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Consistency and reliability are crucial for conducting AI research. Many famous research fields, such as object detection, have been compared and validated with solid benchmark frameworks. After AlphaFold2, the protein folding task has entered a new phase, and many methods are proposed based on the component of AlphaFold2. The importance of a unified research framework in protein folding contains implementations and benchmarks to consistently and fairly compare various approaches. To achieve this, we present Solvent, an protein folding framework that supports significant components of state-of-the-art models in the manner of off-the-shelf interface Solvent contains different models implemented in a unified codebase and supports training and evaluation for defined models on the same dataset. We benchmark well-known algorithms and their components and provide experiments that give helpful insights into the protein structure modeling field. We hope that Solvent will increase the reliability and consistency of proposed models and gives efficiency in both speed and costs, resulting in acceleration on protein folding modeling research. The code is available at https://github.com/kakaobrain/solvent, and the project will continue to be developed., preprint, 8pages

A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected $2$-complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere, if it admits one at all. This can be thought of as a generalisation of the 3-dimensional Schoenflies theorem.

Hansel's lemma states that $\sum_{H\in \mathcal{H}}|H| \geq n \log_2 n$ holds where $\mathcal{H}$ is a collection of bipartite graphs covering all the edges of $K_n$. We generalize this lemma to the corresponding multigraph covering problem and the graphon covering problem. We also prove an upper bound on $\sum_{H\in \mathcal{H}}|H|$ which shows that our generalization is asymptotically tight in some sense., 13 pages

Pedestrian injuries and fatalities due to traffic accidents remain at a high level. Therefore, the need for efforts to reduce this ratio is on the rise. Machine learning models can facilitate the exploration of the various factors that influence the occurrence of pedestrian accidents. In this study, we used data on pedestrian traffic accidents classified into three categories of injury severity: minor, severe, and fatal. To compare the performance of various types of models, logistic regression, Naïve Bayes, XGBoost, CatBoost, and LightGBM were used for analysis. Five machine learning methods were applied to the analysis, and hyperparameter tuning was performed to improve the performance of the model. The performances of the five models were 0.688, 0.577, 0.705, 0.708, and 0.707, respectively, and LightGBM showed the best classification accuracy at 0.708 in this study. Based on SHAP (Shapley additive explanation), one of the explainable artificial intelligence (XAI) techniques, we were able to obtain the variable importance of the LightGBM model, through which we identified the main factors affecting each level of injury severity. In addition, by using LIME (local interpretable model-agnostic explanation), another XAI technique, it was found that the age of the driver and pedestrian was the factor that had the most significant influence on the model’s classification prediction. Specifically, as the size of the vehicle increases, the severity of the accident increases. When the driver is older, the severity of the accident is small, and when the driver is young, the severity of the accident is high.

It is well-known that every tournament contains a Hamilton path, and every strongly connected tournament contains a Hamilton cycle. This paper establishes transversal generalizations of these classical results. For a collection $\mathbf{T}=\{T_1,\dots,T_m\}$ of not-necessarily distinct tournaments on a common vertex set $V$, an $m$-edge directed graph $\mathcal{D}$ with vertices in $V$ is called a $\mathbf{T}$-transversal if there exists a bijection $\phi\colon E(\mathcal{D})\to [m]$ such that $e\in E(T_{\phi(e)})$ for all $e\in E(\mathcal{D})$. We prove that for sufficiently large $m$ with $m=|V|-1$, there exists a $\mathbf{T}$-transversal Hamilton path. Moreover, if $m=|V|$ and at least $m-1$ of the tournaments $T_1,\ldots,T_m$ are assumed to be strongly connected, then there is a $\mathbf{T}$-transversal Hamilton cycle. In our proof, we utilize a novel way of partitioning tournaments which we dub $\mathbf{H}$-partition.

Given a collection $\mathcal{G}=(G_1,\dots, G_h)$ of graphs on the same vertex set $V$ of size $n$, an $h$-edge graph $H$ on the vertex set $V$ is a $\mathcal{G}$-transversal if there exists a bijection $\lambda : E(H) \rightarrow [h]$ such that $e\in E(G_{\lambda(e)})$ for each $e\in E(H)$. The conditions on the minimum degree $\delta(\mathcal{G})=\min_{i\in[h]}\{ \delta(G_i)\}$ for finding a spanning $\mathcal{G}$-transversal isomorphic to a graph $H$ have been actively studied when $H$ is a Hamilton cycle, an $F$-factor, a spanning tree with maximum degree $o(n/\log n)$ and a power of a Hamilton cycle, etc. In this paper, we determined the asymptotically tight threshold on $\delta(\mathcal{G})$ for finding a $\mathcal{G}$-transversal isomorphic to $H$ when $H$ is a general $n$-vertex graph with bounded maximum degree and $o(n)$-bandwidth. This provides a transversal generalization of the celebrated Bandwidth theorem by B\"ottcher, Schacht and Taraz.

