# Browsing by Subject "algorithm"

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Item Open Access Active-Space N-Representability Constraints for Variational Two-Particle Reduced Density Matrix Calculations(2010) Shenvi, Neil; Izmaylov, Artur FThe ground-state energy of a system of fermions can be calculated by minimizing a linear functional of the two-particle reduced density matrix (2-RDM) if an accurate set of N-representability conditions is applied. In this Letter we introduce a class of linear N-representability conditions based on exact calculations on a reduced active space. Unlike wave-function-based approaches, the 2-RDM methodology allows us to combine information from calculations on different active spaces. By adding active-space constraints, we can iteratively improve our estimate for the ground-state energy. Applying our methodology to a 1D Hubbard model yields a significant improvement over traditional 2-positivity constraints with the same computational scaling.Item Open Access Algorithms for Public Decision Making(2019) Fain, Brandon ThomasIn public decision making, we are confronted with the problem of aggregating the conflicting preferences of many individuals about outcomes that affect the group. Examples of public decision making include allocating shared public resources and social choice or voting. We study these problems from the perspective of an algorithm designer who takes the preferences of the individuals and the constraints of the decision making problem as input and efficiently computes a solution with provable guarantees with respect to fairness and welfare, as defined on individual preferences.

Concerning fairness, we develop the theory of group fairness as core or proportionality in the allocation of public goods. The core is a stability based notion adapted from cooperative game theory, and we show extensive algorithmic connections between the core solution concept and optimizing the Nash social welfare, the geometric mean of utilities. We explore applications in public budgeting, multi-issue voting, memory sharing, and fair clustering in unsupervised machine learning.

Regarding welfare, we extend recent work in implicit utilitarian social choice to choose approximately optimal public outcomes with respect to underlying cardinal valuations using limited ordinal information. We propose simple randomized algorithms with strong utilitarian social cost guarantees when the space of outcomes is metric. We also study many other desirable properties of our algorithms, including approximating the second moment of utilitarian social cost. We explore applications in voting for public projects, preference elicitation, and deliberation.

Item Open Access Correlated Polarity Noise Reduction: Development, Analysis, and Application of a Novel Noise Reduction Paradigm(2013) Wells, Jered RImage noise is a pervasive problem in medical imaging. It is a property endemic to all imaging modalities and one especially familiar in those modalities that employ ionizing radiation. Statistical uncertainty is a major limiting factor in the reduction of ionizing radiation dose; patient exposure must be minimized but high image quality must also be achieved to retain the clinical utility of medical images. One way to achieve the goal of radiation dose reduction is through the use of image post processing with noise reduction algorithms. By acquiring images at lower than normal exposure followed by algorithmic noise reduction, it is possible to restore image noise to near normal levels. However, many denoising algorithms degrade the integrity of other image quality components in the process.

In this dissertation, a new noise reduction algorithm is investigated: Correlated Polarity Noise Reduction (CPNR). CPNR is a novel noise reduction technique that uses a statistical approach to reduce noise variance while maintaining excellent resolution and a "normal" noise appearance. In this work, the algorithm is developed in detail with the introduction of several methods for improving polarity estimation accuracy and maintaining the normality of the residual noise intensity distribution. Several image quality characteristics are assessed in the production of this new algorithm including its effects on residual noise texture, residual noise magnitude distribution, resolution effects, and nonlinear distortion effects. An in-depth review of current linear methods for medical imaging system resolution analysis will be presented along with several newly discovered improvements to existing techniques. This is followed by the presentation of a new paradigm for quantifying the frequency response and distortion properties of nonlinear algorithms. Finally, the new CPNR algorithm is applied to computed tomography (CT) to assess its efficacy as a dose reduction tool in 3-D imaging.

