On the axiomatic approach to the maximum entropy principle of inference

Recent axiomatic derivations of the maximum entropy principle from consistency conditions are critically examined. We show that proper application of consistency conditions alone allows a wider class of functionals, essentially of the form ∝ dx p(x)[p(x)/g(x)] s , for some real numbers, to be used for inductive inference and the commonly used form − ∝ dx p(x)ln[p(x)/g(x)] is only a particular case. The role of the prior densityg(x) is clarified. It is possible to regard it as a geometric factor, describing the coordinate system used and it does not represent information of the same kind as obtained by measurements on the system in the form of expectation values.

Measurement of sensitivities for the thermal recording of laser beams

A simple technique for determining the energy sensitivities for the thermographic recording of laser beams is described. The principle behind this technique is that, if a laser beam with a known spatial distribution such as a Gaussian profile is used for imaging, the radius of the thermal image formed depends uniquely on the intensity of the impinging beam. Thus by measuring the radii of the images produced for different incident beam intensities the minimum intensity necessary (that is, the threshold) for thermographic imaging is found. The diameter of the laser beam can also be found from this measurement. A simple analysis based on the temperature distribution in the laser heated material shows that there is an inverse square root dependence on pulse duration or period of exposure for the energy fluence of the laser beam required, both for the threshold and the subsequent increase in the size of the recording. It has also been shown that except for low intensity, long duration exposure on very low conductivity materials, heat losses are not very significant.

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.

Pseudo-time marching schemes for inverse problems in structural health assessment and medical imaging

We propose a self-regularized pseudo-time marching strategy for ill-posed, nonlinear inverse problems involving recovery of system parameters given partial and noisy measurements of system response. While various regularized Newton methods are popularly employed to solve these problems, resulting solutions are known to sensitively depend upon the noise intensity in the data and on regularization parameters, an optimal choice for which remains a tricky issue. Through limited numerical experiments on a couple of parameter re-construction problems, one involving the identification of a truss bridge and the other related to imaging soft-tissue organs for early detection of cancer, we demonstrate the superior features of the pseudo-time marching schemes.

High Resolution Surface Imaging Using a Carbon Nanotube Array with Pointed Height distribution

In this paper we discuss a new technique to image the surfaces of metallic substrates using field emission from a pointed array of carbon nanotubes (CNTs). We consider a pointed height distribution of the CNT array under a diode configuration with two side gates maintained at a negative potential to obtain a highly intense beam of electrons localized at the center of the array. The CNT array on a metallic substrate is considered as the cathode and the test substrate as the anode. Scanning the test Substrate with the cathode reveals that the field emission current is highly sensitive to the surface features with nanometer resolution. Surface features of semi-circular, triangular and rectangular geometries (projections and grooves) are considered for simulation. This surface scanning/mapping technique can be applied for surface roughness measurements with nanoscale accuracy. micro/nano damage detection, high precision displacement sensors, vibrometers and accelerometers. among other applications.

Evaluation of Moderate-Resolution Imaging Spectroradiometer (MODIS) collection 004 (C004) aerosol retrievals at Kanpur, Indo-Gangetic basin

[1] We have compared the spectral aerosol optical depth (AOD, tau lambda) and aerosol fine mode fraction (AFMF) of Collection 004 (C004) derived from Moderate-Resolution Imaging Spectroradiometer (MODIS) on board National Aeronautics and Space Administration's (NASA) Terra and Aqua platforms with that obtained from Aerosol Robotic Network (AERONET) at Kanpur (26.45 degrees N, 80.35 degrees E), India for the period 2001-2005. The spatially-averaged (0.5 degrees x 0.5 degrees centered at AERONET sunphotometer) MODIS Level-2 aerosol parameters (10 km at nadir) were compared with the temporally averaged AERONET-measured AOD (within +/- 30 minutes of MODIS overpass). We found that MODIS systematically overestimated AOD during the pre-monsoon season (March to June, known to be influenced by dust aerosols). The errors in AOD at 0.66 mu m were correlated with the apparent reflectance at 2.1 mu m (rho*(2.1)) which MODIS C004 uses to estimate the surface reflectance in the visible channels (rho(0.47) = rho*(2.1)/ 4, rho(0.66) = rho*(2.1)/ 2). The large errors in AOD (Delta tau(0.66) > 0.3) are found to be associated with the higher values of rho*(2.1) (0.18 to 0.25), where the uncertainty in the ratios of reflectance is large (Delta rho(0.66) +/- 0.04, Delta rho(0.47) +/- 0.02). This could have resulted in lower surface reflectance, higher aerosol path radiance and thus lead to overestimation in AOD. While MODIS-derived AFMF has binary distribution (1 or 0) with too low (AFMF < 0.2) during dust-loading period, and similar to 1 for the rest of the retrievals, AERONET showed range of values (0.4 to 0.9). The errors in tau(0.66) were also high in the scattering angle range 110 degrees - 140 degrees, where the optical effects of nonspherical dust particles are different from that of spherical particles.

