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G Ordaz - One of the best experts on this subject based on the ideXlab platform.
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a two parameter Recursion formula for scalar field theory
Journal of Physics A, 1996Co-Authors: Y Meurice, G OrdazAbstract:We present a two-parameter family of Recursion formulae for scalar field theory. The first parameter is the dimension (D). The second parameter allows one to continuously extrapolate between Wilson's approximate Recursion formula and the Recursion formula of Dyson's hierarchical model. We show numerically that at fixed D, the critical exponent depends continuously on . We suggest the use of the -independence as a guide to construct improved Recursion formulae.
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a two parameter Recursion formula for scalar field theory
arXiv: High Energy Physics - Lattice, 1996Co-Authors: Y Meurice, G OrdazAbstract:We present a two-parameter family of Recursion formulas for scalar field theory. The first parameter is the dimension $(D)$. The second parameter ($\zeta$) allows one to continuously extrapolate between Wilson's approximate Recursion formula and the Recursion formula of Dyson's hierarchical model. We show numerically that at fixed $D$, the critical exponent $\gamma $ depends continuously on $\zeta$. We suggest the use of the $\zeta -$independence as a guide to construct improved Recursion formulas.
Y Meurice - One of the best experts on this subject based on the ideXlab platform.
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a two parameter Recursion formula for scalar field theory
Journal of Physics A, 1996Co-Authors: Y Meurice, G OrdazAbstract:We present a two-parameter family of Recursion formulae for scalar field theory. The first parameter is the dimension (D). The second parameter allows one to continuously extrapolate between Wilson's approximate Recursion formula and the Recursion formula of Dyson's hierarchical model. We show numerically that at fixed D, the critical exponent depends continuously on . We suggest the use of the -independence as a guide to construct improved Recursion formulae.
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a two parameter Recursion formula for scalar field theory
arXiv: High Energy Physics - Lattice, 1996Co-Authors: Y Meurice, G OrdazAbstract:We present a two-parameter family of Recursion formulas for scalar field theory. The first parameter is the dimension $(D)$. The second parameter ($\zeta$) allows one to continuously extrapolate between Wilson's approximate Recursion formula and the Recursion formula of Dyson's hierarchical model. We show numerically that at fixed $D$, the critical exponent $\gamma $ depends continuously on $\zeta$. We suggest the use of the $\zeta -$independence as a guide to construct improved Recursion formulas.
Gregory Berkolaiko - One of the best experts on this subject based on the ideXlab platform.
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analysis of carleman representation of analytical Recursions
Journal of Mathematical Analysis and Applications, 1998Co-Authors: Gregory Berkolaiko, Savely Rabinovich, Shlomo HavlinAbstract:We study a general method to map a nonlinear analytical Recursion onto a linear one. The solution of the Recursion is represented as a product of matrices whose elements depend only on the form of the Recursion and not on initial conditions. First we consider the method for polynomial Recursions of arbitrary degree and then the method is generalized to analytical Recursions. Some properties of these matrices, such as the existence of an inverse matrix and diagonalization, are also studied.
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Solving nonlinear Recursions
Journal of Mathematical Physics, 1996Co-Authors: Savely Rabinovich, Gregory Berkolaiko, Shlomo HavlinAbstract:A general method to map a polynomial Recursion on a matrix linear one is suggested. The solution of the Recursion is represented as a product of a matrix multiplied by the vector of initial values. This matrix is product of transfer matrices whose elements depend only on the polynomial and not on the initial conditions. The method is valid for systems of polynomial Recursions and for polynomial Recursions of arbitrary order. The only restriction on these recurrent relations is that the highest‐order term can be written in explicit form as a function of the lower‐order terms (existence of a normal form). A continuous analog of this method is described as well.
Thomas W. Cusick - One of the best experts on this subject based on the ideXlab platform.
