Statistical physics of hard combinatorial optimization:Vertex cover problem

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomi＇al （NP）-complete combinatorial opti- mization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Constraining Equation of State of Dark Matter:Including Weak Gravitational Lensing

Usually the equation of state （EoS） of dark matter is zero when it is cold, however there exists the possibility of a （effective） nonzero EoS of dark matter due to its decay and interaction with dark energy. In this work, we try to constrain the EoS of dark matter/JAdm using the currently available cosmic observations which include the geometrical and dynamical measurements. For the geometrical measurements, the luminosity distance of type Ia supernovae, the angular diameter distance and comoving sound horizon from baryon acoustic oscillations and the cosmic microwave background radiation will be employed. The data points from the redshift-space distortion and weak gravitational lensing will be taken as dynamical measurements. Using the Markov chain Monte Carlomethod, we obtain a very tight constraint on the-EoS of dark matter：wdm=0.0000532 ＋0.000692＋0.00136＋0.00183 -0.000686-0.00136-0.00177.

Theoretical study on fusion dynamics and evaporation residue cross sections for superheavy elements

The nuclear dynamical deformation,the fusion probability and the evaporation residue(ER) cross sections for the synthesis of superheavy nuclei are studied with the di-nuclear system model and the related dynamical potential energy surface.The intrinsic energy and the maximum dynamical deformations for48Ca+248Cm are calculated.The effect of dynamical deformation on the potential energy surface and fusion is investigated.It is found that the dynamical deformation influences the potential energy surface and fusion probability significantly.The dependence of the fusion probability on the angular momentum is investigated.The ER cross sections for some superheavy nuclei in48Ca induced reactions are calculated and it is found that the theoretical results are in good agreement with the experimental results.

Observation of the Superheavy Nuclide ^(271)Ds

With the recent commissioning of a gas-filled recoil separator at Institute of Modern Physics (IMP) in Lanzhou,the decay properties of 271Ds (Z =110) were studied via the 20sPb(64Ni,n) reaction at a beam energy of 313.3 MeV.Based on the separator coupled with a position sensitive silicon strip detector,we carried out the energy-position-time correlation measurements for the implanted nucleus and its subsequent decay α's.One α-decay chain for 271Ds was established.The α energy and decay time of the 27iDs nucleus were measured to be 10.644 MeV and 96.8ms,which are consistent with the values reported in the literature.

Mechano-chemical selections of two competitive unfolding pathways of a single DNA i-motif

The DNA i-motif is a quadruplex structure formed in tandem cytosine-rich sequences in slightly acidic conditions. Besides being considered as a building block of DNA nano-devices, it may also play potential roles in regulating chromo- some stability and gene transcriptions. The stability of i-motif is crucial for these functions. In this work, we investigated the mechanical stability of a single i-motif formed in the human telomeric sequence 51-（CCCTAA）3CCC, which revealed a novel pH and loading rate-dependent bimodal unfolding force distribution. Although the cause of the bimodal unfolding force species is not clear, we proposed a phenomenological model involving a direct unfolding favored at lower loading rate or higher pH value, which is subject to competition with another unfolding pathway through a mechanically stable inter- mediate state whose nature is yet to be determined. Overall, the unique mechano-chemical responses of i-motif-provide a new perspective to its stability, which may be useful to guide designing new i-motif-based DNA mechanical nano-devices.

Protection-against-water-attack determined difference between strengths of backbone hydrogen bonds in kinesin＇s neck zipper region

Docking of the kinesin＇s neck linker （NL） to the motor domain is the key force-generation process of the kinesin. In this process, NL＇sβ10 portion forms four backbone hydrogen bonds （HBs） with the motor domain. These backbone hydrogen bonds show big differences in their effective strength. The origins of these strength differences are still unclear. Using molecular dynamics method, we investigate the stability of the backbone HBs in explicit water environment. We find that the strength differences of these backbone HBs mainly arise from their relationships with water molecules which are controlled by arranging the surrounding residue sidechains. The arrangement of the residues in the C-terminal part of /310 results in the existence of the water-attack channels around the backbone HBs in this region. Along these channels the water molecules can directly attack the backbone HBs and make these HBs relatively weak. In contrast, the backbone HB at the N-terminus ofβ 10 is protected by the surrounding hydrophobic and hydrophilic residues which cooperate positively with the central backbone HB and make this HB highly strong. The intimate relationship between the effective strength of protein backbone HB and water revealed here should be considered when performing mechanical analysis for protein conformational changes.

