@article{150, abstract = {A short, 14-amino-acid segment called SP1, located in the Gag structural protein1, has a critical role during the formation of the HIV-1 virus particle. During virus assembly, the SP1 peptide and seven preceding residues fold into a six-helix bundle, which holds together the Gag hexamer and facilitates the formation of a curved immature hexagonal lattice underneath the viral membrane2,3. Upon completion of assembly and budding, proteolytic cleavage of Gag leads to virus maturation, in which the immature lattice is broken down; the liberated CA domain of Gag then re-assembles into the mature conical capsid that encloses the viral genome and associated enzymes. Folding and proteolysis of the six-helix bundle are crucial rate-limiting steps of both Gag assembly and disassembly, and the six-helix bundle is an established target of HIV-1 inhibitors4,5. Here, using a combination of structural and functional analyses, we show that inositol hexakisphosphate (InsP6, also known as IP6) facilitates the formation of the six-helix bundle and assembly of the immature HIV-1 Gag lattice. IP6 makes ionic contacts with two rings of lysine residues at the centre of the Gag hexamer. Proteolytic cleavage then unmasks an alternative binding site, where IP6 interaction promotes the assembly of the mature capsid lattice. These studies identify IP6 as a naturally occurring small molecule that promotes both assembly and maturation of HIV-1.}, author = {Dick, Robert and Zadrozny, Kaneil K and Xu, Chaoyi and Schur, Florian and Lyddon, Terri D and Ricana, Clifton L and Wagner, Jonathan M and Perilla, Juan R and Ganser, Pornillos Barbie K and Johnson, Marc C and Pornillos, Owen and Vogt, Volker}, issn = {1476-4687}, journal = {Nature}, number = {7719}, pages = {509–512}, publisher = {Nature Publishing Group}, title = {{Inositol phosphates are assembly co-factors for HIV-1}}, doi = {10.1038/s41586-018-0396-4}, volume = {560}, year = {2018}, } @article{303, abstract = {The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results we need for other articles and also introduces several objects interesting by themselves.}, author = {Kalinin, Nikita and Shkolnikov, Mikhail}, journal = {Discrete and Continuous Dynamical Systems- Series A}, number = {6}, pages = {2827 -- 2849}, publisher = {AIMS}, title = {{Introduction to tropical series and wave dynamic on them}}, doi = {10.3934/dcds.2018120}, volume = {38}, year = {2018}, } @inproceedings{14202, abstract = {Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational family. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with a greedily constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions.}, author = {Locatello, Francesco and Dresdner, Gideon and Khanna, Rajiv and Valera, Isabel and Rätsch, Gunnar}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781510884472}, issn = {1049-5258}, location = {Montreal, Canada}, publisher = {Neural Information Processing Systems Foundation}, title = {{Boosting black box variational inference}}, volume = {31}, year = {2018}, } @inproceedings{14201, abstract = {Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture. However, as is the case with many other variational inference algorithms, its theoretical properties have not been studied. In the present work, we study the convergence properties of this approach from a modern optimization viewpoint by establishing connections to the classic Frank-Wolfe algorithm. Our analyses yields novel theoretical insights regarding the sufficient conditions for convergence, explicit rates, and algorithmic simplifications. Since a lot of focus in previous works for variational inference has been on tractability, our work is especially important as a much needed attempt to bridge the gap between probabilistic models and their corresponding theoretical properties.}, author = {Locatello, Francesco and Khanna, Rajiv and Ghosh, Joydeep and Rätsch, Gunnar}, booktitle = {Proceedings of the 21st International Conference on Artificial Intelligence and Statistics}, location = {Playa Blanca, Lanzarote}, pages = {464--472}, publisher = {ML Research Press}, title = {{Boosting variational inference: An optimization perspective}}, volume = {84}, year = {2018}, } @inproceedings{14198, abstract = {High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose a new representation learning framework building on ideas from interpretable discrete dimensionality reduction and deep generative modeling. This framework allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. We introduce a new way to overcome the non-differentiability in discrete representation learning and present a gradient-based version of the traditional self-organizing map algorithm that is more performant than the original. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the representation space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model in terms of clustering performance and interpretability on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application on the eICU data set. Our learned representations compare favorably with competitor methods and facilitate downstream tasks on the real world data.}, author = {Fortuin, Vincent and Hüser, Matthias and Locatello, Francesco and Strathmann, Heiko and Rätsch, Gunnar}, booktitle = {International Conference on Learning Representations}, location = {New Orleans, LA, United States}, title = {{SOM-VAE: Interpretable discrete representation learning on time series}}, year = {2018}, }