propSym: a tool to establish relationships between property constants for material property tensors of any order

The properties of crystalline materials can be described mathematically by tensors whose components are generally known as property constants. Tabulations of these constants in terms of the independent components are well known for common material properties (e.g. elasticity, piezoelectricity etc.) aptly described by tensors of lower rank (e.g. ranks 2–4). General relationships between constants of higher rank are often unknown and sometimes reported incorrectly. A computer program is developed here to calculate the property constant relationships of a property of any order, represented by a tensor of any rank and point group. Tensors up to rank 12, e.g. the tensor of sixth-order elastic constants c 6 ijklmnpqrs , can be calculated on a standard computer, while ranks higher than 12 are best handled on a supercomputer. Output is provided in either full index form or a reduced index form, e.g. the Voigt index notation common to elasticity. As higher-order tensors are often associated with nonlinear material responses, the program provides an accessible means to investigate the important constants involved in nonlinear material modeling. The routine has been used to discover several incorrect relationships reported in the literature.

Leveraging multi-way interactions for systematic prediction of pre-clinical drug combination effects

We present comboFM, a machine learning framework for predicting the responses of drug combinations in pre-clinical studies, such as those based on cell lines or patient-derived cells. comboFM models the cell context-specific drug interactions through higher-order tensors, and efficiently learns latent factors of the tensor using powerful factorization machines. The approach enables comboFM to leverage information from previous experiments performed on similar drugs and cells when predicting responses of new combinations in so far untested cells; thereby, it achieves highly accurate predictions despite sparsely populated data tensors. We demonstrate high predictive performance of comboFM in various prediction scenarios using data from cancer cell line pharmacogenomic screens. Subsequent experimental validation of a set of previously untested drug combinations further supports the practical and robust applicability of comboFM. For instance, we confirm a novel synergy between anaplastic lymphoma kinase (ALK) inhibitor crizotinib and proteasome inhibitor bortezomib in lymphoma cells. Overall, our results demonstrate that comboFM provides an effective means for systematic pre-screening of drug combinations to support precision oncology applications.

Tensor theta norms and low rank recovery

We study extensions of compressive sensing and low rank matrix recovery to the recovery of tensors of low rank from incomplete linear information. While the reconstruction of low rank matrices via nuclear norm minimization is rather well-understand by now, almost no theory is available so far for the extension to higher order tensors due to various theoretical and computational difficulties arising for tensor decompositions. In fact, nuclear norm minimization for matrix recovery is a tractable convex relaxation approach, but the extension of the nuclear norm to tensors is in general NP-hard to compute. In this article, we introduce convex relaxations of the tensor nuclear norm which are computable in polynomial time via semidefinite programming. Our approach is based on theta bodies, a concept from real computational algebraic geometry which is similar to the one of the better known Lasserre relaxations. We introduce polynomial ideals which are generated by the second-order minors corresponding to different matricizations of the tensor (where the tensor entries are treated as variables) such that the nuclear norm ball is the convex hull of the algebraic variety of the ideal. The theta body of order k for such an ideal generates a new norm which we call the θk-norm. We show that in the matrix case, these norms reduce to the standard nuclear norm. For tensors of order three or higher however, we indeed obtain new norms. The sequence of the corresponding unit-θk-norm balls converges asymptotically to the unit tensor nuclear norm ball. By providing the Gröbner basis for the ideals, we explicitly give semidefinite programs for the computation of the θk-norm and for the minimization of the θk-norm under an affine constraint. Finally, numerical experiments for order-three tensor recovery via θ1-norm minimization suggest that our approach successfully reconstructs tensors of low rank from incomplete linear (random) measurements.

comboFM: leveraging multi-way interactions for systematic prediction of drug combination effects

We present comboFM, a machine learning framework for predicting the responses of drug combinations in preclinical studies, such as those based on cell lines or patient-derived cells. comboFM models the cell context-specific drug interactions through higher-order tensors, and efficiently learns latent factors of the tensor using powerful factorization machines. The approach enables comboFM to leverage information from previous experiments performed on similar drugs and cells when predicting responses of new combinations in so far untested cells; thereby, it achieves highly accurate predictions despite sparsely populated data tensors. We demonstrated high predictive performance of comboFM in various prediction scenarios using data from cancer cell line drug screening. Subsequent experimental validation of a set of previously untested drug combinations further supported the practical and robust applicability of comboFM. For instance, we confirmed a novel synergy between anaplastic lymphoma kinase (ALK) inhibitor crizotinib and proteasome inhibitor bortezomib in lymphoma cells. Overall, our results demonstrate that comboFM provides an effective means for systematic pre-screening of drug combinations to support precision oncology applications.

Short-Term Rental Forecast of Urban Public Bicycle Based on the HOSVD-LSTM Model in Smart City

As a kind of transportation in a smart city, urban public bicycles have been adopted by major cities and bear the heavy responsibility of the “last mile” of urban public transportation. At present, the main problem of the urban public bicycle system is that it is difficult for users to rent a bike during peak h, and real-time monitoring cannot be solved adequately. Therefore, predicting the demand for bicycles in a certain period and performing redistribution in advance is of great significance for solving the lag of bicycle system scheduling with the help of IoT. Based on the HOSVD-LSTM prediction model, a prediction model of urban public bicycles based on the hybrid model is proposed by transforming the source data (multiple time series) into a high-order tensor time series. Furthermore, it uses the tensor decomposition technology (HOSVD decomposition) to extract new features (kernel tenor) from higher-order tensors. At the same time, these kernel tenors are directly used to train tensor LSTM models to obtain new kernel tenors. The inverse tensor decomposition and high-dimensional, multidimensional, and tensor dimensionality reduction were introduced. The new kernel tenor obtains the predicted value of the source sequence. Then the bicycle rental amount is predicted.

Progress in the knowledge of ‘ruby silvers’: New structural and chemical data of pyrostilpnite, Ag3SbS3

The crystal structure of pyrostilpnite from the Plaka mine, Lavrion Mining District, Greece, was refined in the space group P21/c to a final R1 index of 0.0283 on the basis of 2047 reflections with Fo > 4σ(Fo) and 65 refined parameters. Unit-cell parameters of the crystal examined are a = 6.8629(6), b = 15.8800(14), c = 6.2711(5) Å, β = 117.087(2)°, V = 608.48(9) Å3 and Z = 4. Chemical data agree with the stoichiometric formula Ag3SbS3. The crystal structure reported previously was confirmed, although a higher precision of refinement was achieved. It can be described as formed by {010} slabs running along c and connected along a through relatively longer Ag–S bonds. The analysis of the atomic displacement parameters together with a refinement with higher order tensors in the expression of the structure factors revealed no hint for pyrostilpnite as an ionic conductor. A historical background of the ‘ruby silvers’ is also reported.