Bessel processes, the Brownian snake and super-Brownian motion

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in memory of Marc Yo

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Capacity and Opportunity: Predicting Engagement for Middle School Students With Behavioral Disorders

This study examined the capacity and opportunity scores of 36 middle school students with emotional and behavioral disorders (EBD) on the student version of the American Institutes for Research (AIR) Self-Determination Scale across three school engagement factors: grade point averages (GPA), school absences, and frequency of school disciplinary encounters. Poor grades, school absences, and frequency of disciplinary actions pose academic problems for middle school students with EBD. Three multiple regression models determined the predictive relationships between self-determination Capacity and Opportunity subscale scores and GPA, Absences, and Discipline. Higher capacity and opportunity scores predicted greater student GPA, fewer student absences, and fewer disciplinary encounters for students at school. Results of this study demonstrate the need for increased opportunities at school and home for students with EBD to learn and practice self-determination skills.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Human Pose Estimation using Deep Consensus Voting

In this paper we consider the problem of human pose estimation from a single still image. We propose a novel approach where each location in the image votes for the position of each keypoint using a convolutional neural net. The voting scheme allows us to utilize information from the whole image, rather than rely on a sparse set of keypoint locations. Using dense, multi-target votes, not only produces good keypoint predictions, but also enables us to compute image-dependent joint keypoint probabilities by looking at consensus voting. This differs from most previous methods where joint probabilities are learned from relative keypoint locations and are independent of the image. We finally combine the keypoints votes and joint probabilities in order to identify the optimal pose configuration. We show our competitive performance on the MPII Human Pose and Leeds Sports Pose datasets

Confluence of geodesic paths and separating loops in large planar quadrangulations

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding paragraph and one reference added, and several other small correction

Lichens of six vernal pools in Acadia National Park, ME, USA

Whereas lichen-habitat relations have been well-documented globally, literature on lichens of vernal pools is scant. We surveyed six vernal pools at Acadia National Park on Mount Desert Island, Maine, USA for their lichen diversity. Sixty-seven species were identified, including seven species that are new reports for Acadia National Park: Fuscidea arboricola, Hypogymnia incurvoides, Lepraria finkii, Phaeographis inusta, Ropalospora viridis, Usnea flammea, and Violella fucata. Five species are considered uncommon or only locally common in New England: Everniastrum catawbiense, Hypogymnia krogiae, Pseudevernia cladonia, Usnea flammea, and Usnea merrillii. This work represents the first survey of lichens from vernal pools in Acadia National Park and strongly suggests that previous efforts at documenting species at the Park have underestimated its species diversity. More work should be conducted to determine whether a unique assemblage of lichens occurs in association with this unique habitat type

Quantum Algorithms for Matrix Products over Semirings

In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we obtain the following results. We construct a quantum algorithm computing the product of two n x n matrices over the (max,min) semiring with time complexity O(n^{2.473}). In comparison, the best known classical algorithm for the same problem, by Duan and Pettie, has complexity O(n^{2.687}). As an application, we obtain a O(n^{2.473})-time quantum algorithm for computing the all-pairs bottleneck paths of a graph with n vertices, while classically the best upper bound for this task is O(n^{2.687}), again by Duan and Pettie. We construct a quantum algorithm computing the L most significant bits of each entry of the distance product of two n x n matrices in time O(2^{0.64L} n^{2.46}). In comparison, prior to the present work, the best known classical algorithm for the same problem, by Vassilevska and Williams and Yuster, had complexity O(2^{L}n^{2.69}). Our techniques lead to further improvements for classical algorithms as well, reducing the classical complexity to O(2^{0.96L}n^{2.69}), which gives a sublinear dependency on 2^L. The above two algorithms are the first quantum algorithms that perform better than the $\tilde O(n^{5/2})$-time straightforward quantum algorithm based on quantum search for matrix multiplication over these semirings. We also consider the Boolean semiring, and construct a quantum algorithm computing the product of two n x n Boolean matrices that outperforms the best known classical algorithms for sparse matrices. For instance, if the input matrices have O(n^{1.686...}) non-zero entries, then our algorithm has time complexity O(n^{2.277}), while the best classical algorithm has complexity O(n^{2.373}).Comment: 19 page