scholarly journals On Two-Sided Gamma-Positivity for Simple Permutations

10.37236/7472 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Ron M. Adin ◽  
Eli Bagno ◽  
Estrella Eisenberg ◽  
Shulamit Reches ◽  
Moriah Sigron
Keyword(s):  
Negative Integer ◽  
Supporting Evidence ◽  
Decomposition Tree ◽  
Analogous Statement ◽  
Eulerian Polynomial ◽  
Integer Coefficients ◽  
Common Distribution ◽  
Substitution Decomposition ◽  
The Common

Gessel conjectured that the two-sided Eulerian polynomial, recording the common distribution of the descent number of a permutation and that of its inverse, has non-negative integer coefficients when expanded in terms of the gamma basis. This conjecture has been proved recently by Lin.We conjecture that an analogous statement holds for simple permutations, and use the substitution decomposition tree of a permutation (by repeated inflation) to show that this would imply the Gessel-Lin result. We provide supporting evidence for this stronger conjecture.

Optimal selection of stochastic intervals under a sum constraint

1987 ◽  
Vol 19 (2) ◽  
pp. 454-473 ◽  
Author(s):  
E. G. Coffman ◽  
L. Flatto ◽  
R. R. Weber
Keyword(s):  
Decision Rule ◽  
Selection Process ◽  
Random Variables ◽  
Optimal Threshold ◽  
Optimal Selection ◽  
Expected Number ◽  
Common Distribution ◽  
The Common ◽  
Image Position ◽  
Selection Of

We model a selection process arising in certain storage problems. A sequence (X1, · ··, Xn) of non-negative, independent and identically distributed random variables is given. F(x) denotes the common distribution of the Xi′s. With F(x) given we seek a decision rule for selecting a maximum number of the Xi′s subject to the following constraints: (1) the sum of the elements selected must not exceed a given constant c > 0, and (2) the Xi′s must be inspected in strict sequence with the decision to accept or reject an element being final at the time it is inspected.We prove first that there exists such a rule of threshold type, i.e. the ith element inspected is accepted if and only if it is no larger than a threshold which depends only on i and the sum of the elements already accepted. Next, we prove that if F(x) ~ Axα as x → 0 for some A, α> 0, then for fixed c the expected number, En(c), selected by an optimal threshold is characterized by Asymptotics as c → ∞and n → ∞with c/n held fixed are derived, and connections with several closely related, well-known problems are brought out and discussed.

An Evidence-Based Health Information System Theory

2011 ◽  
pp. 1994-2011
Author(s):  
Daniel Carbone
Keyword(s):  
Information Systems ◽  
Systems Theory ◽  
Health Information ◽  
Health Sector ◽  
Health Information System ◽  
Building Blocks ◽  
Evidence Based ◽  
Supporting Evidence ◽  
The Common ◽  
Is Theory

The aim of this chapter is to bridge the gap between what is known about IS theory and the specifics characteristics of health to develop an evidence based health information systems theory. An initial background first sets the significance for the need to have a solid information systems theory in health and then argues that neither the information systems literature nor the health sector have been able to provide any satisfactory pathway to facilitate the adoption of information systems in health settings. The chapter further continues by reviewing the common pathway to develop information systems theory and the knowledge foundations used in the process, and then proceeds to highlight how this theory was developed. Subsequently, the building blocks (constructs, premises, supporting evidence and conclusions) that underpins the constructs and a brief explanation of the relationships between them is included. A discussion and limitation section is then followed by a conclusion.

Caregiver burden and distress

2021 ◽  
pp. 303-310
Author(s):  
Rinat Nissim ◽  
Sarah Hales ◽  
Gary Rodin
Keyword(s):  
Palliative Care ◽  
Family Caregivers ◽  
Personal Growth ◽  
Advanced Disease ◽  
Supporting Evidence ◽  
Care Providers ◽  
Wide Range ◽  
Care Family ◽  
The Common ◽  
Physical Challenges

Caregivers of patients with advanced disease can be seen as both care providers and as receivers of care. Family caregivers frequently face a wide range of their own psychological, spiritual, social, financial, and physical challenges, which may increase in duration due to longer survival and more ambulatory and home care of patients with advanced disease. While support for family caregivers is an integral component of quality palliative care, such support is often unavailable and there is a dearth of evidence-based interventions for caregivers. This chapter will provide an overview of the common issues faced by family caregivers of adults in palliative care, the factors that contribute to or exacerbate these problems, the interventions designed to address them and their supporting evidence, and the potential for personal growth in caregivers. Gaps in clinical practice and research are identified and future directions for clinical attention and research are discussed.

A Note on Normal Attraction to a Stable Law

1971 ◽  
Vol 14 (3) ◽  
pp. 451-452
Author(s):  
M. V. Menon ◽  
V. Seshadri
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Characteristic Exponent ◽  
Random Variables ◽  
Stable Law ◽  
Common Distribution ◽  
Normal Attraction ◽  
Common Distribution Function ◽  
The Common ◽  
Necessary And Sufficient

Let X1, X2, …, be a sequence of independent and identically distributed random variables, with the common distribution function F(x). The sequence is said to be normally attracted to a stable law V with characteristic exponent α, if for some an (converges in distribution to V). Necessary and sufficient conditions for normal attraction are known (cf [1, p. 181]).

