Annals of Mathematics
This paper is the third in a series where we describe the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed 3-manifold. In [CM3]–[CM5] we describe the case where the surfaces are topologically disks on any ﬁxed small scale. Although the focus of this paper, general planar domains, is more in line with [CM6], we will prove a result here (namely, Corollary III.
This paper is the ﬁrst in a series where we describe the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed Riemannian 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 (with the ﬂat metric). This study is undertaken here and completed in [CM6]. These local results are then applied in [CM7] where we describe the general structure of ﬁxed genus surfaces in 3-manifolds. There are two local models for...
Trường phái này nhận được rất nhiều sự chỉ trích từ công chúng vì họ khó có thể chấp nhận được một dãy hình lập phương, hai hình chữ nhật đặt cạnh nhau hay năm khối hình hộp treo trên tường lại có thể được gọi là nghệ thuật. Đơn giản hóa mọi thứ tối đa, kiệm lời là đặc điểm của trường phái Minimalism.
14. Trường phái nghệ thuật nhận thức
The space of embedded minimal surfaces of ﬁxed genus in a 3-manifold II; Multi-valued graphs in disks
By Tobias H. Colding and William P. Minicozzi II*
0. Introduction This paper is the second in a series where we give a description of the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 . We show here that if the curvature of such a disk...
For shipping supplies to sustain troops overseas, airlift or sealift can be used with differential speed and cost. This documented briefing lays out a construct for designing a distribution network that takes advantage of the two transportation modes’ respective strengths to meet combatant command needs while minimizing total
Department of Linguistics The University of Texas at Austin Austin, Texas 78712 email@example.com
or trigram Hidden Markov Model (HMM). Ravi and Knight (2009) achieved the best results thus far (92.3% word token accuracy) via a Minimum Description Length approach using an integer program (IP) that ﬁnds a minimal bigram grammar that obeys the tag dictionary constraints and covers the observed data.
Dialog participants in a non-mixed initiative dialogs, in which one participant asks questions exclusively and the other participant responds to those questions exclusively, can select actions that minimize the expected length of the dialog. The choice of question that minimizes the expected number of questions to be asked can be computed in polynomial time in some cases. The polynomial-time solutions to special cases of the problem suggest a number of strategies for selecting dialog actions in the intractable general case. ...
Minimal Recursion Semantics (MRS) is the standard formalism used in large-scale HPSG grammars to model underspeciﬁed semantics. We present the ﬁrst provably efﬁcient algorithm to enumerate the readings of MRS structures, by translating them into normal dominance constraints.
In this paper, we formulate extractive summarization as a risk minimization problem and propose a unified probabilistic framework that naturally combines supervised and unsupervised summarization models to inherit their individual merits as well as to overcome their inherent limitations. In addition, the introduction of various loss functions also provides the summarization framework with a flexible but systematic way to render the redundancy and coherence relationships among sentences and between sentences and the whole document, respectively. ...
Dependency structures do not have the information of phrase categories in phrase structure grammar. Thus, dependency parsing relies heavily on the lexical information of words. This paper discusses our investigation into the effectiveness of lexicalization in dependency parsing. Speciﬁcally, by restricting the degree of lexicalization in the training phase of a parser, we examine the change in the accuracy of dependency relations. Experimental results indicate that minimal or low lexicalization is sufﬁcient for parsing accuracy. ...
We aim at finding the minimal set of fragments which achieves maximal parse accuracy in Data Oriented Parsing. Experiments with the Penn Wall Street Journal treebank show that counts of almost arbitrary fragments within parse trees are important, leading to improved parse accuracy over previous models tested on this treebank (a precis ion of 90.8% and a recall of 90.6%). We isolate some dependency relations which previous models neglect but which contribute to higher parse accuracy.
The incremental algorithm introduced in (Dale and Reiter, 1995) for producing distinguishing descriptions does not always generate a minimal description. In this paper, I show that when generalised to sets of individuals and disjunctive properties, this approach might generate unnecessarily long and ambiguous and/or epistemically redundant descriptions.
Finding Minimal Neural Networks for Business Intelligence Applications is Introduction; Feed-forward neural networks; Neural network training and pruning; Rule extraction; Business intelligence applications; Conclusion.
Getting an Email Program, Headers, Netiquette, Keyboard Know How, Forwarding Messages, Formatting, Attachments, Security,... As the main contents of the document "The Email Edge: 101 tips for maximizing the power and minimizing the hassle of email". Invite you to consult.
(BQ) Part 1 book "Minimally invasive bariatric surgery" presents the following contents: The global burden of obesity and diabetes, medical management of obesity, medical management of obesity, developing a successful bariatric surgery program, the role of behavioral health in bariatric surgery,...
Minimalism continues to be among the most popular themes in interior design. Inside MNM: Minimalist Interiors explains minimalist concepts and concentrates on private interiors. This guide includes dozens of sophisticated photographs and introductions to each chapter written by leaders of this extraordinary, contemporary design movement. All the examples featured in the book have one thing in common: they feature the essential, but use the minimal.
In this text, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Finobacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization.
This paper is from the SANS Institute Reading Room site. Reposting is not permitted without express written permission.
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