scholarly journals POLYNOMIAL INVARIANTS OF PSEUDO-ANOSOV MAPS

2012 ◽  
Vol 04 (01) ◽  
pp. 13-47 ◽  
Author(s):  
JOAN BIRMAN ◽  
PETER BRINKMANN ◽  
KEIKO KAWAMURO
Keyword(s):  
Characteristic Polynomial ◽  
Transition Matrix ◽  
The Other ◽  
Train Track ◽  
Polynomial Invariants ◽  
Genus 2

We investigate the structure of the characteristic polynomial det (xI - T) of a transition matrix T that is associated to a train track representative of a pseudo-Anosov map [F] acting on a surface. As a result we obtain three new polynomial invariants of [F], one of them being the product of the other two, and all three being divisors of det (xI - T). The degrees of the new polynomials are invariants of [F] and we give simple formulas for computing them by a counting argument from an invariant train-track. We give examples of genus 2 pseudo-Anosov maps having the same dilatation, and use our invariants to distinguish them.

Equilibrium points for three games based on the Poisson process

1993 ◽  
Vol 30 (03) ◽  
pp. 627-638
Author(s):  
M. T. Dixon
Keyword(s):  
Poisson Process ◽  
Equilibrium Point ◽  
Uniform Distribution ◽  
Arbitrary Number ◽  
Transition Matrix ◽  
Equilibrium Points ◽  
Expected Value ◽  
Time Limit ◽  
The Other ◽  
Player Game

An arbitrary number of competitors are presented with independent Poisson streams of offers consisting of independent and identically distributed random variables having the uniform distribution on [0, 1]. The players each wish to accept a single offer before a known time limit is reached and each aim to maximize the expected value of their offer. Rejected offers may not be recalled, but they are passed on to the other players according to a known transition matrix. This paper finds equilibrium points for two such games, and demonstrates a two-player game with an equilibrium point under which the player with the faster stream of offers has a lower expected reward than his opponent.

scholarly journals Improving Distantly Supervised Relation Extraction with Neural Noise Converter and Conditional Optimal Selector

2019 ◽  
Vol 33 ◽  
pp. 7273-7280 ◽  
Author(s):  
Shanchan Wu ◽  
Kai Fan ◽  
Qiong Zhang
Keyword(s):  
Transition Matrix ◽  
Noisy Data ◽  
Relation Extraction ◽  
The Other ◽  
Neural Noise ◽  
Distant Supervision ◽  
Other Hand ◽  
The Impact ◽  
Large Corpus

Distant supervised relation extraction has been successfully applied to large corpus with thousands of relations. However, the inevitable wrong labeling problem by distant supervision will hurt the performance of relation extraction. In this paper, we propose a method with neural noise converter to alleviate the impact of noisy data, and a conditional optimal selector to make proper prediction. Our noise converter learns the structured transition matrix on logit level and captures the property of distant supervised relation extraction dataset. The conditional optimal selector on the other hand helps to make proper prediction decision of an entity pair even if the group of sentences is overwhelmed by no-relation sentences. We conduct experiments on a widely used dataset and the results show significant improvement over competitive baseline methods.

Equilibrium points for three games based on the Poisson process

1993 ◽  
Vol 30 (3) ◽  
pp. 627-638 ◽  
Author(s):  
M. T. Dixon
Keyword(s):  
Poisson Process ◽  
Equilibrium Point ◽  
Uniform Distribution ◽  
Arbitrary Number ◽  
Transition Matrix ◽  
Equilibrium Points ◽  
Expected Value ◽  
Time Limit ◽  
The Other ◽  
Player Game

An arbitrary number of competitors are presented with independent Poisson streams of offers consisting of independent and identically distributed random variables having the uniform distribution on [0, 1]. The players each wish to accept a single offer before a known time limit is reached and each aim to maximize the expected value of their offer. Rejected offers may not be recalled, but they are passed on to the other players according to a known transition matrix. This paper finds equilibrium points for two such games, and demonstrates a two-player game with an equilibrium point under which the player with the faster stream of offers has a lower expected reward than his opponent.

