Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

First-principles study of high conductance DNA sequencing with carbon nanotube electrodes

Rapid and cost-effective DNA sequencing at the single nucleotide level might be achieved by measuring a transverse electronic current as single-stranded DNA is pulled through a nano-sized pore. In order to enhance the electronic coupling between the nucleotides and the electrodes and hence the current signals, we employ a pair of single-walled close-ended (6,6) carbon nanotubes (CNTs) as electrodes. We then investigate the electron transport properties of nucleotides sandwiched between such electrodes by using first-principles quantum transport theory. In particular we consider the extreme case where the separation between the electrodes is the smallest possible that still allows the DNA translocation. The benzene-like ring at the end cap of the CNT can strongly couple with the nucleobases and therefore both reduce conformational fluctuations and significantly improve the conductance. The optimal molecular configurations, at which the nucleotides strongly couple to the CNTs, and which yield the largest transmission, are first identified. Then the electronic structures and the electron transport of these optimal configurations are analyzed. The typical tunneling currents are of the order of 50 nA for voltages up to 1 V. At higher bias, where resonant transport through the molecular states is possible, the current is of the order of several $\mu$A. Below 1 V the currents associated to the different nucleotides are consistently distinguishable, with adenine having the largest current, guanine the second-largest, cytosine the third and finally thymine the smallest. We further calculate the transmission coefficient profiles as the nucleotides are dragged along the DNA translocation path and investigate the effects of configurational variations. Based on these results we propose a DNA sequencing protocol combining three possible data analysis strategies.Comment: 12 pages, 17 figures, 3 table

Spin and orbital valence bond solids in a one-dimensional spin-orbital system: Schwinger boson mean field theory

A generalized one-dimensional $SU(2)\times SU(2)$ spin-orbital model is studied by Schwinger boson mean-field theory (SBMFT). We explore mainly the dimer phases and clarify how to capture properly the low temperature properties of such a system by SBMFT. The phase diagrams are exemplified. The three dimer phases, orbital valence bond solid (OVB) state, spin valence bond solid (SVB) state and spin-orbital valence bond solid (SOVB) state, are found to be favored in respectively proper parameter regions, and they can be characterized by the static spin and pseudospin susceptibilities calculated in SBMFT scheme. The result reveals that the spin-orbit coupling of $SU(2)\times SU(2)$ type serves as both the spin-Peierls and orbital-Peierles mechanisms that responsible for the spin-singlet and orbital-singlet formations respectively.Comment: 6 pages, 3 figure

Topological Gauge Structure and Phase Diagram for Weakly Doped Antiferromagnets

We show that the topological gauge structure in the phase string theory of the {\rm t-J} model gives rise to a global phase diagram of antiferromagnetic (AF) and superconducting (SC) phases in a weakly doped regime. Dual confinement and deconfinement of holons and spinons play essential roles here, with a quantum critical point at a doping concentration $x_c\simeq 0.043$. The complex experimental phase diagram at low doping is well described within such a framework.Comment: 4 pages, 2 figures, modified version, to appear in Phys. Rev. Let

On Fully Dynamic Graph Sparsifiers

We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three main results are as follows. First, we give a fully dynamic algorithm for maintaining a $(1 \pm \epsilon)$-spectral sparsifier with amortized update time $poly(\log{n}, \epsilon^{-1})$. Second, we give a fully dynamic algorithm for maintaining a $(1 \pm \epsilon)$-cut sparsifier with \emph{worst-case} update time $poly(\log{n}, \epsilon^{-1})$. Both sparsifiers have size $n \cdot poly(\log{n}, \epsilon^{-1})$. Third, we apply our dynamic sparsifier algorithm to obtain a fully dynamic algorithm for maintaining a $(1 + \epsilon)$-approximation to the value of the maximum flow in an unweighted, undirected, bipartite graph with amortized update time $poly(\log{n}, \epsilon^{-1})$

Long-term power-law fluctuation in Internet traffic

Power-law fluctuation in observed Internet packet flow are discussed. The data is obtained by a multi router traffic grapher (MRTG) system for 9 months. The internet packet flow is analyzed using the detrended fluctuation analysis. By extracting the average daily trend, the data shows clear power-law fluctuations. The exponents of the fluctuation for the incoming and outgoing flow are almost unity. Internet traffic can be understood as a daily periodic flow with power-law fluctuations.Comment: 10 pages, 8 figure

Poisson homology of r-matrix type orbits I: example of computation

In this paper we consider the Poisson algebraic structure associated with a classical $r$-matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the $r$-matrix type Poisson orbits. Then we describe the $r$-matrix Poisson pencil (i.e the pair of compatible Poisson structures) of rank 1 or $CP^n$-type orbits of $SL(n,C)$. Here we calculate symplectic leaves and the integrable foliation associated with the pencil. We also describe the algebra of functions on $CP^n$-type orbits. In Section 2 we calculate the Poisson homology of Drinfeld--Sklyanin Poisson brackets which belong to the $r$-matrix Poisson family