scholarly journals ENUMERATING THE PRIME ALTERNATING LINKS

2004 ◽  
Vol 13 (01) ◽  
pp. 151-173 ◽  
Author(s):  
STUART RANKIN ◽  
ORTHO FLINT
Keyword(s):  
Finite Sequence ◽  
Efficient Implementation ◽  
The Other ◽  
Large Set ◽  
Basic Scheme ◽  
Group Number ◽  
Alternating Links ◽  
Alternating Link

In [5], four knot operators were introduced and used to construct all prime alternating knots of a given crossing size. An efficient implementation of this construction was made possible by the notion of the master array of an alternating knot. The master array and an implementation of the construction appeared in [6]. The basic scheme (as described in [5]) is to apply two of the operators, D and ROTS, to the prime alternating knots of minimal crossing size n-1, which results in a large set of prime alternating knots of minimal crossing size n, and then the remaining two operators, T and OTS, are applied to these n crossing knots to complete the production of the set of prime alternating knots of minimal crossing size n. In this paper, we show how to obtain all prime alternating links of a given minimal crossing size. More precisely, we shall establish that given any two prime alternating links of minimal crossing size n, there is a finite sequence of T and OTS operations that transforms one of the links into the other. Consequently, one may select any prime alternating link of minimal crossing size n (which is then called the seed link), and repeatedly apply only the operators T and OTS to obtain all prime alternating links of minimal crossing size n from the chosen seed link. The process may be standardized by specifying the seed link to be (in the parlance of [5]) the unique link of n crossings with group number 1, the (n, 2) torus link.

THE ADDITIVITY OF CROSSING NUMBERS

2004 ◽  
Vol 13 (07) ◽  
pp. 857-866 ◽  
Author(s):  
YUANAN DIAO
Keyword(s):  
Knot Theory ◽  
Difficult Problem ◽  
Crossing Number ◽  
The Other ◽  
Connected Sum ◽  
Torus Knots ◽  
Crossing Numbers ◽  
Weaker Conditions ◽  
Alternating Links ◽  
Alternating Link

It has long been conjectured that the crossing numbers of links are additive under the connected sum of links. This is a difficult problem in knot theory and has been open for more than 100 years. In fact, many questions of much weaker conditions are still open. For instance, it is not known whether Cr(K1#K2)≥Cr(K1) or Cr(K1#K2)≥Cr(K2) holds in general, here K1#K2 is the connected sum of K1 and K2 and Cr(K) stands for the crossing number of the link K. However, for alternating links K1 and K2, Cr(K1#K2)=Cr(K1)+Cr(K2) does hold. On the other hand, if K1 is an alternating link and K2 is any link, then we have Cr(K1#K2)≥Cr(K1). In this paper, we show that there exists a wide class of links over which the crossing number is additive under the connected sum operation. This class is different from the class of all alternating links. It includes all torus knots and many alternating links. Furthermore, if K1 is a connected sum of any given number of links from this class and K2 is a non-trivial knot, we prove that Cr(K1#K2)≥Cr(K1)+3.

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

scholarly journals Sentiment Analysis of Suicide Notes: A Shared Task

2012 ◽  
Vol 5s1 ◽  
pp. BII.S9042 ◽  
Author(s):  
John P. Pestian ◽  
Pawel Matykiewicz ◽  
Michelle Linn-Gust ◽  
Brett South ◽  
Ozlem Uzuner ◽  
...  
Keyword(s):  
Preliminary Analysis ◽  
The Other ◽  
Future Research ◽  
Large Set ◽  
Biomedical Domain ◽  
Shared Task ◽  
Clinical Text ◽  
Evaluation Measures ◽  
Suicide Notes ◽  
Data Production

This paper reports on a shared task involving the assignment of emotions to suicide notes. Two features distinguished this task from previous shared tasks in the biomedical domain. One is that it resulted in the corpus of fully anonymized clinical text and annotated suicide notes. This resource is permanently available and will (we hope) facilitate future research. The other key feature of the task is that it required categorization with respect to a large set of labels. The number of participants was larger than in any previous biomedical challenge task. We describe the data production process and the evaluation measures, and give a preliminary analysis of the results. Many systems performed at levels approaching the inter-coder agreement, suggesting that human-like performance on this task is within the reach of currently available technologies.

