An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on $$\left( {{{\frac{{dk}}{{dt}}} \mathord{\left/ {\vphantom {{\frac{{dk}}{{dt}}} k}} \right. \kern-\nulldelimiterspace} k}} \right)$$ is less restrictive than earlier criteria.

Relative stability of DNA as a generic criterion for promoter prediction: whole genome annotation of microbial genomes with varying nucleotide base composition

The rapid increase in genome sequence information has necessitated the annotation of their functional elements, particularly those occurring in the non-coding regions, in the genomic context. Promoter region is the key regulatory region, which enables the gene to be transcribed or repressed, but it is difficult to determine experimentally. Hence an in silico identification of promoters is crucial in order to guide experimental work and to pin point the key region that controls the transcription initiation of a gene. In this analysis, we demonstrate that while the promoter regions are in general less stable than the flanking regions, their average free energy varies depending on the GC composition of the flanking genomic sequence. We have therefore obtained a set of free energy threshold values, for genomic DNA with varying GC content and used them as generic criteria for predicting promoter regions in several microbial genomes, using an in-house developed tool `PromPredict'. On applying it to predict promoter regions corresponding to the 1144 and 612 experimentally validated TSSs in E. coli (50.8% GC) and B. subtilis (43.5% GC) sensitivity of 99% and 95% and precision values of 58% and 60%, respectively, were achieved. For the limited data set of 81 TSSs available for M. tuberculosis (65.6% GC) a sensitivity of 100% and precision of 49% was obtained.

On Guo and Nixon's Criterion for Feature Subset Selection: Assumptions, Implications,and Alternative Options

Guo and Nixon proposed a feature selection method based on maximizing I(x; Y),the multidimensional mutual information between feature vector x and class variable Y. Because computing I(x; Y) can be difficult in practice, Guo and Nixon proposed an approximation of I(x; Y) as the criterion for feature selection. We show that Guo and Nixon's criterion originates from approximating the joint probability distributions in I(x; Y) by second-order product distributions. We remark on the limitations of the approximation and discuss computationally attractive alternatives to compute I(x; Y).

An optimum criterion for eccentrically loaded R. C. columns

An analysis of eccentrically loaded short reinforced concrete columns using a variable failure strain criterion is presented. The method dispenses with the usual procedure of assuming a fixed value for the ultimate strain in concrete. The analysis is based on the use of a simple, single equation for the complete stress-strain curve of concrete and the adoption of a process of maximisation of moment with respect to extreme fibre concrete compressive strain. Columns of rectangular section and loaded eccentrically along one axis only are considered in this paper. A good agreement is observed between the theoretical and experimental values of some test results.

On the bursting criterion for laminar separation bubbles

Traditionally, laminar separation bubbles have been characterised as being 'long' or 'short' on the basis of a two parameter 'bursting' criterion involving a pressure gradient parameter and Reynolds Number at separation. In the present work we suggest a refined bursting criterion, which takes into account not just the length of the bubble but also the maximum height of the bubble, thereby shedding some light on the less understood phenomenon of 'bursting' in laminar separation bubbles.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

A sufficient criterion for Kelvin–Helmholtz instability in the magnetopause boundary‐layer region

The Kelvin–Helmholtz instability has been investigated for the magnetopause boundary‐layer region by the linearized method. The plasma in magnetosheath and magnetopause is assumed to be semi‐infinitely extended homogeneous, nondissipative, and incompressible. It is observed that, if one relation of two plasma speeds on the two sides of the magnetopause, wave number, and boundary‐layer thickness exceeds a certain threshold, the instability sets in. This new analytically sufficient criterion for excitation of instability in the three‐layer plasma flow generalizes the corresponding Chandrasekhar’s instability criterion for two‐layer plasma flow. The known results have been recovered and modified, the new results have been discovered. It is proved that the velocity threshold for the onset of instability is low when the magnitude of the magnetosheath and boundary‐layer region magnetic field and the angle between them are small. Also the threshold depends on the direction of plasma flow. The following results are observed numerically. The growth of the instability is sensitive to the magnetic field direction in the magnetosheath. A slight variation in the magnetic field direction in the second region can substantially change the relative velocity threshold for instability. When the ratio of the density of the second and third layer (magnetosphere) increases or that of the first and third layer decreases, the threshold decreases. Apart from this a necessary criterion for instability is obtained for a particular case.

