The goal of data mining is to help market managers find relationships among items from large datasets to increase profits. Among the mining techniques, the Apriori algorithm is the most basic and important for association rule mining. Although a lot of mining approaches have been proposed based on the Apriori algorithm, most of them focus on positive association rules, such as R1: ¡§If milk is bought, then bread is bought¡¨. However, rule R1 may confuses users and makes wrong decision if the negative relation rules are not considered. For example, the rule such as R2: ¡§If milk is not bought, then bread is bought¡¨ may also be found. Then, the rule R2 conflicts with the positive rule R1. So, if two rules such as ¡§If milk is bought, then bread is bought¡¨ and ¡§If milk is not bought, then bread is not bought¡¨ are found at the same time, the rules which is called coherent rule may be more valuable.In this thesis, we thus propose two algorithms for solving this problem. The first proposed algorithm is named Highly Coherent Rule Mining algorithm (HCRM), which takes the properties of propositional logic into consideration and is based on Apriori approach for finding coherent rules. The lower and upper bounds of itemsets are also tightened to remove unnecessary check. Besides, in order to improve the efficiency of the mining process, the second algorithm, namely Projection-based Coherent Mining Algorithm (PCA), based on data projection is proposed for speeding up the execution time. Experiments are conducted on real and simulation datasets to demonstrate the performance of the proposed approaches and the results show that both HCRM and PCA can find more reliable rules and PCA is more efficient.

The resonant absorption, emission, and scattering of light are the fundamental optical processes that have been used both to probe matter and to manipulate light itself. In the last decade there has been essential progress in coherent control of both linear and nonlinear optical responses based on resonant excitation of atomic coherence in multilevel quantum systems. Some interesting and useful phenomena, resulting from coherent control of absorption and the group index, such as electromagnetically induced transparency, lasing without inversion, and ultra-slow group velocity of light have been widely studied. This work is focused on coherent control of refractive index and resonant fluorescence in multilevel medium. We suggest two promising schemes for resonant enhancement of the refractive index with eliminated absorption and propose their implementation in transition element doped crystals with excited state absorption and in a cell of Rb atoms at natural abundance. We show how to use one of these schemes for spatial variation of the refractive index via its periodic resonant increase/decrease, remarkably keeping at the same time zero absorption/gain. It opens the way to production of transparent photonic structures (such as distributed Bragg reflectors, holey fibers, or photonic crystals) in a homogeneous resonant atomic media such as dielectrics with homogeneously distributed impurities, atomic, or molecular gases. These optically produced photonic structures could easily be controlled (including switching on/off, changing amplitude and period of modulation) and would be highly selective in frequency, naturally limited by the width of the optical resonance. We also derive the optical fluorescence spectra of a three-level medium driven by two coherent fields at the adjacent transitions in a general case when all three transitions are allowed. We show that coherent driving can efficiently control the distribution of intensities between the fluorescent channels. In particular, the total intensity of fluorescence at the transition which is not driven by the optical fields may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. This counter-intuitive effect is due to depletion of the intermediate state via atomic interference.

In the present quantum optics and laser physics study, the non-linear interaction of electromagnetic fields with atomic, molecular and biomolecular media is analyzed. Particular emphasis is given to coherent phenomena, while propagation and dispersion effects are also extensively investigated. The fields involved vary from ultra short pulses to continuous waves; while their energies range from the very strong that are addressed classically, to the very weak which are described quantum mechanically. Applications and problems addressed span a wide range. A scheme for a real time detector of chemical and biological hazards, like anthrax spores, is presented; in it, a strong spectroscopic signature is obtained from complex molecules by using ultrashort, femtosecond, laser pulses and inducing vibrational coherence on them. Furthermore, a way of reversing the phase matching condition in coherent spectroscopy, based on dispersion, is developed; which allows for the use of such spectroscopic methods in remote detection. More fundamental questions addressed include a resolution of the centennial old paradox of Maxwell's demon via quantum thermodynamics, and the role of atomic coherence in enhancing the efficiency of a heat engine as well as in obtaining lasing without population inversion. Additionally, a quantum storage scheme is presented, in which the information contained in an optical pulse is stored and restored via photon echoes.

