On the Robustness of NK-Kauffman Networks Against Changes in their Connections and Boolean Functions

NK-Kauffman networks {\cal L}^N_K are a subset of the Boolean functions on N Boolean variables to themselves, \Lambda_N = {\xi: \IZ_2^N \to \IZ_2^N}. To each NK-Kauffman network it is possible to assign a unique Boolean function on N variables through the function \Psi: {\cal L}^N_K \to \Lambda_N. The probability {\cal P}_K that \Psi (f) = \Psi (f'), when f' is obtained through f by a change of one of its K-Boolean functions (b_K: \IZ_2^K \to \IZ_2), and/or connections; is calculated. The leading term of the asymptotic expansion of {\cal P}_K, for N \gg 1, turns out to depend on: the probability to extract the tautology and contradiction Boolean functions, and in the average value of the distribution of probability of the Boolean functions; the other terms decay as {\cal O} (1 / N). In order to accomplish this, a classification of the Boolean functions in terms of what I have called their irreducible degree of connectivity is established. The mathematical findings are discussed in the biological context where, \Psi is used to model the genotype-phenotype map.Comment: 17 pages, 1 figure, Accepted in Journal of Mathematical Physic

Los derechos humanos desde la emergencia indígena en México

En el presente texto se analiza brevemente un proceso político-jurídico que está ocurriendo desde la emergencia indígena en algunas regiones de México en la segunda década del siglo XXI. Se trata de experiencias autonómicas de comunidades indígenas que, luego de contar con reconocimiento constitucional e internacional de sus derechos humanos, han decidido ejercerlos en tanto derechos colectivos para comenzar a configurar el autogobierno indígena en dos ámbitos: el municipal y el submunicipal. Dichos procesos se están gestando desde el activismo político-social de las propias comunidades, acompañadas de estrategias legales como la judicialización de sus demandas, mismas que se traducen en experiencias exitosas porque han generado importantes precedentes judiciales, a partir de los cuales las demás comunidades indígenas de México encuentran una alternativa para comenzar a reivindicar sus derechos humanos.Lo anterior está generando un fenómeno de transformación considerable en el ámbito comunitario, pero, sobre todo, está poniendo en entredicho la visión oficial o institucional de los derechos humanos indígenas hasta ahora reconocidos.

The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness

We determine the average number $\vartheta (N, K)$, of \textit{NK}-Kauffman networks that give rise to the same binary function. We show that, for $N \gg 1$, there exists a connectivity critical value $K_c$ such that $\vartheta(N,K) \approx e^{\phi N}$ ($\phi > 0$) for $K < K_c$ and $\vartheta(N,K) \approx 1$ for $K > K_c$. We find that $K_c$ is not a constant, but scales very slowly with $N$, as $K_c \approx \log_2 \log_2 (2N / \ln 2)$. The problem of genetic robustness emerges as a statistical property of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints in the average number of epistatic interactions that the genotype-phenotype map can have.Comment: 4 figures 18 page

Discrete Dynamical Systems Embedded in Cantor Sets

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $N$ variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit $N\to\infty$. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological entropy and Lyapunov exponents through the concept of error-profile. We made explicit calculations both numerical and analytic for well known discrete dynamical models.Comment: 36 pages, 13 figures: minor text amendments in places, time running top to bottom in figures, to appear in J. Math. Phy

The Asymptotic Number of Attractors in the Random Map Model

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We derive here explicit formulas for the statistical distribution of the number of attractors in the system. As in related results, the number of operations involved by our formulas increases exponentially with n; therefore, they are not directly applicable to study the behavior of systems where n is large. However, our formulas lend themselves to derive useful asymptotic expressions, as we show.Comment: 16 pages, 1 figure. Minor changes. To be published in Journal of Physics A: Mathematical and Genera

Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity

We establish the relation between the ISO(2,1) homotopy invariants and the polygon representation of (2+1)-dimensional gravity. The polygon closure conditions, together with the SO(2,1) cycle conditions, are equivalent to the ISO(2,1) cycle conditions for the representa- tions of the fundamental group in ISO(2,1). Also, the symplectic structure on the space of invariants is closely related to that of the polygon representation. We choose one of the polygon variables as internal time and compute the Hamiltonian, then perform the Hamilton-Jacobi transformation explicitly. We make contact with other authors' results for g = 1 and g = 2 (N = 0).Comment: 34 pages, Mexico preprint ICN-UNAM-93-1

Effects of heat waves and light deprivation on giant kelp juveniles (Macrocystis pyrifera, Laminariales, Paeophyceae