We investigate quiver representations over $\mathbb{F}_1$. Coefficient quivers are combinatorial gadgets equivalent to $\mathbb{F}_1$-representations of quivers. We focus on the case when the quiver $Q$ is a pseudotree. For such quivers, we first use the notion of coefficient quivers to provide a complete classification of asymptotic behaviors of indecomposable representations over $\mathbb{F}_1$. Then, we prove some fundamental structural results about the Lie algebras associated to pseudotrees. Finally, we construct examples of $\mathbb{F}_1$-representations $M$ of a quiver $Q$ by using coverings, under which the Euler characteristics of the quiver Grassmannians $\textrm{Gr}^Q_{\underline{d}}(M)$ can be computed in a purely combinatorial way., Comment: 26 pages

In 1975, Erd\H{o}s asked the following question: what is the smallest function $f(n)$ for which all graphs with $n$ vertices and $f(n)$ edges contain two edge-disjoint cycles $C_1$ and $C_2$, such that the vertex set of $C_2$ is a subset of the vertex set of $C_1$ and their cyclic orderings of the vertices respect each other? We prove the optimal linear bound $f(n)=O(n)$ using sublinear expanders., Comment: 10 pages, 2 figures

Let $f^{(r)}(n;s,k)$ be the maximum number of edges of an $r$-uniform hypergraph on $n$ vertices not containing a subgraph with $k$ edges and at most $s$ vertices. In 1973, Brown, Erd\H{o}s and S\'os conjectured that the limit $$\lim_{n\to \infty} n^{-2} f^{(3)}(n;k+2,k)$$ exists for all $k$ and confirmed it for $k=2$. Recently, Glock showed this for $k=3$. We settle the next open case, $k=4$, by showing that $f^{(3)}(n;6,4)=\left(\frac{7}{36}+o(1)\right)n^2$ as $n\to\infty$. More generally, for all $k\in \{3,4\}$, $r\ge 3$ and $t\in [2,r-1]$, we compute the value of the limit $\lim_{n\to \infty} n^{-t}f^{(r)}(n;k(r-t)+t,k)$, which settles a problem of Shangguan and Tamo., Comment: 11 pages, 2 figures

Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and R\"{o}dl conjectured that for any given $\mu>0$, there exists $n_0$ such that the following holds. Every $n$-vertex Steiner triple system contains all hypertrees with at most $(1-\mu)n$ vertices whenever $n\geq n_0$. We prove this conjecture., Comment: 19 pages, 2 figures

There has been extensive studies on the following question: given $k$ graphs $G_1,\dots, G_k$ over a common vertex set of size $n$, what conditions on $G_i$ ensures a `colorful' copy of $H$, i.e., a copy of $H$ containing at most one edge from each $G_i$? A lower bound on $\sum_{i\in [k]} e(G_i)$ enforcing a colorful copy of a given graph $H$ was considered by Keevash, Saks, Sudakov, and Verstra\"{e}te. They defined $\operatorname{ex}_k(n,H)$ to be the maximum total number of edges of the graphs $G_1,\dots, G_k$ on a common vertex set of size $n$ having no colorful copy of $H$. They completely determined $\operatorname{ex}_k(n,K_r)$ for large $n$ by showing that, depending on the value of $k$, one of the two natural constructions is always the extremal construction. Moreover, they conjectured the same holds for every color-critical graphs and proved it for 3-color-critical graphs. We prove their conjecture for 4-color-critical graphs and for almost all $r$-color-critical graphs when $r > 4$. Moreover, we show that for every non-color-critical non-bipartite graphs, none of the two natural constructions is extremal for certain values of $k$. This answers a question of Keevash, Saks, Sudakov, and Verstra\"{e}te.

The oriented Ramsey number $\vec{r}(H)$ for an acyclic digraph $H$ is the minimum integer $n$ such that any $n$-vertex tournament contains a copy of $H$ as a subgraph. We prove that the $1$-subdivision of the $k$-vertex transitive tournament $H_k$ satisfies $\vec{r}(H_k)= O(k^2\log\log k)$. This is tight up to multiplicative $\log\log k$-term. We also show that if $T$ is an $n$-vertex tournament with $\Delta^+(T)-\delta^+(T)= O(n/k) - k^2$, then $T$ contains a $1$-subdivision of $\vec{K}_k$, a complete $k$-vertex digraph with all possible $k(k-1)$ arcs. This is tight up to multiplicative constant.

