Abstract:
A perceptron with N random weights can store of the order of N patterns by removing a fraction of the weights without changing their strengths. The critical storage capacity as a function of the concentration of the remaining bonds for random outputs and for outputs given by a teacher perceptron is calculated. A simple Hebb-like dilution algorithm is presented which in the teacher case reaches the optimal generalization ability.

Abstract:
Using a six-orientifold, fourbranes and four fivebranes in type IIA string theory we construct $\mathcal{N}$=1 supersymmetric gauge theories in four dimensions with product group $SU(M)\times SO(N)$ or $SU(M)\times Sp(2N)$, a bifundamental flavor and quarks. We obtain the Seiberg dual for these theories and rederive it via branes. To obtain the complete dual group via branes we have to add semi-infinite fourbranes. We propose that the theory derived from branes has a meson deformation switched on. This deformation implies higgsing in the dual theory. The addition of the semi-infinite fourbranes compensates this effect.

Abstract:
The modern development of new electronic devices requires rapid manufacturing of their prototypes. Printedcircuit boards (PCB) used for this purpose are expensive and, as a rule, time consuming. PCB milling machines arealso expensive. Here we propose a wire board manufacturing method that could be used in any laboratory forrapid prototyping of electronic devices. This method allows us to create wire boards for surface mountingtechnology, with space between pins down to 0.5 mm. This method demands no special equipment and makes itpossible to manufacture a wire board in a few hours.

Abstract:
Conjugated linoleic acid (CLA) is a wide term which groups together a mixture of positional and geometric isomers of C 18:2 fatty acids having conjugated, or contiguous, double bounds. These fatty acids arise along the ruminal process which ends with full saturation into stearic acid, a stepped pathway carried out by rumen bacteria.These naturally occurring groups of dienoic derivatives of linoleic acid are incorporated into the fat in beef and milk of ruminants before the saturation process has been completed. Numerous beneficial effects are attributed to CLA, as in slowing down or even preventing tumor development. CLA decreases body fat storage in animal models [1] and promotes cardiovascular protection against atheroesclerosis [2]. A growing bulk of evidence shows that CLA, mainly as cis-9, trans-11, 18:2 n-6 derivatives, consistently produced antitumor effects, thus reducing the incidence, progression, number of metastases and tumor burden in rats and in murine models of mammary gland, colon, forestomach, skin and prostate tumorigenesis [3]. The evidence became so convincing that the National Academy of Science advised in 1996 that "Conjugated linoleic acid (CLA) is the only fatty acid shown unequivocally to inhibit carcinogenesis in experimental animals" [4]. Beside CLA, other polyunsaturated fatty acids (PUFA) belonging to the essential fatty acid (EFA) n-3 family, whose main source are fish and seafood, are generally believed to act as antipromoters for several cancers.Interestingly enough for those populations having little o negligible fish intake as in the case of the mediterranean population of Argentina [5,6], CLA remains the only source of beneficial fatty acids with respect to tumor prevention and cardiovascular protection.The natural source of CLA are red meats and fatty dairy products, which are mainly bovine derivatives. However, these foods are also heavily suspected to be related to the higher risk of developing colorectal cancer (CRC) in humans.

Abstract:
2-Benzyloxy-1-methylpyridinium triflate (1) is emerging as a mild, convenient, and in some cases uniquely effective new reagent for the synthesis of benzyl ethers and esters. This article provides a revised benzyl transfer protocol in which N-methylation of 2-benzyloxypyridine delivers the active reagent in situ. Observations on the appropriate choice of solvent (toluene vs. trifluorotoluene) and the extension of this methodology to the synthesis of other arylmethyl ethers are included.

Abstract:
We show the existence of a weak solution for the problem $$ -Delta_p u=lambda_1h(x)|u|^{p-2}u+a(x)g(u)+f(x),quad uinmathcal{D}^{1,p}(mathbb{R}^N), $$ where, 2 les than p less than N$, $lambda_1$ is the first eigenvalue of the $p$-Laplacian on $mathcal{D}^{1,p}(mathbb{R}^N)$ relative to the radially symmetric weight $h(x)=h(|x|)$. In this problem, $g(s)$ is a bounded function for all $sinmathbb{R}$, $ain L^{(p^{*})'}(mathbb{R}^N)cap L^{infty}(mathbb{R}^N)$ and $fin L^{(p^{*})'}(mathbb{R}^N)$. To establish an existence result, we employ the Saddle Point Theorem of Rabinowitz [9] and an improved Poincare inequality from an article of Alziary, Fleckinger and Takac [2].

Abstract:
We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the dissipated energy. In the case of a infinitely slow driving rate (quasi-static model) we find that the probability distribution of the released energy shows two different scaling regions separated by a sharp energy crossover. At low energies, the probability of having an event of energy $E$ decays as $\sim E^{-1/2}$, which is robust and independent of the energy quantifier used (or lattice type). At high energies fluctuations dominate the energy distribution leading to a crossover to a different scaling regime, $\sim E^{-2.75}$, whenever the released energy is computed over the whole system. On the contrary, strong finite-size effects are observed if we only consider the energy dissipated at microfractures. In a different numerical experiment the quasi-static dynamics condition is relaxed, so that the system is driven at finite strain load rates, and we find that the energy distribution decays as $\mathcal{P} (E) \sim E^{-1}$ for all the energy range.

Abstract:
We present and analyse new optical images of the dust envelope surrounding the high mass-loss carbon star IRC+10216. This envelope is seen due to external illumination by galactic light. Intensity profiles and colors of the nebula were obtained in the UBV bandpasses. The data are compared with the results of a radiative transfer model calculating multiple scattering of interstellar field photons by dust grains with a single radius. The data show that the observed radial shape of the nebula, especially its half maximum radius, does not depend on wavelength (within experimental errors), suggesting that grains scatter in the grey regime, etc, etc (this abstract has been shortened)

Abstract:
We calculate the storage capacity of a perceptron for correlated gaussian patterns. We find that the storage capacity $\alpha_c$ can be less than 2 if similar patterns are mapped onto different outputs and vice versa. As long as the patterns are in general position we obtain, in contrast to previous works, that $\alpha_c \geq 1$ in agreement with Cover's theorem. Numerical simulations confirm the results.

Agricultural expansion is one
of the prime driving forces of global land cover change. Despite the increasing
attention to the factors that cause it, the patterns and processes associated
with indigenous cultivation systems are not well understood. This study
analyzes agricultural change associated with subsistence-based indigenous
production systems in the lower Pastaza River Basin in the Ecuadorian Amazon
through a spatially explicit dynamic model. The model integrates multiple
logistic regression and cellular automata to simulate agricultural expansion at
a resolution consistent with small scale agriculture and deal with inherently
spatial processes. Data on land use and cultivation practices were collected
through remote sensing and field visits, and processed within a geographic
information system framework. Results show that the probability of an area of
becoming agriculture increases with population pressure, in the vicinity of
existing cultivation plots, and proximity to the center of human settlements.
The positive association between proximity to cultivation areas and the
probability of the presence of agriculture clearly shows the spillover effect
and spatial inertia carried by shifting cultivation practices. The model
depicts an ideal shifting cultivation system, with a complete
cropping-fallow-cropping cycle that shows how agricultural areas expand and
contract across space and over time. The model produced relatively accurate
spatial outputs, as shown by the results of a spatial comparison between the
simulated landscapes and the actual one. The study helped understand local
landscape dynamics associated with shifting cultivation systems and their
implications for land management.