scholarly journals Concatenation of Finite Sequences

2019 ◽  
Vol 27 (1) ◽  
pp. 1-13
Author(s):  
Rafał Ziobro
Keyword(s):  
Finite Sequence ◽  
The Other ◽  
Other Hand ◽  
Finite Sequences ◽  
Initial Object

Summary The coexistence of “classical” finite sequences [1] and their zero-based equivalents finite 0-sequences [6] in Mizar has been regarded as a disadvantage. However the suggested replacement of the former type with the latter [5] has not yet been implemented, despite of several advantages of this form, such as the identity of length and domain operators [4]. On the other hand the number of theorems formalized using finite sequence notation is much larger then of those based on finite 0-sequences, so such translation would require quite an effort. The paper addresses this problem with another solution, using the Mizar system [3], [2]. Instead of removing one notation it is possible to introduce operators which would concatenate sequences of various types, and in this way allow utilization of the whole range of formalized theorems. While the operation could replace existing FS2XFS, XFS2FS commands (by using empty sequences as initial elements) its universal notation (independent on sequences that are concatenated to the initial object) allows to “forget” about the type of sequences that are concatenated on further positions, and thus simplify the proofs.

scholarly journals Planungsrechnungen zur Optimierung von Zuchtplänen der Rasse Merinofleischschaf

1999 ◽  
Vol 42 (3) ◽  
pp. 267-280
Author(s):  
U. Müller ◽  
K. Strittmatter ◽  
G. Nitter
Keyword(s):  
Field Test ◽  
Genetic Gain ◽  
The Other ◽  
Test Scheme ◽  
Progeny Testing ◽  
Basic Scheme ◽  
Lean Meat ◽  
Meat Content ◽  
Selection Strategies ◽  
Step Selection

Abstract. Title of the paper: Alternative selection strategies for the Mutton Merino breed to optimize breedine Systems This paper deals with the investigation of alternative selection strategies for the Mutton Merino breed to improve lamb meat production and fertility. A main topic is the application of ultrasonic scanning to evaluate the meat content on live animals. The aim of model calculations was the optimisation and comparison of five different selection strategies within three different schemes of gene dissimation. First a basic scheme was defined and optimised (selection on field records, one-step selection, no scanning). It was regarded as the reference scheme to which all other breeding Systems were related. The following schemes considered both, selection with and without scanning. A second scheme, also based on field records, includes two-step selection of rams (called improved field test scheme). In a third and fourth scheme a level of uniform environment was assumed for ram progeny testing. These are a central testing Station on the one hand with slaughtering and carcass evaluation on progeny, and one or more contract farms on the other (without slaughtering). For a fifth selection scheme an open nucleus was assumed with ram progeny testing in associated test herds. In a dcterministic approach using the ZPLAN Computer program, the monetary genetic gain for the breeding objeetive (traits lambs weaned, litter weight at weaning, postweaning daily gain and lean meat content) and the profit were calculated for each scheme after optimisation of various biological-technical coefficients. The highest profit was achieved with a nucleus scheme (DM 9,16). Due to low recording costs the basic scheme was second (DM 7,19) and, because of high costs, the Station scheme was last (DM 4,22). The other two schemes were intermediate (DM 6,98 for the scheme with contract farms and DM 6,58 for the improved field test scheme). On an average over all schemes, scanning resulted in a 0,24 DM (i.e. almost 30 per cent) increase of the monetary genetic gain and a threefold higher genetic gain for lean meat percentage. In all schemes scanning lead also to a higher profit because the higher retum of selection based on scanning exceeded the higher costs.

scholarly journals Enhancing direct citations: A comparison of relatedness measures for community detection in a large set of PubMed publications

2020 ◽  
pp. 1-16 ◽  
Author(s):  
Per Ahlgren ◽  
Yunwei Chen ◽  
Cristian Colliander ◽  
Nees Jan van Eck
Keyword(s):  
Community Detection ◽  
Relative Performance ◽  
The Other ◽  
Evaluation Criterion ◽  
Bibliographic Coupling ◽  
Large Set ◽  
Classification Schemes ◽  
Coupling Approach ◽  
Solution Accuracy ◽  
Better Than