It was found that the CPNR algorithm can be used to reduce x ray dose in projection radiography by a factor of at least two without objectionable degradation of image resolution. This is comparable to other nonlinear image denoising algorithms such as the bilateral filter and wavelet denoising. However, CPNR can accomplish this level of dose reduction with few edge effects and negligible nonlinear distortion of the anatomical signal as evidenced by the newly developed nonlinear assessment paradigm. In application to multi-detector CT, XCAT simulations showed that CPNR can be used to reduce noise variance by 40% with minimal blurring of anatomical structures under a filtered back-projection reconstruction paradigm. When an apodization filter was applied, only 33% noise variance reduction was achieved, but the edge-saving qualities were largely retained. In application to cone-beam CT for daily patient positioning in radiation therapy, up to 49% noise variance reduction was achieved with as little as 1% reduction in the task transfer function measured from reconstructed data at the cutoff frequency.

This work concludes that the CPNR paradigm shows promise as a viable noise reduction tool which can be used to maintain current standards of clinical image quality at almost half of normal radiation exposure This algorithm has favorable resolution and nonlinear distortion properties as measured using a newly developed set of metrics for nonlinear algorithm resolution and distortion assessment. Simulation studies and the initial application of CPNR to cone-beam CT data reveal that CPNR may be used to reduce CT dose by 40%-49% with minimal degradation of image resolution.

Item Open Access Essays on Identification and Promotion of Game-Theoretic Cooperation(2018) Moon, CatherineThis dissertation looks at how to identify and promote cooperation in a multiagent system, first theoretically through the lens of computational game theory and later empirically through a human subject experiment. Chapter 2 studies the network dynamics leading to a potential unraveling of cooperation and identify the subset of agents that can form an enforceable cooperative agreement with. This is an important problem, because cooperation is harder to sustain when information of defection, and thus the consequent punishment, transfers slowly through the network structures from a larger community. Chapter 3 examines a model that studies cooperation in a broader strategic context where agents may interact in multiple different domains, or games, simultaneously. Even if a game independently does not give an agent sufficient incentive to play the cooperative action, there may be hope for cooperation when multiple games with compensating asymmetries are put together. Exploiting compensating asymmetries, we can find an institutional arrangement that would either ensure maximum incentives for cooperation or require minimum subsidy to establish sufficient incentives for cooperation. Lastly, Chapter 4 studies a two-layered public good game to empirically examine whether community enforcement through existing bilateral relationships can encourage cooperation in a social dilemma situation. Here, it is found that how the situation is presented matters greatly to real life agents, as their understanding of whether they are in a cooperative or a competitive, strategic setting changes the level of overall cooperation.

Item Open Access Finite density phase transition of QCD with N-f=4 and N-f=2 using canonical ensemble method(2010) Li, A; Alexandru, A; Liu, KF; Meng, XIn a progress toward searching for the QCD critical point, we study the finite density phase transition of N-f = 4 and 2 lattice QCD at finite temperature with the canonical ensemble approach. We develop a winding number expansion method to accurately project out the particle number from the fermion determinant which greatly extends the applicable range of baryon number sectors to make the study feasible. Our lattice simulation was carried out with the clover fermions and improved gauge action. For a given temperature, we calculate the baryon-chemical potential from the canonical approach to look for the mixed phase as a signal for the first-order phase transition. In the case of N-f = 4, we observe an "S-shape'' structure in the chemical potential-density plane due to the surface tension of the mixed phase in a finite volume which is a signal for the first-order phase transition. We use the Maxwell construction to determine the phase boundaries for three temperatures below T-c. The intersecting point of the two extrapolated boundaries turns out to be at the expected first-order transition point at T-c with mu = 0. This serves as a check for our method of identifying the critical point. We also studied the N-f = 2 case, but do not see a signal of the mixed phase for temperature as low as 0.83T(c).Item Open Access Management of Severe Traumatic Brain Injury in Pediatric Patients.(Frontiers in toxicology, 2022-01) Lui, Austin; Kumar, Kevin K; Grant, Gerald AThe optimal management of severe traumatic brain injury (TBI) in the pediatric population has not been well studied. There are a limited number of research articles studying the management of TBI in children. Given the prevalence of severe TBI in the pediatric population, it is crucial to develop a reference TBI management plan for this vulnerable population. In this review, we seek to delineate the differences between severe TBI management in adults and children. Additionally, we also discuss the known molecular pathogenesis of TBI. A better understanding of the pathophysiology of TBI will inform clinical management and development of therapeutics. Finally, we propose a clinical algorithm for the management and treatment of severe TBI in children using published data.Item Open Access Methodologies and analysis of metabolic flux in mammalian systems(2021) Liu, ShiyuQuantification of metabolic fluxes has broad applications in studying metabolic physiology. Isotope tracing with heavy labeled carbon (13C labeled metabolic flux analysis, 13C-MFA) is a promising strategy due to its ability to compute metabolic fluxes from isotope tracing profiles without relying on assumptions such as metabolic objectives or enzyme kinetic parameters. However, most current 13C-MFA methods have limitations on model scope, algorithmic efficacy and user interaction, especially given the availability of modern mass spectrometry-based metabolomics techniques and computational resources. In this study, a new 13C-MFA framework is developed, with emphasis on flux resolution in larger-sized metabolic network. Novel simulation methods of isotope tracing data are also used to guide algorithm development. The new MFA methodology has been applied to isotope-labeled cultured cancer cell line and isotope-infused mice. In cultured cancer cell line, the new MFA framework enabled the discovery of long-term interaction from one-carbon metabolism to pentose phosphate pathway and TCA cycle. In isotope-infused mice, the new MFA framework directly measured systemic glucose and lactate contribution to TCA cycle under physiological condition, which confirms the conventional knowledge that glucose is the main direct energy source in body. Taken together the new MFA methodology will offer unprecedented opportunities for expanding research in metabolic physiology.

