Normal Surfaces Research Articles

Non-symplectic involutions of normal K3 surfaces associated with Hirzebruch surfaces

For a non-symplectic involution g of a K3 surface X, the fixed point set of g and the quotient space X/⟨g⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X/\\langle g\\rangle $$\\end{document} are well studied. In this paper, we study a non-symplectic involution f of a normal K3 surface Y such that the smooth model of Y is a double cover K3 surface of a Hirzebruch surface and f is induced by its covering involution. We determine the fixed point set of f, the singular points of Y, and the quotient space Y/⟨f⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Y/\\langle f\\rangle $$\\end{document}.

Castelnuovo–Mumford regularity and splitting criteria for logarithmic bundles over rational normal scroll surfaces

We introduce and study a notion of Castelnuovo–Mumford regularity suitable for rational normal scroll surfaces. In this setting we prove analogs of some classical properties. We prove splitting criteria for coherent sheaves and a characterization of Ulrich bundles. Finally we study logarithmic bundles associated to arrangements of lines and rational curves.

Effects of Aging on Patellofemoral Joint Stress during Stair Negotiation on Challenging Surfaces.

This study examined the effect of age and surface on patellofemoral joint (PFJ) stress magnitude and waveform during stair ascent and descent tasks. A total of 12 young and 12 older adults had knee biomechanics quantified while they ascended and descended stairs on normal, slick, and uneven surfaces. The peak of stance (0-100%) PFJ stress and associated components were submitted to a two-way repeated measures ANOVA, while the PFJ stress waveform was submitted to statistical parametric mapping two-way ANOVA. During stair ascent, older adults exhibited greater PFJ stress waveforms, from 55 to 59% and 74 to 84% of stance (p < 0.001) as well as greater PFJ stress-time integral across stance (p = 0.003), and later peak PFJ stress, than young adults (p = 0.002). When ascending on the uneven surface, participants exhibited smaller PFJ stress from 9 to 24% of stance compared to the normal surface, but greater PFJ stress from 75 to 88% and from 63 to 68% of stance (p < 0.001) as well as greater PFJ stress-time integrals compared to normal and slick surfaces (p < 0.032). During stair descent, older adults exhibited a smaller PFJ contact area range (p = 0.034) and peak knee flexion angle (p = 0.022) than young adults. When descending on the slick surface, participants exhibited smaller PFJ stress from 5 to 18% of stance, but greater stress, from 92 to 98% of stance (both: p < 0.001), compared to the normal surface. Negotiating slick and uneven stairs may produce knee biomechanics that increase PFJ stress, and the larger, later PFJ stress exhibited by older adults may further increase their risk of PFJ pain.

Lectin-glycan interactions: a comprehensive cataloguing of cancer-associated glycans for biorecognition and bio-alteration: a review.

This comprehensive review meticulously compiles data on an array of lectins and their interactions with different cancer types through specific glycans. Crucially, it establishes the link between aberrant glycosylation and cancer types. This repository of lectin-defined glycan signatures, assumes paramount importance in the realm of cancer and its dynamic nature. Cancer, known for its remarkable heterogeneity and individualized behaviour, can be better understood through these glycan signatures. The current review discusses the important lectins and their carbohydrate specificities, especially recognizing glycans of cancer origin. The review also addresses the key aspects of differentially expressed glycans on normal and cancerous cell surfaces. Specific cancer types highlighted in this review include breast cancer, colon cancer, glioblastoma, cervical cancer, lung cancer, liver cancer, and leukaemia. The glycan profiles unveiled through this review hold the key to tailor-made treatment and precise diagnostics. It opens up avenues to explore the potential of targeting glycosyltransferases and glycosidases linked with cancer advancement and metastasis. Armed with knowledge about specific glycan expressions, researchers can design targeted therapies to modulate glycan profiles, potentially hampering the advance of this relentless disease.

MR imaging for preoperative characterization of pelvic adhesions: role in diagnosis and surgical planning.

