On the Cubicity of Interval Graphs

A k-cube (or ``a unit cube in k dimensions'') is defined as the Cartesian product R-1 x . . . x R-k where R-i (for 1 <= i <= k) is an interval of the form [a(i), a(i) + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes corresponding to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity of a graph G, denoted as cub(G), is defined as the minimum dimension k such that G has a k-cube representation. An interval graph is a graph that can be represented as the intersection of intervals on the real line - i. e., the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. We show that for any interval graph G with maximum degree Delta, cub(G) <= inverted right perpendicular log(2) Delta inverted left perpendicular + 4. This upper bound is shown to be tight up to an additive constant of 4 by demonstrating interval graphs for which cubicity is equal to inverted right perpendicular log(2) Delta inverted left perpendicular.

ESTIMATION OF EVAPOTRANSPIRATION IN AN EXPERIMENTAL WATERSHED IN A DECIDUOUS FOREST OF SOUTH INDIA

Forested areas play a dominant role in the global hydrological cycle. Evapotranspiration is a dominant component most of the time catching up with the rainfall. Though there are sophisticated methods which are available for its estimation, a simple reliable tool is needed so that a good budgeting could be made. Studies have established that evapotranspiration in forested areas is much higher than in agricultural areas. Latitude, type of forests, climate and geological characteristics also add to the complexity of its estimation. Few studies have compared different methods of evapotranspiration on forested watersheds in semi arid tropical forests. In this paper a comparative study of different methods of estimation of evapotranspiration is made with reference to the actual measurements made using all parameter climatological station data of a small deciduous forested watershed of Mulehole (area of 4.5 km2 ), South India. Potential evapotranspiration (ETo) was calculated using ten physically based and empirical methods. Actual evapotranspiration (AET) has been calculated through computation of water balance through SWAT model. The Penman-Montieth method has been used as a benchmark to compare the estimates arrived at using various methods. The AET calculated shows good agreement with the curve for evapotranspiration for forests worldwide. Error estimates have been made with respect to Penman-Montieth method. This study could give an idea of the errors involved whenever methods with limited data are used and also show the use indirect methods in estimation of Evapotranspiration which is more suitable for regional scale studies.

Site classification and estimation of surface level seismic hazard using geophysical data and probabilistic approach

This paper presents the site classification of Bangalore Mahanagar Palike (BMP) area using geophysical data and the evaluation of spectral acceleration at ground level using probabilistic approach. Site classification has been carried out using experimental data from the shallow geophysical method of Multichannel Analysis of Surface wave (MASW). One-dimensional (1-D) MASW survey has been carried out at 58 locations and respective velocity profiles are obtained. The average shear wave velocity for 30 m depth (Vs(30)) has been calculated and is used for the site classification of the BMP area as per NEHRP (National Earthquake Hazards Reduction Program). Based on the Vs(30) values major part of the BMP area can be classified as ``site class D'', and ``site class C'. A smaller portion of the study area, in and around Lalbagh Park, is classified as ``site class B''. Further, probabilistic seismic hazard analysis has been carried out to map the seismic hazard in terms spectral acceleration (S-a) at rock and the ground level considering the site classes and six seismogenic sources identified. The mean annual rate of exceedance and cumulative probability hazard curve for S. have been generated. The quantified hazard values in terms of spectral acceleration for short period and long period are mapped for rock, site class C and D with 10% probability of exceedance in 50 years on a grid size of 0.5 km. In addition to this, the Uniform Hazard Response Spectrum (UHRS) at surface level has been developed for the 5% damping and 10% probability of exceedance in 50 years for rock, site class C and D These spectral acceleration and uniform hazard spectrums can be used to assess the design force for important structures and also to develop the design spectrum.

Multiresolution Area-based Fractal Dimension Estimation of Signals Applied to EEG Data

In this paper, we present an approach to estimate fractal complexity of discrete time signal waveforms based on computation of area bounded by sample points of the signal at different time resolutions. The slope of best straight line fit to the graph of log(A(rk)A / rk(2)) versus log(l/rk) is estimated, where A(rk) is the area computed at different time resolutions and rk time resolutions at which the area have been computed. The slope quantifies complexity of the signal and it is taken as an estimate of the fractal dimension (FD). The proposed approach is used to estimate the fractal dimension of parametric fractal signals with known fractal dimensions and the method has given accurate results. The estimation accuracy of the method is compared with that of Higuchi's and Sevcik's methods. The proposed method has given more accurate results when compared with that of Sevcik's method and the results are comparable to that of the Higuchi's method. The practical application of the complexity measure in detecting change in complexity of signals is discussed using real sleep electroencephalogram recordings from eight different subjects. The FD-based approach has shown good performance in discriminating different stages of sleep.

