Group Normalization

International Journal of Computer Vision - Batch Normalization (BN) is a milestone technique in the development of deep learning, enabling various networks to train. However, normalizing along the...     

Normalization of rings

We present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. A modification, applicable in positive characteristic, where actually all computations are over the original ring, is also described. The new algorithm of this paper has been implemented in Singular, for localizations of affine rings with respect to arbitrary monomial orderings. Benchmark tests show that it is in general much faster than any other implementation of normalization algorithms known to us.     

离散余弦变换的归一化正交性

在以前提出的离散余弦变换(DCT)类定义的基础上，给出了一维DCT的归一化正交性的一种简洁证明，为同类问题的证明奠定了基础．     

DTD的规范化

一个设计良好的DTD对于XML应用来说是必须的,从消除文档内数据冗余的角度出发研究了这一问题。函数依赖是数据语义的重要组成部分,将它引入到XML的领域中。给出的函数依赖可以是绝对的,也可以是相对的,键只是它的一种特例。讨论了逻辑蕴涵及其相应的推理规则,并证明了推理规则集的正确性和完备性。基于函数依赖,提出了规范化的DTD概念,并给出了一个将DTD转化为规范化形式的算法。     

Strong Normalization from Weak Normalization by Translation into the Lambda-I-Calculus

This paper offers a systematic account of techniques to infer strong normalization from weak normalization that make use of syntactic translations from -terms to I-terms. We present variants of such techniques due to Klop, Sørensen, Xi, Gandy, and Loader.We show that all the translations, in some cases via adjustments, are special cases of a generic scheme of translations, known as permutative inner interpretations. Having established this, which is easy, the fact that all the translations can be used to reduce strong normalization to weak normalization can be obtained from a single, general result concerning permutative inner interpretations.Furthermore, we show that each of the translations can be obtained as the composition of Klop's well-known -translation and some other translation of independent interest. For instance, in the case of Xi's translation, this other translation is a thunkification translation.Finally we compare the above techniques in some detail to the intimately related techniques by de Vrijer and Girard.A main contribution of the paper is to compare the techniques of Gandy, Klop, and Girard in detail. For instance, we prove the main property of Gandy's translation without reference to functionals using instead ideas from Klop's translation.     

Normalization and optimization of schema mappings

Schema mappings are high-level specifications that describe the relationship between database schemas. They are an important tool in several areas of database research, notably in data integration and data exchange. However, a concrete theory of schema mapping optimization including the formulation of optimality criteria and the construction of algorithms for computing optimal schema mappings is completely lacking to date. The goal of this work is to fill this gap. We start by presenting a system of rewrite rules to minimize sets of source-to-target tuple-generating dependencies. Moreover, we show that the result of this minimization is unique up to variable renaming. Hence, our optimization also yields a schema mapping normalization. By appropriately extending our rewrite rule system, we also provide a normalization of schema mappings containing equality-generating target dependencies. An important application of such a normalization is in the area of defining the semantics of query answering in data exchange, since several definitions in this area depend on the concrete syntactic representation of the mappings. This is, in particular, the case for queries with negated atoms and for aggregate queries. The normalization of schema mappings allows us to eliminate the effect of the concrete syntactic representation of the mapping from the semantics of query answering. We discuss in detail how our results can be fruitfully applied to aggregate queries.     

Non-Linear Rewrite Closure and Weak Normalization

A rewrite closure is an extension of a term rewrite system with new rules, usually deduced by transitivity. Rewrite closures have the nice property that all rewrite derivations can be transformed into derivations of a simple form. This property has been useful for proving decidability results in term rewriting. Unfortunately, when the term rewrite system is not linear, the construction of a rewrite closure is quite challenging. In this paper, we construct a rewrite closure for term rewrite systems that satisfy two properties: the right-hand side term in each rewrite rule contains no repeated variable (right-linear) and contains no variable occurring at depth greater than one (right-shallow). The left-hand side term is unrestricted, and in particular, it may be non-linear. As a consequence of the rewrite closure construction, we are able to prove decidability of the weak normalization problem for right-linear right-shallow term rewrite systems. Proving this result also requires tree automata theory. We use the fact that right-shallow right-linear term rewrite systems are regularity preserving. Moreover, their set of normal forms can be represented with a tree automaton with disequality constraints, and emptiness of this kind of automata, as well as its generalization to reduction automata, is decidable. A preliminary version of this work was presented at LICS 2009 (Creus 2009).     