Pelvic adhesions are nonanatomic connections between organs and normal peritoneal surfaces that develop secondary to a maladaptive inflammatory response to tissue insults. Comprised of fibrous tissue, adhesions can result in the distortion of operative dissection planes, which can complicate the establishment of abdominal access in patients undergoing surgery, prolong the length of surgery, and increase the risk of injury to bowel and other structures if involved by extensive adhesive disease. This can adversely impact patient outcomes by increasing the risk of surgical complications including bleeding, infection, and prolonging postoperative length of stay. Literature on the characterization of adhesions with imaging is limited and a systematic framework for evaluating adhesive disease on cross-sectional imaging of the pelvis does not currently exist. In this review, we discuss the MR imaging features of pelvic adhesions, highlighting unique teaching cases in which surgical exploration was significantly complicated by the presence of adhesive disease. We will also review the correlation between MR imaging and intraoperative findings in these cases. A proposed standardized framework for the detection and characterization of adhesions on pelvic MRI will be reviewed with multiple imaging examples. Identification and characterization of pelvic adhesive disease on preoperative imaging provides radiologists with an opportunity to inform the referring clinician of their presence, potentially improving outcomes and the quality of patient care.

Predicting the Shape of Corneas from Clinical Data with Machine Learning Models

ObjectiveIn ophthalmology, there is a need to explore the relationships between clinical parameters of the cornea and the corneal shape. This study explores the paradigm of machine learning with nonlinear regression methods to verify whether corneal shapes can effectively be predicted from clinical data only, in an attempt to better assess and visualize their effects on the corneal shape. MethodsThe dimensionality of a database of normal anterior corneal surfaces was first reduced by Zernike modeling into short vectors of 12 to 20 coefficients used as targets. The associated structural, refractive and demographic corneal parameters were used as predictors. The nonlinear regression methods were borrowed from the scikit-learn library. All possible regression models (method + predictors + targets) were pre-tested in an exploratory step and those that performed better than linear regression were fully tested with 10-fold validation. The best model was selected based on mean RMSE scores measuring the distance between the predicted corneal surfaces of a model and the raw (non-modeled) true surfaces. The quality of the best model's predictions was visually assessed thanks to atlases of average elevation maps that displayed the centroids of the predicted and true surfaces on a number of clinical variables. ResultsThe best model identified was gradient boosting regression using all available clinical parameters to predict 16 Zernike coefficients. The predicted and true corneal surfaces represented in average elevation maps were remarkably similar. The most explicative predictor was the radius of the best-fit sphere, and departures from that sphere were mostly explained by the eye side and by refractive parameters (axis and cylinder). ConclusionIt is possible to make a reasonably good prediction of the normal corneal shape solely from a set of clinical parameters. In so doing, one can visualize their effects on the corneal shape and identify its most important contributors.

Extensions of curves with high degree with respect to the genus

We classify linearly normal surfaces $S \subset \mathbf{P}^{r+1}$ of degree $d$ such that $4g-4 \leq d \leq 4g+4$, where $g&gt;1$ is the sectional genus (it is a classical result that for larger $d$ there are only cones). We apply this to the study of the extension theory of pluricanonical curves and genus $3$ curves, whenever they verify Property $N_2$, using and slightly expanding the theory of integration of ribbons of the authors and E.~Sernesi. We compute the corank of the relevant Gaussian maps, and we show that all ribbons over such curves are integrable, and thus there exists a universal extension. We carry out a similar program for linearly normal hyperelliptic curves of degree $d\geq 2g+3$. We classify surfaces having such a curve $C$ as a hyperplane section, compute the corank of the relevant Gaussian maps, and prove that all ribbons over $C$ are integrable if and only if $d=2g+3$. In the latter case we obtain the existence of a universal extension.

An integral version of Zariski decompositions on normal surfaces

An integral version of Zariski decompositions on normal surfaces

The Picard index of a surface with torus action

AbstractWe consider normal rational projective surfaces with torus action and provide a formula for their Picard index, that means the index of the Picard group inside the divisor class group. As an application, we classify the log del Pezzo surfaces with torus action of Picard number one up to Picard index $$ 10\,000 $$ 10 000 .

Bridgeland stability conditions on normal surfaces

We prove a new version of Bogomolov’s inequality on normal proper surfaces. This allows to construct Bridgeland’s stability condition on such surfaces. In particular, this gives the first known examples of stability conditions on non-projective, proper schemes.

