On partially ordered patterns of length 4 and 5 in permutations

Partially ordered patterns (POPs) generalize the notion of classical patterns studied widely in the literature in the context of permutations, words, compositions and partitions. In an occurrence of a POP, the relative order of some of the elements is not important. Thus, any POP of length k is defined by a partially ordered set on k elements, and classical patterns correspond to k-element chains. The notion of a POP provides a convenient language to deal with larger sets of permutation patterns. This paper contributes to a long line of research on classical permutation patterns of length 4 and 5, and beyond, by conducting a systematic search of connections between sequences in the Online Encyclopedia of Integer Sequences (OEIS) and permutations avoiding POPs of length 4 and 5. As the result, we (i) obtain 13 new enumerative results for classical patterns of length 4 and 5, and a number of results for patterns of arbitrary length, (ii) collect under one roof many sporadic results in the literature related to avoidance of patterns of length 4 and 5, and (iii) conjecture 6 connections to the OEIS. Among the most intriguing bijective questions we state, 7 are related to explaining Wilf-equivalence of various sets of patterns, e.g. 5 or 8 patterns of length 4, and 2 or 6 patterns of length 5

Optimization of protein extraction from tree peony (Paeonia suffruticosa Andr.) seed using response surface methodology

Optimization of extraction ratio (ER) of tree peony seed protein (TPSP) was investigated using response surface methodology (RSM). The second-degree equation for ER of TPSP had high coeffi cient (0.9625) of determination. The probability (P) value of regression model signifi cance was less than 0.001 by analysis of central composite rotatable design. Relationships of ER to pH, liquid/solid ratio, squares of all factors, and cross-product factors (x2x3, x2x4, x3x4) were signifi cant (P1x2, x1x3, x1x4) were not signifi cant factors (P>0.05). Optimum extraction conditions were 3.42 h, pH 9.50, 50.80 ºC, and 9.54 ml g–1 of liquid/solid ratio with the maximum ER (43.60%) . SDS-PAGE indicated TPSP had mainly four proteins (180, 100, 60, and 35 kDa) with four subunits of 60, 48, 38, and 23 kDa. TPSP had a good amino acid composition with abundant essential amino acids (39.76%) determined by amino acid analysis

On a greedy algorithm to construct universal cycles for permutations

A universal cycle for permutations of length n is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length n, and containing all permutations of length n as factors. It is well known that universal cycles for permutations of length n exist. However, all known ways to construct such cycles are rather complicated. For example, in the original paper establishing the existence of the universal cycles, constructing such a cycle involves finding an Eulerian cycle in a certain graph and then dealing with partially ordered sets. In this paper, we offer a simple way to generate a universal cycle for permutations of length n, which is based on applying a greedy algorithm to a permutation of length n - 1. We prove that this approach gives a unique universal cycle In for permutations, and we study properties of I n

In vitro and in vivo anticancer activity of steroid saponins of paris polyphylla var. yunnanensis

Aim: To confirm the anticancer activity of steroid saponins isolated from the rhizome of Paris polyphylla var. yunnanensis and evaluate the structure-activity relationships of these steroid saponins in vitro and in vivo. Materials and Methods: Eight known steroid saponins were isolated from the rhizome of Paris polyphylla. The LA795 lung adenocarcinoma cell line from mice was chosen to evaluate cytotoxicity by means of MTT assay, and to study apoptosis by means of AnnexinV-FITC/PI flow cytometry. Diosgenin-3-α-L-arabinofuranosyl(1→4)-[α-L-rhamnopyranosyl(1→2)]-β-D-glycopyranoside (compound 1), the main steroid saponin of Paris polyphylla, and diosgenin (Dio), the aglycone of major steroid saponins, were evaluated for antitumor activity on LA795 lung adenocarcinoma in T739 inbred mice. Results: The steroid saponins showed remarkable cytotoxicity and caused typical apoptosis in a dose-dependent manner. They were evaluated in vivo by their effect on tumor developed in T739 inbred mice. The oral administration to T739 mice bearing LA795 lung adenocarcinoma of compound 1 and diosgenin significantly inhibited tumor growth, by 29.44% and 33.94%, respectively. HE staining showed that lungs and livers of treated mice underwent various levels of histopathological alterations. It was demonstrated by TUNEL assay that apoptosis rate in tumor cells was increased in comparison to cells in control mice. The 3-O-glycoside moiety and spirostanol structure played an important role in the anticancer activity of steroid saponins, and the number and the variety of glycosides of compounds strongly influenced on their anticancer activity. Conclusion: Rhizoma Paridis saponins showed anticancer activity against lung adenocarcinoma cell line, both in vitro and in vivo, and their effect was dependent on compounds’ structure in a certain degree