Due to climate change, the incidence of marine heat waves (MHWs) has increased, yet their effects on seaweeds are still not well understood. Adult sporophytes of Macrocystis pyrifera, the species forming the iconic giant kelp forests, can be negatively affected by thermal stress and associated environmental factors (e.g., nutrient depletion, light deprivation); however, little is known about the tolerance/vulnerability of juvenile sporophytes. Simultaneously to MHWs, juveniles can be subjected to light limitation for extended periods of time (days–weeks) due to factors causing turbidity, or even because of shading by understory canopyforming seaweeds. This study evaluated the effects of a simulated MHW (24°C, 7 d) in combination (or not) with light deprivation, on the hotosynthetic capacities, nutrient uptake, and tissue composition, as well as oxidative stress descriptors of M. pyrifera juvenile sporophytes (single blade stage, up to 20 cm length). Maximum quantum yield (Fv/Fm) decreased in juveniles under light at 24°C, likely reflecting some damage on the photosynthetic apparatus or dynamic photoinhibition; however, no other sign of physiological alteration was found in this treatment (i.e., pigments, nutrient reserves and uptake, oxidative stress). Photosynthetic capacities were maintained or even enhanced in plants under light deprivation, likely supported by photoacclimation (pigments increment); by contrast, nitrate uptake and internal storage of carbohydrates were strongly reduced, regardless of temperature. This study indicated that light limitation can be more detrimental to juvenile survival, and therefore recruitment success of M. pyrifera forests, than episodic thermal stress from MHWs.En prensa2,23

Weyl's law and quantum ergodicity for maps with divided phase space

For a general class of unitary quantum maps, whose underlying classical phase space is divided into several invariant domains of positive measure, we establish analogues of Weyl's law for the distribution of eigenphases. If the map has one ergodic component, and is periodic on the remaining domains, we prove the Schnirelman-Zelditch-Colin de Verdiere Theorem on the equidistribution of eigenfunctions with respect to the ergodic component of the classical map (quantum ergodicity). We apply our main theorems to quantised linked twist maps on the torus. In the Appendix, S. Zelditch connects these studies to some earlier results on `pimpled spheres' in the setting of Riemannian manifolds. The common feature is a divided phase space with a periodic component.Comment: Colour figures. Black & white figures available at http://www2.maths.bris.ac.uk/~majm. Appendix by Steve Zelditc

Nitrogen uptake and internal recycling in Zostera marina exposed to oyster farming: eelgrass potential as a natural biofilter

Oyster farming in estuaries and coastal lagoons frequently overlaps with the distribution of seagrass meadows, yet there are few studies on how this aquaculture practice affects seagrass physiology. We compared in situ nitrogen uptake and the productivity of Zostera marina shoots growing near off-bottom longlines and at a site not affected by oyster farming in San Quintin Bay, a coastal lagoon in Baja California, Mexico. We used benthic chambers to measure leaf NH4 (+) uptake capacities by pulse labeling with (NH4)-N-15 (+) and plant photosynthesis and respiration. The internal N-15 resorption/recycling was measured in shoots 2 weeks after incubations. The natural isotopic composition of eelgrass tissues and vegetative descriptors were also examined. Plants growing at the oyster farming site showed a higher leaf NH4 (+) uptake rate (33.1 mmol NH4 (+) m(-2) day(-1)) relative to those not exposed to oyster cultures (25.6 mmol NH4 (+) m(-2) day(-1)). We calculated that an eelgrass meadow of 15-16 ha (which represents only about 3-4 % of the subtidal eelgrass meadow cover in the western arm of the lagoon) can potentially incorporate the total amount of NH4 (+) excreted by oysters (similar to 5.2 x 10(6) mmol NH4 (+) day(-1)). This highlights the potential of eelgrass to act as a natural biofilter for the NH4 (+) produced by oyster farming. Shoots exposed to oysters were more efficient in re-utilizing the internal N-15 into the growth of new leaf tissues or to translocate it to belowground tissues. Photosynthetic rates were greater in shoots exposed to oysters, which is consistent with higher NH4 (+) uptake and less negative delta C-13 values. Vegetative production (shoot size, leaf growth) was also higher in these shoots. Aboveground/belowground biomass ratio was lower in eelgrass beds not directly influenced by oyster farms, likely related to the higher investment in belowground biomass to incorporate sedimentary nutrients

Aislamiento de Levaduras Killer en Alimentos.

Las levaduras killer, se caracterizan por secretar una toxina proteica, llamada “toxina killer” que es letal para cepas sensibles de su misma especie o especies de diferentes géneros, pero siendo ellas mismas inmunes a sus propias toxinas. Estas pueden ser utilizadas como biocontrol en la poscosecha de alimentos. Se tomaron muestras de tepache y queso fresco del cual se aislaron 7 y 8 levaduras en el medio YEPD (Extracto de levadura, peptona, dextrosa y agar bacteriológico) se incubaron a 25ºC por 48h. Se realizó el ensayo Killer para dichas levaduras en placas con agar YEPD-MB (Extracto de levadura, peptona, dextrosa, agar bacteriológico con azul de metileno), realizando 8 divisiones en la placa cada levadura susceptible del panel se inoculó a manera de césped (ATCC26609, Ca023, VG028, Derma5, RG001 y WG002) para posteriormente agregar en cada división una levadura aislada y la levadura control LALVIN (Killer) y se incubaron a 25ºC por 48 horas. Obteniendo 6 levaduras con el fenotipo Killer para el tepache y 7 levaduras en el queso fresco, la conservación de las cepas se llevó a cabo en tubos falcón con una solución de glicerol 20% y agua destilada 80%. Posteriormente permanecenen congelación a 4º C