Ingenuity in performing replica permutation: How to order the state labels for improving sampling efficiency

In the replica-permutation method, an advanced version of the replica-exchange method, all combinations of replicas and parameters are considered for parameter permutation, and a list of all the combinations is prepared. Here, we report that the temperature transition probability depends on how the list is created, especially in replica permutation with solute tempering (RPST). We found that the transition probabilities decrease at large replica indices when the combinations are sequentially assigned to the state labels as in the originally proposed list. To solve this problem, we propose to modify the list by randomly assigning the combinations to the state labels. We performed molecular dynamics simulations of amyloid-β(16–22) peptides using RPST with the “randomly assigned” list (RPST-RA) and RPST with the “sequentially assigned” list (RPST-SA). The results show the decreases in the transition probabilities in RPST-SA are eliminated, and the sampling efficiency is improved in RPST-RA.     

A longitudinal view of mathematics achievement of primary students: case studies from Japan, Singapore, and the United States

This paper shares results from a secondary analysis of data from the participation of Japanese, Singaporean, and U.S. students in the International Project on Mathematical Attainment (IPMA). IPMA was a longitudinal study to assess the mathematics achievement of primary students from their first year of schooling through the end of fifth grade. Tests were constructed to enable achievement on the same items to be assessed over multiple years, thus permitting the assessment of growth in achievement throughout primary school. Achievement is compared to the grade at which the content is introduced so that achievement can be related to students’ opportunity to learn.     

On singularities arising from the contraction op the minimal section of a ruled surface

We will discuss the Gorenstein property of the singularity which is blown down from the minimal section of a ruled surface in terms of the extension class. In the case that the base field has positive characteristic, we find a new example (3.4) of Gorenstein singularity in connection with Theorem B.     

Hardness measures for gridworld benchmarks and performance analysis of real-time heuristic search algorithms

Gridworlds are one of the most popular settings used in benchmark problems for real-time heuristic search algorithms. However, no comprehensive studies have been published so far on how the difference in the density of randomly positioned obstacles affects the hardness of the problems. This paper presents two measures for characterizing the hardness of gridworld problems parameterized by obstacle ratio, and relates them to the performance of the algorithms. We empirically show that the peak locations of those measures and actual performance degradation of the basic algorithms (RTA* and LRTA*) almost coincide with each other for a wide variety of problem settings. Thus the measures uncover some interesting aspects of the gridworlds.     

Symmetry-Breaking Phenomena in an Optimization Problem for some Nonlinear Elliptic Equation

Let $\Omega$ be a bounded domain in ${\bf R^n}$ with Lipschitz boundary, $\lambda >0,$ and $1\le p \le (n+2)/(n-2)$ if $n\ge 3$ and $1\le p< +\infty$ if $n=1,2$. Let $D$ be a measurable subset of $\Omega$ which belongs to the class $ {\cal C}_{\beta}=\{D\subset \Omega \quad | \quad |D|=\beta\} $ for the prescribed $\beta\in (0, |\Omega|).$ For any $D\in{\cal C}_{\beta}$, it is well known that there exists a unique global minimizer $u\in H^1_0(\Omega)$, which we denote by $u_D$, of the functional \[\quad J_{\Omega,D}(v)=\frac12\int_{\Omega}|\nabla v|^2\, dx+\frac{\lambda}{p+1}\int_{\Omega}|v|^{p+1}\, dx -\int_{\Omega}\chi_Dv\,dx \] on $H^1_0(\Omega)$. We consider the optimization problem $ E_{\beta,\Omega}=\inf_{D\in {\cal C}_{\beta}} J_D(u_D) $ and say that a subset $D^*\in {\cal C}_{\beta}$ which attains $E_{\beta,\Omega}$ is an optimal configuration to this problem. In this paper we show the existence, uniqueness and non-uniqueness, and symmetry-preserving and symmetry-breaking phenomena of the optimal configuration $D^*$ to this optimization problem in various settings.     

A note on the uniqueness and the non-degeneracy of positive radial solutions for semilinear elliptic problems and its application

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE analysis, we extend previous results to cases where nonlinear terms may have sublinear growth.As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified Schr¨odinger equations.     

Infinitely many solutions for a nonlinear Schrödinger equation with general nonlinearity

We prove the existence of infinitely many solutions for

$$\begin{aligned} - \Delta u + V(x) u = f(u) \quad \text { in } \mathbb {R}^N, \quad u \in H^1(\mathbb {R}^N), \end{aligned}$$

where V(x) satisfies \(\lim _{|x| \rightarrow \infty } V(x) = V_\infty >0\) and some conditions. We require conditions on f(u) only around 0 and at \(\infty \).

     

Visible-light photocatalysis of ZnO deposited on nanoporous Au

ZnO deposited on nanoporous Au showed photocatalytic decomposition toward methyl orange under visible light, unlike ZnO sputtered on flat Au without a nanoporous structure. First-principles calculations suggested that the surface lattice disorder in nanoporous Au induced a band gap narrowing and a large built-in electric field in the adjacent ZnO, resulting in the visible-light photocatalytic response.     

Absorption of millimeter to submillimeter waves by atmospheric water molecules

Using the values of the rotational molecular parameters (including cencrifugal distortion terms) of the H₂ ¹⁶O molecule, which can explain 12 observed transitions below 800 GHz, all rotational energy levels with normalized Boltzmann factors larger than 5×10^–8 at 300°K are calculated. Probabilities of all possible electric dipole transitions among these states, 2277 lines, are calculated using the eigenfunctions thus obtained, and the permanent electric dipole moment of 1.8546 Debye. Assuming the single and full Lorentzian line forms, we calculated the absorption coefficient for millimeter to submillimeter region. Our result, using the single term Lorentzian line form, agrees quite well with experiment for 1 Torr of water vapor in 760 Torr air at 300°K.     

Synthesis of water-soluble C60-porphyrin hybrid compounds

Water-soluble C60-porphyrin hybrid molecules were first synthesized toward their pharmaceutical applications.