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Abstract.A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is plausible for infinitely large systems, in conjunction with the introduction of a Lagrange multiplier for constraining the length of the eigenvector, the eigenvalue problem is reduced to a bunch of optimization problems of a quadratic function of a single variable, and the coefficients of the first and the second order terms of the functions act as cavity fields that are handled in cavity analysis. We show that the first eigenvalue is determined in such a way that the distribution of the cavity fields has a finite value for the second order moment with respect to the cavity fields of the first order coefficient. The validity and utility of the developed methodology are examined by applying it to two analytically solvable and one simple but non-trivial examples in conjunction with numerical justification.

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The present study compared the abilities of the spectral vegetation indices (VI) of Advanced Very High Resolution Radiometer (AVHRR) and Moderate Resolution Imaging Spectroradiometer (MODIS) sensors in accurately detecting seasonal vegetation changes (phenology) with regard to forage quantity and quality. The normalized difference vegetation index (NDVI) and enhanced vegetation index (EVI) were computed with a 10-day maximum value composite from April 1 to October 31, 2002. The study sites included four meadow steppes and six typical steppes in the Xilingol steppe area of central Inner Mongolia, China. Comparisons of the MODIS-NDVI and AVHRR-NDVI profiles revealed that the MODIS-NDVI temporal profile had a higher fidelity. The dynamic range of the MODIS-NDVI was then analyzed and its sensitivity in discriminating between vegetation differences was evaluated in sparsely and densely vegetated areas. Estimations of the live, dead standing, total biomass and crude protein (CP) concentration and standing CP were obtained using AVHRR-NDVI (1.1 km pixels), MODIS-NDVI and -EVI (500 m pixels). Regression analysis revealed that the MODIS-VI showed a good coefficient of determination ( R 2 = 0.77-0.83) with regard to estimations of the total and live biomass. Furthermore, the MODIS-EVI was a good predictor of standing CP ( R 2 = 0.74) compared with AVHRR ( R 2 = 0.53). These results suggest that the MODIS-VI can reliably detect the phenology and forage quantity and quality of grassland steppe areas.

Scalability is a key requirement for any KDD and data mining algorithm, and one of the biggest research challenges is to develop methods that allow to use large amounts of data. One possible approach for dealing with huge amounts of data is to take a random sample and do data mining on it, since for many data mining applications approximate answers are acceptable. However, as argued by several researchers, random sampling is difficult to use due to the difficulty of determining an appropriate sample size. In this paper, we take a sequential sampling approach for solving this difficulty, and propose an adaptive sampling algorithm that solves a general problem covering many problems arising in applications of discovery science. The algorithm obtains examples sequentially in an on-line fashion, and it determines from the obtained examples whether it has already seen a large enough number of examples. Thus, sample size is not fixed a priori; instead, it adaptively depends on the situation. Due to this adaptiveness, if we are not in a worst case situation as fortunately happens in many practical applications, then we can solve the problem with a number of examples much smaller than the required in the worst case. For illustrating the generality of our approach, we also describe how different instantiations of it can be applied to scale up knowledge discovery problems that appear in several areas.

A self-cross-linking polymer electrolyte based on polystyrene-incorporated poly͑ethylene oxide͒ ͑PEO͒ containing LiTFSI has been tested in an all solid-state lithium-polymer battery (Li/SP-E/Li x MnO 2 with a solid polymer electrolyte. The polymer electrolyte showed high stability toward metallic lithium. Mechanical properties of the electrolyte film were much improved by incorporating the polystyrene, but ion conductivity was decreased to half of the value obtained in pure PEO electrolyte film. The cell was charged and discharged at a high temperature ͑80°C͒, providing about 80% utilization of the positive electrode. The cell showed good cycle life at 80°C, keeping 90% of the initial capacity after 50 cycles.Lithium-ion technology is rapidly contributing to the state-of-art of secondary systems and has been commercially used in popular portable devices such as cellular phones and note-size computers. However, such batteries are not being rapidly developed for electric vehicles ͑EVs͒ in view of the safety of the devices because the use of a liquid electrolyte may result in problems, i.e., leakage of a flammable electrolyte, production of gases upon overcharge or overdischarge, and a thermal runaway reaction when the battery is heated to high temperatures. On the other hand, an all solid-state lithium/polymer battery ͑LPB͒ using a metallic lithium anode and solvent-free polymer electrolyte has been demonstrated to be the most promising secondary battery for EV applications because of its absence of risk for leakage of liquid electrolyte, its higher energy density, and its shape flexibility. One of the paramount approaches is to use a thin film of polymer electrolyte with high ionic conductivity and strong mechanical integrity. 1-9 High ionic conductivity is expected to improve rate capability. Good mechanical properties are required to protect against shortages, to assure safety reliability, and to make a feasible thin film, thus improving battery-specific energy and rate capability. However, it is difficult to optimize both the energy and rate capability. In the present work, we used a polystyrene-poly͑ethylene oxide͒ ͑PEO͒ block-graft copolymer, which has a microphase-separated structure, a lamellar shape, good ionic conductivity, and excellent mechanical properties, as the polymer electrolyte for a Li/Li x MnO 2 cell. The electrochemical performance, especially the effect of the film thickness on rate capability, was evaluated. ExperimentalThe detailed synthesis condition of the polystyrene-poly͑ethylene oxide͒ block-graft copolymer ͑SE-P͒ is reported elsewhere. 10 The structure of the polymer is shown in Fig. 1. The average molecular weight is 3.4 ϫ 10 5 with an ethylene oxide ͑EO͒ content of 60 wt %. Battery-grade lithium bis͑trifluoromethanesulfonyl͒imide ͑LiTFSI Kishida Chemical Co., Ltd͒ was used as the electrolyte salt and was vacuum dried for 24 h before use. The polymer electrolyte film was prepared by a well-known solvent-casting technique: a known amount of SE-P and LiTFSI, normally an EO/Li ratio of ...

We present persistence length measurements on neurofilaments (NFs), an intermediate filament with protruding side arms, of the neuronal cytoskeleton. Tapping mode atomic force microscopy enabled us to visualize and trace at subpixel resolution photoimmobilized NFs, assembled at various subunit protein ratios, thereby modifying the side-arm length and chain density charge distribution. We show that specific polyampholyte sequences of the side arms can form salt-switchable intrafilament attractions that compete with the net electrostatic and steric repulsion and can reduce the total persistence length by half. The results are in agreement with present X-ray and microscopy data yet present a theoretical challenge for polyampholyte interchain interactions.

We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomial-time hierarchy PH to ZPP(NP) under the assumption that NP has polynomial-size circuits. This improves on the well-known result of Karp, Lipton, and Sipser [KL80] stating a collapse of PH to its second level Σ P 2 under the same assumption. As a further consequence, we derive new collapse consequences under the assumption that complexity classes like UP, FewP, and C = P have polynomialsize circuits. Finally, we investigate the circuit-size complexity of several language classes. In particular, we show that for every fixed polynomial s, there is a set in ZPP(NP) which does not have O(s(n))-size circuits.