Two linear beetle-type scanning tunneling microscopes

Two beetle-type scanning tunneling microscopes are described. Both designs have the thermal stability of the Besocke beetle and the simplicity of the Wilms beetle. Moreover, sample holders were designed that also allow both semiconductor wafers and metal single crystals to be studied. The coarse approach is a linear motion of the beetle towards the sample using inertial slip–stick motion. Ten wires are required to control the position of the beetle and scanner and measure the tunneling current. The two beetles were built with different sized piezolegs, and the vibrational properties of both beetles were studied in detail. It was found, in agreement with previous work, that the beetle bending mode is the lowest principal eigenmode. However, in contrast to previous vibrational studies of beetle-type scanning tunneling microscopes, we found that the beetles did not have the “rattling” modes that are thought to arise from the beetle sliding or rocking between surface asperities on the raceway. The mass of our beetles is 3–4 times larger than the mass of beetles where rattling modes have been observed. We conjecture that the mass of our beetles is above a “critical beetle mass.” This is defined to be the beetle mass that attenuates the rattling modes by elastically deforming the contact region to the extent that the rattling modes cannot be identified as distinct modes in cross-coupling measurements.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Activities in the $FeTiO_{3}-NiTiO_{3}$ Solid Solution from Alloy-Oxide Equilibria at 1273 K

Nine tie-lines between Fe-Ni alloys and FeTiO3-NiTiO3 solid solutions were determined at 1273 K. Samples were equilibrated in evacuated quartz ampoules for periods up to 10 days. Compositions of the alloy and oxide phases at equilibrium were determined by energy-dispersive x-ray spectroscopy. X-ray powder diffraction was used to confirm the results. Attainment of equilibrium was verified by the conventional tie-line rotation technique and by thermodynamic analysis of the results. The tie-lines are skewed toward the FeTiO3 corner. From the tie-line data and activities in the Fe-Ni alloy phase available in the literature, activities of FeTiO3 and NiTiO3 in the ilmenite solid solution were derived using the modified Gibbs-Duhem technique of Jacob and Jeffes [K.T. Jacob and J.H.E. Jeffes, An Improved Method for Calculating Activities from Distribution Equilibria, High Temp. High Press., 1972, 4, p 177-182]. The components of the oxide solid solution exhibit moderate positive deviations from Raoult's law. Within experimental error, excess Gibbs energy of mixing for the FeTiO3-NiTiO3 solid solution at 1273 K is a symmetric function of composition and can be represented as: Delta G(E) = 8590 (+/- 200) X-FeTiO3 X-NiTiO3 J/mol Full spectrum of tie-lines and oxygen potentials for the three-phase equilibrium involving Fe-Ni alloys, FeTiO3-NiTiO3 solid solutions, and TiO2 at 1273 K were computed using results obtained in this study and data available in the literature.

The Parallel Complexity Of Propagation In Boolean Circuits

We consider the problem of deciding whether the output of a boolean circuit is determined by a partial assignment to its inputs. This problem is easily shown to be hard, i.e., co-Image Image -complete. However, many of the consequences of a partial input assignment may be determined in linear time, by iterating the following step: if we know the values of some inputs to a gate, we can deduce the values of some outputs of that gate. This process of iteratively deducing some of the consequences of a partial assignment is called propagation. This paper explores the parallel complexity of propagation, i.e., the complexity of determining whether the output of a given boolean circuit is determined by propagating a given partial input assignment. We give a complete classification of the problem into those cases that are Image -complete and those that are unlikely to be Image complete.

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

Linear filtering in DCT IV/DST IV and MDCT/MDST domain

In this paper, expressions for convolution multiplication properties of DCT IV and DST IV are derived starting from equivalent DFT representations. Using these expressions methods for implementing linear filtering through block convolution in the DCT IV and DST IV domain are proposed. Techniques developed for DCT IV and DST IV are further extended to MDCT and MDST where the filter implementation is near exact for symmetric filters and approximate for non-symmetric filters. No additional overlapping is required for implementing the symmetric filtering in the MDCT domain and hence the proposed algorithm is computationally competitive with DFT based systems. Moreover, inherent 50% overlap between the adjacent frames used for MDCT/MDST domain reduces the blocking artifacts due to block processing or quantization. The techniques are computationally efficient for symmetric filters and provides a new alternative to DFT based convolution.

Secondary attribute retrieval using tree data structures

Several techniques are known for searching an ordered collection of data. The techniques and analyses of retrieval methods based on primary attributes are straightforward. Retrieval using secondary attributes depends on several factors. For secondary attribute retrieval, the linear structures—inverted lists, multilists, doubly linked lists—and the recently proposed nonlinear tree structures—multiple attribute tree (MAT), K-d tree (kdT)—have their individual merits. It is shown in this paper that, of the two tree structures, MAT possesses several features of a systematic data structure for external file organisation which make it superior to kdT. Analytic estimates for the complexity of node searchers, in MAT and kdT for several types of queries, are developed and compared.

