An LU-fuzzy calculator for the basic fuzzy calculus

The LU-model for fuzzy numbers has been introduced in [4] and applied to fuzzy calculus in [9]; in this paper we build an LU-fuzzy calculator, in order to explain the use of the LU-fuzzy representation and to show the advantage of the parametrization. The calculator produces the basic fuzzy calculus: the arithmetic operations (scalar multiplication, addition, subtraction, multiplica- tion, division) and the fuzzy extension of many univariate functions (power with integer positive or negative exponent, exponential , logarithm, general power function with numeric or fuzzy exponent, sin, arcsin, cos, arccos, tan, arctan, square root, Gaussian and standard Gaussian functions, hyperbolic sinh, cosh, tanh and inverses, erf error function and complementary erfc error function, cu- mulative standard normal distribution). The use of the calculator is illustrated.Fuzzy Sets, LU-fuzzy Calculator, Fuzzy Calculus

Representing fuzzy numbers for fuzzy calculus

In this paper we illustrate the LU representation of fuzzy numbers and present an LU-fuzzy calculator, in order to explain the use of the LU-fuzzy model and to show the advantage of the parametrization. The model can be applied either in the level-cut or in generalized LR frames. The hand-like fuzzy calculator has been developed for the MSWindows platform and produces the basic fuzzy calculus: the arithmetic operations (scalar multiplication, addition, subtraction, multiplication, division) and the fuzzy extension of many univariate functions (exponential, logarithm, power with numeric or fuzzy exponent, sin, arcsin, cos, arccos, tan, arctan, square root, Gaussian, hyperbolic sinh, cosh, tanh and inverses, erf and erfc error functions, cumulative standard normal distribution).Fuzzy Sets, LU-fuzzy Calculator, Fuzzy Calculus, Parametric LU represemtation

The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity

Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.Comment: 29 pages, 13 figure

PuFFIN--a parameter-free method to build nucleosome maps from paired-end reads.

BackgroundWe introduce a novel method, called PuFFIN, that takes advantage of paired-end short reads to build genome-wide nucleosome maps with larger numbers of detected nucleosomes and higher accuracy than existing tools. In contrast to other approaches that require users to optimize several parameters according to their data (e.g., the maximum allowed nucleosome overlap or legal ranges for the fragment sizes) our algorithm can accurately determine a genome-wide set of non-overlapping nucleosomes without any user-defined parameter. This feature makes PuFFIN significantly easier to use and prevents users from choosing the "wrong" parameters and obtain sub-optimal nucleosome maps.ResultsPuFFIN builds genome-wide nucleosome maps using a multi-scale (or multi-resolution) approach. Our algorithm relies on a set of nucleosome "landscape" functions at different resolution levels: each function represents the likelihood of each genomic location to be occupied by a nucleosome for a particular value of the smoothing parameter. After a set of candidate nucleosomes is computed for each function, PuFFIN produces a consensus set that satisfies non-overlapping constraints and maximizes the number of nucleosomes.ConclusionsWe report comprehensive experimental results that compares PuFFIN with recently published tools (NOrMAL, TEMPLATE FILTERING, and NucPosSimulator) on several synthetic datasets as well as real data for S. cerevisiae and P. falciparum. Experimental results show that our approach produces more accurate nucleosome maps with a higher number of non-overlapping nucleosomes than other tools