Abstract
For any positive integer , we show that every maximal ‐free graph with at least edges contains an induced complete bipartite subgraph on vertices. We also show that this is the best possible.
Hoffmann–Ostenhof's conjecture states that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a 2-regular subgraph. In this paper, we show that the ...conjecture holds for claw-free subcubic graphs and 4-chordal subcubic graphs.
The fuzzy membership function has non-collapsability and can be used to characterize uncertainties that cannot be explored by sudden events. As the membership function does not satisfy the ...complementarity law, a single membership function cannot simultaneously characterize the positive and negative aspects of things. This article considers structured fuzzy data with negative uncertainty information, which is modeled using bipolar fuzzy graphs. On this basis, we consider the connectivity remainder of the model and obtain the corresponding theoretical results. In addition, we have discussed some related fractional factor issues.
Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical ...properties of the measured signals. Conditions for generic identifiability of multiple modules, i.e. a subnetwork, are developed for the situation that all node signals are measured and excitation of the network is provided by both measured excitation signals and unmeasured disturbance inputs. Additionally, the network model set is allowed to contain non-parametrized modules that are fixed, and e.g. reflect modules of which the dynamics are known to the user. The conditions take the form of path-based conditions on the graph of the network model set. Based on these conditions, synthesis results are formulated for allocating external excitation signals to achieve generic identifiability of particular subnetworks. If there are a sufficient number of measured external excitation signals, the formulated results give rise to a generalized indirect type of identification algorithm that requires only the measurement of a subset of the node signals in the network.
Abstract In current assembly process of the aircraft complex structural parts, there are problems such as nonlinear, multilevel strong coupling and large uncertainty transfer relationship between ...assembly quality and its deviation sources. In this paper, an assembly deviation transfer method based on transfer entropy network graph is proposed to address the challenges. Firstly, the source of assembly deviation is analysed by constructing a multi-level assembly coordination network with assembly deviation detection data. Secondly, an assembly deviation propagation model is established by combining transfer entropy and complex network graph theory. This model provides insights into the topological relationship of assembly deviations and introduces causal metrics for evaluation. The effectiveness of method is demonstrated through its application in the assembly of an aircraft nose, thereby verifying its practicality and utility.
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.
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