Supersymmetric methods in the traveling variable: inside neurons and at the brain scale

We apply the mathematical technique of factorization of differential operators to two different problems. First we review our results related to the supersymmetry of the Montroll kinks moving onto the microtubule walls as well as mentioning the sine-Gordon model for the microtubule nonlinear excitations. Second, we find analytic expressions for a class of one-parameter solutions of a sort of diffusion equation of Bessel type that is obtained by supersymmetry from the homogeneous form of a simple damped wave equations derived in the works of P.A. Robinson and collaborators for the corticothalamic system. We also present a possible interpretation of the diffusion equation in the brain contextComment: 14 pages, 1 figur

Cohomological Finiteness Conditions in Bredon Cohomology

We show that any soluble group $G$ of type Bredon-\FP_{\infty} with respect to the family of all virtually cyclic subgroups such that centralizers of infinite order elements are of type \FP_{\infty} must be virtually cyclic. To prove this, we first reduce the problem to the case of polycyclic groups and then we show that a polycyclic-by-finite group with finitely many conjugacy classes of maximal virtually cyclic subgroups is virtually cyclic. Finally we discuss refinements of this result: we only impose the property Bredon-\FP_n for some $n \leq 3$ and restrict to abelian-by-nilpotent, abelian-by-polycyclic or (nilpotent of class 2)-by-abelian groups.Comment: Corrected a mistake in Lemma 2.4 of the previous version, which had an effect on the results in Section 5 (the condition that all centralisers of infinite order elements are of type $FP_\infty$ was added

Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA

In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. They eliminated the polynomial background at^b through the direct fitting of the polynomial coefficients a and b. We here reconsider their work eliminating the polynomial trend by means of the multifractal-based detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution property is employed to filter out the trend in a more speedy way than the direct polynomial fitting and also with respect to the wavelet transform modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet transform is used to calculate the trend as a local feature that enters the so-called details signal. We illustrate our result for three representative ECA rules: 90, 105, and 150. We confirm their multifractal behavior and provide our results for the scaling parametersComment: 8 pages, 5 figures, 21 reference

Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA

In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. They eliminated the polynomial background at^b through the direct fitting of the polynomial coefficients a and b. We here reconsider their work eliminating the polynomial trend by means of the multifractal-based detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution property is employed to filter out the trend in a more speedy way than the direct polynomial fitting and also with respect to the wavelet transform modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet transform is used to calculate the trend as a local feature that enters the so-called details signal. We illustrate our result for three representative ECA rules: 90, 105, and 150. We confirm their multifractal behavior and provide our results for the scaling parametersComment: 8 pages, 5 figures, 21 reference

VLT and GTC observations of SDSS J0123+00: a type 2 quasar triggered in a galaxy encounter?

We present long-slit spectroscopy, continuum and [OIII]5007 imaging data obtained with the Very Large Telescope and the Gran Telescopio Canarias of the type 2 quasar SDSS J0123+00 at z=0.399. The quasar lies in a complex, gas-rich environment. It appears to be physically connected by a tidal bridge to another galaxy at a projected distance of ~100 kpc, which suggests this is an interacting system. Ionized gas is detected to a distance of at least ~133 kpc from the nucleus. The nebula has a total extension of ~180 kpc. This is one of the largest ionized nebulae ever detected associated with an active galaxy. Based on the environmental properties, we propose that the origin of the nebula is tidal debris from a galactic encounter, which could as well be the triggering mechanism of the nuclear activity. SDSS J0123+00 demonstrates that giant, luminous ionized nebulae can exist associated with type 2 quasars of low radio luminosities, contrary to expectations based on type 1 quasar studies.Comment: 6 pages, 5 figures. Accepted for publication in MNRAS Letter

Length-weight relationships of coral reef fishes from the Alacran Reef, Yucatan, Mexico

Length-weight relationships were computed for 42 species of coral reef fishes from 14 families from the Alacran Reef (Yucatan, Mexico). A total of 1 892 individuals was used for this purpose. The fish species were caught by different fishing techniques such as fishhooks, harpoons, gill and trawl nets. The sampling period was from March 1998 to January 2000