Some Exact Results on the Potts Model Partition Function in a Magnetic Field

We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for $Z$ for cyclic strip graphs.Comment: 5 pages, late

Miro, MCU, and calcium: Bridging our understanding of mitochondrial movement in axons

Neurons are extremely polarized structures with long axons and dendrites, which require proper distribution of mitochondria and maintenance of mitochondrial dynamics for neuronal functions and survival. Indeed, recent studies show that various neurological disorders are linked to mitochondrial transport in neurons. Mitochondrial anterograde transport is believed to deliver metabolic energy to synaptic terminals where energy demands are high, while mitochondrial retrograde transport is required to repair or remove damaged mitochondria in axons. It has been suggested that Ca2+ plays a key role in regulating mitochondrial transport by altering the configuration of mitochondrial protein, miro. However, molecular mechanisms that regulate mitochondrial transport in neurons still are not well characterized. In this review, we will discuss the roles of miro in mitochondrial transport and how the recently identified components of the mitochondrial calcium uniporter add to our current model of mitochondrial mobility regulation.open2

Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions

We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with a variety of boundary conditions, and with $Q$ and $v$ restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two-dimensional lattices. From these calculations, in the limit $L_x \to \infty$, we determine the continuous accumulation loci ${\cal B}$ of the partition function zeros in the $v$ and $Q$ planes. Strips of the honeycomb lattice are also considered. We discuss some general features of these loci.Comment: 12 pages, 12 figure

Juvenile Justice and Racial Disproportionality: A Presentation to the Washington State Supreme Court

Juvenile Justice and Racial Disproportionality: A Presentation to the Washington State Supreme Cour

Brief of Amicus Curiae, Fred T. Korematsu Center for Law and Equality in Support of Petitioner

State v. Garcia-Buen

Brief of Amicus Curiae, Fred T. Korematsu Center for Law and Equality in Support of Petitioner

State v. Garcia-Buen

Too real for comfort? Uncanny responses to computer generated faces

As virtual humans approach photorealistic perfection, they risk making real humans uncomfortable. This intriguing phenomenon, known as the uncanny valley, is well known but not well understood. In an effort to demystify the causes of the uncanny valley, this paper proposes several perceptual, cognitive, and social mechanisms that have already helped address riddles like empathy, mate selection, threat avoidance, cognitive dissonance, and psychological defenses. In the four studies described herein, a computer generated human character’s facial proportions, skin texture, and level of detail were varied to examine their effect on perceived eeriness, human likeness, and attractiveness. In Study I, texture photorealism and polygon count increased human likeness. In Study II, texture photorealism heightened the accuracy of human judgments of ideal facial proportions. In Study III, atypical facial proportions were shown to be more disturbing on photorealistic faces than on other faces. In Study IV, a mismatch in the size and texture of the eyes and face was especially prone to make a character eerie. These results contest the depiction of the uncanny valley as a simple relation between comfort level and human likeness. This paper concludes by introducing a set of design principles for bridging the uncanny valley

High Temperature Dynamic Pressure Measurements Using Silicon Carbide Pressure Sensors

Un-cooled, MEMS-based silicon carbide (SiC) static pressure sensors were used for the first time to measure pressure perturbations at temperatures as high as 600 C during laboratory characterization, and subsequently evaluated in a combustor rig operated under various engine conditions to extract the frequencies that are associated with thermoacoustic instabilities. One SiC sensor was placed directly in the flow stream of the combustor rig while a benchmark commercial water-cooled piezoceramic dynamic pressure transducer was co-located axially but kept some distance away from the hot flow stream. In the combustor rig test, the SiC sensor detected thermoacoustic instabilities across a range of engine operating conditions, amplitude magnitude as low as 0.5 psi at 585 C, in good agreement with the benchmark piezoceramic sensor. The SiC sensor experienced low signal to noise ratio at higher temperature, primarily due to the fact that it was a static sensor with low sensitivity

Atmosphere of Callisto

During the Galileo flybys of Callisto in 1999, a CO_2 atmosphere and an ionosphere were detected. Using the Caltech/Jet Propulsion Laboratory one-dimensional KINETICS model, we have successfully simulated the observed electron density within a factor of 2, while satisfying the observational constraints on carbon and oxygen atoms. We conclude that photoionization of CO_2 alone is insufficient to produce the observed electron density. An atmosphere 20–100 times denser than the CO_2 atmosphere must be introduced, as suggested by Kliore et al. (2002). We show that an O_2-rich atmosphere is highly probable. However, the atomic oxygen produced from O_2 photodissociation is 2 orders of magnitude greater than the upper limit given by Strobel et al. (2002). The introduction of reactive hydrogen chemistry assuming a surface abundance of H_2O of ∼2 × 10^9 cm^(−3) (4 × 10^(−8) mbar) is required to reduce the excess atomic O abundance. The calculated atomic O column density is >5 × 10^(12) cm^(−2), which is about the observed upper limit, suggesting we should be able to detect O in the atmosphere of Callisto