scholarly journals A CLASSIFICATION OF 2-CHAINS HAVING 1-SHELL BOUNDARIES IN ROSY THEORIES

2015 ◽  
Vol 80 (1) ◽  
pp. 322-340 ◽  
Author(s):  
BYUNGHAN KIM ◽  
SUNYOUNG KIM ◽  
JUNGUK LEE
Keyword(s):  
Upper Bound ◽  
Homology Group ◽  
Strong Type ◽  
Simple Theories ◽  
Shell Boundary ◽  
Rosy Theories

AbstractWe classify, in a nontrivial amenable collection of functors, all 2-chains up to the relation of having the same 1-shell boundary. In particular, we prove that in a rosy theory, every 1-shell of a Lascar strong type is the boundary of some 2-chain, hence making the 1st homology group trivial. We also show that, unlike in simple theories, in rosy theories there is no upper bound on the minimal lengths of 2-chains whose boundary is a 1-shell.

Supervised Adaptive Hamming Net for Classification of Multiple-Valued Patterns

1997 ◽  
Vol 08 (02) ◽  
pp. 181-200
Author(s):  
Cheng-An Hung ◽  
Sheng-Fuu Lin
Keyword(s):  
Upper Bound ◽  
Incremental Learning ◽  
Arbitrary Sequence ◽  
Input Output ◽  
Multiple Valued Logic

A Supervised Adaptive Hamming Net (SAHN) is introduced for incremental learning of recognition categories in response to arbitrary sequence of multiple-valued or binary-valued input patterns. The binary-valued SAHN derived from the Adaptive Hamming Net (AHN) is functionally equivalent to a simplified ARTMAP, which is specifically designed to establish many-to-one mappings. The generalization to learning multiple-valued input patterns is achieved by incorporating multiple-valued logic into the AHN. In this paper, we examine some useful properties of learning in a P-valued SAHN. In particular, an upper bound is derived on the number of epochs required by the P-valued SAHN to learn a list of input-output pairs that is repeatedly presented to the architecture. Furthermore, we connect the P-valued SAHN with the binary-valued SAHN via the thermometer code.

scholarly journals DENSE CODING WITH MULTIPARTITE QUANTUM STATES

2006 ◽  
Vol 04 (03) ◽  
pp. 415-428 ◽  
Author(s):  
DAGMAR BRUß ◽  
MACIEJ LEWENSTEIN ◽  
ADITI SEN(DE) ◽  
UJJWAL SEN ◽  
GIACOMO MAURO D'ARIANO ◽  
...  
Keyword(s):  
Quantum State ◽  
Upper Bound ◽  
Arbitrary Number ◽  
Information Transfer ◽  
Quantum States ◽  
Dense Coding ◽  
Joint Operations ◽  
Single Receiver

We consider generalizations of the dense coding protocol with an arbitrary number of senders and either one or two receivers, sharing a multiparty quantum state, and using a noiseless channel. For the case of a single receiver, the capacity of such information transfer is found exactly. It is shown that the capacity is not enhanced by allowing the senders to perform joint operations. We provide a nontrivial upper bound on the capacity in the case of two receivers. We also give a classification of the set of all multiparty states in terms of their usefulness for dense coding. We provide examples for each of these classes, and discuss some of their properties.

scholarly journals On the Number of Similar Instances of a Pattern in a Finite Set

10.37236/4972 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Bernardo M. Ábrego ◽  
Silvia Fernández-Merchant ◽  
Daniel J. Katz ◽  
Levon Kolesnikov
Keyword(s):  
Arithmetic Progression ◽  
Finite Subset ◽  
Upper Bound ◽  
Point Subset ◽  
Finite Set ◽  
Equilateral Triangles ◽  
Optimal Configurations ◽  
Full Classification ◽  
General Method

New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is shown to be no more than $\lfloor{(4 n-1)(n-1)/18}\rfloor$. The number of $k$-term arithmetic progressions that lie within an $n$-point subset of the line is shown to be at most $(n-r)(n+r-k+1)/(2 k-2)$, where $r$ is the remainder when $n$ is divided by $k-1$. This upper bound is achieved when the $n$ points themselves form an arithmetic progression, but for some values of $k$ and $n$, it can also be achieved for other configurations of the $n$ points, and a full classification of such optimal configurations is given. These results are achieved using a new general method based on ordering relations.

ON AN INVERSE PROBLEM TO FROBENIUS' THEOREM II

2012 ◽  
Vol 11 (05) ◽  
pp. 1250092 ◽  
Author(s):  
WEI MENG ◽  
JIANGTAO SHI ◽  
KELIN CHEN
Keyword(s):  
Inverse Problem ◽  
Finite Group ◽  
Positive Integer ◽  
Upper Bound ◽  
Complete Classification ◽  
Frobenius Theorem ◽  
A Finite Group

Let G be a finite group and e a positive integer dividing |G|, the order of G. Denoting Le(G) = {x ∈ G|xe = 1}. Frobenius proved that |Le(G)| = ke for some positive integer k ≥ 1. Let k(G) be the upper bound of the set {k||Le(G)| = ke, ∀ e ||G|}. In this paper, a complete classification of the finite group G with k(G) = 3 is obtained.

scholarly journals An improvement of a transcendence measure of Galochkin and Mahler's S-numbers

1992 ◽  
Vol 52 (1) ◽  
pp. 130-140 ◽  
Author(s):  
Masaaki Amou
Keyword(s):  
Upper Bound ◽  
Functional Equations ◽  
Special Values ◽  
Transcendental Numbers ◽  
Transcendence Measure

AbstractWe give a transcendence measure of special values of functions satisfying certain functional equations. This improves an earlier result of Galochkin, and gives a better upper bound of the type for such a number as an S-number in the classification of transcendental numbers by Mahler.

