Affine Space Research Articles

Evaluation of natural compounds as VEGFR-2 inhibitors for breast cancer therapy: insights from molecular docking and drug-likeness analysis

Breast cancer remains one of the most common cancers worldwide, with VEGFR-2 (KDR) playing a key role in tumor angiogenesis. Inhibiting VEGFR-2 is a promising therapeutic strategy. Natural compounds are increasingly studied for their potential to inhibit VEGFR-2. This study aims to assess the binding affinity of 11 natural compounds (andrographolide, alpha-mangostin, pinostrobin, pinocembrin, ethyl-p-methoxycinnamate (EPMS), xanthorrhizol, galangin, gamma-mangostin, curcumin, cinnamaldehyde, and alashanoid B) to the VEGFR-2 protein through molecular docking and Lipinski's rule analysis, identifying promising candidates for breast cancer treatment. Molecular docking simulations were performed for 11 compounds and sunitinib as a control, with binding energies and interactions analyzed. The compounds were also evaluated for drug-likeness using Lipinski’s rule of five. Curcumin showed the highest binding affinity to VEGFR-2 with a binding energy of -9.9 kcal/mol, surpassing sunitinib (-9.4 kcal/mol). Key interactions were observed with active site residues Cys919 and Asp1046. All tested compounds met the criteria for oral bioavailability per Lipinski’s rules. Curcumin demonstrates potential as a VEGFR-2 inhibitor due to its favorable binding affinity and drug-like properties. Enhancing curcumin’s bioavailability is recommended for effective therapeutic application.

Images of dominant endomorphisms of affine space

A basic problem in algebraic morphisms is which sets can be the image of an endomorphism of affine space. This paper extends the results previously obtained by the first author on the question of existence of surjective maps F : A n → A n ∖ Z , where Z is an algebraic subvariety of A n of codimension at least 2. In particular, we show that for any (affine) algebraic variety Z of dimension at most n − 2 , there is an algebraic variety W ⊂ A n birational to Z and a surjective algebraic morphism A n → A n ∖ W . We also propose a conjectural approach toward resolving unknown cases.

Выбор аналитической модели и количественных показателей для геоинформационного анализа устойчивого развития территориальных образований

Currently, there are no generally accepted algorithms for assessing, analyzing and forecasting the sustainable development of administrative-territorial units. The authors introduce the definition of this term, which implies the successful functioning of a human community over time carrying out economic activities without threats to its environment. Also, an analytical model for representation of its regional integrated indicator in the form of a vector with differential components, which characterize economic growth, environmental and social metrics, in a three-dimensional affine space, is proposed. Furthermore, we present a multiplicative criterion for assessing partial criteria of sustainable development efficiency and the basic expression for its parameters computation based on the set of economic, environmental and social ones, including such as the availability and quality of natural resources, regional labour resources, eco-factors, etc. The proposed vector model is based on the geoinformation approach and can be deployed within the framework of GIS of sustainable development for geo-analysis, modeling and mapping of natural resource potential and ecological state of intensively advancing territories, considering the dynamics of this process. Important properties of the geoinformation approach to assessing territorial entities’ forward growth, spatial and semantic scalability, are noted. In addition, the functional requirements and preliminary architecture of the core, modules, clients and layers of the related thematic geographic information system for the management, planning and forecasting the said indicator within the framework of digital economy are described

Graded Lie algebras, compactified Jacobians and arithmetic statistics

A simply laced Dynkin diagram gives rise to a family of curves over \mathbb{Q} and a coregular representation, using deformations of simple singularities and Vinberg theory, respectively. Thorne conjectured and partially proved a strong link between the arithmetic of these curves and the rational orbits of these representations. In this paper, we complete Thorne’s picture and show that 2-Selmer elements of the Jacobians of the smooth curves in each family can be parametrised by integral orbits of the corresponding representation. Using geometry-of-numbers techniques, we deduce statistical results on the arithmetic of these curves. We prove these results in a uniform manner. This recovers and generalises results of Bhargava, Gross, Ho, Shankar, Shankar and Wang. The main innovations are an analysis of torsors on affine spaces using results of Colliot-Thélène and the Grothendieck–Serre conjecture, a study of geometric properties of compactified Jacobians using the Białynicki-Birula decomposition, and a general construction of integral orbit representatives.

