Polar Decomposition Research Articles

Higham's approximations of polar factors of operators

In this paper, we first present a necessary and sufficient condition for a class of block matrices to be positive semidefinite. Second, we demonstrate the significance of a known inequality (as presented in [5]) through a norm inequality. Finally, utilizing the polar decomposition, we provide a functional version of a singular value inequality.

Acetylated chitosan scaffolds modulate the micro-environment and promote peripheral nerve regeneration through macrophage TLR2/4 pathway activation

To identify the core immune regulatory gene ELANE in sepsis and explore its mechanism in regulating sepsis through macrophage polarization. Peripheral blood RNA sequencing and bioinformatics analysis were performed on 20 sepsis patients and 10 healthy controls. Differential gene expression (DEGs) screening, functional enrichment (GO/KEGG/GSEA), and protein-protein interaction (PPI) network analysis were conducted. Meta-analysis validated ELANE expression trends across GEO datasets, while survival analysis assessed its prognostic relevance. Single-cell sequencing localized ELANE expression, and in vitro experiments using LPS-stimulated macrophages and siRNA-mediated ELANE inhibition evaluated its role in M1/M2 macrophage polarization and inflammatory factor release (flow cytometry, ELISA). 948 DEGs were identified, with ELANE significantly upregulated in sepsis. PPI and MCC algorithms identified ELANE as a top core gene. Meta-analysis confirmed ELANE overexpression in sepsis, and survival analysis linked high ELANE levels to poor 28-day prognosis. Single-cell sequencing localized ELANE predominantly in macrophages. LPS stimulation increased ELANE expression and M1 polarization (CD86+), while ELANE inhibition reduced M1 polarization and suppressed IL-1β/TNF-α levels. ELANE exacerbates sepsis by promoting M1 macrophage polarization and proinflammatory cytokine release, highlighting its potential as a therapeutic target.

Target cell recognition by cytotoxic T lymphocytes (CTLs) triggers rapid delivery of cytolytic granules to the immune synapse directed by the centrosome. Recent studies have also identified a rapid burst of T cell receptor (TCR)-activated transcription that contributes to CTL-mediated killing. To determine how de novo transcription might be coordinated with intracellular polarization, we asked when transcription factor translocation to the nucleus occurs relative to TCR activation and centrosome polarization within individual CTLs. Upon target cell recognition, the nucleus polarized to and contacted the immune synapse, preceding centrosome docking. The nucleus distorted as it moved, with transcription factors NFAT and NF-κB accumulating in the nucleus during polarization. Inhibition or deletion of myosin IIA prevented both nuclear polarization and transcription factor translocation. Thus, nuclear polarization facilitates an early transcriptional burst that occurs as CTLs encounter targets and the consequent delivery of newly synthesized cytokines to the immune synapse.

The singular value decomposition and left and right polar decompositions are well known for (in particular) all n × n complex matrices A, but, as customarily formulated, they are not meaningful for elements a of semigroups S other than S = M n ( C ) . For elements a of any ★-semigroup S with 1, this article presents new definitions of the singular value and polar decompositions which extend those for the matrix case, and examines the equivalence of these and other related weaker conditions on elements a of S.

Macrophages (MΦs) are integral cellular components responsible for immune response and tissue homeostasis. Evaluation of their pro-inflammatory (M1) and anti-inflammatory (M2) polarization states, along with their metabolic profiles, typically conducted via flow cytometry, is crucial for assessing the immune status of an organism. Traditional flow cytometry relies on extrinsic fluorescent labels, which may interfere with cellular function. Here, using multispectral flow cytometry, we demonstrate how the autofluorescence profiles of human monocyte-derived macrophages change under M1/M2 polarization, hypoxia and starvation stress factors, and interaction with low-density lipoproteins as an atherosclerosis model. Extending these findings to clinical samples, we demonstrated that leukocyte AF profiles could distinguish atherosclerosis patients from healthy controls with a ROC-AUC of 0.84 ± 0.09, advanced predictive models. These findings highlight AF as a sensitive, non-invasive tool for assessing macrophage activation and metabolic states, with potential applications in atherosclerosis diagnostics and immune cell phenotyping.

