210,791 research outputs found
Reconstructing complex lineage trees from scRNA-seq data using MERLoT
Advances in single-cell transcriptomics techniques are revolutionizing studies of cellular differentiation and heterogeneity. It has become possible to track the trajectory of thousands of genes across the cellular lineage trees that represent the temporal emergence of cell types during dynamic processes. However, reconstruction of cellular lineage trees with more than a few cell fates has proved challenging. We present MERLoT (https://github.com/soedinglab/merlot), a flexible and user-friendly tool to reconstruct complex lineage trees from single-cell transcriptomics data. It can impute temporal gene expression profiles along the reconstructed tree. We show MERLoT’s capabilities on various real cases and hundreds of simulated datasets
Active dendrites enhance neuronal dynamic range
Since the first experimental evidences of active conductances in dendrites,
most neurons have been shown to exhibit dendritic excitability through the
expression of a variety of voltage-gated ion channels. However, despite
experimental and theoretical efforts undertaken in the last decades, the role
of this excitability for some kind of dendritic computation has remained
elusive. Here we show that, owing to very general properties of excitable
media, the average output of a model of active dendritic trees is a highly
non-linear function of their afferent rate, attaining extremely large dynamic
ranges (above 50 dB). Moreover, the model yields double-sigmoid response
functions as experimentally observed in retinal ganglion cells. We claim that
enhancement of dynamic range is the primary functional role of active dendritic
conductances. We predict that neurons with larger dendritic trees should have
larger dynamic range and that blocking of active conductances should lead to a
decrease of dynamic range.Comment: 20 pages, 6 figure
The number and degree distribution of spanning trees in the Tower of Hanoi graph
The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of spanning trees and the study of their properties remain a challenge, particularly for large networks. In this paper, we study the number and degree distribution of the spanning trees in the Hanoi graph. We first establish recursion relations between the number of spanning trees and other spanning subgraphs of the Hanoi graph, from which we find an exact analytical expression for the number of spanning trees of the n-disc Hanoi graph. This result allows the calculation of the spanning tree entropy which is then compared with those for other graphs with the same average degree. Then, we introduce a vertex labeling which allows to find, for each vertex of the graph, its degree distribution among all possible spanning trees.Postprint (author's final draft
Distributed Maintenance of Anytime Available Spanning Trees in Dynamic Networks
We address the problem of building and maintaining distributed spanning trees
in highly dynamic networks, in which topological events can occur at any time
and any rate, and no stable periods can be assumed. In these harsh
environments, we strive to preserve some properties such as cycle-freeness or
the existence of a root in each tree, in order to make it possible to keep
using the trees uninterruptedly (to a possible extent). Our algorithm operates
at a coarse-grain level, using atomic pairwise interactions in a way akin to
recent population protocol models. The algorithm relies on a perpetual
alternation of \emph{topology-induced splittings} and \emph{computation-induced
mergings} of a forest of spanning trees. Each tree in the forest hosts exactly
one token (also called root) that performs a random walk {\em inside} the tree,
switching parent-child relationships as it crosses edges. When two tokens are
located on both sides of a same edge, their trees are merged upon this edge and
one token disappears. Whenever an edge that belongs to a tree disappears, its
child endpoint regenerates a new token instantly. The main features of this
approach is that both \emph{merging} and \emph{splitting} are purely localized
phenomenons. In this paper, we present and motivate the algorithm, and we prove
its correctness in arbitrary dynamic networks. Then we discuss several
implementation choices around this general principle. Preliminary results
regarding its analysis are also discussed, in particular an analytical
expression of the expected merging time for two given trees in a static
context.Comment: Distributed Maintenance of Anytime Available Spanning Trees in
Dynamic Networks, Poland (2013
Compositional synthesis of temporal fault trees from state machines
Dependability analysis of a dynamic system which is embedded with several complex interrelated components raises two main problems. First, it is difficult to represent in a single coherent and complete picture how the system and its constituent parts behave in conditions of failure. Second, the analysis can be unmanageable due to a considerable number of failure events, which increases with the number of components involved. To remedy this problem, in this paper we outline an analysis approach that converts failure behavioural models (state machines) to temporal fault trees (TFTs), which can then be analysed using Pandora -- a recent technique for introducing temporal logic to fault trees. The approach is compositional and potentially more scalable, as it relies on the synthesis of large system TFTs from smaller component TFTs. We show, by using a Generic Triple Redundant (GTR) system, how the approach enables a more accurate and full analysis of an increasingly complex system
Parameterized Approximation Schemes using Graph Widths
Combining the techniques of approximation algorithms and parameterized
complexity has long been considered a promising research area, but relatively
few results are currently known. In this paper we study the parameterized
approximability of a number of problems which are known to be hard to solve
exactly when parameterized by treewidth or clique-width. Our main contribution
is to present a natural randomized rounding technique that extends well-known
ideas and can be used for both of these widths. Applying this very generic
technique we obtain approximation schemes for a number of problems, evading
both polynomial-time inapproximability and parameterized intractability bounds
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