Tilted Axis Rotation of ^(57)Mn in Covariant Density Functional Theory

The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction is applied to investigate the tilted axis rotation in ^57 Mn. The observed data for band C are reproduced well with the assigned configuration eonfig 1. The shears mechanism for magnetic rotation is examined by investigating microscopically the orientation of angular momentum and the corresponding contributions. It is found that config 1 and config 3 correspond to a rotation of high-K character. Config 2 corresponds to a rotation of magnetic character. However, due to the presence of electromagnetic transition B（M1） and B（E2）, collective rotation plays an essential role in the competition with magnetic rotation.

Specific Heat of a Unitary Fermi Gas Including Particle-Hole Fluctuation

We investigate the particle-hole fluctuation correction to the specific heat of an ultracold Fermi gas at unitarity within the framework of the non-self-consistent T-matrix approximation in the normal phase. We find good agreement between our theoretical predictions and the experimental data measured by the MIT group, apart from discrepancies near the transition temperature. At high temperature, our calculated specific heat has the tendency to approach the specific heat of the Boltzmann gas.

Schrdinger Equation of a Particle on a Rotating Curved Surface

We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.

Covalent intermolecular interaction of the nitric oxide dimer (NO)_2

Covalent bonds arise from the overlap of the electronic clouds in the internucleus region, which is a pure quantum effect and cannot be obtained in any classical way. If the intermolecular interaction is of covalent character, the result from direct applications of classical simulation methods to the molecular system would be questionable. Here, we analyze the special intermolecular interaction between two NO molecules based on quantum chemical calculation. This weak intermolecular interaction, which is of covalent character, is responsible for the formation of the NO dimer,（NO）2, in its most stable conformation, a cis conformation. The natural bond orbital（NBO） analysis gives an intuitive illustration of the formation of the dimer bonding and antibonding orbitals concomitant with the breaking of the πbonds with bond order 0.5of the monomers. The dimer bonding is counteracted by partially filling the antibonding dimer orbital and the repulsion between those fully or nearly fully occupied nonbonding dimer orbitals that make the dimer binding rather weak. The direct molecular mechanics（MM） calculation with the UFF force fields predicts a trans conformation as the most stable state, which contradicts the result of quantum mechanics（QM）. The lesson from the investigation of this special system is that for the case where intermolecular interaction is of covalent character, a specific modification of the force fields of the molecular simulation method is necessary.

Theoretical studies on s RNA-mediated regulation in bacteria

Small RNA（sRNA）-mediated post-transcriptional regulation differs from protein-mediated regulation. Through basepairing, sRNA can regulate the target m RNA in a catalytic or stoichiometric manner. Some theoretical models were built for comparison of the protein-mediated and sRNA-mediated modes in the steady-state behaviors and noise properties. Many experiments demonstrated that a single sRNA can regulate several m RNAs, which causes crosstalk between the targets.Here, we focus on some models in which two target mRNAs are silenced by the same sRNA to discuss their crosstalk features. Additionally, the sequence-function relationship of sRNA and its role in the kinetic process of base-pairing have been highlighted in model building.

Formation and dissociation of protonated cytosine–cytosine base pairs in i-motifs by ab initio quantum chemical calculations

Formation and dissociation mechanisms of C-C＋ base pairs in acidic and alkaline environments are investigated, employing ab initio quantum chemical calculations. Our calculations suggest that, in an acidic environment, a cytosine monomer is first protonated and then dimerized with an unprotonated cytosine monomer to form a C-C＋ base pair; in an alkaline environment, a protonated cytosine dimer is first unprotonated and then dissociated into two cytosine monomers. In addition, the force for detaching a C-C＋ base pair was found to be inversely proportional to the distance between the two cytosine monomers. These results provide a microscopic mechanism to qualitatively explain the experimentally observed reversible formation and dissociation of i-motifs.

Quantum and semiclassical studies on photodetachment cross sections of H^- in a harmonic potential

The photodetachment cross section of H- in a linear harmonic oscillator potential is investigated. This system pro- vides a rare example that can be studied analytically by both quantum and semiclassical methods with some approxi- mations. The formulas of the cross section for different laser polarization directions are explicitly derived by both the traditional quantum approach and closed-orbit theory. In the traditional quantum approach, we calculate the cross sections in coordinate representation and momentum representation, and get the same formulas. We compare the quantum formulas with closed-orbit theory formulas, and find that when the detachment electron energy is larger than hco, where co is the frequency of the oscillator potential, the quantum results are shown to be in good agreement with the semiclassical results.