Effect of substituent on the thermodynamics of D-glucopyranoside binding to concanavalin A, pea (Pisum sativum) lectin and lentil (Lens culinaris) lectin

Titration calorimetry measurements of the binding of phenyl-alpha (alpha PhOGlu), 3-methoxy (3MeOGlu), fluorodeoxy and deoxy derivatives of alpha-D-glucopyranose (Glu) to concanavalin A (conA), pea lectin and lentil lectin were performed at approx. 10 and 25 degrees C in 0.01 M dimethylglutaric acid/NaOH buffer, pH 6.9, containing 0.15 M NaCl and Mn2+ and Ca2+ ions. Apparently the 3-deoxy, 4-deoxy and 6-deoxy as well as the 4-fluorodeoxy and 6-fluorodeoxy derivatives of Glu do not bind to the lectins because no heat release was observed on the addition of aliquots of solutions of these derivatives to the lectin solutions. The binding enthalpies, delta H0b, and entropies, delta S0b, determined from the measurements were compared with the same thermodynamic binding parameters for Glu, D-mannopyranoside and methyl-alpha- D-glucopyranoside (alpha MeOGlu). The binding reactions are enthalpically driven with little change in the heat capacity on binding, and exhibit enthalpy-entropy compensation. Differences between the thermodynamic binding parameters can be rationalized in terms of the interactions apparent in the known crystal structures of the methyl-alpha-D-mannopyranoside-conA [Derewenda, Yariv, Helliwell, Kalb (Gilboa), Dodson, Papiz, Wan and Campbell (1989) EMBO J. 8, 2189-2193] and pea lectin-trimanno-pyranoside [Rini, Hardman, Einspahr, Suddath and Carber (1993) J. Biol. Chem. 268, 10126-10132] complexes. Increases in the entropy change on binding are observed for alpha MeOGlu binding to pea and lentil lectin, for alpha PhOGlu binding to conA and pea lectin, and for 3MeOGlu binding to pea lectin relative to the entropy change for Glu binding, and imply that the phenoxy and methoxy substituents provide additional hydrophobic interactions in the complex. Increases in the binding enthalpy relative to that of Glu are observed for deoxy and fluoro derivatives in the C-1 and C-2 positions and imply that these substituents weaken the interaction with the surrounding water, thereby strengthening the interaction with the binding site.

Thermodynamics of monosaccharide binding to concanavalin A, pea (Pisum sativum) lectin, and lentil (Lens culinaris) lectin

