Resolution limit in community detection

Detecting community structure is fundamental to clarify the link between structure and function in complex networks and is used for practical applications in many disciplines. A successful method relies on the optimization of a quantity called modularity [Newman and Girvan, Phys. Rev. E 69, 026113 (2004)], which is a quality index of a partition of a network into communities. We find that modularity optimization may fail to identify modules smaller than a scale which depends on the total number L of links of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined. The probability that a module conceals well-defined substructures is the highest if the number of links internal to the module is of the order of \sqrt{2L} or smaller. We discuss the practical consequences of this result by analyzing partitions obtained through modularity optimization in artificial and real networks.Comment: 8 pages, 3 figures. Clarification of definition of community in Section II + minor revision

Natural clustering: the modularity approach

We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally in the case of clustering algorithms that are rooted in Statistical Mechanics and use the analogy with a physical system.Comment: 11 pages, 5 figure enlarged versio

심층학습을 이용한 액체계의 성질 예측

학위논문(박사)--서울대학교 대학원 :자연과학대학 화학부,2020. 2. 정연준.최근 기계학습 기술의 급격한 발전과 이의 화학 분야에 대한 적용은 다양한 화학적 성질에 대한 구조-성질 정량 관계를 기반으로 한 예측 모형의 개발을 가속하고 있다. 용매화 자유 에너지는 그러한 기계학습의 적용 예중 하나이며 다양한 용매 내의 화학반응에서 중요한 역할을 하는 근본적 성질 중 하나이다. 본 연구에서 우리는 목표로 하는 용매화 자유 에너지를 원자간의 상호작용으로부터 구할 수 있는 새로운 심층학습 기반 용매화 모형을 소개한다. 제안된 심층학습 모형의 계산 과정은 용매와 용질 분자에 대한 부호화 함수가 각 원자와 분자들의 구조적 성질에 대한 벡터 표현을 추출하며, 이를 토대로 원자간 상호작용을 복잡한 퍼셉트론 신경망 대신 벡터간의 간단한 내적으로 구할 수 있다. 952가지의 유기용질과 147가지의 유기용매를 포함하는 6,493가지의 실험치를 토대로 기계학습 모형의 교차 검증 시험을 실시한 결과, 평균 절대 오차 기준 0.2 kcal/mol 수준으로 매우 높은 정확도를 가진다. 스캐폴드-기반 교차 검증의 결과 역시 0.6 kcal/mol 수준으로, 외삽으로 분류할 수 있는 비교적 새로운 분자 구조에 대한 예측에 대해서도 우수한 정확도를 보인다. 또한, 제안된 특정 기계학습 모형은 그 구조 상 특정 용매에 특화되지 않았기 때문에 높은 양도성을 가지며 학습에 이용할 데이터의 수를 늘이는 데 용이하다. 원자간 상호작용에 대한 분석을 통해 제안된 심층학습 모형 용매화 자유 에너지에 대한 그룹-기여도를 잘 재현할 수 있음을 알 수 있으며, 기계학습을 통해 단순히 목표로 하는 성질만을 예측하는 것을 넘어 더욱 상세한 물리화학적 이해를 하는 것이 가능할 것이라 기대할 수 있다.Recent advances in machine learning technologies and their chemical applications lead to the developments of diverse structure-property relationship based prediction models for various chemical properties; the free energy of solvation is one of them and plays a dominant role as a fundamental measure of solvation chemistry. Here, we introduce a novel machine learning-based solvation model, which calculates the target solvation free energy from pairwise atomistic interactions. The novelty of our proposed solvation model involves rather simple architecture: two encoding function extracts vector representations of the atomic and the molecular features from the given chemical structure, while the inner product between two atomistic features calculates their interactions, instead of black-boxed perceptron networks. The cross-validation result on 6,493 experimental measurements for 952 organic solutes and 147 organic solvents achieves an outstanding performance, which is 0.2 kcal/mol in MUE. The scaffold-based split method exhibits 0.6 kcal/mol, which shows that the proposed model guarantees reasonable accuracy even for extrapolated cases. Moreover, the proposed model shows an excellent transferability for enlarging training data due to its solvent-non-specific nature. Analysis of the atomistic interaction map shows there is a great potential that our proposed model reproduces group contributions on the solvation energy, which makes us believe that the proposed model not only provides the predicted target property, but also gives us more detailed physicochemical insights.1. Introduction 1 2. Delfos: Deep Learning Model for Prediction of Solvation Free Energies in Generic Organic Solvents 7 2.1. Methods 7 2.1.1. Embedding of Chemical Contexts 7 2.1.2. Encoder-Predictor Network 9 2.2. Results and Discussions 13 2.2.1. Computational Setup and Results 13 2.2.2. Transferability of the Model for New Compounds 17 2.2.3. Visualization of Attention Mechanism 26 3. Group Contribution Method for the Solvation Energy Estimation with Vector Representations of Atom 29 3.1. Model Description 29 3.1.1. Word Embedding 29 3.1.2. Network Architecture 33 3.2. Results and Discussions 39 3.2.1. Computational Details 39 3.2.2. Prediction Accuracy 42 3.2.3. Model Transferability 44 3.2.4. Group Contributions of Solvation Energy 49 4. Empirical Structure-Property Relationship Model for Liquid Transport Properties 55 5. Concluding Remarks 61 A. Analyzing Kinetic Trapping as a First-Order Dynamical Phase Transition in the Ensemble of Stochastic Trajectories 65 A1. Introduction 65 A2. Theory 68 A3. Lattice Gas Model 70 A4. Mathematical Model 73 A5. Dynamical Phase Transitions 75 A6. Conclusion 82 B. Reaction-Path Thermodynamics of the Michaelis-Menten Kinetics 85 B1. Introduction 85 B2. Reaction Path Thermodynamics 88 B3. Fixed Observation Time 94 B4. Conclusions 101Docto

