Mott Transition in Quasi-One-Dimensional Systems

We report the application of the density-matrix renormalization group method to a spatially anisotropic two-dimensional Hubbard model at half-filling. We find a deconfinement transition induced by the transverse hopping parameter $t_y$ from an insulator to a metal. Therefore, if $t_y$ is fixed in the metallic phase, increasing the interaction $U$ leads to a metal-to-insulator transition at a finite critical $U$. This is in contrast to the weak-coupling Hartree-Fock theory which predicts a nesting induced antiferromagnetic insulator for any $U>0$.Comment: 4 pages, 3 figure

Lingual infarction in Wegener's Granulomatosis: A case report and review of the literature

Wegener's granulomatosis (WG) is a multi-system disease, characterised by the triad of necrotising granulomata affecting the upper and lower respiratory tracts, disseminated vasculitis and glomerulonephritis. Oral lesions are associated with up to 50% of cases, although are rare as a presenting feature. The most common oral lesions associated with WG are ulceration and strawberry gingivitis. We review the literature regarding oral manifestations of WG and present a case of lingual infarction, an extremely rare oral lesion associated with WG, in a severe, rapidly progressive and ultimately fatal form of the disease

Characterizing the Google Books corpus: Strong limits to inferences of socio-cultural and linguistic evolution

It is tempting to treat frequency trends from the Google Books data sets as indicators of the true popularity of various words and phrases. Doing so allows us to draw quantitatively strong conclusions about the evolution of cultural perception of a given topic, such as time or gender. However, the Google Books corpus suffers from a number of limitations which make it an obscure mask of cultural popularity. A primary issue is that the corpus is in effect a library, containing one of each book. A single, prolific author is thereby able to noticeably insert new phrases into the Google Books lexicon, whether the author is widely read or not. With this understood, the Google Books corpus remains an important data set to be considered more lexicon-like than text-like. Here, we show that a distinct problematic feature arises from the inclusion of scientific texts, which have become an increasingly substantive portion of the corpus throughout the 1900s. The result is a surge of phrases typical to academic articles but less common in general, such as references to time in the form of citations. We use information theoretic methods to highlight these dynamics by examining and comparing major contributions via a divergence measure of English data sets between decades in the period 1800-2000. We find that only the English Fiction data set from the second version of the corpus is not heavily affected by professional texts. Overall, our findings call into question the vast majority of existing claims drawn from the Google Books corpus, and point to the need to fully characterize the dynamics of the corpus before using these data sets to draw broad conclusions about cultural and linguistic evolution

Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure

In this paper, the worst-case probability measure over the data is introduced as a tool for characterizing the generalization capabilities of machine learning algorithms. More specifically, the worst-case probability measure is a Gibbs probability measure and the unique solution to the maximization of the expected loss under a relative entropy constraint with respect to a reference probability measure. Fundamental generalization metrics, such as the sensitivity of the expected loss, the sensitivity of the empirical risk, and the generalization gap are shown to have closed-form expressions involving the worst-case data-generating probability measure. Existing results for the Gibbs algorithm, such as characterizing the generalization gap as a sum of mutual information and lautum information, up to a constant factor, are recovered. A novel parallel is established between the worst-case data-generating probability measure and the Gibbs algorithm. Specifically, the Gibbs probability measure is identified as a fundamental commonality of the model space and the data space for machine learning algorithms.Comment: To appear in the Proceedings of the AAAI Conference on Artificial Intelligence (7 + 2 pages

The human controller : usability and accessibility in video game interfaces

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (leaves 41-43).Despite the advances in user interfaces and the new gaming genres, not all people can play all games - disabled people are frequently excluded from game play experiences. On the one hand this adds to the list of discriminations disabled people face in our society, while on the other hand actively including them potentially results in games that are better for everyone. The largest hurdle to involvement is the user interface, or how a player interacts with the game. Analyzing usability and adhering to accessibility design principles makes it both possible and practical to develop fun and engaging game user interfaces that a broader range of the population can play. To demonstrate these principles we created AudiOdyssey, a PC rhythm game that is accessible to both sighted and non-sighted audiences. By following accessibility guidelines we incorporated a novel combination of features resulting in a similar play experience for both groups. Testing AudiOdyssey yielded useful insights into which interface elements work and which don't work for all users. Finally a case is made for considering accessibility when designing future versions of gaming user interfaces, and speculative scenarios are presented for what such interfaces might look like.by Eitan M. Glinert.M.Eng

Cyclic cocycles on twisted convolution algebras

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to a construction of Mathai and Stevenson. When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras. The results in this article were originally published in the author's Ph.D. thesis.Comment: 39 page

Coherent control of correlated nanodevices: A hybrid time-dependent numerical renormalization-group approach to periodic switching

The time-dependent numerical renormalization-group approach (TD-NRG), originally devised for tracking the real-time dynamics of quantum-impurity systems following a single quantum quench, is extended to multiple switching events. This generalization of the TD-NRG encompasses the possibility of periodic switching, allowing for coherent control of strongly correlated systems by an external time-dependent field. To this end, we have embedded the TD-NRG in a hybrid framework that combines the outstanding capabilities of the numerical renormalization group to systematically construct the effective low-energy Hamiltonian of the system with the prowess of complementary approaches for calculating the real-time dynamics derived from this Hamiltonian. We demonstrate the power of our approach by hybridizing the TD-NRG with the Chebyshev expansion technique in order to investigate periodic switching in the interacting resonant-level model. Although the interacting model shares the same low-energy fixed point as its noninteracting counterpart, we surprisingly find the gradual emergence of damped oscillations as the interaction strength is increased. Focusing on a single quantum quench and using a strong-coupling analysis, we reveal the origin of these interaction-induced oscillations and provide an analytical estimate for their frequency. The latter agrees well with the numerical results.Comment: 20 pager, Revtex, 10 figures, submitted to Physical Review