Abstract PO2-23-12: Innovative Metastatic Breast Cancer Therapy, CBT300, Reverses Drug and Immune Resistance

Abstract For many patients with metastatic breast cancer (MBC), their disease is treatable but incurable. Although the rate of death from MBC has significantly decreased over the last 10 years due to early detection and new treatment options, MBC still accounts for over 40,000 deaths each year in the US that has been consistent for the past 30 years. Recently, it is estimated that 90% of those deaths were due to drug resistant recurrent disease. Nearly 45% of MBC deaths can be attributed to a subpopulation of patients with metastatic triple negative breast cancer (mTNBC). Despite MBC’s initial sensitivity to chemotherapy, it often recurs at greater than 40% in stage I-III patients and greater than 80% in stage IV patients which have a dismal 5-year survival of 12%. African American women have a 40% greater incidence of death from MBC despite a 4% lower risk of diagnosis. Unfortunately, current therapies do little to reduce drug resistance and death for recurrent drug resistant MBC. Currently, the only therapies approved by the FDA for recurrent TNBC patients are Keytruda plus chemotherapy and an Antibody Drug Conjugate (ADC) called Sacituzumab Govitecan. Keytruda (anti-PD-L1) is an immune checkpoint inhibitor(ICI) given with chemotherapy (nab-paclitaxel, paclitaxel, or gemcitabine plus carboplatin). The second recently approved therapy, Sacituzumab Govitecan (SG), is composed of an antibody to human trophoblast cell-surface antigen 2 (Trpo-2) coupled to SN-38 (topoisomerase I inhibitor). Although these results are very encouraging, the 80% of TNBC patients that either do not have high positive PD-L1 tumors, or don’t respond to these therapies and become drug resistant suggests that most patients with TNBC will have recurrent disease with little or no hope for survival. For contrast, our novel MBC therapy, CBT300, targets cell surface GRP78 that has been found in over 95% of MBC and in 93% of TNBC tumors. We can now show that inhibition of cell surface GRP78 can a) induce apoptosis of drug resistant TNBC cells in vitro and in vivo, b) eliminate drug resistance showing synergistic effects with chemotherapy in vitro and in vivo, c) decrease amount of chemotherapy in combination with CBT300 and d) reduce immune suppression. Recent publications show that GRP78 is found on many types of tumor cell surfaces but not on normal cell surfaces. In fact, tumor cell surface GRP78 (csGRP78) is important for many aspects of MBC development, including cell survival, proliferation, chemoresistance, angiogenesis, metastasis formation, immune suppression, and stem cell formation. Recently, it has been shown that increased cell surface GRP78 expression in TNBC patients was significantly associated with later stage, increased distant metastasis, increased aggressiveness, shorter disease-free survival, and decreased overall survival. In studies to help understand how cell surface GRP78 causes MBC progression and drug resistance, we discovered a novel GRP78 binding transmembrane protein on TNBC cells called Receptor Tyrosine Kinase Orphan Receptor-1 (ROR1). Using the GRP78 binding domain from ROR1 and a human Fc IgG1 domain, we created a biologic fusion protein that is a potent and cell surface specific GRP78 inhibitor, CBT300. We now show that CBT300’s elimination of cell surface GRP78 destabilizes and removes oncofetal proteins ROR1, Cripto-1, and checkpoint protein PD-L1 from tumor cell surfaces resulting in reversal of chemoresistance, reduction in immune suppression, inhibition of stem cell phenotype and increased tumor cell apoptosis. Since ROR1, Cripto-1 and PD-L1 are three of the major redundant pathways for tumor drug resistance, immune suppression and stem cell formation, the ability to inhibit all these pathways with CBT300, a single safe and very efficacious therapy, is very innovative and could be a significant advance for the treatment of MBC. Citation Format: Elizabeth Stolarik, Jorryn Zelek, Mariah Thigpen, Anita Davidson, Donald Davidson. Innovative Metastatic Breast Cancer Therapy, CBT300, Reverses Drug and Immune Resistance [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO2-23-12.

Influence of fluoride characteristics on tooth surface protection in an erosive condition: A multifaceted characterization approach.

To evaluate the effect of fluoride consistency and composition to protect enamel and dentin against the dental erosion. Bovine enamel and dentin specimens were treated with artificial saliva, neutral fluoride gel (NFG), acidulated phosphate fluoride gel (AFG), neutral fluoride foam (NFF), and acidulated phosphate fluoride foam. The samples were subjected to cycling. Micro energy-dispersive X-ray fluorescence spectrometry, surface roughness (Ra), contact angle (CA), and scanning electron microscopy (SEM) were performed. Composition, CA and Ra data were analyzed by ANOVA and multiple comparison test (p < 0.05). The dentin protected had a significantly higher mineral content than in the control. Eroded unprotected enamel had higher Ra values than normal surfaces. Fluoride treatments increased the Ra in dentin samples. AFG increased the CA in enamel. Fluoride foams increased CA in dentin with reduced mineral loss. SEM analysis found a deposited layer on enamel treated with AFG and remnants of deposits on dentin treated with NFG and NFF. Regardless of the form of application, fluoride provided protection against erosion, however with different levels. Applying the adequate fluoride form is relevant since the formulations have different effects on both enamel and dentin.

