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We discuss 1-2 matchings, which are matchings in bipartite graphs G = (S S′, E) where their elements are pairs of edges with common endpoints in S. An algorithm to find an optimal 1-2 matching is d...

We discuss the eigenvalue problem in the max-plus algebra. For a max-plus square matrix, the roots of its characteristic polynomial are not its eigenvalues. In this paper, we give the notion of algebraic eigenvectors associated with the roots of characteristic polynomials. Algebraic eigenvectors are the analogues of the usual eigenvectors in the following three senses: (1) An algebraic eigenvector satisfies an equation similar to the equation A ⊗ x = λ ⊗ x for usual eigenvectors. Under a suitable assumption, the equation has a nontrivial solution if and only if λ is a root of the characteristic polynomial. (2) The set of algebraic eigenvectors forms a max-plus subspace called algebraic eigenspace. (3) The dimension of each algebraic eigenspace is at most the multiplicity of the corresponding root of the characteristic polynomial.

The tropical kernel of a Min-Plus matrix is a linear space. It has a finite basis that is uniquely determined up to scalar multiplication. In this paper, we give a characterization of vectors in a basis of the kernel using the tropical analogue of Cramer's rule. We first show that each finite vector in a basis can be obtained by applying Cramer's rule to a submatrix consisting of certain rows of the original matrix. We prove the main results by presenting an algorithm for choosing such rows. Further, we extend the result for kernel vectors that contain infinity in its entries.

Vanadium dioxide (VO2) exhibits a metal-insulator phase transition at approximately 70 °C. Two different crystal structures, M1 and M2 phases, in the insulating state have been reported. The M2 phase is expected to be a Mott insulator, whereas the M1 phase is expected to act as a band insulator. It is important to clarify the origin and transition properties of the M2 phase. In this study, we fabricated VO2 nanostructures via sputtering deposition and subsequent lamp annealing at various O2 pressures. Temperature-dependent XRD measurements revealed that the nanostructured VO2 exhibits the M2 phase in temperatures just before the phase transition from M1 to R (metal state) during the heating process. The ratio of V5+/(V4+ + V5+) in nanostructured VO2 was estimated from XPS results; an increase in this ratio resulted in the broadening of the temperature range of the M2 phase. Furthermore, in the cooling process, direct phase transitions from R to M1 were observed. Structural changes are likely to occur in different pathways during heating and cooling. Our findings should contribute to the identification of the phase transition mechanism and to the development of a Mott field-effect transistor that utilizes nanostructured VO2 in the M2 phase.

Platinum nanocatalysts play critical roles in CO oxidation, an important catalytic conversion process. As the catalyst size decreases, the influence of the support material on catalysis increases which can alter the chemical states of Pt atoms in contact with the support. Herein, we demonstrate that under-coordinated Pt atoms at the edges of the first cluster layer are rendered cationic by direct contact with the Al2O3 support, which affects the overall CO oxidation activity. The ratio of neutral to cationic Pt atoms in the Pt nanocluster is strongly correlated with the CO oxidation activity, but no correlation exists with the total surface area of surface-exposed Pt atoms. The low oxygen affinity of cationic Pt atoms explains this counterintuitive result. Using this relationship and our modified bond-additivity method, which only requires the catalyst–support bond energy as input, we successfully predict the CO oxidation activities of various sized Pt clusters on TiO2., Platinum nanocatalysts play critical roles in CO oxidation. Herein, the authors discover that under-coordinated Pt atoms at the edges of the first cluster layer are rendered cationic by direct contact with the Al2O3 support, which affects the overall CO oxidation activity.

