VictorJuiz/thesis huggingface dataset:
Clause Learning, Resolution Space, and Pebbling
Keywords: Proof Complexity
Black-White Pebbling

Currently, the most effective complete SAT solvers are based on the DPLL algorithm augmented by Clause Learning. These solvers can handle many real-world problems from application areas like verification, diagnosis, planning, and design. Clause Learning works by storing previously computed, intermediate results and then reusing them to prune the future search tree. Without Clause Learning, however, DPLL loses most of its effectiveness on real world problems. Recently there has been some work on obtaining a deeper understanding of the technique of Clause Learning. In this thesis, we contribute to the understanding of Clause Learning, and the Resolution proof system that underlies it, in a number of ways. We characterize Clause Learning as a new, intuitive Resolution refinement which we call CL. We then show that CL proofs can effectively p-simulate general Resolution. Furthermore, this result holds even for the more restrictive class of greedy, unit propagating CL proofs, which more accurately characterize Clause Learning as it is used in practice. This result is surprising and indicates that Clause Learning is significantly more powerful than was previously known. Since Clause Learning makes use of previously derived clauses, it motivates the study of Resolution space. We contribute to this area of study by proving that determining the variable space of a Resolution derivation is PSPACE-complete. The reduction also yields a surprising exponential size/space trade-off for Resolution in which an increase of just 3 units of variable space results in an exponential decrease in proofsize. This result runs counter to the intuitions of many in the SAT-solving community who have generally believed that proof-size should decrease smoothly as available space increases. In order to prove these Resolution results, we need to make use of some intuition regarding the relationship between Black-White Pebbling and Resolution. In fact, determining the complexity of Resolution variable space required us to first prove that Black-White Pebbling is PSPACE-complete. The complexity of the Black-White Pebbling Game has remained an open problem for 30 years and resisted numerous attempts to solve it. Its solution is the primary contribution of this thesis.
Applications of Games to Propositional Proof Complexity
Keywords: Proof Complexity
Computational Complexity
Resolution Space
Automated Theorem Proving
Combinatorial Games

In this thesis we explore a number of ways in which combinatorial games can be used to help prove results in the area of propositional proof complexity. The results in this thesis can be divided into two sets, the first being dedicated to the study of Resolution space (memory) requirements, whereas the second is centered on formalizing the notion of `dangerous' reductions. The first group of results investigate Resolution space measures by asking questions of the form, `Given a formula F and integer k, does F have a [Type of Resolution] proof with [Type of Resource] at most k?'. We refer to this as a proof complexity resource problem, and provide comprehensive results for several forms of Resolution as well as various resources. These results include the PSPACE-Completeness of Tree Resolution clause space (and the Prover/Delayer game), the PSPACE-Completeness of Input Resolution derivation total space, and the PSPACE-Hardness of Resolution variable space. This research has theoretical as well as practical motivations: Proof complexity research has focused on the size of proofs, and Resolution space requirements are an interesting new theoretical area of study. In more practical terms, the Resolution proof system forms the underpinnings of all modern SAT-solving algorithms, including clause learning. In practice, the limiting factor on these algorithms is memory space, so there is a strong motivation for better understanding it as a resource. With the second group of results in this thesis we investigate and formalize what it means for a reduction to be `dangerous'. The area of SAT-solving necessarily employs reductions in order to translate from other domains to SAT, where the power of highly-optimized algorithms can be brought to bear. Researchers have empirically observed that it is unfortunately possible for reductions to map easy instances from the input domain to hard SAT instances. We develop a non-Hamiltonicity proof system and combine it with additional results concerning the Prover/Delayer game from the first part of this thesis as well as proof complexity results for intuitionistic logic in order to provide the first formal examples of harmful and beneficial reductions, ultimately leading to the development of a framework for studying and comparing translations from one language to another.
Variable-aperture Photography
Keywords: computer vision
computer graphics
computational photography
3D reconstruction
shape-from-focus
shape-from-defocus
image-based rendering
high dynamic range imaging
camera calibration
multiview stereo
optics

