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We study the complexity of high-dimensional approximation in the $L_2$-norm when different classes of information are available; we compare the power of function evaluations with the power of arbitrary continuous linear measurements. Here, we discuss the situation when the number of linear measurements required to achieve an error $\varepsilon \in (0,1)$ in dimension $d\in\mathbb{N}$ depends only poly-logarithmically on $\varepsilon^{-1}$. This corresponds to an exponential order of convergence of the approximation error, which often happens in applications. However, it does not mean that the high-dimensional approximation problem is easy, the main difficulty usually lies within the dependence on the dimension $d$. We determine to which extent the required amount of information changes, if we allow only function evaluation instead of arbitrary linear information. It turns out that in this case we only lose very little, and we can even restrict to linear algorithms. In particular, several notions of tractability hold simultaneously for both types of available information.

In this paper we revisit the classical problem of polynomial interpolation, with a slight twist; namely, polynomial evaluations are available up to a group action of the unit circle on the complex plane. It turns out that this new setting allows for a phaseless recovery of a polynomial in a polynomial time., Comment: Corrected formatting

In recent years machine learning (ML) took bio- and cheminformatics fields by storm, providing new solutions for a vast repertoire of problems related to protein sequence, structure, and interactions analysis. ML techniques, deep neural networks especially, were proven more effective than classical models for tasks like predicting binding affinity for molecular complex. In this work we investigated the earlier stage of drug discovery process - finding druggable pockets on protein surface, that can be later used to design active molecules. For this purpose we developed a 3D fully convolutional neural network capable of binding site segmentation. Our solution has high prediction accuracy and provides intuitive representations of the results, which makes it easy to incorporate into drug discovery projects. The model's source code, together with scripts for most common use-cases is freely available at http://gitlab.com/cheminfIBB/kalasanty

BackgroundOur previous work has shown peroxiredoxin-1 (PRDX1), one of major antioxidant enzymes, to be a biomarker in human breast cancer. Hereby, we further investigate the role of PRDX1, compared to its close homolog PRDX2, in mammary malignant cells.MethodsCRISPR/Cas9- or RNAi-based methods were used for genetic targeting PRDX1/2. Cell growth was assessed by crystal violet, EdU incorporation or colony formation assays. In vivo growth was assessed by a xenotransplantation model. Adenanthin was used to inhibit the thioredoxin-dependent antioxidant defense system. The prooxidant agents used were hydrogen peroxide, glucose oxidase and sodium L-ascorbate. A PY1 probe or HyPer-3 biosensor were used to detect hydrogen peroxide content in samples.ResultsPRDX1 downregulation significantly impaired the growth rate of MCF-7 and ZR-75-1 breast cancer cells. Likewise, xenotransplanted PRDX1-deficient MCF-7 cells presented a retarded tumour growth. Furthermore, genetic targeting of PRDX1 or adenanthin, but not PRDX2, potently sensitised all six cancer cell lines studied, but not the non-cancerous cells, to glucose oxidase and ascorbate.ConclusionsOur study pinpoints the dominant role for PRDX1 in management of exogeneous oxidative stress by breast cancer cells and substantiates further exploration of PRDX1 as a target in this disease, especially when combined with prooxidant agents.

Structure based ligand discovery is one of the most successful approaches for augmenting the drug discovery process. Currently, there is a notable shift towards machine learning (ML) methodologies to aid such procedures. Deep learning has recently gained considerable attention as it allows the model to "learn" to extract features that are relevant for the task at hand. We have developed a novel deep neural network estimating the binding affinity of ligand-receptor complexes. The complex is represented with a 3D grid, and the model utilizes a 3D convolution to produce a feature map of this representation, treating the atoms of both proteins and ligands in the same manner. Our network was tested on the CASF "scoring power" benchmark and Astex Diverse Set and outperformed classical scoring functions. The model, together with usage instructions and examples, is available as a git repository at http://gitlab.com/cheminfIBB/pafnucy