We investigated the reduction of a CeO2(111) surface after the deposition of size-selected Pt8 clusters on it via x-ray photoelectron spectroscopy (XPS). Electron transfer from Pt to CeO2(111) results in the reduction of Ce4+ to Ce3+ and the subsequent formation of Ptδ+ atoms at the interface. We quantitatively estimated the reduction from the Ce3+/(Ce3+ + Ce4+) ratio determined from the Ce3d spectra. Approximately 30% of Ce4+ under or in the perimeter of the Pt8 cluster was reduced to Ce3+. The XPS spectra showed an increase in the ratio of Ce3+/(Ce3+ + Ce4+) with an increase in the amount of Pt8 clusters deposited on the CeO2(111) surface. The reduction of 3.7 Ce4+ to Ce3+ per Pt8 clusters, followed by the formation of 3.7 Ptδ+ atoms per Pt8 clusters was observed at 0.006 ML (mono layer) Pt coverage. The actual Ce3+ formation influenced by Pt deposition was approximately 2.5%. We estimate that approximately 30% of Ce4+ under or in the perimeter of a Pt8 cluster was reduced to Ce3+. At a higher coverage of 0.015 ML, the reduction of 2.2 Ce4+ to Ce3+ per Pt8 cluster, followed by the formation of 3.2 Ptδ+ atoms per Pt8 cluster was observed. This implies the aggregation of Pt clusters occurred at a higher Pt coverage. Atomically precise quantification of the electron transfer across the Pt–CeO2(111) interface can enable an improved understanding of the metal-support interaction.

The measurement procedure of oxophilicity and electrocatalytic activity for oxygen reduction reaction (ORR) on size-selected Au clusters was developed and applied. Mass-selected Au9 clusters were deposited on a glassy carbon substrate under ultrahigh vacuum (UHV) conditions, and the model electrode was transferred to an electrochemical cell with the rotating disk electrode (RDE) configuration. Cyclic voltammetry exhibited a significantly lower oxide-reduction peak potential of the Au clusters than that of bulk Au in the first cycle, thus confirming the exceptionally higher oxophilicities for the former. After performing cyclic voltammetry with an upper limit potential of 1.8 V versus a reversible hydrogen electrode, the ORR activity of the Au clusters was lower than that of bulk Au and bulk Pt. This result was partially ascribed to aggregations of Au clusters during the potential cycles.

Catalytic CO oxidation is unveiled on size-selected Pt-10 clusters deposited on two very different ultrathin (approximate to 0.5-0.7 nm thick) alumina films: (i) a highly ordered alumina obtained under ultra-high vacuum (UHV) by oxidation of the NiAl(110) surface and (ii) amorphous alumina obtained by atomic layer deposition (ALD) on a silicon chip that is a close model of real-world supports. Notably, when exposed to realistic reaction conditions, the Pt-10/UHV-alumina system undergoes a morphological transition in both the clusters and the substrate, and becomes closely akin to Pt-10/ALD-alumina, thus reconciling UHV-type surface-science and real-world experiments. The Pt-10 clusters, thoroughly characterized via combined experimental techniques and theoretical analysis, exhibit among the highest CO oxidation activity per Pt atom reported for CO oxidation catalysts, due to the interplay of ultra-small size and support effects. A coherent interdisciplinary picture then emerges for this catalytic system.

Supported Pt catalysts and ceria are well known for their application in automotive exhaust catalysts. Size-selected Pt clusters supported on a CeO

In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which causes the infinite loop in the algorithm, does not occur in the network simplex algorithm associated with the maximum flow problem., Comment: 13pages

Reduction of CeO 2 (111)/Ru(0001) surface by atomic hydrogen was investigated using scanning tunneling microscopy (STM) and X-ray photoelectron spectroscopy (XPS). We observed the formation of oxygen vacancy trimers and hydroxyl trimers on the stoichiometric CeO 2 (111) surface when it was exposed to atomic hydrogen at room temperature. The reaction of an impinging hydrogen atom with a surface oxygen atom yields a hydroxyl species, which diffuse on the surface until stabilized by the formation of OH trimers. The hydrogen atoms were located at atop sites of the oxygen atoms in the topmost surface layer. A reaction between the hopping hydrogen atom and the hydroxyl species yields a water molecule, which is desorbed from the surface leaving an oxygen defect. The oxygen vacancies were also observed as a trimer of vacancies. XPS measurements showed an increase of a reduced Ce and hydroxyl species with an amount of exposed hydrogen atoms. The former was estimated by measuring the ratio of Ce 3 + /Ce 4 + in the Ce 3d components. Our study shows the formation of hydroxyl trimer species in atomic scale upon atomic hydrogen exposure to CeO 2 (111) surface which could offer new catalytic activity.