While modern digital cameras incorporate sophisticated engineering, in terms of their core functionality, cameras have changed remarkably little in more than a hundred years. In particular, from a given viewpoint, conventional photography essentially remains limited to manipulating a basic set of controls: exposure time, focus setting, and aperture setting. In this dissertation we present three new methods in this domain, each based on capturing multiple photos with different camera settings. In each case, we show how defocus can be exploited to achieve different goals, extending what is possible with conventional photography. These methods are closely connected, in that all rely on analyzing changes in aperture. First, we present a 3D reconstruction method especially suited for scenes with high geometric complexity, for which obtaining a detailed model is difficult using previous approaches. We show that by controlling both the focus and aperture setting, it is possible compute depth for each pixel independently. To achieve this, we introduce the "confocal constancy" property, which states that as aperture setting varies, the pixel intensity of an in-focus scene point will vary in a scene-independent way that can be predicted by prior calibration. Second, we describe a method for synthesizing photos with adjusted camera settings in post-capture, to achieve changes in exposure, focus setting, etc. from very few input photos. To do this, we capture photos with varying aperture and other settings fixed, then recover the underlying scene representation best reproducing the input. The key to the approach is our layered formulation, which handles occlusion effects but is tractable to invert. This method works with the built-in "aperture bracketing" mode found on most digital cameras. Finally, we develop a "light-efficient" method for capturing an in-focus photograph in the shortest time, or with the highest quality for a given time budget. While the standard approach involves reducing the aperture until the desired region is in-focus, we show that by "spanning" the region with multiple large-aperture photos,we can reduce the total capture time and generate the in-focus photo synthetically. Beyond more efficient capture, our method provides 3D shape at no additional cost.
Interaction with Volumetric Displays
Keywords: Volumetric Display
3D Interaction

For almost 50 years, researchers have been exploring the use of stereoscopic displays for visualizing and interacting with three-dimensional (3D) data. Unfortunately, a number of unfavorable qualitative properties have impeded the wide-spread adoption of traditional 3D displays. The volumetric display, a more recent class of 3D display to emerge, possesses unique features which potentially makes it more suitable for integration into workplace, classroom, and even home environments. In this dissertation we investigate volumetric displays as an interactive platform for 3D applications. We identify the inherent affordances unique to volumetric displays, such as their true 3D display volume, 360° viewing angle, and enclosing surface. Identifying these properties exposes human factor issues which we investigate and interaction issues which we address. First, we evaluate the user’s ability perceive imagery displayed by a volumetric display. In a formal experiment, we show that depth perception can be improved, in comparison to more traditional platforms. We then perform an experiment which evaluates users’ ability to read text under 3D rotations, and present a new algorithm which optimizes text rotation when viewed my multiple users. Next, we investigate the user’s ability to select 3D imagery within the display. Results show that the dimension defining the depth of the object can constrain user performance as much as or more than the other two dimensions of the target. This leads us to explore alternative methods of selection which are less constraining to the user. We define a suite of new selection techniques, of which several are found to have significant benefits in comparison to techniques traditionally used in 3D user interfaces. Next, we describe our development of the first working interactive application, where a volumetric display is the sole device for input and display. The application presents a first glance at what the equivalent of today’s graphical user interface might be on a volumetric display. We then develop a prototype application which allows multiple users to simultaneously interact with the volumetric display. We discuss and address the core issues related to providing such a collaborative user interface, and report feedback obtained from usage sessions and expert interviews.
The Development and Evolution of Complex Patterns: The Drosophila Sex Comb as a Model System
Keywords: evolution
development
complexity
patterning
developmental constraints
Drosophila
sex comb
tarsus
bristle pattern
live imaging
convergent extension
cell intercalation

