Families of weighted sum formulas for multiple zeta values

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.Comment: The conjecture at the end is reformulate

Experimental study on Gaussian-modulated coherent states quantum key distribution over standard telecom fiber

In this paper, we present a fully fiber-based one-way Quantum Key Distribution (QKD) system implementing the Gaussian-Modulated Coherent States (GMCS) protocol. The system employs a double Mach-Zehnder Interferometer (MZI) configuration in which the weak quantum signal and the strong Local Oscillator (LO) go through the same fiber between Alice and Bob, and are separated into two paths inside Bob's terminal. To suppress the LO leakage into the signal path, which is an important contribution to the excess noise, we implemented a novel scheme combining polarization and frequency multiplexing, achieving an extinction ratio of 70dB. To further minimize the system excess noise due to phase drift of the double MZI, we propose that, instead of employing phase feedback control, one simply let Alice remap her data by performing a rotation operation. We further present noise analysis both theoretically and experimentally. Our calculation shows that the combined polarization and frequency multiplexing scheme can achieve better stability in practice than the time-multiplexing scheme, because it allows one to use matched fiber lengths for the signal and the LO paths on both sides of the double MZI, greatly reducing the phase instability caused by unmatched fiber lengths. Our experimental noise analysis quantifies the three main contributions to the excess noise, which will be instructive to future studies of the GMCS QKD systems. Finally, we demonstrate, under the "realistic model" in which Eve cannot control the system within Bob's terminal, a secure key rate of 0.3bit/pulse over a 5km fiber link. This key rate is about two orders of magnitude higher than that of a practical BB84 QKD system.Comment: 21 pages, 9 figure

Sub-array normalization subject to differentiation

From microarray measurement, we seek differentiation of mRNA expressions among different biological samples. However, each array has a ‘block effect’ due to uncontrolled variation. The statistical treatment of reducing the block effect is usually referred to as normalization. Our perspective is to find a transformation that matches the distributions of hybridization levels of those probes corresponding to undifferentiated genes between arrays. We address two important issues. First, array-specific spatial patterns exist due to uneven hybridization and measurement process. Second, in some cases a substantially large portion of genes are differentially expressed between a target and a reference array. For the purpose of normalization we need to identify a subset that exclude those probes corresponding to differentially expressed genes and abnormal probes due to experimental variation. Least trimmed squares (LTS) is a natural choice to achieve this goal. Substantial differentiation is protected in LTS by setting an appropriate trimming fraction. To take into account any spatial pattern of hybridization, we divide each array into sub-arrays and normalize probe intensities within each sub-array. We illustrate the problem and solution through an Affymetrix spike-in dataset with defined perturbation and a dataset of primate brain expression

Single-breath-hold photoacoustic computed tomography of the breast

We have developed a single-breath-hold photoacoustic computed tomography (SBH-PACT) system to reveal detailed angiographic structures in human breasts. SBH-PACT features a deep penetration depth (4 cm in vivo) with high spatial and temporal resolutions (255 µm in-plane resolution and a 10 Hz 2D frame rate). By scanning the entire breast within a single breath hold (~15 s), a volumetric image can be acquired and subsequently reconstructed utilizing 3D back-projection with negligible breathing-induced motion artifacts. SBH-PACT clearly reveals tumors by observing higher blood vessel densities associated with tumors at high spatial resolution, showing early promise for high sensitivity in radiographically dense breasts. In addition to blood vessel imaging, the high imaging speed enables dynamic studies, such as photoacoustic elastography, which identifies tumors by showing less compliance. We imaged breast cancer patients with breast sizes ranging from B cup to DD cup, and skin pigmentations ranging from light to dark. SBH-PACT identified all the tumors without resorting to ionizing radiation or exogenous contrast, posing no health risks

Systematic identification of cell cycle regulated transcription factors from microarray time series data

<p>Abstract</p> <p>Background</p> <p>The cell cycle has long been an important model to study the genome-wide transcriptional regulation. Although several methods have been introduced to identify cell cycle regulated genes from microarray data, they can not be directly used to investigate cell cycle regulated transcription factors (CCRTFs), because for many transcription factors (TFs) it is their activities instead of expressions that are periodically regulated across the cell cycle. To overcome this problem, it is useful to infer TF activities across the cell cycle by integrating microarray expression data with ChIP-chip data, and then examine the periodicity of the inferred activities. For most species, however, large-scale ChIP-chip data are still not available.</p> <p>Results</p> <p>We propose a two-step method to identify the CCRTFs by integrating microarray cell cycle data with ChIP-chip data or motif discovery data. In <it>S. cerevisiae</it>, we identify 42 CCRTFs, among which 23 have been verified experimentally. The cell cycle related behaviors (e.g. at which cell cycle phase a TF achieves the highest activity) predicted by our method are consistent with the well established knowledge about them. We also find that the periodical activity fluctuation of some TFs can be perturbed by the cell synchronization treatment. Moreover, by integrating expression data with in-silico motif discovery data, we identify 8 cell cycle associated regulatory motifs, among which 7 are binding sites for well-known cell cycle related TFs.</p> <p>Conclusion</p> <p>Our method is effective to identify CCRTFs by integrating microarray cell cycle data with TF-gene binding information. In <it>S. cerevisiae</it>, the TF-gene binding information is provided by the systematic ChIP-chip experiments. In other species where systematic ChIP-chip data is not available, in-silico motif discovery and analysis provide us with an alternative method. Therefore, our method is ready to be implemented to the microarray cell cycle data sets from different species. The C++ program for AC score calculation is available for download from URL <url>http://leili-lab.cmb.usc.edu/yeastaging/projects/project-base/</url>.</p

Prevalence and antimicrobial resistance of Salmonella in retail foods in northern China

A total of 387 retail meat, seafood and milk powder samples were collected from nine cities in northern China in 2005 and screened for the presence of Salmonella. Salmonella strains isolated were subjected to serotyping and antimicrobial susceptibility testing. Salmonella was isolated from 81 (20.9%, 81/387) samples and classified into 23 serotypes. The isolates were frequently resistant to sulfamethoxazole (86.4%), sulfamethoxazole/trimethoprim (48.1%), nalidixic acid (30.9%), tetracycline (19.8%), carboxybenzylpenicillin (17.3%), amoxicillin (17.3%) and ampicillin (16.0%). The multiple resistance (resistance to ≥ 3 antibiotics) was found in 29.6% (n = 24) isolates. Additionally, 4 isolates from chicken displayed the ACSSuTNx profile, resistant to ampicillin, chloramphenicol, streptomycin, sulfonamide, tetracycline and nalidixic acid, in particular, strain HBS084 showing the resistance to as many as 20 antibiotics. Salmonella from chicken showed the higher frequency of antimicrobial resistance. Our findings indicate that in northern China food products of animal origin can be a source of exposure for consumers to multiresistant Salmonella strain