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Computational Experiences on the Distances of Polynomials to Irreducible Polynomials
 Mathematics of Computation
, 1997
"... Abstract. In this paper we deal with a problem of Turán concerning the ‘distance ’ of polynomials to irreducible polynomials. Using computational methods we prove that for any monic polynomial P ∈ Z[x] ofdegree≤22 there exists a monic polynomial Q ∈ Z[x]withdeg(Q)=deg(P) such that Q is irreducible o ..."
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Abstract. In this paper we deal with a problem of Turán concerning the ‘distance ’ of polynomials to irreducible polynomials. Using computational methods we prove that for any monic polynomial P ∈ Z[x] ofdegree≤22 there exists a monic polynomial Q ∈ Z[x]withdeg(Q)=deg(P) such that Q is irreducible
The Distance to an Irreducible Polynomial
 CONTEMPORARY MATHEMATICS
, 2009
"... An old problem of P. Turán asks if every polynomial with integer coefficients lies close to an irreducible polynomial of the same degree or less, where the distance between two polynomials f and g is measured as the sum of the absolute values of the coefficients of f − g. We develop some algorithms ..."
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An old problem of P. Turán asks if every polynomial with integer coefficients lies close to an irreducible polynomial of the same degree or less, where the distance between two polynomials f and g is measured as the sum of the absolute values of the coefficients of f − g. We develop some
Large margin methods for structured and interdependent output variables
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary ..."
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Cited by 607 (12 self)
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that solves the optimization problem in polynomial time for a large class of problems. The proposed method has important applications in areas such as computational biology, natural language processing, information retrieval/extraction, and optical character recognition. Experiments from various domains
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 3307 (12 self)
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large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization
THE DISTANCE TO AN IRREDUCIBLE POLYNOMIAL, II
"... Abstract. P. Turán asked if there exists an absolute constant C such that for every polynomial f ∈ Z[x] there exists an irreducible polynomial g ∈ Z[x] with deg(g) ≤ deg(f) and L(f − g) ≤ C, where L(·) denotes the sum of the absolute values of the coefficients. We show that C = 5 suffices for all ..."
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integer polynomials of degree at most 40 by investigating analogous questions in Fp[x] for small primes p. We also prove that a positive proportion of the polynomials in F2[x] have distance at least 4 to an arbitrary irreducible polynomial. 1.
On Approximate Irreducibility of Polynomials in Several Variables
"... We study the problem of bounding a polynomial away from polynomials which are absolutely irreducible. Such separation bounds are useful for testing whether a numerical polynomial is absolutely irreducible, given a certain tolerance on its coefficients. Using an absolute irreducibility criterion due ..."
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Cited by 19 (7 self)
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We study the problem of bounding a polynomial away from polynomials which are absolutely irreducible. Such separation bounds are useful for testing whether a numerical polynomial is absolutely irreducible, given a certain tolerance on its coefficients. Using an absolute irreducibility criterion due
Polynomials
, 2006
"... Time series are unstructured data; they are difficult to monitor, summarize and predict. Weather forecasts, stock market prices, medical data (ECG, EEG) are examples of nonstationary time series we wish to clean, classify and index. Segmentation organizes time series into few intervals having unifo ..."
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uniform characteristics (flatness, linearity, modality, monotonicity and so on). The popular piecewise linear model can determine where the data goes up or down and at what rate. Unfortunately, when the data does not follow a linear model, the computation of the local slope creates overfitting. We propose
Results 1  10
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331,044