Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.

Separating DNA with different topologies by atomic force microscopy in comparison with gel electrophoresis.

Atomic force microscopy, which is normally used for DNA imaging to gain qualitative results, can also be used for quantitative DNA research, at a single-molecular level. Here, we evaluate the performance of AFM imaging specifically for quantifying supercoiled and relaxed plasmid DNA fractions within a mixture, and compare the results with the bulk material analysis method, gel electrophoresis. The advantages and shortcomings of both methods are discussed in detail. Gel electrophoresis is a quick and well-established quantification method. However, it requires a large amount of DNA, and needs to be carefully calibrated for even slightly different experimental conditions for accurate quantification. AFM imaging is accurate, in that single DNA molecules in different conformations can be seen and counted. When used carefully with necessary correction, both methods provide consistent results. Thus, AFM imaging can be used for DNA quantification, as an alternative to gel electrophoresis.

Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

A kinesin motor in a force-producing conformation.

BACKGROUND: Kinesin motors hydrolyze ATP to produce force and move along microtubules, converting chemical energy into work by a mechanism that is only poorly understood. Key transitions and intermediate states in the process are still structurally uncharacterized, and remain outstanding questions in the field. Perturbing the motor by introducing point mutations could stabilize transitional or unstable states, providing critical information about these rarer states. RESULTS: Here we show that mutation of a single residue in the kinesin-14 Ncd causes the motor to release ADP and hydrolyze ATP faster than wild type, but move more slowly along microtubules in gliding assays, uncoupling nucleotide hydrolysis from force generation. A crystal structure of the motor shows a large rotation of the stalk, a conformation representing a force-producing stroke of Ncd. Three C-terminal residues of Ncd, visible for the first time, interact with the central beta-sheet and dock onto the motor core, forming a structure resembling the kinesin-1 neck linker, which has been proposed to be the primary force-generating mechanical element of kinesin-1. CONCLUSIONS: Force generation by minus-end Ncd involves docking of the C-terminus, which forms a structure resembling the kinesin-1 neck linker. The mechanism by which the plus- and minus-end motors produce force to move to opposite ends of the microtubule appears to involve the same conformational changes, but distinct structural linkers. Unstable ADP binding may destabilize the motor-ADP state, triggering Ncd stalk rotation and C-terminus docking, producing a working stroke of the motor.

Ambient aerosol size distributions and number concentrations measured during the Pittsburgh Air Quality Study (PAQS)

Twelve months of aerosol size distributions from 3 to 560nm, measured using scanning mobility particle sizers are presented with an emphasis on average number, surface, and volume distributions, and seasonal and diurnal variation. The measurements were made at the main sampling site of the Pittsburgh Air Quality Study from July 2001 to June 2002. These are supplemented with 5 months of size distribution data from 0.5 to 2.5μm measured with a TSI aerosol particle sizer and 2 months of size distributions measured at an upwind rural sampling site. Measurements at the main site were made continuously under both low and ambient relative humidity. The average Pittsburgh number concentration (3-500nm) is 22,000cm-3 with an average mode size of 40nm. Strong diurnal patterns in number concentrations are evident as a direct effect of the sources of particles (atmospheric nucleation, traffic, and other combustion sources). New particle formation from homogeneous nucleation is significant on 30-50% of study days and over a wide area (at least a hundred kilometers). Rural number concentrations are a factor of 2-3 lower (on average) than the urban values. Average measured distributions are different from model literature urban and rural size distributions. © 2004 Elsevier Ltd. All rights reserved.

Convergent Surface Water Distributions in U.S. Cities

Earth's surface is rapidly urbanizing, resulting in dramatic changes in the abundance, distribution and character of surface water features in urban landscapes. However, the scope and consequences of surface water redistribution at broad spatial scales are not well understood. We hypothesized that urbanization would lead to convergent surface water abundance and distribution: in other words, cities will gain or lose water such that they become more similar to each other than are their surrounding natural landscapes. Using a database of more than 1 million water bodies and 1 million km of streams, we compared the surface water of 100 US cities with their surrounding undeveloped land. We evaluated differences in areal (A WB) and numeric densities (N WB) of water bodies (lakes, wetlands, and so on), the morphological characteristics of water bodies (size), and the density (D C) of surface flow channels (that is, streams and rivers). The variance of urban A WB, N WB, and D C across the 100 MSAs decreased, by 89, 25, and 71%, respectively, compared to undeveloped land. These data show that many cities are surface water poor relative to undeveloped land; however, in drier landscapes urbanization increases the occurrence of surface water. This convergence pattern strengthened with development intensity, such that high intensity urban development had an areal water body density 98% less than undeveloped lands. Urbanization appears to drive the convergence of hydrological features across the US, such that surface water distributions of cities are more similar to each other than to their surrounding landscapes. © 2014 The Author(s).

Using ground reaction force to predict knee kinetic asymmetry following anterior cruciate ligament reconstruction.

