The Characterization of Graphs Whose Sandpile Group has Fixed Number of Generators

AbstractIt is well known that simply typed λ-terms can be used to represent numbers, as well as some other data types. We show that λ-terms of each fixed (but possibly very complicated) type can be described by a finite piece of information (a set of appropriately defined intersection types) and by a vector of natural numbers. On the one hand, the description is compositional: having only the finite piece of information for two closed λ-terms M and N, we can determine its counterpart for MN, and a linear transformation that applied to the vectors of numbers for M and N gives us the vector for MN. On the other hand, when a λ-term represents a natural number, then this number is approximated by a number in the vector corresponding to this λ-term. As a consequence, we prove that in a λ-term of a fixed type, we can store only a fixed number of natural numbers, in such a way that they can be extracted using λ-terms. More precisely, while representing k numbers in a closed λ-term of some type, we only require that there are k closed λ-terms M1,. . .,Mk such that Mi takes as argument the λ-term representing the k-tuple, and returns the i-th number in the tuple (we do not require that, using λ-calculus, one can construct the representation of the k-tuple out of the k numbers in the tuple). Moreover, the same result holds when we allow that the numbers can be extracted approximately, up to some error (even when we only want to know whether a set is bounded or not). All the results remain true when we allow the Y combinator (recursion) in our λ-terms, as well as uninterpreted constants.

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Free generators in free inverse semigroups

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700045251 ◽

1972 ◽

Vol 7 (3) ◽

pp. 407-424 ◽

Cited By ~ 26

Author(s):

N.R. Reilly

Keyword(s):

Inverse Semigroup ◽

Inverse Semigroups ◽

Idempotent Element ◽

Necessary And Sufficient Condition ◽

Countable Number ◽

Number Of Generators ◽

Free Inverse Semigroup ◽

Free Generators ◽

Necessary And Sufficient

Using the characterization of the free inverse semigroup F on a set X, given by Scheiblich, a necessary and sufficient condition is found for a subset K of an inverse semigroup S to be a set of free generators for the inverse sub semigroup of S generated by K. It is then shown that any non-idempotent element of F generates the free inverse semigroup on one generator and that if |X| > 2 then F contains the free inverse semigroup on a countable number of generators. In addition, it is shown that if |X| = 1 then F does not contain the free inverse semigroup on two generators.

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The Alternation Hierarchy for the Theory of mu-lattices

BRICS Report Series ◽

10.7146/brics.v7i29.20163 ◽

2000 ◽

Vol 7 (29) ◽

Cited By ~ 2

Author(s):

Luigi Santocanale

Keyword(s):

Fixed Point ◽

Fixed Number ◽

Hierarchy Problem ◽

Explicit Characterization

The alternation hierarchy problem asks whether every mu-term, that is a term built up using also a least fixed point constructor as well as a greatest fixed point constructor, is equivalent to a mu-term where the number of nested fixed point of a different type is bounded by a fixed number. In this paper we give a proof that the alternation hierarchy for the theory of mu-lattices is strict, meaning that such number does not exist if mu-terms are built up from the basic lattice operations and are interpreted as expected. The proof relies on the explicit characterization of free mu-lattices by means of games and strategies.

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On Realization and Characterization of Topological Indices

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.a4135.119119 ◽

2019 ◽

Vol 9 (1) ◽

pp. 715-718

Keyword(s):

Topological Index ◽

Fixed Number ◽

Topological Indices ◽

Molecular Structures ◽

Real Numbers ◽

Graph Invariants ◽

Chemical Graph ◽

Zagreb Indices ◽

Chemical Graph Theory

In chemical graph theory, topological index is one of the graph invariants which is a fixed number based on structure of a graph. Topological index is used as one of the tool to analyze molecular structures and for proper and optimal design of nanostructure. In this paper we realize the real numbers that are topological indices such as Zagreb indices, Randic index, NK-index, multiplicative F-index and multiplicative Zagreb indices along with some characterizations.

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m-full ideals

Nagoya Mathematical Journal ◽

10.1017/s0027763000000908 ◽

1987 ◽

Vol 106 ◽

pp. 101-111 ◽

Cited By ~ 28

Author(s):

Junzo Watanabe

Keyword(s):

Local Ring ◽

Dimensional Case ◽

Flat Extension ◽

Basic Properties ◽

Number Of Generators ◽

Low Dimensional

An ideal a of a local ring (R, m) is called m-full if am: y = a for some y in a certain faithfully flat extension of R. The definition is due to Rees (unpublished) and he had obtained some elementary results (also unpublished). The present paper concerns some basic properties of m-full ideals. One result is the characterization of m-fullness in terms of the minimal number of generators of ideal, generalizing his result in a low dimensional case (Theorem 2, § 2).

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Firing Patterns in the Parallel Chip-Firing Game

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.2421 ◽

2014 ◽

Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽

Author(s):

Ziv Scully ◽

Tian-Yi Jiang ◽

Yan Zhang

Keyword(s):

