Visualizing classification of natural video sequences using sparse, hierarchical models of cortex.

Recent work on hierarchical models of visual cortex has reported state-of-the-art accuracy on whole-scene labeling using natural still imagery. This raises the question of whether the reported accuracy may be due to the sophisticated, non-biological back-end supervised classifiers typically used (support vector machines) and/or the limited number of images used in these experiments. In particular, is the model classifying features from the object or the background? Previous work (Landecker, Brumby, et al., COSYNE 2010) proposed tracing the spatial support of a classifier’s decision back through a hierarchical cortical model to determine which parts of the image contributed to the classification, compared to the positions of objects in the scene. In this way, we can go beyond standard measures of accuracy to provide tools for visualizing and analyzing high-level object classification. We now describe new work exploring the extension of these ideas to detection of objects in video sequences of natural scenes

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

A note on dimer models and McKay quivers

We give one formulation of an algorithm of Hanany and Vegh which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following Feng, He, Kennaway and Vafa.Comment: 25 pages, 35 figures. v3:completely rewritte

The TAOS Project: Upper Bounds on the Population of Small KBOs and Tests of Models of Formation and Evolution of the Outer Solar System

We have analyzed the first 3.75 years of data from TAOS, the Taiwanese American Occultation Survey. TAOS monitors bright stars to search for occultations by Kuiper Belt Objects (KBOs). This dataset comprises 5e5 star-hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this dataset. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari (2005), Kenyon & Bromley (2004), Benavidez & Campo Bagatin (2009), and Fraser (2009). A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is comprised of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.Comment: 18 pages, 16 figures, Aj submitte

Planet formation around low mass stars: the moving snow line and super-Earths

We develop a semi-analytic model for planet formation during the pre-main sequence contraction phase of a low mass star. During this evolution, the stellar magnetosphere maintains a fixed ratio between the inner disk radius and the stellar radius. As the star contracts at constant effective temperature, the `snow line', which separates regions of rocky planet formation from regions of icy planet formation, moves inward. This process enables rapid formation of icy protoplanets that collide and merge into super-Earths before the star reaches the main sequence. The masses and orbits of these super-Earths are consistent with super-Earths detected in recent microlensing experiments.Comment: accepted by ApJ Letter

The interaction of a gap with a free boundary in a two dimensional dimer system

Let $\ell$ be a fixed vertical lattice line of the unit triangular lattice in the plane, and let \Cal H be the half plane to the left of $\ell$. We consider lozenge tilings of \Cal H that have a triangular gap of side-length two and in which $\ell$ is a free boundary - i.e., tiles are allowed to protrude out half-way across $\ell$. We prove that the correlation function of this gap near the free boundary has asymptotics $\frac{1}{4\pi r}$, $r\to\infty$, where $r$ is the distance from the gap to the free boundary. This parallels the electrostatic phenomenon by which the field of an electric charge near a conductor can be obtained by the method of images.Comment: 34 pages, AmS-Te

A Spectroscopic Survey of Subarcsecond Binaries in the Taurus-Auriga Dark Cloud with the Hubble Space Telescope

We report the results of a spectroscopic survey of 20 close T Tauri binaries in the Taurus-Auriga dark cloud where the separations between primaries and their secondaries are less than the typical size of a circumstellar disk around a young star. Analysis of low-resolution and medium-resolution STIS spectra yields the stellar luminosities, reddenings, ages, masses, mass accretion rates, IR excesses, and emission line luminosities for each star in each pair. We examine the ability of IR color excesses, H-alpha equivalent widths, [O I] emission, and veiling to distinguish between weak emission and classical T Tauri stars. Four pairs have one cTTs and one wTTs; the cTTs is the primary in three of these systems. This frequency of mixed pairs among the close T Tauri binaries is similar to the frequency of mixed pairs in wider young binaries. Extinctions within pairs are usually similar; however, the secondary is more heavily reddened than the primary in some systems, where it may be viewed through the primary's disk. Mass accretion rates of primaries and secondaries are strongly correlated, and H-alpha luminosities, IR excesses, and ages also correlate within pairs. Primaries tend to have somewhat larger accretion rates than their secondaries do, and are typically slightly older than their secondaries according to three different sets of modern pre-main-sequence evolutionary tracks. Age differences for XZ Tau and FS Tau, systems embedded in reflection nebulae, are striking; the secondary in each pair is less massive but more luminous than the primary. The stellar masses of the UY Aur and GG Tau binaries measured from their rotating molecular disks are about 30% larger than the masses inferred from the spectra and evolutionary tracks

The Size Distribution of Kuiper Belt Objects

We describe analytical and numerical collisional evolution calculations for the size distribution of icy bodies in the Kuiper Belt. For a wide range of bulk properties, initial masses, and orbital parameters, our results yield power-law cumulative size distributions, N_C propto r^{-q}, with q_L = 3.5 for large bodies with radii of 10-100 km, and q_s = 2.5-3 for small bodies with radii lesss than 0.1-1 km. The transition between the two power laws occurs at a break radius of 1-30 km. The break radius is more sensitive to the initial mass in the Kuiper Belt and the amount of stirring by Neptune than the bulk properties of individual Kuiper Belt objects (KBOs). Comparisons with observations indicate that most models can explain the observed sky surface density of KBOs for red magnitudes, R = 22-27. For R 28, the model surface density is sensitive to the amount of stirring by Neptune, suggesting that the size distribution of icy planets in the outer solar system provides independent constraints on the formation of Neptune.Comment: 24 pages of text, 12 figures; to appear in the Astronomical Journal, October 200