One of the central problems limiting the application of accurate {em ab initio} methods to large molecular systems is their high computational costs, i.e., their computing and storage requirements exhibit polynomial scaling with the size of the system. For example, the coupled cluster singles and doubles method with the perturbative inclusion of triples: the CCSD(T) model, which is considered to be the ``gold standard'' of quantum chemistry scales as 𝑂(N⁷) in its canonical formulation, where $N$ is a measure of the system size. However, the steep scaling associated with these methods is unphysical since the property of dynamic electron correlation or dispersion (for insulators) is local in nature and decays as R⁻⁶ power of distance. Different reduced-scaling techniques which attempt to exploit this inherent sparsity in the wavefunction have been used in conjunction with the coupled cluster theory to calculate ground-state properties of molecular systems with hundreds of heavy atoms in reasonable computational time. However, efforts towards extension of these methods for describing response properties like polarizabilities, optical rotations, etc., which are related to the derivative of the wavefunction with respect to external electric or/and magnetic fields, have been fairly limited and conventional reduced-scaling algorithms have been shown to yield large and often erratic deviations from the full canonical results. Accurate simulation of response properties like optical rotation is highly desirable as it can help the experimental chemists in understanding the structure-activity relationship of different chiral drug candidates. In this work, we identify the reasons behind the unsatisfactory performance of the pair natural orbital (PNO) based reduced-scaling approach for calculating linear response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}) that can provide the necessary accuracy at significantly lower computational costs. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. {em J. Phys. Chem. A}, 2017, 121(3), pp 708 716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}). The essence of these modified schemes (FVNO++ and PNO++) lie in finding suitable field perturbed one-electron densities to construct ``perturbation aware" virtual spaces which, by construction, are much more compact for describing response properties, making them ideal for applications on large molecular systems. / Ph. D. / Since its inception, quantum mechanics has been widely used by theoretical chemists to study, model and predict a variety of molecular properties and reactions accurately and reliably. Central to the field of quantum mechanics is the Schr¨odinger equation, whose exact solution is only known for one electron systems. As such, numerous quantum mechanical models have been proposed over the years which attempt to solve the many body Schrodinger equation approximately. A very good example in this regard is the coupled cluster (CC) family of methods wherein the CCSD(T) model is considered as the “gold standard” of quantum chemistry due to its high accuracy. However, one major bottleneck which prevents the use of accurate CC models to study biological systems which routinely involve hundreds of atoms, is the issue of high computational expenses. For example, doubling the system size in a CCSD(T) calculation can lead to more than a hundred-fold increase in the computational costs, which limits the application of this model to systems with 10 to 20 atoms. However, this unfavorable scaling with respect to system size is unphysical for large molecules as inter-electron interactions decay rapidly with distance, or are in other words, a local phenomenon. Reduced-scaling methods attempt to exploit this property of locality by finding a compact representation of the wavefunction. Various reduced-scaling approaches like pair natural orbitals (PNOs), projected atomic orbitals (PAOs) have been proposed and developed over the years which have extended the applicability of the CC methods to systems as large as proteins and DNA fragments. While these methods have been shown to be quite reliable for calculating properties like molecular energies, much more work needs to be done to guarantee similar levels of accuracy and computational cost for describing molecular response properties like polarizabilities and optical rotations. As the name suggests, response properties are related to the response or the change induced in the wavefunction in the presence of external electromagnetic fields like visible light. Accurate simulation of response properties like optical rotation is highly desirable as it can help the experimental chemists in understanding the structure-activity relationship of different drug candidates, an important part of the drug discovery process. However, limited applications of the reduced-scaling algorithms to these properties have been shown to yield large and often erratic errors. In this work, we identify the reasons behind the unsatisfactory performance of the PNO based reduced-scaling approach for calculating response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, manuscript in preparation) which can provide the desired accuracy reliably at significantly lower computational costs than the regular PNO method. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. J. Phys. Chem. A, 2017, 121(3), pp 708-716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, manuscript in preparation). The essence of these modified schemes (FVNO++ and PNO++) lie in choosing a “field aware” representation of the wavefunction, which by construction, is much more compact than their conventional counterparts for calculating response properties. Thus, these schemes are ideal for applications to larger and chemically interesting systems like molecules in solutions, biomolecules, etc.