The families $\mathcal F_0,\ldots,\mathcal F_s$ of $k$-element subsets of $[n]:=\{1,2,\ldots,n\}$ are called cross-union if there is no choice of $F_0\in \mathcal F_0, \ldots, F_s\in \mathcal F_s$ such that $F_0\cup\ldots\cup F_s=[n]$. A natural generalization of the celebrated Erd\H{o}s--Ko--Rado theorem, due to Frankl and Tokushige, states that for $n\le (s+1)k$ the geometric mean of $\lvert \mathcal F_i\rvert$ is at most $\binom{n-1}{k}$. Frankl conjectured that the same should hold for the arithmetic mean under some mild conditions. We prove Frankl's conjecture in a strong form by showing that the unique (up to isomorphism) maximizer for the arithmetic mean of cross-union families is the natural one $\mathcal F_0=\ldots=\mathcal F_s={[n-1]\choose k}$., Comment: 14 pages, 1 figure Accepted at Combinatorial Theory

A celebrated theorem of Pippenger, and Frankl and R\"odl states that every almost-regular, uniform hypergraph $\mathcal{H}$ with small maximum codegree has an almost-perfect matching. We extend this result by obtaining a ``conflict-free'' matching, where conflicts are encoded via a collection $\mathcal{C}$ of subsets $C\subseteq E(\mathcal{H})$. We say that a matching $\mathcal{M}\subseteq E(\mathcal{H})$ is conflict-free if $\mathcal{M}$ does not contain an element of $\mathcal{C}$ as a subset. Under natural assumptions on $\mathcal{C}$, we prove that $\mathcal{H}$ has a conflict-free, almost-perfect matching. This has many applications, one of which yields new asymptotic results for so-called ``high-girth'' Steiner systems. Our main tool is a random greedy algorithm which we call the ``conflict-free matching process''., Comment: 58 pages

Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and Rödl conjectured that for any given $μ>0$, there exists $n_0$ such that the following holds. Every $n$-vertex Steiner triple system contains all hypertrees with at most $(1-μ)n$ vertices whenever $n\geq n_0$. We prove this conjecture., 19 pages, 2 figures

Let $f^{(r)}(n;s,k)$ be the maximum number of edges of an $r$-uniform hypergraph on $n$ vertices not containing a subgraph with $k$ edges and at most $s$ vertices. In 1973, Brown, Erdős and Sós conjectured that the limit $$\lim_{n\to \infty} n^{-2} f^{(3)}(n;k+2,k)$$ exists for all $k$ and confirmed it for $k=2$. Recently, Glock showed this for $k=3$. We settle the next open case, $k=4$, by showing that $f^{(3)}(n;6,4)=\left(\frac{7}{36}+o(1)\right)n^2$ as $n\to\infty$. More generally, for all $k\in \{3,4\}$, $r\ge 3$ and $t\in [2,r-1]$, we compute the value of the limit $\lim_{n\to \infty} n^{-t}f^{(r)}(n;k(r-t)+t,k)$, which settles a problem of Shangguan and Tamo., 11 pages, 2 figures

We prove that every properly edge-colored $n$-vertex graph with average degree at least $100(\log n)^2$ contains a rainbow cycle, improving upon $(\log n)^{2+o(1)}$ bound due to Tomon. We also prove that every properly colored $n$-vertex graph with at least $10^5 k^2 n^{1+1/k}$ edges contains a rainbow $2k$-cycle, which improves the previous bound $2^{ck^2}n^{1+1/k}$ obtained by Janzer. Our method using homomorphism inequalities and a lopsided regularization lemma also provides a simple way to prove the Erd\H{o}s--Simonovits supersaturation theorem for even cycles, which may be of independent interest.

For a given graph $H$, its subdivisions carry the same topological structure. The existence of $H$-subdivisions within a graph $G$ has deep connections with topological, structural and extremal properties of $G$. One prominent examples of such connections, due to Bollob\'{a}s and Thomason and independently Koml\'os and Szemer\'edi, asserts that the average degree of $G$ being $d$ ensures a $K_{\Omega(\sqrt{d})}$-subdivision in $G$. Although this square-root bound is best possible, various results showed that much larger clique subdivisions can be found in a graph from many natural classes. We investigate the connection between crux, a notion capturing the essential order of a graph, and the existence of large clique subdivisions. This reveals the unifying cause underpinning all those improvements for various classes of graphs studied. Roughly speaking, when embedding subdivisions, natural space constraints arise; and such space constraints can be measured via crux. Our main result gives an asymptotically optimal bound on the size of a largest clique subdivision in a generic graph $G$, which is determined by both its average degree and its crux size. As corollaries, we obtain (1) a characterisation of extremal graphs for which the square-root bound above is tight: they are essentially disjoint union of graphs each of which has the crux size linear in $d$; (2) a unifying approach to find a clique subdivision of almost optimal size in graphs which does not contain a fixed bipartite graph as a subgraph; (3) and that the clique subdivision size in random graphs $G(n,p)$ witnesses a dichotomy: when $p = \omega(n^{-1/2})$, the barrier is the space, while when $p=o( n^{-1/2})$, the bottleneck is the density., Comment: 37 pages, 2 figures