Comparison Of If Estimation Methods For Noise Robustness

Non-stationary signal modeling is a well addressed problem in the literature. Many methods have been proposed to model non-stationary signals such as time varying linear prediction and AM-FM modeling, the later being more popular. Estimation techniques to determine the AM-FM components of narrow-band signal, such as Hilbert transform, DESA1, DESA2, auditory processing approach, ZC approach, etc., are prevalent but their robustness to noise is not clearly addressed in the literature. This is critical for most practical applications, such as in communications. We explore the robustness of different AM-FM estimators in the presence of white Gaussian noise. Also, we have proposed three new methods for IF estimation based on non-uniform samples of the signal and multi-resolution analysis. Experimental results show that ZC based methods give better results than the popular methods such as DESA in clean condition as well as noisy condition.

Spectral Sensing for Cognitive Radio: Estimation of Adaptive Frequency Hopping Signal

The issue of dynamic spectrum scene analysis in any cognitive radio network becomes extremely complex when low probability of intercept, spread spectrum systems are present in environment. The detection and estimation become more complex if frequency hopping spread spectrum is adaptive in nature. In this paper, we propose two phase approach for detection and estimation of frequency hoping signals. Polyphase filter bank has been proposed as the architecture of choice for detection phase to efficiently detect the presence of frequency hopping signal. Based on the modeling of frequency hopping signal it can be shown that parametric methods of line spectral analysis are well suited for estimation of frequency hopping signals if the issues of order estimation and time localization are resolved. An algorithm using line spectra parameter estimation and wavelet based transient detection has been proposed which resolves above issues in computationally efficient manner suitable for implementation in cognitive radio. The simulations show promising results proving that adaptive frequency hopping signals can be detected and demodulated in a non cooperative context, even at a very low signal to noise ratio in real time.

Estimation of gear tooth deflection by the finite element method

The finite element method (FEM) is used to determine for pitch-point, mid-point and tip loading, the deflection curve of a Image 1 diamentral pitch (DP) standard spur gear tooth corresponding to number of teeth of 14, 21, 26 and 34. In all these cases the deflection of the gear tooth at the point of loading obtained by FEM is in good agreement with the experimental value. The contraflexure in the deflection curve at the point of loading observed experimentally in the cases of pitch-point and mid-point loading, is predicted correctly by the FEM analysis.

Swarm intelligence-based solver for parameter estimation of laboratory through-diffusion transport of contaminants

Theoretical approaches are of fundamental importance to predict the potential impact of waste disposal facilities on ground water contamination. Appropriate design parameters are generally estimated be fitting theoretical models to data gathered from field monitoring or laboratory experiments. Transient through-diffusion tests are generally conducted in the laboratory to estimate the mass transport parameters of the proposed barrier material. Thes parameters are usually estimated either by approximate eye-fitting calibration or by combining the solution of the direct problem with any available gradient-based techniques. In this work, an automated, gradient-free solver is developed to estimate the mass transport parameters of a transient through-diffusion model. The proposed inverse model uses a particle swarm optimization (PSO) algorithm that is based on the social behavior of animals searching for food sources. The finite difference numerical solution of the forward model is integrated with the PSO algorithm to solve the inverse problem of parameter estimation. The working principle of the new solver is demonstrated and mass transport parameters are estimated from laboratory through-diffusion experimental data. An inverse model based on the standard gradient-based technique is formulated to compare with the proposed solver. A detailed comparative study is carried out between conventional methods and the proposed solver. The present automated technique is found to be very efficient and robust. The mass transport parameters are obtained with great precision.

Estimation of red blood cell lifespan from alveolar carbon monoxide measurements

Measurement of alveolar carbon monoxide (CO) presents a facile technique to estimate the lifespan, L, of red blood cells (RBCs) in vivo. Several recent studies employ this technique and calculate L (in days) using the expression, L = 13.8 (Hb)/P-CO(end), where (Hb) is the concentration (in g/dL) of hemoglobin in blood, and P-CO(end) is the endogenous production of CO (in ppm). Implicit in this calculation is the assumption that the fraction, f, of endogenous CO production due to RBC turnover is a constant equal to 0.7, which yields the expected RBC lifespan, L approximate to 120 days, in normal controls. In anemic patients, however, enhanced RBC turnover may increase f substantially above 0.7. The above expression then overestimates L. Here, we deriv an alternative tive expression, L = 3390[Hb]/322P(CO (end)-110, that accounts explicitly for the dependence of f on the rate of RBC turnover and thereby provides more accurate estimates of L without requiring additional measurements. Using the latter expression, we recalculate L from recent measurements on hepatitis C virus infected patients undergoing treatment with ribavirin. We find that our estimates of L in these patients (39 +/- 13 days) are significantly lower than current estimates (46 +/- 14 days), indicating that ribavirin affects RBC survival more severely than expected from current studies. Our expression for L is simple to employ in a clinical setting and would render the broadly applicable technique of alveolar CO measurement for the estimation of RBC lifespan more accurate.