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Affine equivalence for quadratic rotation symmetric Boolean functions
Designs Codes and Cryptography, 2020Co-Authors: Alexandru Chirvasitu, Thomas W. CusickAbstract:Let $$f_n(x_0, x_1, \ldots , x_{n-1})$$ f n ( x 0 , x 1 , … , x n - 1 ) denote the algebraic normal form (polynomial form) of a rotation symmetric (RS) Boolean function of degree d in $$n \ge d$$ n ≥ d variables and let $$wt(f_n)$$ w t ( f n ) denote the Hamming weight of this function. Let $$(0, a_1, \ldots , a_{d-1})_n$$ ( 0 , a 1 , … , a d - 1 ) n denote the function $$f_n$$ f n of degree d in n variables generated by the monomial $$x_0x_{a_1} \ldots x_{a_{d-1}}.$$ x 0 x a 1 … x a d - 1 . Such a function $$f_n$$ f n is called monomial rotation symmetric (MRS). It was proved in a 2012 paper that for any MRS $$f_n$$ f n with $$d=3,$$ d = 3 , the sequence of weights $$\{w_k = wt(f_k):~k = 3, 4, \ldots \}$$ { w k = w t ( f k ) : k = 3 , 4 , … } satisfies a homogeneous linear Recursion with integer coefficients. This result was gradually generalized in the following years, culminating around 2016 with the proof that such Recursions exist for any rotation symmetric function $$f_n.$$ f n . Recursions for quadratic RS functions were not explicitly considered, since a 2009 paper had already shown that the quadratic weights themselves could be given by an explicit formula. However, this formula is not easy to compute for a typical quadratic function. This paper shows that the weight Recursions for the quadratic RS functions have an interesting special form which can be exploited to solve various problems about these functions, for example, deciding exactly which quadratic RS functions are balanced.
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Theory of 2-rotation symmetric cubic Boolean functions
Designs Codes and Cryptography, 2015Co-Authors: Thomas W. Cusick, Bryan JohnsAbstract:A Boolean function in $$n$$ n variables is $$2$$ 2 - rotation symmetric if it is invariant under even powers of the cyclic permutation $$\rho (x_1,\ldots ,x_n)=(x_2,\ldots ,x_n,x_1)$$ ρ ( x 1 , … , x n ) = ( x 2 , … , x n , x 1 ) of the variables, but not under the first power (ordinary rotation symmetry); for brevity, we call such a function a $$2$$ 2 -function. A $$2$$ 2 -function is said to be monomial rotation symmetric (MRS) if it is generated by applying powers of $$\rho ^2$$ ρ 2 to a single monomial. This paper develops the theory of cubic MRS $$2$$ 2 -functions in $$2n$$ 2 n variables generated by a monomial $$x_1 x_r x_s$$ x 1 x r x s with $$1 2. An exact count of the equivalence classes is given and their number is proved to be very small, in fact $$O(n^{\epsilon })$$ O ( n ϵ ) for any $$\epsilon > 0.$$ ϵ > 0 . It is proved that the sequence of Hamming weights $$\{wt(2 \text {-}(1,r,s)_{2n}):~2n \ge s\}$$ { w t ( 2 - ( 1 , r , s ) 2 n ) : 2 n ≥ s } satisfies a linear Recursion with integer coefficients. A similar result for ordinary cubic MRS functions was proved recently (papers by Bileschi, Cusick and Padgett, and by Brown and Cusick), but this paper uses a new method for the $$2$$ 2 -functions proof. Unlike the ordinary MRS function case, both the orders of the Recursions for the $$2$$ 2 -functions and the precise values of the roots of the corresponding Recursion polynomials can be given explicitly. Finally, a precise value for the weights of the $$2$$ 2 -functions is proved, using a 2011 formula of Cusick and Padgett. These weights are connected to powers of members of the well known Lucas sequence, and so the weights can be found without computing initial values for the Recursions.
Wayne M Getz - One of the best experts on this subject based on the ideXlab platform.
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methods for assessing movement path Recursion with application to african buffalo in south africa
Ecology, 2009Co-Authors: Shirli Bardavid, Israel Bardavid, Paul C Cross, Sadie J Ryan, Christiane U Knechtel, Wayne M GetzAbstract:Recent developments of automated methods for monitoring animal movement, e.g., global positioning systems (GPS) technology, yield high-resolution spatiotemporal data. To gain insights into the processes creating movement patterns, we present two new techniques for extracting information from these data on repeated visits to a particular site or patch (“Recursions”). Identification of such patches and quantification of Recursion pathways, when combined with patch-related ecological data, should contribute to our understanding of the habitat requirements of large herbivores, of factors governing their space-use patterns, and their interactions with the ecosystem. We begin by presenting output from a simple spatial model that simulates movements of large-herbivore groups based on minimal parameters: resource availability and rates of resource recovery after a local depletion. We then present the details of our new techniques of analyses (Recursion analysis and circle analysis) and apply them to data generated by our model, as well as two sets of empirical data on movements of African buffalo (Syncerus caffer): the first collected in Klaserie Private Nature Reserve and the second in Kruger National Park, South Africa. Our Recursion analyses of model outputs provide us with a basis for inferring aspects of the processes governing the production of buffalo Recursion patterns, particularly the potential influence of resource recovery rate. Although the focus of our simulations was a comparison of movement patterns produced by different resource recovery rates, we conclude our paper with a comprehensive discussion of how Recursion analyses can be used when appropriate ecological data are available to elucidate various factors influencing movement. Inter alia, these include the various limiting and preferred resources, parasites, and topographical and landscape factors.
