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Showing papers on "Class (philosophy) published in 2017"


Journal ArticleDOI
TL;DR: The genesis of these two formulas are reviewed, their effectiveness with that of a number of instances taken from the well-known Glänzel–Schubert class of models for the h-index are compared, and the Lambert-W formula provides a quite robust and effective ready-to-use rule that should be preferred to other known formulas if one’s goal is to derive a reliable estimate of theh-index.
Abstract: Of the existing theoretical formulas for the h-index, those recently suggested by Burrell (J Informetr 7:774---783, 2013b) and by Bertoli-Barsotti and Lando (J Informetr 9(4):762---776, 2015) have proved very effective in estimating the actual value of the h-index Hirsch (Proc Natl Acad Sci USA 102:16569---16572, 2005), at least at the level of the individual scientist. These approaches lead (or may lead) to two slightly different formulas, being based, respectively, on a "standard" and a "shifted" version of the geometric distribution. In this paper, we review the genesis of these two formulas--which we shall call the "basic" and "improved" Lambert-W formula for the h-index--and compare their effectiveness with that of a number of instances taken from the well-known Glanzel---Schubert class of models for the h-index (based, instead, on a Paretian model) by means of an empirical study. All the formulas considered in the comparison are "ready-to-use", i.e., functions of simple citation indicators such as: the total number of publications; the total number of citations; the total number of cited paper; the number of citations of the most cited paper. The empirical study is based on citation data obtained from two different sets of journals belonging to two different scientific fields: more specifically, 231 journals from the area of "Statistics and Mathematical Methods" and 100 journals from the area of "Economics, Econometrics and Finance", totaling almost 100,000 and 20,000 publications, respectively. The citation data refer to different publication/citation time windows, different types of "citable" documents, and alternative approaches to the analysis of the citation process ("prospective" and "retrospective"). We conclude that, especially in its improved version, the Lambert-W formula for the h-index provides a quite robust and effective ready-to-use rule that should be preferred to other known formulas if one's goal is (simply) to derive a reliable estimate of the h-index.

75 citations


Patent
Rajeev Dubey1, Navendu Jain1
14 Apr 2017
TL;DR: In this paper, a knowledge base can include a dictionary associated with classes of a model, e.g., an ontology, and a text segment that is not found in the dictionary can be received.
Abstract: A knowledge base can include a dictionary associated with classes of a model, e.g., an ontology. A text segment that is not found in the dictionary can be received. Feature(s) can be determined for the text segment and, based partly on providing the feature(s) to a classifier, a set of values can be determined. The distribution can include values respectively corresponding to the classes. One of the values can be greater than a predetermined threshold. That value can correspond to a class. An indication identifying the class can be presented via a user interface having functionality to provide input that the text segment is associated with the class, is not associated with the class, or is associated with another class. Based at least partly on adding a new class to the ontology, a precedence table indicating priorities between motifs defining relationships between classes of the ontology can be updated.

16 citations


Journal ArticleDOI
TL;DR: A generic set of midlevel visual shape features forms the basis for superordinate classification of novel objects along the animacy continuum, suggesting a class-like organization of items.
Abstract: Superordinate visual classification-for example, identifying an image as "animal," "plant," or "mineral"-is computationally challenging because radically different items (e.g., "octopus," "dog") must be grouped into a common class ("animal"). It is plausible that learning superordinate categories teaches us not only the membership of particular (familiar) items, but also general features that are shared across class members, aiding us in classifying novel (unfamiliar) items. Here, we investigated visual shape features associated with animate and inanimate classes. One group of participants viewed images of 75 unfamiliar and atypical items and provided separate ratings of how much each image looked like an animal, plant, and mineral. Results show systematic tradeoffs between the ratings, indicating a class-like organization of items. A second group rated each image in terms of 22 midlevel shape features (e.g., "symmetrical," "curved"). The results confirm that superordinate classes are associated with particular shape features (e.g., "animals" generally have high "symmetry" ratings). Moreover, linear discriminant analysis based on the 22-D feature vectors predicts the perceived classes approximately as well as the ground truth classification. This suggests that a generic set of midlevel visual shape features forms the basis for superordinate classification of novel objects along the animacy continuum.

