54 research outputs found
Modeling Flocks and Prices: Jumping Particles with an Attractive Interaction
We introduce and investigate a new model of a finite number of particles
jumping forward on the real line. The jump lengths are independent of
everything, but the jump rate of each particle depends on the relative position
of the particle compared to the center of mass of the system. The rates are
higher for those left behind, and lower for those ahead of the center of mass,
providing an attractive interaction keeping the particles together. We prove
that in the fluid limit, as the number of particles goes to infinity, the
evolution of the system is described by a mean field equation that exhibits
traveling wave solutions. A connection to extreme value statistics is also
provided.Comment: 35 pages, 9 figures. A shortened version appears as arXiv:1108.243
The measurable Kesten theorem
We give explicit estimates between the spectral radius and the densities of
short cycles for finite d-regular graphs. This allows us to show that the
essential girth of a finite d-regular Ramanujan graph G is at least c log log
|G|.
We prove that infinite d-regular Ramanujan unimodular random graphs are
trees. Using Benjamini-Schramm convergence this leads to a rigidity result
saying that if most eigenvalues of a d-regular finite graph G fall in the
Alon-Boppana region, then the eigenvalue distribution of G is close to the
spectral measure of the d-regular tree.
Kesten showed that if a Cayley graph has the same spectral radius as its
universal cover, then it must be a tree. We generalize this to unimodular
random graphs.Comment: The previous, longer version 1 has been split in two parts: the
present paper, and a more group-theoretic one with the title "Kesten's
theorem for Invariant Random Subgroups
Kesten's theorem for Invariant Random Subgroups
An invariant random subgroup of the countable group {\Gamma} is a random
subgroup of {\Gamma} whose distribution is invariant under conjugation by all
elements of {\Gamma}. We prove that for a nonamenable invariant random subgroup
H, the spectral radius of every finitely supported random walk on {\Gamma} is
strictly less than the spectral radius of the corresponding random walk on
{\Gamma}/H. This generalizes a result of Kesten who proved this for normal
subgroups. As a byproduct, we show that for a Cayley graph G of a linear group
with no amenable normal subgroups, any sequence of finite quotients of G that
spectrally approximates G converges to G in Benjamini-Schramm convergence. In
particular, this implies that infinite sequences of finite d-regular Ramanujan
Schreier graphs have essentially large girth.Comment: 19 page
Discrete Scale Axis Representations for 3D Geometry
This paper addresses the fundamental problem of computing stable medial representations of 3D shapes. We propose a spatially adaptive classification of geometric features that yields a robust algorithm for generating medial representations at different levels of abstraction. The recently introduced continuous scale axis transform serves as the mathematical foundation of our algorithm. We show how geometric and topological properties of the continuous setting carry over to discrete shape representations. Our method combines scaling operations of medial balls for geometric simplification with filtrations of the medial axis and provably good conversion steps to and from union of balls, to enable efficient processing of a wide variety shape representations including polygon meshes, 3D images, implicit surfaces, and point clouds. We demonstrate the robustness and versatility of our algorithm with an extensive validation on hundreds of shapes including complex geometries consisting of millions of triangles
OCC: A Smart Reply System for Efficient In-App Communications
Smart reply systems have been developed for various messaging platforms. In
this paper, we introduce Uber's smart reply system: one-click-chat (OCC), which
is a key enhanced feature on top of the Uber in-app chat system. It enables
driver-partners to quickly respond to rider messages using smart replies. The
smart replies are dynamically selected according to conversation content using
machine learning algorithms. Our system consists of two major components:
intent detection and reply retrieval, which are very different from standard
smart reply systems where the task is to directly predict a reply. It is
designed specifically for mobile applications with short and non-canonical
messages. Reply retrieval utilizes pairings between intent and reply based on
their popularity in chat messages as derived from historical data. For intent
detection, a set of embedding and classification techniques are experimented
with, and we choose to deploy a solution using unsupervised distributed
embedding and nearest-neighbor classifier. It has the advantage of only
requiring a small amount of labeled training data, simplicity in developing and
deploying to production, and fast inference during serving and hence highly
scalable. At the same time, it performs comparably with deep learning
architectures such as word-level convolutional neural network. Overall, the
system achieves a high accuracy of 76% on intent detection. Currently, the
system is deployed in production for English-speaking countries and 71% of
in-app communications between riders and driver-partners adopted the smart
replies to speedup the communication process.Comment: link to demo: https://www.youtube.com/watch?v=nOffUT7rS0A&t=32
Metatranscriptomics reveals contrasting effects of elevation on the activity of bacteria and bacterial viruses in soil
Soil microbial diversity affects ecosystem functioning and global biogeochemical cycles. Soil bacterial communities catalyse a diversity of biogeochemical reactions and have thus sparked considerable scientific interest. One driver of bacterial community dynamics in natural ecosystems has so far been largely neglected: the predator-prey interactions between bacterial viruses (bacteriophages) and bacteria. To generate ground level knowledge on environmental drivers of these particular predator-prey dynamics, we propose an activity-based ecological framework to simultaneous capture community dynamics of bacteria and bacteriophages in soils. An ecological framework and specifically the analyses of community dynamics across latitudinal and elevational gradients have been widely used in ecology to understand community-wide responses of innumerable taxa to environmental change, in particular to climate. Here, we tested the hypothesis that the activity of bacteria and bacteriophages codeclines across an elevational gradient. We used metatranscriptomics to investigate bacterial and bacteriophage activity patterns at five sites across 400 elevational metres in the Swiss Alps in 2015 and 2017. We found that metabolic activity (transcription levels) of bacteria declined significantly with increasing elevation, but activity of bacteriophages did not. We showed that bacteriophages are consistently active in soil along the entire gradient, making bacteriophage activity patterns divergent from that of their putative bacterial prey. Future efforts will be necessary to link the environment-activity relationship to predator-prey dynamics, and to understand the magnitude of viral contributions to carbon, nitrogen and phosphorus cycling when infection causes bacterial cell death, a process that may represent an overlooked component of soil biogeochemical cycles
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