The switch operators and push-the-button games: a sequential compound over rulesets

We study operators that combine combinatorial games. This field was initiated by Sprague-Grundy (1930s), Milnor (1950s) and Berlekamp-Conway-Guy (1970-80s) via the now classical disjunctive sum operator on (abstract) games. The new class consists in operators for rulesets, dubbed the switch-operators. The ordered pair of rulesets (R 1 , R 2) is compatible if, given any position in R 1 , there is a description of how to move in R 2. Given compatible (R 1 , R 2), we build the push-the-button game R 1 R 2 , where players start by playing according to the rules R 1 , but at some point during play, one of the players must switch the rules to R 2 , by pushing the button ". Thus, the game ends according to the terminal condition of ruleset R 2. We study the pairwise combinations of the classical rulesets Nim, Wythoff and Euclid. In addition, we prove that standard periodicity results for Subtraction games transfer to this setting, and we give partial results for a variation of Domineering, where R 1 is the game where the players put the domino tiles horizontally and R 2 the game where they play vertically (thus generalizing the octal game 0.07).Comment: Journal of Theoretical Computer Science (TCS), Elsevier, A Para{\^i}tr

Shear thickening of highly viscous granular suspensions

We experimentally investigate shear thickening in dense granular suspensions under oscillatory shear. Directly imaging the suspension-air interface, we observe dilation beyond a critical strain $\gamma_c$ and the end of shear thickening as the maximum confining stress is reached and the contact line moves. Analyzing the shear profile, we extract the viscosity contributions due to hydrodynamics $\eta_\mu$, dilation $\eta_c$ and sedimentation $\eta_g$. While $\eta_g$ governs the shear thinning regime, $\eta_\mu$ and $\eta_c$ together determine the shear thickening behavior. As the suspending liquid's viscosity varies from 10 to 1000 cst, $\eta_\mu$ is found to compete with $\eta_c$ and soften the discontinuous nature of shear thickening

SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels

We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors. For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domain-independence.Comment: Presented at CVPR 201

Access to Effective Teaching for Disadvantaged Students

Recent federal initiatives in education, such as Race to the Top, the Teacher Incentive Fund, and the flexibility policy for the Elementary and Secondary Education Act are designed in part to ensure that disadvantaged students have equal access to effective teaching. The initiatives respond to the concern that disadvantaged students may be taught by less effective teachers and that this could contribute to the achievement gap between disadvantaged students and other students. To address the need for evidence on this issue, the Institute of Education Sciences at the U.S. Department of Education initiated a study to examine access to effective teaching for disadvantaged students in 29 diverse school districts. Mathematica Policy Research and its partner, the American Institutes for Research, conducted the study, which focused on English/ language arts (ELA) and math teachers in grades 4 through 8 from the 2008 -- 2009 to the 2010 -- 2011 school year

Strain-stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model polymer system to investigate the contribution of entanglements to strain-stiffening in the absence of Brownian motion. The chain packings are sheared in triaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds a the scale of the confining pressure, similar to packings of spherical particles. In contrast, packings of chains which are long enough to form loops exhibit strain-stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.Comment: 4 pages, 4 figures. submitted to Physical Review Letter