Through the exploitation of data-sparsity ---a catch all term for savings gained from a variety of approximations--- it is possible to reduce the computational cost of accurate electronic structure calculations to linear. Meaning, that the total time to solution for the calculation grows at the same rate as the number of particles that are correlated. Multiple techniques for exploiting data-sparsity are discussed, with a focus on those that can be systematically improved by tightening numerical parameters such that as the parameter approaches zero the approximation becomes exact. These techniques are first applied to Hartree-Fock theory and then we attempt to design a linear scaling massively parallel electron correlation strategy based on second order perturbation theory. / Ph. D. / The field of Quantum Chemistry is highly dependent on a vast hierarchy of approximations; all carefully balanced, so as to allow for fast calculation of electronic energies and properties to an accuracy suitable for quantitative predictions. Formally, computing these energies should have a cost that increases exponentially with the number of particles in the system, but the use of approximations based on local behavior, or nearness, of the particles reduces this scaling to low order polynomials while maintaining an acceptable amount of accuracy. In this work, we introduce several new approximations that throw away information in a specific fashion that takes advantage of the fact that the interactions between particles decays in magnitude with the distance between them (although sometimes very slowly) and also exploits the smoothness of those interactions, by factorizing their numerical representation into a linear combination of simpler items. These factorizations, while technical in nature, have benefits that are hard to obtain by merely ignoring interactions between distant particles. Through the development of new factorizations and a careful neglect of interactions between distant particles, we hope to be able to compute properties of molecules in such a way that accuracy is maintained, but that the cost of the calculations only grows at the same rate as the number of particles. It seems that very recently, circa 2015, that this goal may actually soon become a reality, potentially revolutionizing the ability of quantum chemistry to make quantitative predictions for properties of large molecules.

A comparison of available fluid-to-fluid scaling laws for scaling convective heat transfer at supercritical pressures showed that the ones suggested by Zahlan, Groeneveld and Tavoularis (ZGT) have some advantages. The applicability of the ZGT laws was tested for pairs of fluids including carbon dioxide, water or Refrigerant R134a. The conditions of previous measurements taken in the Supercritical University of Ottawa Loop with CO2 flowing vertically upwards in an electrically heated tube with 8 mm ID were scaled to equivalent conditions in R134a and new measurements of the heat transfer coefficient (HTC) were taken in the same tube using the latter fluid. The inlet pressure was 1.13 times the critical pressure (4.06 MPa), the mass flux was in the range from 212 kg/m^2 s to 1609 kg/m^2 s, the heat flux was in the range from 2 kW/m^2 to 137 kW/m^2, and the inlet temperature was in the range from 62 ℃ to 105 ℃. The HTC at equivalent conditions in water was also determined with the use of transcritical look-up tables. Average and linearly varying corrections to the ZGT scaling laws were derived by statistical analysis for each pair of fluids under NHT or DHT conditions. Such corrections reduced the standard deviation of the scaling error but did not eliminate the presence of large errors under many sets of conditions. As expected, scaling errors were in general larger for DHT than NHT conditions. The present results did not reveal any systematic and correctable dependence of the scaling error upon the mass flux or heat flux but showed that scaling errors became particularly large as the bulk temperature T_b approached the pseudocritical temperature T_pc. In conclusion, the ZGT scaling laws appear to be fairly accurate for the three pairs of fluids considered in the liquid-like region with T_b/T_pc ≤ 0.94 and possibly in the gas-like region with T_b/T_pc ≥ 1.02, whereas outside this range scaling errors could be significant. It was also found that the ZGT scaling laws do not scale accurately the onset of DHT in different fluids.

abstract: Body size plays a pervasive role in determining physiological and behavioral performance across animals. It is generally thought that smaller animals are limited in performance measures compared to larger animals; yet, the vast majority of animals on earth are small and evolutionary trends like miniaturization occur in every animal clade. Therefore, there must be some evolutionary advantages to being small and/or compensatory mechanisms that allow small animals to compete with larger species. In this dissertation I specifically explore the scaling of flight performance (flight metabolic rate, wing beat frequency, load-carrying capacity) and learning behaviors (visual differentiation visual Y-maze learning) across stingless bee species that vary by three orders of magnitude in body size. I also test whether eye morphology and calculated visual acuity match visual differentiation and learning abilities using honeybees and stingless bees. In order to determine what morphological and physiological factors contribute to scaling of these performance parameters I measure the scaling of head, thorax, and abdomen mass, wing size, brain size, and eye size. I find that small stingless bee species are not limited in visual learning compared to larger species, and even have some energetic advantages in flight. These insights are essential to understanding how small size evolved repeatedly in all animal clades and why it persists. Finally, I test flight performance across stingless bee species while varying temperature in accordance with thermal changes that are predicted with climate change. I find that thermal performance curves varied greatly among species, that smaller species conform closely to air temperature, and that larger bees may be better equipped to cope with rising temperatures due to more frequent exposure to high temperatures. This information may help us predict whether small or large species might fare better in future thermal climate conditions, and which body-size related traits might be expected to evolve. / Dissertation/Thesis / Doctoral Dissertation Biology 2018

This study examined the validity of various scaling methods, isometric mid-thigh pull (IMTP) peak force using various scaling methods, and the relationships between IMTP peak force and countermovement jump height. Fifty-one collegiate baseball and soccer athletes performed two maximal IMTPs. Absolute peak force was compared between teams and when data were scaled using ratio (RS), traditional allometric (ALLOTrad), and fitted allometric (ALLOFit) scaling. ALLOTrad and ALLOFit validity was violated because different derived exponents existed for baseball (b = 0.20) and soccer (b = 1.20). Soccer athletes produced greater RS peak force compared to baseball (p = 0.012), while no difference existed with absolute, ALLOTrad or ALLOFit (all p > 0.05) peak force. Moderate relationships existed between body mass and absolute (r = 0.402, p = 0.003) and RS (r = -0.328, p = 0.019) peak force, while trivial relationships existed with ALLOTrad and ALLOFit (both r < -0.10, p > 0.05). Trivial relationships existed between countermovement jump height and absolute, RS, ALLOTrad, and ALLOFit (all r < 0.20, p > 0.05) peak force. The current dataset violated allometric scaling assumptions, making it inappropriate to use ALLOTrad and ALLOFit scaling. Practitioners must understand the assumptions, limitations, and purpose of scaling methods.

