Power-Partible Reduction and Congruences

Based on the polynomial reduction, a holonomic (or, P-recursive) sequence $F(k)$ can be decomposed into a summable part and a reduced part. In this paper, we show that when $F(k)$ has a certain kind of symmetry, the reduced part contains only odd or even powers. The reduction in this case is called a power-partible reduction, which is then applied to obtain new series of congruences for Ap\'ery numbers $A_k$ and central Delannoy polynomials $D_k(z)$. In particular, when $p>3$ is a prime, we prove that for each r\in\bN, there is a $p$-adic integer $c_r$ such that \begin{equation*} \sum_{k=0}^{p-1}(2k+1)^{2r+1}A_k\equiv c_r p \pmod {p^3}. \end{equation*

Power-partible Reduction and Congruences for Schr\"oder Polynomials

In this note, we apply the power-partible reduction to show the following arithmetic properties of large Schr\"oder polynomials $S_n(z)$ and little Schr\"oder polynomials $s_n(z)$: for any odd prime $p$, nonnegative integer $r\in\mathbb{N}$, $\varepsilon\in\{-1,1\}$ and $z\in\mathbb{Z}$ with $\gcd(p,z(z+1))=1$, we have $$\sum_{k=0}^{p-1}(2k+1)^{2r+1}\varepsilon^k S_k(z)\equiv 1\pmod {p}\quad \text{and} \quad \sum_{k=0}^{p-1}(2k+1)^{2r+1}\varepsilon^k s_k(z)\equiv 0\pmod {p}.$$Comment: 1

Nanopore-facilitated single molecule detection of circulating microRNAs in cancer patients

Developing new technologies for cancer screening and early diagnosis is a critical issue for saving cancer patients' lives. MicroRNAs (miRNAs) are a class of short (~18-24-nt) non-coding RNAs molecules that regulate gene expression at the post-transcriptional level. Aberrant expression of miRNAs has been found in all types of tumors. Thus miRNAs have been recognized as potential cancer biomarkers. Most notably, specific miRNAs are released from the primary tumor into blood circulation, making the detection of circulating miRNAs profile a powerful tool for noninvasive cancer detection, diagnosis, staging, and monitoring. We developed a robust nanopore sensor that selectively detects single molecules of circulating miRNAs derived from primary cancer. The nanopore is a fabricated 2-nm molecular pore. Such a tiny pore can generate a signature current signal when a miRNA molecule is specifically captured in it. These signals function as fingerprints that enable us to identify a specific miRNA and quantify its concentration. The prototype of nanopore sensor has demonstrated the capability to discriminate single nucleotide difference between miRNAs (single nucleotide polymorphisms, SNPs). In clinical tests, the nanopore has shown the power to differentiate miRNA levels in blood from lung cancer patients and healthy people. Due to the label-free single molecule detection without nucleic acids amplification, the nanopore sensor is higher selective, precise and accurate over the gold standard RT-PCR and microarray. This noninvasive clinical test requires a mere 5 ml of peripheral blood, with a reduced cost from several hundred dollars today to less than 20 dollars per sample. The developing nanopore array would give a high throughput capability for detecting miRNA profile. If validated in clinical trial, the nanopore sensor will become a system available to monitor cancer patients and to screen high risk populations for early diagnosis of cancers which will potentially save the lives of millions. Potential Areas of Applications: * Detection of microRNAs, study of DNA, RNA, DNA/RNA hybrid unzipping kinetics * Study of miRNA mechanism and principle of regulation * Drug discovery and development * Biomarker characterization * Diagnostics and prognostics

Functional protease-activated receptors in the dorsal motor nucleus of the vagus

Protease-activated receptors (PARs), a family member of G-protein coupled receptors, are present and functionally active in a wide variety of cells. The object of this study was to demonstrate the presence and function of PAR-1 and PAR-2 in the dorsal motor nucleus of the vagus (DMV).DMNV neurons were isolated from neonatal rat brainstems using micro-dissection and enzymatic digestion. Neurons were cultured in Neurobasal medium A containing 2% B27 supplement. Intracellular calcium concentration ([Ca 2 +  ] i ) was measured using fura-2 based microspectrometry. Expression of PARs was detected by RT-PCR and immunofluorescent staining.Thrombin and PAR-1 agonist peptide activate PAR-1 with a maximum change in [Ca 2 +  ] i expressed as δF/F0 of 229 ± 14% and 137 ± 7%, respectively. Trypsin and PAR-2 agonist peptide activate PAR-2 with a maximum δF/F0 change of 258 ± 12% and 242 ± 10%, respectively. Inhibition of phospholipase C (PLC) by U73312 (1 μm) decreased the maximal change in δF/F0 induced by PAR-1 activation from 140 ± 17% to 21 ± 3%, while the PAR-2-mediated maximal change in δF/F0 decreased from 185 ± 21% to 19 ± 6%. Blockade of IP3 receptor with 2APB inhibited the maximal change in δF/F0 due to PAR-1 and PAR-2 activation by 72 ± 13% and 71 ± 20% respectively. PAR-1 immnuoreactivity was present in DMV neurons. Increase in transcripts for PAR-1 and PAR-2 were detected in DMV tissues derived from IBD rats relative to control animals. Our results indicate that PAR-1 and PAR-2 are present in the DMV neurons, and their activation leads to increases in intracellular calcium via signal transduction mechanism that involves activation of PLC and the production of IP3.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79371/1/j.1365-2982.2009.01391.x.pd

Three-dimensional topological lattice models with surface anyons

We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they may well capture the topological behavior of some strongly correlated systems. In this work we give a full pedagogical treatment of a special simple case of these models, which we call the 3D semion model: We calculate its ground state degeneracies for a variety of boundary conditions, and classify its low-lying excitations. While point defects in the bulk are confined in pairs connected by energetic strings, the surface excitations are more interesting: the model has deconfined point defects pinned to the boundary of the lattice, and these exhibit semionic braiding statistics. The surface physics is reminiscent of a $\nu=1/2$ bosonic fractional quantum Hall effect in its topological limit, and these considerations help motivate an effective field theoretic description for the lattice models as variants of $bF$ theories. Our special example of the 3D semion model captures much of the behavior of more general `confined Walker-Wang models'. We contrast the 3D semion model with the closely related 3D version of the toric code (a lattice gauge theory) which has deconfined point excitations in the bulk and we discuss how more general models may have some confined and some deconfined excitations. Having seen that there exist lattice models whose surfaces have the same topological order as a bosonic fractional quantum Hall effect on a confining bulk, we construct a lattice model whose surface has similar topological order to a fermionic quantum hall effect. We find that in these models a fermion is always deconfined in the three dimensional bulk

Various Correlations in Anisotropic Heisenberg XYZ Model with Dzyaloshinski-Moriya Interaction

Various thermal correlations as well as the effect of intrinsic decoherence on the correlations are studied in a two-qubit Heisenberg XYZ spin chain with the Dzyaloshinski--Moriya (DM) interaction along the z direction, i.e. Dz. It is found that tunable parameter Dz may play a constructive role on the concurrence (C), classical correlation (CC) and quantum discord (QD) in thermal equilibrium while it plays a destructive role on the correlations in the intrinsic decoherence case. The entanglement and quantum discord exhibit collapse and revival under the phase decoherence. With a proper combination of the system parameters, the correlations can effectively be kept at high steady state values despite the intrinsic decoherence.Comment: 4 pages, 4 figure