15 citations


Posted Content
TL;DR: It is shown that under mild assumptions, both the global and local clustering coefficients converge to constants which may or may not be the same, and a central limit theorem for the number of nodes is derived.
Abstract: This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense regime, (ii) a sparse almost dense regime, (iii) a sparse regime with power-law behaviour, and (iv) an almost extremely sparse regime. We show that under mild assumptions, both the global and local clustering coefficients converge to constants which may or may not be the same. We also derive a central limit theorem for the number of nodes. Finally, we propose a class of models within this framework where one can separately control the latent structure and the global sparsity/power-law properties of the graph.

12 citations


Journal ArticleDOI
TL;DR: In this paper, a parameterized/schematic version of the CLA11 (P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11,P12,P13,P14,P15,P16,P17,P18,P19,P20,P21,P22,P23,P24,P25,P26,P27,P28,P29,P30,P31,P32,P33,P
Abstract: Clarithmetics are number theories based on computability logic (see http://www.csc.villanova.edu/~japaridz/CL/ ). Formulas of these theories represent interactive computational problems, and their "truth" is understood as existence of an algorithmic solution. Various complexity constraints on such solutions induce various versions of clarithmetic. The present paper introduces a parameterized/schematic version CLA11(P1,P2,P3,P4). By tuning the three parameters P1,P2,P3 in an essentially mechanical manner, one automatically obtains sound and complete theories with respect to a wide range of target tricomplexity classes, i.e. combinations of time (set by P3), space (set by P2) and so called amplitude (set by P1) complexities. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a solution from the given tricomplexity class and, furthermore, such a solution can be automatically extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a solution from the given tricomplexity class is represented by some theorem of the system. Furthermore, through tuning the 4th parameter P4, at the cost of sacrificing recursive axiomatizability but not simplicity or elegance, the above extensional completeness can be strengthened to intensional completeness, according to which every formula representing a problem with a solution from the given tricomplexity class is a theorem of the system. This article is published in two parts. The present Part I introduces the system and proves its completeness, while Part II is devoted to proving soundness.

12 citations


31 May 2017
TL;DR: This work presents a new approach to multi-class probability estimation by turning IVAPs and CVAPs into multiclass probabilistic predictors, which are experimentally more accurate than both uncalibrated predictors and existing calibration methods.
Abstract: Inductive (IVAP) and cross (CVAP) Venn–Abers predictors are computationally efficient algorithms for probabilistic prediction in binary classification problems. We present a new approach to multi-class probability estimation by turning IVAPs and CVAPs into multiclass probabilistic predictors. The proposed multi-class predictors are experimentally more accurate than both uncalibrated predictors and existing calibration methods.

10 citations


Posted Content
TL;DR: This work uses general discrete simulations of classical infinite-precision protocols to roughly partition the various fair-allocation problems into 3 classes: "easy" (constant number of rounds of logarithmic many bits), "medium" (poly-logarithsmic total communication), and "hard".
Abstract: We study classic cake-cutting problems, but in discrete models rather than using infinite-precision real values, specifically, focusing on their communication complexity Using general discrete simulations of classical infinite-precision protocols (Robertson-Webb and moving-knife), we roughly partition the various fair-allocation problems into 3 classes: "easy" (constant number of rounds of logarithmic many bits), "medium" (poly-logarithmic total communication), and "hard" Our main technical result concerns two of the "medium" problems (perfect allocation for 2 players and equitable allocation for any number of players) which we prove are not in the "easy" class Our main open problem is to separate the "hard" from the "medium" classes

8 citations


Journal ArticleDOI
TL;DR: The existence of infinitely many low-lying fundamental geodesics was proved in this article, answering a question of Einsiedler-Lindenstrauss-Michel-Venkatesh.
Abstract: A closed geodesic on the modular surface is "low-lying" if it does not travel "high" into the cusp. It is "fundamental" if it corresponds to an element in the class group of a real quadratic field. We prove the existence of infinitely many low-lying fundamental geodesics, answering a question of Einsiedler-Lindenstrauss-Michel-Venkatesh.

