A Stochastic Comparison for Arrangement Increasing Functions

1994 ◽  
Vol 3 (3) ◽  
pp. 345-348 ◽  
Author(s):  
Abba M. Krieger ◽  
Paul R. Rosenbaum
Keyword(s):  
Distributive Lattice ◽  
Partial Order ◽  
Random Permutation ◽  
The Other ◽  
Stochastic Comparison ◽  
Finite Distributive Lattice ◽  
Set Of Permutations ◽  
Arrangement Increasing ◽  
Increasing Functions ◽  
Increasing Function

Let h(·) be an arrangement increasing function, let X have an arrangement increasing density, and let XE be a random permutation of the coordinates of X. We prove E{h(XE)} ≤ E{h(X)}. This comparison is delicate in that similar results are sometimes true and sometimes false. In a finite distributive lattice, a similar comparison follows from Holley's inequality, but the set of permutations with the arrangement order is not a lattice. On the other hand, the set of permutations is a lattice, though not a distributive lattice, if it is endowed with a different partial order, but in this case the comparison does not hold.

Initial segments of the lattice of Π10 classes

2001 ◽  
Vol 66 (4) ◽  
pp. 1749-1765 ◽  
Author(s):  
Douglas Cenzer ◽  
Andre Nies
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Limit Point ◽  
Finite Differences ◽  
Boolean Algebras ◽  
The Other ◽  
Finite Distributive Lattice ◽  
Property A ◽  
Decidable Theory ◽  
Reduction Property

Abstract.We show that in the lattice of classes there are initial segments [∅, P] = (P) which are not Boolean algebras, but which have a decidable theory. In fact, we will construct for any finite distributive lattice L which satisfies the dual of the usual reduction property a class P such that L is isomorphic to the lattice (P)*, which is (P). modulo finite differences. For the 2-element lattice, we obtain a minimal class, first constructed by Cenzer, Downey, Jockusch and Shore in 1993. For the simplest new class P constructed, P has a single, non-computable limit point and (P)* has three elements, corresponding to ∅, P and a minimal class P0 ⊂ P, The element corresponding to P0 has no complement in the lattice. On the other hand, the theory of (P) is shown to be decidable.A class P is said to be decidable if it is the set of paths through a computable tree with no dead ends. We show that if P is decidable and has only finitely many limit points, then (P)* is always a Boolean algebra. We show that if P is a decidable class and (P) is not a Boolean algebra, then the theory of (P) interprets the theory of arithmetic and is therefore undecidable.

Special Items: A Descriptive Analysis

2011 ◽  
Vol 25 (3) ◽  
pp. 511-536 ◽  
Author(s):  
Peter M. Johnson ◽  
Thomas J. Lopez ◽  
Juan Manuel Sanchez
Keyword(s):  
Firm Value ◽  
Temporal Frequency ◽  
Descriptive Analysis ◽  
Financial Statements ◽  
Comprehensive Analysis ◽  
The Other ◽  
Future Earnings ◽  
Special Items ◽  
Increasing Function ◽  
Frequency Magnitude

SYNOPSIS We provide a comprehensive analysis of special items and the characteristics of the firms that recognize them. Our analysis reveals that the temporal frequency, magnitude, and persistence of special items has increased significantly in the last 30 years, and that such increases are primarily driven by negative special items. More recently, however, our evidence is consistent with both a decline in frequency and magnitude of negative special items. On the other hand, we find that the frequency of reporting of positive special items, which remained relatively constant through 2002, has increased in more recent years. We also find strong evidence that subsequent special item reporting is an increasing function of the frequency of “prior” special item reporting. Using a random subsample of firms reporting special items, we document that 22 percent of the amounts reported in Compustat do not reconcile with the amounts reported on the firms' actual financial statements. Our comprehensive analysis should be of interest to regulators, academics, and managers interested in the implications of special items on firm-related consequences such as future earnings and firm value. Our examination can also serve as a catalyst for researchers interested in extending this important area of inquiry.

New kinds of multidimensional IFR distribution

1990 ◽  
Vol 22 (1) ◽  
pp. 251-253 ◽  
Author(s):  
Yuedong Wang ◽  
Jinhua Cao
Keyword(s):  
Partial Order ◽  
Shock Model ◽  
Closure Properties ◽  
Increasing Function

Two kinds of multidimensional IFR distribution are defined by using a partial order in Rn+, which is derived from a non-negative, strictly increasing function in Rn+. Some closure properties under operations and an application to a shock model are discussed.

