scholarly journals Counting peaks and valleys in $k$-colored Motzkin paths

10.37236/1913 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
A. Sapounakis ◽  
P. Tsikouras
Keyword(s):  
Fixed Number ◽  
Dyck Paths ◽  
Special Cases ◽  
Left And Right ◽  
High Level ◽  
Motzkin Paths

This paper deals with the enumeration of $k$-colored Motzkin paths with a fixed number of (left and right) peaks and valleys. Further enumeration results are obtained when peaks and valleys are counted at low and high level. Many well-known results for Dyck paths are obtained as special cases.

scholarly journals On Exact Sampling of Nonnegative Infinitely Divisible Random Variables

2012 ◽  
Vol 44 (3) ◽  
pp. 842-873 ◽  
Author(s):  
Zhiyi Chi
Keyword(s):  
Basic Result ◽  
Random Variables ◽  
Random Variable ◽  
Fixed Number ◽  
Rejection Sampling ◽  
Infinitely Divisible ◽  
Exact Sampling ◽  
Special Cases ◽  
Wide Range ◽  
Lévy Density

Nonnegative infinitely divisible (i.d.) random variables form an important class of random variables. However, when this type of random variable is specified via Lévy densities that have infinite integrals on (0, ∞), except for some special cases, exact sampling is unknown. We present a method that can sample a rather wide range of such i.d. random variables. A basic result is that, for any nonnegative i.d. random variable X with its Lévy density explicitly specified, if its distribution conditional on X ≤ r can be sampled exactly, where r > 0 is any fixed number, then X can be sampled exactly using rejection sampling, without knowing the explicit expression of the density of X. We show that variations of the result can be used to sample various nonnegative i.d. random variables.

scholarly journals Modular action language

2015 ◽  
Vol 16 (2) ◽  
pp. 189-235 ◽  
Author(s):  
DANIELA INCLEZAN ◽  
MICHAEL GELFOND
Keyword(s):  
Logic Programming ◽  
Medium Size ◽  
Programming System ◽  
Problem Structuring ◽  
System Description ◽  
Action Languages ◽  
Special Cases ◽  
Action Language ◽  
Stepwise Development ◽  
High Level

AbstractThe paper introduces a new modular action language,${\mathcal ALM}$, and illustrates the methodology of its use. It is based on the approach of Gelfond and Lifschitz (1993,Journal of Logic Programming 17, 2–4, 301–321; 1998,Electronic Transactions on AI 3, 16, 193–210) in which a high-level action language is used as a front end for a logic programming system description. The resulting logic programming representation is used to perform various computational tasks. The methodology based on existing action languages works well for small and even medium size systems, but is not meant to deal with larger systems that requirestructuring of knowledge.$\mathcal{ALM}$is meant to remedy this problem. Structuring of knowledge in${\mathcal ALM}$is supported by the concepts ofmodule(a formal description of a specific piece of knowledge packaged as a unit),module hierarchy, andlibrary, and by the division of a system description of${\mathcal ALM}$into two parts:theoryandstructure. Atheoryconsists of one or more modules with a common theme, possibly organized into a module hierarchy based on adependency relation. It contains declarations of sorts, attributes, and properties of the domain together with axioms describing them.Structuresare used to describe the domain's objects. These features, together with the means for defining classes of a domain as special cases of previously defined ones, facilitate the stepwise development, testing, and readability of a knowledge base, as well as the creation of knowledge representation libraries.

Joint distributions of successes, failures and patterns in enumeration problems

2000 ◽  
Vol 32 (3) ◽  
pp. 866-884 ◽  
Author(s):  
S Chadjiconstantinidis ◽  
D. L. Antzoulakos ◽  
M. V. Koutras
Keyword(s):  
Joint Distribution ◽  
Joint Probability ◽  
Fixed Number ◽  
Composite Pattern ◽  
Joint Distributions ◽  
Special Cases ◽  
Enumeration Problems ◽  
Binomial Type ◽  
Probability Mass ◽  
Mass Functions

