Contraction Operators Research Articles

Exploring the prognostic role of microbial and genetic markers in lung squamous cell carcinoma

Despite advances in diagnostic and therapeutic strategies, the prognosis of lung squamous cell carcinoma (LUSC) patients remains poor, and the potential of microbiome-based prognostic biomarkers and therapeutic targets remains largely unexplored. LUSC patient data from The Cancer Genome Atlas (TCGA), including microbial genus level abundance data and RNA sequencing (RNA-Seq) data, were used as a training dataset. Two other independent datasets GSE19188 and GSE157009 serve as validation datasets. A microbiome-based risk score (RS) model was constructed by univariate Cox regression analysis combined with the least absolute contraction and selection operator (LASSO) regression. 18 microbial genera were found to be significantly associated with RFS in LUSC patients. The microbial signature built with these microbial genera, exhibited robust predictive accuracy in both the training and validation datasets. Furthermore, hub mRNA between high- and low-risk groups were selected by XGBOOST and intersect with mRNAs screened by univariate Cox regression analysis, finally identifying four mRNA significantly associated with LUSC prognosis. This study reveals a complex interplay between the lung microbiome and genetic biomarkers, and identifies specific microbial-based and mRNA associated with prognosis in LUSC. These findings provide a basis for future studies aimed to elucidate the mechanisms underlying these associations and provide potential biomarkers for guiding treatment decisions and improving patient outcomes.

Exact and Heuristic Solution Approaches for the Cluster Deletion Problem on General Graphs

ABSTRACTA cluster graph is a disjoint union of cliques, obtained by clustering the nodes of a given network and then removing the edges between nodes assigned to different clusters. The Cluster Deletion problem asks for the smallest subset of edges to be removed from a network in order to produce a cluster graph, which is equivalent to determining the largest subset of edges to be preserved. The problem finds application in many fields, including computational biology, bioinformatics, and wireless sensor networks, and it is known to be ‐hard on general graphs. In this work, we formulate the problem as an integer linear program, and we devise a heuristic approach based on edge contraction operations. We test the proposed approaches on both artificial instances and benchmark biological networks.

On a New Stochastic Space with Applications to Nonlinear Economic Models

This article will utilize a weighted regular matrix composed of Fibonacci numbers and variable exponent sequence spaces to create a novel stochastic space with certain geometric and topological properties. This area demonstrates the new form of the Kannan contraction operator with a fixed point. In mathematical economics, we represent economic entities, processes, and phenomena by mathematically structured functional equations, either as summable equations or integral equations. We investigate a category of Volterra-type non-linear dynamical systems, similar to an economic model. We employ our acquired results to formulate new solvability criteria for a unique solution of these non-linear discrete economic dynamical systems. Ultimately, we illustrate our findings with specific instances and applications related to the presence of solutions in non-linear dynamical systems of Volterra-type.

A Rigorous Integrator and Global Existence for Higher-Dimensional Semilinear Parabolic PDEs via Semigroup Theory

In this paper, we introduce a general constructive method to compute solutions of initial value problems of semilinear parabolic partial differential equations on hyper-rectangular domains via semigroup theory and computer-assisted proofs. Once a numerical candidate for the solution is obtained via a finite dimensional projection, Chebyshev series expansions are used to solve the linearized equations about the approximation from which a solution map operator is constructed. Using the solution operator (which exists from semigroup theory), we define an infinite dimensional contraction operator whose unique fixed point together with its rigorous bounds provide the local inclusion of the solution. Applying this technique for multiple time steps leads to constructive proofs of existence of solutions over long time intervals. As applications, we study the 3D/2D Swift–Hohenberg, where we combine our method with explicit constructions of trapping regions to prove global existence of solutions of initial value problems converging asymptotically to nontrivial equilibria. A second application consists of the 2D Ohta–Kawasaki equation, providing a framework for handling derivatives in nonlinear terms.

Construction and validation of prognosis and treatment outcome models based on plasma membrane tension characteristics in bladder cancer.