Asymmetries in sagittal plane knee kinetics have been identified as a risk factor for anterior cruciate ligament (ACL) re-injury. Clinical tools are needed to identify the asymmetries. This study examined the relationships between knee kinetic asymmetries and ground reaction force (GRF) asymmetries during athletic tasks in adolescent patients following ACL reconstruction (ACL-R). Kinematic and GRF data were collected during a stop-jump task and a side-cutting task for 23 patients. Asymmetry indices between the surgical and non-surgical limbs were calculated for GRF and knee kinetic variables. For the stop-jump task, knee kinetics asymmetry indices were correlated with all GRF asymmetry indices (P < 0.05), except for loading rate. Vertical GRF impulse asymmetry index predicted peak knee moment, average knee moment, and knee work (R(2)  ≥ 0.78, P < 0.01) asymmetry indices. For the side-cutting tasks, knee kinetic asymmetry indices were correlated with the peak propulsion vertical GRF and vertical GRF impulse asymmetry indices (P < 0.05). Vertical GRF impulse asymmetry index predicted peak knee moment, average knee moment, and knee work (R(2)  ≥ 0.55, P < 0.01) asymmetry indices. The vertical GRF asymmetries may be a viable surrogate for knee kinetic asymmetries and therefore may assist in optimizing rehabilitation outcomes and minimizing re-injury rates.

Spanning the scales of granular materials through microscopic force imaging.

If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. Here we describe experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combination of packing structure and contact deformations produce the observed nontrivial mechanical response of the packing, revealing a surprising microscopic particle deformation enhancement mechanism.

In vivo visualization of abdominal malignancies with acoustic radiation force elastography.

The utility of acoustic radiation force impulse (ARFI) imaging for real-time visualization of abdominal malignancies was investigated. Nine patients presenting with suspicious masses in the liver (n = 7) or kidney (n = 2) underwent combined sonography/ARFI imaging. Images were acquired of a total of 12 tumors in the nine patients. In all cases, boundary definition in ARFI images was improved or equivalent to boundary definition in B-mode images. Displacement contrast in ARFI images was superior to echo contrast in B-mode images for each tumor. The mean contrast for suspected hepatocellular carcinomas (HCCs) in B-mode images was 2.9 dB (range: 1.5-4.2) versus 7.5 dB (range: 3.1-11.9) in ARFI images, with all HCCs appearing more compliant than regional cirrhotic liver parenchyma. The mean contrast for metastases in B-mode images was 3.1 dB (range: 1.2-5.2) versus 9.3 dB (range: 5.7-13.9) in ARFI images, with all masses appearing less compliant than regional non-cirrhotic liver parenchyma. ARFI image contrast (10.4 dB) was superior to B-mode contrast (0.9 dB) for a renal mass. To our knowledge, we present the first in vivo images of abdominal malignancies in humans acquired with the ARFI method or any other technique of imaging tissue elasticity.

In vivo guidance and assessment of liver radio-frequency ablation with acoustic radiation force elastography.

The initial results from clinical trials investigating the utility of acoustic radiation force impulse (ARFI) imaging for use with radio-frequency ablation (RFA) procedures in the liver are presented. To date, data have been collected from 6 RFA procedures in 5 unique patients. Large displacement contrast was observed in ARFI images of both pre-ablation malignancies (mean 7.5 dB, range 5.7-11.9 dB) and post-ablation thermal lesions (mean 6.2 dB, range 5.1-7.5 dB). In general, ARFI images provided superior boundary definition of structures relative to the use of conventional sonography alone. Although further investigations are required, initial results are encouraging and demonstrate the clinical promise of the ARFI method for use in many stages of RFA procedures.

Intracardiac acoustic radiation force impulse imaging: a novel imaging method for intraprocedural evaluation of radiofrequency ablation lesions.

BACKGROUND: Arrhythmia recurrence after cardiac radiofrequency ablation (RFA) for atrial fibrillation has been linked to conduction through discontinuous lesion lines. Intraprocedural visualization and corrective ablation of lesion line discontinuities could decrease postprocedure atrial fibrillation recurrence. Intracardiac acoustic radiation force impulse (ARFI) imaging is a new imaging technique that visualizes RFA lesions by mapping the relative elasticity contrast between compliant-unablated and stiff RFA-treated myocardium. OBJECTIVE: To determine whether intraprocedure ARFI images can identify RFA-treated myocardium in vivo. METHODS: In 8 canines, an electroanatomical mapping-guided intracardiac echo catheter was used to acquire 2-dimensional ARFI images along right atrial ablation lines before and after RFA. ARFI images were acquired during diastole with the myocardium positioned at the ARFI focus (1.5 cm) and parallel to the intracardiac echo transducer for maximal and uniform energy delivery to the tissue. Three reviewers categorized each ARFI image as depicting no lesion, noncontiguous lesion, or contiguous lesion. For comparison, 3 separate reviewers confirmed RFA lesion presence and contiguity on the basis of functional conduction block at the imaging plane location on electroanatomical activation maps. RESULTS: Ten percent of ARFI images were discarded because of motion artifacts. Reviewers of the ARFI images detected RFA-treated sites with high sensitivity (95.7%) and specificity (91.5%). Reviewer identification of contiguous lesions had 75.3% specificity and 47.1% sensitivity. CONCLUSIONS: Intracardiac ARFI imaging was successful in identifying endocardial RFA treatment when specific imaging conditions were maintained. Further advances in ARFI imaging technology would facilitate a wider range of imaging opportunities for clinical lesion evaluation.

