scholarly journals Lempel-Ziv Parsing for Sequences of Blocks

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 359
Author(s):  
Dmitry Kosolobov ◽  
Daniel Valenzuela

The Lempel-Ziv parsing (LZ77) is a widely popular construction lying at the heart of many compression algorithms. These algorithms usually treat the data as a sequence of bytes, i.e., blocks of fixed length 8. Another common option is to view the data as a sequence of bits. We investigate the following natural question: what is the relationship between the LZ77 parsings of the same data interpreted as a sequence of fixed-length blocks and as a sequence of bits (or other “elementary” letters)? In this paper, we prove that, for any integer b>1, the number z of phrases in the LZ77 parsing of a string of length n and the number zb of phrases in the LZ77 parsing of the same string in which blocks of length b are interpreted as separate letters (e.g., b=8 in case of bytes) are related as zb=O(bzlognz). The bound holds for both “overlapping” and “non-overlapping” versions of LZ77. Further, we establish a tight bound zb=O(bz) for the special case when each phrase in the LZ77 parsing of the string has a “phrase-aligned” earlier occurrence (an occurrence equal to the concatenation of consecutive phrases). The latter is an important particular case of parsing produced, for instance, by grammar-based compression methods.

1977 ◽  
Vol 9 (1) ◽  
pp. 191-195 ◽  
Author(s):  
Thomas L. Sporleder ◽  
Robert A. Skinner

Several definitions of diversification exist. Typically, the concept is dynamic and refers to the relationship among various activities or enterprises in which the firm is engaged. As new activities are acquired by a firm from some existing base of activities, complementarity of the newly acquired activity relative to the existing base is subjectively determined. Judgment is rendered on whether the result represents diversification or conglomeration.Conventional wisdom has not succinctly differentiated between diversification and conglomeration. Some writers have considered conglomeration a special case of diversification [2, 7]. For purposes of this paper, this taxonomic argument need not be settled.


2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.


2021 ◽  
Vol 18 (180) ◽  
pp. 20210334
Author(s):  
Liane Gabora ◽  
Mike Steel

Natural selection successfully explains how organisms accumulate adaptive change despite that traits acquired over a lifetime are eliminated at the end of each generation. However, in some domains that exhibit cumulative, adaptive change—e.g. cultural evolution, and earliest life—acquired traits are retained; these domains do not face the problem that Darwin’s theory was designed to solve. Lack of transmission of acquired traits occurs when germ cells are protected from environmental change, due to a self-assembly code used in two distinct ways: (i) actively interpreted during development to generate a soma, and (ii) passively copied without interpretation during reproduction to generate germ cells. Early life and cultural evolution appear not to involve a self-assembly code used in these two ways. We suggest that cumulative, adaptive change in these domains is due to a lower-fidelity evolutionary process, and model it using reflexively autocatalytic and foodset-generated networks. We refer to this more primitive evolutionary process as self–other reorganization (SOR) because it involves internal self-organizing and self-maintaining processes within entities, as well as interaction between entities. SOR encompasses learning but in general operates across groups. We discuss the relationship between SOR and Lamarckism, and illustrate a special case of SOR without variation.


2020 ◽  
Vol 34 (04) ◽  
pp. 5444-5453
Author(s):  
Edward Raff ◽  
Charles Nicholas ◽  
Mark McLean

Prior work inspired by compression algorithms has described how the Burrows Wheeler Transform can be used to create a distance measure for bioinformatics problems. We describe issues with this approach that were not widely known, and introduce our new Burrows Wheeler Markov Distance (BWMD) as an alternative. The BWMD avoids the shortcomings of earlier efforts, and allows us to tackle problems in variable length DNA sequence clustering. BWMD is also more adaptable to other domains, which we demonstrate on malware classification tasks. Unlike other compression-based distance metrics known to us, BWMD works by embedding sequences into a fixed-length feature vector. This allows us to provide significantly improved clustering performance on larger malware corpora, a weakness of prior methods.


2021 ◽  
pp. 54-77
Author(s):  
Daniel Greco

This chapter defends the possible worlds framework for modeling the contents of belief. Both the threats against which the chapter defends it—the problems of coarse grain—and the ‘fragmentationist’ response it offers are familiar. At least as a sociological matter, the fragmentationist response has been unpersuasive, likely because it can look like an ad hoc patch—an unmotivated epicycle aimed at saving a flailing theory from decisive refutation. The chapter offers two responses to this charge. First, the problems of coarse grain aren’t unique to the possible worlds framework and indeed arise for anyone who accepts certain very attractive views about the relationship between beliefs, desires, and action. Second, the fragmentationist response to these problems is in fact a special case of an independently motivated, ‘modest’ approach to model-building in philosophy.


Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].


