Matrix Pencils and Entanglement Classification

In this paper, we study pure state entanglement in systems of dimension $2\otimes m\otimes n$. Two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local quantum resources and classical communication (SLOCC). We introduce a connection between entanglement manipulations in these systems and the well-studied theory of matrix pencils. All previous attempts to study general SLOCC equivalence in such systems have relied on somewhat contrived techniques which fail to reveal the elegant structure of the problem that can be seen from the matrix pencil approach. Based on this method, we report the first polynomial-time algorithm for deciding when two $2\otimes m\otimes n$ states are SLOCC equivalent. Besides recovering the previously known 26 distinct SLOCC equivalence classes in $2\otimes 3\otimes n$ systems, we also determine the hierarchy between these classes

Target prediction and a statistical sampling algorithm for RNA-RNA interaction

It has been proven that the accessibility of the target sites has a critical influence for miRNA and siRNA. In this paper, we present a program, rip2.0, not only the energetically most favorable targets site based on the hybrid-probability, but also a statistical sampling structure to illustrate the statistical characterization and representation of the Boltzmann ensemble of RNA-RNA interaction structures. The outputs are retrieved via backtracing an improved dynamic programming solution for the partition function based on the approach of Huang et al. (Bioinformatics). The $O(N^6)$ time and $O(N^4)$ space algorithm is implemented in C (available from \url{http://www.combinatorics.cn/cbpc/rip2.html})Comment: 7 pages, 10 figure

The effects of death and post-mortem cold ischemia on human tissue transcriptomes

Post-mortem tissues samples are a key resource for investigating patterns of gene expression. However, the processes triggered by death and the post-mortem interval (PMI) can significantly alter physiologically normal RNA levels. We investigate the impact of PMI on gene expression using data from multiple tissues of post-mortem donors obtained from the GTEx project. We find that many genes change expression over relatively short PMIs in a tissue-specific manner, but this potentially confounding effect in a biological analysis can be minimized by taking into account appropriate covariates. By comparing ante- and post-mortem blood samples, we identify the cascade of transcriptional events triggered by death of the organism. These events do not appear to simply reflect stochastic variation resulting from mRNA degradation, but active and ongoing regulation of transcription. Finally, we develop a model to predict the time since death from the analysis of the transcriptome of a few readily accessible tissues.Peer ReviewedPostprint (published version

Slow and fast inhibition and an H-current interact to create a theta rhythm in a model of CA1 interneuron network

The oriens-lacunosum moleculare (O-LM) subtype of interneuron is a key component in the formation of the theta rhythm (8–12 Hz) in the hippocampus. It is known that the CA1 region of the hippocampus can produce theta rhythms in vitro with all ionotropic excitation blocked, but the mechanisms by which this rhythmicity happens were previously unknown. Here we present a model suggesting that individual O-LM cells, by themselves, are capable of producing a single-cell theta-frequency firing, but coupled O-LM cells are not capable of producing a coherent population theta. By including in the model fast-spiking (FS) interneurons, which give rise to IPSPs that decay faster than those of the O-LM cells, coherent theta rhythms are produced. The inhibition to O-LM cells from the FS cells synchronizes the O-LM cells, but only when the FS cells themselves fire at a theta frequency. Reciprocal connections from the O-LM cells to the FS cells serve to parse the FS cell firing into theta bursts, which can then synchronize the O-LM cells. A component of the model O-LM cell critical to the synchronization mechanism is the hyperpolarization-activated h-current. The model can robustly reproduce relative phases of theta frequency activity in O-LM and FS cells

Transcriptome analysis reveals high tumor heterogeneity with respect to re-activation of stemness and proliferation programs

Significant alterations in signaling pathways and transcriptional regulatory programs together represent major hallmarks of many cancers. These, among all, include the reactivation of stemness, which is registered by the expression of pathways that are active in the embryonic stem cells (ESCs). Here, we assembled gene sets that reflect the stemness and proliferation signatures and used them to analyze a large panel of RNA-seq data from The Cancer Genome Atlas (TCGA) Consortium in order to specifically assess the expression of stemness-related and proliferation-related genes across a collection of different tumor types. We introduced a metric that captures the collective similarity of the expression profile of a tumor to that of ESCs, which showed that stemness and proliferation signatures vary greatly between different tumor types. We also observed a high degree of intertumoral heterogeneity in the expression of stemness- and proliferation-related genes, which was associated with increased hazard ratios in a fraction of tumors and mirrored by high intratumoral heterogeneity and a remarkable stemness capacity in metastatic lesions across cancer cells in single cell RNA-seq datasets. Taken together, these results indicate that the expression of stemness signatures is highly heterogeneous and cannot be used as a universal determinant of cancer. This calls into question the universal validity of diagnostic tests that are based on stem cell markers

Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies

Deciphering the universe of RNA structures and trans RNA-RNA interactions of transcriptomes in vivo: from experimental protocols to computational analyses

The last few years have seen an explosion of experimental and computational methods for investigating RNA structures of entire transcriptomes in vivo. Very recent experimental protocols now also allow trans RNA–RNA interactions to be probed in a transcriptome-wide manner. All of the experimental strategies require comprehensive computational pipelines for analysing the raw data and converting it back into actual RNA structure features or trans RNA–RNA interactions. The overall performance of these methods thus strongly depends on the experimental and the computational protocols employed. In order to get the best out of both worlds, both aspects need to be optimised simultaneously. This review introduced the methods and proposes ideas how they could be further improved