Plasma membrane tension-related genes (MTRGs) are known to play a crucial role in tumor progression by influencing cell migration and adhesion. However, their specific mechanisms in bladder cancer (BLCA) remain unclear. Transcriptomic, clinical and mutation data from BLCA patients were collected from The Cancer Genome Atlas (TCGA) and Gene Expression Omnibus (GEO) databases. Clusters associated with MTRGs were identified by consensus unsupervised cluster analysis. The genes of different clusters were analyzed by GO and KEGG gene enrichment analysis. Differentially expressed genes (DEGs) were screened from different clusters. Consensus cluster analysis of prognostic DEGs was performed to identify gene subtypes. Patients were then randomly divided into training and validation groups, and MTRG scores were constructed by logistic minimum absolute contraction and selection operator (LASSO) and Cox regression analysis. We assessed changes in clinical outcomes and immune-related factors between different patient groups. The single-cell RNA sequencing (scRNA-seq) dataset for BLCA was collected and analyzed from the Tumor Immune Single-cell Hub (TISCH) database. Biological functions were investigated using a series of experiments including quantitative reverse transcriptase polymerase chain reaction (qRT-PCR), wound healing, transwell, etc. Our MTRG score is based on eight genes (HTRA1, GOLT1A, DCBLD2, UGT1A1, FOSL1, DSC2, IGFBP3 and TAC3). Higher scores were characterized by lower cancer stem cell (CSC) indices, as well as higher tumor microenvironment (TME) stromal and immune scores, suggesting that high scores were associated with poorer prognosis. In addition, some drugs such as cisplatin, paclitaxel, doxorubicin, and docetaxel exhibited lower IC50 values in the high MTRG score group. Functional experiments have demonstrated that downregulation of DCBLD2 affects tumor cell migration, but not proliferation. Our study sheds light on the prognostic significance of MTRGs within the TME and their correlation with immune infiltration patterns, ultimately impacting patient survival in BLCA. Notably, our findings highlight DCBLD2 as a promising candidate for targeted therapeutic interventions in the clinical management of BLCA.

Ciric-Rhoades-Type Contractive Mappings

The available literature shows that weakly contractive operators have been thoroughly researched in relation to metric spaces and associated fixed point theorems. These efforts, which broaden the concept of symmetric and asymmetric spaces, however, have not yet fully grasped the context of metric-like spaces.Considering this gap, this manuscripts introduces the notion of generalized weakly quasi contractive operators in metric-like space and investigates the existence and uniqueness of these operators' fixed points. Non-trivial comparative examples are constructed to support the assertions forming the main ideas herein. Some corollaries indicating that the idea of this paper encompasses a few related ones in the literature are highlighted and addressed.

Decision-making on A Novel Stochastic Space-I of Solutions for Fuzzy Volterra-Type Non-linear Dynamical Economic Models

In this paper, we explain the sufficient conditions on a novel constructed stochastic space by weighted generalized Gamma matrix and variable exponent sequence spaces of fuzzy functions, for the Kannan contraction operator to have a unique fixed point. Finally, we discuss the numerous applications of solutions to Fuzzy Volterra-Type Non-linear Dynamical Economic Models and illustrate them with some examples.

Approximation to the optimal allocation for response adaptive designs.

We investigate the optimal allocation design for response adaptive clinical trials, under the average reward criterion. The treatment randomization process is formatted as a Markov decision process and the Bayesian method is used to summarize the information on treatment effects. A span-contraction operator is introduced and the average reward generated by the policy identified by the operator is shown to converge to the optimal value. We propose an algorithm to approximate the optimal treatment allocation using the Thompson sampling and the contraction operator. For the scenario of two treatments with binary responses and a sample size of 200 patients, simulation results demonstrate efficient learning features of the proposed method. It allocates a high proportion of patients to the better treatment while retaining a good statistical power and having a small probability for a trial going in the undesired direction. When the difference in success probability to detect is 0.2, the probability for a trial going in the unfavorable direction is < 1.5%, which decreases further to < 0.9% when the difference to detect is 0.3. For normally distribution responses, with a sample size of 100 patients, the proposed method assigns 13% more patients to the better treatment than the traditional complete randomization in detecting an effect size of difference 0.8, with a good statistical power and a < 0.7% probability for the trial to go in the undesired direction.

Contraction Heuristics for Tensor Decision Diagrams.

In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a crucial impact on efficiency, which is why many heuristics have been proposed. In this work, we use an efficient representation of tensors as a tensor decision diagram. Since existing contraction heuristics do not perform well in combination with these diagrams, we propose two new contraction heuristics. We demonstrate experimentally that our heuristics outperform other state-of-the-art heuristics. We also demonstrate that our framework yields state-of-the-art performance for equivalence checking.

Construction of a cuproptosis-tricarboxylic acid cycle-associated lncRNA model to predict the prognosis of non-small cell lung cancer.

