A sharp log-Sobolev inequality for the multislice

We determine the log-Sobolev constant of the multi-urn Bernoulli-Laplace diffusion model with arbitrary parameters, up to a small universal multiplicative constant. Our result extends a classical estimate of Lee and Yau (1998) and confirms a conjecture of Filmus, O'Donnell and Wu (2018). Among other applications, we completely quantify the "small-set expansion" phenomenon on the multislice, and obtain sharp mixing-time estimates for the colored exclusion process on various graphs.Comment: 23 pages, comments welcom

Application of Dual-Energy Computed Tomography to the Evalution of Coronary Atherosclerotic Plaque

Atherosclerotic coronary artery disease is responsible for around 50 of cardiovascular deaths in USA. Early detection and characterization of coronary artery atherosclerotic plaque could help prevent cardiac events. Computed tomography (CT) is an excellent modality for imaging calcifications and has higher spatial resolution than other common non-invasive modalities (e.g MRI), making it more suitable for coronary plaque detection. However, attenuation-based classification of non-calcified plaques as fibrous or lipid is difficult with conventional CT, which relies on a single x-ray energy. Dual-energy CT (DECT) may provide additional attenuation data for the identification and discrimination of plaque components. The purpose of this research was to evaluate the feasibility of DECT imaging for coronary plaque characterization and further, to explore the limits of CT for non-invasive plaque analysis. DECT techniques were applied to plaque classification using a clinical CT system. Saline perfused coronary arteries from autopsies were scanned at 80 and 140 kVp, prior to and during injection of iodinated contrast. Plaque attenuation was measured from CT images and matched to histology. Measurements were compared to assess differences among plaque types. Although calcified and non-calcified plaques could be identified and differentiated with DECT, further characterization of non-calcified plaques was not possible. The results also demonstrated that calcified plaque and iodine could be discriminated. The limits of x-ray based non-calcified plaque discrimination were assessed using microCT, a pre-clinical x-ray based high spatial resolution modality. Phantoms and tissues of different composition were scanned using different tube voltages (i.e., different energies) and resulting attenuation values were compared. Better vessel wall visualization and increase in tissue contrast resolution was observed with decrease in x-ray energy. Feasibility of calcium quantification from contrast-enhanced scans by creating virtual n

Application of Dual-Energy Computed Tomography to the Evalution of Coronary Atherosclerotic Plaque

Atherosclerotic coronary artery disease is responsible for around 50 of cardiovascular deaths in USA. Early detection and characterization of coronary artery atherosclerotic plaque could help prevent cardiac events. Computed tomography (CT) is an excellent modality for imaging calcifications and has higher spatial resolution than other common non-invasive modalities (e.g MRI), making it more suitable for coronary plaque detection. However, attenuation-based classification of non-calcified plaques as fibrous or lipid is difficult with conventional CT, which relies on a single x-ray energy. Dual-energy CT (DECT) may provide additional attenuation data for the identification and discrimination of plaque components. The purpose of this research was to evaluate the feasibility of DECT imaging for coronary plaque characterization and further, to explore the limits of CT for non-invasive plaque analysis. DECT techniques were applied to plaque classification using a clinical CT system. Saline perfused coronary arteries from autopsies were scanned at 80 and 140 kVp, prior to and during injection of iodinated contrast. Plaque attenuation was measured from CT images and matched to histology. Measurements were compared to assess differences among plaque types. Although calcified and non-calcified plaques could be identified and differentiated with DECT, further characterization of non-calcified plaques was not possible. The results also demonstrated that calcified plaque and iodine could be discriminated. The limits of x-ray based non-calcified plaque discrimination were assessed using microCT, a pre-clinical x-ray based high spatial resolution modality. Phantoms and tissues of different composition were scanned using different tube voltages (i.e., different energies) and resulting attenuation values were compared. Better vessel wall visualization and increase in tissue contrast resolution was observed with decrease in x-ray energy. Feasibility of calcium quantification from contrast-enhanced scans by creating virtual n