On affine spaces of rectangular matrices with constant rank

Let F be a field, and n≥p≥r>0 be integers. In a recent article, Rubei has determined, when F is the field of real numbers, the greatest possible dimension for an affine subspace of n–by–p matrices with entries in F in which all the elements have rank r. In this note, we generalize her result to an arbitrary field with more than r+1 elements, and we classify the spaces that reach the maximal dimension as a function of the classification of the affine subspaces of invertible matrices of Ms(F) with dimension (s2). The latter is known to be connected to the classification of nonisotropic quadratic forms over F up to congruence.

Exploring the Affordances of Vernacular Digital Games in Developing 21st-Century Skills

The past decade has witnessed an unprecedented surge in technological advancements and an exponential growth in mobile device ownership world-wide. Such transformations have intensified access to digital content, opening up new avenues for non-formal learning. This was particularly true during subsequent crises such as the COVID-19 Pandemic and natural and man-made disasters which have disrupted formal learning and left many learners immobilised. This paper contends that capitalising on the intersection of formal and non-formal learning experiences is integral to innovative planning and value-added education. To dismiss engagement in non-formal leaning transactions is to exclude a significant part of learners’ cognitive processes, preferences and experiences. In particular, this paper focuses on vernacular digital games as an apt example of pervasive technology and a non-formal learning arena. Described as a popular culture text, vernacular games are originally intended for entertainment, as opposed to pedagogical, purposes. However, embedded in their designs are social and developmental affordances that render them potent tools for serendipitous learning and dynamic spaces for developing competencies. In the light of this, this paper proposes a move from gamification, i.e. adding a gaming layer to non-gaming contexts, to adding an educational layer to non-formal digital gaming contexts. To consolidate this proposal, it investigates the 21st-century competencies reportedly acquired and developed through digital gameplay. It also delves into possible design-related paradoxes. More precisely, the paper reflects on how key game design features such as multimodality, adaptivity, cultural narratives and affinity spaces can be harnessed to better cultivate much in-demand 21st-century skills. Although learning skills (in their metacognitive form of higher-order thinking) are part and parcel of 21st-century skills, literacy skills and life skills are equally important. The further longer-term aim is to map development opportunities and optimise learning in ways that are in harmony with today’s changing scenarios, demands and objectives.

Smooth connectivity in real algebraic varieties

AbstractA standard question in real algebraic geometry is to compute the number of connected components of a real algebraic variety in affine space. This manuscript provides algorithms for computing the number of connected components, the Euler characteristic, and deciding the connectivity between two points for a smooth manifold arising as the complement of a real hypersurface of a real algebraic variety. When considering the complement of the set of singular points of a real algebraic variety, this yields an approach for determining smooth connectivity in a real algebraic variety. The method is based upon gradient ascent/descent paths on the real algebraic variety inspired by a method proposed by Hong, Rohal, Safey El Din, and Schost for complements of real hypersurfaces. Several examples are included to demonstrate the approach.

Boosting Barlow Twins Reduced Order Modeling for Machine Learning‐Based Surrogate Models in Multiphase Flow Problems

AbstractWe present an innovative approach called boosting Barlow Twins reduced order modeling (BBT‐ROM) to enhance the reliability of machine learning surrogate models for multiphase flow problems. BBT‐ROM builds upon Barlow Twins reduced order modeling that leverages self‐supervised learning to effectively handle linear and nonlinear manifolds by constructing well‐structured latent spaces of input parameters and output quantities. To address the challenge of high contrast data in multiphase flow problems due to injection wells and faults, we employ a boosting algorithm within BBT‐ROM. This algorithm sequentially trains a set of weak models (i.e., inaccurate models), improving prediction accuracy through ensemble learning. To evaluate the performance of BBT‐ROM, we conduct three three‐dimensional multiphase flow problems, including waterflooding and geologic carbon storage (GCS), with varying numbers of input parameter cases and model domain features. The results demonstrate that BBT‐ROM excels at predicting non‐wetting phase saturation (e.g., oil or saturation) and fluid pressure, with average relative errors ranging from 0.5% to 3%. Importantly, BBT‐ROM showcases robustness when faced with limited input parameter space during GCS testing.

