Related papers: Reply to comment by P.Markos [arXiv:1205.0689]
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
In [Chu12], Church used representation stability to prove that the space of configurations of distinct unordered points in a closed manifold exhibit rational homological stability. A second proof was also given by Randal-Williams in [RW11]…
This note replies Dr. Jensen (2010) comments on Problem 2.3, which was left in Fuh (2010). In the following, we use the same notations and definitions in Fuh (2006) unless specified.
Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.
We introduce and study effective versions of the localization numbers introduced by Newelski and Roslanowski (cite in paper). We show that proper hierarchies are produced, and that the corresponding highness notions are relatively weak, in…
The first result in this paper provides a very general $\epsilon$-removal argument for the multilinear restriction estimate. The second result provides a refinement of the multilinear restriction estimate in the case when some terms have…
We propose a new inference framework called localized conformal prediction. It generalizes the framework of conformal prediction by offering a single-test-sample adaptive construction that emphasizes a local region around this test sample,…
Over the last few years, we have witnessed tremendous progress on many subtasks of autonomous driving, including perception, motion forecasting, and motion planning. However, these systems often assume that the car is accurately localized…
We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (resp. connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple…
Conformal prediction has become increasingly popular for quantifying the uncertainty associated with machine learning models. Recent work in graph uncertainty quantification has built upon this approach for conformal graph prediction. The…
In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…
Would it be possible to automatically associate ancient pictures to modern ones and create fancy cultural heritage city maps? We introduce here the task of recognizing the location depicted in an old photo given modern annotated images…
Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…
Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the…
We suggest new types and interpretation of complex and hypercomplex numbers for which the commutative, associative, and distributive laws and the norm axioms are trivially satisfied.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
One proves that any everywhere defined constructive mapping from a complete metric space into a complete metric space which preserves the property of precompacity of subsets is locally uniformly continuous. This fact can be viewed as…
Local linearization is highlighted to explain the success of the orbital approximation in positive response to Scerri's comments on the electronic configuration model. The relevance of Rydberg states is made clear.
We interpret part of the experimental results of Shwartz-Ziv and Tishby [2017]. Inspired by these results, we established a conjecture of the dynamics of the machinary of deep neural network. This conjecture can be used to explain the…