Benchmarking of cell type deconvolution pipelines for transcriptomics data

Many computational methods have been developed to infer cell type proportions from bulk transcriptomics data. However, an evaluation of the impact of data transformation, pre-processing, marker selection, cell type composition and choice of methodology on the deconvolution results is still lacking. Using five single-cell RNA-sequencing (scRNA-seq) datasets, we generate pseudo-bulk mixtures to evaluate the combined impact of these factors. Both bulk deconvolution methodologies and those that use scRNA-seq data as reference perform best when applied to data in linear scale and the choice of normalization has a dramatic impact on some, but not all methods. Overall, methods that use scRNA-seq data have comparable performance to the best performing bulk methods whereas semi-supervised approaches show higher error values. Moreover, failure to include cell types in the reference that are present in a mixture leads to substantially worse results, regardless of the previous choices. Altogether, we evaluate the combined impact of factors affecting the deconvolution task across different datasets and propose general guidelines to maximize its performance. Inferring cell type proportions from transcriptomics data is affected by data transformation, normalization, choice of method and the markers used. Here, the authors use single-cell RNAseq datasets to evaluate the impact of these factors and propose guidelines to maximise deconvolution performance

Ode and Diffusion Limits in Large Symmetric Circuit Switched Networks.

This paper considers a large symmetric star-shaped circuit- switched network where each route requires one circuit from each of two links. Interarrival and holding times of calls are exponential. The process of the number of free circuits in each link is analyzed. An ordinary differential equation limit is established along with a diffusion approximation limit conjectured by Whitt [Wh]

Stochastic Monotonicity of the Output Process of Parallel Queues.

This paper considers the output process of a system of K DOT /M/I queues in parallel with Bernoulli routing of jobs upon arrival. It is shown that the output process is stochastically increasing as the routing probabilities approach 1/K in a certain sense. The proof crucially depends on the fact that the absolute value of a simple random walk is a time-homogeneous birth and death process

Transient Behavior of Circuit-Switched Networks.

This paper is concerned with strong approximation in queueing networks. A model of a circuit-switched network with fixed routes is considered in the limiting regime where the link capacities and the offered traffic are increased at the same rate. The process of normalized queue lengths is shown to converge almost surely to a sliding mode solution of an ordinary differential equation. The solution is shown to possess a unique stable point. It is reached exponentially fast or in finite time, depending on the values of the parameters. This has implications on the settling time of the network. The technique is applicable to closed Jackson networks and their settling times. In contrast with other asymptotic results on queueing networks it does not make use of product form distributions and extends easily to non- Markovian models

Concavity of Throughput in Series of Queues with Finite Buffers.

Concavity of the output process with respect to buffer size is established in a series of DOT/M/1/B queues with loss at the first node. Similarly, one shows concavity of the throughput with respect to the number of servers and the buffer sizes in a node belonging to a series of DOT/M/s/B queues

Monotonicity of Throughput in Non-Markovian Networks.

Monotonicity of throughput is established in some non-Markovian queueing networks by means of path-wise comparisons. In a series of DOT/GI/s/N queues with loss at the first node it is proved that increasing the waiting room and/or the number of servers increases the throughput. For a closed network of DOT/GI/s queues it is shown that the throughput increases as the total number of jobs increases. The technique used for these results does not apply to blocking systems with finite buffers and feedback. Using a stronger coupling argument we prove throughput monotonicity as a function of buffer size for a series of two DOT/M/1/N queues with loss and feedback from the second to the first node

A proof of the markov chain tree theorem

Abstract: Let X be a finite set, P be a stochastic matrix on X, and P = lim,,_,(l/n)X$LAPk. Let C=(X, E) be the weighted directed graph on X associated to P, with weights p,;. An arborescence is a subset a c E which has at most one edge out of every node, contains no cycles, and has maximum possible cardinahty. The weight of an arborescence is the product of its edge weights. Let _z? denote the set of all arborescences. Let dI, denote the set of all arborescences which have j as a root and in which there is a directed path from i to j. Let 1) & 11, resp. II_@‘,, 11, be the sum of the weights of the arborescences in &, resp. &,j. The Markov chain tree theorem states that p,, = Ij zz!,, II / II _&II. We give a proof of this theorem which is probabilistic in nature

A proof of the Markov chain tree theorem

Let X be a finite set, P be a stochastic matrix on X, and = limn --> [infinity] (1/n)[summation operator]n-1k=0Pk. Let G = (X, E) be the weighted directed graph on X associated to P, with weights pij. An arborescence is a subset a [subset, double equals] E which has at most one edge out of every node, contains no cycles, and has maximum possible cardinality. The weight of an arborescence is the product of its edge weights. Let denote the set of all arborescences. Let ij denote the set of all arborescences which have j as a root and in which there is a directed path from i to j. Let [short parallel][short parallel], resp. [short parallel]ij[short parallel], be the sum of the weights of the arborescences in , resp. ij. The Markov chain tree theorem states that ij = [short parallel]ij[short parallel]/[short parallel][short parallel]. We give a proof of this theorem which is probabilistic in nature.arborescence Markov chain stationary distribution time reversal tree