Counterfactual Explanations for Medical Image Classification and Regression using Diffusion Autoencoder

Counterfactual explanations (CEs) aim to enhance the interpretability of machine learning models by illustrating how alterations in input features would affect the resulting predictions. Common CE approaches require an additional model and are typically constrained to binary counterfactuals. In contrast, we propose a novel method that operates directly on the latent space of a generative model, specifically a Diffusion Autoencoder (DAE). This approach offers inherent interpretability by enabling the generation of CEs and the continuous visualization of the model’s internal representation across decision boundaries. Our method leverages the DAE’s ability to encode images into a semantically rich latent space in an unsupervised manner, eliminating the need for labeled data or separate feature extraction models. We show that these latent representations are helpful for medical condition classification and the ordinal regression of severity pathologies, such as vertebral compression fractures (VCF) and diabetic retinopathy (DR). Beyond binary CEs, our method supports the visualization of ordinal CEs using a linear model, providing deeper insights into the model’s decision-making process and enhancing interpretability. Experiments across various medical imaging datasets demonstrate the method’s advantages in interpretability and versatility. The linear manifold of the DAE’s latent space allows for meaningful interpolation and manipulation, making it a powerful tool for exploring medical image properties. Our code is available at <a href='https://github.com/matanat/dae_counterfactual'>https://github.com/matanat/dae_counterfactual</a>

Investigating the binding affinity, molecular dynamics, and ADMET properties of curcumin-IONPs as a mucoadhesive bioavailable oral treatment for iron deficiency anemia

Iron deficiency anemia (IDA) is a common health issue, and researchers are interested in overcoming it. Nanotechnology green synthesis is one of the recent approaches to making efficient drugs. In this study, we modeled curcumin-coated iron oxide nanoparticles (cur-IONPs) to study their predicted toxicity and drug-likeness properties, then to investigate mucoadhesive behavior by docking cur-IONPs with two main mucin proteins in gastrointestinal tract (GIT) mucosa (muc 5AC and muc 2). Furthermore, the stability of cur-IONPs/protein complexes was assessed by molecular dynamics. Our in-silico studies results showed that cur-IONPs were predicted to be potential candidates to treat IDA due to its mucoadhesive properties, which could enhance the bioavailability, time residency, and iron absorbance through GIT, in addition to its high safety profile with high drug-likeness properties and oral bioavailability. Finally, molecular dynamic simulation studies revealed stable complexes supporting strength docking studies. Our results focus on the high importance of in-silico drug design studies; however, they need to be supported with in vitro and in vivo studies to reveal the efficacy, toxicity, and bioavailability of cur-IONPs.

Specific isolation and quantification of PD-L1 positive tumor derived exosomes for accurate breast cancer discrimination via aptamer-functionalized magnetic composites and SERS immunoassay

PD-L1 positive tumor derived exosomes (TEXsPD−L1) play a significant role in disease progression, tumor metastasis and cancer immunotherapy. However, the overlap of PD-L1 between TEXs and non-tumor derived exosomes (non-TEXs) restricts the specific isolation and quantification of TEXPD−L1 from clinical samples. Herein, a new aptamer-functionalized and hydrophilic immunomagnetic substrate was designed by decorating generation 5 polyamidoamine dendrimers (G5 PAMAM), zwitterionic trimethylamine N-oxide (TMAO) and EpCAM (Epithelial cell adhesion molecule) aptamers on magnetic cores sequentially (Fe3O4@PAMAM@TMAO@Aptamer, named as FPTA) for rapid target and efficient capture of TEXs. The FPTA substrate gathered excellent characters of strong magnetic responsiveness of Fe3O4, abundant affinity sites of PAMAM, strong hydrophilicity of TMAO and enhanced affinity properties of EpCAM aptamers. Because of these advantages, FPTA can isolate TEXs quickly within 30min with high capture efficiency of 90.5 % ± 3.0 % and low nonspecific absorption of 8.2 % ± 2.0 % for non-TEXs. Furthermore, PD-L1 (Programmed cell death-ligand 1) positive TEXs (TEXsPD−L1) from the captured TEXs were recognized and quantitatively analyzed by utilizing SERS (surface-enhanced Raman spectroscopy) reporter molecules 4-NTP (4-Nitrothiophenol) on PD-L1 aptamers-functionalized gold immunoaffinity probe. The signal of TEXsPD−L1 was converted to SERS signal of 4-NTP at 1344 cm−1 which exhibited a linear correlation to concentration of TEXsPD−L1(R2 = 0.9905). With these merits, this strategy was further applied to clinical plasma samples from breast cancer (BC) patients and healthy controls (HC), exhibited an excellent diagnosis accuracy with area under curve (AUC) of receiver operating characteristic (ROC) curve reaching 0.988. All these results demonstrate that the FPTA immunomagnetic substrate combined with SERS immunoaffinity probe may become a generic tool for specific isolation and quantitative analysis of PD-L1 positive tumor-derived exosomes in clinics.

