Spiders for rank 2 Lie algebras

A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. We define certain combinatorial spiders by generators and relations that are isomorphic to the representation theories of the three rank two simple Lie algebras, namely A2, B2, and G2. They generalize the widely-used Temperley-Lieb spider for A1. Among other things, they yield bases for invariant spaces which are probably related to Lusztig's canonical bases, and they are useful for computing quantities such as generalized 6j-symbols and quantum link invariants.Comment: 33 pages. Has color figure

A pilot study of law ernforcement officer (LEO) anthropometry with applications to vehicle design for safety and accommodation

Law enforcement officers (LEO) are at relatively high risk of back pain and other musculoskeletal disorders. The risk is exacerbated by the poor accommodation provided by their vehicles, which are usually modified civilian vehicles. LEO are also involved in vehicle crashes at a higher rate than most other occupations, yet officers report difficulty in wearing a safety belt due to interference with their body-borne equipment. To begin to address these issues, a pilot study was conducted to demonstrate the application of three-dimensional anthropometric techniques to quantifying the influence of body-borne gear on space claim and posture in vehicles. The results demonstrated that three exemplar vehicles accommodated the officers poorly due to interference between the seat or other vehicle features and the body-borne gear. Belt fit was also adversely affected, and vehicle modifications and additions, such as the now-common center-mounted laptop computer, create awkward postures for driving, in-vehicle work, and ingress and egress. A large-scale, population-based study aimed at developing seat and vehicle design guidelines using three-dimensional anthropometric techniques is needed.Anthrotech, Inc.http://deepblue.lib.umich.edu/bitstream/2027.42/116202/1/103221.pdfDescription of 103221.pdf : Final repor

Combinatorial expression for universal Vassiliev link invariant

The most general R-matrix type state sum model for link invariants is constructed. It contains in itself all R-matrix invariants and is a generating function for "universal" Vassiliev link invariants. This expression is more simple than Kontsevich's expression for the same quantity, because it is defined combinatorially and does not contain any integrals, except for an expression for "the universal Drinfeld's associator".Comment: 20 page

Naturalistic Passenger Behavior: Posture and Activities

Technical Report FinalVideo cameras were installed in the passenger cabins of 75 vehicles to monitor the postures and activities of front-seat passengers. Video frames from a total of 2733 trips were coded for 306 unique front-seat passengers. During these trips, a total of 13638 frames were coded; each frame represents about four minutes of travel time. The median trip duration was 12.2 minutes and 5% of trips were longer than 54 minutes. The distribution of trip durations was similar to that for the general population of US travelers. The front seat passenger was female in 72% of frames and most often judged to be between 17 and 30 years of age. The seat belt was worn 97% of the time, with visibly poor fit (belt on belly or lateral to the clavicle) in about 30% of frames. The most common passenger interaction was talking with the driver, while interactions with hand-held devices (typically phones) occurred in 26% of frames. Phone use was associated with a downward pitched head. The head was rotated left or right in 33% of frames, and the torso was rotated left or right about 10% of the time and pitched forward in almost 10% of frames. The front of the thighs was lifted off the seat due to the feet being shifted rearward about 40% of the time and the legs were crossed in about 5% of frames. Resting behavior was observed more frequently in longer-duration trips and when traveling at higher speeds, while phone use increased and talking with vehicle occupants decreased with increased sitting time. No seat position or seat back angle change was noted in 40 (53%) of vehicles. In the remaining 35 vehicles, seat back angle and seat position were observed to change only 16 and 61 times, respectively, so that the distributions of seat position and seat back angle on arrival were essentially unchanged during travel. The seat was positioned full-rear on the seat track about 23% of the time and rearward of the mid-track position in 81% of frames. The mean seat back angle was 25.4 degrees (standard deviation 6.4 degrees); seat back angle was greater than 30 degrees in 15% of frames and greater than 35 degrees in less than 1% of frames. Seat back angles greater than 30 degrees were more common on longer trips and associated with a greater likelihood of the head touching the seat, lower phone use, and slightly greater frequency of resting behavior. When a second-row passenger was present behind the front-seat passenger, the seat was 5 mm further forward and 1.4 degrees more upright, on average. This study is the first to report distributions of seat positions and seat back angles for front-seat passengers and the first to provide details of passenger posture and activities from a large sample of individuals. The findings have implications for the design of current vehicles and also provide insight into the likely postures and activities of the occupants of future driverless vehicles.Toyota Collaborative Safety Research Centerhttps://deepblue.lib.umich.edu/bitstream/2027.42/154855/1/UMTRI-2020-2.pdfDescription of UMTRI-2020-2.pdf : Technical Report Fina

On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date

The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix detailing some long calculations. arXiv admin note: text overlap with arXiv:1110.454

A-dependence of nuclear transparency in quasielastic A(e,e'p) at high Q^2

The A-dependence of the quasielastic A(e,e'p) reaction has been studied at SLAC with H-2, C, Fe, and Au nuclei at momentum transfers Q^2 = 1, 3, 5, and 6.8 (GeV/c)^2. We extract the nuclear transparency T(A,Q^2), a measure of the average probability that the struck proton escapes from the nucleus A without interaction. Several calculations predict a significant increase in T with momentum transfer, a phenomenon known as Color Transparency. No significant rise within errors is seen for any of the nuclei studied.Comment: 5 pages incl. 2 figures, Caltech preprint OAP-73