One of the best-known structures in Drosophila is the sex comb, an arrangement of modified bristles on the tarsal forelegs of males. This complex, sexually-dimorphic trait shows striking variation among closely related species, although most other aspects of the tarsal bristle pattern have been conserved. I studied the development of the sex comb in the model organism Drosophila melanogaster and six related species. I confirmed that the D. melanogaster sex comb, although longitudinal in the adult, originates in a transverse orientation and rotates during development, and showed that this process occurs through male-specific convergent extension. However, in the species that I examined that have longitudinally-oriented sex combs that extend the full length of the tarsus, including D. ficusphila and two species of the montium subgroup, the sex comb does not rotate, and instead forms from two longitudinal rows that converge during development. Another species of the montium subgroup, D. nikananu, has a sex comb that is convergently similar to D. melanogaster, but forms in a manner typical of its subgroup, showing that very similar combs can be formed through different processes. In all species, there is a strong correlation between the position of the sex comb and the transverse bristle row on the foreleg tarsus just proximal to it. To test whether it is possible to violate this apparent constraint on development, I perturbed the expression of the leg patterning gene dachshund to generate ectopic sex combs in D. melanogaster. I found that while most patterns showed the same correlation, a few circumvent the constraint. I also demonstrated that the ectopic combs were formed non-autonomously and that overexpression of dachshund can transform certain aspects of the sex comb phenotype to resemble the transverse bristles to which they are homologous.
An Integrated Multi-model Approach for Predicting the Impact of Household Travel on Urban Air Quality and Simulating Population Exposure
Keywords: Transportation Emissions Modelling
Air Quality Modelling
Transport Policy Appraisal
Environmental Impacts of Transport

The population and economic growth experienced by Canadian metropolitan areas in the past twenty years, has been associated with increased levels of car ownership and vehicle kilometres travelled leading to a deterioration of air quality and public health and an increase in greenhouse gas emissions. The need to modify urban growth patterns has motivated planning agencies in Canada to develop a broad range of policies aiming at achieving a more sustainable transportation sector. The challenge however, remains in the ability to test the effectiveness of proposed policy measures. This situation has led to a renewed interest in integrated land-use and transport models to support transport policy appraisal. This research is motivated by the need to improve transport policy appraisal through the use of integrated land-use and transport models linked with a range of sub-models that can reflect transport externalities. This research starts with an exploration of the transport policy environment in Canada through a questionnaire-based survey conducted with planners and policy-makers. The survey results highlight the need for tools reflecting the sustainability impacts of proposed policies. While the second part of this research explores sustainability indicators and recommends a set of social, economic, and environmental measures, linked with integrated land-use and transport models; effort is dedicated to estimate the environmental indicators as part of this thesis. As such, the third part of this research involves the development of an emission-dispersion-exposure modelling framework. The framework includes a suite of sub-models including an activity-based travel demand model (TASHA), an emission factor model (Mobile6.2C), a meteorological model (CALMET), and a dispersion model (CALPUFF). The framework is used to estimate link-based emissions of light-duty vehicles in the Greater Toronto Area under a base scenario for 2001. Dispersion of emissions is then conducted and linked with population in order to estimate exposure to air pollution.
Performance Assessment of Shear-critical Reinforced Concrete Plane Frames
Keywords: shear-critical
reinforced concrete
nonlinear
analysis
performance
frame
shear
non-linear

Current analysis procedures for new reinforced concrete structures are typically based on linear-elastic principles. However, under certain conditions, it may be necessary to analyze a structure to more accurately predict its structural behaviour. Such an analysis can be performed using nonlinear analysis procedures which typically require specialized software. This type of software is limited in number and most available programs do not adequately capture shear-related influences, potentially severely overestimating strength and ductility in shear-critical structures. The purpose of this study is to develop and verify an analytical procedure for the nonlinear analysis of frame structures with the aim of capturing shear-related mechanisms as well as flexural and axial effects. A previously developed analysis program, VecTor5, is further developed for this purpose. Originally formulated in the early 1980s at the University of Toronto, VecTor5 is based on the Modified Compression Field Theory (MCFT) and is capable of performing nonlinear frame analyses under temperature and monotonic loading conditions. Although providing generally satisfactory simulations, there are a number of deficiencies present in its computational algorithms. This study consists of three major parts: improvement of the original analysis procedure for monotonic loading conditions, expansion of the procedure for general loading conditions including the special cases of cyclic and reversed-cyclic loading, and further development of the procedure for dynamic loading conditions including time-varying base accelerations, impulse, impact and blast forces, initial mass velocities, and constant mass accelerations. Each part is supported by verification studies performed on a large number and variety of previously tested structures available in the literature. In addition, considerations in nonlinear modelling are discussed with the aim of providing guidelines for general modelling applications. Analyses of 63 previously tested structures, half of which are shear-critical, demonstrate that the developed analytical procedure is highly successful in simulating the experimental responses in terms of load-deflection response, reinforcement strains, crack widths, failure mode, failure displacement, total energy dissipation, displacement ductility ratio, and post-peak vibrational characteristics.
Developing New Strategies for the Preparation of Micro- and Nano-structured Polymer Materials
Keywords: microfluidics, microreactors, polymer particles, core-shell, microcapsules, Janus particles, three-phasic particles, self-assembly, gold nanorods, block copolymers, plasmonic band

