Provable randomized rounding for minimum-similarity diversification.

When searching for information in a data collection, we are often interested not only in finding relevant items, but also in assembling a diverse set, so as to explore different concepts that are present in the data. This problem has been researched extensively. However, finding a set of items with minimal pairwise similarities can be computationally challenging, and most existing works striving for quality guarantees assume that item relatedness is measured by a distance function. Given the widespread use of similarity functions in many domains, we believe this to be an important gap in the literature. In this paper we study the problem of finding a diverse set of items, when item relatedness is measured by a similarity function. We formulate the diversification task using a flexible, broadly applicable minimization objective, consisting of the sum of pairwise similarities of the selected items and a relevance penalty term. To find good solutions we adopt a randomized rounding strategy, which is challenging to analyze because of the cardinality constraint present in our formulation. Even though this obstacle can be overcome using dependent rounding, we show that it is possible to obtain provably good solutions using an independent approach, which is faster, simpler to implement and completely parallelizable. Our analysis relies on a novel bound for the ratio of Poisson-Binomial densities, which is of independent interest and has potential implications for other combinatorial-optimization problems. We leverage this result to design an efficient randomized algorithm that provides a lower-order additive approximation guarantee. We validate our method using several benchmark datasets, and show that it consistently outperforms the greedy approaches that are commonly used in the literature.

Strengthening ties towards a highly-connected world.

Online social networks provide a forum where people make new connections, learn more about the world, get exposed to different points of view, and access information that were previously inaccessible. It is natural to assume that content-delivery algorithms in social networks should not only aim to maximize user engagement but also to offer opportunities for increasing connectivity and enabling social networks to achieve their full potential. Our motivation and aim is to develop methods that foster the creation of new connections, and subsequently, improve the flow of information in the network. To achieve our goal, we propose to leverage the strong triadic closure principle, and consider violations to this principle as opportunities for creating more social links. We formalize this idea as an algorithmic problem related to the densest k-subgraph problem. For this new problem, we establish hardness results and propose approximation algorithms. We identify two special cases of the problem that admit a constant-factor approximation. Finally, we experimentally evaluate our proposed algorithm on real-world social networks, and we additionally evaluate some simpler but more scalable algorithms.

Joint B0 and image estimation integrated with model based reconstruction for field map update and distortion correction in prostate diffusion MRI.

In prostate Diffusion Weighted MRI, differences in susceptibility values exist at the interface between the prostate and rectal-air. This can result in off-resonance magnetic field leading to geometric distortions including signal stretching and signal pile-up in the reconstructed images. Using a set of EPI data acquired with blip-up and blip-down phase encoding gradient directions, model based reconstruction has recently been proposed that can correct these distortions by using a B0 field estimated from a separate B0 scan. However, change in the size of the rectal air region across time can occur that can result in a mismatch of the B0 field to the EPI scan. Also, the measured B0 field itself can be erroneous in regions of low Signal to Noise ratio around the prostate rectal air interface. In this work, using a set of single shot EPI data acquired with blip-up and blip-down phase encoding gradient directions, a novel joint model based reconstruction is proposed that can account for changes in the off resonance effects between the B0 and EPI scans. For ten prostate patients, using a measured B0 field as an initial B0 estimate, on a 5-point scale (1-5) image quality scores evaluated by an experienced radiologist, the proposed framework achieved scores of 3.50 ±â€¯0.85 and 3.40 ±â€¯0.51 for b-values of 0 and 500 s/mm2, respectively compared to 3.40 ±â€¯0.70 and 3.30 ±â€¯0.67 for model based reconstruction. The proposed framework is also capable of estimating a distortion corrected EPI image even without an initial B0 field estimate in situations where a separate B0 scan cannot be obtained due to time constraint.

A Robust Method for Estimating B0 Inhomogeneity Field in the Liver by Mitigating Fat Signals and Phase-Wrapping.

We developed an optimized and robust method to estimate liver B0 field inhomogeneity for monitoring and correcting susceptibility-induced geometric distortion in magnetic resonance images for precision therapy. A triple-gradient-echo acquisition was optimized for the whole liver B0 field estimation within a single-exhale breath-hold scan on a 3 T scanner. To eliminate chemical-shift artifacts, fat signals were chosen in-phase between 2 echoes with an echo time difference (ΔTE) of 2.3 milliseconds. To avoid phase-wrapping, other 2 echoes provided a large field dynamic range (1/ΔTE) to cover the B0 field inhomogeneity. In addition, using high parallel imaging factor of 4 and a readout-bandwidth of 1955 Hz/pixel, an ~18-second acquisition time for breath-held scans was achieved. A 2-step, 1-dimensional regularized method for the ΔB0 field map estimation was developed, tested and validated in phantom and patient studies. Our method was validated on a water phantom with fat components and air pockets; it yielded ΔB0-field maps that had no chemical-shift and phase-wrapping artifacts, and it had a <0.5 mm of geometric distortion near the air pockets. The ΔB0-field maps of the patients' abdominal regions were also free from phase-wrapping and chemical-shift artifacts. The maximum field inhomogeneity was found near the lung-liver interface, up to ~300 Hz, resulting in ~2 mm of distortions in anatomical images with a readout-bandwidth of 440 Hz/pixel. The field mapping method in the abdominal region is robust; it can be easily integrated in clinical workflow for patient-based quality control of magnetic resonance imaging geometric integrity.