Highly Durable Chemoresistive Micropatterned PdAu Hydrogen Sensors: Performance and Mechanism.

Hydrogen (H2) is a promising alternative energy source for Net-zero, but the risk of explosion requires accurate and rapid detection systems. As the use of H2 energy expands, sensors require high performance in a variety of properties. Palladium (Pd) is an attractive material for H2 detection due to its high H2 affinity and catalytic properties. However, poor stability caused by volume changes and reliability due to environmental sensitivity remain obstacles. This study proposes a micropatterned thin film of PdAu with optimized composition (Pd0.62Au0.38) as a chemoresistive sensor to overcome these issues. At room temperature, the sensor has a wide detection range of 0.0002% to 5% and a fast response time of 9.5 s. Significantly, the sensor exhibits excellent durability for repeated operation (>35 h) in 5% H2 and resistance to humidity and carbon monoxide. We also report a negative resistivity change in PdAu, which is opposite to that of Pd. Density functional theory (DFT) calculations were performed to investigate the resistance change. DFT analysis revealed that H2 penetrates specific interstitial sites, causing partial lattice compression. The lattice compression causes a decrease in electrical resistance. This work is expected to contribute to the development of high-performance H2 sensors using Pd-based alloys.

On the v-Picard Group of Stein Spaces

Abstract We study the image of the Hodge–Tate logarithm map (in any cohomological degree), defined by Heuer, in the case of smooth Stein varieties. Heuer, motivated by the computations for the affine space of any dimension, raised the question whether this image is always equal to the group of closed differential forms. We show that it indeed always contains such forms but the quotient can be non-trivial: it contains a slightly mysterious $\mathbf{Z}_{p}$-module that maps, via the Bloch–Kato exponential map, to integral classes in the pro-étale cohomology. This quotient is already non-trivial for open unit disks of dimension strictly greater than $1$.

An invariant for affine maximal type equations

Let y:M→Rn+1 be a locally strongly convex hypersurface immersion of a smooth, connected manifold into the real affine space Rn+1, given as the graph of a smooth, strictly convex function xn+1=f(x1,...,xn) defined on a domain Ω⊂Rn. Considering the α-relative normalization of the graph of the convex function f, we will prove a Bernstein theorem for a class of nonlinear, fourth order partial differential equations of affine maximal type. As applications, we define an invariant of the equations and prove a rigidity result of the complete Tn-invariant Kähler metric on complex torus (C⁎)n with vanishing scalar curvature for n≤5.

Aqueous extract of CAP-ash: A greener benchmark for Suzuki-Miyaura coupling reaction in palladium catalyzed ligand-free condition

Synthesis, molecular, spectroscopic properties, and electronic structure calculations of biphenyls derivatives have been achieved using a highly efficient catalytic amount of Pd(OAc)2 in aqueous extract of custard apple peels (CAP)-ash (AECAP) a green, highly cost-effective, operationally convenient and environmentally benign media at ambient temperature. The analytical reports showed the presence of metal oxides which are probably extracted in water produces corresponding hydroxides, which provide alkaline media in water which shows dual performance (solvent and base) for said cross-coupling transformation. The catalytic system is generated in situ based on aqueous extract and Pd(OAc)2 which requires no external base and ligand. Moreover, the study also offers insights into the frontier molecular orbitals (FMO), electronegativity, chemical potential, global electrophilicity index, ionization potential, electron affinity, chemical hardness, and softness properties of the synthesized biphenyl derivatives for understanding their stability, active sites, and biological activity using density functional theory (DFT) at the B3LYP/6–311G(d,p) level/basis.

