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Accepted financial theory holds that stock splits provide no wealth benefits to stock-holders. The corporate management view is that stock splits add value by placing the stock in a more liquid price range. Empirical explanations of excess returns near the split rely principally upon an information effect. Other findings are that (1) an unexplained, sustained jump in returns' variance occurs at the split, and (2) there appears to be a coincidental decrease in liquidity, not an increase. Daily returns from CRSP and daily and intradaily returns and daily trading volumes and price change information from trade-by-trade data are used to examine the returns variance increase and any connection it may have with any liquidity change. Binomial probability comparisons of returns' variance measures each side of the split ex-date are used to examine the variance change and liquidity change phenomena. T-tests are also used to examine the mean-variance change and the possible change in several liquidity measures. Linear regression is used to detect impact of the general market variance level, firm-specific variables, and microstructure measures, and liquidity measures upon the returns’ variance change. Findings include: (1) the variance increase is significant and exhibits a firm size effect and is affected by the previous history of splits use and. dividend payout, (2) the increase is primarily related to the price level adjustment and changes in the liquidity measures, (3) a slight change in the demand to hold as measured by the percentage of the firm traded takes place for firms with an increase in variance (4) the bid-ask spread decreases, but increases relative to the new price. Stock splits with increased returns’ variance have significantly different liquidity measures from splits where the variance declined. / Ph. D. / incomplete_metadata

No / This paper presents a novel and hardware-efficient architecture for power-of-two FFT processors. The proposed design is based on the phase-amplitude splitting technique which converts a DFT to cyclic convolutions and additions. The cyclic convolutions are implemented with a filter-like structure and the additions are computed with several stages of butterfly processing units. The proposed architecture requires no multiplier, and comparisons with other designs show it can save up to 39% total equivalent gates for an 8-bit 16-point FPGA-based FFT processor.

When-issued trading, the contractual agreement for the sale and purchase of shares to be issued in the future (when-issued securities), typically occurs after stock split announcements. Curiously, when-issued trading does not always exist for a stock-splitting firm's shares even though the shares are eligible for when-issued trading. Although stock splits have been the subject of a large number of studies, intriguing questions concerning these events remain unanswered. In particular, academia has yet to explain adequately the positive average abnormal returns associated with stock split announcements. These two peculiar phenomena are examined. A major objective of this dissertation is to determine whether there are systematic differences between those stock-splitting firms whose shares are traded on a when-issued basis and those whose shares arc not. A logistic regression model was constructed, using information with respect to nine accounting variables, to determine if there are systematic differences in accounting information that are useful in classifying stock-splitting firms as being associated with when-issued trading. The classification accuracy of the logistic regression model was significantly better than a random walk model, but was not better than the maximum chance model. The results of the final model indicate that size of the stock-splitting firm is the most significant factor affecting the probability that a stock-splitting firm's shares are traded on a when-issued basis. The probability that a stock-splitting firm's shares will be traded on a when-issued basis increases with firm size. The presence/absence of when-issued trading indicates that investors do not react to stock splits in a consistent manner. Therefore, the stock price behavior around the stock split announcements was examined and the difference in the reaction to announcements of when-issued traded and non-when-issued traded firms was tested for statistical significance. The results indicate that the market responds more favorably to the stock split announcements made by non-when-issued traded firms. The variation in the stock price behavior over a two-day stock split announcement period was analyzed cross-sectionally to determine whether the market reaction displayed through stock prices is related to selected accounting variables. Again, size was the most significant factor. In this case, size was negatively related to the stock price behavior suggesting that stockholders of larger firms earn lower abnormal returns. Another interpretation would be that stock splits are viewed more favorably if authorized by smaller firms. Overall, the results of this study suggest that all stock-splitting firms are not similar and that the market does not react consistently to the announcement of stock splits of all firms. It seems that the larger the firm, the more likely its shares will be traded on a when-issued basis after the stock split is announced. Furthermore, the market does not react as positively to stock split announcements of larger firms as it does to announcements of smaller firms. My conclusion is that larger firms are more efficiently valued and, accordingly, the announcements of stock splits by larger firms are less informative than for smaller ones. / Ph. D.