Correlation of creep rate with microstructural changes during high temperature creep

Creep tests were conducted on Haynes 188 cobalt-base alloy and alpha titanium. The tests on Haynes 188 were conducted at 1600 F and 1800 F for stresses from 3 to 20 ksi, and the as-received, mill-annealed results were compared to specimens given 5%, 10%, and 15% room temperature prestrains and then annealed one hour at 1800 F. The tests on alpha titanium were performed at 7,250 and 10,000 psi at 500 C. One creep test was done at 527 C and 10,000 psi to provide information on kinetics. Results for annealed titanium were compared to specimens given 10% and 20% room temperature prestrains followed by 100 hours recovery at 550 C. Electron microscopy was used to relate dislocation and precipitate structure to the creep behavior of the two materials. The results on Haynes 188 alloy reveal that the time to reach 0.5% creep strain at 1600 F increases with increasing prestrain for exposure times less than 1,000 hours, the increase at 15% prestrain being more than a factor of ten

Simple models of protein folding and of non--conventional drug design

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the three--dimensional, biologically active, native conformation of a protein whose sequence is known. Using insight obtained from simple model simulations of the folding of proteins, in particular of the fact that this phenomenon is essentially controlled by conserved (native) contacts among (few) strongly interacting ("hot"), as a rule hydrophobic, amino acids, which also stabilize local elementary structures (LES, hidden, incipient secondary structures like $\alpha$--helices and $\beta$--sheets) formed early in the folding process and leading to the postcritical folding nucleus (i.e., the minimum set of native contacts which bring the system pass beyond the highest free--energy barrier found in the whole folding process) it is possible to work out a succesful strategy for reading the native structure of designed proteins from the knowledge of only their amino acid sequence and of the contact energies among the amino acids. Because LES have undergone millions of years of evolution to selectively dock to their complementary structures, small peptides made out of the same amino acids as the LES are expected to selectively attach to the newly expressed (unfolded) protein and inhibit its folding, or to the native (fluctuating) native conformation and denaturate it. These peptides, or their mimetic molecules, can thus be used as effective non--conventional drugs to those already existing (and directed at neutralizing the active site of enzymes), displaying the advantage of not suffering from the uprise of resistance

Ordinal Motifs in Lattices

Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of understandably large parts. With the present work we propose /ordinal motifs/ as analytical units of meaning. We study these ordinal substructures (or standard scales) through (full) scale-measures of formal contexts from the field of formal concept analysis. We show that the underlying decision problems are NP-complete and provide results on how one can incrementally identify ordinal motifs to save computational effort. Accompanying our theoretical results, we demonstrate how ordinal motifs can be leveraged to retrieve basic meaning from a medium sized ordinal data set