Fiber-optic networks are continually evolving to accommodate the ever increasing data rates demanded by modern applications and devices. The current state-of-the art systems are being deployed with 100 Gb/s rates per wavelength while maintaining the 50 GHz channel spacing established for 10 Gb/s dense wavelength division multiplexed (DWDM) systems. Phase modulation formats (in particular quadrature phase shift keying - QPSK) are necessary to meet the spectral efficiency (SE) requirements of the application. The main challenge for phase modulated optical systems is fiber nonlinearities, where changes in intensity of the combined optical signal result in changes to the fiber's refractive index. Limiting launch power is the primary means to avoid dramatic intensity fluctuations, a strategy which in turn limits the available signal-to-noise ratio (SNR) within the channel. Continuous phase modulation (CPM) is a format in which data is encoded in the phase, while the amplitude is constant throughout all transmission (even during transitions between symbols). With the goal of reducing the impact of nonlinearities, the purpose of this research was to identify a set of CPM signals best suited for high speed fiber-optic transmission, and quantify their performance against other formats. The secondary goal was to identify techniques appropriate for demodulation of high speed fiber-optic systems and implement them for simulation and experimental research. CPM encompasses a number of variable parameters that combine to form an infinite number of unique schemes, each of which is characterized by its own SE, minimum distance, and implementation complexity. A method for computing minimum distance of DWDM-filtered CPM formats is presented and utilized to narrow down to a range of candidate schemes. A novel transmitter design is presented for CPM signal generation, as well as a number of novel reception techniques to achieve proper demodulation of the CPM signal from the coherent optical receiver. Using these methods, the identified range of candidate schemes was compared in simulation to the conventional QPSK format, showing that some modest gain can be expected from CPM. Through these and other simulations, it is revealed that fiber nonlinearities depend on the aggregate sum of all wavelengths rather than the imposition of each separate carrier on its neighbors. Therefore the constant envelope of CPM does not directly impact the nonlinearities since multiple carriers will photonically interfere and result in intensity fluctuations regardless of modulation format. Additionally, dispersive effects in fiber decompose the underlying channels so that the intensity throughout propagation is nearly Gaussian distributed, regardless of format. The benefits gained from CPM are thus limited to schemes that attain a higher minimum distance than alternative formats (in the given channel passband), and for optically compensated links in which low dispersion is maintained throughout the fiber link.

Thesis (Ph. D.)--University of Chicago, Dept. of Chemistry, August 2001. / Includes bibliographical references. Also available on the Internet.

Nonlinear magneto-optical effects, originated from atomic coherence, are studied both theoretically and experimentally in thermal Rb vapor. The analytical description of the fundamental properties of coherent media are based on the simplified three- and four-level systems, and then verified using numerical simulations and experimental measurements. In particular, we analyze the modification of the long-lived atomic coherence due to various physical effects, such as reabsorption of spontaneous radiation, collisions with a buffer gas atoms, etc. We also discuss the importance of the high-order nonlinearities in the description of the polarization rotation for the elliptically polarized light. The effect of self-rotation of the elliptical polarization is also analyzed. Practical applications of nonlinear magneto-optical effects are considered in precision metrology and magnetometery, and for the generation of non-classical states of electromagnetic field.

Properties of coherent media in the regime of electromagnetically induced transparency (EIT) are studied. A study of the shape and width of the EIT resonance is presented for coherent media with buffer gas. Observation of an absorption-like resonance for large one-photon detunings in a medium with buffer gas and its properties are shown. The regime of ``slow'' and ``fast'' group velocities are studied. Observation of narrow resonances with a phase broadened probe field is presented, and possible application of this regime are outlined.