Discrete-Time Controlled Markov Processes with Average Cost Criterion: A Survey

This work is a survey of the average cost control problem for discrete-time Markov processes. The authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. The exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. The authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. The authors have also identified several important questions that are still open to investigation.

A thermodynamic criterion for selection of gas compositions for diamond deposition

Isoactivity lines for carbon with respect to diamond as the standard state have been calculated in the ternary system C-H-O at 1223 K to identify the diamond deposition domain. The gas composition is calculated by suppressing the formation of all condensed forms of carbon using the SOLGASMIX free-energy minimization program. Thirty six gas species were included in the calculation. From the gas composition, isoactivity lines are computed using recent data on the Gibbs energy of diamond. Except for activities less than 0.1, the isoactivity lines are almost linear on the C-H-O ternary diagram. Gas compositions which generate activity of diamond ranging from 1 to 100 at 1223 K fall inside a narrow wedge originating from the point representing CO. This wedge is very similar to the revised lens-shaped diamond growth domain identified by Bachman et al., using inputs from experiment. The small difference between the calculated and observed domains may be attributed to variation in the supersaturation required for diamond deposition with gas composition. The diamond solubility in the gas phase along the isoactivity line for a(di)=100 and P=6.7 kPa exhibits a minimum at 1280 K, which is close to the optimum temperature found experimentally. At higher supersaturations, non-diamond forms of carbon, including amorphous varieties, are expected. The results suggest that thermodynamic calculations can be useful for locating diamond growth domains in more complex CVD systems containing halogens, for which very little experimental data is available.

A New Full-diversity Criterion and Low-complexity STBCs with Partial Interference Cancellation Decoding

Recently, Guo and Xia gave sufficient conditions for an STBC to achieve full diversity when a PIC (Partial Interference Cancellation) or a PIC-SIC (PIC with Successive Interference Cancellation) decoder is used at the receiver. In this paper, we give alternative conditions for an STBC to achieve full diversity with PIC and PIC-SIC decoders, which are equivalent to Guo and Xia's conditions, but are much easier to check. Using these conditions, we construct a new class of full diversity PIC-SIC decodable codes, which contain the Toeplitz codes and a family of codes recently proposed by Zhang, Xu et. al. as proper subclasses. With the help of the new criteria, we also show that a class of PIC-SIC decodable codes recently proposed by Zhang, Shi et. al. can be decoded with much lower complexity than what is reported, without compromising on full diversity.

Least path criterion (LPC) for unique indexing in a two-dimensional decagonal quasilattice

The least path criterion or least path length in the context of redundant basis vector systems is discussed and a mathematical proof is presented of the uniqueness of indices obtained by applying the least path criterion. Though the method has greater generality, this paper concentrates on the two-dimensional decagonal lattice. The order of redundancy is also discussed; this will help eventually to correlate with other redundant but desirable indexing sets.

Collocated and Distributed STBCs with Partial Interference Cancellation Decoding, Part I: Full-Diversity Criterion

Low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, were given by Guo and Xia along with sufficient conditions for a Space-Time Block Code (STBC) to achieve full diversity with PIC/PIC-SIC decoding for point-to-point MIMO channels. In Part-I of this two part series of papers, we give new conditions for an STBC to achieve full diversity with PIC and PIC-SIC decoders, which are equivalent to Guo and Xia's conditions, but are much easier to check. We then show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks and give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders. In Part-II, we construct new low complexity full-diversity PIC/PIC-SIC decodable STBCs and DSTBCs that achieve higher rates than the known full-diversity low complexity ML decodable STBCs and DSTBCs.