2014 ◽  
Vol 8 (2) ◽  
Author(s):  
Simone Elisabeth Lang

AbstractIn describing the position of the narrator, research in literary studies generally follows Gérard Genette’s pioneering theory of narrative in distinguishing between the homo- and heterodiegetic type of narrator. This categorization is not sufficient to allow the position of the narrator to be described properly. The different ways in which the terms are used in literary studies reveal a shortcoming in the distinction behind them. Even in Genette’s work, there is a contradiction between the definition and the names of the two categories: Genette defines homo- and heterodiegesis with reference to the narrator’s presence in the narrated story, whereas he elsewhere states that the diegesis (in the sense of FrenchThe present article aims to do just that, starting from a theoretical standpoint. Thus, the different types of narrator that are possible are sketched in outline, and then explained with the help of examples.I begin by exposing the problems that result from using the terms in Genette’s manner (1), in order then to develop a list of possible narratorial standpoints based on the one hand on the involvement of the narratorial instance in the narrated world and on the other on its involvement in the story. By establishing separation of the two aspects as a ground rule in this way, a number of misunderstandings that are due to the varied ways in which the terminology has been used to date can be overcome.There follows a description of those cases that are unambiguously hetero- and homodiegetic (2), after which the problematic cases are considered (3), yielding the different types of homodiegetic narration that are possible. This latter set of distinctions will, like the others, shed light on the contours of the different narratorial positions and thus be capable of being put profitably into practice in textual interpretation. Accordingly, what is suggested is a way of using the terms that is first unambiguous and second beneficial to the interpretation of works, thus doing justice to the heuristic importance of narratology (see Kindt/Müller 2003; Stanzel 2002, 19).Thus, whereas the concept of diegesis provides the foundation for a distinction based on an ontological criterion that divides homo- and heterodiegesis from each other, the relationship between story and narrator is used to describe various types of homodiegetic narration. In the process, there come to light two types that are distinguished from each other by involvement in events (›homodiegetic, in the story‹ and ›homodiegetic, not in the story‹ narrators). If the narrator is not involved in events, the question arises of whether it would in principle have been possible for him to be involved in events, which is the norm with ›homodiegetic, not in the story‹ narrators, or whether a physical impossibility is the reason for his lack of involvement in the story. A special case of the ›homodiegetic, not in the story‹ narrator can be derived from this: peridiegetic narration: whereas narratorial instances of the ›homodiegetic, in the story‹ and ›homodiegetic, not in the story‹ types could in principle have been involved in the action and those of the ›homodiegetic, in the story‹ type actually were, peridiegetic narrators are marked by the fact that they cannot have been involved in the events.In summary, it will be shown that the concept of homodiegesis – in particular in the form in which it has previously been used, where links with the action and appearance in the story were not kept distinct – is in effect an umbrella term that brings together a number of possible forms. There is a prominent distinction between the ›homodiegetic, in the story‹ and the ›homodiegetic, not in the story‹ types of narrator (these types are represented in the present article by the old lawyer in Leo Perutz’s »The Beaming Moon« and the narrator who is a friend of Nathanael in E. T. A. Hoffmann’s »Sandman« respectively). The different degrees of homodiegetic narrator, which have often been mentioned in previous research and are defined by the strength of the character’s presence in the narrated world (from an uninvolved witness to an autodiegetic protagonist), are also to be situated between these two poles.It will also be shown in the process that the case of the narrator who is, for reasons of physical difference, not involved in events (the peridiegetic narrator) should be treated as a form of homodiegesis (for instance the schoolmaster in Theodor Storm’s


1999 ◽  
Vol 11 (4) ◽  
pp. 274-282 ◽  
Author(s):  
Takayoshi Yamada ◽  
◽  
Sushanta Kumar Saha ◽  
Nobuharu Mimura ◽  
Yasuyuki Funahashi ◽  
...  

We analyze stability of planar grasp using a 2D virtual spring model. A 2D virtual spring model is widely used to explore frictionless grasp, but the direction of contact force has not been studied for a grasped object displaced by external disturbance. Finger displacement is restricted to the normal at initial contact. We introduce a 2D spring model for a frictionless case. The direction of contact force is explicitly formulated. Using potential energy, we analyze stability of frictionless grasp and show that the 1D-spring model is a special case of our proposed 2D-spring model. Frictional grasp stability is also studied using rolling contact. Numerical examples of 2-fingered grasp demonstrate the effects of parameters such as spring stiffness and contact force. It is shown that an optimum force exists for stabilizing frictionless grasp. It is proved that friction enhances grasp stability from the relationship between frictionless and frictional stiffness matrices. Stiffness conditions for stabilizing 3-fingered grasp is clarified.


1978 ◽  
Vol 83 (2) ◽  
pp. 269-272 ◽  
Author(s):  
R. M. Loynes

1. Summary and introductionIn (5) a weak convergence result for U-statistics was obtained as a special case of a reverse martingale theorem; in (7) Miller and Sen obtained another such result for U-statistics by a direct argument. As they stand these results are not very closely connected, since one is concerned with U-statistics Uk for k ≥ n, while the other deals with Uk for k ≤ n, but if one instead thinks of k as unrestricted and transforms the random functions Xn which enter into one of these results into new functions Yn by setting Yn(t) = tXn(t−1) one finds that the Yn are (aside from variations in interpolated values) just the functions with which the other result is concerned. As the limiting Wiener process W is well-known to have the property that tW(t−1) is another Wiener process it is not too surprising that both results should hold, and part of the purpose of this paper is to provide a general framework within which the relationship between these results will become clear. A second purpose is to illustrate the simplification that the martingale property brings to weak convergence studies; this is shown both in the U-statistic example and in a new proof of the convergence of the empirical process.


1969 ◽  
Vol 47 (22) ◽  
pp. 2519-2524 ◽  
Author(s):  
A. P. Verma

In this paper, one special case of oil–water imbibition phenomena in a cracked porous medium of a finite length is analytically discussed. The equation for the linear countercurrent imbibition is a nonlinear differential equation whose solution has been obtained by a perturbation technique. For definiteness, specific results have been used for the relationship between relative permeability and phase saturation) impregnation function, oil–water viscosity ratio, and capillary pressure dependence on phase saturation due to Jones, Bokserman et al., Evgen'ev, and Oroveanu, respectively. An expression for the wetting phase saturation has been derived.


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