Infinite horizon disturbance attenuation for discrete-time systems. A Popov-Yakubovich approach

It is proved that for the discrete-time linear systems with time-varying coefficients the existence of a controller which simultaneously stabilizes and provides prescribed disturbance attenuation for the resultant closed-loop system, implies the existence of global solutions to several Kalman-Szegö-Popov-Yakubovich systems. It is also proved that this fact is equivalent to the existence of the positive semidefinite stabilizing solutions to corresponding game-theoretic Riccati equations. The family of all controllers with the above mentioned properties is constructed in terms of the solutions to the cited Kalman-Szegö-Popov-Yakubovich systems. The main tool is the generalized Popov-Yakubovich theory which is essentially developed in an operator-theoretic framework.     

Synthesis of isoagathane aldehydes representing metabolites of the spongeSpongia officinalis

The synthesis has been performed of (14R)-15-acetoxyisoagath-12-en-16-al and of (14R)- and (14S)-isoagath-12-ene-15,16-dials, which are metabolites of the marine spongeSpongia officinalis, and alos of a number of substances related to them starting from (14R)- and (14S)-isoagath-12-en-15-ols.Institute of Chemistry, Academy of Sciences of the Moldavian SSR, Kishinev. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 45–51, January–February, 1985.     

On the positivity of symmetric polynomial functions. Part II: Lattice general results and positivity criteria for degrees 4 and 5

We prove that homogeneous symmetric polynomial inequalities of degree p∈{4,5} in n positive¹ variables can be algorithmically tested, on a finite set depending on the given inequality (Theorem 13); the test-set can be obtained by solving a finite number of equations of degree not exceeding p−2. Section 3 discusses the structure of the ordered vector spaces and . In Section 4, positivity criteria for degrees 4 and 5 are stated and proved. The main results are Theorems 10-14. Part III of this work will be concerned with the construction of extremal homogeneous symmetric polynomials (best inequalities) of degree 4 in n positive variables.     

Transition event statistics in genetics and disordered kinetics. Theoretical approaches for extracting rate distributions from experimental data

We study the analogies between the theory of rate processes in disordered systems and the overdispersed molecular clocks in evolutionary biology. A biological "molecular clock" expresses the statistics of the number of amino acid or nucleotide substitutions during evolution. Random variations of the evolution rates lead to statistical (overdispersed) molecular clocks which are described by random point processes with random substitution rates. We find that the models for overdispersed molecular clocks are equivalent to those of the random-rate or random channel models used in disordered kinetics. The number of transport (reaction) events in disordered kinetics plays the same role as the number of substitution events in molecular biology. We study the connections between the (observed) statistics of the transition events and the statistics of random rate coefficients and random channels; a unified approach is developed which is valid both in molecular biology and in disordered kinetics. We develop methods for extracting statistical information about the variations of rate coefficients from experimental or observed data regarding the fluctuations of the numbers of substitution, reaction, or transport events. For systems with static disorder, the observed statistics of the number of reaction events, expressed in terms of probabilities at a given time or by the cumulants of the number of transition events at a given time, contains the information necessary for evaluating the cumulants or the probability density of the rate coefficients or the density of states for random channel kinetics. For dynamic disorder this is not possible; further information about multitime probability distributions of the reaction events is needed.     

The Sobolev Stability Threshold for 2D Shear Flows Near Couette

We consider the 2D Navier–Stokes equation on \(\mathbb T \times \mathbb R\), with initial datum that is \(\varepsilon \)-close in \(H^N\) to a shear flow (U(y), 0), where \(\Vert U(y) - y\Vert _{H^{N+4}} \ll 1\) and \(N>1\). We prove that if \(\varepsilon \ll \nu ^{1/2}\), where \(\nu \) denotes the inverse Reynolds number, then the solution of the Navier–Stokes equation remains \(\varepsilon \)-close in \(H^1\) to \((e^{t \nu \partial _{yy}}U(y),0)\) for all \(t>0\). Moreover, the solution converges to a decaying shear flow for times \(t \gg \nu ^{-1/3}\) by a mixing-enhanced dissipation effect, and experiences a transient growth of gradients. In particular, this shows that the stability threshold in finite regularity scales no worse than \(\nu ^{1/2}\) for 2D shear flows close to the Couette flow.     

Lower bounds for densities of Asian type stochastic differential equations

We obtain lower bounds for densities of solutions of certain hypoelliptic two-dimensional stochastic differential equations where one of the components is the Lebesgue integral of the other. These results are non-trivial extensions of previous work of the authors. In particular, these type of equations are linked to the so-called Asian option set-up.     

Micellization of a Siloxane‐Based Segmented Copolymer in Organic Solvents and its Use as a Tool for Metal Complex Nanoparticles

The micellization of a polysiloxane‐ketimine has been studied in solvents of different polarity, i.e., dimethylformamide (DMF) and toluene. The critical micelle concentration was determined from surface tension measurements ‐in DMF‐, and from viscosity variation with concentration. Metal complex nanoparticles have been synthesized from this macromolecular ligand in DMF and in toluene, using the formed micelles as templates. Spectroscopic data (IR and UV‐vis) confirmed the metal complexation. TEM observations revealed the formation of nanoparticles with different morphologies, which were consistent with the assumed conformation of the ligand in solutions of the two selective solvents.

     

Automated species recognition of antbirds in a Mexican rainforest using hidden Markov models

Behavioral and ecological studies would benefit from the ability to automatically identify species from acoustic recordings. The work presented in this article explores the ability of hidden Markov models to distinguish songs from five species of antbirds that share the same territory in a rainforest environment in Mexico. When only clean recordings were used, species recognition was nearly perfect, 99.5%. With noisy recordings, performance was lower but generally exceeding 90%. Besides the quality of the recordings, performance has been found to be heavily influenced by a multitude of factors, such as the size of the training set, the feature extraction method used, and number of states in the Markov model. In general, training with noisier data also improved recognition in test recordings, because of an increased ability to generalize. Considerations for improving performance, including beamforming with sensor arrays and design of preprocessing methods particularly suited for bird songs, are discussed. Combining sensor network technology with effective event detection and species identification algorithms will enable observation of species interactions at a spatial and temporal resolution that is simply impossible with current tools. Analysis of animal behavior through real-time tracking of individuals and recording of large amounts of data with embedded devices in remote locations is thus a realistic goal.     

Visible-Light Augmented Lithium Storage Capacity in a Ruthenium(II) Photosensitizer Conjugated with a Dione-Catechol Redox Couple

Controlling redox activity of judiciously appended redox units on a photo-sensitive molecular core is an effective strategy for visible light energy harvesting and storage. The first example of a photosensitizer - electron donor coordination compound in which the photoinduced electron transfer step is used for light to electrical energy conversion and storage is reported. A photo-responsive Ru-diimine module conjugated with redox-active catechol groups in [Ru(II)(phenanthroline-5,6-diolate)₃]⁴⁻ photosensitizer can mediate photoinduced catechol to dione oxidation in the presence of a sacrificial electron acceptor or at the surface of an electrode. Under potentiostatic condition, visible light triggered current density enhancement confirmed the light harvesting ability of this photosensitizer. Upon implementation in galvanostatic charge-discharge of a Li battery configuration, the storage capacity was found to be increased by 100 %, under 470 nm illumination with output power of 4.0 mW/cm⁻². This proof-of-concept molecular system marks an important milestone towards a new generation of molecular photo-rechargeable materials.