8 citations


Journal ArticleDOI
30 Jun 2017
TL;DR: The algorithm of the definition of dimension of link mechanism lengths of high classes (MHC) and their metric parameters at successive approach is offered in this work.
Abstract: It is necessary to make link mechanisms calculation to the strength at designing of flat link mechanisms of high class after definition of block diagrams and link linear sizes i.e. it is rationally to choose their forms and to determine the section sizes. The algorithm of the definition of dimension of link mechanism lengths of high classes (MHC) and their metric parameters at successive approach is offered in this work.

6 citations


Posted Content
TL;DR: An almost precise result in case of even $n$ is provided by proving that for $n \ge 4$ even, and some bounds on the number of queries needed to ask for larger $k$ are proved.
Abstract: The Plurality problem - introduced by Aigner \cite{A2004} - has many variants. In this article we deal with the following version: suppose we are given $n$ balls, each of them colored by one of three colors. A \textit{plurality ball} is one such that its color class is strictly larger than any other color class. Questioner wants to find a plurality ball as soon as possible or state there is no, by asking triplets (or $k$-sets, in general), while Adversary partition the triplets into color classes as an answer for the queries and wants to postpone the possibility of determining a plurality ball (or stating there is no). We denote by $A_p(n,3)$ the largest number of queries needed to ask if both play optimally (and Questioner asks triplets). We provide an almost precise result in case of even $n$ by proving that for $n \ge 4$ even we have $$\frac{3}{4}n-2 \le A_p(n,3) \le \frac{3}{4}n-\frac{1}{2},$$ and for $n \ge 3$ odd we have $$\frac{3}{4}n-O(\log n) \le A_p(n,3) \le \frac{3}{4}n-\frac{1}{2}.$$ We also prove some bounds on the number of queries needed to ask for larger $k$.

5 citations


Book ChapterDOI
28 Jul 2017
TL;DR: In this article, a rule-like semantics is proposed to treat meanings of names as known to every member of a society in a like manner, such that a name has an identical meaning not only every time it is used but for every member speaking to any other member.
Abstract: Structural semantics treats meanings of names as known to every member of a society in a like manner. That is, the name has an identical meaning not only every time it is used but for every member speaking to any other member. Members of both of these latter schools have proposed that the semantic aspects of language, like the grammatical aspects, have a rulelike character in the gametheoretic sense of rules. The consequences of proposing a rulelike semantics rather than focusing on the indexical properties of everyday language use may be seen by examining the nature of a society that members would experience if they did speak with a rulelike semantics. A phoneme, as a class of noncontrastive phone types that share a distinctive bundle of phonetic features that members of a society are presumed to use in discriminating between sounds, is analogous to a kin class.

Posted Content
TL;DR: In this paper, the authors argue that classical and Bayesian ideas about stopping rules do in fact "lend each other" the kind of "mutual support and clarification" that Savage had originally hoped to find.
Abstract: L.J. Savage once hoped to show that "the superficially incompatible systems of ideas associated on the one hand with [subjective Bayesianism] and on the other hand with [classical statistics]...lend each other mutual support and clarification." By 1972, however, he had largely "lost faith in the devices" of classical statistics. One aspect of those "devices" that he found objectionable is that differences among the "stopping rules" that are used to decide when to end an experiment which are "noninformative" from a Bayesian perspective can affect decisions made using a classical approach. Two experiments that produce the same data using different stopping rules seem to differ only in the intentions of the experimenters regarding whether or not they would have carried on if the data had been different, which seem irrelevant to the evidential import of the data and thus to facts about what actions the data warrant. I argue that classical and Bayesian ideas about stopping rules do in fact "lend each other" the kind of "mutual support and clarification" that Savage had originally hoped to find. They do so in a kind of case that is common in scientific practice, in which those who design an experiment have different interests from those who will make decisions in light of its results. I show that, in cases of this kind, Bayesian principles provide qualified support for the classical statistical practice of "penalizing" "biased" stopping rules. However, they require this practice in a narrower range of circumstances than classical principles do, and for different reasons. I argue that classical arguments for this practice are compelling in precisely the class of cases in which Bayesian principles also require it, and thus that we should regard Bayesian principles as clarifying classical statistical ideas about stopping rules rather than the reverse.

