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[Link to my homepage](https://sites.google.com/view/danisch/home) ## I will read the following papers. - [PageRank as a Function of the Damping Factor](https://papers-gamma.link/paper/106) - [Graph Stream Algorithms: A Survey](https://papers-gamma.link/paper/102) - [Network Sampling: From Static to Streaming Graphs](https://papers-gamma.link/paper/122) - [The Protein-Folding Problem, 50 Years On](https://papers-gamma.link/paper/78) - [Computational inference of gene regulatory networks: Approaches, limitations and opportunitie](https://papers-gamma.link/paper/77) - [Graph complexity analysis identifies an ETV5 tumor-specific network in human and murine low-grade glioma](https://papers-gamma.link/paper/79) - [Gene Networks in Plant Biology: Approaches in Reconstruction and Analysis](https://papers-gamma.link/paper/76) - [The non-convex Burer–Monteiro approach works on smooth semidefinite programs](https://papers-gamma.link/paper/80) - [Solving SDPs for synchronization and MaxCut problems via the Grothendieck inequality](https://papers-gamma.link/paper/81) - [Influence maximization in complex networks through optimal percolation](https://papers-gamma.link/paper/70) - [Motifs in Temporal Networks](https://papers-gamma.link/paper/61) - [Deep Sparse Rectifier Neural Networks](https://papers-gamma.link/paper/69) - [Sparse Convolutional Neural Networks](https://papers-gamma.link/paper/67) - [A fast and simple algorithm for training neural probabilistic language models](https://papers-gamma.link/paper/58) - [Adding One Neuron Can Eliminate All Bad Local Minima](https://papers-gamma.link/paper/71) ## I read the following papers. ### 2018-2019: - [Hierarchical Taxonomy Aware Network Embedding](https://papers-gamma.link/paper/116) - [Billion-scale Network Embedding with Iterative Random Projection](https://papers-gamma.link/paper/110) - [HARP: Hierarchical Representation Learning for Networks](https://papers-gamma.link/paper/109/) - [Layered Label Propagation: A MultiResolution Coordinate-Free Ordering for Compressing Social Networks](https://papers-gamma.link/paper/105) ### 2017-2018: - [Link Prediction in Graph Streams](https://papers-gamma.link/paper/101) - [The Community-search Problem and How to Plan a Successful Cocktail Party](https://papers-gamma.link/paper/74) - [A Nonlinear Programming Algorithm for Solving Semidefinite Programs via Low-rank Factorization](https://papers-gamma.link/paper/55) - [Deep Learning](https://papers-gamma.link/paper/68) - [Reducing the Dimensionality of Data with Neural Networks](https://papers-gamma.link/paper/65) - [Representation Learning on Graphs: Methods and Applications](https://papers-gamma.link/paper/60) - [Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION](https://papers-gamma.link/paper/56) - [Cauchy Graph Embedding](https://papers-gamma.link/paper/53) - [Phase Transitions in Semidefinite Relaxations](https://papers-gamma.link/paper/57) - [Graph Embedding Techniques, Applications, and Performance: A Survey](https://papers-gamma.link/paper/52) - [VERSE: Versatile Graph Embeddings from Similarity Measures](https://papers-gamma.link/paper/48) - [Hierarchical Clustering Beyond the Worst-Case](https://papers-gamma.link/paper/45) - [Scalable Motif-aware Graph Clustering](https://papers-gamma.link/paper/18) - [Practical Algorithms for Linear Boolean-width](https://papers-gamma.link/paper/40) - [New Perspectives and Methods in Link Prediction](https://papers-gamma.link/paper/28/New%20Perspectives%20and%20Methods%20in%20Link%20Prediction) - [In-Core Computation of Geometric Centralities with HyperBall: A Hundred Billion Nodes and Beyond](https://papers-gamma.link/paper/37) - [Diversity is All You Need: Learning Skills without a Reward Function](https://papers-gamma.link/paper/36) - [When Hashes Met Wedges: A Distributed Algorithm for Finding High Similarity Vectors](https://papers-gamma.link/paper/23) - [Fast Approximation of Centrality](https://papers-gamma.link/paper/35/Fast%20Approximation%20of%20Centrality) - [Indexing Public-Private Graphs](https://papers-gamma.link/paper/19/Indexing%20Public-Private%20Graphs) - [On the uniform generation of random graphs with prescribed degree sequences](https://papers-gamma.link/paper/26/On%20the%20uniform%20generation%20of%20random%20graphs%20with%20prescribed%20d%20egree%20sequences) - [Linear Additive Markov Processes](https://papers-gamma.link/paper/21/Linear%20Additive%20Markov%20Processes) - [ESCAPE: Efficiently Counting All 5-Vertex Subgraphs](https://papers-gamma.link/paper/17/ESCAPE:%20Efficiently%20Counting%20All%205-Vertex%20Subgraphs) - [The k-peak Decomposition: Mapping the Global Structure of Graphs](https://papers-gamma.link/paper/16/The%20k-peak%20Decomposition:%20Mapping%20the%20Global%20Structure%20of%20Graphs) - [A Fast and Provable Method for Estimating Clique Counts Using Turán’s Theorem](https://papers-gamma.link/paper/24)

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### Very nice associated website: http://web.stanford.edu/~montanar/SDPgraph/ Slides: http://www.lps.ens.fr/~krzakala/LESHOUCHES2017/talks/LesHouches2017_RicciTersenghi.pdf ### Generalising to the Goemans-Williamson algorithm: Can we implement the Goemans-Williamson algorithm using this "spin technique"? This is a try: https://github.com/maxdan94/spingraphSDP I think that it may be interesting as it could lead to a scalable implementation of the Goemans-Williamson algorithm. ### Minors: - In the main text, some equation numbers correspond to the equations in the supplementary material, e.g. "(42)", "(49)" or "(288)". This makes the paper hard to read. "(288)" should be replaced by "(10)". - "solving the combinatorial optimization problem in Eq. (5) is a prototypical NP-complete problem." This is not a decision problem and thus it cannot be NP-complete by definition. - "(total CPU time was about 10 years)" This is not clear: what does it mean exactly? Which type of machines were used?
### Wrong reference: I read "It is also known that, for $m >\sqrt{2 n}$, the problem (49) has no local optima except the global ones [BM03]." In [BM03], which is [this paper](https://papers-gamma.link/paper/55), there is no such proof! We can only read: "Theorem 2.2. There exists an optimal solution $X^∗$ of (1) with rank r satisfying the inequality $r(r+ 1)/2 ≤ m$." and "we present computational results which show that the method finds optimal solutions to (2) quite reliably, and although we are able to derive some amount of theoretical justification for this, our belief that the method is not strongly affected by the inherent nonconvexity of (2) is largely experimental" but not that any local minimum is a global minimum.
> ### Minors: > > - "(total CPU time was about 10 years)" This is not clear: what does it mean exactly? Which type of machines were used? Although the algorithm based on the minimization of a non-convex cost function in terms of m-component variables is extremely fast to solve a single SBM problem (see e.g. figure 5 in https://arxiv.org/pdf/1603.09045, where many numerical experiments are reported) the precise determination of the critical threshold in the sparse case (i.e. SBM) required a large numerical effort of more than 80,000 core hours (we run all out simulations on Intel(R) Xeon(R) CPU E5-2670 @ 2.60GHz).
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