Title: Structure of partially hyperbolic Hénon maps
We describe the structure of “substantially dissipative” complex Hénon maps admitting a dominated splitting on the Julia set. We prove that the Fatou set consists of only finitely many components, each either attracting or parabolic periodic. In particular, there are no wandering components and no rotation domains. more »« less
Bera, Sabyasachi; Chatterjee, Snigdhansu
(, Statistics in Transition New Series)
Okrasa, Włodzimierz; Lahiri, Partha
(Ed.)
Abstract We develop a technique for record linkage on high dimensional data, where the two datasets may not have any common variable, and there may be no training set available. Our methodology is based on sparse, high dimensional principal components. Since large and high dimensional datasets are often prone to outliers and aberrant observations, we propose a technique for estimating robust, high dimensional principal components. We present theoretical results validating the robust, high dimensional principal component estimation steps, and justifying their use for record linkage. Some numeric results and remarks are also presented.
Kim, Tae Soo; Jones, Jonathan; Peven, Michael; Xiao, Zihao; Bai, Jin; Zhang, Yi; Qiu, Weichao; Yuille, Alan; Hager, Gregory D
(, Proceedings of the AAAI Conference on Artificial Intelligence)
There are many realistic applications of activity recognition where the set of potential activity descriptions is combinatorially large. This makes end-to-end supervised training of a recognition system impractical as no training set is practically able to encompass the entire label set. In this paper, we present an approach to fine-grained recognition that models activities as compositions of dynamic action signatures. This compositional approach allows us to reframe fine-grained recognition as zero-shot activity recognition, where a detector is composed “on the fly” from simple first-principles state machines supported by deep-learned components. We evaluate our method on the Olympic Sports and UCF101 datasets, where our model establishes a new state of the art under multiple experimental paradigms. We also extend this method to form a unique framework for zero-shot joint segmentation and classification of activities in video and demonstrate the first results in zero-shot decoding of complex action sequences on a widely-used surgical dataset. Lastly, we show that we can use off-the-shelf object detectors to recognize activities in completely de-novo settings with no additional training.
The Event Horizon Telescope (EHT) is taking the first images of black holes resolved at horizon scales to measure their shadows and probe accretion physics. A promising avenue for testing the hypothesis that astrophysical black holes are described by the Kerr solution to Einstein’s equations is to compare the size and shape of the shadow a black hole casts on the surrounding emission to the predictions of the Kerr metric. We develop here an efficient parametric framework to perform this test. We carry out ray-tracing simulations for several parametrized non-Kerr metrics to create a large data set of non-Kerr shadows that probe the allowed parameter space for the free parameters of each metric. We then perform principal components analysis (PCA) on this set of shadows and show that only a small number of components are needed to accurately reconstruct all shadows within the set. We further show that the amplitude of the PCA components are smoothly related to the free parameters in the metrics, and therefore, that these PCA components can be fit to EHT observations in order to place constraints on the free parameters of these metrics that will help quantify any potential deviations from the Kerr solution.
Guo, Zheng; James, Michael; Justo, David; Zhou, Jiaxiao; Wang, Ziteng; Jhala, Ranjit; Polikarpova, Nadia
(, Proceedings of the ACM on Programming Languages)
We consider the problem of type-directed component-based synthesis where, given a set of (typed) components and a querytype, the goal is to synthesize atermthat inhabits the query. Classical approaches based on proof search in intuitionistic logics do not scale up to the standard libraries of modern languages, which span hundreds or thousands of components. Recent graph reachability based methods proposed for Java do scale, but only apply to monomorphic data and components: polymorphic data and components infinitely explode the size of the graph that must be searched, rendering synthesis intractable. We introducetype-guided abstraction refinement(TYGAR), a new approach for scalable type-directed synthesis over polymorphic datatypes and components. Our key insight is that we can overcome the explosion by building a graph overabstract typeswhich represent a potentially unbounded set of concrete types. We show how to use graph reachability to search for candidate terms over abstract types, and introduce a new algorithm that usesproofs of untypeabilityof ill-typed candidates to iterativelyrefinethe abstraction until a well-typed result is found. We have implemented TYGAR in H+, a tool that takes as input a set of Haskell libraries and a query type, and returns a Haskell term that uses functions from the provided libraries to implement the query type. Our support for polymorphism allows H+ to work with higher-order functions and type classes, and enables more precise queries due to parametricity. We have evaluated H+ on 44 queries using a set of popular Haskell libraries with a total of 291 components. H+ returns an interesting solution within the first five results for 32 out of 44 queries. Our results show that TYGAR allows H+ to rapidly return well-typed terms, with the median time to first solution of just 1.4 seconds. Moreover, we observe that gains from iterative refinement over exhaustive enumeration are more pronounced on harder queries.
Bhat, Ganapati; Gupta, Ujjwal; Tran, Nicholas; Park, Jaehyun; Ozev, Sule; Ogras, Umit Y.
(, 2016 IEEE/ACM International Conference on Computer-Aided Design (ICCAD))
Flexible systems that can conform to any shape are desirable for wearable applications. Over the past decade, there have been tremendous advances in the domain of flexible electronics which enabled printing of devices, such as sensors on a flexible substrate. Despite these advances, pure flexible electronics systems are limited by poor performance and large feature sizes. Flexible hybrid electronics (FHE) is an emerging technology which addresses these issues by integrating high performance rigid integrated circuits and flexible devices. Yet, there are no system-level design flows and algorithms for the design of FHE systems. To this end, this paper presents a multi-objective design algorithm to implement a target application optimally using a library of rigid and flexible components. Our algorithm produces a set of Pareto frontiers that optimize the physical flexibility, energy per operation and area metrics. Simulation studies show a 32× range in area and 4× range in flexibility across the set of Pareto-optimal design points.
Lyubich, Mikhail, and Peters, Hans. Structure of partially hyperbolic Hénon maps. Retrieved from https://par.nsf.gov/biblio/10467873. Journal of the European Mathematical Society 23. Web. doi:10.4171/JEMS/1074.
Lyubich, Mikhail, & Peters, Hans. Structure of partially hyperbolic Hénon maps. Journal of the European Mathematical Society, 23 (). Retrieved from https://par.nsf.gov/biblio/10467873. https://doi.org/10.4171/JEMS/1074
Lyubich, Mikhail, and Peters, Hans.
"Structure of partially hyperbolic Hénon maps". Journal of the European Mathematical Society 23 (). Country unknown/Code not available: JOURNALSJEMSVOL. 23, NO. 9PP. 3075–3128. https://doi.org/10.4171/JEMS/1074.https://par.nsf.gov/biblio/10467873.
@article{osti_10467873,
place = {Country unknown/Code not available},
title = {Structure of partially hyperbolic Hénon maps},
url = {https://par.nsf.gov/biblio/10467873},
DOI = {10.4171/JEMS/1074},
abstractNote = {We describe the structure of “substantially dissipative” complex Hénon maps admitting a dominated splitting on the Julia set. We prove that the Fatou set consists of only finitely many components, each either attracting or parabolic periodic. In particular, there are no wandering components and no rotation domains.},
journal = {Journal of the European Mathematical Society},
volume = {23},
publisher = {JOURNALSJEMSVOL. 23, NO. 9PP. 3075–3128},
author = {Lyubich, Mikhail and Peters, Hans},
}
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