Journal ArticleDOI
TL;DR: In this paper, a parameterized/schematic version of the CLA11 (P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11,P12,P13,P14,P15,P16,P17,P18,P19,P20,P21,P22,P23,P24,P25,P26,P27,P28,P29,P30,P31,P32,P33,P
Abstract: Clarithmetics are number theories based on computability logic (see http://www.csc.villanova.edu/~japaridz/CL/ ). Formulas of these theories represent interactive computational problems, and their "truth" is understood as existence of an algorithmic solution. Various complexity constraints on such solutions induce various versions of clarithmetic. The present paper introduces a parameterized/schematic version CLA11(P1,P2,P3,P4). By tuning the three parameters P1,P2,P3 in an essentially mechanical manner, one automatically obtains sound and complete theories with respect to a wide range of target tricomplexity classes, i.e. combinations of time (set by P3), space (set by P2) and so called amplitude (set by P1) complexities. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a solution from the given tricomplexity class and, furthermore, such a solution can be automatically extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a solution from the given tricomplexity class is represented by some theorem of the system. Furthermore, through tuning the 4th parameter P4, at the cost of sacrificing recursive axiomatizability but not simplicity or elegance, the above extensional completeness can be strengthened to intensional completeness, according to which every formula representing a problem with a solution from the given tricomplexity class is a theorem of the system. This article is published in two parts. The previous Part I has introduced the system and proved its completeness, while the present Part II is devoted to proving soundness.

01 Jan 2017
TL;DR: In this paper, the authors used the National Research Foundation (NRF) grant for research supported by the South African Broadcasting Service (SBS) in South Africa to investigate the effect of gender discrimination.
Abstract: This work is based upon research supported by the National Research Foundation, South Africa (ref. CPRR13090132066 grant nr: 91497).

Posted Content
01 Jan 2017
TL;DR: In this paper, a class of sequential non-revelation mechanisms where hospitals make simultaneous take-it-or-leave-it o?ers to doctors that either accept or reject them is studied.
Abstract: We study a class of sequential non-revelation mechanisms where hospitals make simultaneous take-it-or-leave-it o?ers to doctors that either accept or reject them. We show that the mechanisms in this class are equivalent. They (weakly) implement the set of stable allocations in subgame perfect equilibrium. When all preferences are substitutable, the set of equilibria of the mechanisms in the class forms a lattice. Our results reveal a first-mover advantage absent in the model without contracts. We apply our findings to centralize school admissions problems, and we show obtaining pairwise stable allocations is possible through the immediate acceptance mechanism.Economic Literature Classification Numbers: C78, D78. Key words: Keywords: Many-to-many, contracts, ultimatum games.

Journal ArticleDOI
01 Oct 2017
TL;DR: In this paper, an approach to the synthesis of a neural network for a class of logical-arithmetic problems, based on the formation of a network of pre-constructed elementary functions, is proposed.
Abstract: One of the main problems facing the developer of a system with a neural network is the choice of the structure of a neural network that could solve the tasks. At present there are no unambiguous recommendations for choosing such a structure and such parameters as: the number of layers, the number of neurons in the layer, the type of neuron nonlinearity, the training method, the parameters of the training method, and others. The article considers an approach to the synthesis of a neural network for a class of logical-arithmetic problems, based on the formation of a network of pre-constructed elementary functions. The novelty of the proposed approach is the formation of a neural network using a well-known algorithm using pre-built functions. Thus, in the article elementary logical-arithmetic functions such as "and", "or", "exclusive or", "and-not", "or-not", "", "", ">", "

Journal ArticleDOI
TL;DR: A two- person game is defined and it is demonstrated that it can be used in order to define a model for any given intensional program of the class introduced in [13] and this model is shown to be identical to the minimum model constructed.

Posted Content
TL;DR: In this article, the authors studied monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary, following an original idea of the first author: tete-a-tete graphs and twists.
Abstract: We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary, following an original idea of the first author: tete-a-tete graphs and twists. We completely characterize mapping classes that can be represented by tete-a-tete twists, and generalize the notion to be able to represent any class of the mapping class group relative to the boundary which is boundary-free periodic. This improves previous work on the subject by C. Graf. Furthermore, we introduce the class of mixed tete-a-tete graphs and twists, and prove that mixed tete-a-tete twists contain monodromies of irreducible plane curve singularities. In a sequel paper, the fourth author and B. Sigurdsson have extended this to the reducible case.