Item Open Access PSTD Method for Thermoacoustic Tomography (TAT) and Related Experimental Investigation(2009) Ye, GangIn this work, the simulation (forward problem) and reconstruction (inverse problem) in Thermoacoustic Tomography (TAT) are studied using a pseudospectral time-domain (PSTD) method with 4th-order time integration.

The objective of the TAT simulation is to solve for the thermoacoustic pressure field in an inhomogeneous medium. Using the PSTD method, the spatial derivatives of pressure field and particle velocity can be obtained using fast fourier transform (FFT). Since the Fourier transforms used to represent the spatial derivatives of smooth functions are exact, only 2 points per wavelength are needed in the spatial discretization. The time integration is achieved by a 4th-order method to effectively reduce the computational time. The results of the algorithm are validated by analytical solutions. Perfectly Matched Layers (PMLs) are applied to absorb the outgoing waves and avoid ``wraparound'' effect. The maximum attenuation coefficient of the PMLs has an optimum value to minimize the reflections due to discretization and wraparound effect for 2D and 3D problems. Different PML profiles are also compared, quadratic profile is chosen because it can minimize the overall reflection. Spatial smoothing is needed for PSTD to avoid Gibbs' phenomenon in the modeling of a point source, and the effect of the smoothing function is studied.

In the TAT reconstruction problem, the PSTD method is used to reconstruct the thermoacoustic sources by solving the thermoacoustic wave equations in a reversed temporal order within the framework of time reversal imaging. The back-propagated pressure waves then refocus at the spatial locations of the original sources. Most other TAT reconstruction algorithms are based on the assumption that the tissue medium is acoustically homogeneous. In practice, however, even the mild tissue inhomogeneity will cause large phase errors and cause spatial misplacement and distortion of the sources. The proposed PSTD method utilizes a two-step process to solve this problem. In the first step, a homogeneous time reversal reconstruction is performed. Since an inhomogeneity itself is usually a source because of spatially dependent electrical conductivity (thus microwave absorption), the spatial location and the shape of the inhomogeneity can be estimated. In the second step, the updated acoustic property map is loaded followed by an inhomogeneous reconstruction. Numerical results show that this method greatly improves the reconstruction results. Images with improved quality are reconstructed from experimental data.

A 3D PSTD algorithm is developed and validated. Numerical results show that the PSTD algorithm with the 4th-order time integration is capable of simulating large 3D acoustic problems accurately and efficiently. A 3D breast phantom model is used to study the inhomogeneous reconstruction in 3D. Improved results over the homogeneous method are observed.

A preliminary study of the Thermoacoustic Tomography (TAT) using continuous-wave (CW) modulated microwaves is summarized. The theoretical background, system configuration, experiment setup, and measurement results are presented.