The following question was proposed by Nenadov and Pehova and reiterated by Knierim and Su: Given integers $\ell,r$ and $n$ with $n\in r\mathbb{N}$, is it true that every $n$-vertex graph $G$ with $\delta(G) \ge \max \{ \frac{1}{2},\frac{r - \ell}{r} \}n + o(n)$ and $\alpha_{\ell}(G) = o(n) $ contains a $K_{r}$-factor? We give a negative answer for the case when $\ell\ge \frac{3r}{4}$ by giving a family of constructions using the so-called cover thresholds and show that the minimum degree condition given by our construction is asymptotically best possible. That is, for all integers $r,\ell$ with $r > \ell \ge \frac{3}{4}r$ and $\mu >0$, there exist $\alpha > 0$ and $N$ such that for every $n\in r\mathbb{N}$ with $n>N$, every $n$-vertex graph $G$ with $\delta(G) \ge \left( \frac{1}{2-\varrho_{\ell}(r-1)} + \mu \right)n $ and $\alpha_{\ell}(G) \le \alpha n$ contains a $K_{r}$-factor. Here $\varrho_{\ell}(r-1)$ is the Ramsey--Tur\'an density for $K_{r-1}$ under the $\ell$-independence number condition., Comment: 23 pages,2 figures

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Let the kissing number $K(d)$ be the maximum number of non-overlapping unit balls in $\mathbb R^d$ that can touch a given unit ball. Determining or estimating the number $K(d)$ has a long history, with the value of $K(3)$ being the subject of a famous discussion between Gregory and Newton in 1694. We prove that, as the dimension $d$ goes to infinity, $$ K(d)\ge (1+o(1)){\frac{\sqrt{3\pi}}{4\sqrt2}}\,\log\frac{3}{2}\cdot d^{3/2}\cdot \Big(\frac{2}{\sqrt{3}}\Big)^{d}, $$ thus improving the previously best known bound of Jenssen, Joos and Perkins by a factor of $\log(3/2)/\log(9/8)+o(1)=3.442...$. Our proof is based on the novel approach from Jenssen, Joos and Perkins that uses the hard core sphere model of an appropriate fugacity. Similar constant-factor improvements in lower bounds are also obtained for general spherical codes, as well as for the expected density of random sphere packings in the Euclidean space $\mathbb R^d$., Comment: 20 pages

For a graph $H$, a graph $G$ is $H$-saturated if $G$ does not contain $H$ as a subgraph but for any $e \in E(\overline{G})$, $G+e$ contains $H$. In this note, we prove a sharp lower bound for the number of paths and walks on length $2$ in $n$-vertex $K_{r+1}$-saturated graphs. We then use this bound to give a lower bound on the spectral radii of such graphs which is asymptotically tight for each fixed $r$ and $n\to\infty$.

We prove that for every integer $k$, there exists $\varepsilon > 0$ such that for every n-vertex graph $G$ with no pivot-minor isomorphic to $C_k$, there exist disjoint sets $A,B \subseteq V(G)$ such that $|A|,|B| \geq \varepsilon n$, and $A$ is either complete or anticomplete to $B$. This proves the analog of the Erd��s-Hajnal conjecture for the class of graphs with no pivot-minor isomorphic to $C_k$., 13 pages, 4 figures

The famous Erd\H{o}s-Rademacher problem asks for the smallest number of $r$-cliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asymptotic value of this extremal function for all $r$ was determined only recently, by Reiher [Annals of Mathematics, 184 (2016) 683--707]. Here we describe the asymptotic structure of all almost extremal graphs. This task for $r=3$ was previously accomplished by Pikhurko and Razborov [Combinatorics, Probability and Computing, 26 (2017) 138--160].

We investigate how minor-monotone graph parameters change if we add a few random edges to a connected graph $H$. Surprisingly, after adding a few random edges, its treewidth, treedepth, genus, and the size of a largest complete minor become very large regardless of the shape of $H$. Our results are close to best possible for various cases., Comment: 19 pages

In this work, we propose the use of the d-band width of the muffin-tin orbital theory (to account for the local coordination environment) plus electronegativity (to account for adsorbate renormalization) as a simple set of alternative descriptors for chemisorption which do not require ab initio calculations for large-scale first-hand screening., In a conventional chemisorption model, the d-band center theory (augmented sometimes with the upper edge of the d-band for improved accuracy) plays a central role in predicting adsorption energies and catalytic activity as a function of the d-band center of solid surfaces, but it requires density functional calculations that can be quite costly for the purposes of large scale screening of materials. In this work, we propose to use the d-band width of the muffin-tin orbital theory (to account for the local coordination environment) plus electronegativity (to account for adsorbate renormalization) as a simple set of alternative descriptors for chemisorption which do not require ab initio calculations for large-scale first-hand screening. This pair of descriptors is then combined with machine learning methods, namely, neural network (NN) and kernel ridge regression (KRR). We show, for a toy set of 263 alloy systems, that the CO adsorption energy on the (100) facet can be predicted with a mean absolute deviation error of 0.05 eV. We achieved this high accuracy by utilizing an active learning algorithm, without which the accuracy was 0.18 eV. In addition, the results of testing the method with other facets such as (111) terrace and (211) step sites suggest that the present model is also capable of handling different coordination environments effectively. As an example of the practical application of this machine, we identified Cu3Y@Cu* as an active and cost-effective electrochemical CO2 reduction catalyst to produce CO with an overpotential ∼1 V lower than a Au catalyst.