When solving problems involving quantum mechanical systems, it is frequently desirable to find the matrix elements of a unitary representation $T$ of a real algebraic Lie group $G$. This requires defining an inner product on the Hilbert space $\mathbb{H}$ that carries the representation $T$. In the case where the representation is determined by a representation of a subgroup containing the lowest weight vector of $T$, this can be achieved through the coherent state construction. In both the scalar and vector coherent state methods, the process of finding the overlaps can be simplified by introducing the coherent state triplet ($\mathfrak{F}_{\mathbb{H}_D}$, $\mathbb{H}_D$, $\mathfrak{F}^{\mathfrak{H}_D}$) of Bargmann spaces. Coherent state wave functions -- the elements of $\mathfrak{F}_{\mathbb{H}_D}$ and of $\mathfrak{F}^{\mathbb{H}_D}$ -- are used to define the inner product on $\mathbb{H}_D$ in a way that simplifies the calculation of the overlaps. This inner product and the group action $\Gamma$ of $G$ on $\mathfrak{F}^{\mathbb{H}_D}$ are used to formulate expressions for the matrix elements of $T$ with coefficients from the given subrepresentation. The process of finding an explicit expression for $\Gamma$ relies on matrix factorizations in the complexification of $G$ even though the representation $T$ does not extend to the complexification. It will be shown that these factorizations are, in fact, justified, that the overlaps and $\Gamma$ action can be expressed in terms of the given subrepresentation, and that it is possible to find numerical values for the inner product in $\mathbb{H}$. The scalar and vector coherent state methods will both be applied to Sp($n$) and Sp($n,\mathbb{R}$).

Coherent optical data processing is recognised, for many applications, as a viable alternative to digital electronic signal processing; the case for using coherent optics is particularly strong when the data to be processed is two dimensional in nature. It has long been accpeted that, in order for coherent optical processing to achieve its full performance potential, two dimensional spatial light modulators - capable of operating in real time - are essential at both the object plane (where the data is input to the system) and the Fourier plane (where the operation carried out on the data is determined). Most previous research in the field of spatial modulators has concentrated on optically addressed devices for use in the object plane. This thesis describes a prototype liquid crystal over silicon spatial light modulator built to test the feasibility of using such devices in a coherent optical processor. Optically, the device operates as a binary amplitude modulator, consisting of a square array of 16x16 pixels, each of size 100x100 m^2 and located at 200m centres. The integrated circuit is designed for a 6m wafer fabrication process. Each pixel of the IC contains a static memory element (which stores a digital logic voltage corresponding to the optical state of that pixel) and provides a stable square wave voltage signal to drive the liquid crystal layer. The component parts of the spatial light modulator are tested individually: the liquid crystal, in test cells, for contrast and switching speed; the IC for electrical performance and optical (flatness) characteristics. The effect of pixellation on optical performance is investigated. The performance of live devices is demonstrated. The results indicate the feasibility of using such a device as a binary amplitude spatial light modulator.

When solving problems involving quantum mechanical systems, it is frequently desirable to find the matrix elements of a unitary representation $T$ of a real algebraic Lie group $G$. This requires defining an inner product on the Hilbert space $\mathbb{H}$ that carries the representation $T$. In the case where the representation is determined by a representation of a subgroup containing the lowest weight vector of $T$, this can be achieved through the coherent state construction. In both the scalar and vector coherent state methods, the process of finding the overlaps can be simplified by introducing the coherent state triplet ($\mathfrak{F}_{\mathbb{H}_D}$, $\mathbb{H}_D$, $\mathfrak{F}^{\mathfrak{H}_D}$) of Bargmann spaces. Coherent state wave functions -- the elements of $\mathfrak{F}_{\mathbb{H}_D}$ and of $\mathfrak{F}^{\mathbb{H}_D}$ -- are used to define the inner product on $\mathbb{H}_D$ in a way that simplifies the calculation of the overlaps. This inner product and the group action $\Gamma$ of $G$ on $\mathfrak{F}^{\mathbb{H}_D}$ are used to formulate expressions for the matrix elements of $T$ with coefficients from the given subrepresentation. The process of finding an explicit expression for $\Gamma$ relies on matrix factorizations in the complexification of $G$ even though the representation $T$ does not extend to the complexification. It will be shown that these factorizations are, in fact, justified, that the overlaps and $\Gamma$ action can be expressed in terms of the given subrepresentation, and that it is possible to find numerical values for the inner product in $\mathbb{H}$. The scalar and vector coherent state methods will both be applied to Sp($n$) and Sp($n,\mathbb{R}$).