Single-cell expression profiling reveals the molecular states of individual cells with unprecedented detail. Because these methods destroy cells in the process of analysis, they cannot measure how ...gene expression changes over time. However, some information on dynamics is present in the data: the continuum of molecular states in the population can reflect the trajectory of a typical cell. Many methods for extracting single-cell dynamics from population data have been proposed. However, all such attempts face a common limitation: for any measured distribution of cell states, there are multiple dynamics that could give rise to it, and by extension, multiple possibilities for underlying mechanisms of gene regulation. Here, we describe the aspects of gene expression dynamics that cannot be inferred from a static snapshot alone and identify assumptions necessary to constrain a unique solution for cell dynamics from static snapshots. We translate these constraints into a practical algorithmic approach, population balance analysis (PBA), which makes use of a method from spectral graph theory to solve a class of high-dimensional differential equations. We use simulations to show the strengths and limitations of PBA, and then apply it to single-cell profiles of hematopoietic progenitor cells (HPCs). Cell state predictions from this analysis agree with HPC fate assays reported in several papers over the past two decades. By highlighting the fundamental limits on dynamic inference faced by any method, our framework provides a rigorous basis for dynamic interpretation of a gene expression continuum and clarifies best experimental designs for trajectory reconstruction from static snapshot measurements.
Let D be a digraph of order p and size q. For an integer k ⩾ 1 and ν ∈ V(D), let \(\sum _{e\in {E}_{k}(v)}f(e)\) where Ek (v) is the set of all in-arcs which are at distance at most k from ν. A V k ...-super vertex in-magic labeling (Vk -SVIML) is an one-to-one onto function f : V(D) ∪ A(D) → {1,2…, P + q} such that f(V(D)) = {1,2…, p} and for every ν ∈ V(D), f(ν) + ω k(ν) = M for some positive integer M. A digraph that admits a V k -SVIML is called V k -super vertex in-magic (V k -SVIM). In this paper, we study some properties of V k -SVIML in digraphs. We characterized the digraphs which are V k -SVIM. Also, we find the magic constant for Ek -regular digraphs. Farther, we characterized the unidirectional cycles and union of unidirectional cycles which are V 2-SMM.
On analysis of iron Zhou, Hao; Hanif, Muhammad Farhan; Mahmood, Hasan ...
PloS one,
01/2024, Letnik:
19, Številka:
1
Journal Article
Recenzirano
The crystalline material that is greenish-white and dissolves in water is iron chloride. It is utilized in sewage treatment, dyeing, and medicine. Graph entropy plays a significant role in measuring ...the complexity of atoms, molecules, and structures in nature. It has specific chemical applications in biology, neuroscience, and chemistry. A compound's molecular structure consists of many atoms. Particularly, hydrocarbons are a chemical combination of hydrogen and carbon atoms. In this article, we discuss the entropy of the chemical structure Iron (II) Chloride. Additionally, we discuss the idea of degree-based indices and compute the Shannon entropy(ENT) using these indices. The linear regression(LR) of various indices and entropies for iron chloride, FeCl.sub.2, is also discussed. Also, we link the degree-based indices and entropies via line fit.
In this paper we survey methods for performing a comparative graph analysis and explain the history, foundations and differences of such techniques of the last 50 years. While surveying these ...methods, we introduce a novel classification scheme by distinguishing between methods for deterministic and random graphs. We believe that this scheme is useful for a better understanding of the methods, their challenges and, finally, for applying the methods efficiently in an interdisciplinary setting of data science to solve a particular problem involving comparative network analysis.
Kochen-Specker contextuality Budroni, Costantino; Cabello, Adán; Gühne, Otfried ...
Reviews of modern physics,
10/2022, Letnik:
94, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a ...measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained, and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.
This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are ...relatively prime. By finding the pattern elements of resolving set and local resolving set, it can be shown the value of the metric dimension and the local metric dimension of graphs are and respectively, where is the number of vertices groups that formed multiple 2,3, … , and is the cardinality of set . This research can be developed by determining the value of the fractional metric dimension, local fractional metric dimension and studying the advanced properties of graphs related to their forming rings.Key Words : metric dimension; modulo ; relative prime graph; resolving set; rings.
Given a simple graph G, a set Formula omitted is a neighborhood cover set if every edge and vertex of G belongs to some Gv with Formula omitted, where Gv denotes the subgraph of G induced by the ...closed neighborhood of the vertex v. Two elements of Formula omitted are neighborhood-independent if there is no vertex Formula omitted such that both elements are in Gv. A set Formula omitted is neighborhood-independent if every pair of elements of S is neighborhood-independent. Let Formula omitted be the size of a minimum neighborhood cover set and Formula omitted of a maximum neighborhood-independent set. Lehel and Tuza defined neighborhood-perfect graphs G as those where the equality Formula omitted holds for every induced subgraph Formula omitted of G. In this work we prove forbidden induced subgraph characterizations of the class of neighborhood-perfect graphs, restricted to two superclasses of cographs: Formula omitted-tidy graphs and tree-cographs. We give as well linear-time algorithms for solving the recognition problem of neighborhood-perfect graphs and the problem of finding a minimum neighborhood cover set and a maximum neighborhood-independent set in these same classes. Finally we prove that although for complements of trees finding these optimal sets can be achieved in linear-time, for complements of bipartite graphs it is Formula omitted-hard.
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