BLTSA: pseudotime prediction for single cells by branched local tangent space alignment.

MOTIVATION: The development of single-cell RNA sequencing (scRNA-seq) technology makes it possible to study the cellular dynamic processes such as cell cycle and cell differentiation. Due to the difficulties in generating genuine time-series scRNA-seq data, it is of great importance to computationally infer the pseudotime of the cells along differentiation trajectory based on their gene expression patterns. The existing pseudotime prediction methods often suffer from the high level noise of single-cell data, thus it is still necessary to study the single-cell trajectory inference methods. RESULTS: In this study, we propose a branched local tangent space alignment (BLTSA) method to infer single-cell pseudotime for multi-furcation trajectories. By assuming that single cells are sampled from a low-dimensional self-intersecting manifold, BLTSA first identifies the tip and branching cells in the trajectory based on cells' local Euclidean neighborhoods. Local coordinates within the tangent spaces are then determined by each cell's local neighborhood after clustering all the cells to different branches iteratively. The global coordinates for all the single cells are finally obtained by aligning the local coordinates based on the tangent spaces. We evaluate the performance of BLTSA on four simulation datasets and five real datasets. The experimental results show that BLTSA has obvious advantages over other comparison methods. AVAILABILITY AND IMPLEMENTATION: R codes are available at https://github.com/LiminLi-xjtu/BLTSA. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MicroRNA-disease association prediction by matrix tri-factorization.

BACKGROUND: Biological evidence has shown that microRNAs(miRNAs) are greatly implicated in various biological progresses involved in human diseases. The identification of miRNA-disease associations(MDAs) is beneficial to disease diagnosis as well as treatment. Due to the high costs of biological experiments, it attracts more and more attention to predict MDAs by computational approaches. RESULTS: In this work, we propose a novel model MTFMDA for miRNA-disease association prediction by matrix tri-factorization, based on the known miRNA-disease associations, two types of miRNA similarities, and two types of disease similarities. The main idea of MTFMDA is to factorize the miRNA-disease association matrix to three matrices, a feature matrix for miRNAs, a feature matrix for diseases, and a low-rank relationship matrix. Our model incorporates the Laplacian regularizers which force the feature matrices to preserve the similarities of miRNAs or diseases. A novel algorithm is proposed to solve the optimization problem. CONCLUSIONS: We evaluate our model by 5-fold cross validation by using known MDAs from HMDD V2.0 and show that our model could obtain the significantly highest AUCs among all the state-of-art methods. We further validate our method by applying it on colon and breast neoplasms in two different types of experiment settings. The new identified associated miRNAs for the two diseases could be verified by two other databases including dbDEMC and HMDD V3.0, which further shows the power of our proposed method.

Integrative subspace clustering by common and specific decomposition for applications on cancer subtype identification.

BACKGROUND: Recent high throughput technologies have been applied for collecting heterogeneous biomedical omics datasets. Computational analysis of the multi-omics datasets could potentially reveal deep insights for a given disease. Most existing clustering methods by multi-omics data assume strong consistency among different sources of datasets, and thus may lose efficacy when the consistency is relatively weak. Furthermore, they could not identify the conflicting parts for each view, which might be important in applications such as cancer subtype identification. METHODS: In this work, we propose an integrative subspace clustering method (ISC) by common and specific decomposition to identify clustering structures with multi-omics datasets. The main idea of our ISC method is that the original representations for the samples in each view could be reconstructed by the concatenation of a common part and a view-specific part in orthogonal subspaces. The problem can be formulated as a matrix decomposition problem and solved efficiently by our proposed algorithm. RESULTS: The experiments on simulation and text datasets show that our method outperforms other state-of-art methods. Our method is further evaluated by identifying cancer types using a colorectal dataset. We finally apply our method to cancer subtype identification for five cancers using TCGA datasets, and the survival analysis shows that the subtypes we found are significantly better than other compared methods. CONCLUSION: We conclude that our ISC model could not only discover the weak common information across views but also identify the view-specific information.

Distributed atomic quantum information processing via optical fibers.

The qudit system may offer great flexibilities for quantum information processing. We investigate the possibility of realizing elementary quantum gates between two high-dimensional atoms in distant cavities coupled by an optical fiber. We show that highly reliable special swap gate is achievable by different detuning. The numerical simulation shows that the proposed elementary gate is robust against the atomic spontaneous decay, photon leakage of cavities and optical fibers by choosing the experimental parameters appropriately.

Quantum computation based on photonic systems with two degrees of freedom assisted by the weak cross-Kerr nonlinearity.

Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.

Quantum Computation Based on Photons with Three Degrees of Freedom.

Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems.

Photonic ququart logic assisted by the cavity-QED system.

Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions of qubit systems, we investigate the possibility of ququart systems (four-dimensional states) dependent on two DOFs of photon systems. We propose some useful one-parameter four-dimensional quantum transformations for the construction of universal ququart logic gates. The interface between the spin of a photon and an electron spin confined in a quantum dot embedded in a microcavity is applied to build universal ququart logic gates on the photon system with two freedoms. Our elementary controlled-ququart gates cost no more than 8 CNOT gates in a qubit system, which is far less than the 104 CNOT gates required for a general four-qubit logic gate. The ququart logic is also used to generate useful hyperentanglements and hyperentanglement-assisted quantum error-correcting code, which may be available in modern physical technology.