Three-Dimensional Turbulent Simulation of Bivariate Normal Distribution Protection Device

In response to the deficiencies in existing bridge pier scour protection technologies, this paper introduces a novel protective device, namely a normal distribution-shaped surface (BND) protection devices formed by rotating a concave normal curve. A three-dimensional turbulent SST k−ω model is constructed, and physical model experiments of conical surfaces are conducted to validate the mathematical model. The simulation analyzes longitudinal water flow, downflow, vorticity intensity, and shear stress within normal and conical surfaces. The results show that the downflow distribution in front of the pier spans a relative water depth of (−0.45, 0.67), with a peak velocity approximately 70% of the longitudinal flow velocity. Circulation forms within the surfaces, with the main vortex flux inside the BND being 33% lower than that inside the conical surface. The maximum shear stress coefficient inside the BND can reach 9, and the protective surface isolates the bed from the flow to prevent scouring by high shear stress. The velocity gradient at the edge of the surface is small, and the edge shear stress of the 3D normal distribution-shaped surface (BND) protection device is only one-third of that of the conical surface, preventing edge scouring. The large shear stress and its distribution area decrease monotonically with the increase in surface width. When the surface width is four times the diameter, the distribution range of the shear stress coefficient greater than 1 is very small. The study of three-Dimensional turbulence within the BND provides a numerical basis for an anti-scour design.

Abstract 4755: Extracellular GRP78 inhibition reverses drug and immune resistance in cancer cells

Abstract CBT300 was created from Creative BioTherapeutics’ discovery that drug resistant recurrent cancer cells up-regulate a survival pathway that results in the expression of extracellular Glucose-Regulated Protein 78 (ecGRP78) in the tumor microenvironment (TME). This TME ecGRP78 binds to cancer and immune cell surfaces, which induces a cascade of events to increase drug resistance, immune suppression, and cancer stem cell (CSC) formation. CBT300 targets surface bound ecGRP78 that has been found on breast, lung, ovarian, prostate, melanoma, multiple myeloma, colon, pediatric and adult brain tumors. We can now show that inhibition of ecGRP78 can a) induce apoptosis of drug resistant tumor cells, b) eliminate drug and immune resistance showing synergistic effects with chemotherapy and immunotherapy, c) decrease the amount of chemotherapy about 90% in combination with CBT300. Recent publications show that ecGRP78 is found on many types of tumor cell surfaces but not on normal cell surfaces. In fact, cell surface bound ecGRP78 is important for many aspects of cancer development, including cell survival, proliferation, chemoresistance, angiogenesis, metastasis formation, immune suppression, and stem cell formation. Recently, it has been shown that increased ecGRP78 expression in metastatic breast cancer, glioblastoma and multiple myeloma patients was significantly associated with later stage, increased distant metastasis, increased aggressiveness, shorter disease-free survival, and decreased overall survival. In studies to help understand how ecGRP78 causes tumor progression and drug and immune resistance, we discovered a novel ecGRP78 binding transmembrane protein on TNBC, and brain cancer cells called Receptor Tyrosine Kinase Orphan Receptor-1 (ROR1). Using the GRP78 binding domain from ROR1 and a human Fc domain, we created a biologic fusion protein that is a potent and specific ecGRP78 inhibitor called CBT300. We now show that CBT300’s elimination of csGRP78 destabilizes and removes oncofetal proteins ROR1, and Cripto, and checkpoint protein PD-L1 from tumor cell surfaces resulting in reversal of chemoresistance, reduction in immune suppression, inhibition of stem cell phenotype and increased tumor cell apoptosis. Our results with CBT300 demonstrate proof of concept data in vitro and in vivo for our novel ecGRP78 inhibitor on several drug resistant cancers demonstrating the potential to provide a major advance in the treatment of drug resistant cancers either alone or in combination with lower doses of chemotherapy. Exploiting a novel mechanism of action with a non-toxic, efficacious and cost effective biologic therapy that has shown increased survival in recurrent cancers will bring new hope for these patients. Citation Format: Donald J. Davidson, Jorryn Zelek, Elizabeth Stolarik, Mariah Thigpen, Anita Davidson, DPT. Extracellular GRP78 inhibition reverses drug and immune resistance in cancer cells [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 4755.