Alcohol expectancies have been shown to be predictive of risk for alcohol problems. Experimental research studies have challenged participants' expectancies with the end result demonstrating a mediational effect on participant drinking. Cognitive research using priming and word recognition tasks have led to the theory that expectancies operate in an associative network. Using dissimilarities information this network has been mapped using multidimensional scaling. The current techniques for collecting dissimilarities information directly in alcohol expectancy research has been limited to the use of the paired comparisons tasks. In order to investigate the utility of a different similarities task a comparison was made between a card sorting task and paired comparisons. The overall comparisons of matrices and Individual Difference Scaling (INDSCAL; Carroll & Chang, 1970) results followed the expected trends and generally supported the hypotheses that the two methods would provide essentially the same information. However, a possible method effect for gender was observed. The method effect was seen when comparing across methods within the females dichotomized by drinker category. Further studies are necessary to replicate these findings and to attempt to identify which method has the effect.

Title from PDF of title page. / Document formatted into pages; contains 64 pages. / Thesis (M.A.)--University of South Florida, 2003. / Includes bibliographical references. / Text (Electronic thesis) in PDF format. / ABSTRACT: Alcohol expectancies have been shown to be predictive of risk for alcohol problems. Experimental research studies have challenged participants' expectancies with the end result demonstrating a mediational effect on participant drinking. Cognitive research using priming and word recognition tasks have led to the theory that expectancies operate in an associative network. Using dissimilarities information this network has been mapped using multidimensional scaling. The current techniques for collecting dissimilarities information directly in alcohol expectancy research has been limited to the use of the paired comparisons tasks. In order to investigate the utility of a different similarities task a comparison was made between a card sorting task and paired comparisons. / ABSTRACT: The overall comparisons of matrices and Individual Difference Scaling (INDSCAL; Carroll & Chang, 1970) results followed the expected trends and generally supported the hypotheses that the two methods would provide essentially the same information. However, a possible method effect for gender was observed. The method effect was seen when comparing across methods within the females dichotomized by drinker category. Further studies are necessary to replicate these findings and to attempt to identify which method has the effect. / System requirements: World Wide Web browser and PDF reader. / Mode of access: World Wide Web.

Branches of complexity theory have been widely employed in geographic information systems (GIS) to explore phenomena that appear in urban environments. Among these, space syntax, as an urban morphological application of complexity theory, has attracted increasing attention in recent years. Accordingly, many computer-based tools have been developed to realize related analysis spatially, especially those that can be integrated as functions with GIS. In this thesis, a space syntax tool – Axwoman – is redeveloped and tested as an extension of ESRI ArcGIS Desktop in order to fulfill certain specific needs in urban morphological analysis. It is primarily used to calculate all space syntax measures for several urban systems and to explore the relationships between these measures. To meet the needs for this new version of Axwoman, several functions have been updated and changed, for drawing, coloring, and classifying axial lines as maps for visual thinking; ticking overpasses and excluding them from computing space syntax parameters; and integrating AxialGen and Axwoman. In accordance with this, several case studies have been performed on the urban street networks in large cities. In this paper, Stockholm was chosen as the study object at both the urban level and the building level. After the scaling analysis and time efficiency analysis, the results are also interpreted from a structural point of view and in terms of how the function of space is subject to its morphological structure. Finally, the connectivity of axial lines (a spatial measurement in space syntax theory) was found to follow a power-law distribution. Through this work, the new edition of Axwoman generating satisfactory outputs, the research have proved that the connectivity of axial lines follows a lognormal distribution or a power-law-like distribution, which is one of the heavy-tailed distributions. In addition, it was have found that axial lines better for capture the underlying urban morphologies showed in their study on redefining the generated axial lines from street center lines. Moreover, fewer longest axial lines will show up on the maps, just as coincidental as the shape of mental maps, which proved that the axial line representations can be a powerful tool for urban studies.

In modern digital audio applications, a continuous audio signal stream is sampled at a fixed sampling rate, which is always greater than twice the highest frequency of the input signal, to prevent aliasing. A more energy efficient approach is to dynamically change the sampling rate based on the input signal. In the dynamic sampling rate technique, fewer samples are processed when there is little frequency content in the samples. The perceived quality of the signal is unchanged in this technique. Processing fewer samples involves less computation work; therefore processor speed and voltage can be reduced. This reduction in processor speed and voltage has been shown to reduce power consumption by up to 40% less than if the audio stream had been run at a fixed sampling rate.

Thesis (M.S.)--University of Michigan, 1966.