关系数据库设计与规范化

数据库模式直接决定和影响了数据的完整性、准确性和一致性,它对数据库的性能有致关重要的影响。关系数据库设计的目标就是要从各种可能的关系模式组合中选取一组关系模式来构成一个数据库模式,使得我们既不必存储不必要的重复信息,又可以方便地获取信息。在进行关系数据库设计时,一般是通过设计满足某一范式的模式来获得一个好的数据库模式,通常认为3NF在性能、扩展性和数据完整性方面达到了最好的平衡,故一般数据库设计要求达到3NF。     

Normalization of informal text

This paper describes a noisy-channel approach for the normalization of informal text, such as that found in emails, chat rooms, and SMS messages. In particular, we introduce two character-level methods for the abbreviation modeling aspect of the noisy channel model: a statistical classifier using language-based features to decide whether a character is likely to be removed from a word, and a character-level machine translation model. A two-phase approach is used; in the first stage the possible candidates are generated using the selected abbreviation model and in the second stage we choose the best candidate by decoding using a language model. Overall we find that this approach works well and is on par with current research in the field.     

Normalization of satellite imagery

Abstract

Sets of Thematic Mapper (TM) imagery taken over the Washington DC metropolitan area during the months of November, March and May were converted into a form of ground reflectance imagery. This conversion was accomplished by adjusting the incident sunlight and view angles and by applying a pixel-by-pixel correction for atmospheric effects. Seasonal colour changes of the area can be better observed when such normalization is applied to space imagery taken in time series. In normalized imagery, the grey scale depicts variations in surface reflectance and tonal signature of multi-band colour imagery can be directly interpreted for quantitative information of the target.     

数据库的规范化理论与非规范化设计

关系数据库设计的目标就是要得到一组关系模式来组成一个最优的数据库模式,使得我们既不必存储不必要的重复数据,又可以方便地查询数据。这组关系模式首先要用关系规范化理论规范化,构造好的逻辑结构,然后根据需要,从提高数据库性能的角度,进行非规范化处理。规范化和非规范化各有其优缺点,需要我们根据实际需求权衡处理。     

XML文档中的数据依赖及其规范化

对XML文档中存在的异常数据依赖进行了分析,提出了规范化所对应的范式及规则.     

数据库的规范化理论与非规范化设计

关系数据库设计的目标就是要得到一组关系模式采组成一个最优的数据库模式，使得我们既不必存储不必晏的重复数据．又可以方便地查询数据。这组关系模式首先要用关系规范化理论规范化。构造好的逻辑结构，然后根据需要，从提高数据库性能的角度．进行非规范化处理。规范化和非规范化各有其优缺点，需要我们根据实际需求权衡处理。     

From Reduction-based to Reduction-free Normalization

We present a systematic construction of a reduction-free normalization function. Starting from a reduction-based normalization function, i.e., the transitive closure of a one-step reduction function, we successively subject it to refocusing (i.e., deforestation of the intermediate reduced terms), simplification (i.e., fusing auxiliary functions), refunctionalization (i.e., Church encoding), and direct-style transformation (i.e., the converse of the CPS transformation). We consider two simple examples and treat them in detail: for the first one, arithmetic expressions, we construct an evaluation function; for the second one, terms in the free monoid, we construct an accumulator-based flatten function. The resulting two functions are traditional reduction-free normalization functions.The construction builds on previous work on refocusing and on a functional correspondence between evaluators and abstract machines. It is also reversible.     

Normalization of discrete planar objects

The case is made for normalization of discrete planar objects prior to comparison with test objects and an expression for normalization is derived using a Euclidean distance function based on the underlying continuous boundaries of the objects and their prototypes. The results are given in both the spatial and the frequency domain; an analysis of errors due to the quantization introduced by using a discrete grid is also given.     

Normalization of Chinese chat language

Real-time communication platforms such as ICQ, MSN and online chat rooms are getting more popular than ever on the Internet. There are, however, real risks where criminals and terrorists can perpetrate illegal and criminal abuses. This highlights the security significance of accurate detection and translation of the chat language to its stand language counterpart. The language used on these platforms differs significantly from the standard language. This language, referred to as chat language, is comparatively informal, anomalous and dynamic. Such features render conventional language resources such as dictionaries, and processing tools such as parsers ineffective. In this paper, we present the NIL corpus, a chat language text collection annotated to facilitate training and testing of chat language processing algorithms. We analyse the NIL corpus to study the linguistic characteristics and contextual behaviour of a chat language. First we observe that majority of the chat terms, i.e. informal words in a chat text, is formed by phonetic mapping. We then propose the eXtended Source Channel Model (XSCM) for the normalization of the chat language, which is a process to convert messages expressed in a chat language to its standard language counterpart. Experimental results indicate that the performance of XSCM in terms of chat term recognition and normalization accuracy is superior to its Source Channel Model (SCM) counterparts, and is also more consistent over time.

存在多值依赖(MVD)的XML文档的规范化

讨论了在XML文档中存在多值依赖的情况下,如何规范XML文档,从而使XML文档有更小的冗余,以及更新、删除、插入异常。并在此基础上提出了一个规范化算法,来规范存在多值依赖的XML文档。并给出了算法的说明。