Background: Diabetes mellitus (DM) is a global health concern, with 90% of cases diagnosed as type 2 DM (DM2). Objective: We evaluated the effects of photobiomodulation (PBM) plus adipose-derived stem (ADS) cells, alone and together, during the inflammation (day 4) and proliferation (day 8) stages of the wound healing process (WHP) in an infected ischemic wound model in DM2 rats. Stereological parameters and immunohistological assessments of M1 and M2 macrophage phenotypes, as well as mRNA expression levels of four genes, were assessed. Materials and Methods: We assigned 48 rats to 4 groups: control, PBM, ADS, and PBM+ADS. Results: On day 4, the treatment groups had significantly reduced neutrophil, macrophage, and M1 counts compared to the control group (all p < 0.001). PBM+ADS showed the greatest reduction (p < 0.001). The treatment groups had higher fibroblast and M2 counts (p < 0.001), with PBM+ADS showing the largest increase (p < 0.01). Vascular length was significantly greater in the PBM+ADS and PBM groups (p < 0.001), with PBM+ADS showing the highest increase (p < 0.001). New epidermis and dermis volumes were significantly higher in all treatment groups (p < 0.001), with PBM+ADS showing the greatest improvements (p < 0.001). On day 8, neutrophil, macrophage, and M1 counts remained significantly lower in all treated groups (p < 0.001), with PBM+ADS showing the most reduction. Fibroblasts and M2 counts remained elevated, with PBM+ADS having the highest values (p < 0.001). Vascular length, epidermis, and dermis volumes increased significantly in the PBM+ADS group (all p < 0.001). There were significant increases in basic fibroblast growth factor, vascular endothelial growth factor A, stromal cell-derived factor-1α, and hypoxia-inducible factor 1-alpha in all treatment groups (all p < 0.001), especially the PBM+ADS and PBM groups. Conclusion: Although PBM outperformed ADS in enhancing WHP in a DM2 rat model, the combination of PBM+ADS showed the best results.

Osteosarcoma is a highly aggressive cancer, and the efficacy of existing therapies has plateaued. Multiomics integration analysis can identify novel therapeutic targets for various cancers and therefore shows potential toward osteosarcoma treatment. This study aimed to leverage multiomics integration to develop a new risk model, characterizing the immune features of osteosarcoma to uncover novel therapeutic targets. Metabolomics profiling was conducted to identify key metabolites in osteosarcoma. Transcriptomic sequencing datasets were analyzed to identify prognostic genes related to key metabolic pathways and develop a prognostic risk model. Patients were then divided into high-risk and low-risk groups with distinct clinical outcomes based on the risk model. The single-sample gene set enrichment analysis, Estimation of Stromal and Immune cells in Malignant Tumor tissues using Expression data (ESTIMATE) algorithm, and xCell algorithms were used to evaluate the immune cell infiltration and activity. Single-cell RNA sequencing was used to explore cell-to-cell interactions within the tumor microenvironment. In vitro coculture functional assays were performed to validate the role of macrophage migration inhibitory factor (MIF) in macrophage polarization and chemotaxis. In vivo studies were used to evaluate the effectiveness of MIF inhibition in combination with immune checkpoint blockade in murine models. Elevated lactate levels in osteosarcoma patients correlated with poorer overall survival. We identified SLC7A7 and CYP27A1 as prognostic lactate metabolism genes and developed a risk model to stratify patients into high-risk and low-risk groups with distinct outcomes. Bioinformatics analyses highlighted the differences in immune infiltration patterns and activity between the groups. Notably, the infiltration and phenotype of macrophages varied significantly between the groups, and MIF was identified as a critical mediator in this process. In osteosarcoma cells, lactate regulated MIF expression through histone H3K9 lactylation. Combining the MIF inhibitor 4-IPP with a programmed cell death 1 (PD-1) monoclonal antibody treatment demonstrated a significant antitumor effect. MIF acts as a novel therapeutic target by regulating macrophage polarization and chemotaxis. Lactate regulated MIF expression through histone lactylation. Targeting MIF holds promise for enhancing the efficacy of anti-PD-1 treatment.

Thanks to the ability to obtain Muller matrix of targets, Mueller matrix polarimeters are critical to many applications. However, for optical components such as submersible observation windows, which work in complex environments, the existing Mueller matrix polarimeters are infeasible. To achieve non-contact, real-time measurements for these special targets, a measurement method based on bidirectional optical path is proposed to obtain their polarization properties. The measured results are bidirectional Mueller matrixes. However, they combine forward and backward optical path effects so that they cannot directly characterize polarization properties of measured components. In this case, a decomposition method based on polar decomposition is developed to obtain a single forward Mueller matrix from a measured bidirectional Mueller matrix. To verify the proposed decomposition method and improve measurement accuracy, both simulations and the impacts of various systematic errors are analyzed and summarized carefully. Furthermore, an in-situ calibration scheme is proposed to eliminate the influences of several systemic errors. Based on the simulation results and the proposed calibration scheme, an optical path is built in laboratory. Both air and wave plates are measured so that the proposed measurement method, decomposition method and measurement accuracy are verified. Hence, the proposed measurement method is a good supplement to the existing Mueller matrix polarimeters and would play important roles in areas such as deep-sea exploration.