In vivo comparative study of linear versus geometrically correct three-dimensional reconstruction of coronary arteries.

Although conventional linear 3-dimensional (3D) reconstruction of coronary arteries by intravascular ultrasound has been widely used for the assessment of plaque volume and progression; the volumetric error (VE) that is produced has not been adequately studied. Linear and geometrically correct 3D reconstruction was applied in 16 coronary arterial segments from 9 patients. Using geometrically correct reconstruction as reference, VE was assessed in 1-mm-long arterial slices. Although for the entire length of the coronary arteries VEs for lumen, external elastic membrane (EEM), and intima-media volumes were minimal (lumen VE 0.4%, -0.8 to 1.8; EEM VE 0.3%, -0.9 to 1.9; intima-media VE 0.4%, -1.4 to 2.2), the VE in each arterial slice exhibited a large variation from -15.6% to 36.2% for lumen volume, from -12.9% to 33.1% for EEM volume, and from -17.2% to 46.7% for intima-media volume, suggesting that linear reconstruction over- or underestimates the true arterial volumes. Lumen VE, EEM VE, and intima-media VE were also significantly higher in curved arterial subsegments than in relatively straight arterial subsegments (p <0.05). In conclusion, in highly curved arterial subsegments, the VE that is produced by linearly stacking the intravascular ultrasound images may be not negligible. Geometrically correct reconstruction of coronary arteries provides more reliable arterial reconstructions and plaque volume measurements. It is anticipated that clinical application of this technique will contribute to more accurate follow-up of the progression of atherosclerosis and assessment of arterial remodeling.

In-vivo validation of spatially correct three-dimensional reconstruction of human coronary arteries by integrating intravascular ultrasound and biplane angiography.

OBJECTIVES: The in-vivo validation of geometrically correct three-dimensional reconstruction of human coronary arteries by integrating intravascular ultrasound and biplane coronary angiography has not been adequately investigated. The purpose of this study was to describe the reconstruction method and investigate its in-vivo feasibility and accuracy. METHODS: In 17 coronary arteries (mean length, 85.7+/-17.1 mm) from nine patients, an intravascular ultrasound procedure along with a biplane coronary angiography was performed. From each angiographic projection, a single end-diastolic frame was selected in order to reconstruct the intravascular ultrasound catheter trajectory in space. In each end-diastolic intravascular ultrasound image, the lumen and media-adventitia contours were detected semi-automatically by an active contour algorithm. Each pair of contours was located on the catheter trajectory appropriately and interpolated with the adjacent pairs creating a three-dimensional volume of the arterial lumen and wall. The reconstructed lumen was back-projected onto both angiographic planes and the agreement between the back-projected and the angiographic luminal outlines was calculated. RESULTS: The angiogram-derived catheter length showed very high correlation (y=0.97 x + 1.8, P<0.001) and agreement with the corresponding pullback-derived values. Accordingly, the semi-automated segmentation of intravascular ultrasound images was also in significant correlation (r> or =0.96, P<0.001) and agreement with the reference manual tracing. The back-projected luminal borders showed good overall association with the corresponding angiographic ones (r=0.78, P<0.001) as well as remarkable agreement. CONCLUSIONS: Spatially correct three-dimensional reconstruction of human coronary arteries constitutes an imaging method with considerably high in-vivo feasibility and accuracy.

In-vivo accuracy of geometrically correct three-dimensional reconstruction of human coronary arteries: is it influenced by certain parameters?

OBJECTIVE: The geometrically correct three-dimensional reconstruction of human coronary arteries by integrating intravascular ultrasound (IVUS) and biplane angiography constitutes a promising imaging method for coronaries with broad clinical potential. The determinants of the accuracy of the method, however, have not been investigated before. METHODS: In total, 17 arterial segments (right coronary artery, n=7; left anterior descending, n=4; left circumflex, n=6) derived from nine patients were three-dimensionally reconstructed by applying three-dimensional intravascular ultrasound. The degree of matching between the reconstructed lumen back-projected onto each angiographic plane and the actual lumen in each plane was used as a measure of method's accuracy. The investigated factors that could potentially affect the reliability of the method included the type of the artery (left anterior descending, left circumflex, right coronary artery) and several geometrical and morphological characteristics of the reconstructed arteries. RESULTS: The correlation between the back-projected reconstructed lumens and the actual angiographic ones was found to be high (r=0.78, P<0.001). Neither the category of the reconstructed arteries nor their particular geometrical and morphological characteristics influenced the accuracy of the reconstruction method significantly. Nonetheless, the method exhibited slightly less accuracy in the reconstruction of right coronary arteries, an observation that could be attributed to the more intense pulsatile motion that this artery experiences during the cardiac cycle compared to the left anterior descending and left circumflex artery. CONCLUSIONS: The in-vivo accuracy of three-dimensional intravascular ultrasound (3D IVUS) is significantly high regardless of the type of the coronary arteries or their particular geometrical and morphological characteristics. This finding further supports the applicability of the method for either diagnostic or investigational purposes.