Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Structure and anti-HIV activity of micrandilactones B and C, new nortriterpenoids possessing a unique skeleton from Schisandra micrantha

Two new highly oxygenated nortriterpenoids with a unique norcycloartane skeleton, micrandilactones B and C (1-2), were isolated from Schisandra micrantha; micrandilactone C ( 2) exhibited an EC50 value of 7.71 mu g/mL (SI > 25.94) against HIV-1 replication with minimal cytotoxicity, and the potent anti-HIV-1 activity and unique structural features of 2 make it a promising lead for therapeutic development of a new generation of anti-HIV drug.

Lancifodilactone F: A novel nortriterpenoid possessing a unique skeleton from Schisandra lancifolia and its anti-HIV activity

Lancifodilactone F (1), possessing an unprecedented rearranged pentanortriterpenoid backbone derived from cycloartane, was isolated from the leaves and stems of Schisandra lancifolia (Rehd. et Wils) A. C. Smith. Its structure was established by comprehensive NMR and MS spectroscopic analysis, coupled with single-crystal X-ray experiment. Compound 1 exerted minimal cytotoxicity against C8166 cells (CC50 > 200 mu g/mL) and showed anti-HIV activity with EC50 = 20.69 +/- 3.31 mu g/mL and a selectivity index > 6.62.

Przewalskin A: A new C-23 terpenoid with a 6/6/7 carbon ring skeleton from Salvia przewalskii maxim

Przewalskin A (1), a novel C-23 terpenoid with a 6/6/7 carbon ring skeleton, was isolated from Salvia przewalskii. Its structure was determined by comprehensive 1D NMR, 2D NMR, and MS spectroscopic analysis and subsequently confirmed by a single-crystal X

Isatisine a, a novel alkaloid with an unprecedented skeleton from leaves of isatis indigotica

9 alpha,13 alpha-Dihydroxylisopropylidenylisatisine A (1), which was derived from isatisine A (2) and possessed an unprecedented fused pentacyclic skeleton, was isolated from the leaves of Isatis indigotica Fort. The structure and relative configuration w

Przewalskin B, a novel diterpenoid with an unprecedented skeleton from Salvia przewalskii maxim

[GRAPHIC] Przewalskin B (1), a novel diterpenoid possessing a unique skeleton, was isolated from a Chinese medicinal plant Salvia przewalskii. Its structure and relative stereochemistry were elucidated by extensive NMR analysis and a single-crystal X-ray

Schilancidilactones A and B: two novel tetranortriterpenoids with an unprecedented skeleton from Schisandra lancifolia

Schilancidilactones A (1) and B (2). two novel tetranortriterpenoids possessing an unprecedented skeleton, have been isolated from the stems of Schisandra lancifolia. Their structures were elucidated on the basis of extensive spectroscopic analysis. The r

Insulin-like growth factor-binding protein-3 plays an important role in regulating pharyngeal skeleton and inner ear formation and differentiation

Insulin-like growth factor-binding protein (IGFBP)-3 is the major insulin-like growth factor (IGF) carrier protein in the bloodstream. IGFBP-3 prolongs the half-life of circulating IGFs and prevents their potential hypo-glycemic effect. IGFBP-3 is also expressed in many peripheral tissues in fetal and adult stages. In vitro, IGFBP-3 can inhibit or potentiate IGF actions and even possesses IGF-independent activities, suggesting that local IGFBP-3 may also have paracrine/autocrine function(s). The in vivo function of IGFBP-3, however, is unclear. In this study, we elucidate the developmental role of IGFBP-3 using the zebrafish model. IGFBP-3 mRNA expression is first detected in the migrating cranial neural crest cells and subsequently in pharyngeal arches in zebrafish embryos. IGFBP-3 mRNA is also persistently expressed in the developing inner ears. To determine the role of IGFBP-3 in these tissues, we ablated the IGFBP-3 gene product using morpholino-modified antisense oligonucleotides (MOs). The IGFBP-3 knocked down embryos had delayed pharyngeal skeleton morphogenesis and greatly reduced pharyngeal cartilage differentiation. Knockdown of IGFBP-3 also significantly decreased inner ear size and disrupted hair cell differentiation and semicircular canal formation. Furthermore, reintroduction of a MO-resistant form of IGFBP-3 "rescued" the MO-induced defects. These findings suggest that IGFBP-3 plays an important role in regulating pharyngeal cartilage and inner car development and growth in zebrafish.