Dans cette thèse nous considérons une population branchante générale où les individus vivent et se reproduisent de manière i.i.d. La durée de vie de chaque individu est distribuée suivant une mesure de probabilité arbitraire et chacun d'eux donne naissance à taux exponentiel. L'arbre décrivant la dynamique de cette population est connu sous le nom de splitting tree. Le processus comptant le nombre d’individus vivant au temps t est connu sous le nom de processus de Crump-Mode-Jagers binaire homogène, et il est connu que ce processus, quand correctement renormalisé, converge presque sûrement en temps long vers une variable aléatoire. Grâce à l'étude du splitting tree sous-jacent à la population via les outils introduit par A. Lambert en 2010, nous montrons un théorème central limite pour cette convergence p.s. dans le cas surcritique. Nous supposons, de plus, que les individus subissent des mutations à taux exponentiel sous l'hypothèse d'infinité d'allèles. Nous nous intéressons alors au spectre de fréquence allélique de la population qui compte la fréquence des tailles de familles dans la population à un instant donnée. Grâce aux méthodes développées dans cette thèse, nous obtenons des résultats d’approximations du spectre de Fréquence. Enfin nous nous intéressons à des questions statistiques sur des arbres de Galton-Watson conditionnés par leurs tailles. Le but est d'estimer la variance de la loi de naissance rendue inaccessible par le conditionnement. On utilise le fait que le processus de contour d'un tel arbre converge vers une excursion Brownienne quand la taille de l'arbre grandit afin de construire des estimateurs de la variance à partir de forêts / In this thesis we consider a general branching population. The lifetimes of the individuals are supposed to be i.i.d. random variables distributed according to an arbitrary distribution. Moreover, each individual gives birth to new individuals at Poisson rate independently from the other individuals. The tree underlying the dynamics of this population is called a splitting tree. The process which count the number of alive individuals at given times is known as binary homogeneous Crump-Mode-Jagers processes. Such processes are known, when properly renormalized, to converge almost surely to some random variable. Thanks to the study of the underlying splitting tree through the tools introduced by A. Lambert in 2010, we show a central limit theorem associated to this a.s. convergence. Moreover, we suppose that individuals undergo mutation at Poisson rate under the infinitely many alleles assumption. We are mainly interested in the so called allelic frequency spectrum which describes the frequency of sizes of families (i.e. sets of individuals carrying the same type) at fixed times. Thanks to the methods developedin this thesis, we are able to get approximation results for the frequency spectrum. In a last part, we study some statistical problems for size constrained Galton-Watson trees. Our goal is to estimate the variance of the birth distribution. Using that the contour process of such tree converges to a Brownian excursion as the size of the tree growth, we construct estimators of the variance of the birth distribution

This thesis presents the numerical algorithms to carry out the face transformation. The main efforts are denoted to the finite volume method (FVM) with the Delaunay triangulation to solve the Laplace equations in the harmonic transformation undergone in face images. The advantages of the FVM with the Delaunay triangulation are: (1) Easy to formulate the linear algebraic equations, (2) Good to retain the geometric and physical properties, (3) less CPU time needed. The numerical and graphical experiments are reported for the face transformations from a female to a male, and vice versa. The computed sequential and absolute errors are and , where N is division number of a pixel into subpixels. Such computed errors coincide with the analysis on the splitting-shooting method (SSM) with piecewise constant interpolation in [Li and Bui, 1998c].

Cette thèse contient deux parties: la simulation des événements rares et le rééchantillonnage non-intrusif stratifié pour la programmation dynamique. La première partie consiste à quantifier des statistiques liées aux événements très improbables mais dont les conséquences sont sévères. Nous proposons des transformations markoviennes sur l'espace des trajectoires et nous les combinons avec les systèmes de particules en interaction et l'ergodicité de chaîne de Markov, pour proposer des méthodes performantes et applicables en grande généralité. La deuxième partie consiste à résoudre numériquement le problème de programmation dynamique dans un contexte où nous avons à disposition seulement des données historiques en faible nombre et nous ne connaissons pas les valeurs des paramètres du modèle. Nous développons et analysons un nouveau schéma composé de stratification et rééchantillonnage / This thesis contains two parts: rare events simulation and non-intrusive stratified resampler for dynamic programming. The first part consists of quantifying statistics related to events which are unlikely to happen but which have serious consequences. We propose Markovian transformation on path spaces and combine them with the theories of interacting particle system and of Markov chain ergodicity to propose methods which apply very generally and have good performance. The second part consists of resolving dynamic programming problem numerically in a context where we only have historical observations of small size and we do not know the values of model parameters. We propose and analyze a new scheme with stratification and resampling techniques.