본 연구는 지난 1999년도부터 시작되어 현재까지 수행되고 있는 예비타당성조사에서 중요하게 고려되고 있는 요인이 무엇인지 살펴보는 것을 목적으로 한다. 분석결과, AHP평점에 영향을 미치는 요인은 B/C, 경제성 분석 가중치, 지역균형발전 가중치, 부정적인 특수평가항목, 사업계획 변경 여부, 집권당의 성향 등인 것으로 나타났다. 또한 분석과정에서 AHP활용의 적합성에 대해서도 재검토의 여지가 있을 것으로 판단하여 이에 대해 제언하였다. 본 연구는 예비타당성조사가 여러 항목을 아우르는 평가를 수행하고 있는지 여부를 확인할 수 있는 계기를 마련하고, 예비타당성조사의 종합판단을 위해 고안된 AHP방법론이 적합한 것인가에 대한 시사점을 제안하는데 의의를 가진다.

The extremal number $\mathrm{ex}(n,F)$ of a graph $F$ is the maximum number of edges in an $n$-vertex graph not containing $F$ as a subgraph. A real number $r \in [1,2]$ is realisable if there exists a graph $F$ with $\mathrm{ex}(n , F) = \Theta(n^r)$. Several decades ago, Erd\H{o}s and Simonovits conjectured that every rational number in $[1,2]$ is realisable. Despite decades of effort, the only known realisable numbers are $0,1, \frac{7}{5}, 2$, and the numbers of the form $1+\frac{1}{m}$, $2-\frac{1}{m}$, $2-\frac{2}{m}$ for integers $m \geq 1$. In particular, it is not even known whether the set of all realisable numbers contains a single limit point other than two numbers $1$ and $2$. In this paper, we make progress on the conjecture of Erd\H{o}s and Simonovits. First, we show that $2 - \frac{a}{b}$ is realisable for any integers $a,b \geq 1$ with $b>a$ and $b \equiv \pm 1 ~({\rm mod}\:a)$. This includes all previously known ones, and gives infinitely many limit points $2-\frac{1}{m}$ in the set of all realisable numbers as a consequence. Secondly, we propose a conjecture on subdivisions of bipartite graphs. Apart from being interesting on its own, we show that, somewhat surprisingly, this subdivision conjecture in fact implies that every rational number between 1 and 2 is realisable.

We prove several results on approximate decompositions of edge-coloured quasirandom graphs into rainbow spanning structures. More precisely, we say that an edge-colouring of a graph is locally $\ell$-bounded if no vertex is incident to more than $\ell$ edges of any given colour, and that it is (globally) $g$-bounded if no colour appears more than $g$ times in the colouring. Note that every proper colouring of an $n$-vertex graph is locally $1$-bounded, and (globally) $n/2$-bounded. Our results imply the following: (i) The existence of approximate decompositions of edge-coloured $K_n$ into rainbow almost-spanning cycles, provided that the colouring is $\frac{n}{2}$-bounded and locally $o(n)$-bounded. (ii) The existence of approximate decompositions of edge-coloured $K_n$ into rainbow Hamilton cycles, provided that the colouring is $(1-o(1))\frac n2$-bounded and locally $o\big(\frac{n}{\log^4 n}\big)$-bounded. (iii) A bipartite version of our results implies that every $n\times n$ array, where each symbol appears $(1-o(1))n$ times in total and appears only $o\big(\frac{n}{\log^2 n}\big)$ times in each row or column, has an approximate decomposition into full transversals. We also prove analogues of (i) and (ii) for $F$-factors, where $F$ is any fixed graph. Apart from the logarithmic factor in (ii), all these bounds are essentially best possible. (i) can be viewed as a generalization of a recent result of Alon, Pokrovskiy and Sudakov, who showed the existence of an almost spanning cycle in a properly coloured complete graph. Both (i) and (ii) imply approximate versions of a conjecture of Brualdi and Hollingsworth, stating that every properly edge-coloured complete graph can be decomposed into rainbow spanning trees., final version, to appear in Random Structures and Algorithms