The unique skeleton of siliceous sponges (Porifera; Hexactinellida and Demospongiae) that evolved first from the Urmetazoa during the Proterozoic: a review

Sponges (phylum Porifera) had been considered as an enigmatic phylum, prior to the analysis of their genetic repertoire/tool kit. Already with the isolation of the first adhesion molecule, galectin, it became clear that the sequences of sponge cell surface receptors and of molecules forming the intracellular signal transduction pathways triggered by them, share high similarity with those identified in other metazoan phyla. These studies demonstrated that all metazoan phyla, including Porifera, originate from one common ancestor, the Urmetazoa. The sponges evolved prior to the Ediacaran-Cambrian boundary (542 million years ago [myr]) during two major "snowball earth events", the Sturtian glaciation (710 to 680 myr) and the Varanger-Marinoan ice ages (605 to 585 myr). During this period the ocean was richer in silica due to the silicate weathering. The oldest sponge fossils (Hexactinellida) have been described from Australia, China and Mongolia and are thought to have existed coeval with the diverse Ediacara fauna. Only little younger are the fossils discovered in the Sansha section in Hunan (Early Cambrian; China). It has been proposed that only the sponges possessed the genetic repertoire to cope with the adverse conditions, e.g. temperature-protection molecules or proteins protecting them against ultraviolet radiation. The skeletal elements of the Hexactinellida (model organisms Monorhaphis chuni and Monorhaphis intermedia or Hyalonema sieboldi) and Demospongiae (models Suberites domuncula and Geodia cydonium), the spicules, are formed enzymatically by the anabolic enzyme silicatein and the catabolic enzyme silicase. Both, the spicules of Hexactinellida and of Demospongiae, comprise a central axial canal and an axial filament which harbors the silicatein. After intracellular formation of the first lamella around the channel and the subsequent extracellular apposition of further lamellae the spicules are completed in a net formed of collagen fibers. The data summarized here substantiate that with the finding of silicatein a new aera in the field of bio/inorganic chemistry started. For the first time strategies could be formulated and experimentally proven that allow the formation/synthesis of inorganic structures by organic molecules. These findings are not only of importance for the further understanding of basic pathways in the body plan formation of sponges but also of eminent importance for applied/commercial processes in a sustainable use of biomolecules for novel bio/inorganic materials.

Skeleton-rearranged pentacyclic diterpenoids possessing a cyclobutane ring from Euphorbia wallichii

Two novel rearranged trachylobane diterpenoids, designated as wallichanol A (2) and wallichanol B (3), consisting of an unprecedented pentacyclic skeleton named wallichane with a cyclobutane ring, and a new ent-trachylobane diterpenoid, 3-oxo-ent-trachyloban-17-oic acid (1), were isolated from the roots of Euphorbia wallichii. Their structures were elucidated by comprehensive analysis of 2D-NMR spectroscopic data, with the stereochemistry of 1 confirmed by X-ray crystallographic study. All of these compounds potently block osteoclastogenesis in vitro, suggesting a potential therapeutic application in prevention of osteoporosis.

Identification of Nonlinear Systems Through Time-Frequency Filtering Technique

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

Contingent sensitivity to configuration in a nonlinear evolution system

A trans-scopic sensitivity of macroscopic failure to slight differentiation in the meso-scopic structure of a system with nonlinear evolution is reported. A periodical chain following a non-local load-sharing evolution was applied as a propotype in failure study. The results demonstrate that there is a transition region composed of globally stable (GS) and evolution induced catastrophic (EIC) modes. That is different from a critical threshold as predicted by percolation and renormalization group theories. Moreover, the EIC mode shows a distinctive sample specific behaviour. For instance, some neighbouring initial states may evolve into completely different final states, though different initial states can evolve into the same final states. As an example, a marginal configuration of EIC mode, a quasi-Fibonacci skeleton, is constructed.

Formation Mechanism of Cracks in Saturated Sand

The formation mechanism of “water film” (or crack) in saturated sand is analyzed theoretically and numerically. The theoretical analysis shows that there will be no stable “water film” in the saturated sand if the strength of the skeleton is zero and no positions are choked. It is shown by numerical simulation that stable water films initiate and grow if the choking state keeps unchanged once the fluid velocities decrease to zero in the liquefied sand column. The developments of “water film” based on the model presented in this paper are compared with experimental results.