EIGENTIME IDENTITY OF THE WEIGHTED KOCH NETWORKS

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850042 ◽  
Author(s):  
YU SUN ◽  
JIAHUI ZOU ◽  
MEIFENG DAI ◽  
XIAOQIAN WANG ◽  
HUALONG TANG ◽  
...  
Keyword(s):  
Transition Matrix ◽  
Small World ◽  
Laplacian Matrix ◽  
Block Matrix ◽  
The Other ◽  
Small World Networks ◽  
Eigenvalues And Eigenvectors ◽  
Two Factors ◽  
Analytical Research ◽  
Definition Of

The eigenvalues of the transition matrix of a weighted network provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to biased walks. Although various dynamical processes have been investigated in weighted networks, analytical research about eigentime identity on such networks is much less. In this paper, we study analytically the scaling of eigentime identity for weight-dependent walk on small-world networks. Firstly, we map the classical Koch fractal to a network, called Koch network. According to the proposed mapping, we present an iterative algorithm for generating the weighted Koch network. Then, we study the eigenvalues for the transition matrix of the weighted Koch networks for weight-dependent walk. We derive explicit expressions for all eigenvalues and their multiplicities. Afterwards, we apply the obtained eigenvalues to determine the eigentime identity, i.e. the sum of reciprocals of each nonzero eigenvalues of normalized Laplacian matrix for the weighted Koch networks. The highlights of this paper are computational methods as follows. Firstly, we obtain two factors from factorization of the characteristic equation of symmetric transition matrix by means of the operation of the block matrix. From the first factor, we can see that the symmetric transition matrix has at least [Formula: see text] eigenvalues of [Formula: see text]. Then we use the definition of eigenvalues and eigenvectors to calculate the other eigenvalues.

scholarly journals Indecomposable orthogonal invariants of several matrices over a field of positive characteristic

2020 ◽  
pp. 1-11
Author(s):  
Artem Lopatin
Keyword(s):  
Characteristic Polynomial ◽  
Orthogonal Group ◽  
General Linear Group ◽  
Positive Characteristic ◽  
The Other ◽  
Symmetric Matrices ◽  
Maximal Degree ◽  
Infinite Field ◽  
The Given ◽  
Field Of Positive Characteristic

We consider the algebra of invariants of [Formula: see text]-tuples of [Formula: see text] matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic [Formula: see text] different from two. It is well known that this algebra is generated by the coefficients of the characteristic polynomial of all products of generic and transpose generic [Formula: see text] matrices. We establish that in case [Formula: see text] the maximal degree of indecomposable invariants tends to infinity as [Formula: see text] tends to infinity. In other words, there does not exist a constant [Formula: see text] such that it only depends on [Formula: see text] and the considered algebra of invariants is generated by elements of degree less than [Formula: see text] for any [Formula: see text]. This result is well-known in case of the action of the general linear group. On the other hand, for the rest of [Formula: see text] the given phenomenon does not hold. We investigate the same problem for the cases of symmetric and skew-symmetric matrices.

scholarly journals Genus-2 curves and Jacobians with a given number of points

2015 ◽  
Vol 18 (1) ◽  
pp. 170-197 ◽  
Author(s):  
Reinier Bröker ◽  
Everett W. Howe ◽  
Kristin E. Lauter ◽  
Peter Stevenhagen
Keyword(s):  
Finite Field ◽  
Elliptic Curves ◽  
Polynomial Time ◽  
Rational Points ◽  
The Other ◽  
Base Field ◽  
Arbitrary Base ◽  
The Family ◽  
Genus 2 ◽  
Genus 2 Curves