ABSTRACTIn two studies conducted in Spain, we identified asymmetries in moral judgements, showing that leftist political topics and individuals were perceived as more moral than their rightist counterparts. Study 1 assessed the participants’ perceived moral obligation to defend topics traditionally associated with leftist or rightist ideologies. Both leftist and rightist participants reported stronger moral obligations towards leftist than rightist topics. Study 2 investigated moral, meta‐ and self‐stereotypes within leftist and rightist political topics. Rightists viewed leftists more positively in moral terms than leftists viewed rightists, particularly in the context of leftist topics. Rightists also anticipated harsher moral judgements from leftists (meta‐stereotypes), whereas leftists did not reciprocate. Moral self‐stereotypes were similar across groups. These findings reveal moral asymmetry favouring leftist topics and individuals. We discuss the implications for political polarization, intergroup relations and contextual factors that shape these perceptions.

The polarization reflection model is a fundamental framework describing the changes in both intensity and polarization of light following reflection. Materials with distinct properties exhibit unique polarization reflection characteristics. However, traditional models assume that the scattered light from diffuse reflection is completely depolarized after undergoing internal scattering, regardless of the scattering properties of the object. In reality, multiple scattering events do not completely depolarize the scattered light. To address this discrepancy, we first established a reference coordinate system for the scattering process. Subsequently, we employed polar decomposition methods to analyze the subsurface scattering Mueller matrix. Building upon this analysis, we introduced polarization Monte Carlo simulations to empirically construct a novel polarimetric bidirectional subsurface scattering reflectance distribution function (pBSSRDF) model. We also explored the relationship between the depolarization and scattering coefficient and developed a comprehensive optimization process for the object's pBSSRDF parameters, thereby avoiding the limitations associated with coaxial and coplanar assumptions. Our experiments, conducted on both synthetic and real data for opaque and translucent objects, demonstrate high accuracy in representing the polarization states of scattered light.

Tongue cancer, the most aggressive subtype of oral cancer, presents critical challenges due to the limited number of specialists available and the time-consuming nature of conventional histopathological diagnosis. To address these issues, we developed an intelligent diagnostic system integrating Mueller matrix microscopy with deep learning to enhance diagnostic accuracy and efficiency. Through Mueller matrix polar decomposition and transformation, micro-polarization feature parameter images were extracted from tongue cancer tissues, and purity parameter images were generated by calculating the purity of the Mueller matrices. A multi-stage feature dataset of Mueller matrix parameter images was constructed using histopathological samples of tongue cancer tissues with varying stages. Based on this dataset, the clinical potential of Mueller matrix microscopy was preliminarily validated for histopathological diagnosis of tongue cancer. Four mainstream medical image classification networks—AlexNet, ResNet50, DenseNet121 and VGGNet16—were employed to quantitatively evaluate the classification performance for tongue cancer stages. DenseNet121 achieved the highest classification accuracy of 98.48%, demonstrating its potential as a robust framework for rapid and accurate intelligent diagnosis of tongue cancer.

The aim of the study is to identify the functional features of generational neologisms in English as factors of cognitive and social polarization both between and within generations. The article examines the phenomenon of lexemes marked by cohort affiliation and traces their role in shaping symbolic boundaries and intergenerational opposition in English-language discourse. The semantic and pragmatic characteristics of such units are revealed, and their dichotomizing function in communication is substantiated. The scientific novelty of the research lies in identifying and describing cognitive and discursive mechanisms of generational lexical polarization, manifested in the functioning of neologisms with a pronounced cohort affiliation. The novelty also consists in developing and applying the author’s dynamic conceptual modeling scheme, which makes it possible to reconstruct the transformational trajectory of conflictogenic lexemes from primary affiliation to ambivalent functioning and stable contradiction of cognitive attitudes. In addition, the pragmatic status of such neologisms as instruments of cohort self-identification, symbolic differentiation, and reinterpretation of sociocultural norms is clarified, which expands our understanding of the polarization potential of lexical innovations in English-language discourse. As a result, key cognitive features of conflictogenic generational neologisms, their semantic and pragmatic transformations, as well as the discursive scenarios in which they are actualized, have been identified.