Patent
09 Mar 2017
TL;DR: In this paper, a method for generating rules for rule-based reasoning includes the steps of starting from a set of generic reasoning rules and generating a set specific reasoning rules by substituting in at least one of the generic rules having more than one variable.
Abstract: A method for generating rules for rule-based reasoning includes the steps of starting from a set of generic reasoning rules generating a set of specific reasoning rules by substituting in at least one of the generic reasoning rules having more than one variable, at least one of the variables with (a) class(es) defined in an ontology.

Posted Content
TL;DR: It is proved that the iterative redefinition process in Constant structure closed semantic systems will quickly degenerate into a series of pairwise isomorphic states.
Abstract: Constant structure closed semantic systems are the systems each element of which receives its definition through the correspondent unchangeable set of other elements of the system. Discrete time means here that the definitions of the elements change iteratively and simultaneously based on the "neighbor portraits" from the previous iteration. I prove that the iterative redefinition process in such class of systems will quickly degenerate into a series of pairwise isomorphic states and discuss some directions of further research.

Posted Content
TL;DR: This work introduces a Boolean algebraic approach to formulate a general class of judgment aggregation problems and finds that, as the size of a group goes to infinity, PDW ensures the probability that the voting outcome is correct converges to one, while this holds for CDW only if an additional condition is satisfied.
Abstract: Imagine a group of individuals facing with a complicated yes-no question whose truth value is logically driven from multiple premises. Their purpose is to make a correct group judgment on the question based on their individual judgments. There are two types of ways to aggregate individual judgments: "the premise driven way" (PDW) and "the conclusion driven way" (CDW). We analyze which way is superior to the other to find a correct answer. In our analysis, we introduce a Boolean algebraic approach to formulate a general class of such judgment aggregation problems. We find that if a decision problem is conjunctive, then PDW is more likely to avoid "false acquittance," while CDW is more likely to avoid "false conviction". If a decision problem is disjunctive, the converse of this result holds. These conditions are sufficient to characterize intrinsic biases of aggregation procedures when an aggregation rule possesses no veto power. We also study the asymptotic properties of aggregation procedures, and find that, as the size of a group goes to infinity, PDW ensures the probability that the voting outcome is correct converges to one, while this holds for CDW only if an additional condition is satisfied.

Posted Content
TL;DR: A theoretical framework is developed that leads to the definition of the abstract concept of flow size in connection with the global quality of service (QoS) requirements of a network and shows that if a partitioned QoS problem is nested convex as formally defined in this work, then it can be solved in polynomial time.
Abstract: The problem of elephant flow detection has been the subject of intense research for the last fifteen years at least. However, previous research presumes the existence of the abstract concept of flow size, for which the current literature has no formal mathematical definition. In this paper, we develop a theoretical framework that leads to the definition of the abstract concept of flow size in connection with the global quality of service (QoS) requirements of a network. Our framework demonstrates that the problem of elephant flow detection is a particular case of the more general problem of mapping groups of flows onto an arbitrary number of network policies. With this view we introduce the concept of partitioned QoS and identify the convexity properties that lead to a formal definition of the concept of flow size. We demonstrate that metric-based approaches found in the existing literature provide a solution to one particular class of network problems, and that a precise definition of flow size can only be constructed starting from the partitioned QoS problem. Further, we show that if a partitioned QoS problem is nested convex as formally defined in this work, then it can be solved in polynomial time.

Patent
24 May 2017
TL;DR: In this article, a method and a device for pushing multimedia information is presented, which comprises steps: a target member whose age information is not determined yet in already-built class groups is searched in a client; a target class group to which the target member belongs is determined in the class groups; age information of known members whose age is determined already in the target class groups are acquired; according to the age of the known members, the target information of the target members is determined; and multimedia information corresponding to the ages of the targeted member is pushed to the target person.
Abstract: The invention discloses a method and a device for pushing multimedia information. The method comprises steps: a target member whose age information is not determined yet in already-built class groups is searched in a client; a target class group to which the target member belongs is determined in the class groups; age information of known members whose age information is determined already in the target class group is acquired; according to the age information of the known members, the age information of the target member is determined; and multimedia information corresponding to the age information of the target member is pushed to the target member. Thus, the technical problem that the multimedia information pushed to a user in the prior art is low in accuracy is solved.