Extinction in the Pigeon after Continuous Reinforcement: Effect of Number of Reinforced Responses

1971 ◽  
Vol 28 (1) ◽  
pp. 331-338 ◽  
Author(s):  
Laurel Furumoto
Keyword(s):  
Animal Studies ◽  
Food Pellet ◽  
Key Peck ◽  
Continuous Reinforcement ◽  
Gm Food ◽  
Free Operant ◽  
Time To Extinction ◽  
Monotonically Increasing Function ◽  
Increasing Functions ◽  
Increasing Function

Number of responses and time to extinction were measured after 3, 10, 1000, 3000, 5000, and 10,000 reinforced key-peck responses during conditioning. Each response was reinforced with a 045-gm. food pellet. The number of responses in extinction was a monotonically increasing function which became asymptotic beyond 1000 reinforced responses. Number of reinforced responses during conditioning significantly affected the number of responses in extinction ( p < .001) but not the time to extinction. The results support the findings of previous free-operant bar-press studies with rats. Free-operant animal studies of extinction after continuous reinforcement have consistently produced monotonically increasing functions and have typically employed relatively small amounts of reinforcement. Amount of reward may be an important parameter determining the shape of the extinction function in the free-operant studies.

scholarly journals Congruence Lattices of Finite Semimodular Lattices

1998 ◽  
Vol 41 (3) ◽  
pp. 290-297 ◽  
Author(s):  
G. Grätzer ◽  
H. Lakser ◽  
E. T. Schmidt
Keyword(s):  
Distributive Lattice ◽  
Congruence Lattice ◽  
Finite Distributive Lattice ◽  
Congruence Lattices ◽  
Semimodular Lattices

AbstractWe prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.

scholarly journals The Lattice of Definable Equivalence Relations in Homogeneous $n$-Dimensional Permutation Structures

10.37236/5980 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Samuel Braunfeld
Keyword(s):  
Distributive Lattice ◽  
Equivalence Relations ◽  
Electronic Journal ◽  
Finite Distributive Lattice ◽  
Linear Orders ◽  
Finite Dimensional ◽  
Homogeneous Structures ◽  
Special Case

In Homogeneous permutations, Peter Cameron [Electronic Journal of Combinatorics 2002] classified the homogeneous permutations (homogeneous structures with 2 linear orders), and posed the problem of classifying the homogeneous $n$-dimensional permutation structures (homogeneous structures with $n$ linear orders) for all finite $n$. We prove here that the lattice of $\emptyset$-definable equivalence relations in such a structure can be any finite distributive lattice, providing many new imprimitive examples of homogeneous finite dimensional permutation structures. We conjecture that the distributivity of the lattice of $\emptyset$-definable equivalence relations is necessary, and prove this under the assumption that the reduct of the structure to the language of $\emptyset$-definable equivalence relations is homogeneous. Finally, we conjecture a classification of the primitive examples, and confirm this in the special case where all minimal forbidden structures have order 2. 

Undirected Graphs Realizable as Graphs of Modular Lattices

1965 ◽  
Vol 17 ◽  
pp. 923-932 ◽  
Author(s):  
Laurence R. Alvarez
Keyword(s):  
Distributive Lattice ◽  
Partial Order ◽  
Directed Graph ◽  
Undirected Graph ◽  
Single Edge ◽  
Undirected Graphs ◽  
Modular Lattices

If (L, ≥) is a lattice or partial order we may think of its Hesse diagram as a directed graph, G, containing the single edge E(c, d) if and only if c covers d in (L, ≥). This graph we shall call the graph of (L, ≥). Strictly speaking it is the basis graph of (L, ≥) with the loops at each vertex removed; see (3, p. 170).We shall say that an undirected graph Gu can be realized as the graph of a (modular) (distributive) lattice if and only if there is some (modular) (distributive) lattice whose graph has Gu as its associated undirected graph.

scholarly journals Stochastic comparison of point random fields

1997 ◽  
Vol 34 (04) ◽  
pp. 868-881 ◽  
Author(s):  
Hans-Otto Georgii ◽  
Torsten Küneth
Keyword(s):  
Point Process ◽  
Random Fields ◽  
Alternative Proof ◽  
Probability Measures ◽  
Stochastic Comparison ◽  
Sufficient Condition ◽  
Stochastic Domination ◽  
Positive Correlations ◽  
Increasing Functions

We give an alternative proof of a point-process version of the FKG–Holley–Preston inequality which provides a sufficient condition for stochastic domination of probability measures, and for positive correlations of increasing functions.

New kinds of multidimensional IFR distribution

1990 ◽  
Vol 22 (01) ◽  
pp. 251-253
Author(s):  
Yuedong Wang ◽  
Jinhua Cao
Keyword(s):  
Partial Order ◽  
Shock Model ◽  
Closure Properties ◽  
Increasing Function

Two kinds of multidimensional IFR distribution are defined by using a partial order in R n +, which is derived from a non-negative, strictly increasing function in R n +. Some closure properties under operations and an application to a shock model are discussed.

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