Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K

We consider systems A_\ell(t) y(q^\ell t) + ... + A_0(t) y(t) = b(t) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.Comment: 8 page

Constructing the space of visual attention

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Page 180 blank. Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 168-171).This thesis explores the nature of a human experience in space through a primary inquiry into vision. This inquiry begins by questioning the existing methods and instruments employed to capture and represent a human experience of space. While existing qualitative and quantitative methods and instruments -- from "subjective" interviews to "objective" photographic documentation -- may lead to insight in the study of a human experience in space, we argue that they are inherently limited with respect to physiological realities. As one moves about the world, one believes to see the world as continuous and fully resolved. However, this is not how human vision is currently understood to function on a physiological level. If we want to understand how humans visually construct a space, then we must examine patterns of visual attention on a physiological level. In order to inquire into patterns of visual attention in three dimensional space, we need to develop new instruments and new methods of representation. The instruments we require, directly address the physiological realities of vision, and the methods of representation seek to situate the human subject within a space of their own construction. In order to achieve this goal we have developed PUPIL, a custom set of hardware and software instruments, that capture the subject's eye movements. Using PUPIL, we have conducted a series of trials from proof of concept -- demonstrating the capabilities of our instruments -- to critical inquiry of the relationship between a human subject and a space. We have developed software to visualize this unique spatial experience, and have posed open questions based on the initial findings of our trials. This thesis aims to contribute to spatial design disciplines, by providing a new way to capture and represent a human experience of space.by Moritz Philipp Kassner [and] William Rhoades Patera.S.M

Worst Case and the Worst Example: An Agenda for Any Young Lawyer Who Wants to Save the World from Climate Chaos

Wherever you turn with regard to climate change, you\u27ll hear about the worst, and the worst of the worst, and the worst that will happen after that. Young lawyers should put themselves in the right frame of mind to tackle all these worsts that are headed our way. In the interest of keeping it simple, we would suggest a personal strategy for every young lawyer that would entail: (I) Honoring Knowledge and Learning; (II) Protecting Your Institutions and Loving Your Country; (III) Planning and Conducting Your Personal War on Bad Law; and (IV) Rejecting Defeatism and Impossibility Theorems. Let\u27s consider these strategies in order. Knowing your circumstance is followed by the occasion of improving your circumstance. This captures the power of positive thinking. If the flaws in human nature that are so celebrated by pessimists could stop effective action, human progress would have been stanched long ago. Despite all talk of futility, impossibility, and resignation, the entire legal scene is a frenzy of hope, effort, creative initiative, and change. That unwarranted optimism of the human species and of the legal profession appears to have seized momentary control in the rush to protect our world and our climate from unprecedented challenge. It\u27s a nice place to end a legal story. Impossible problems can only succumb to implacable convictions. Humans created the conditions for this climate change catastrophe. Perhaps they can stumble into ultimate triumph

Past, present and future distribution of the yellow fever mosquito Aedes aegypti: The European paradox

The global distribution of the yellow fever mosquito Aedes aegypti is the subject of considerable attention because of its pivotal role as a biological vector of several high profile disease pathogens including dengue, chikungunya, yellow fever, and Zika viruses. There is also a lot of interest in the projected future species' distribution. However, less effort has been focused on its historical distribution, which has changed substantially over the past 100 years, especially in southern Europe where it was once widespread, but largely disappeared by the middle of the 20th century. The present work utilises all available historical records of the distribution of Ae. aegypti in southern Europe, the Near East within the Mediterranean Basin and North Africa from the late 19th century until the 1960's to construct a spatial distribution model using matching historical climatic and demographic data. The resulting model was then implemented using current climate and demographic data to assess the potential distribution of the vector in the present. The models were rerun with several different assumptions about the thresholds that determine habitat suitability for Ae. aegypti. The historical model matches the historical distributions well. When it is run with current climate values, the predicted present day distribution is somewhat broader than it used to be particularly in north-west France, North Africa and Turkey. Though it is beginning to reappear in the eastern Caucasus, this 'potential' distribution clearly does not match the actual distribution of the species, which suggests some other factors are responsible for its absence. Future distributions based on the historical model also do not match future distributions derived from models based only on present day vector distributions, which predict little or no presence in the Mediterranean Region. At the same time, the vector is widespread in the USA which is predicted to consolidate its range there in future. This contradiction and the implication for possible re-invasion of Europe are discussed

Evolution of Initiation Rites During the Austronesian Dispersal

As adaptive systems, kinship and its accompanying rules have co-evolved with elements of complex societies, including wealth inheritance, subsistence, and power relations. Here we consider an aspect of kinship evolution in the Austronesian dispersal that began from about 5500 BP in Taiwan, reaching Melanesia about 3200 BP, and dispersing into Micronesia by 1500 BP. Previous, foundational work has used phylogenetic comparative methods and ethnolinguistic information to infer matrilocal residence in proto-Austronesian societies. Here we apply Bayesian phylogenetic analyses to a data set on Austronesian societies that combines existing data on marital residence systems with a new set of ethnographic data, introduced here, on initiation rites. Transition likelihoods between cultural-trait combinations were modeled on an ensemble of 1000 possible Austronesian language trees, using Reversible Jump Markov Chain Monte Carlo (RJ-MCMC) simulations. Compared against a baseline phylogenetic model of independent evolution, a phylogenetic model of correlated evolution between female and male initiation rites is substantially more likely (log Bayes factor: 17.9). This indicates, over the generations of Austronesian dispersal, initiation rites were culturally stable when both female and male rites were in the same state (both present or both absent), yet relatively unstable for female-only rites. The results indicate correlated phylogeographic evolution of cultural initiation rites in the prehistoric dispersal of Austronesian societies across the Pacific. Once acquired, male initiation rites were more resilient than female-only rites among Austronesian societies