Estimation of peak ground acceleration and spectral acceleration for South India with local site effects: probabilistic approach

In this work an attempt has been made to evaluate the seismic hazard of South India (8.0 degrees N-20 degrees N; 72 degrees E-88 degrees E) based on the probabilistic seismic hazard analysis (PSHA). The earthquake data obtained from different sources were declustered to remove the dependent events. A total of 598 earthquakes of moment magnitude 4 and above were obtained from the study area after declustering, and were considered for further hazard analysis. The seismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones in the study area which are associated with earthquakes of magnitude 4 and above. For assessing theseismic hazard, the study area was divided into small grids of size 0.1 degrees x0.1 degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources with in a radius of 300 km. Rock level peak horizontal acceleration (PHA) and spectral acceleration (SA) values at 1 corresponding to 10% and 2% probability of exceedance in 50 years have been calculated for all the grid points. The contour maps showing the spatial variation of these values are presented here. Uniform hazard response spectrum (UHRS) at rock level for 5% damping and 10% and 2% probability of exceedance in 50 years were also developed for all the grid points. The peak ground acceleration (PGA) at surface level was calculated for the entire South India for four different site classes. These values can be used to find the PGA values at any site in South India based on site class at that location. Thus, this method can be viewed as a simplified method to evaluate the PGA values at any site in the study area.

Direct estimation of an element of order matrix from H-1 NMR spectra of strongly dipolar coupled spins

NMR spectra of molecules oriented in thermotropic liquid crystalline media provide information on the molecular structure and order. The spins are generally strongly dipolar coupled and the spectral analyse require the tedious and time consuming numerical iterative calculations. The present study demonstrates the application of multiple quantum spin state selective detection of single quantum transitions for mimicking the homonuclear decoupling and the direct estimation of an element of ordering matrix. This information is utilized to estimate the nearly accurate starting dipolar couplings for iterative calculations. The studies on the spectra of strongly dipolar coupled five and six interacting spin systems are reported.

Estimation of Cavitation Erosion with Incubation Periods and Material Properties

A detailed study of the normalized correlations between the incubation period tc and the properties of various materials tested in a rotating disk device indicates that, at very high intensities, the strength properties influence the duration of tc. The analysis of extensive data from other laboratories for cavitation and liquid impingement erosion also indicates that, while both energy and strength properties influence the duration of tc, the latter ones predominate for a majority of cases. A fatigue-type failure occurs during tc. For estimating the time required to pierce a metallic specimen in a rotating device a relationship tp = 160 tc0.44 is proposed. A detailed study of normalized correlations between erosion resistance (inverse of erosion rate) and tc values of different materials tested in the rotating disk shows that correlations are good. Analysis of data from eight other investigators clearly points out the validity and the usefulness of this type of prediction.

Estimation of fuzzy memberships from histograms

Based on the conclusions drawn in the bijective transformation between possibility and probability, a method is proposed to estimate the fuzzy membership function for pattern recognition purposes. A rational function approximation to the probability density function is obtained from the histogram of a finite (and sometimes very small) number of samples. This function is normalized such that the highest ordinate is one. The parameters representing the rational function are used for classifying the pattern samples based on a max-min decision rule. The method is illustrated with examples.

A rapid and sensitive method for the estimation of individual tRNA pools

A rapid and sensitive method is described to quantitatively compare tRNA pools for individual aminoacids in a single experiment. The procedure comprises of: (i) charging of total tRNA with a mixture of radiolabeled aminoacids, (ii) deacylation of the esterified tRNA with a volatile base and the recovery of the labeled aminoacid, (iii) derivatisation of the aminoacid with phenylisothiocyanate after mixing with excess of nonradioactive aminoacids, (iv) baseline separation of the phenylthiocarbamyl aminoacids by reverse phase high performance liquid chromatography monitored by A254nm and (v) quantitation of the radioactivity in individual aminoacid peaks. The radioactivity in the aminoacid peak corresponds to the quantity of the aminoacylated tRNA. The method has been successfully applied to quantitate the individual tRNA pools in the developing silk glands of Bombyx mori, a functionally adapted tissue which undergoes considerable variations in tRNA content. PSG, posterior silk gland; PITC, phenylisothiocyanate; DMAA, N,N-dimethyl-N-allylamine; APH, algal protein hydrolysate; ptc-, phenylthiocarbamyl; HPLC, high performance liquid chromatography.

Automated estimation of fatigue crack length and closure/opening stress

An experimental technique is proposed for the estimation of crack length as well as crack closure/opening stress during fatigue crack growth. A specially designed, single cantilever, crack opening displacement gauge is used to monitor these variables during fatigue crack propagation testing. The technique was experimentally validated through electronfractography.