This thesis described the development of new strategies for the preparation of micro- and nano-structured polymer materials. In particular, this thesis focused on: i) the synthesis of polymer particles in microreactors, and ii) the self-assembly of inorganic nanorods. First, this thesis presented the synthesis of polymer particles and capsules with pre-determined sizes and narrow size distributions (CV<2%) in continuous microfluidic reactors. The method includes (i) the emulsification of monomers in a microfluidic flow-focusing device and (ii) in-situ solidification of droplets via photopolymerization. This microfluidic synthesis provides a novel strategy for the control over the shapes, compositions, and morphologies of polymer particles. In particular, we demonstrated the control over particle shapes by producing polymer ellipsoids, disks, rods, hemispheres, plates, and bowls. We produced polymer particles loaded with dyes, liquid crystals, quantum dots, and magnetic nanoparticles. We generated core-shell particles, microcapsules, Janus and three-phasic polymer particles. Control over the number of cores per droplet was achieved by manipulating the flow rates of liquids in the microchannels. We further investigated the hydrodynamic mechanism underlying the emulsification of droplets, which helps in guiding scientists and engineers to utilize this technique. Second, we described the self-assembly of inorganic nanorods by using a striking analogy between amphiphilic ABA triblock copolymers and the hydrophilic nanorods tethered with hydrophobic polystyrene chains at both ends. We organized metal nanorods in structures with various geometries such as nanorings, nanochains, bundles, bundled nanochains, and nanospheres by tuning solely the quality of solvents. The self-assembly was tunable and reversible. This approach paved the way for the organization of anisotropic nanoparticles by using the strategies that are well-established for the self-assembly of block copolymers. We further described a systematic study of the self-assembly of polymer-tethered gold nanorods as a function of solvent composition in the system and the molecular weight of the polystyrene blocks. We found that the structure of the polymer pom-poms played an important role on the organization of polymer-tethered gold NRs. The 'supramolecular' assembly was governed by the competition between the end-to-end and side-by-side association of NRs and resulted in the controlled variation of the plasmonic properties of NRs, reflected in a 3-D plasmonic graph.
Phase Transitions in Polymeric Systems: A Directed Walk Study
Keywords: statistical mechanics
polymers
directed walks
phase transition

In this thesis several classes of directed paths are considered as models of linear polymers in a dilute solution. We obtain the generating functions for each model by considering factorization arguments. Information about the polymer behaviour can be extracted from the singularity structure of the associated generating functions. By using modified versions of these models we study the adsorption and localization of polymer molecules, the behaviour of polymers subject to a tensile force, the effects of stiffness, as well as the behaviour of polymers in confined geometries. In each of these situations the resulting generating functions contain at least two physical singularities. We identify the phase transitions in these systems by a changeover in the dominant singularity of the generating function. In the study of localization and polymers subject to a force, we utilize both homopolymer and random copolymer models. For copolymers, the physically relevant properties are obtained by considering a quenched average of the free energy over all possible monomer sequences. This procedure is intractable even for the simplest models. By considering the Morita approximation for several walk models we obtain results which give a bound on the corresponding features of the quenched system. We use a mapping between a simple model of duplex DNA and an adsorbing Motzkin path in order to study the mechanical unzipping of duplex DNA. From this model, we obtain force-temperature diagrams which show re-entrant behaviour of the force. We also develop a simple low temperature theory to describe the behaviour of the force close to T=0 and find that the shape of the force-temperature curve is associated with entropy in the ground state of the system. We consider the effect of stiffness on polymer adsorption and find that the phase transition is second order for all finite stiffness parameters. For systems of polymers in confined geometries, we find that the behaviour of the polymer depends on the distance between the confining surfaces and the associated interactions with each surface. In this problem, there exist regimes where the polymer exerts a force on the surfaces which can be attractive, repulsive or zero.