The adsorption states of size-selected Ptn clusters (7 ≤ n ≤ 20) soft-landed on an Al2O3/NiAl(110) substrate were investigated using scanning tunneling microscopy, infrared reflection absorption spectroscopy, and temperature programmed desorption. Ptn clusters lay flat on the surface with a planar structure (n ≤ 18), and three-dimensional two-layer clusters start to appear at n ≥ 19. By considering the Pt-Pt and Pt-oxide bonds in the cluster, the morphological transition could be reasonably explained. Using CO probe molecules, the chemical states of the Pt atoms inside the clusters were investigated. Two ontop CO species were observed inside the clusters, and were assigned as adsorbed CO on neutral and slightly cationic Pt atoms. Despite the first layer Pt atoms, the Ptn clusters are composed of two kinds of Pt atoms. The observed size dependence of the Pt atoms inside the clusters may contribute to the size-dependent chemical reactivity of Ptn clusters on the Al2O3 surface.

We present an algorithm for solving the maximum 1-2 matching problem in bipartite graphs by reducing it to solving the 1-1 matching in general undirected graphs. Further, we propose two variants of the maximum 1-2 matching problem: one is the maximum 1-2 matching problem of the different kind in divided bipartite graphs and the other is the maximum 1-2 matching problem of the same kind in divided bipartite graphs. The former one is shown to be solved by a similar algorithm to that of the maximum 1-2 matching problem by reducing it to solve the maximum 1-1 matching problem in bipartite graphs. For the latter one, we can only present the augmenting subgraph theorem, which is an extension of our augmenting trail theorem for the maximum 1-2 matching problem.

組合せ最適化問題の多くは,線形計画問題として定式化することができるため,それぞれの問題に合った組合せ論的アルゴリズムだけでなく,線形計画問題におけるアルゴリズムを使っても解くことが出来る.本論文で取り上げる最適化問題は,フローネットワークにおける最適化問題の代表例である最短路問題と最長路問題である.最短路問題とは重みが最小となる道を求める問題で,最長路問題とはその逆に,重みが最大となる道を求める問題である.本研究の目的は,最短路問題と最長路問題の線形計画問題としての定式化と,最長路問題を解く組合せ論的アルゴリズムを見つけることである.本論文では,最短路問題の線形計画問題としての定式化は与えるが,最長路問題については,線形計画問題としてではない定式化を与えるにとどまる.最長路問題については,組合せ論的アルゴリズムを与える., Many of combinatorial optimization problems can be formulated as the linear programming (LP) problem. So they can be solved not only by their proper combinatorial algorithms but also by the algorithm in the LP problem. In the present paper, we focus on the shortest path problem and the longest path problem which are typical examples of the combinatorial optimization problem on the flow-networks. The shortest path problem is the problem for finding the path whose weight is minimal. Conversely, the longest path problem is the problem for finding the path whose weight is maximal. The purpose of our study is to formulate the shortest path problem and the longest path problem as the LP problem, and to find an algorithm for solving the longest path problem. In the present paper, we give the formulation of the shortest path problem as the LP problem. However, the longest path problem is not easy to formulate as the LP problem. So we give one formulation of the longest path problem by using rank condition, and give a combinatorial algorithm for the longest path problem.

