Strong practical stability based robust stabilization of uncertain discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest whose dynamics evolve over a subset of the positive quadrant in the 2D plane. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass respectively where the former is a necessary condition for the latter. Stability along the pass demands a bounded-input bounded-output property over the complete positive quadrant of the 2D plane and this is a very strong requirement, especially in terms of control law design. A more feasible alternative for some cases is strong practical stability, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality (LMI) based tests, which then extend to allow control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that extend to allow control law design in the presence of uncertainty in process model

Floral structure of Kirkia (Kirkiaceae) and its position in Sapindales

BACKGROUND AND AIMS: The monogeneric Kirkiaceae (Sapindales) were formerly placed as Kirkioideae in Simaroubaceae. However, recent molecular phylogenetic studies indicate that they are not in Simaroubaceae and they appear to be sister to the clade of Anacardiaceae plus Burseraceae. Such affinity was never considered or discussed since the first description of Kirkia. The present study is the first detailed analysis of the floral structure of a representative of Kirkiaceae and the first comparison with other sapindalean families, especially Anacardiaceae and Burseraceae. METHODS: Floral structure of Kirkia wilmsii was studied using transversal and longitudinal microtome section series, scanning electron microscopy and light microscopy. KEY RESULTS: The flowers of Kirkia wilmsii are morphologically bisexual but functionally unisexual. They are polysymmetric, isomerous (tetramerous) and haplostemonous. The ovary is syncarpous and entirely synascidiate. The floral apex forms a hemispherical protrusion on top of the ovary. The styles are free but postgenitally united and apically form a stigmatic head with a compitum. Each carpel is uniovulate (biovulate in a few other species) and ovules are crassinucellar, bitegmic and slightly campylotropous. The micropyle is formed by both integuments and is unusually long. The unusual two radially disposed locules in each carpel in the former genus Pleiokirkia can be explained developmentally by the two offset and tightly contiguous lateral placentae. CONCLUSIONS: Paralleling the molecular results, a suite of floral features supports the position of Kirkiaceae close to the Anacardiaceae-Burseraceae clade, and not in Simaroubacea

An Outlook on Correlations in Stock Prices

We present an outlook of the studies on correlations in the price timeseries of stocks, discussing the construction and applications of "asset tree". The topic discussed here should illustrate how the complex economic system (financial market) enrichens the list of existing dynamical systems that physicists have been studying for long.Comment: 6 pages, RevTeX format. To appear in the Conference Proceedings of ECONOPHYS-KOLKATA II: International Workshop on Econophysics of Stock Markets and Minority Games", February 14-17, 2006, SINP, Kolkata, as a book chapter in Eds. A. Chatterjee and B.K. Chakrabarti, Econophysics of Stock and other Markets, (Springer-Verlag (Italia), Milan, 2006

Collective behavior of stock price movements in an emerging market

To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack of distinct sector identity in emerging markets is explicitly shown by reconstructing the network of mutually interacting stocks. Spectral analysis of C for NSE reveals that, the few largest eigenvalues deviate from the bulk of the spectrum predicted by random matrix theory, but they are far fewer in number compared to, e.g., NYSE. We show this to be due to the relative weakness of intra-sector interactions between stocks, compared to the market mode, by modeling stock price dynamics with a two-factor model. Our results suggest that the emergence of an internal structure comprising multiple groups of strongly coupled components is a signature of market development.Comment: 10 pages, 10 figure

Analysis of aggregated tick returns: evidence for anomalous diffusion

In order to investigate the origin of large price fluctuations, we analyze stock price changes of ten frequently traded NASDAQ stocks in the year 2002. Though the influence of the trading frequency on the aggregate return in a certain time interval is important, it cannot alone explain the heavy tailed distribution of stock price changes. For this reason, we analyze intervals with a fixed number of trades in order to eliminate the influence of the trading frequency and investigate the relevance of other factors for the aggregate return. We show that in tick time the price follows a discrete diffusion process with a variable step width while the difference between the number of steps in positive and negative direction in an interval is Gaussian distributed. The step width is given by the return due to a single trade and is long-term correlated in tick time. Hence, its mean value can well characterize an interval of many trades and turns out to be an important determinant for large aggregate returns. We also present a statistical model reproducing the cumulative distribution of aggregate returns. For an accurate agreement with the empirical distribution, we also take into account asymmetries of the step widths in different directions together with crosscorrelations between these asymmetries and the mean step width as well as the signs of the steps.Comment: 9 pages, 10 figures, typos correcte

Vortex-forced-oscillations of thin flexible plates

Fluid-structure interaction of a slender flexible cantilevered-element and vortices in an otherwise steady flow is considered here by investigating the dynamics of thin low-density polyethylene sheets subject to periodic forcing due to B\'enard-K\`arm\`an vortices in a $2$-meter long narrow water channel. The vortex shedding frequency $f_v$ is varied via the mean flow speed $U_0$ and the cylinder diameter $d_0 = 10$, $20$ and $40$ mm, while the structures' bending resistance is properly controlled via its Young's modulus $E$, thickness $e_b$ and length $L_b$. Thereby, it is first shown that the non-dimensional time-averaged sheet deflection, namely, the sheet \textit{reconfiguration} $\bar{h}_b/L_b \sim C_y^{\mathcal{V}/2}$ and also, the time-averaged \textit{drag force} $\bar{F}_d \propto U_0^{2+\mathcal{V}}$, where $\mathcal{V} \leq 0$ is the well-known Vogel number for flexible structures in a steady flow and $C_y = 12 \left({C_d \frac{1}{2} \rho U_0^2}/{E}\right) \left({ L_b^3/}{e_b^3} \right)$ is the Cauchy number comparing the relative magnitude of the profile drag force over a typical elastic restoring force, if the sheet were rigid. Measurements and a simple model based on torsional-spring-mounted flat plate illustrate that the tip amplitude $\delta_b$ is not only directly proportional to the characteristic size of the eddies, say $d_v$, but also to the sheet mechanical properties and the vortex flow characteristics such that $\delta_b/d_v \sim C_y^{(1+\mathcal{V})/2} \sqrt{U_0/f_v d_v}$. Furthermore, a rich phenomenology of structural dynamics including vortex-forced-vibration, lock-in with the sheet natural frequency, flow-induced vibration due to the sheet wake, multiple-frequency and modal response is reported

Determinants of immediate price impacts at the trade level in an emerging order-driven market

The common wisdom argues that, in general, large trades cause large price changes, while small trades cause small price changes. However, for extremely large price changes, the trade size and news play a minor role, while the liquidity (especially price gaps on the limit order book) is a more influencing factor. Hence, there might be other influencing factors of immediate price impacts of trades. In this paper, through mechanical analysis of price variations before and after a trade of arbitrary size, we identify that the trade size, the bid-ask spread, the price gaps and the outstanding volumes at the bid and ask sides of the limit order book have impacts on the changes of prices. We propose two regression models to investigate the influences of these microscopic factors on the price impact of buyer-initiated partially filled trades, seller-initiated partially filled trades, buyer-initiated filled trades, and seller-initiated filled trades. We find that they have quantitatively similar explanation powers and these factors can account for up to 44% of the price impacts. Large trade sizes, wide bid-ask spreads, high liquidity at the same side and low liquidity at the opposite side will cause a large price impact. We also find that the liquidity at the opposite side has a more influencing impact than the liquidity at the same side. Our results shed new lights on the determinants of immediate price impacts.Comment: 21 IOP tex pages including 5 figures and 5 tables. Accepted for publication in New Journal of Physic