Aluthge transform is a well-known mapping defined on bounded linear operators. Especially, the convergence property of its iteration has been studied by many authors. In this paper, we discuss the problem for the induced Aluthge transforms which is a generalization of the Aluthge transform defined in 2021. We give the polar decomposition of the induced Aluthge transformations of centered operators and show its iteration converges to a normal operator. In particular, if T T is an invertible centered matrix, then iteration of any induced Aluthge transformations converges. Using the canonical standard form of matrix algebras we show that the iteration of any induced Aluthge transformations with respect to the weighted arithmetic mean and the power mean converge. Those observation are extended to the C ∗ C^* -algebra of compact operators on an infinite dimensional Hilbert space, and as an application we show the stability of A N \mathcal {AN} and A M \mathcal {AM} properties under the iteration of the induced Aluthge transformations. We also provide concrete forms of their limit points for centered matrices and several examples. Moreover, we discuss the limit point of the induced Aluthge transformation with respect to the power mean in the injective I I 1 II_1 -factor M \mathcal {M} and determine the form of its limit for some centered operators in M \mathcal {M} .

Abstract The Cartan decomposition of a semisimple Lie algebra is pivotal in both theoretical exploration and practical application. It generalizes the classical spectral, polar, and singular value decompositions found in linear algebra. This paper explores an advanced refinement of the Cartan decomposition of $$\mathfrak {su}(2^{n})$$ su ( 2 n ) , arising from the parameterization of a Hamiltonian for quantum simulation. Specifically, given an AI-type Cartan decomposition $${\mathfrak {g}} = {\mathfrak {k}} \oplus {\mathfrak {p}}$$ g = k ⊕ p of any Lie subalgebra $${\mathfrak {g}}$$ g in $$\mathfrak {su}(2^{n})$$ su ( 2 n ) , where $${\mathfrak {p}} = \widetilde{{\mathfrak {p}}} \oplus {\mathfrak {h}}$$ p = p ~ ⊕ h and $${\mathfrak {h}}$$ h is the maximal abelian subalgebra in $${\mathfrak {p}}$$ p , it is revealed that both the subalgebra $${\mathfrak {k}}$$ k and the corresponding $$\widetilde{{\mathfrak {p}}}$$ p ~ (which is generally not a subalgebra) can further be partitioned, respectively, as the direct sums of equal-dimensional commutative Lie subalgebras. With respect to the involution $$\theta (g)=-g^{\top }$$ θ ( g ) = - g ⊤ , any Lie subalgebra $${\mathfrak {g}}$$ g in $$\mathfrak {su}(2^{n})$$ su ( 2 n ) with nondegenerate Cartan decomposition can thus be fully decomposed as the orthogonal direct sum of $${\mathfrak {h}}$$ h and pairs of commutative Lie subalgebras over $${\mathfrak {k}}$$ k and $$\widetilde{{\mathfrak {p}}}$$ p ~ , all of which, except $${\mathfrak {h}}$$ h , share the same dimension.

This study analyzes the strategic challenges and optimization pathways for human resource development through Indonesia’s Free Nutritious Meal Program (MBG), which is aligned with the national vision of Golden Indonesia 2045. The research addresses critical gaps stemming from persistent stunting rates (19.8%), heavy reliance on food imports (80% of milk needs), and ongoing public concerns over program transparency and accountability, despite a substantial budget allocation of IDR 71 trillion serving 19.47 million beneficiaries. Using a qualitative descriptive approach, the study integrates big data from social media, online news, and academic publications. The analysis uses NVivo 15 Plus software to explore word frequency, sentiment polarity, and thematic factor categorization related to MBG implementation. Results reveal key challenges such as infrastructure limitations, import dependency, perceived corruption risks, and predominantly neutral public sentiment. To optimize outcomes, the study recommends three strategic directions: (1) enhancing national food self-sufficiency, (2) establishing Nutrition Food Processing Centers (Sentra Pengolahan Pangan Gizi, SPPG) across all regions, and (3) recruiting Indonesian Development Driving Graduates (Sarjana Penggerak Pembangunan Indonesia, SPPI) to ensure professional program management and policy compliance. The MBG initiative represents a transformative step in reshaping Indonesia’s nutrition and education landscape, catalyzing the development of competitive, high-quality human capital essential for achieving Indonesia’s long-term socio-economic vision.