3D Imaging for Planning of Minimally Invasive Surgical Procedures

Novel minimally invasive surgeries are used for treating cardiovascular diseases and are performed under 2D fluoroscopic guidance with a C-arm system. 3D multidetector row computed tomography (MDCT) images are routinely used for preprocedural planning and postprocedural follow-up. For preprocedural planning, the ability to integrate the MDCT with fluoroscopic images for intraprocedural guidance is of clinical interest. Registration may be facilitated by rotating the C-arm to acquire 3D C-arm CT images. This dissertation describes the development of optimal scan and contrast parameters for C-arm CT in 6 swine. A 5-s ungated C-arm CT acquisition during rapid ventricular pacing with aortic root injection using minimal contrast (36 mL), producing high attenuation (1226), few artifacts (2.0), and measurements similar to those from MDCT (p\u3e0.05) was determined optimal. 3D MDCT and C-arm CT images were registered to overlay the aortic structures from MDCT onto fluoroscopic images for guidance in placing the prosthesis. This work also describes the development of a methodology to develop power equation (R2\u3e0.998) for estimating dose with C-arm CT based on applied tube voltage. Application in 10 patients yielded 5.48┬▒177 2.02 mGy indicating minimal radiation burden. For postprocedural follow-up, combinations of non-contrast, arterial, venous single energy CT (SECT) scans are used to monitor patients at multiple time intervals resulting in high cumulative radiation dose. Employing a single dual-energy CT (DECT) scan to replace two SECT scans can reduce dose. This work focuses on evaluating the feasibility of DECT imaging in the arterial phase. The replacement of non-contrast and arterial SECT acquisitions with one arterial DECT acquisition in 30 patients allowed generation of virtual non-contrast (VNC) images with 31 dose savings. Aortic luminal attenuation in VNC (32┬▒177 2 HU) was similar to true non-contrast images (35┬▒177 4 HU) indicating presence of unattenuated blood. To improve discrimination between c

3D Imaging for Planning of Minimally Invasive Surgical Procedures

Novel minimally invasive surgeries are used for treating cardiovascular diseases and are performed under 2D fluoroscopic guidance with a C-arm system. 3D multidetector row computed tomography (MDCT) images are routinely used for preprocedural planning and postprocedural follow-up. For preprocedural planning, the ability to integrate the MDCT with fluoroscopic images for intraprocedural guidance is of clinical interest. Registration may be facilitated by rotating the C-arm to acquire 3D C-arm CT images. This dissertation describes the development of optimal scan and contrast parameters for C-arm CT in 6 swine. A 5-s ungated C-arm CT acquisition during rapid ventricular pacing with aortic root injection using minimal contrast (36 mL), producing high attenuation (1226), few artifacts (2.0), and measurements similar to those from MDCT (p\u3e0.05) was determined optimal. 3D MDCT and C-arm CT images were registered to overlay the aortic structures from MDCT onto fluoroscopic images for guidance in placing the prosthesis. This work also describes the development of a methodology to develop power equation (R2\u3e0.998) for estimating dose with C-arm CT based on applied tube voltage. Application in 10 patients yielded 5.48┬▒177 2.02 mGy indicating minimal radiation burden. For postprocedural follow-up, combinations of non-contrast, arterial, venous single energy CT (SECT) scans are used to monitor patients at multiple time intervals resulting in high cumulative radiation dose. Employing a single dual-energy CT (DECT) scan to replace two SECT scans can reduce dose. This work focuses on evaluating the feasibility of DECT imaging in the arterial phase. The replacement of non-contrast and arterial SECT acquisitions with one arterial DECT acquisition in 30 patients allowed generation of virtual non-contrast (VNC) images with 31 dose savings. Aortic luminal attenuation in VNC (32┬▒177 2 HU) was similar to true non-contrast images (35┬▒177 4 HU) indicating presence of unattenuated blood. To improve discrimination between c

Hypercontractivity on high dimensional expanders

We prove hypercontractive inequalities on high dimensional expanders. As in the settings of the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities are effective for global functions, which are functions that are not significantly affected by a restriction of a small set of coordinates. As applications, we obtain Fourier concentration, small-set expansion, and Kruskal–Katona theorems for high dimensional expanders. Our techniques rely on a new approximate Efron–Stein decomposition for high dimensional link expanders