Let ε be a (single or composite) pattern defined over a sequence of Bernoulli trials. This article presents a unified approach for the study of the joint distribution of the number Sn of successes (and Fn of failures) and the number Xn of occurrences of ε in a fixed number of trials as well as the joint distribution of the waiting time Tr till the rth occurrence of the pattern and the number STr of successes (and FTr of failures) observed at that time. General formulae are developed for the joint probability mass functions and generating functions of (Xn,Sn), (Tr,STr) (and (Xn,Sn,Fn),(Tr,STr,FTr)) when Xn belongs to the family of Markov chain imbeddable variables of binomial type. Specializing to certain success runs, scans and pattern problems several well-known results are delivered as special cases of the general theory along with some new results that have not appeared in the statistical literature before.

scholarly journals The Politicization of Society and the Religious Issues in Modern Russia

2020 ◽  
Vol 22 (4) ◽  
pp. 647-663
Author(s):  
Vasily K. Pinkevich
Keyword(s):  
The State ◽  
Private Life ◽  
Russian Society ◽  
Ruling Class ◽  
Extensive Discussion ◽  
Religious Policy ◽  
Special Cases ◽  
The One ◽  
The Right ◽  
High Level

The purpose of the article is to trace the connection between the change in the religious policy of the state and the anti-clerical protests of the 2016-2020s. Statements against Church restitution and the construction of churches have caused extensive discussion, which has given rise to a number of contradictory, sometimes mutually exclusive interpretations. According to the author, the reason for these protests was not private reasons, but deeper reasons related to the religious policy of the state. The author pays special attention to changes in religious legislation, which led to increased control over the private life of citizens and infringement of the right to freedom of ideological choice. The article points out that the religious issue has divided Russian society: the ruling class on the one hand, and a significant part of citizens on the other, have become increasingly different in understanding the place and role of religion in the life of the country. According to the author, the protests in Yekaterinburg, St. Petersburg, and Moscow were special cases of numerous manifestations of politicization of society and growing dissatisfaction with the state of state-confessional relations in modern Russia. The author concludes that the degree of conflict, the high level of solidarity actions, a diverse and resonant series of events, as well as the level of ideological discussion allow us to classify these events as political and plebiscite.

scholarly journals Constructing combinatorial operads from monoids

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Samuele Giraudo
Keyword(s):  
Rooted Trees ◽  
Parking Functions ◽  
Combinatorial Objects ◽  
Dyck Paths ◽  
International Audience ◽  
Motzkin Paths ◽  
Planar Rooted Trees

International audience We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar combinatorial objects: parking functions, packed words, planar rooted trees, generalized Dyck paths, Schröder trees, Motzkin paths, integer compositions, directed animals, etc. We also retrieve some known operads: the magmatic operad, the commutative associative operad, and the diassociative operad.

scholarly journals A Short Approach to Catalan Numbers Modulo $2^r$

10.37236/664 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Guoce Xin ◽  
Jing-Feng Xu
Keyword(s):  
Catalan Numbers ◽  
Binary Expansion ◽  
Dyck Paths ◽  
Combinatorial Interpretations ◽  
Recent Classification ◽  
Motzkin Paths

We notice that two combinatorial interpretations of the well-known Catalan numbers $C_n=(2n)!/n!(n+1)!$ naturally give rise to a recursion for $C_n$. This recursion is ideal for the study of the congruences of $C_n$ modulo $2^r$, which attracted a lot of interest recently. We present short proofs of some known results, and improve Liu and Yeh's recent classification of $C_n$ modulo $2^r$. The equivalence $C_{n}\equiv_{2^r} C_{\bar n}$ is further reduced to $C_{n}\equiv_{2^r} C_{\tilde{n}}$ for simpler $\tilde{n}$. Moreover, by using connections between weighted Dyck paths and Motzkin paths, we find new classes of combinatorial sequences whose $2$-adic order is equal to that of $C_n$, which is one less than the sum of the digits of the binary expansion of $n+1$.

scholarly journals Digital reconstruction of the mandible of an adultLesothosaurus diagnosticuswith insight into the tooth replacement process and diet