The Quark Number Susceptibility of QCD at Finite Temperature and Chemical Potential

We calculate the quark number density and quark number susceptibility (QNS) of QCD at finite chemical potential μ and finite temperature T in the framework of a new nonperturbative QCD model. Analysis and discussions of the calculated results of the QNS are given. It is found that the quark number density has a singularity when μ comes close to a critical value μ0, and the QNS χ(μ,T) becomes discontinuous at some values of T. At high temperature the QNS approaches the free quark gas result, while at very low temperature the QNS equals zero. Importantly, the QNS shows a sudden increase near some temperature (T~120 MeV), which may be regarded as the signal of a crossover.

Radio-Frequency Spectra of Ultracold Fermi Gases Including a Generalized GMB Approximation at Unitarity

Taking into account the effect of the generalized Gor'kov and Melik-Barkhudarov(GMB)approximation,we calculate the radio-frequency spectra of balanced and homogeneous ultracold Fermi gases within the framework of the non-self-consistent T-matrix approximation at unitarity in the normal phase.The corresponding equations are numerically calculated on the real frequency axis directly.It is found that our results agree well with the experimental result of the radio-frequency spectroscopy[Phys.Rev.Lett.101(2008)140403].

Initiation Mechanism of Kinesin's Neck Linker Docking Process

The neck linker （NL） docking to the motor domain is the key force generation process of a kinesin motor. In the initiation step of NL docking the first three residues （LYS325, THR326 and ILE327 in 2KIN） of the NL must form an ＇extra turn＇, thus the other parts of the NL could dock to the motor domain. How the extra turn is formed remains elusive. We investigate the extra turn formation mechanism using structure-based mechanical analysis via molecular dynamics simulation. We find that the motor head rotation induced by ATP binding first drives ILE327 to move towards a hydrophobic pocket on the motor domain. The driving force, together with the hydrophobic interaction of ILE327 with the hydrophobic pocket, then causes a clockwise rotation of THR326, breaks the locking of LYS325, and finally drives the extra turn formation. This extra turn formation mechanism provides a clear pathway from ATP binding to NL docking of kinesin.

A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.

Discussion of Various Susceptibilities within Thermal and Dense Quantum Chromodynamics

It is commonly accepted that the system undergoes a crossover at high temperature and low chemical potential beyond the chiral limit case, and the properties of the crossover region are important for researchers to understand the nature of strong interacting matters of quantum chromodynamics （QCD）. Since at present there is no exact order of parameters of the phase transitions beyond the chiral limit, QCD susceptibilities are widely used as indicators. In this work various susceptibilities are discussed in the framework of Dyson-Schwinger equations. The results show that different kinds of susceptibilities give the same critical end point, which is the bifurcation point of the crossover region and the first order phase transition line of QCD. Nevertheless, different pseudo- critical points are found in the temperature axis. We think that defining a critical band is more suitable in the crossover region.

Characteristics of Double Gamma-Ray Bursts

Double gamma-ray bursts （DGRBs） have two well-separated sub-bursts in the main prompt emission and the typical time interval between them is in the hundreds of seconds. Among DGRBs, gamma-ray bursts （DGRBs） 110801A and 120716A are the ones with known redshifts. However, unlike GRB 110801A, we show that the two sub-bursts of GRB 120716A is severally similar to the short- and long-duration GRBs, thus it is difficult to explain the origin of GRB 120716A by the popular models on the central engine of GRBs. We suggest that some mechanisms of x-ray flares in GRBs, i.e., a post-merger millisecond pulsars or the jet precession in a black hole hyperaccretion system may produce the DGRB.

Theoretical study of fusion reactions ^(32)S + ^(94,96)Zr and ^(40)Ca + ^(94,96)Zr and quadrupole deformation of ^(94)Zr

The dynamic coupling effects on fusion cross sections for reactions^(32)S + ^(94,96)Zr and ^(40)Ca + ^(94,96)Zr are studied with the universal fusion function formalism and an empirical coupled channel(ECC) model. An examination of the reduced fusion functions shows that the total effect of couplings to inelastic excitations and neutron transfer channels on fusion in ^(32)S +^(94)Zr(^(40)Ca +^(94)Zr) is almost the same as that in ^(32)S +^(96)Zr(^(40)Ca +^(96)Zr). The enhancements of the fusion cross section at sub-barrier energies due to inelastic channel coupling and neutron transfer channel coupling are evaluated separately by using the ECC model. The results show that effect of couplings to inelastic excitations channels in the reactions with94 Zr as target should be similar as that in the reactions with ^(96) Zr as target. This implies that the quadrupole deformation parameters β_2of ^(94)Zr and^(96) Zr should be similar to each other.However, β_2 's predicted from the finite-range droplet model, which are used in the ECC model, are quite different. Experiments on^(48) Ca +^(94)Zr or^(36) S +^(94)Zr are suggested to solve the puzzling issue concerning β_2for^(94)Zr.