Given graphs $H_1,\ldots, H_k$, a graph $G$ is $(H_1,\ldots, H_k)$-free if there is a $k$-edge-colouring $\phi:E(G)\rightarrow [k]$ with no monochromatic copy of $H_i$ with edges of colour $i$ for each $i\in[k]$. Fix a function $f(n)$, the Ramsey-Tur\'an function $\textrm{RT}(n,H_1,\ldots,H_k,f(n))$ is the maximum number of edges in an $n$-vertex $(H_1,\ldots,H_k)$-free graph with independence number at most $f(n)$. We determine $\textrm{RT}(n,K_3,K_s,\delta n)$ for $s\in\{3,4,5\}$ and sufficiently small $\delta$, confirming a conjecture of Erd\H{o}s and S\'os from 1979. It is known that $\textrm{RT}(n,K_8,f(n))$ has a phase transition at $f(n)=\Theta(\sqrt{n\log n})$. However, the values of $\textrm{RT}(n,K_8, o(\sqrt{n\log n}))$ was not known. We determined this value by proving $\textrm{RT}(n,K_8,o(\sqrt{n\log n}))=\frac{n^2}{4}+o(n^2)$, answering a question of Balogh, Hu and Simonovits. The proofs utilise, among others, dependent random choice and results from graph packings., Comment: 20 pages, 2 figures, 2 pages appendix

Given graphs $H_1,\ldots, H_k$, a graph $G$ is $(H_1,\ldots, H_k)$-free if there is a $k$-edge-colouring $��:E(G)\rightarrow [k]$ with no monochromatic copy of $H_i$ with edges of colour $i$ for each $i\in[k]$. Fix a function $f(n)$, the Ramsey-Tur��n function $\textrm{RT}(n,H_1,\ldots,H_k,f(n))$ is the maximum number of edges in an $n$-vertex $(H_1,\ldots,H_k)$-free graph with independence number at most $f(n)$. We determine $\textrm{RT}(n,K_3,K_s,��n)$ for $s\in\{3,4,5\}$ and sufficiently small $��$, confirming a conjecture of Erd��s and S��s from 1979. It is known that $\textrm{RT}(n,K_8,f(n))$ has a phase transition at $f(n)=��(\sqrt{n\log n})$. However, the values of $\textrm{RT}(n,K_8, o(\sqrt{n\log n}))$ was not known. We determined this value by proving $\textrm{RT}(n,K_8,o(\sqrt{n\log n}))=\frac{n^2}{4}+o(n^2)$, answering a question of Balogh, Hu and Simonovits. The proofs utilise, among others, dependent random choice and results from graph packings., 20 pages, 2 figures, 2 pages appendix

The extremal number $\mathrm{ex}(n,F)$ of a graph $F$ is the maximum number of edges in an $n$-vertex graph not containing $F$ as a subgraph. A real number $r \in [1,2]$ is realisable if there exists a graph $F$ with $\mathrm{ex}(n , F) = ��(n^r)$. Several decades ago, Erd��s and Simonovits conjectured that every rational number in $[1,2]$ is realisable. Despite decades of effort, the only known realisable numbers are $0,1, \frac{7}{5}, 2$, and the numbers of the form $1+\frac{1}{m}$, $2-\frac{1}{m}$, $2-\frac{2}{m}$ for integers $m \geq 1$. In particular, it is not even known whether the set of all realisable numbers contains a single limit point other than two numbers $1$ and $2$. In this paper, we make progress on the conjecture of Erd��s and Simonovits. First, we show that $2 - \frac{a}{b}$ is realisable for any integers $a,b \geq 1$ with $b>a$ and $b \equiv \pm 1 ~({\rm mod}\:a)$. This includes all previously known ones, and gives infinitely many limit points $2-\frac{1}{m}$ in the set of all realisable numbers as a consequence. Secondly, we propose a conjecture on subdivisions of bipartite graphs. Apart from being interesting on its own, we show that, somewhat surprisingly, this subdivision conjecture in fact implies that every rational number between 1 and 2 is realisable.

International audience; The Set1 family of histone H3 lysine 4 (H3K4) methyltransferases is highly conserved from yeast to human. Here we show that the Set1 complex (Set1C) directly binds RNA in vitro through the regions that comprise the double RNA recognition motifs (dRRM) and N-SET domain within Set1 and its subunit Spp1. To investigate the functional relevance of RNA binding, we performed UV RNA crosslinking (CRAC) for Set1 and RNA polymerase II in parallel with ChIP-seq experiments. Set1 binds nascent transcripts through its dRRM. RNA binding is important to define the appropriate topology of Set1C distribution along transcription units and correlates with the efficient deposition of the H3K4me3 mark. In addition, we uncovered that Set1 binds to different classes of RNAs to levels that largely exceed the levels of binding to the general population of transcripts, suggesting the Set1 persists on these RNAs after transcription. This class includes RNAs derived from SET1, Ty1 retrotransposons, specific transcription factors genes and snRNAs (small nuclear RNAs). We propose that Set1 modulates adaptive responses, as exemplified by the post-transcriptional inhibition of Ty1 retrotransposition.