Optical microcavities (OMs) are receiving increasing attention owing to their potential applications ranging from cavity quantum electrodynamics, optical detection to photonic devices. Recently, rolled-up structures have been demonstrated as OMs which have gained considerable attention owing to their excellent customizability. To fully exploit this customizability, asymmetric and topological rolled-up OMs are proposed and investigated in addition to conventional rolled-up OMs in this thesis. By doing so, novel phenomena and applications are demonstrated in OMs. The fabrication of conventional rolled-up OMs is presented in details. Then, dynamic mode tuning by a near-field probe is performed on a conventional rolled-up OM. Next, mode splitting in rolled-up OMs is investigated. The effect of single nanoparticles on mode splitting in a rolled-up OM is studied. Because of a non-synchronized oscillating shift for different azimuthal split modes induced by a single nanoparticle at different positions, the position of the nanoparticle can be determined on the rolled-up OM. Moreover, asymmetric rolled-up OMs are fabricated for the purpose of introducing coupling between spin and orbital angular momenta (SOC) of light into OMs. Elliptically polarized modes are observed due to the SOC of light. Modes with an elliptical polarization can also be modeled as coupling between the linearly polarized TE and TM mode in asymmetric rolled-up OMs. Furthermore, by adding a helical geometry to rolled-up structures, Berry phase of light is introduced into OMs. A -π Berry phase is generated for light in topological rolled-up OMs so that modes have a half-integer number of wavelengths. In order to obtain a deeper understanding for existing rolled-up OMs and to develop the new type of rolled-up OMs, complete theoretical models are also presented in this thesis.

In this study, the spin-splitting energy of the lowest conduction bands in bulk zincblende and wurtzite structures of III-V semiconductors had been investigated by the linear combination of atomic orbital (LCAO) method, the atomic bond-orbital model (ABOM), and the two-band k¡Dp (2KP) model. Spin-splitting calculation for zincblende structures: We develop a 16-band atomic bond-orbital model (ABOM) to compute the spin splitting induced by bulk inversion asymmetry in zincblende materials. This model is derived from the linear combination of atomic orbital (LCAO) scheme such that the characteristics of the real atomic orbitals can be preserved to calculate the spin splitting. The Hamiltonian of 16-band center-zone ABOM (CZABOM) is based on a similarity transformation performed on the nearest-neighbor LCAO Hamiltonian with a second-order Taylor expansion over k at the £F point. The spin-splitting energies in bulk zincblende semiconductors, GaAs and InSb, are calculated, and the results agree with the LCAO and first-principles calculations. However, we find that the spin-orbit coupling between bonding and antibonding p-like states, evaluated by the 16CZABOM, dominates the spin splitting of the lowest conduction bands in the zincblende materials. Spin-splitting calculation for wurtzite structures: The spin-splitting energies in biaxially strained bulk wurtzite material AlN are calculated using the linear combination of atomic orbital (LCAO) method, and the equi-spin-splitting distributions in k-space near the minimum-spin-splitting (MSS) surfaces are illustrated. These data are compared with those derived analytically by two-band k¡Dp (2KP) model. It is found that the results from these two methods are in good agreement for small k. However, the ellipsoidal MSS surface under biaxial compressive strain does not exist in the 2KP model, because the data points are far from the £F point. Instead, three basic shapes of the MSS surface occur in the wurtzite Brillouin zone: a hyperboloid of two sheets, a hexagonal cone, and a hyperboloid of one sheet, evaluated from the LCAO method across the range of biaxial strains from compressive to tensile. The shapes of the equi-spin-splitting (ESS) surfaces near these MSS surfaces have also three types: a hyperboloid of one sheet, an approximate, asymmetric hyperboloid surface, and an opposing hyperboloid of one sheet.

