No abstract

We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the literature, which includes notable entries like the Diagonal Symmetric states and the Choi-type maps, we show that this class of matrices (and maps) encompasses a wide variety of scenarios, thereby unifying their study. We examine their linear algebraic structure and investigate different notions of positivity through their convex conic manifestations. In particular, we generalize the well-known cone of completely positive matrices to that of triplewise completely positive matrices and connect it to the separability of the relevant invariant states (or the entanglement breaking property of the corresponding quantum channels). For linear maps, we provide explicit characterizations of the stated covariance in terms of their Kraus, Stinespring, and Choi representations, and systematically analyze the usual properties of positivity, decomposability, complete positivity, and the like. We also describe the invariant subspaces of these maps and use their structure to provide necessary and sufficient conditions for separability of the associated invariant bipartite states.

The applicability domain of machine learning models trained on structural fingerprints for the prediction of biological endpoints is often limited by the lack of diversity of chemical space of the training data. In this work, we developed similarity-based merger models which combined the outputs of individual models trained on cell morphology (based on Cell Painting) and chemical structure (based on chemical fingerprints) and the structural and morphological similarities of the compounds in the test dataset to compounds in the training dataset. We applied these similarity-based merger models using logistic regression models on the predictions and similarities as features and predicted assay hit calls of 177 assays from ChEMBL, PubChem and the Broad Institute (where the required Cell Painting annotations were available). We found that the similarity-based merger models outperformed other models with an additional 20% assays (79 out of 177 assays) with an AUC > 0.70 compared with 65 out of 177 assays using structural models and 50 out of 177 assays using Cell Painting models. Our results demonstrated that similarity-based merger models combining structure and cell morphology models can more accurately predict a wide range of biological assay outcomes and further expanded the applicability domain by better extrapolating to new structural and morphology spaces. Graphical Abstract

Determining whether a noisy quantum channel can be used to reliably transmit quantum information is a challenging problem in quantum information theory. This is because it requires computation of the channel’s coherent information for an unbounded number of copies of the channel. In this paper, we devise an elementary perturbative technique to solve this problem in a wide variety of circumstances. Our analysis reveals that a channel’s ability to transmit information is intimately connected to the relative sizes of its input, output, and environment spaces. We exploit this link to develop easy tests which can be used to detect positivity of quantum channel capacities simply by comparing the channels’ input, output, and environment dimensions. Several noteworthy examples, such as the depolarizing and transpose-depolarizing channels (including the Werner-Holevo channel), dephasing channels, generalized Pauli channels, multi-level amplitude damping channels, and (conjugate) diagonal unitary covariant channels, serve to aptly exhibit the utility of our method. Notably, in all these examples, the coherent information of a single copy of the channel turns out to be positive.

The applicability domain of machine learning models trained on structural fingerprints for the prediction of biological endpoints is often limited by the diversity of chemical space of the training data. In this work, we developed similarity-based merger models which combined the output of individual models trained on cell morphology (based on Cell Painting) and chemical structure (based on chemical fingerprints). Using a combination of a decision tree and logistic regression models on the structural versus morphological feature space of the training data, which leveraged the similarity of test compounds to training compounds, the similarity-based merger models used logistic equations to weigh individual model outputs. We applied these models to predict assay hit calls of 92 assays from ChEMBL and PubChem and 89 anonymised assays released by the Broad Institute, where the required Cell Painting annotations were available. We found that for the 181 assays used in this study the similarity-based merger model improved AUC in relative terms by 16.3% compared to the models using chemical structure alone (mean AUC of 0.75 vs. 0.64), and by 21.3% compared to the models using Cell Painting data alone (mean AUC of 0.62). Our results demonstrate that similarity-based merger models combining structure and cell morphology models can more accurately predict a wide range of biological assay outcomes and expand the applicability domain by better extrapolating to new structural and morphology spaces.