In cuproptosis, excess copper ions induce cell death via fatty acylation in the tricarboxylic acid (TCA) cycle. However, the effects of cuproptosis-TCA-related long non-coding RNAs (lncRNAs) on the clinical prognosis of non-small cell lung cancer (NSCLC) and the associated tumor microenvironment remain unclear. The purpose of this study is to use cuproptosis-TCA related lncRNAs to predict the prognosis of NSCLC. Molecular signature databases and cuproptosis-related publications were made use of identifying cuproptosis-TCA-related genes. They were identified based on Pearson correlation analysis. The prognostic features associated with these lncRNAs were evaluated using the absolute contraction and selection operator and a receiver operating characteristic curve analysis. Additionally, downstream functional enrichment and immunoinfiltration were analyzed to examine the immunotherapeutic responses of patients with NSCLC. Eleven cuproptosis-TCA-associated lncRNAs were identified. A high-risk group was compared with a low-risk group based on risk scores, and the high-risk group had a significantly lower overall survival (OS). We established a prognostic risk profile, and based on these characteristics and clinical staging, a nomogram was constructed. An analysis of functional enrichment revealed the involvement of pathways associated with cellular and humoral immunity and fatty acylation. Risk scores differed significantly based on immune cells and pathways (antigen-presenting cell co-stimulation). Moreover, TP53, TTN, and MUC16 mutation status were strongly associated with risk scores, with patients identified as having a higher risk of NSCLC being more responsive to immunotherapy. Eleven cuproptosis-TCA-associated lncRNAs can be used to predict the prognosis of NSCLC patients, thereby providing a new theoretical basis for immunotherapy.

Notes on quasi contractive operators and their applications

Notes on quasi contractive operators and their applications

Common Attractors of Generalized Hutchinson–Wardowski Contractive Operators

The aim of this paper is to obtain a fractal set of ℑ-iterated function systems comprising generalized ℑ-contractions. For a variety of Hutchinson–Wardowski contractive operators, we prove that this kind of system admits a unique common attractor. Consequently, diverse outcomes are obtained for generalized iterated function systems satisfying various generalized contractive conditions. An illustrative example is also provided. Finally, the existence results of common solutions to fractional boundary value problems are obtained.

Iterative algorithm for computing magnetic field considering remanent magnetization and demagnetization

SUMMARY Efficient and high-precision methods for performing large-scale numerical calculations under high magnetic susceptibility conditions are essential for magnetic exploration applications. This paper proposes an algorithm for magnetic field modelling considering both demagnetization and remanent magnetization. The 3-D partial differential equation of magnetic potential is reduced to a 1-D ordinary differential equation in the space-wavenumber domain through a 2-D Fourier transform in the horizontal direction. Using the quadratic interpolation finite element method to obtain the pentagonal equation, the chasing method is used to solve the equation efficiently, and a contraction operator based on electromagnetic integral equation method is introduced to ensure stable iteration convergence. The validity of the algorithm was confirmed by comparing it with analytical solutions. Numerical examples demonstrate the importance of considering demagnetization under high magnetization conditions. Test results reveal that magnetic susceptibility is the sole factor affecting convergence among the factors examined. Further analysis showed that, for the same magnetic susceptibility, the algorithm converges with the same number of iterations and higher precision is achieved with an increasing number of nodes. Under the same grid configuration, higher magnetic susceptibility requires more iterations to converge and results in lower algorithm precision. The algorithm presented in this paper shows higher efficiency compared to those based on integral equations. Moreover, we demonstrate the algorithm's high accuracy when applied to models with anomalies near boundaries. Finally, the adaptability of the algorithm to complex geological models and undulating topography is verified by combining model tests with DEM data. This algorithm presents an efficient and high-precision method for magnetic field calculations under conditions of high susceptibility and strong remanent magnetization, offering promising prospects for geoscience applications.

Minor-closed classes of binary functions

Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and contraction. We give the excluded minor characterisations for the classes of binary functions with well defined minors, and those with an associated rank function. Within these classes, we also characterise the classes of binary functions corresponding to polymatroids, matroids and binary matroids by their excluded minors. This gives a new proof of Tutte's excluded minor characterisation of binary matroids in the more generalised space of binary functions.

Explore the expression of mitochondria-related genes to construct prognostic risk model for ovarian cancer and validate it, so as to provide optimized treatment for ovarian cancer.