AbstractWe study the problem of efficiently constructing a curve $C$ of genus $2$ over a finite field $\mathbb{F}$ for which either the curve $C$ itself or its Jacobian has a prescribed number $N$ of $\mathbb{F}$-rational points.In the case of the Jacobian, we show that any ‘CM-construction’ to produce the required genus-$2$ curves necessarily takes time exponential in the size of its input.On the other hand, we provide an algorithm for producing a genus-$2$ curve with a given number of points that, heuristically, takes polynomial time for most input values. We illustrate the practical applicability of this algorithm by constructing a genus-$2$ curve having exactly $10^{2014}+9703$ (prime) points, and two genus-$2$ curves each having exactly $10^{2013}$ points.In an appendix we provide a complete parametrization, over an arbitrary base field $k$ of characteristic neither two nor three, of the family of genus-$2$ curves over $k$ that have $k$-rational degree-$3$ maps to elliptic curves, including formulas for the genus-$2$ curves, the associated elliptic curves, and the degree-$3$ maps.Supplementary materials are available with this article.

scholarly journals Osserman pseudo-Riemannian manifolds of signature (2,2)

2001 ◽  
Vol 71 (3) ◽  
pp. 367-396 ◽  
Author(s):  
Novica Blažić ◽  
Neda Bokan ◽  
Zoran Rakić
Keyword(s):  
Riemannian Manifold ◽  
Characteristic Polynomial ◽  
Riemannian Manifolds ◽  
Jacobi Operator ◽  
Tangent Vector ◽  
Jordan Form ◽  
The Other ◽  
Jacobi Operators ◽  
Osserman Manifold ◽  
Rank One

AbstractA pseudo-Riemannian manifold is said to be timelike (spacelike) Osserman if the Jordan form of the Jacobi operator Kx is independent of the particular unit timelike (spacelike) tangent vector X. The first main result is that timelike (spacelike) Osserman manifold (M, g) of signature (2, 2) with the diagonalizable Jacobi operator is either locally rank-one symmetric or flat. In the nondiagonalizable case the characteristic polynomial of Kx has to have a triple zero, which is the other main result. An important step in the proof is based on Walker's study of pseudo-Riemannian manifolds admitting parallel totally isotropic distributions. Also some interesting additional geometric properties of Osserman type manifolds are established. For the nondiagonalizable Jacobi operators some of the examples show a nature of the Osserman condition for Riemannian manifolds different from that of pseudo-Riemannian manifolds.

scholarly journals On the characteristic polynomial of power graphs

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4375-4387
Author(s):  
Modjtaba Ghorbani ◽  
Fatemeh Abbasi-Barfaraz
Keyword(s):  
Finite Group ◽  
Characteristic Polynomial ◽  
The Other ◽  
Power Graph ◽  
Graphs Of Groups ◽  
Vertex Set

The power graph P(G) of finite group G is a graph whose vertex set is G and two distinct vertices are adjacent if one is a power of the other. In this paper, we determine the characteristic polynomial of the power graphs of groups of order a product of three primes.

scholarly journals Overdominant Alleles in a Population of Variable Size

Genetics ◽  
1999 ◽  
Vol 152 (2) ◽  
pp. 775-781 ◽  
Author(s):  
Montgomery Slatkin ◽  
Christina A Muirhead
Keyword(s):  
Markov Chain ◽  
Approximate Method ◽  
Population Size ◽  
Transition Matrix ◽  
Markov Chain Model ◽  
Population Bottleneck ◽  
The Other ◽  
Chain Model ◽  
Variable Size ◽  
Constant Size

Abstract An approximate method is developed to predict the number of strongly overdominant alleles in a population of which the size varies with time. The approximation relies on the strong-selection weak-mutation (SSWM) method introduced by J. H. Gillespie and leads to a Markov chain model that describes the number of common alleles in the population. The parameters of the transition matrix of the Markov chain depend in a simple way on the population size. For a population of constant size, the Markov chain leads to results that are nearly the same as those of N. Takahata. The Markov chain allows the prediction of the numbers of common alleles during and after a population bottleneck and the numbers of alleles surviving from before a bottleneck. This method is also adapted to modeling the case in which there are two classes of alleles, with one class causing a reduction in fitness relative to the other class. Very slight selection against one class can strongly affect the relative frequencies of the two classes and the relative ages of alleles in each class.

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