Fixing the functoriality of Khovanov homology

We describe a modification of Khovanov homology (math.QA/9908171), in the spirit of Bar-Natan (math.GT/0410495), which makes the theory properly functorial with respect to link cobordisms. This requires introducing `disorientations' in the category of smoothings and abstract cobordisms between them used in Bar-Natan's definition. Disorientations have `seams' separating oppositely oriented regions, coming with a preferred normal direction. The seams satisfy certain relations (just as the underlying cobordisms satisfy relations such as the neck cutting relation). We construct explicit chain maps for the various Reidemeister moves, then prove that the compositions of chain maps associated to each side of each of Carter and Saito's movie moves (MR1238875, MR1445361) always agree. These calculations are greatly simplified by following arguments due to Bar-Natan and Khovanov, which ensure that the two compositions must agree, up to a sign. We set up this argument in our context by proving a result about duality in Khovanov homology, generalising previous results about mirror images of knots to a `local' result about tangles. Along the way, we reproduce Jacobsson's sign table (math.GT/0206303) for the original `unoriented theory', with a few disagreements.Comment: 91 pages. Added David Clark as co-author. Further detail on variations of third Reidemeister moves, to allow treatment of previously missing cases of movie move six. See changelog section for more detai

Differences in fMRI intersubject correlation while viewing unedited and edited videos of dance performance

Intersubject Correlation (ISC) analysis of fMRI data provides insight into how continuous streams of sensory stimulation are processed by groups of observers. Although edited movies are frequently used as stimuli in ISC studies, there has been little direct examination of the effect of edits on the resulting ISC maps. In this study we showed 16 observers two audiovisual movie versions of the same dance. In one experimental condition there was a continuous view from a single camera (Unedited condition) and in the other condition there were views from different cameras (Edited condition) that provided close up views of the feet or face and upper body. We computed ISC maps for each condition, as well as created a map that showed the difference between the conditions. The results from the Unedited and Edited maps largely overlapped in the occipital and temporal cortices, although more voxels were found for the Edited map. The difference map revealed greater ISC for the Edited condition in the Postcentral Gyrus, Lingual Gyrus, Precentral Gyrus and Medial Frontal Gyrus, while the Unedited condition showed greater ISC in only the Superior Temporal Gyrus. These findings suggest that the visual changes associated with editing provide a source of correlation in maps obtained from edited film, and highlight the utility of using maps to evaluate the difference in ISC between conditions

Using natural viewing behavior to screen for and reconstruct visual field defects

There is a need for simple and effective ways to screen for visual field defects (VFD). Watching a movie is a simple task most humans are familiar with. Therefore we assessed whether it is possible to detect and reconstruct visual field defects based on free viewing eye movements, recorded while watching movie clips. Participants watched 90 movie clips of one minute, with and without simulated visual field defects (sVFD), while their eye movements were tracked. We simulated homonymous hemianopia (HH) (left and right sided) and glaucoma (small nasal arc, large nasal arc, and tunnel vision). We generated fixation density maps of the visual field and trained a linear support vector machine to predict the viewing conditions of each trial of each participant based on these maps. To reconstruct the visual field defect, we computed "viewing priority" maps and maps of differences in fixation density of the visual field of each participant. We were able to classify the simulated visual field condition with more than 85% accuracy. In simulated HH, the viewing priority distribution over the visual field indicated the location of the sVFD in the simulated HH condition. In simulated glaucoma the difference in fixation density to the control condition indicated the location of the sVFD. It is feasible to use natural viewing behavior to screen for and reconstruct (simulated) visual field defects. Movie clip viewing in combination with eye tracking may thus provide an alternative to or supplement standard automated perimetry, in particular in patients who cannot perform the latter technique

Subject and group level changes and comparison in functional connectivity under low vs. high cognitively demanding naturalistic viewing conditions using fmri

Resting State fMRI is used extensively for analysing brain regions. fMRI is also used to determine task induced activations from cerebral networks. This study involves both rest and task activation data and implements statistical methods applied on Blood Oxygenation Level Dependent (BOLD) signals. The conventional task based designs are very specific and may not reflect day to day activities. The two task conditions in this study are watching a movie called INSCAPE with low cognitive load and segments of contextual Hollywood movies under continuous and natural conditions. The aim is to investigate individual and group level Functional Connectivity changes between REST and the two conditions - INSCAPE and MOVIE. The hypothesis is that the functional networks of INSCAPE emulate Resting State networks more closely than traditional MOVIES if the consistent group level effect is regressed out. Voxel wise regression is used on individual subjects across sessions and between subjects per session. Network Wise Correlation Coefficient Maps were also generated using Power\u27s 264 ROIs. Group level concatenated (cICA), for all conditions, and tensor ICA (tICA) maps for only natural viewing conditions were also generated. A paired t-test was performed between INSCAPE vs. REST and MOVIE vs. REST conditions. The results show that ROIS with significant differences were considerably lower for INSCAPE than MOVIE for an FDR corrected arbitrary threshold of p \u3c 0.0005

Experience + Interaction

What do our historic sites and museums offer to visitors? More importantly, what should we strive to offer? Right now, I think many of our historic sites offer two different things: a variety of experiences and access to a wealth of information. Sites like Antietam offer a number of different experiences – from taking a tour over the battleground where so many fought and died, to driving through the battlefield at night seeing thousands of luminaries, each one representing a life. Our historic sites also offer access to knowledge and information – many times through those experiences they offer. Continuing to use Antietam as our guide, this access to information includes things such as a talk with a park ranger who has studied the battle for many years, to a movie that explains the battle complete with maps and reenactments in the park theater. [excerpt

Denver goes to the movies: engaging national-scale identity shifts from movie house to movie palace, 1900-1940

2012 Summer.Includes bibliographical references.This thesis examines the relationship between film history and movie theater architecture at local and national levels as a window into early twentieth century identity shifts. The argument is that Denver films and movie theaters from 1900 to 1940 manifested national-level identity shifts as well as influenced them. The identity shifts included attitudes of innovation, decadence, and endurance that roughly characterized the 1900s and 1910s, 1920s, and 1930s. These identities represented the dominant identities that were part of the broad shift from nineteenth century frontier identity to post-WWII modern identity. This thesis draws from Denver newspapers, architectural and cinema journals, early film histories, Denver Householder and City Directories, Denver Sanborn Fire Insurance maps, other historic maps, memoirs, and photographs. Through close study of these sources and balancing the national history with Denver history, there emerges a story of how Denverites and Americans have selected ideals to maintain and adopted others as they chase their ever-changing dreams

Functoriality for the su(3) Khovanov homology

We prove that Morrison and Nieh's categorification of the su(3) quantum knot invariant is functorial with respect to tangle cobordisms. This is in contrast to the categorified su(2) theory, which was not functorial as originally defined. We use methods of Bar-Natan to construct explicit chain maps for each variation of the third Reidemeister move. Then, to show functoriality, we modify arguments used by Clark, Morrison, and Walker to show that induced chain maps are invariant under Carter and Saito's movie moves.Comment: 65 page