Nuclear transparency from quasielastic A(e,e'p) reactions uo to Q^2=8.1 (GeV/c)^2

The quasielastic (e,e$^\prime$p) reaction was studied on targets of deuterium, carbon, and iron up to a value of momentum transfer $Q^2$ of 8.1 (GeV/c)$^2$. A nuclear transparency was determined by comparing the data to calculations in the Plane-Wave Impulse Approximation. The dependence of the nuclear transparency on $Q^2$ and the mass number $A$ was investigated in a search for the onset of the Color Transparency phenomenon. We find no evidence for the onset of Color Transparency within our range of $Q^2$. A fit to the world's nuclear transparency data reflects the energy dependence of the free proton-nucleon cross section.Comment: 11 pages, 6 figure

Measurements of the observed cross sections for e+e−→e^+e^-\to exclusive light hadrons containing π0π0\pi^0\pi^0 at s=3.773\sqrt s= 3.773, 3.650 and 3.6648 GeV

By analyzing the data sets of 17.3, 6.5 and 1.0 pb$^{-1}$ taken, respectively, at $\sqrt s= 3.773$, 3.650 and 3.6648 GeV with the BES-II detector at the BEPC collider, we measure the observed cross sections for $e^+e^-\to \pi^+\pi^-\pi^0\pi^0$, $K^+K^-\pi^0\pi^0$, $2(\pi^+\pi^-\pi^0)$, $K^+K^-\pi^+\pi^-\pi^0\pi^0$ and $3(\pi^+\pi^-)\pi^0\pi^0$ at the three energy points. Based on these cross sections we set the upper limits on the observed cross sections and the branching fractions for $\psi(3770)$ decay into these final states at 90% C.L..Comment: 7 pages, 2 figure

Partial wave analysis of J/\psi \to \gamma \phi \phi

Using $5.8 \times 10^7 J/\psi$ events collected in the BESII detector, the radiative decay $J/\psi \to \gamma \phi \phi \to \gamma K^+ K^- K^0_S K^0_L$ is studied. The $\phi\phi$ invariant mass distribution exhibits a near-threshold enhancement that peaks around 2.24 GeV/$c^{2}$. A partial wave analysis shows that the structure is dominated by a $0^{-+}$ state ($\eta(2225)$) with a mass of $2.24^{+0.03}_{-0.02}{}^{+0.03}_{-0.02}$ GeV/$c^{2}$ and a width of $0.19 \pm 0.03^{+0.06}_{-0.04}$ GeV/$c^{2}$. The product branching fraction is: $Br(J/\psi \to \gamma \eta(2225))\cdot Br(\eta(2225)\to \phi\phi) = (4.4 \pm 0.4 \pm 0.8)\times 10^{-4}$.Comment: 11 pages, 4 figures. corrected proof for journa

Direct Measurements of Absolute Branching Fractions for D0 and D+ Inclusive Semimuonic Decays

By analyzing about 33 $\rm pb^{-1}$ data sample collected at and around 3.773 GeV with the BES-II detector at the BEPC collider, we directly measure the branching fractions for the neutral and charged $D$ inclusive semimuonic decays to be $BF(D^0 \to \mu^+ X) =(6.8\pm 1.5\pm 0.7)$ and $BF(D^+ \to \mu^+ X) =(17.6 \pm 2.7 \pm 1.8)$, and determine the ratio of the two branching fractions to be $\frac{BF(D^+ \to \mu^+ X)}{BF(D^0 \to \mu^+ X)}=2.59\pm 0.70 \pm 0.25$

New Physics and CP Violation in Hyperon Nonleptonic Decays

The sum of the CP-violating asymmetries A(Lambda_-^0) and A(Xi_-^-) in hyperon nonleptonic decays is presently being measured by the E871 experiment. We evaluate contributions to the asymmetries induced by chromomagnetic-penguin operators, whose coefficients can be enhanced in certain models of new physics. Incorporating recent information on the strong phases in Xi->Lambda pi decay, we show that new-physics contributions to the two asymmetries can be comparable. We explore how the upcoming results of E871 may constrain the coefficients of the operators. We find that its preliminary measurement is already better than the epsilon parameter of K-Kbar mixing in bounding the parity-conserving contributions.Comment: 12 pages, 2 figure