Asymptotic distributions of extremes of extremal Markov sequences

1994 ◽  
Vol 31 (01) ◽  
pp. 256-261
Author(s):  
S. R. Adke ◽  
C. Chandran
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Asymptotic Distributions ◽  
Arbitrary Distribution ◽  
Extreme Statistics ◽  
Common Distribution ◽  
Common Distribution Function ◽  
The Common

Let {ξ n , n ≧1} be a sequence of independent real random variables, F denote the common distribution function of identically distributed random variables ξ n , n ≧1 and let ξ 1 have an arbitrary distribution. Define Xn+ 1 = k max(Xn, ξ n +1), Yn + 1 = max(Yn, ξ n +1) – c, Un +1 = l min(Un, ξ n +1), Vn+ 1 = min(Vn, ξ n +1) + c, n ≧ 1, 0 < k < 1, l > 1, 0 < c < ∞, and X 1 = Υ 1 = U 1 = V 1 = ξ 1. We establish conditions under which the limit law of max(X 1, · ··, Xn ) coincides with that of max(ξ 2, · ··, ξ n+ 1) when both are appropriately normed. A similar exercise is carried out for the extreme statistics max(Y 1, · ··, Yn ), min(U 1,· ··, Un ) and min(V 1, · ··, Vn ).

An extension of a lemma of Wald

1966 ◽  
Vol 3 (01) ◽  
pp. 272-273 ◽  
Author(s):  
H. Robbins ◽  
E. Samuel
Keyword(s):  
Natural Extension ◽  
Random Variables ◽  
Random Variable ◽  
Common Distribution ◽  
The Common ◽  
Image Position ◽  
Independent Identically Distributed

We define a natural extension of the concept of expectation of a random variable y as follows: M(y) = a if there exists a constant − ∞ ≦ a ≦ ∞ such that if y 1, y 2, … is a sequence of independent identically distributed (i.i.d.) random variables with the common distribution of y then

scholarly journals The central limit theorem for Euclidean minimal spanning trees II

1999 ◽  
Vol 31 (04) ◽  
pp. 969-984 ◽  
Author(s):  
Sungchul Lee
Keyword(s):  
Central Limit ◽  
Spanning Tree ◽  
Limit Theorems ◽  
Spanning Trees ◽  
Regularity Conditions ◽  
Minimal Spanning Tree ◽  
The Central Limit Theorem ◽  
Common Distribution ◽  
The Common ◽  
Minimal Spanning Trees

Let X i : i ≥ 1 be i.i.d. points in ℝ d , d ≥ 2, and let T n be a minimal spanning tree on X 1,…,X n . Let L(X 1,…,X n ) be the length of T n and for each strictly positive integer α let N(X 1,…,X n ;α) be the number of vertices of degree α in T n . If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L(X 1,…,X n ) and N(X 1,…,X n ;α). We also study the rate of convergence for EL(X 1,…,X n ).

An extension of a lemma of Wald

1966 ◽  
Vol 3 (1) ◽  
pp. 272-273 ◽  
Author(s):  
H. Robbins ◽  
E. Samuel
Keyword(s):  
Natural Extension ◽  
Random Variables ◽  
Random Variable ◽  
Common Distribution ◽  
The Common ◽  
Image Position ◽  
Independent Identically Distributed

We define a natural extension of the concept of expectation of a random variable y as follows: M(y) = a if there exists a constant − ∞ ≦ a ≦ ∞ such that if y1, y2, … is a sequence of independent identically distributed (i.i.d.) random variables with the common distribution of y then

scholarly journals The central limit theorem for Euclidean minimal spanning trees II

1999 ◽  
Vol 31 (4) ◽  
pp. 969-984 ◽  
Author(s):  
Sungchul Lee
Keyword(s):  
Central Limit ◽  
Spanning Tree ◽  
Limit Theorems ◽  
Spanning Trees ◽  
Regularity Conditions ◽  
Minimal Spanning Tree ◽  
The Central Limit Theorem ◽  
Common Distribution ◽  
The Common ◽  
Minimal Spanning Trees

Let Xi : i ≥ 1 be i.i.d. points in ℝd, d ≥ 2, and let Tn be a minimal spanning tree on X1,…,Xn. Let L(X1,…,Xn) be the length of Tn and for each strictly positive integer α let N(X1,…,Xn;α) be the number of vertices of degree α in Tn. If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L(X1,…,Xn) and N(X1,…,Xn;α). We also study the rate of convergence for EL(X1,…,Xn).

Some asymptotic results on multiple matching

1974 ◽  
Vol 11 (3) ◽  
pp. 479-492 ◽  
Author(s):  
R. Hafner ◽  
W. Sendler
Keyword(s):  
Finite Number ◽  
Random Variable ◽  
Limiting Distribution ◽  
Equal Probability ◽  
Asymptotic Results ◽  
Main Result Theorem ◽  
Common Distribution ◽  
Result Theorem ◽  
The Common

We consider s ≦ n randomly chosen permutations of the numbers 1, 2, …, n, and write them under each other, thus forming an s × n matrix, called “random-batch”. A rule, prescribing how many elements of a column may occur exactly one time, how many may occur exactly two times, etc., is called a fixpoint-structure. Assuming each possible permutation to be chosen with equal probability, the number of columns having a certain fixpoint-structure F is a random variable X(F). The limiting distribution of X(F) for n→ ∞ is considered for different cases of s = s(n). The main result (Theorem 4) says, that the common distribution of a finite number t of given fixpoint-structures tends to the product of t Poisson-laws, n→ ∞.

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