The kinetic schemes, also known as Boltzmann schemes are based on the moment-method-strategy, where an upwind scheme is first developed at the Boltzmann level and after taking suitable moments we arrive at an upwind scheme for the governing Euler or Navier-Stokes equations. The Kinetic Flux Vector Splitting (KFVS)scheme, which belongs to the family of kinetic schemes is being extensively used to compute inviscid as well as viscous flows around many complex configurations of practical interest over the past two decades. To resolve many flow features accurately, like suction peak, minimising the loss in stagnation pressure, shocks, slipstreams, triple points, vortex sheets, shock-shock interaction, mixing layers, flow separation in viscous flows require an accurate and low dissipative numerical scheme. The first order KFVS method even though is very robust suffers from the problem of having much more numerical diffusion than required, resulting in very badly smearing of the above features. However, numerical dissipation can be reduced considerably by using higher order kinetic schemes. But they require more points in the stencil and hence consume more computational time and memory. The second order schemes require flux or slope limiters in the neighbourhood of discontinuities to avoid spurious and physically meaningless wiggles or oscillations in pressure, temperature or density. The limiters generally restrict the residue fall in second order schemes while in first order schemes residue falls up to machine zero. Further, pressure and density contours or streamlines are much smoother for first order accurate schemes than second order accurate schemes. A question naturally arises about the possibility of constructing first order upwind schemes which retain almost all advantages mentioned above while at the same time crisply capture the flow features. In the present work, an attempt has been made to address the above issues by developing yet another kinetic scheme, known as the low dissipative modified KFVS (m-KFVS) method based on modified CIR (MCIR) splitting with molecular velocity dependent dissipation control function. Different choices for the dissipation control function are presented. A detailed mathematical analysis and the underlying physical arguments behind these choices are presented. The expressions for the m-KFVS fluxes are derived. For one of the choices, the expressions for the split fluxes are similar to the usual first order KFVS method. The mathematical properties of 1D m-KFVS fluxes and the eigenvalues of the corresponding flux Jacobians are studied numerically. The analysis of numerical dissipation is carried out both at Boltzmann and Euler levels. The expression for stability criterion is derived. In order to be consistent with the interior scheme, modified solid wall and outer boundary conditions are derived by extending the MCIR idea to boundaries. The cell-centred finite volume method based on m-KFVS is applied to several standard test cases for 1D, 2D and 3D inviscid flows. In the case of subsonic flows, the m-KFVS method produces much less numerical entropy compared to first order KFVS method and the results are comparable to second order accurate q-KFVS method. In transonic and supersonic flows, m-KFVS generates much less numerical dissipation compared to first order KFVS and even less compared to q-KFVS method. Further, the m-KFVS method captures the discontinuities more sharply with contours being smooth and near second order accuracy has been achieved in smooth regions, by still using first order stencil. Therefore, the numerical dissipation generated by m-KFVS is considerably reduced by suitably choosing the dissipation control variables. The Euler code based on m-KFVS method almost takes the same amount of computational time as that of KFVS method. Although, the formal accuracy is of order one, the m-KFVS method resolves the flow features much more accurately compared to first order KFVS method but the numerical dissipation generated by m-KFVS method may not be minimal. Hence, the dissipation control vector is in general not optimal. If we can find the optimal dissipation control vector then we will be able to achieve the minimal dissipation. In the present work, the above objective is attained by posing the minimisation of numerical dissipation in m-KFVS method as an optimal control problem. Here, the control variables are the dissipation control vector. The discrete form of the cost function, which is to be minimised is considered as the sum of the squares of change in entropy at all cells in the computational domain. The number of control variables is equal to the total number of cells or finite volumes in the computational domain, as each cell has only one dissipation control variable. In the present work, the minimum value of cost function is obtained by using gradient based optimisation method. The sensitivity gradients of the cost function with respect to the control variables are obtained using discrete adjoint approach. The discrete adjoint equations for the optimisation problem of minimising the numerical dissipation in m-KFVS method applied to 2D and 3D Euler equations are derived. The method of steepest descent is used to update the control variables. The automatic differentiation tool Tapenade has been used to ease the development of adjoint codes. The m-KFVS code combined with discrete adjoint code is applied to several standard test cases for inviscid flows. The test cases considered are, low Mach number flows past NACA 0012 airfoil and two element Williams airfoil, transonic and supersonic flows past NACA 0012 airfoil and finally, transonic flow past Onera M6 wing. Numerical results have shown that the m-KFVS-adjoint method produces even less numerical dissipation compared to m-KFVS method and hence results in more accurate solution. The m-KFVS-adjoint code takes more computational time compared to m-KFVS code. The present work demonstrates that it is possible to achieve near second order accuracy by formally first order accurate m-KFVS scheme while retaining advantages of first order accurate methods.