The effects of enhancing direct citations, with respect to publication–publication relatedness measurement, by indirect citation relations (bibliographic coupling, cocitation, and extended direct citations) and text relations on clustering solution accuracy are analyzed. For comparison, we include each approach that is involved in the enhancement of direct citations. In total, we investigate the relative performance of seven approaches. To evaluate the approaches we use a methodology proposed by earlier research. However, the evaluation criterion used is based on MeSH, one of the most sophisticated publication-level classification schemes available. We also introduce an approach, based on interpolated accuracy values, by which overall relative clustering solution accuracy can be studied. The results show that the cocitation approach has the worst performance, and that the direct citations approach is outperformed by the other five investigated approaches. The extended direct citations approach has the best performance, followed by an approach in which direct citations are enhanced by the BM25 textual relatedness measure. An approach that combines direct citations with bibliographic coupling and cocitation performs slightly better than the bibliographic coupling approach, which in turn has a better performance than the BM25 approach.

scholarly journals Modifications and Cobounding Manifolds

1960 ◽  
Vol 12 ◽  
pp. 503-528 ◽  
Author(s):  
Andrew H. Wallace
Keyword(s):  
Algebraic Variety ◽  
Finite Sequence ◽  
Differentiable Manifold ◽  
The Other ◽  
Algebraic Varieties ◽  
The Given ◽  
Hyperplane Sections

The object of this paper is to establish a simple connection between Thorn's theory of cobounding manifolds and the theory of modifications. The former theory is given in detail in (8) and sketched in (3), while the latter is worked out in (1). In particular in (1) it is shown that the only modifications which can transform one differentiable manifold into another are what I call below spherical modifications, which consist in taking out a sphere from the given manifold and replacing it by another. The main result is that manifolds cobound if and only if each is obtainable from the other by a finite sequence of spherical modifications.The technique consists in approximating the manifolds by pieces of algebraic varieties. Thus if M1 and M2 form the boundary of M, the last is taken to be part of an algebraic variety such that M1 and M2 are two members of a pencil of hyperplane sections.

scholarly journals Stably Stratified Flows: A Model with No Ri(cr)*

2008 ◽  
Vol 65 (7) ◽  
pp. 2437-2447 ◽  
Author(s):  
V. M. Canuto ◽  
Y. Cheng ◽  
A. M. Howard ◽  
I. N. Esau
Keyword(s):  
Numerical Simulation ◽  
Large Eddy Simulation ◽  
Direct Numerical Simulation ◽  
Turbulent Mixing ◽  
Stratified Flows ◽  
The Other ◽  
Large Set ◽  
Eddy Simulation ◽  
Stably Stratified Flows ◽  
Large Eddy

Abstract A large set of laboratory, direct numerical simulation (DNS), and large eddy simulation (LES) data indicates that in stably stratified flows turbulent mixing exists up to Ri ∼ O(100), meaning that there is practically no Ri(cr). On the other hand, traditional local second-order closure (SOC) models entail a critical Ri(cr) ∼ O(1) above which turbulence ceases to exist and are therefore unable to explain the above data. The authors suggest how to modify the recent SOC model of Cheng et al. to reproduce the above data for arbitrary Ri.

POSITIVE ALTERNATING LINKS ARE POSITIVELY ALTERNATING

2000 ◽  
Vol 09 (01) ◽  
pp. 107-112 ◽  
Author(s):  
TAKUJI NAKAMURA
Keyword(s):  
Alternating Links ◽  
Alternating Link

By using a result of P. R. Cromwell on homogeneous links which contain both positive links and alternating links, we prove that any reduced alternating diagram of a positive alternating link is positive.

scholarly journals GRAPH SMALL CANCELLATION THEORY APPLIED TO ALTERNATING LINK GROUPS

2012 ◽  
Vol 21 (11) ◽  
pp. 1250113
Author(s):  
RÉMI CUNÉO ◽  
HAMISH SHORT
Keyword(s):  
Small Cancellation ◽  
Cancellation Condition ◽  
Small Cancellation Theory ◽  
Link Group ◽  
Finite Sums ◽  
Small Cancellation Condition ◽  
Alternating Links ◽  
Alternating Link

We show that the Wirtinger presentation of a prime alternating link group satisfies a generalized small cancellation condition. This new version of Weinbaum's solution to the word and conjugacy problems for these groups easily extends to finite sums of alternating links.

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