Intracardiac acoustic radiation force impulse (ARFI) and shear wave imaging in pigs with focal infarctions.

Four pigs, three with focal infarctions in the apical intraventricular septum (IVS) and/or left ventricular free wall (LVFW), were imaged with an intracardiac echocardiography (ICE) transducer. Custom beam sequences were used to excite the myocardium with focused acoustic radiation force (ARF) impulses and image the subsequent tissue response. Tissue displacement in response to the ARF excitation was calculated with a phase-based estimator, and transverse wave magnitude and velocity were each estimated at every depth. The excitation sequence was repeated rapidly, either in the same location to generate 40 Hz M-modes at a single steering angle, or with a modulated steering angle to synthesize 2-D displacement magnitude and shear wave velocity images at 17 points in the cardiac cycle. Both types of images were acquired from various views in the right and left ventricles, in and out of infarcted regions. In all animals, acoustic radiation force impulse (ARFI) and shear wave elasticity imaging (SWEI) estimates indicated diastolic relaxation and systolic contraction in noninfarcted tissues. The M-mode sequences showed high beat-to-beat spatio-temporal repeatability of the measurements for each imaging plane. In views of noninfarcted tissue in the diseased animals, no significant elastic remodeling was indicated when compared with the control. Where available, views of infarcted tissue were compared with similar views from the control animal. In views of the LVFW, the infarcted tissue presented as stiff and non-contractile compared with the control. In a view of the IVS, no significant difference was seen between infarcted and healthy tissue, whereas in another view, a heterogeneous infarction was seen to be presenting itself as non-contractile in systole.

Acoustic radiation force impulse imaging (ARFI) on an IVUS circular array.

Our long-term goal is the detection and characterization of vulnerable plaque in the coronary arteries of the heart using intravascular ultrasound (IVUS) catheters. Vulnerable plaque, characterized by a thin fibrous cap and a soft, lipid-rich necrotic core is a precursor to heart attack and stroke. Early detection of such plaques may potentially alter the course of treatment of the patient to prevent ischemic events. We have previously described the characterization of carotid plaques using external linear arrays operating at 9 MHz. In addition, we previously modified circular array IVUS catheters by short-circuiting several neighboring elements to produce fixed beamwidths for intravascular hyperthermia applications. In this paper, we modified Volcano Visions 8.2 French, 9 MHz catheters and Volcano Platinum 3.5 French, 20 MHz catheters by short-circuiting portions of the array for acoustic radiation force impulse imaging (ARFI) applications. The catheters had an effective transmit aperture size of 2 mm and 1.5 mm, respectively. The catheters were connected to a Verasonics scanner and driven with pushing pulses of 180 V p-p to acquire ARFI data from a soft gel phantom with a Young's modulus of 2.9 kPa. The dynamic response of the tissue-mimicking material demonstrates a typical ARFI motion of 1 to 2 microns as the gel phantom displaces away and recovers back to its normal position. The hardware modifications applied to our IVUS catheters mimic potential beamforming modifications that could be implemented on IVUS scanners. Our results demonstrate that the generation of radiation force from IVUS catheters and the development of intravascular ARFI may be feasible.

Contrast in intracardiac acoustic radiation force impulse images of radiofrequency ablation lesions.

We have previously shown that intracardiac acoustic radiation force impulse (ARFI) imaging visualizes tissue stiffness changes caused by radiofrequency ablation (RFA). The objectives of this in vivo study were to (1) quantify measured ARFI-induced displacements in RFA lesion and unablated myocardium and (2) calculate the lesion contrast (C) and contrast-to-noise ratio (CNR) in two-dimensional ARFI and conventional intracardiac echo images. In eight canine subjects, an ARFI imaging-electroanatomical mapping system was used to map right atrial ablation lesion sites and guide the acquisition of ARFI images at these sites before and after ablation. Readers of the ARFI images identified lesion sites with high sensitivity (90.2%) and specificity (94.3%) and the average measured ARFI-induced displacements were higher at unablated sites (11.23 ± 1.71 µm) than at ablated sites (6.06 ± 0.94 µm). The average lesion C (0.29 ± 0.33) and CNR (1.83 ± 1.75) were significantly higher for ARFI images than for spatially registered conventional B-mode images (C = -0.03 ± 0.28, CNR = 0.74 ± 0.68).