最尤復号とは,受信後と同じシンドロームを持つベクトルの中でハミング重みが最小の誤りベクトルを選ぶことによって実行される.したがって,最尤復号は有限体上の整数計画問題として定式化できる.整数計画問題をグレブナー基底を使って解く方法としてConti-Traversoのアルゴリズムが有名である.このアルゴリズムをもとに,池上と楫はグレブナー基底を用いて最尤復号を解くアルゴリズムを提唱した.しかし,池上・楫アルゴリズムにはグレブナー基底の計算量について,重大な問題点がある.本論文では,2元符号に付随するグレブナー基底の計算量を減らすため,2つの試みを行っている.1つはFaugéreらによるグレブナー基底変換を用いる方法で,もう1つはグレブナー基底の中で最尤復号に必要なものだけを取り出す方法である.2元符号に付随するイデアルの辞書式順序に関するグレブナー基底が容易に得られることは知られている.このグレブナー基底をFGLMアルゴリズムを用いて適合順序に関するグレブナー基底に変換する.この方法は我々の目的に有効ではなかった.2つ目の方法については,復号に有効であると思われる特定のグレブナー基底を見出すことができた., Maximum likelihood decoding (MLD) is performed by choosing the error vector with the minimal Hamming weight among the set of vectors having the same syndromes as the received word. Thus, it is formulated as an integer programming (IP) problem on finite fields. There is a famous algorithm by Conti and Traverso for solving IP problems using the Gröbner basis in the polynomial ideal theory. Ikegami and Kaji have presented the algorithm for solving MLD using Gröbner basis; which is an analogue of the Conti and Traverso's algorithm. Once we have the Gröbner basis with respect to the adapted ordering of the ideal associated with the binary code, we efficiently perform MLD by computing the normal form of the monomials corresponding to the received word. However the algorithm has a serious problem on the computational complexity of the Gröbner basis. The present paper is an attempt to reduce the computational complexity of the Gröbner basis of the ideals associated with binary codes. We take two approaches: One is to apply the Gröbner basis conversion algorithm by Faugére et al. and the other is to determine the subset of binomials in the Gröbner basis that are indispensable for MLD. It is known that the Gröbner basis of the ideals associated with binary code with respect to the lexicographic ordering can be obtained easily. We convert this Gröbner basis to the Gröbner basis with respect to the adapted ordering by using FGLM algorithm. We have shown that this approach is not effective for our purpose. As for the second approach we have found the specified subset of the Gröbner basis that seems to be effective for the decoding.

Co-adsorption states and thermal stability of NO + CO on Ni(111) were investigated using infrared reflection absorption spectroscopy and temperature programed desorption. The mechanism for the displacement of CO by NO was clarified. Co-adsorbed NO induced hollow-to-ontop site-conversion of CO; NO molecules occupied hollow sites. Ontop and two hollow CO species were observed in the co-adsorbed phase. The ontop and lower frequency hollow CO were assigned to CO neighboring hollow NO; higher frequency hollow CO were assigned to CO forming those domain. The hollow-to-ontop site-conversion of CO occurred due to local interactions between CO and NO, which destabilized the CO by 0.5 eV. This destabilization afforded facile displacement of CO by NO at 300 K.

Adsorption states of size-selected Pt 7 clusters soft-landed on an Al 2 O 3 /NiAl(1 1 0) were investigated using scanning tunneling microscopy and spectroscopy at 300 K. Pt 7 clusters lay flat on the surface with a planar structure and were preferentially adsorbed on domain boundaries (DBs) of the Al 2 O 3 film. Because the clusters are thermally immobile, adsorption to DBs is controlled by transient mobility on the surface. The mean lateral displacement by transient migration is estimated to be ∼8 nm. Distinct conductivity resonances through unoccupied states of the Pt 7 clusters were observed near 2 V.