The use of gene development data from public database has become a new starting point to explore mitochondrial related gene expression and construct a prognostic prediction model of ovarian cancer. Data were obtained from the TCGA and ICGC databases, and the intersection with mitochondrial genes was used to obtain the differentially expressed genes. q-PCR, Cox proportional risk regression, minimal absolute contraction and selection operator regression analysis were performed to construct the prognostic risk model, and ROC curve was used to evaluate the model for centralized verification. The association between risk scores and clinical features, tumor mutation load, immune cell infiltration, macrophage activation analysis, immunotherapy, and chemosensitivity was further evaluated. A prognostic risk score model for ovarian cancer patients was constructed based on 12 differentially expressed genes. The score was highly correlated with ovarian cancer macrophage infiltration and was a good predictor of the response to immunotherapy. M1 and M2 macrophages in the ovarian tissue in the OV group were significantly activated, providing a reference for the study of the polarity change of tumor-related macrophages for the prognosis and treatment of ovarian cancer. In terms of drug sensitivity, the high-risk group was more sensitive to vinblastine, Acetalax, VX-11e, and PD-0325901, while the low-risk group was more sensitive to Sabutoclax, SB-505124, cisplatin, and erlotinib. The prognostic risk model of ovarian cancer associated to mitochondrial genes built on the basis of public database better evaluated the prognosis of ovarian cancer patients and guided individual treatment.

Portfolio problem for the α−hypergeometric stochastic volatility model with consumption

This paper solves the finite horizon optimal consumption-investment problem for an investor that trades in the α−hypergeometric stochastic volatility model, with preferences based on a power utility function. To find the optimal strategy, we follow the dynamic programming approach. First, we perform a suitable change of variables in order to fully transform the non-linear Hamilton-Jacobi-Bellman (HJB) equation into a semilinear one. Next, we apply the Girsanov theorem to deduce an implicit Feynman-Kac formula depending upon the volatility process. The operator defined by the Feynman-Kac representation is shown to be a contraction operator on a designed function space. Finally, the Banach fixed point theorem yields the existence of a solution to the HJB equation in the designed space. Moreover, we apply a verification theorem to guarantee that the solution of the HJB equation coincides with the value function.

Exploring resveratrol against Alzheimer's disease and Parkinson's disease through integrating network pharmacology, bioinformatics, and experimental validation strategy in vitro

BackgroundThe study aims to investigate the pharmacological basis and molecular mechanisms of resveratrol in the treatment of Alzheimer's disease (AD) and Parkinson's disease (PD) through the approach of treating different diseases with the same method, guided by traditional Chinese medicine theory. Utilizing network pharmacology and bioinformatics methods, this research aims to provide modern medical evidence for the theory of treating different diseases with the same method in traditional Chinese medicine. MethodsOmnibus from Swiss Target Prediction, TCMSP, SuperPred, SEA, HIT, CTD, TCMIP and Gene Expression Disease datasets for resveratrol related genes, Alzheimer's disease, and Parkinson's disease were obtained from the GEO database. Core targets were identified by weighted gene coexpression network analysis (WGCNA) and minimum absolute contraction and selection operator (LASSO). The expression of core targets was verified in AD and PD cell models. The immune characteristics of AD and PD were analyzed by CIBERSORT algorithm. Finally, the potential mechanism of resveratrol intervention on the core target was studied by molecular docking technique. ResultsThe results of network pharmacological analysis showed that resveratrol acted on 85 common targets such as STAT3 and CASP3, affected AGE-RAGE signaling pathway and PI3K-Akt signaling pathway, and showed the effect of "same disease and different treatment" for AD and PD. Three core targets associated with AD and PD (PLK4, FCGRT, and PRKAR2A) were finally identified through comprehensive transcriptome analysis, and experimentally verified in cell models of AD and PD. At the same time, the analysis of immune cell infiltration suggested that AD and PD had dysregulation of inflammation, and the core target was significantly related to M2 macrophages. ConclusionResveratrol may play a potential mechanism of "treating the same disease with different diseases" and target three core targets (PLK4, FCGRT and PRKAR2A) to improve the disease process of AD and PD by participating in the regulation of immune and inflammatory pathways. These findings have potential implications for clinical practice and future research.

Integrated single-cell and bulk RNA sequencing analyses identify an immunotherapy nonresponse-related fibroblast signature in gastric cancer.

