Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero

Let $\mathbf{X}_p=(\mathbf{s}_1,...,\mathbf{s}_n)=(X_{ij})_{p \times n}$ where $X_{ij}$'s are independent and identically distributed (i.i.d.) random variables with $EX_{11}=0,EX_{11}^2=1$ and $EX_{11}^4<\infty$. It is showed that the largest eigenvalue of the random matrix $\mathbf{A}_p=\frac{1}{2\sqrt{np}}(\mathbf{X}_p\mathbf{X}_p^{\prime}-n\mathbf{I}_p)$ tends to 1 almost surely as $p\rightarrow\infty,n\rightarrow\infty$ with $p/n\rightarrow0$.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ381 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

In-situ electrochemical fabrication of natural contacts on single nanowires

We report a template-based in-situ electrochemical method for fabricating natural electric contacts on single nanowires using a pair of cross-patterned electrodes. Such electric contacts are highly stable upon thermal cycling between room temperature and milli-Kelvin temperatures. Direct imaging of the single-nanowire contacts using scanning electron microscopy is also demonstrated.Comment: 13 pages, 4 figure

Prediction of the post-fire flexural capacity of RC beam using GA-BPNN Machine Learning

To accurately predict the flexural capacity of post-fire RC beams is imperative for fire safety design. In this paper, the residual flexural capacity of post-fire RC beams is predicted based on a back-propagation (BP) neural network (NN) optimized by a genetic algorithm (GA). First, the temperature distribution of the beams was determined using the finite element analysis software ABAQUS, and the strength reduction factor of materials was determined. The flexural capacity of the RC beams after fire is calculated by the flexural strength reduction calculation model. The model is used to generate the training data for the NN. To enable machine learning, 480 datasets are produced, of which 360 datasets are used to train the network; the remaining 120 datasets are used to test the network. The predictive models are constructed using BPNN and GA-BPNN respectively. The prediction accuracy is evaluated by comparing the predicted values and the target values. The comparison shows that the GA-BPNN has a faster convergence speed, higher stability, and can reach the goal more times, reducing the possibility of BPNN falling into the local optimum and achieving the global optimum. The proposed GA-BPNN model for predicting the flexural capacity of post-fire RC beams provides a new approach for design practice

Application of Information Theory in Nuclear Liquid Gas Phase Transition

Information entropy and Zipf's law in the field of information theory have been used for studying the disassembly of nuclei in the framework of the isospin dependent lattice gas model and molecular dynamical model. We found that the information entropy in the event space is maximum at the phase transition point and the mass of the cluster show exactly inversely to its rank, i.e. Zipf's law appears. Both novel criteria are useful in searching the nuclear liquid gas phase transition experimentally and theoretically.Comment: 5 pages, 5 figure

On the Reconstructed Fermi Surface in the Underdoped Cuprates

The Fermi surface topologies of underdoped samples the high-Tc superconductor Bi2212 have been measured with angle resolved photoemission. By examining thermally excited states above the Fermi level, we show that the Fermi surfaces in the pseudogap phase of underdoped samples are actually composed of fully enclosed hole pockets. The spectral weight of these pockets is vanishingly small at the anti-ferromagnetic zone boundary, which creates the illusion of Fermi "arcs" in standard photoemission measurements. The area of the pockets as measured in this study is consistent with the doping level, and hence carrier density, of the samples measured. Furthermore, the shape and area of the pockets is well reproduced by a phenomenological model of the pseudogap phase as a spin liquid.Comment: 4 pages, 4 figures. Submitted to Physics Review Letter

Atmospheric input of nitrogen and phosphorus to the Southeast Mediterranean: Sources, fluxes, and possible impact

Estimates of the sources and wet deposition fluxes of inorganic nutrients (PO43-, NO3-, NO2-, NH4+) have been made using a long-term wet atmospheric deposition measurement at three sites along the Mediterranean coast of Israel. The nutrient composition in rainwater indicated a dominant anthropogenic source for NO, and NH: and a continental, natural, and anthropogenic, rock/soil source for PO43-. The calculated long-term dissolved inorganic N (IN) and inorganic P (IP) fluxes were 0.28 and 0.009 g m(-2) yr(-1) to the coastal zone and estimated as 0.24 and 0.008 g m(-2) yr(-1) to the Southeast (SE) Mediterranean, with a possible increasing pattern of the annual dissolved IN fluxes. Concentration of total and seawater leachable LP (LIP) from dust was examined on 20 Whatman 41 filters collected during 1996. The mean total IP concentration in dust was 0.13 +/- 0.11% (geomean = 0.09%), with a mean of 387 +/- 205 mu g IP per g of dust leached by seawater. LIP from dust varies between 6 and 85% (mean of 38%) of the dry total IF. Dust of desert-type (Saharan) events exhibited lower LIP solubility in seawater (similar to 25%, median) than air masses of European origin (similar to 45%, median). The calculated ratio of wet deposition to total (wet and dry) deposition here of 0.2 showed the importance of dry deposition of P in the SE Mediterranean basin compared to atmospheric inputs into the northwestern basin. The total IP and seawater LIP fluxes from dry deposition were estimated as 0.04 and 0.01 g m(-2) yr(-1), respectively. Atmospheric inputs of bioavailable N and P represent an imbalanced contribution to the new production of 8-20 and 4-11%, respectively, and reinforce the unusual N: P ratios (similar to 27) and possible P limitation in the SE Mediterranean