本論文では,フローネットワークにおける最適化問題の1つである,最小費用流問題に着目する.最小費用流問題とは,容量制約と需要条件を満たすフローの中で,そのコストが最小となるフローを求める問題で,実社会に広く応用されている問題である.この最小費用流問題を解くアルゴリズムとして,最も効率的であるのがネットワークシンプレックス法である.このアルゴリズムは木構造と呼ばれるものを更新し,最小費用流問題の最適解を求めるアルゴリズムであるが,更新が収束しない現象が頻繁に起こる.この現象は巡回と呼ばれ,巡回は強認容木構造をと呼ばれる特別な木構造を保つことで防ぐことができる.本論文では,この強認容木構造を保ちながら更新するための新しい方法について述べる.この新しい方法を第一閉鎖辺選択規則と呼ぶ.この方法はネットワークシンプレックス法における巡回の数学的構造をあきらかにする,重要な役割を果たす., In the present paper, we focus on the minimum cost flow problem which is one of the well-known optimization problems on flow-networks. The minimum cost flow problem is the problem for finding the minimum cost flow which satisfies the given capacity conditions and the demand conditions. It is known to have wide applications to real fields. The network simplex algorithm is known as the most efficient algorithm for solving the minimum cost flow problem. This algorithm gives an optimal solution to the minimal cost flow problem by updating the so called tree structure, but it does not necessarily terminate in a finite number of steps, even for small networks. This infinite iteration is caused by the cycling of tree structure. It is known that the cycling in the network simplex algorithm can be prevented by maintaining a special type of the tree structure, that is called a strongly admissible tree structure. In the present paper, we give a new rule for updating the tree structure, by which the strongly admissible tree structure is maintained. We call this new rule, rule of the first blocking edge. This will play a key role in clarifying the mathematical structure of the cycling in the network simplex algorithm.

Relaxation dynamics of hot metal clusters on oxide surfaces play a crucial role in a variety of physical and chemical processes. However, their transient mobility has not been investigated as much as other systems such as atoms and molecules on metal surfaces due to experimental difficulties. To study the role of the transient mobility of clusters on the oxide surface, we investigated the initial adsorption process of size-selected Pt clusters on a thin Al2O3 film. Soft-landing the size-selected clusters while suppressing the thermal migration resulted in the transient migration controlling the initial adsorption states as an isolated and aggregated cluster, as revealed using scanning tunneling microscopy. We demonstrate that transient migration significantly contributes to the initial cluster adsorption process; the cross section for aggregation is seven times larger than the expected value from geometrical considerations, indicating that metal clusters are highly mobile during a energy dissipation proce...

Low-temperature (25 K) adsorption states and the site conversion of adsorbed CO between the ontop and the hollow sites on Ni(111) were studied by means of temperature programmed desorption and infrared reflection absorption spectroscopy. The activation energy and pre-exponential factor of desorption were estimated to be 1.2 eV and 2.6 × 1013 s− 1, respectively, in the limit of zero coverage. At low coverage, CO molecules preferentially adsorbed at the hollow sites below 100 K. With increasing temperature, the ontop sites were also occupied. Using a van't Hoff plot, the enthalpy and the entropy differences between the hollow and ontop CO were estimated to be 36 meV and 0.043 meV K− 1, respectively, and the vibrational entropy difference was estimated to be 0.085 meV K− 1. The positive entropy difference was the result of the low-energy frustrated translational mode of the ontop CO, which was estimated to be 4.6 ± 0.3 meV. With the harmonic approximation, the upper limit of the activation energy of site hopping from ontop sites to hollow sites was estimated to be 61 meV. In addition, it was suggested that the activation energy of hollow-to-hollow site hopping via a bridge site was less than 37 meV.