Characterizing an online, science-based affinity space using topic modelling, diversity indices, and social network analysis

Characterizing an online, science-based affinity space using topic modelling, diversity indices, and social network analysis

The primacy model and the structure of olfactory space.

Understanding sensory processing relies on the establishment of a consistent relationship between the stimulus space, its neural representation, and perceptual quality. In olfaction, the difficulty in establishing these links lies partly in the complexity of the underlying odor input space and perceptual responses. Based on the recently proposed primacy model for concentration invariant odor identity representation and a few assumptions, we have developed a theoretical framework for mapping the odor input space to the response properties of olfactory receptors. We analyze a geometrical structure containing odor representations in a multidimensional space of receptor affinities and describe its low-dimensional implementation, the primacy hull. We propose the implications of the primacy hull for the structure of feedforward connectivity in early olfactory networks. We test the predictions of our theory by comparing the existing receptor-ligand affinity and connectivity data obtained in the fruit fly olfactory system. We find that the Kenyon cells of the insect mushroom body integrate inputs from the high-affinity (primacy) sets of olfactory receptors in agreement with the primacy theory.

Identification of Difference Equations by Observations of Solutions with Perturbations from a Linear Manifold

Identification of Difference Equations by Observations of Solutions with Perturbations from a Linear Manifold

Affinity Uncertainty-Based Hard Negative Mining in Graph Contrastive Learning.

Hard negative mining has shown effective in enhancing self-supervised contrastive learning (CL) on diverse data types, including graph CL (GCL). The existing hardness-aware CL methods typically treat negative instances that are most similar to the anchor instance as hard negatives, which helps improve the CL performance, especially on image data. However, this approach often fails to identify the hard negatives but leads to many false negatives on graph data. This is mainly due to that the learned graph representations are not sufficiently discriminative due to oversmooth representations and/or non-independent and identically distributed (non-i.i.d.) issues in graph data. To tackle this problem, this article proposes a novel approach that builds a discriminative model on collective affinity information (i.e., two sets of pairwise affinities between the negative instances and the anchor instance) to mine hard negatives in GCL. In particular, the proposed approach evaluates how confident/uncertain the discriminative model is about the affinity of each negative instance to an anchor instance to determine its hardness weight relative to the anchor instance. This uncertainty information is then incorporated into the existing GCL loss functions via a weighting term to enhance their performance. The enhanced GCL is theoretically grounded that the resulting GCL loss is equivalent to a triplet loss with an adaptive margin being exponentially proportional to the learned uncertainty of each negative instance. Extensive experiments on ten graph datasets show that our approach does the following: 1) consistently enhances different state-of-the-art (SOTA) GCL methods in both graph and node classification tasks and 2) significantly improves their robustness against adversarial attacks. Code is available at https://github.com/mala-lab/AUGCL.

Recent Advances in Trifluoromethylation of Olefins, Aldehydes, and Ketones

: Due to the robust electrophilic properties of the trifluoromethyl group (-CF3), its incorporation into organic compounds can markedly alter their ester affinity, stability, bioavailability, and other properties. The trifluoromethylation reaction is currently experiencing rapid advancement, with an expanding array of substrates and the emergence of novel methodologies. Consequently, compounds containing the -CF3 moiety find extensive utility across diverse fields. This article aims to comprehensively review the latest advancements in trifluoromethylation reaction of olefins, aldehydes, and ketones, encompassing nucleophilic trifluoromethylation, electrophilic trifluoromethylation, and radical trifluoromethylation. The discussion includes an exploration of the types and broadening scope of applicable substrates. Furthermore, this article addresses the associated challenges and delineates prospective directions for future developments in trifluoromethyl reaction.