Simple Model ◽

Complete Characterization ◽

Local Behavior ◽

Emergent Complexity ◽

Self Organized ◽

Chip Firing ◽

Self Organized Criticality ◽

International Audience ◽

Sandpile Group

International audience The $\textit{parallel chip-firing game}$ is an automaton on graphs in which vertices "fire'' chips to their neighbors. This simple model, analogous to sandpiles forming and collapsing, contains much emergent complexity and has connections to different areas of mathematics including self-organized criticality and the study of the sandpile group. In this work, we study $\textit{firing sequences}$, which describe each vertex's interaction with its neighbors in this game. Our main contribution is a complete characterization of the periodic firing sequences that can occur in a game, which have a surprisingly simple combinatorial description. We also obtain other results about local behavior of the game after introducing the concept of $\textit{motors}$. Le $\textit{parallel chip-firing game}$, c’est une automate sur les graphiques, dans lequel les sommets “tirent” des jetons à leurs voisins. Ce modèle simple, semblable aux tas de sable qui forment et s’affaissent, contient beaucoup de complexité émergente et a des connections avec différents domaines de mathématiques, incluant le $\textit{self-organized criticality}$ et l’étude du $\textit{sandpile group}$. Dans ce projet, on étudie les $\textit{firing sequences}$, qui décrivent les interactions de chaque sommet avec ses voisins dans le jeu. Notre contribution principale est une caractérisation complète des séquences de tir qui peuvent arriver dans une jeu, qui ont une description combinatoire assez simple. Nous obtenonsaussi d'autres résultats sur le conduite locale du jeu après l’introduction du concept des $\textit{motors}$.

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A novel image-processing based method for the automatic detection, extraction and characterization of marine mammal tonal calls

Journal of the Marine Biological Association of the United Kingdom ◽

10.1017/s0025315409000927 ◽

2009 ◽

Vol 90 (8) ◽

pp. 1667-1684 ◽

Cited By ~ 6

Author(s):

Antonio Sánchez-García ◽

Patricio Muñoz-Esparza ◽

José Luis Sancho-Gomez

Keyword(s):

Image Processing ◽

Radial Basis Function ◽

Basis Function ◽

Marine Mammal ◽

Automatic Detection ◽

Fixed Number ◽

Automatic Method ◽

Contour Extraction ◽

Time Frequency

A novel, automatic method for the detection, extraction and characterization of marine mammal tonal calls is presented. Signals are automatically detected from the spectrogram, isolated using region-based segmentation, extracted and finally characterized by means of a fixed number of radial basis function (RBF) coefficients. A total of sixteen RBF coefficients are sufficient to accurately capture the time–frequency information contained in the calls. These coefficients can be later used to classify signals based on their characteristics. New specific functions for contour extraction and cross-resolution have been developed. The performance of the method has been extensively tested using simulated signals and a set of recordings covering a significant range of situations that can be encountered at sea.

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Structural Health Monitoring for Rotating Imbalance and Misalignment

Manufacturing ◽

10.1115/imece2003-42322 ◽

2003 ◽

Author(s):

S. G. Mattson ◽

S. M. Pandit ◽

S. A. Kubow

Keyword(s):

Pulse Signal ◽

Fixed Number ◽

Second Development ◽

Gear Mesh ◽

Characteristic Roots ◽

Spectral Estimates ◽

Spectral Peaks ◽

Shaft Misalignment ◽

Single Number

The dynamics of rotating machinery are dominated by responses due to shaft and drive train characteristics such as imbalance, misalignment, gear mesh, and bearings. These phenomena occur a fixed number of times every revolution, and are related to rotational speed. This paper presents a new method for condition monitoring of such phenomena. An autoregressive model used for condition assessment is fit to the pulse signal. Decomposition of the model yields its characteristic roots, which contain the frequency, damping value, and variance of the signal component. The model also provides an analytical spectrum yielding clear spectral peaks with extremely accurate levels. The illustrated results are based on an experiment built to simulate a rotating imbalance, shaft misalignment, or a combination of the two. Three areas of improvement are identified. The first is characterization of extra information in the speed signal, eliminating the need for an added measurement that must be related to the speed. The second development is a single number estimate of energies at defect frequencies, eliminating subjective interpretation of spectral plots. The third enhancement is the technique’s ability to make accurate spectral estimates based on limited data, allowing the technician to handle situations where rapid speed changes are unavoidable.

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Epidemiologic characterization of bovine tuberculosis in the State of Rondônia, Brazil

Semina Ciências Agrárias ◽

10.5433/1679-0359.2016v37n5supl2p3639 ◽

2016 ◽

Vol 37 (5Supl2) ◽

pp. 3639 ◽

Cited By ~ 1

Author(s):

Fabiano Benitez Vendrame ◽

Marcos Amaku ◽

Fernando Ferreira ◽

Evelise Oliveira Telles ◽

José Henrique Hildebrand Grisi-Filho ◽

...

Keyword(s):

Bovine Tuberculosis ◽

Tuberculin Test ◽

Reproductive Activity ◽

Cross Sectional Study ◽

Fixed Number ◽

The State ◽

Cross Sectional ◽

Apparent Prevalence ◽

Primary Sample

A cross sectional study was performed between June 2009 and March 2010 to determine the situation of bovine tuberculosis (bTB) in Rondônia. The state was divided into three regions and, in each of them, 300 farms with reproductive activity were randomly chosen and considered as primary sample units. In the selected farms, an epidemiologic questionnaire was applied. A fixed number of bovine females older than two years of age was randomly selected and tested through comparative cervical tuberculin test. Considering the State of Rondônia, the apparent prevalence of bTB positive farms was 2.3% (95% CI = 1.5–3.5%). The prevalence in the regions varied from 1.7% (95% CI = 0.7 – 4%) to 3% (95% CI = 1.6–5.7%). The apparent prevalence of bTB positive animals in the State of Rondônia was 0.12% (95% CI = 0.06–0.25%) and varied from 0.08% (95% CI = 0.04–0.18%) to 0.15% (95% CI = 0.07–0.33%) in the regions. The risk factor associated to tuberculosis in the State of Rondônia was the acquisition of animals (OR = 7.1; 95% CI = 1.6–31.1). The State of Rondônia should implement a surveillance system to detect bTB-infected herds to certify them as bTB-free. Moreover, an efficient health education program to inform farmers to test replacement animals for bTB prior to introduction in their herds should also be implemented.

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