Patent
27 Apr 2017
TL;DR: In this article, a computer stores a generic class attribute associated with a definition of generic classes, which includes a type variable declaration (TVD) associated with usage entries (VUEs) within the definition.
Abstract: Techniques herein process type variables to transform type parameters (TPs) of generic classes. In an embodiment, a computer stores a generic class attribute associated with a definition of a generic class. The generic class attribute includes a type variable declaration (TVD) for each TP. Each TVD is associated with usage entries (VUEs) within the definition. Each VUE indicates an actual type for use, within a portion of the definition, as the TP represented by the VUE. Based on how a particular portion of the definition uses a particular TP represented by a particular TVD of a particular VUE, the computer determines whether the particular VUE is to be assigned to a particular type or erased. In response to determining that the particular VUE is to be erased, the computer configures the particular VUE to indicate erasure. Otherwise, the computer assigns the particular type to the particular VUE.

Patent
Wang Lan1
04 May 2017
TL;DR: In this paper, the authors propose a system design device and method with which it is possible to increase description capability with a modeling language by making an expanded definition of a meta-model.
Abstract: [Problem] To provide a system design device and method with which it is possible to increase description capability with a modeling language by making an expanded definition of a meta-model. [Solution] The system design device according to one embodiment of the present invention is provided with a meta-model definition unit, a model construction unit, and a script file generation unit. The meta-model definition unit generates a second meta-model on the basis of a first meta-model described with the modeling language. The second meta-model includes: the first meta-model; a meta-model of a constraint condition class for describing constraint conditions; and a meta-model for defining the relationship (Association) between the constraint condition class and a relationship class in order to distinguish between the presence and absence of constraint conditions for the relationship class (Trace). The model construction unit constructs a model according to the second meta-model. The script file generation unit generates a script file that corresponds to the model.

Journal ArticleDOI
TL;DR: Eisenhauer et al. as mentioned in this paper proposed a more general definition of the wealthy, which encompasses that definition as well as ones based on the ability to live at higher standards of living than the poverty level over longer periods of time than one year while living off interest income alone.
Abstract: A definition of the wealthy was proposed in this journal [Eisenhauer, J. G. (2008). An economic definition of the middle class. Forum for Social Economics, 37, 103–113]. According to the definition, “the wealthy” are people who could live poorly for a year while living off the interest on their wealth. This paper suggests a more general definition of the wealthy, which encompasses that definition as well as ones based on the ability to live at higher standards of living than the poverty level over longer periods of time than one year while living off interest income alone. Previous empirical work is revisited to show new insights offered by the new definition. The evidence points to the reemergence of a rentier class.

Posted Content
TL;DR: In this article, it was shown that the generalized shift dynamical system is Li-Yorke sensitive if and only if it has at least one non-quasi-periodic point.
Abstract: In the following text, for finite discrete $X$ with at least two elements, nonempty countable $\Gamma$, and $\varphi:\Gamma\to\Gamma$ we prove the generalized shift dynamical system $(X^\Gamma,\sigma_\varphi)$ is densely chaotic if and only if $\varphi:\Gamma\to\Gamma$ does not have any (quasi-)periodic point. Hence the class of all densely chaotic generalized shifts on $X^\Gamma$ is intermediate between the class of all Devaney chaotic generalized shifts on $X^\Gamma$ and the class of all Li-Yorke chaotic generalized shifts on $X^\Gamma$. In addition, these inclusions are proper for infinite countable $\Gamma$. Moreover we prove $(X^\Gamma,\sigma_\varphi)$ is Li-Yorke sensitive (resp. sensitive, strongly sensitive, asymptotic sensitive, syndetically sensitive, cofinitely sensitive, multi-sensitive, ergodically sensitive, spatiotemporally chaotic, Li-Yorke chaotic) if and only if $\varphi:\Gamma\to\Gamma$ has at least one non-quasi-periodic point.