Abstract:
In this paper we construct a mathematical model for excitable membranes by introducing circuit characteristics for ion pump, ion current activation, and voltage-gating. The model is capable of reestablishing the Nernst resting potentials, all-or-nothing action potentials, absolute refraction, anode break excitation, and spike bursts. We propose to replace the Hodgkin-Huxley model by our model as the basis template for neurons and excitable membranes.

Abstract:
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

Abstract:
Chargaff's second parity rule holds empirically for most types of DNA that along single strands of DNA the base contents are equal for complimentary bases, A = T, G = C. A Markov chain model is constructed to track the evolution of any single base position along single strands of genomes whose organisms are equipped with replication mismatch repair. Under the key assumptions that mismatch error rates primarily depend the number of hydrogen bonds of nucleotides and that the mismatch repairing process itself makes strand recognition error, the model shows that the steady state probabilities for any base position to take on one of the 4 nucleotide bases are equal for complimentary bases. As a result, Chargaff's second parity rule is the manifestation of the Law of Large Number acting on the steady state probabilities. More importantly, because the model pinpoints mismatch repair as a basis of the rule, it is suitable for experimental verification.

Abstract:
Sexual reproduction in Nature requires two sexes, which raises the question why the reproductive scheme did not evolve to have three or more sexes. Here we construct a constrained optimization model based on the communication theory to analyze trade-offs among reproductive schemes with arbitrary number of sexes. More sexes on one hand lead to higher reproductive diversity, but on the other hand incur greater cost in time and energy for reproductive success. Our model shows that the two-sexes reproduction scheme maximizes the recombination entropy-to-cost ratio, and hence is the optimal solution to the problem.

Abstract:
Effects of static magnetic field on optic properties of water are investigated by infrared spectroscopy, ultraviolet spectroscopy and X-ray diffraction, respectively. The ultraviolet spectroscopy experiments show the changes of properties of water under action of static magnetic field, in the region of 191 to 400 nm. The infrared experiment shows that the water exposed in a magnetic field had saturation and memory effects. The magnetized effects increased with increasing exposed time, but were weakened with increasing of time when the magnetic field was removed. In the X-ray experiment, the strength of diffraction increased also, after the water was exposed in magnetic field. Meanwhile, the shift of peak and increase of strength of X-ray diffraction of magnetized water added with nanoFe3O4 occurred as compared with that of pure water added with nano Fe3O4. This result suggests that the magnetized water has certain magnetism. Finally, these phenomena are simply explained by the molecular structure of water and the theory of magnetization of water.

Abstract:
In 2003 Matveev suggested a new version of the Diamond Lemma suitable for topological applications. We apply this result to different situations and get a new conceptual proof of theorem on decomposition of three-dimensional manifolds into boundary connected sum of prime components. 1. Introduction Since 2003 Matveev [1–3] had suggested a new version of the Diamond Lemma [4] of great importance for various fields of mathematics, which is suitable for and efficient solving topological problems. In this paper we apply this result to get a new conceptual proof of theorem on decomposition of three-dimensional manifolds into boundary connected sum of prime components. 2. Definition, Lemma, and -Irreducible Manifolds Diamond Lemma (see [5]). If an oriented graph has the properties (FP) and (MF), then each of its vertices has a unique root. Definition 1. Let be a proper disk in a compact connected 3-manifold . A disk reduction of along consists in cutting along the disk . Its result is a new manifold . We apply nontrivial disk reductions to a given manifold as many times as possible. If this process stops, then we obtain a set of new manifolds, which is called a root of .(1)If the disk is splitting, the manifold is obtained by gluing the manifolds and together along disks on their boundaries. Then is called a boundary connected sum of the manifolds and and denoted by .(2)If the disk is nonsplitting, then is also connected. Definition 2. is said to be irreducible if every properly embedded disk in is trivial. Lemma 3 (see [6]). Let be a -irreducible manifold. Let be the manifold obtained from by attaching a 1-handle to make the boundary connected. Then is a prime which is not irreducible. 3. Proof of Theorem？？4 Theorem 4. Any connected irreducible compact 3-manifold different from a ball and with nonempty boundary is homeomorphism to a boundary connected sum of prime manifolds. All the summands are defined uniquely up to reordering and, if is non-Orientale, replacing solid tori by solid Klein bottles . We apply the universal scheme [4] in two stages. First, by considering reductions along all disks we establish uniqueness of the -irreducible manifolds . Then we restrict ourselves to reductions only along splitting disks and by lemma [3] complete the proof of the theorem. We construct the graph [5] whose vertices are compact connected irreducible manifolds, considered up to addition or deletion of three-dimensional balls. The edges of the graph correspond to reductions along both splitting and nonsplitting disks. Lemma 5 (see [7]). Each essential disks reduction

The exact evolutionary history of any set of biological taxa is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this paper we propose a game theoretic approach to constructing biological networks. The key hypothesis is that evolution is driven by distinct mechanisms that seek to maximize two competing objectives, taxonomic conservation and diversity. One branch of the mathematical theory of games is brought to bear. It translates this evolutionary game hypothesis into a mathematical model in two-player zero-sum games, with the zero-sum assumption conforming to one of the fundamental constraints in nature in mass and energy conservation. We demonstrate why and how a mechanistic and localized adaptation to seek out greater information for conservation and diversity may always lead to a global Nash equilibrium in phylogenetic affinity. Our game theoretic method, referred to as bioinformatic game theory, is used to construct network clusters. As an example, we applied this method to clustering of a multidomain protein family. The protein clusters identified were consistent with known protein subfamilies, indicating that this game-theoretic approach provides a new framework in biological sequence analysis, especially in studying gene-genome and domain-protein relationships.

Abstract:
Based on the characteristics of wireless communication technology and
Wireless Sensor Network, this paper studies the well site environmental monitoring
system. The relevant hardware and software of the system are designed to monitor
the well site environment, thus preventing downhole accidents. The system uses
the wireless ZigBee technology as the transmission mode, and combines the
virtual instrument technology to design the upper machine interface. The test results
show that the system can monitor the outdoor environment in real time. When the
environmental parameters exceed the set value, the corresponding location of
the LabVIEW interface will send an alarm.

Abstract:
An analytical solution is presented to describe the emission/sorption of volatile organic compounds (VOCs) from/on multiple single-layer materials coexisting in buildings. The diffusion of VOCs within each material is described by a transient diffusion equation. All diffusion equations are coupled with each other through the equation of mass conservation in the air. The analytical solution is validated by the experimental data in literature. Compared to the one-material case, the coexistence of multiple materials may decrease the emission rate of VOCs from each material. The smaller the diffusion coefficient is, the more the emission rate decreases. Whether a material is a source or a sink in the case of multiple materials coexisting is not affected by the diffusion coefficient. For the case of multiple materials with different partition coefficients, a material with a high partition coefficient may become a sink. This may promote the emission of VOCs from other materials.

Abstract:
A sharp bending scheme for the self-collimation of acoustic waves is proposed by simply truncating the sonic crystals. An all-angle and wide-band 90{\deg}-bending wave guide is demonstrated with nearly perfect transmissions for Gaussian beams at a wide range of incident angles. A 90{\deg}-bended imaging for a point source with a subwavelength resolution of 0 0.37{\lambda} is also realized by the proposed structure. These results will find applicability in the manipulation of acoustic waves by sonic crystals.