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1
Content available remote

Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers

100%
Bułatek W., Kwiatkowski J.
Studia Mathematica
|
1992
|
tom 103
|
nr 2
133-142
EN
A class of strictly ergodic Toeplitz flows with positive entropies and trivial topological centralizers is presented.
2
Content available remote

The use of information and information gain in the analysis of attribute dependencies

80%
Moliński K., Dobek A., Tomaszyk K.
Biometrical Letters
|
2012
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tom 49
|
nr 2
149-158
EN
This paper demonstrates the possible conclusions which can be drawn from an analysis of entropy and information. Because of its universality, entropy can be widely used in different subjects, especially in biomedicine. Based on simulated data the similarities and differences between the grouping of attributes and testing of their independencies are shown. It follows that a complete exploration of data sets requires both of these elements. A new concept introduced in this paper is that of normed information gain, allowing the use of any logarithm in the definition of entropy.
3
Content available remote

On Entropy Bumps for Calderón-Zygmund Operators

80%
Lacey M. T., Spencer S.
Concrete Operators
|
2015
|
tom 2
|
nr 1
EN
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).
4
Content available remote

On Entropy Bumps for Calderón-Zygmund Operators

80%
Lacey M. T., Spencer S.
Concrete Operators
|
2015
|
tom 2
|
nr 1
EN
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ℇ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on Rd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound [...]
5
Content available remote

Dynamic stability and spatial heterogeneityin the individualbased modelling of a lotkavolterra gas

80%
Waniewski J., Jędruch W., Żołek N. S.
International Journal of Applied Mathematics and Computer Science
|
2004
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tom 14
|
nr 2
139-147
EN
Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the mathematical description by the Lotka-Volterra equations. The spatial patterns were evaluated using entropy and a cross correlation coefficient for the spatial distribution of both populations. In some simulations the system oscillated with variable amplitude but rather stable period, but the particle distribution departed from the (quasi) homogeneous state and did not return to it. The distribution entropy oscillated in the same rhythm as the population, but its value was smaller than in the initial homogeneous state. The cross correlation coefficient oscillated between positive and negative values. Its average value depended on the space scale applied for its evaluation with the negative values on the small scale (separation of preys from predators) and the positive values on the large scale (aggregation of both populations). The stability of such oscillation patterns was based on a balance of the population parameters and particle mobility. The increased mobility (particle mixing) resulted in unstable oscillations with high amplitude, sustained homogeneity of the particle distribution, and final extinction of one or both populations.
6
Content available remote

Mixing properties of nearly maximal entropy measures for $ℤ^{d}$ shifts of finite type

80%
E. Arthur Robinson, Jr., Şahin A. A.
Colloquium Mathematicum
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2000
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tom 84/85
|
nr 1
43-50
EN
We prove that for a certain class of $ℤ^d$ shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.
7
Content available remote

Detection of outlying observations using the Akaike information criterion

70%
Kornacki A.
Biometrical Letters
|
2013
|
tom 50
|
nr 2
117-126
EN
For the detection of outliers (observations which are seemingly different from the others) the method of testing hypotheses is most often used. This approach, however, depends on the level of significance adopted by the investigator. Moreover, it can lead to the undesirable effect of “masking” of the outliers. This paper presents an alternative method of outlier detection based on the Akaike information criterion. The theory presented is applied to analysis of the results of beet leaf mass determination.
8
Content available remote

Relatively perfect σ-algebras for flows

70%
Blanchard F., Kamiński B.
Studia Mathematica
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1995
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tom 114
|
nr 1
71-85
EN
We show that for every ergodic flow, given any factor σ-algebra ℱ, there exists a σ-algebra which is relatively perfect with respect to ℱ. Using this result and Ornstein's isomorphism theorem for flows, we give a functorial definition of the entropy of flows.
9
Content available remote

Generalized interval exchanges and the 2–3 conjecture

70%
Friedland S., Weiss B.
Open Mathematics
|
2005
|
tom 3
|
nr 3
412-429
EN
We introduce the notion of a generalized interval exchange $$\phi _\mathcal{A} $$ induced by a measurable k-partition $$\mathcal{A} = \left\{ {A_1 ,...,A_k } \right\}$$ of [0,1). $$\phi _\mathcal{A} $$ can be viewed as the corresponding restriction of a nondecreasing function $$f_\mathcal{A} $$ on ℝ with $$f_\mathcal{A} (0) = 0, f_\mathcal{A} (k) = 1$$ . A is called λ-dense if λ(A i∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that $$f_\mathcal{A} \circ f_\mathcal{B} = f_\mathcal{B} \circ f_\mathcal{A} $$ . We give necessary and sufficient conditions for this equality to hold. We show that for each integer m≥2, such that 3∤2m+1, there exist 2 and 3 non λ-dense partitions A and B of [0,1), corresponding to the interval exchanges on 2m intervals, for which $$f_\mathcal{A} $$ and $$f_\mathcal{B} $$ commute.
10
Content available remote

Average convergence rate of the first return time

61%
Choe G. H., Kim D. H.
Colloquium Mathematicum
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2000
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tom 84/85
|
nr 1
159-171
EN
The convergence rate of the expectation of the logarithm of the first return time $R_{n}$, after being properly normalized, is investigated for ergodic Markov chains. I. Kontoyiannis showed that for any β > 0 we have $log[R_{n}(x)P_{n}(x)] =o(n^{β})$ a.s. for aperiodic cases and A. J. Wyner proved that for any ε >0 we have $-(1 + ε)log n ≤ log[R_{n}(x)P_{n}(x)] ≤ loglog n$ eventually, a.s., where $P_{n}(x)$ is the probability of the initial n-block in x. In this paper we prove that $ E[log R_{(L,S)} - (L-1)h]$ converges to a constant depending only on the process where $R_{(L,S)}$ is the modified first return time with block length L and gap size S. In the last section a formula is proposed for measuring entropy sharply; it may detect periodicity of the process.
11
Content available remote

The use of outlier detection methods in the log-normal distribution for the identification of atypical varietal experiments

61%
Kornacki A., Bochniak A.
Biometrical Letters
|
2015
|
tom 52
|
nr 2
75-84
EN
In this study the Akaike information criterion for detecting outliers in a log-normal distribution is used. Theoretical results were applied to the identification of atypical varietal trials. This is an alternative to the tolerance interval method. Detection of outliers with the help of the Akaike information criterion represents an alternative to the method of testing hypotheses. This approach does not depend on the level of significance adopted by the investigator. It also does not lead to the masking effect of outliers.
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