Cell division cycle protein 42 (Cdc42) is a member of the Rho GTPase subfamily that serves as a signal mediating factor in cell cycle division, cytoskeleton arrangement, cell polarization, membrane trafficking and signal transduction. However, the role of Cdc42 in cardiac remodeling, including hypertrophy and fibrosis, remains controversial. This study aimed to clarify the role and underlying mechanism of Cdc42 in cardiac remodeling. Cardiac Cdc42 knockout (Cdc42CKO) mice were generated by crossing Cdc42loxP/loxP mice with MLC2v-Cre mice. Mouse cardiac remodeling models were induced by subcutaneous administration of AngII (1500 ng/kg/min) for 7 days or transverse aortic constriction (TAC) for 2 or 8 weeks. Our results showed that cardiac Cdc42 deletion significantly suppressed AngII- or TAC-induced cardiac hypertrophy and fibrosis and improved cardiac function in mice. Cdc42CKO or specific inhibition of Cdc42, markedly inhibited Ang II-mediated activation of the MKK3/6-p38 cascade in the heart and in isolated newborn/adult mouse cardiomyocytes or H9c2 cells. Furthermore, Cdc42 overexpression increased the surface area and hypertrophic gene expression in myocytes, whereas ML141 (a Cdc42 inhibitor) and SB203580 (a p38 inhibitor) specifically decreased p38 activation and hypertrophy in Cdc42-overexpressing or AngII-induced hypertrophic cardiomyocytes, indicating that p38 is a downstream effector of Cdc42 in cardiac hypertrophy. Taken together, our results demonstrated that Cdc42 is a key driver of cardiac remodeling via activation of the p38 signaling pathway.Graphical abstract

Anti-inflammatory M2 macrophages are highly relevantin variousphysiological processes ranging from tissue regeneration to cancerprogression. However, conventional two-dimensional (2D) invitro cell cultures limit our understanding of macrophagephenotypes and how they can be modulated for immunotherapeutic approaches.Moreover, there is a growing demand for scalable, animal-free hydrogelsto replace animal-derived materials in three-dimensional (3D) in vitro models. In this study, we explore hydrogels basedon plant-derived nanofibrillar cellulose (NFC), also known as cellulosenanofibrils (CNFs) or microfibrillated cellulose (MFC), for generating3D in vitro models of M2-like macrophages from humanblood monocytes. Notably, flow cytometry analysis shows that cellscultured in 3D phosphorylated NFC hydrogels show enhanced expressionof the M2 macrophage marker CD206 compared to cells cultured in othernegatively charged hydrogels prepared from native NFC or NFCs withcarboxylate or sulfate modifications. Furthermore, the upregulationof CD206 expression in 3D phosphorylated NFC is comparable to theinduction of CD206 in interleukin 4 (IL-4)-differentiated M2a macrophages.In addition, the cells in the phosphorylated NFC hydrogel show a differentialcytokine profile compared to 2D cultured cells, secreting similarlevels of tumor necrosis factor α (TNF-α), but 2.6-foldhigher amounts of IL-1β and 1.2-fold higher amounts of IL-10.The results suggest that the conversion of monocytes to M2-like macrophagescan be controlled by the phosphorylation of NFC, a strategy whichdoes not require the addition of polarization factors like growthfactors and cytokines conventionally used to generate macrophages in vitro. The findings highlight the importance of surfacechemistry in matrix-guided macrophage polarization, paving the wayfor xeno-free yet bioactive 3D macrophage culture scaffolds for immunologicalresearch.

Abstract In recent years, plastic materials have increasingly been employed in the automotive and electronics industries due to their advantageous properties, such as lightweight and electrical insulation. Polypropylene (PP), in particular, is favored for its exceptional chemical resistance, low cost, and versatility, making it a popular choice in these sectors. Among various manufacturing techniques, injection molding is widely utilized for fabricating PP components. However, the complex thermo-mechanical conditions of the injection molding process, including high pressures and significant temperature gradients, often lead to the accumulation of internal residual stresses in PP components. These stresses can induce dimensional instability and mechanical degradation over time. In this study, we utilized a continuous-wave (CW) terahertz (THz) source to assess the internal residual stress in injection-molded square PP components. The polarization-dependent THz response exhibited a strong correlation with the molecular orientation of the polymer, which was associated with the internal residual stress distribution. We further validated this correlation by measuring the dimensional changes in PP specimens after precise cutting, confirming a positive relationship between residual stress and the THz polarization factor. Additionally, the influence of injection molding parameters on polymer orientation and residual stress in PP was investigated. The results demonstrated that the distance from the injection molding gate had the most significant impact on polymer chain alignment, thereby affecting both THz polarization characteristics and the residual stress distribution. This study not only confirms the utility of the previously developed THz waves-based evaluation system but also provides insights into optimizing injection molding parameters to improve residual stress management in PP materials.&amp;#xD;