Abstract:
In this work, a rumor’s spreading and controlling in a directed Micro-blog user network being consisted with 580 000 nodes are simulated. By defining some authority nodes that release anti-rumor information as the prevention strategy, the effect of the nodes’ role in network on rumor’s suppression is studied. The findings show that rumor will be spread out fast and reach a stable level within limited steps. The suppression of rumor is more predominated by the intervening opportunity, the earlier the intervention strategy was implemented, the better the rumor’s controlling could be achieved. The controlling effect is less relevant with the role of the authority nodes in network.

Abstract:
Objective: To explore the effects of psoralen (PSO) plus long-wave ultraviolet-A (PUVA) on apoptosis and expression of Fas ligand (FasL) in HL-60 leukemia cells. Methods: The HL-60 cells were taken as the study objects and their apoptosis rates, ultrastructure changes and the expression of FasL were detected in order to observe the effects of PSO and ultraviolet-A (UVA) of wave length 360 nm. The factorial design and analysis of variance were used to analyze the interaction among the factors. Results: PSO, UVA and PUVA all induced the apoptosis and the effects of PUVA were stronger than those of the other two. After HL-60 cells had been treated with PUVA, they all showed obvious ultrastructure changes due to apoptosis observed under the electron microscope. PSO, UVA and PUVA all decreased the expressions of FasL gene and protein. The effects of PUVA were stronger than those of the other two. Conclusions: PUVA can induce the apoptosis of HL-60 cells and the effects are stronger than those of PSO or UVA alone. The expression of FasL gene in HL-60 cells is down-regulated during the apoptosis induced by PUVA.

Abstract:
More and more proxy records approved that the periodicity of the glacial cycles is about 40 ka before MPT (middle Pleistocene transition) as early as late Tertiary from 3.0 Ma to 0.9 Ma, whereas it changes to about 100 ka after MPT. Summer insolation at high latitude in Northern Hemisphere, usually considered as the main external force for the ice age, is dominated by the 23 ka precession period, which does not match the period of the glacial cycles. In this paper, we define an energy index C and its threshold Ct that indicate the net energy supply and the overall response of the climate system. The difference between these two parameters determines whether the ice sheet melts or not, and accordingly the start and termination of the interglacial stages, as well as the periodicity of glacial oscillations. Based on the energy threshold hypothesis, the preliminary simulation experiments are made to test the period of the glacial cycles and driven factors from a conceptual model. The results indicate that energy index C and threshold Ct can interpret not only the 40 ka periodicity before MPT, but also the quasi-100 ka periodicity after MPT to some extent, and the 40 ka is the basic period of the glacial cycles, which discloses the inherent continuity of climatic change before and after MPT.

Abstract:
A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same time can predict the three dimensional structure of a protein with a given sequence in reasonable time. For this purpose, rather than focusing on the real folding dynamics or full structural details at the atomic scale, we adopt the Monte Carlo method and the coarse-grained representation of the protein in which both side-chains and the backbones are replaced by suitable geometrical objects in consistent with the known structure. On top of the coarse-grained representation, our effective potential can be developed. Two new interactions, the dipole-dipole interactions and the local hydrophobic interactions, are introduced and are shown to be as crucial as the hydrogen bonds for forming the secondary structures. In particular, for the first time, we demonstrate that the resulting reduced model can successfully fold proteins with both helix and sheet structures without using any biased potential. Further analyses show that this model can also fold other proteins in reasonable accuracy and thus provides a promising starting point for the problem of protein folding.

Abstract:
Chaos control in Random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. This paper proposes a new control method in which controlled nodes can exert an active impact on the network. Controlled nodes and frozen values are deliberately selected according to the information of connection and Boolean functions. Simulation results show that the number of nodes needed to achieve control is largely reduced compared to previous method. Theoretical analysis is also given to estimate the least fraction of nodes needed to achieve control.

Abstract:
The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and Smith normal form of integral matrices with integer parameters are also given.

Abstract:
Let A(n) be a $k\times s$ matrix and $m(n)$ be a $k$ dimensional vector, where all entries of A(n) and $m(n)$ are integer-valued polynomials in $n$. Suppose that $$t(m(n)|A(n))=#\{x\in\mathbb{Z}_{+}^{s}\mid A(n)x=m(n)\}$$ is finite for each $n\in \mathbb{N}$, where $Z_+$ is the set of nonnegative integers. This paper conjectures that $t(m(n)|A(n))$ is an integer-valued quasi-polynomial in $n$ for $n$ sufficiently large and verifies the conjecture in several cases.

Abstract:
Suppose that $a_1(n),a_2(n),...,a_s(n),m(n)$ are integer-valued polynomials in $n$ with positive leading coefficients. This paper presents Popoviciu type formulas for the generalized restricted partition function $$p_{A(n)}(m(n)):=#\{(x_1,...,x_s)\in \mathbb{Z}^{s}: all x_j\geqslant 0, x_1a_1(n)+...+x_sa_s(n)=m(n) \}$$ when $s=2$ or 3. In either case, the formula implies that the function is an integer-valued quasi-polynomial. The main result is proved by a reciprocity law for a class of fractional part sums and the theory of generalized Euclidean division.

Abstract:
Given an equilateral triangle with $a$ the square of its side length and a point in its plane with $b$, $c$, $d$ the squares of the distances from the point to the vertices of the triangle, it can be computed that $a$, $b$, $c$, $d$ satisfy $3(a^2+b^2+c^2+d^2)=(a+b+c+d)^2$. This paper derives properties of quadruples of nonnegative integers $(a,\, b,\, c,\, d)$, called triangle quadruples, satisfying this equation. It is easy to verify that the operation generating $(a,\, b,\, c,\, a+b+c-d)$ from $(a,\, b,\, c,\, d)$ preserves this feature and that it and analogous ones for the other elements can be represented by four matrices. We examine in detail the triangle group, the group with these operations as generators, and completely classify the orbits of quadruples with respect to the triangle group action. We also compute the number of triangle quadruples generated after a certain number of operations and approximate the number of quadruples bounded by characteristics such as the maximal element. Finally, we prove that the triangle group is a hyperbolic Coxeter group and derive information about the elements of triangle quadruples by invoking Lie groups. We also generalize the problem to higher dimensions.