An $r$-matching in a graph $G$ is a collection of edges in $G$ such that the distance between any two edges is at least $r$. A $2$-matching is also called an induced matching. In this paper, we estimate the maximum number of $r$-matchings in a tree of fixed order. We also prove that the $n$-vertex path has the maximum number of induced matchings among all $n$-vertex trees.

Koml\'os conjectured in 1981 that among all graphs with minimum degree at least $d$, the complete graph $K_{d+1}$ minimises the number of Hamiltonian subsets, where a subset of vertices is Hamiltonian if it contains a spanning cycle. We prove this conjecture when $d$ is sufficiently large. In fact we prove a stronger result: for large $d$, any graph $G$ with average degree at least $d$ contains almost twice as many Hamiltonian subsets as $K_{d+1}$, unless $G$ is isomorphic to $K_{d+1}$ or a certain other graph which we specify., Comment: 33 pages, to appear in Proceedings of the London Mathematical Society

Koml��s conjectured in 1981 that among all graphs with minimum degree at least $d$, the complete graph $K_{d+1}$ minimises the number of Hamiltonian subsets, where a subset of vertices is Hamiltonian if it contains a spanning cycle. We prove this conjecture when $d$ is sufficiently large. In fact we prove a stronger result: for large $d$, any graph $G$ with average degree at least $d$ contains almost twice as many Hamiltonian subsets as $K_{d+1}$, unless $G$ is isomorphic to $K_{d+1}$ or a certain other graph which we specify., 33 pages, to appear in Proceedings of the London Mathematical Society

In conventional chemisorption model, the d-band center theory (augmented sometimes with the upper edge of d-band for imporved accuarcy) plays a central role in predicting adsorption energies and catalytic activity as a function of d-band center of the solid surfaces, but it requires density functional calculations that can be quite costly for large scale screening purposes of materials. In this work, we propose to use the d-band width of the muffin-tin orbital theory (to account for local coordination environment) plus electronegativity (to account for adsorbate renormalization) as a simple set of alternative descriptors for chemisorption, which do not demand the ab initio calculations. This pair of descriptors are then combined with machine learning methods, namely, artificial neural network (ANN) and kernel ridge regression (KRR), to allow large scale materials screenings. We show, for a toy set of 263 alloy systems, that the CO adsorption energy can be predicted with a remarkably small mean absolute deviation error of 0.05 eV, a significantly improved result as compared to 0.13 eV obtained with descriptors including costly d-band center calculations in literature. We achieved this high accuracy by utilizing an active learning algorithm, without which the accuracy was 0.18 eV otherwise. As a practical application of this machine, we identified Cu3Y@Cu as a highly active and cost-effective electrochemical CO2 reduction catalyst to produce CO with the overpotential 0.37 V lower than Au catalyst., Comment: Under review and including Electronic Supplementary Information (ESI)

We develop a new method for constructing approximate decompositions of dense graphs into sparse graphs and apply it to longstanding decomposition problems. For instance, our results imply the following. Let $G$ be a quasi-random $n$-vertex graph and suppose $H_1,\dots,H_s$ are bounded degree $n$-vertex graphs with $\sum_{i=1}^{s} e(H_i) \leq (1-o(1)) e(G)$. Then $H_1,\dots,H_s$ can be packed edge-disjointly into $G$. The case when $G$ is the complete graph $K_n$ implies an approximate version of the tree packing conjecture of Gy\'arf\'as and Lehel for bounded degree trees, and of the Oberwolfach problem. We provide a more general version of the above approximate decomposition result which can be applied to super-regular graphs and thus can be combined with Szemer\'edi's regularity lemma. In particular our result can be viewed as an extension of the classical blow-up lemma of Koml\'os, S\'ark\H{o}zy and Szemer\'edi to the setting of approximate decompositions., Comment: Final version, to appear in Transactions of the American Mathematical Society

In laser wakefield accelerator, usually a gas target is used to generate plasma medium. With this gas target, the pressure of the system cannot be keep as low as possible for electron beam application such as seeding the storage ring. To reduce this vacuum problem in LWFA, a plasma generated from solid Al target was used as plasma medium. A fundamental beam from the Q-switched ns pump laser in the Ti:sapphire power amplifier was used to generate a plasma from solid Al target. The plasma density was controlled by changing the distance between the main laser pulse for electron acceleration and the solid target. The plasma density was measured by the interferometer. The measured density indicates that the average charge of the ion in pre-plasma was 4.4. The main pulse ionized the Al plasma up to Al XII which means that the ionization injection could be used as an injection scheme. A 28 TW fs laser was used to accelerate the electron. A quasi-monochromatic electron was generated. The peak energy was 70 MeV and energy spread was 15 %. The divergence of the beam was 12 mrad in horizontal direction and 6 mrad in vertical direction., Proceedings of the 37th International Free Electron Laser Conference, FEL2015, Daejeon, Republic of Korea