本論文では,フローネットワーク最適化問題の1つとして有名な最大流問題に注目する.最大流問題とは,ネットワークにおいて2つの制約,容量制約と流量保存則のもとでフローの値が最大となるフローを見つける問題である.多くの組み合わせ最適化問題は線形計画問題(LP問題)として定式化され,最大流問題についてもLPへの定式化の方法は知られている.一方で,組み合わせ最適化問題において有名な定理,最大フロー・最小カットセット定理はネットワークにおけるフローとカットセットの双対性を表したものだと知られている.我々の研究の目的は,フローとカットセットの双対性をLP問題を通して明らかにすることである.本論文では知られている定式化とは違う新しい最大流問題の定式化を行った.実験結果によると,新しい定式化の双対問題は解として0-1ベクトルが現れ,これは最小カットセットを与えていた.この結果よりこの定式化は我々の意図するものだといえる.しかし,LP問題の双対問題を作ったのにもかかわらず,0-1ベクトルが解として現れた理由についてはまだ分かっておらず,これを今後の課題とする., In the present paper, we focus on the maximum flow problem which is one of the well-known optimization problems on flow-networks. The maximum flow problem is the problem for finding the flow such that the flow value is maximal among the flows subject to the capacity restriction and the flow conservation laws. Many of the combinatorial optimization problems can be formulated as linear programming (LP) problems, and it is known that the maximum flow problem can be formulated as an LP problem. On the other hand, the max-flow min-cutset theorem which is one of the famous results in combinatorial optimization, suggests the duality between flows and cutsets in networks. The purpose of our study is to clarify the duality between flows and cutsets in the maximum flow problem through the LP problem. In the present paper, we give a new formulation of the maximum flow problem as an LP problem which is slightly different from the one in the references. Computational experiments show that the dual of the LP problem computes a binary vector as the optimal solution, which presents the min-cutset. This implies that our formulation in the present paper is adequate for our purpose. However, we cannot make clear the reason why the optimal solution of the dual problem of the maximum flow problem becomes the binary vector, though the dual problem is an LP problem. This remains as a future subject of study.

本論文では,Min-Plus代数における行列の固有値問題を取り上げる.Min-Plus代数とは様々な数学の分野で研究がされているベキ等な半環構造を持つ代数系の1つである.Min-Plus代数では一般の線形代数における様々な性質や定理がそのまま従うように思えるが,検証はされていない.そこで我々はこのMin-Plus代数における行列の固有値を調べ,何らかの特徴付けができないかを考えた.そしてMin-Plus代数における重み付き隣接行列の固有値が,その行列で実現できる重みの付いた有向グラフ(ネットワーク)の閉路平均重みと対応していることがわかり,それを証明することができた.しかし,ネットワークの全ての閉路に対して,その平均重みが重み付き隣接行列の固有値として現れるかについてはまだわかっておらず,今後の課題といえるだろう., In the present paper, we focus on the eigenvalue problem of matrices with entries in min-plus algebra. Min-plus algebra is one of many idempotent semirings which have been studied in various fields of mathematics. Many of the theorems and techniques that we use in classical linear algebra seems to have analogues in linear algebra over min-plus algebra. However, such kinds of investigation have not yet exploited sufficiently. In the present paper, we try to give a characterization of eigenvalues of matrices with entries in min-plus algebra. We prove that eigenvalues of the weighted adjacency matrix of the network on digraphs with entries in min-plus algebra correspond to the average weight of the directed circuits. However, it is impossible for us to prove that there always exists an eigenvalue of weighted adjacency matrices for an arbitrary circuit of the network. So, the problem to characterize circuits for which there exits eigenvalues that are equal to the average weight of the circuit is left as an open problem.

本論文の主題は,最少費用粒問題の解法アルゴリズムであるネットワークシンプレックス法をMATLABへ実装することである.最小費用流問題とは,与えられた需要条件と容量条件の下で,コストが最少であるフローをみつける問題である.この問題は実社会の問題に広く応用がある問題であるにも関わらず,知られている解法アルゴリズムは少ない.ネットワークシンプレックス法はもっとも効率的なものであるが,多くの部分アルゴリズムから構成されており,きわめて複雑なアルゴリズムである.従って,実装は容易ではなく,部分アルゴリズムの組み合わせにおいて多様性がある.本論文においては,最短経路問題の解法アルゴリズムであるダイクストラ法やフロイド・ワーシャル法を部分アルゴリズムとして効率的に用いたネットワークシンプレックス法の実装を提案する.本実装は,非常に効率的であるとは言い難いが,グラフ理論における様々なアルゴリズムに対する知識を少ししか必要としない理解しやすい実装となっている., The main theme of the present paper is an implementation of the Network Simplex Algorithm for solving the minimum cost flow problem to MATLAB. The minimum cost flow problem is the problem for finding the minimum cost flow which satisfies the given capacity conditions and the demand and supply conditions. Although it is known to have a wide application to real fields, there have been known a few algorithms for solving the minimum cost flow problem. The Network Simplex Algorithm is known as the most efficient one, but it is a very complicated algorithm consisting of lots of sub-algorithms. So the implementation of the algorithm is not easy and it has varieties of combinations of sub-algorithms. In the present paper, we provide an implementation of the Network Simplex Algorithm using algorithms for the shortest path problems such as the Dijkstra algorithm or the Floyd-Warshall algorithm efficiently as sub-algorithms. We cannot say that the present implementation is quite efficient but it is easy to understand and requires a little knowledge about algorithms on graph theory.

