Eigenvalues of Random Power law Graphs

Many graphs arising in various information networks exhibit the "power law" behavior -the number of vertices of degree k is proportional to k^-# for some positive #. We show that if # > 2.5, the largest eigenvalue of a random power law graph is almost surely(1+ o(1))?m (1+ o(1))\sqrt{m} where m is the maximum degree. Moreover, the klargest eigenvalues of a random power law graph with exponent # have power law distribution with exponent 2# if the maximum degree is sufficiently large, where k is a function depending on #, mand d, the average degree. When 2<#< 2.5, the largest eigenvalue is heavily concentrated at cm^3-# for some constant c depending on # and the average degree. This result follows from a more general theorem which shows that the largest eigenvalue of a random graph with a given expected degree sequence is determined by m, the maximum degree, and [(d)\tilde] \tilde{d} , the weighted average of the squares of the expected degrees. We show that the k-th largest eigenvalue is almost surely (1+ o(1))?{m_k} (1+ o(1))\sqrt{m_k} where m_k is the k-th largest expected degree provided m_k is large enough. These results have implications on the usage of spectral techniques in many areas related to pattern detection and information retrieval.     

Small Complete Arcs in Projective Planes

In the late 1950s, B. Segre introduced the fundamental notion of arcs and complete arcs [48,49]. An arc in a nite projective plane is a set of points with no three on a line and it is complete if cannot be extended without violating this property. Given a projective plane , determining , the size of its smallest complete arc, has been a major open question in finite geometry for several decades. Assume that has order q, it was shown by Lunelli and Sce [41], more than 40 years ago, that . Apart from this bound, practically nothing was known about , except for the case is the Galois plane. For this case, the best upper bound, prior to this paper, was O(q ^3/4) obtained by Sznyi using the properties of the Galois field GF(q).In this paper, we prove that for any projective plane of order q, where c is a universal constant. Together with Lunelli-Sces lower bound, our result determines up to a polylogarithmic factor. Our proof uses a probabilistic method known as the dynamic random construction or Rödls nibble. The proof also gives a quick randomized algorithm which produces a small complete arc with high probability.The key ingredient of our proof is a new concentration result, which applies for non-Lipschitz functions and is of independent interest.* Research supported in part by grant RB091G-VU from UCSD, by NSF grant DMS-0200357 and by an A. Sloan fellowship.Part of this work was done at AT&T Bell Labs and Microsoft Research     

Synthesis of multi-walled carbon nanotubes for NH3 gas detection

It has been recently demonstrated that carbon nanotubes (CNTs) represent a new type of chemical sensor capable of detecting a small concentration of molecules such as CO, NO₂, NH₃.In this work, CNTs were synthesized by chemical vapor deposition (CVD) on the SiO₂/Si substrate by decomposition of acetylene (C₂H₂) on sputtered Ni catalyst nanoparticles. Their structural properties are studied by atomic force microscopy, high-resolution scanning electron microscopy (HRSEM) and Raman spectroscopy. The CNTs grown at 700 °C exhibit a low dispersion in size, are about 1 μm long and their average diameter varies in the range 25–60 nm as a function of the deposition time. We have shown that their diameter can be reduced either by annealing in oxygen environment or by growing at lower temperature (less than 600 °C).We developed a test device with interdigital Pt electrodes on an Al₂O₃ substrate in order to evaluate the CNTs-based gas sensor capabilities. We performed room temperature current–voltage measurements for various gas concentrations. The CNT films are found to exhibit a fast response and a high sensitivity to NH₃ gas.     

RF generation of the plasma jet channel for the jet PCVD

Breakdown conditions for creation of the hollow cathode discharge in the nozzle passed through the rf powered electrode and creation of the plasma jet channel in PCVD reactor are studied. Pure nitrogen is used for measurements. The creation of jet channel is easier for smaller rf electrodes. The breakdown depends on the pressure and on the gas inflow rate. The plasma potential and the self-bias potential is influenced by the covering of reactor walls and the rf electrode by a dielectric layer.     

Determination of Spectra of Functions

Boundaries of convex and compact spectra of functions on plane are fully described without passing to the complexification and the Fourier transform.     

Production of Acetone–Butanol–Ethanol (ABE) in Direct Fermentation of Cassava by Clostridium saccharoperbutylacetonicum N1-4

In this work, acetone–butanol–ethanol (ABE) fermentation characteristics of cassava starch and cassava chips when using Clostridium saccharoperbutylacetonicum N1-4 was presented. The obtained results in batch mode using a 1-L fermenter showed that C. saccharoperbutylacetonicum N1-4 was a hyperamylolytic strain and capable of producing solvents efficiently from cassava starch and cassava chips, which was comparable to when glucose was used. Batch fermentation of cassava starch and cassava chips resulted in 21.0 and 19.4 g/L of total solvent as compared with 24.2 g/L of total solvent when using glucose. Solvent productivity in fermentation of cassava starch was from 42% to 63% higher than that obtained in fermentation using corn and sago starches in the same condition. In fermentation of cassava starch and cassava chips, maximum butanol concentration was 16.9 and 15.5 g/L, respectively. Solvent yield and butanol yield (based on potential glucose) was 0.33 and 0.41, respectively, for fermentation of cassava starch and 0.30 and 0.38, respectively for fermentation using cassava chips.     

Designing an intelligent teaching simulator for learning to teach by practicing

Learning to teach is difficult for prospective teachers because of the complex nature of the work of teaching. Practicing (Lampert in J Teach Educ 61(1–2):21–34, 2010), interacting with the practice of teaching from a first-person perspective, may give them a unique experience in learning to teach. Computer-based simulators in which the apprentice teacher can interact with virtual students may be used to create that kind of experience. In this paper, we show how to apply techniques in artificial intelligence to design an intelligent learning environment. We show how to model the apprentice’s decision making and resources that can help him or her improve the practice of teaching.