The substantial influence of CEOs diminishes the oversight function of the board of directors. Many outside directors have social ties with CEOs and their behavioral patterns are inconsistent with those of vigilant monitors. Dissents are rare, and those who do dissent are highly likely to be replaced. Further, the director ratio tends to be lower when more supervisory items are on the board agenda. In order for the outside director system to operate properly, the voting rights of minority shareholders should be respected, outside directors and agenda selection must remain independent from CEOs, and objective evaluation and disclosure of outside directors' board activities must ensue. - Analysis on corporate data shows that, under the current outside director system, CEOs can immobilize oversight by outside directors. - There is a low possibility of dissent on boards that lack independence from management. - The attendance pattern of friendly outside directors is consistent with delegating decision making to inside directors. - Outside directors rarely cast a dissenting vote, but once they do, they face a higher risk of being replaced. - Outside directors with the same regional or high school background as the CEO face lower replacement risks than those without such connections. - It seems that practical influence of outside directors on boards is low during times when their supervisory role is critical. The situation also implies that CEOs have of the windows of opportunity to obtain approval on sensitive issues at board meetings. - In order to restrict CEOs from intervening in the process of outside director recommendation, it is necessary to strengthen the role of outside directors in the composition of the candidate recommendation committee and to mandate the committee to recommend more than one candidate. - The general shareholders' meeting should be provided with information on objective indices regarding how the board of directors has operated on essential issues. - The CEO should not be allowed to hold the position of board chairman.

A family $\mathcal{F}$ is $t$-$\it{intersecting}$ if any two members have at least $t$ common elements. Erd\H os, Ko, and Rado proved that the maximum size of a $t$-intersecting family of subsets of size $k$ is equal to $ {{n-t} \choose {k-t}}$ if $n\geq n_0(k,t)$. Alon, Aydinian, and Huang considered families generalizing intersecting families, and proved the same bound. In this paper, we give a strengthening of their result by considering families generalizing $t$-intersecting families for all $t \geq 1$. In 2004, Talbot generalized Bollob\'{a}s's Two Families Theorem to $t$-intersecting families. In this paper, we proved a slight generalization of Talbot's result by using the probabilistic method.

Hiring former government officials can provide benefits in utilizing the accumulated knowledge, but also creates problems in that they can be abused as lobbying channels. - One of the primary causes of Korea's savings bank collapse was the hiring of former oversight agency officials and their prominent role in illegal lobbying. - The primary reason for the usage of former government employees as lobbying arms is to the close, personal ties between former and current officials, reinforced by the closed recruitment system. - The possibility exists that retired officials with close ties to current officials may be used as lobbying channels. - Closed recruitment practices were also implicated in a recent controversy over nuclear power plant corruption. - In order to weaken the close ties between current officials and former officials and to utilize the skills of private sector experts in the public sector, it is imperative to adopt a more advanced HR system, expand the open recruitment system, and increase the number of private sector experts across all departments. - Open recruitment was introduced in January 2000, with 20 percent of the total senior official positions selected from a pool of candidates from both inside and outside the government. However, questions have been raised about the system's effectiveness in terms of attracting experts from the private sector. - An advanced version of civil service HR system and improvements on the current state of partial application of the open recruitment and private sector expert recruitment is essential. This should be followed by large-scale expansion and application.

Using the nonlinear interaction between the high power laser and the plasma, we can generate strong acceleration field, called the laser wake field acceleration. The plasma density is very crucial to generate high energy electron. In this work, we studied the effect of the plasma density structure on the accelerated electron energy. We used 20 TW, 40 fs laser system to generate the plasma wakefield. A gas jet was used as a target. The plasma density was controlled by the back pressure of the gas nozzle and measured by the interferometer. The accelerated electron energy was measured using the electron energy spectrometer with 0.5 T magnet. The bunch charge was measured integrated charge transformer (ICT). When the plasma density is uniform, 2×10¹⁹ cm⁻³ we can generate 200 MeV electron beam with bunch charge 33 pC. The electron beam divergence was less than 5 degree. If there exists the downward density tramp, the electron energy is only 50 MeV. The PIC simulation also indicates that if there is density ramp structure, the electron is not accelerated well. In this presentation, the overall experimental and simulation results are presented., Proceedings of the 1st International Particle Accelerator Conference, IPAC2010, Kyoto, Japan

This study describes the tensile test results of AISI type 304 deformed at room and elevated temperatures. It has been known that the normal distribution fits well with the strength of typical structural materials. The Weibull distribution has many characteristics in the reliability design. In this paper, we showed that the Weibull distribution can be used to describe the scattering of strength data as well as normal distribution by testing goodness of fit. It is found that the parameters of Weibull distribution have decreasing tendency for temperature rise and the coefficient of variation has increasing tendency for temperature rise.

The journal of chemical physics 155(8), 084801 (2021). doi:10.1063/5.0055522, Published by American Institute of Physics, Melville, NY