Definability in low simple theories

2000 ◽  
Vol 65 (4) ◽  
pp. 1481-1490 ◽  
Author(s):  
Ziv Shami
Keyword(s):  
Amalgamation Property ◽  
Simple Theory ◽  
Weak Version ◽  
Strong Type ◽  
Simple Theories ◽  
New Class ◽  
Bounded Set ◽  
Almost All ◽  
Independence Theorem ◽  
Mutually Independent

In 1978 Shelah introduced a new class of theories, called simple (see [Shi]) which properly contained the class of stable theories. Shelah generalized part of the theory of forking to the simple context. After approximately 15 years of neglecting the general theory (although there were works by Hrushovski on finite rank with a definability assumption, as well as deep results on specific simple theories by Cherlin, Hrushovski, Chazidakis, Macintyre and Van den dries, see [CH], [CMV], [HP1], [HP2], [ChH]) there was a breakthrough, initiated with the work of Kim ([K1]). Kim proved that almost all the technical machinery of forking developed in the stable context could be generalized to simple case. However, the theory of multiplicity (i.e., the description of the (bounded) set of non forking extensions of a given complete type) no longer holds in the context of simple theories. Indeed, by contrast to simple theories, stable theories share a strong amalgamation property of types, namely if p and q are two “free” complete extensions over a superset of A, and there is no finite equivalence relation over A which separates them, then the conjunction of p and q is consistent (and even free over A.) In [KP] Kim and Pillay proved a weak version of this property for any simple theory, namely “the Independence Theorem for Lascar strong types”. This was a weaker version both because of the requirement that the sets of parameters of the types be mutually independent, as well as the use of Lascar strong types instead of the usual strong types. A very fundamental and interesting problem is whether the independence theorem can be proved for any simple theory, using only the usual strong types. In 1997 Buechler proved ([Bu]) the strong-type version of the independence theorem for an important subclass of simple theories, namely the class of low theories (which includes the class of stable theories and the class of supersimple theories of finite D-rank.)

scholarly journals Wilf-Classification of Mesh Patterns of Short Length

10.37236/4678 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Ísak Hilmarsson ◽  
Ingibjörg Jónsdóttir ◽  
Steinunn Sigurðardóttir ◽  
Lína Viðarsdóttir ◽  
Henning Ulfarsson
Keyword(s):  
Upper Bound ◽  
Short Length ◽  
Actual Number ◽  
Automatic Methods

This paper starts the Wilf-classification of mesh patterns of length 2. Although there are initially 1024 patterns to consider we introduce automatic methods to reduce the number of potentially different Wilf-classes to at most 65. By enumerating some of the remaining classes we bring that upper-bound further down to 56. Finally, we conjecture that the actual number of Wilf-classes of mesh patterns of length 2 is 46.

scholarly journals Convex Geometries are Extremal for the Generalized Sauer-Shelah Bound

10.37236/7217 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Bogdan Chornomaz
Keyword(s):  
Upper Bound ◽  
Closure Systems ◽  
Np Complete ◽  
Convex Geometries

The Sauer-Shelah lemma provides an exact upper bound on the size of set families with bounded Vapnik-Chervonekis dimension. When applied to lattices represented as closure systems, this lemma outlines a class of extremal lattices obtaining this bound. Here we show that the Sauer-Shelah bound can be easily generalized to arbitrary antichains, and extremal objects for this generalized bound are exactly convex geometries. We also show that the problem of classification of antichains admitting such extremal objects is NP-complete. 

Lascar strong types in some simple theories

1999 ◽  
Vol 64 (2) ◽  
pp. 817-824 ◽  
Author(s):  
Steven Buechler
Keyword(s):  
Strong Type ◽  
Simple Theories ◽  
Low Theory

AbstractIn this paper a class of simple theories, called the low theories is developed, and the following is proved.Theorem. Let T be a low theory, A a set and a, b elements realizing the same strong type over A. Then, a and b realize the same Lasear strong type over A.

scholarly journals Regular dessins uniquely determined by a nilpotent automorphism group

2018 ◽  
Vol 21 (3) ◽  
pp. 397-415 ◽  
Author(s):  
Na-Er Wang ◽  
Roman Nedela ◽  
Kan Hu
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Upper Bound ◽  
Automorphism Groups ◽  
Nilpotency Class ◽  
Isomorphism Classes ◽  
One To One

Abstract It is well known that the automorphism group of a regular dessin is a two-generator finite group, and the isomorphism classes of regular dessins with automorphism groups isomorphic to a given finite group G are in one-to-one correspondence with the orbits of the action of {{\mathrm{Aut}}(G)} on the ordered generating pairs of G. If there is only one orbit, then up to isomorphism the regular dessin is uniquely determined by the group G and it is called uniquely regular. In this paper we investigate the classification of uniquely regular dessins with a nilpotent automorphism group. The problem is reduced to the classification of finite maximally automorphic p-groups G, i.e., the order of the automorphism group of G attains Hall’s upper bound. Maximally automorphic p-groups of nilpotency class three are classified.

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