Distribution of black nodes at various levels in a linear quadtree

The distribution of black leaf nodes at each level of a linear quadtree is of significant interest in the context of estimation of time and space complexities of linear quadtree based algorithms. The maximum number of black nodes of a given level that can be fitted in a square grid of size 2n × 2n can readily be estimated from the ratio of areas. We show that the actual value of the maximum number of nodes of a level is much less than the maximum obtained from the ratio of the areas. This is due to the fact that the number of nodes possible at a level k, 0≤k≤n − 1, should consider the sum of areas occupied by the actual number of nodes present at levels k + 1, k + 2, …, n − 1.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Influence of environmental and instrumental variables on the non-invasive prediction of Brix in pineapple using near infrared spectroscopy

The Brix content of pineapple fruit can be non-invasively predicted from the second derivative of near infrared reflectance spectra. Correlations obtained using a NIRSystems 6500 spectrophotometer through multiple linear regression and modified partial least squares analyses using a post-dispersive configuration were comparable with that from a pre-dispersive configuration in terms of accuracy (e.g. coefficient of determination, R2, 0.73; standard error of cross validation, SECV, 1.01°Brix). The effective depth of sample assessed was slightly greater using the post-dispersive technique (about 20 mm for pineapple fruit), as expected in relation to the higher incident light intensity, relative to the pre-dispersive configuration. The effect of such environmental variables as temperature, humidity and external light, and instrumental variables such as the number of scans averaged to form a spectrum, were considered with respect to the accuracy and precision of the measurement of absorbance at 876 nm, as a key term in the calibration for Brix, and predicted Brix. The application of post-dispersive near infrared technology to in-line assessment of intact fruit in a packing shed environment is discussed.

Non-invasive assessment of pineapple and mango fruit quality using near infra-red spectroscopy

The potential of near infra-red (NIR) spectroscopy for non-invasive measurement of fruit quality of pineapple (Ananas comosus var. Smooth Cayenne) and mango (Magnifera indica var. Kensington) fruit was assessed. A remote reflectance fibre optic probe, placed in contact with the fruit skin surface in a light-proof box, was used to deliver monochromatic light to the fruit, and to collect NIR reflectance spectra (760–2500 nm). The probe illuminated and collected reflected radiation from an area of about 16 cm2. The NIR spectral attributes were correlated with pineapple juice Brix and with mango flesh dry matter (DM) measured from fruit flesh directly underlying the scanned area. The highest correlations for both fruit were found using the second derivative of the spectra (d2 log 1/R) and an additive calibration equation. Multiple linear regression (MLR) on pineapple fruit spectra (n = 85) gave a calibration equation using d2 log 1/R at wavelengths of 866, 760, 1232 and 832 nm with a multiple coefficient of determination (R2) of 0.75, and a standard error of calibration (SEC) of 1.21 °Brix. Modified partial least squares (MPLS) regression analysis yielded a calibration equation with R2 = 0.91, SEC = 0.69, and a standard error of cross validation (SECV) of 1.09 oBrix. For mango, MLR gave a calibration equation using d2 log 1/R at 904, 872, 1660 and 1516 nm with R2 = 0.90, and SEC = 0.85% DM and a bias of 0.39. Using MPLS analysis, a calibration equation with R2 = 0.98, SEC = 0.54 and SECV = 1.19 was obtained. We conclude that NIR technology offers the potential to assess fruit sweetness in intact whole pineapple and DM in mango fruit, respectively, to within 1° Brix and 1% DM, and could be used for the grading of fruit in fruit packing sheds.

Low PAPR Square STBCs from Complex Partial-Orthogonal Designs (CPODs)

Space-time codes from complex orthogonal designs (CODs) with no zero entries offer low Peak to Average Power Ratio (PAPR) and avoid the problem of switching off antennas. But square CODs for 2(a) antennas with a + 1. complex variables, with no zero entries were discovered only for a <= 3 and if a + 1 = 2(k), for k >= 4. In this paper, a method of obtaining no zero entry (NZE) square designs, called Complex Partial-Orthogonal Designs (CPODs), for 2(a+1) antennas whenever a certain type of NZE code exists for 2(a) antennas is presented. Then, starting from a so constructed NZE CPOD for n = 2(a+1) antennas, a construction procedure is given to obtain NZE CPODs for 2n antennas, successively. Compared to the CODs, CPODs have slightly more ML decoding complexity for rectangular QAM constellations and the same ML decoding complexity for other complex constellations. Using the recently constructed NZE CODs for 8 antennas our method leads to NZE CPODs for 16 antennas. The class of CPODs do not offer full-diversity for all complex constellations. For the NZE CPODs presented in the paper, conditions on the signal sets which will guarantee full-diversity are identified. Simulation results show that bit error performance of our codes is same as that of the CODs under average power constraint and superior to CODs under peak power constraint.

Linear time geometrical design rule checker based on quadtree representation of VLSI mask layouts

An efficient geometrical design rule checker is proposed, based on operations on quadtrees, which represent VLSI mask layouts. The time complexity of the design rule checker is O(N), where N is the number of polygons in the mask. A pseudoPascal description is provided of all the important algorithms for geometrical design rule verification.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.