention to the approximate algorithms for finding the LCS of $k$ input sequence ($k$-LCS problem), the merged LCS problem, and the mosaic LCS problem. These three problems try to hunt out the identical relationships among the $k$ sequences, the interleaving relationship between a target sequence and a merged sequence of a pair of sequences, and the mosaic relationship between a target sequence and a set of sequences, respectively. Given $k$ input sequences, the $k$-LCS problem is to find the LCS which is common in all sequences. We first propose two $sigma$-approximate algorithms for the $k$-LCS problem with time complexities $O(sigma k n)$ and $O(sigma^{2} k n + sigma^{3} n)$ respectively, where $sigma$ and $n$ are the alphabet size and length of sequences, respectively. Experimental results show that our algorithms for 2-LCS could be a good filter to select the candidate sequences in database searching. Given a target sequence $T$ and a pair of merging sequences $A$ and $B$, the merged LCS problem is to find the LCS of $T$ and the optimally merged sequence by merging $A$ and $B$ alternately. Its goal is to find a merging way for understanding the interleaving relationship of sequences. We first propose an algorithm with $O(n^{3})$ time for solving the problem, where $n$ is the sequence length. We further add the block information of input sequences in the blocked merged LCS problem. To solve the latter problem, we propose an algorithm with time complexity $O(n^{2}m_{b})$, where $m_{b}$ is the number of blocks. Based on the S-table technique, we can design an improved algorithm with $O(n^{2} + nm_{b}^{2})$ time. Additionally, we desire to obtain the relationship between one sequence and a set of sequences. Given a target sequence $T$ and a set $S$ of source sequences, the mosaic LCS problem is to find the LCS of $T$ and a mosaic sequence $C$, composed of repeatable $k$ sequences in $S$. Based on the concept of break points in $T$, a divide and conquer algorithm is proposed with $O(n^2m|S|+ n^3log k)$ time, where $n$ and $m$ are the lengths of $T$ and the maximal length of sequences in $S$, respectively. Again, based on the S-table technique, an improved algorithm with $O(n(m+k)|S|)$ time is proposed by applying an efficient preprocessing.

A huge number of genomic information, including protein and DNA sequences, is generated by the human genome project. Deciphering these sequences and detecting local residue patterns of multiple sequences are very difficult. One of the ways to decipher these biological sequences is to detect local residue patterns from them. However, detecting unknown patterns from multiple sequences is still very difficult. In this thesis, we propose an algorithm, based on the Gibbs sampler method, for identifying local consensus patterns (motifs) in monomolecular sequences. We first designed an ACO (ant colony optimization) algorithm to find a good initial solution and a set of better candidate positions for revising the motif. Then the Gibbs sampler method is applied with these better candidate positions as the input. The required time for finding motifs using our algorithm is reduced drastically. It takes only 20 % of time of the Gibbs sampler method and it maintains the comparable quality.

Thesis--M. Phil., University of Hong Kong, 1986.

The thesis offers an investigation into the analysis of so-called iterated generating functions and the schemes that produce them. Beginning with the study of some ad hoc scheme formulations, the notion of an iterated generating function is introduced and a mechanism to produce arbitrary finite sequences established. The development of schemes to accommodate infinite sequences leads – in the case of the Catalan sequence – to the discovery of what are termed Catalan polynomials whose properties are examined. Results are formulated for these polynomials through the algebraic adaptation of classical root-finding algorithms, serving as a basis for the synthesis of new generalised results for other infinite sequences and their associated polynomials.

published_or_final_version / Mathematics / Master / Master of Philosophy

In 1912 Axel Thue sparked the study of combinatorics on words when he showed that the Thue-Morse sequence contains no overlaps, that is, factors of the form ayaya. Since then many interesting properties of sequences began to be discovered and studied. In this thesis, we consider a class of infinite sequences generated by automata, called the k-automatic sequences. In particular, we present a logical theory in which many properties of k-automatic sequences can be expressed as predicates and we show that such predicates are decidable. Our main contribution is the implementation of a theorem prover capable of practically characterizing many commonly sought-after properties of k-automatic sequences. We showcase a panoply of results achieved using our method. We give new explicit descriptions of the recurrence and appearance functions of a list of well-known k-automatic sequences. We define a related function, called the condensation function, and give explicit descriptions for it as well. We re-affirm known results on the critical exponent of some sequences and determine it for others where it was previously unknown. On the more theoretical side, we show that the subword complexity p(n) of k-automatic sequences is k-synchronized, i.e., the language of pairs (n, p(n)) (expressed in base k) is accepted by an automaton. Furthermore, we prove that the Lyndon factorization of k-automatic sequences is also k-automatic and explicitly compute the factorization for several sequences. Finally, we show that while the number of unbordered factors of length n is not k-synchronized, it is k-regular.

No description available.

The offshore facies of the basal Lias of S.Britain was studied as a typical example of an open-marine cyclic sequence. The sedimentology, geochemistry and power-spectral analysis were investigated in order to understand the cause of the interbedded rock types. Three sediment types were deposited on the sea-floor: light marl, dark marl and laminated carbonate-rich shale. Calcite microspar, the dominant carbonate component, appears to have been formed from the neomorphic aggradation of coccoliths supplied in zooplankton faecal pellets. During sulphate reduction, the most carbonate-rich horizons in the light marl and laminated shale beds were cemented by carbonate, producing early diagenetic limestone and laminated limestone beds and nodules. Walsh power-spectral analysis of several measured sections in the basal Lias indicate that two regular sedimentary cycles, with periods of tens of thousands of years, are present. The regularity, stability and periods of the cycles invokes the Milankovitch Theory of orbital forcing of sedimentation; the cycles thus probably represent periods of 41,000 and 21,000 years. The sedimentation appears to have been linked to climatic variation by the levels of runoff and the formation and destruction of wedges of brackish water. During dry periods relatively little runoff and low clay input allowed turbulent, oxygenated bottom-waters and the deposition of burrowed, organic-poor marl. During wet periods, brackish wedges caused widespread density stratification, bottom-water anoxia and high clay inputs that resulted in laminated shale beds. Walsh power spectra were generated for one Silurian, five Upper Lower Jurassic, one Kimmeridgian and one Oligocene formation. Unexpectedly the Early Jurassic appears to have been dominated by the Milankovitch cycles related to obliquity and precession rather than eccentricity. Of the thirteen spectra produced, including five from the basal Lias, ten (or about 80%) contain evidence for regular sedimentary cycles consistent with orbital forcing of sedimentation. Therefore the Milankovitch Theory should be considered whilst investigating open-marine 'cyclic' sequences.

For a given graph, G, the crossing number crₐ(G) denotes the minimum number of edge crossings when a graph is drawn on an orientable surface of genus a. The sequence cr₀(G), cr₁(G), ... is said to be the crossing sequence of a G. An equivalent definition exists for non-orientable surfaces. In 1983, Jozef Širáň proved that for every decreasing, convex sequence of non-negative integers, there is a graph G such that this sequence is the crossing sequence of G. This main result of this thesis proves the existence of a graph with non-convex crossing sequence of arbitrary length.