Motivation: Considerable attention has been focused on predicting RNA–RNA interaction since it is a key to identifying possible targets of non-coding small RNAs that regulate gene expression post-transcriptionally. A number of computational studies have so far been devoted to predicting joint secondary structures or binding sites under a specific class of interactions. In general, there is a trade-off between range of interaction type and efficiency of a prediction algorithm, and thus efficient computational methods for predicting comprehensive type of interaction are still awaited. Results: We present RactIP, a fast and accurate prediction method for RNA–RNA interaction of general type using integer programming. RactIP can integrate approximate information on an ensemble of equilibrium joint structures into the objective function of integer programming using posterior internal and external base-paring probabilities. Experimental results on real interaction data show that prediction accuracy of RactIP is at least comparable to that of several state-of-the-art methods for RNA–RNA interaction prediction. Moreover, we demonstrate that RactIP can run incomparably faster than competitive methods for predicting joint secondary structures. Availability: RactIP is implemented in C++, and the source code is available at http://www.ncrna.org/software/ractip/ Contact: ykato@kuicr.kyoto-u.ac.jp; satoken@k.u-tokyo.ac.jp Supplementary information: Supplementary data are available at Bioinformatics online.

In order to examine cluster size dependence, mass-selected platinum clusters, Ptn (n=2–5, 7, 8, 10, 15), were deposited on TiO2(110) surfaces at room temperature under soft landing conditions, and their core levels were investigated by x-ray photoelectron spectroscopy. Pt core-level shifts with cluster size are observed. The binding energies of Pt 4f7/2 decrease steeply with increasing cluster size up to n=7 for Ptn and decrease gradually for n≥8. This inflection point (n=8) agrees well with the cluster size at a geometric transition (planar-to-three-dimensional) seen with scanning tunneling microscopy (STM) [N. Isomura, X. Wu, and Y. Watanabe, J. Chem. Phys. 131, 164707 (2009)]. It was found that the core-level shifts of mass-selected Pt clusters deposited on TiO2 are closely correlated with cluster geometries determined directly by atomic-resolution STM imaging.

The objectives of this research is to demonstrate that street stall operations that are conducted in street spaces of structure unique to Bangkok, Thailand and forms part of the informal sector, supports the livelihood of many urban migrants, and is closely related and integral to daily life, particularly eating habits and dwelling types, of urban dwellers in the city. The results of the on-site survey conducted in Sukhumvit Area reveal that street stalls located along Soi of dead-end streets basically are required for daily life particularly for maintenance of unique eating habits. To maintain the lifestyle unique to Thais, it is necessary and important to maintain street spaces of unique structure for street stall operation by not placing uniform restrictions as premises for excluding the street stalls in the informal sector but in accordance with site-oriented and flexible guidelines.

A new experimental setup to study catalytic and electronic properties of size-selected clusters on metal oxide substrates from the viewpoint of cluster-support interaction and to formulate a method for the development of heterogeneous catalysts such as automotive exhaust catalysts has been developed. The apparatus consists of a size-selected cluster source, a photoemission spectrometer, a scanning tunneling microscope (STM), and a high-pressure reaction cell. The high-pressure reaction cell measurements provided information on catalytic properties in conditions close to practical use. The authors investigated size-selected platinum clusters deposited on a TiO2(110) surface using a reaction cell and STM. Catalytic activity measurements showed that the catalytic activities have a cluster-size dependency.