Related papers: Backbone decomposition of multitype superprocesses
A general theoretical framework is put forth to organize and understand various observed phenomena and mathematical relationships in the field of molecular biology. By modeling each cell in eukaryotic organisms as a processor having a…
Although bulk transcriptomic analyses have significantly contributed to an enhanced comprehension of multifaceted diseases, their exploration capacity is impeded by the heterogeneous compositions of biological samples. Indeed, by averaging…
In many data sets, crucial elements co-exist with non-essential ones and noise. For data represented as networks in particular, several methods have been proposed to extract a "network backbone", i.e., the set of most important links.…
Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. These models are widely used in biology, materials science and nuclear physics, and their asymptotic…
Multistate models offer a powerful framework for studying disease processes and can be used to formulate intensity-based and more descriptive marginal regression models. They also represent a natural foundation for the construction of joint…
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
Deep learning is extensively used in many areas of data mining as a black-box method with impressive results. However, understanding the core mechanism of how deep learning makes predictions is a relatively understudied problem. Here we…
Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem…
We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…
Proteins are macromolecules that mediate a significant fraction of the cellular processes that underlie life. An important task in bioengineering is designing proteins with specific 3D structures and chemical properties which enable…
The decomposable branching processes are relatively less studied objects, particularly in the continuous time framework. In this paper, we consider various variants of decomposable continuous time branching processes. As usual practice in…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
The process of decomposing a complex system into simpler subsystems has been of interest to computer scientists over many decades, for instance, for the field of distributed computing. In this paper, motivated by the desire to distribute…
We revisit certain decompositions of continuous-state branching processes (CSBPs), commonly referred to as skeletal decompositions, through the lens of intertwining of semi-groups. Precisely, we associate to a CSBP $X$ with branching…
Interest in development of brain prostheses, which might be proposed to recover mental functions lost due to neuron-degenerative disease or trauma, requires new methods in molecular engineering and nanotechnology to build artificial brain…
The long-term behaviors of flows of continuous-state branching processes are characterized through subordinators and extremal processes. The extremal processes arise in the case of supercritical processes with infinite mean and of…
The article develops marginal models for multivariate longitudinal responses. Overall, the model consists of five regression submodels, one for the mean and four for the covariance matrix, with the latter resulting by considering various…
We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations. We provide sufficient conditions on pivotal operations that guarantee that the corresponding classes of pivotally decomposable operations…
There are different concepts regarding to tree decomposition of a graph $G$. For the Hypercube $Q_n$, these concepts have been shown to have many applications. But some diverse papers on this subject make it difficult to follow what is…