Factors that determine nonresponse to immune checkpoint inhibitor (ICI) remain unclear. The protumor activities of cancer-associated fibroblasts (CAFs) suggest that they are potential therapeutic targets for cancer treatment. There is, however, a lack of CAF-related signature in predicting response to immunotherapy in gastric cancer (GC). Single-cell RNA sequencing (scRNA-seq) and RNA sequencing (RNA-seq) data of GC immunotherapy were downloaded from the Gene Expression Omnibus database. Bulk RNA-seq data were obtained from The Cancer Genome Atlas. The R package 'Seurat' was used for scRNA-seq data processing. Cellular infiltration, receptor-ligand interactions, and evolutionary trajectory analysis were further explored. Differentially expressed genes affecting overall survival were obtained using the limma package. Weighted Gene Correlation Network Analysis was used to identify key modules of immunotherapy nonresponder. Prognostic model was constructed by univariate Cox and least absolute contraction and selection operator analysis using the intersection of activated fibroblast genes (AFGs) with key module genes. The differences in clinicopathological features, immune microenvironment, immunotherapy prediction, and sensitivity to small molecule agents between the high- and low-risk groups were further investigated. Based on scRNA-seq, we finally identified 20 AFGs associations with the prognosis of GC patients. AFGs' high expression levels were correlated with both poor prognosis and tumor progression. Three genes ( FRZB , SPARC , and FKBP10 ) were identified as immunotherapy nonresponse-related fibroblast genes and used to construct the prognostic signature. This signature is an independent significant risk factor affecting the clinical outcomes of GC patients. Remarkably, there were more CD4 memory T cells, resting mast cells, and M2 macrophages infiltrating in the high-risk group, which was characterized by higher tumor immune exclusion. Moreover, patients with higher risk scores were more prone to not respond to immunotherapy but were more sensitive to various small molecule agents, such as memantine. In conclusion, this study constructed a fibroblast-associated ICI nonresponse gene signature, which could predict the response to immunotherapy. This study potentially revealed a novel way to overcome immune resistance in GC.

Convergence of power sequences of operators via their stability

This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where “convergence” and “stability” are considered with respect to weak, strong and norm topologies. It is proved that an operator has a convergent power sequence if and only if it is a (not necessarily orthogonal) direct sum of an identity operator and a stable operator. This reduces the issue of convergence of the power sequence of an operator T to the study of stability of T. The question of when the limit of the power sequence is an orthogonal projection is investigated. Among operators sharing this property are hyponormal and contractive ones. In particular, a hyponormal or a contractive operator with no identity part is stable if and only if its power sequence is convergent. In turn, a unitary operator has a weakly convergent power sequence if and only if its singular-continuous part is weakly stable and its singular-discrete part is the identity. Characterizations of the convergence of power sequences and stability of subnormal operators are given in terms of semispectral measures.

Acetylation model predicts prognosis of patients and affects immune microenvironment infiltration in epithelial ovarian carcinoma

BackgroundEpithelial ovarian carcinoma (EOC) is a prevalent gynaecological malignancy. The prognosis of patients with EOC is related to acetylation modifications and immune responses in the tumour microenvironment (TME). However, the relationships between acetylation-related genes, patient prognosis, and the tumour immune microenvironment (TIME) are not yet understood. Our research aims to investigate the link between acetylation and the tumour microenvironment, with the goal of identifying new biomarkers for estimating survival of patients with EOC.MethodsUsing data downloaded from the tumour genome atlas (TCGA), genotypic tissue expression (GTEx), and gene expression master table (GEO), we comprehensively evaluated acetylation-related genes in 375 ovarian cancer specimens and identified molecular subtypes using unsupervised clustering. The prognosis, TIME, stem cell index and functional concentration analysis were compared among the three groups. A risk model based on differential expression of acetylation-related genes was established through minimum absolute contraction and selection operator (LASSO) regression analysis, and the predictive validity of this feature was validated using GEO data sets. A nomogram is used to predict a patient's likelihood of survival. In addition, different EOC risk groups were evaluated for timing, tumour immune dysfunction and exclusion (TIDE) score, stemness index, somatic mutation, and drug sensitivity.ResultsWe used the mRNA levels of the differentially expressed genes related to acetylation to classify them into three distinct clusters. Patients with increased immune cell infiltration and lower stemness scores in cluster 2 (C2) exhibited poorer prognosis. Immunity and tumourigenesis-related pathways were highly abundant in cluster 3 (C3). We developed a prognostic model for ten differentially expressed acetylation-related genes. Kaplan–Meier analysis demonstrated significantly worse overall survival (OS) in high-risk patients. Furthermore, the TIME, tumour immune dysfunction and exclusion (TIDE) score, stemness index, tumour mutation burden (TMB), immunotherapy response, and drug sensitivity all showed significant correlations with the risk scores.ConclusionsOur study demonstrated a complex regulatory mechanism of acetylation in EOC. The assessment of acetylation patterns could provide new therapeutic strategies for EOC immunotherapy to improve the prognosis of patients.