Working with Nonstandard Models
Most of the research in foundations of mathematics that I do in some way or another involves the use of nonstandard models. I will give a few examples, and indicate what is involved.
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OF THE DISSERTATION Relational Models for Human-Object Interactions and Object Affordances By Chaitanya Desai Doctor of Philosophy in Computer Science University of California, Irvine, 2013 Professor Deva Ramanan, Chair Humans have the remarkable ability to look at an image and decipher a wealth of information about the scene it depicts. In particular, humans are very good at the following: 1) Locating various objects in the scene and telling how they are oriented, and 2) Understanding the different activities that the people in the scene are engaged in. In this thesis, we tackle the problem of helping a vision system achieve these two goals. Our techniques build on the observation that human activities, their poses and the nature of their interaction with objects in their environment are all dependent on each other. The thesis proposes techniques to model such dependencies and learns the nature of person-object interactions from training examples. While previous approaches typically deal with problems of object-detection, human-body pose estimation and activity recognition as isolated problems, the thesis proposes a framework that jointly addresses them. We show superior empirical performance to state-of-the-art techniques designed for each of the three tasks. A 2D pictorial structure framework is at the core of our approach. By handling appearance changes due to viewpoint, 3D pose and occlusions in a principled fashion, we show that such models can be quite powerful and versatile.
O2 constraints from Paleoproterozoic detrital pyrite and uraninite
Redox-sensitive detrital grains such as pyrite and uraninite in sedimentary successions provide one of the most conspicuous geological clues to a different composition of the Archean and early Paleoproterozoic atmosphere. Today, these minerals are rapidly chemically weathered within short transport distances. Prior to the rise of oxygen, low O2 concentrations allowed their survival in siliciclastic deposits with grain erosion tied only to physical transport processes. After the rise of oxygen, redox-sensitive detrital grains effectively vanish from the sedimentary record. To get a better understanding of the timing of this transition, we examined sandstones recorded in a scientifi c drill core from the South African 2.415 Ga Koegas Subgroup, a mixed siliciclastic and iron formation–bearing unit deposited on the western deltaic margin of the Kaapvaal craton in early Paleoproterozoic time. We observed detrital pyrite and uraninite grains throughout all investigated sandstone beds in the section, indicating the rise of oxygen is younger than 2.415 Ga. To better understand how observations of detrital pyrite and uraninite in sedimentary rocks can quantitatively constrain Earth surface redox conditions, we constructed a model of grain erosion from chemical weathering and physical abrasion to place an upper limit on ancient environmental O2 concentrations. Even conservative model calculations for deltaic depositional systems with suffi cient transport distances (approximately hundreds of kilometers) show that redox-sensitive detrital grains are remarkably sensitive to environmental O2 concentrations, and they constrain the Archean and early Paleoproterozoic atmosphere to have <3.2 × 10 –5 atm of molecular O2. These levels are lower than previously hypothesized for redox-sensitive detrital grains, but they are consistent with estimates made from other redox proxy data, including the anomalous fractionation of sulfur isotopes. The binary loss of detrital pyrite and uraninite from the sedimentary record coincident with the rise of oxygen indicates that atmospheric O2 concentrations rose substantially at this time and were never again suffi ciently low (<0.01 atm) to enable survival and preservation of these grains in short transport systems.