Titration calorimetry measurements of the binding of methyl alpha-D-mannopyranoside (Me alpha Man), D-mannopyranoside (Man), methyl alpha-D-glucopyranoside (Me alpha Glu), and D-glucopyranoside (Glu) to concanavalin A (Con A), pea lectin, and lentil lectin were performed at 281 and 292 K in 0.01 M dimethylglutaric acid-NaOH buffer (pH 6.9) containing 0.15 M NaCl and Mn+2 and Ca+2 ions. The site binding enthalpies, delta H, are the same at both temperatures and range from -28.4 +/- 0.9 (Me alpha Man) to -16.6 +/- 0.5 kJ mol-1 (Glu) for Con A, from -26.2 +/- 1.1 (Me alpha Man) to -12.8 +/- 0.4 kJ mol-1 (Me alpha Glu) for pea lectin, and from -16.6 +/- 0.7 (Me alpha Man) to -8.0 +/- 0.2 kJ mol-1 (Me alpha Glu) for lentil lectin. The site binding constants range from 17 +/- 1 x 10(3) M-1 (Me alpha Man to Con A at 281.2 K) to 230 +/- 20 M-1 (Glu to lentil lectin at 292.6 K) and exhibit high specificity for Con A where they are in the Me alpha Man:Man:Me alpha Glu:Glu ratio of 21:4:5:1, while the corresponding ratio is 5:2:1.5:1 for pea lectin and 4:2:2:1 for lentil lectin. The higher specificity for Con A indicates more interactions between the amino acid residues at the binding site and the carbohydrate ligand than for the pea and lentil lectin-carbohydrate complexes. The carbohydrate-lectin binding results exhibit enthalpy-entropy compensation in that delta Hb (kJ mol-1) = -1.67 +/- 0.06 x 10(4) + (1.30 +/- 0.12)T(K) delta Sb (J mol-1K-1). Differential scanning calorimetry measurements on the thermal denaturation of the lectins and their carbohydrate complexes show that the Con A tetramer dissociates into monomers, while the pea and lentil lectin dimers dissociate into two submonomer fragments. At the denaturation temperature, one carbohydrate binds to each monomer of Con A and the pea and lentil lectins. Complexation with the carbohydrate increases the denaturation temperature of the lectin and the magnitude of the increases yield binding constants in agreement with the determinations from titration calorimetry.

Improved k-t BLAST for fast fMR imaging

A popular dynamic imaging technique, k-t BLAST (ktB) is studied here for BAR imaging. ktB utilizes correlations in k-space and time, to reconstruct the image time series with only a fraction of the data. The algorithm works by unwrapping the aliased Fourier conjugate space of k-t (y-f-space). The unwrapping process utilizes the estimate of the true y-f-space, by acquiring densely sampled low k-space data. The drawbacks of this method include separate training scan, blurred training estimates and aliased phase maps. The proposed changes are incorporation of phase information from the training map and using generalized-series-extrapolated training map. The proposed technique is compared with ktB on real fMRI data. The proposed changes allow for ktB to operate at an acceleration factor of 6. Performance is evaluated by comparing activation maps obtained using reconstructed images. An improvement of up to 10 dB is observed in thePSNR of activation maps. Besides, a 10% reduction in RMSE is obtained over the entire time series of fMRI images. Peak improvement of the proposed method over ktB is 35%, averaged over five data sets. (C)2010 Elsevier Inc. All rights reserved.

Novel composite coded pattern for small angle measurement using imaging method -art.no.62891D

A novel approach for measurement of small rotation angles using imaging method is proposed and demonstrated. A plane mirror placed on a precision rotating table is used for imaging the newly designed composite coded pattern. The imaged patterns are captured with the help of a CCD camera. The angular rotation of the plane mirror is determined from a pair of the images of the pattern, captured once before and once after affecting the tilt of the mirror. Both simulation and experimental results suggest that the proposed approach not only retains the advantages of the original imaging method but also contributes significantly to the enhancement of its measuring range (+/- 4.13 degrees with accuracy of the order of 1 arcsec).

Multiple imaging with an aberration optimized hololens array

The imaging performance of hololenses formed with four different geometries were studied through an analysis of their third-order aberration coefficients. It is found that the geometry proposed by Brandt (1969) gives the least residual aberration with minimum variation of this aberration with the reconstruction angle. When the ideal position of one of the construction beams is changed in order to generate a hololens array, the residual aberration is found to increase sharply, which in turn affects the image resolution among the multiplied images in the output. A hololens array was generated using Brandt's geometry with the help of a one-dimensional sinusoidal grating. The results of multiple imaging with the hololens array are presented. The image resolution is reasonably high and can be further improved by reducing the f-number of the hololenses.

Imaging with oriented photographic diffusers

We analyse the imaging property of an oriented photographic diffuser which is the record of an elongated speckle pattern. It is found that the contrast transfer, when gratings are imaged through the slits in the diffuser, is considerably higher compared to imaging through a circular pinhole of comparable dimensions. We use the diffuser to produce high frequency gratings through multiple imaging a low frequency grating. The grating is used to demonstrate optical image subtraction.

Multiplexing in multiple imaging through the theta modulation technique

We apply the theta modulation technique to simultaneously multiple image more than one object independently with a Fourier plane sampling type of multiple imaging system. Experimental results of multiple imaging two objects is presented.