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e3054 ◽  
Author(s):  
Lara Sciscio ◽  
Fabien Knoll ◽  
Emese M. Bordy ◽  
Michiel O. de Kock ◽  
Ragna Redelstorff
Keyword(s):  
Ct Scanning ◽  
Lower Jurassic ◽  
Micro Ct ◽  
Tooth Replacement ◽  
Dental Wear ◽  
Digital Reconstruction ◽  
Replacement Process ◽  
Left And Right ◽  
High Level ◽  
Insight Into

Fragmentary caudal ends of the left and right mandible assigned toLesothosaurus diagnosticus, an early ornithischian, was recently discovered in the continental red bed succession of the upper Elliot Formation (Lower Jurassic) at Likhoele Mountain (Mafeteng District) in Lesotho. Using micro-CT scanning, this mandible could be digitally reconstructed in 3D. The replacement teeth within the better preserved (left) dentary were visualised. The computed tomography dataset suggests asynchronous tooth replacement in an individual identified as an adult on the basis of bone histology. Clear evidence for systematic wear facets created by attrition is lacking. The two most heavily worn teeth are only apically truncated. Our observations of this specimen as well as others do not support the high level of dental wear expected from the semi-arid palaeoenvironment in whichLesothosaurus diagnosticuslived. Accordingly, a facultative omnivorous lifestyle, where seasonality determined the availability, quality, and abundance of food is suggested. This would have allowed for adaptability to episodes of increased environmental stress.

scholarly journals Dyck paths, Motzkin paths and traffic jams

2004 ◽  
Vol 2004 (10) ◽  
pp. P10007 ◽  
Author(s):  
R A Blythe ◽  
W Janke ◽  
D A Johnston ◽  
R Kenna
Keyword(s):  
Traffic Jams ◽  
Dyck Paths ◽  
Motzkin Paths

scholarly journals Party Control, Party Competition and Public Service Performance

2012 ◽  
Vol 42 (3) ◽  
pp. 641-660 ◽  
Author(s):  
George A. Boyne ◽  
Oliver James ◽  
Peter John ◽  
Nicolai Petrovsky
Keyword(s):  
Public Service ◽  
Local Governments ◽  
Mixed Model ◽  
Party Competition ◽  
Service Performance ◽  
Right Wing ◽  
Party Control ◽  
Left And Right ◽  
And Performance ◽  
High Level

This article assesses party effects on the performance of public services. A policy-seeking model, hypothesizing that left and right party control affects performance, and an instrumental model, where all parties strive to raise performance, are presented. The framework also suggests a mixed model in which party effects are contingent on party competition, with parties raising performance as increasing party competition places their control of government at increasing risk. These models are tested against panel data on English local governments’ party control and public service performance. The results question the traditional account of left and right parties, showing a positive relationship between right-wing party control and performance that is contingent on a sufficiently high level of party competition. The findings suggest left–right models should be reframed for the contemporary context.

scholarly journals Generalized locomotion of brittle stars with a flexible number of arms

2019 ◽  
Author(s):  
Daiki Wakita ◽  
Katsushi Kagaya ◽  
Hitoshi Aonuma
Keyword(s):  
Single Species ◽  
Fixed Number ◽  
Nerve Ring ◽  
Brittle Stars ◽  
Decentralized System ◽  
Quantitative Indices ◽  
Front Position ◽  
Symmetrical Body ◽  
Left And Right ◽  
Bayesian Statistical Modeling

AbstractTypical brittle stars have five radially symmetrical arms, which coordinate to move their body in a certain direction. However, some species of them show individual difference in the number of arms. We found this trait unique since intact legged animals each own a fixed number of limbs in general. How does a single species manage such different numbers of motile organs to realize adaptive locomotion? We here described four-, five-, six-, and seven-armed locomotion with the aim to generalize a common rule which is flexible with arm numbers in brittle stars. We mechanically stimulated an arm inOphiactis brachyaspisto analyze escape direction and arm movements. Gathering quantitative indices and employing Bayesian statistical modeling, we figured out an average locomotion: regardless of the total number of arms, a front position emerges at one of the second neighboring arms to a mechanically stimulated arm, while side arms adjacent to the front synchronously work as left and right rowers. We suggest a model where some afferent signal runs either clockwise or anticlockwise along the nerve ring while linearly counting how many arms it passes. This idea would explain how ‘left and right’ emerges in a radially symmetrical body via a decentralized system.

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