Enhancing automatic inspection and characterization of carbon fiber composites through hyperspectral diffuse reflection analysis and k-means clustering

Numerous industries utilize carbon fiber composites (CFC) for their exceptional strength-to-weight ratio and stiffness. However, inherent manufacturing defects such as voids and delamination can undermine the material’s structural integrity and performance. This study introduces an advanced imaging technique employing hyperspectral imaging (HSI) to effectively detect and characterize flaws within CFC materials. HSI provides high-resolution spectral data, enabling precise analysis of material properties. Initial observations indicate a distinctive peak variability in dispersed reflectance spanning 440 nm to 600 nm for both pristine surfaces and defective regions of CFC sheets. The proposed methodology entails the automated characterization of CFC through a combination of HSI and an advanced clustering technique, k-means clustering (k-mc). The application of k-mc facilitates rapid and accurate categorization of defect locations. Statistical analysis reveals mean and standard deviation (SD) values of 0.34 and 0.33, respectively, for normal CFC surfaces, compared to 0.43 and 0.29 for cracked CFC sections. These discernible variations enable precise differentiation between defect-free and defective CFC specimens. By employing spectral signatures at 445 nm, 546 nm, and 585 nm as optical markers, the study accurately measures fracture penetration depths. Implementation of this approach generates 3D-resolved images, offering a comprehensive visualization of CFC imperfections. The proposed methodology presents a more automated and objective strategy for defect identification and categorization. This unique approach holds significant potential for industrial applications, particularly in scenarios necessitating efficient and precise evaluation of numerous CFC components.

Aphids increase their rate of survival on emergent aquatic plants through niche construction.

Flooding or rain is a threat to many insects in nature, including herbivorous invertebrates whose hosts are emergent aquatic plants. They may thus have developed particular adaptations to withstand the flooding that is a feature of emergent plants' environment. The aphid Hyalopterus pruni (Hemiptera: Aphididae) modifies the physical and chemical conditions of its habitat by periodically spreading wax around itself with its hind legs. This behaviour constitutes a form of niche construction. We hypothesized that the aphid decreases its risk of death of own or around other individuals when submerged in water by spreading wax powder secreted from its body onto the leaves of its host plant, Phragmites australis. We compared the hydrophobicity of waxed and normal leaf surfaces. Next, we compared the survival rates of wax-powdering and nonwax-powdering aphids under submerged and rainy conditions in the laboratory and in the field. Finally, we examined whether the aphids' wax-powdering behaviour increased as a result of experiencing brief submergence or rain. The surface of the waxed area was significantly more water-repellent than the surface of unwaxed leaves. The waxed areas held air bubbles when under water. In experiments, aphids without wax around themselves exhibited lower survival rates: 22.9% in laboratory conditions and 15.7% in field conditions after 48 hr underwater. In contrast, aphids that secreted wax had higher survival rates, with 41.5% and 38.2% under laboratory and field conditions, respectively, after the same duration. Aphids exposed to rainfall showed similar results. Moreover, aphids that had experienced rain or submersion for 24 hr engaged in increased wax-powdering behaviour. These results indicate that aphids reduce their risk of drowning by powdering secreted wax onto the surface of leaves around them. Our findings suggest that niche construction by herbivorous invertebrates supports their ability to utilize host plants that grow under stressful conditions, such as emergent plants that are subject to periodic inundation.

Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space

&lt;abstract&gt;&lt;p&gt;In the present paper, we defined the circular evolutes and involutes for a given spacelike framed curve with respect to Bishop directions in Minkowski 3-space. Then, we studied the essential duality relations among parallel curves, normal surfaces, and circular evolutes and involutes. Furthermore, we also studied the duality relations of their singularities. Based on these studies, we found that it is crucially important to consider the duality relations among different geometric objects for the research of submanifolds with singularities.&lt;/p&gt;&lt;/abstract&gt;

Bounding geometrically integral del Pezzo surfaces

Abstract We prove several boundedness statements for geometrically integral normal del Pezzo surfaces X over arbitrary fields. We give an explicit sharp bound on the irregularity if X is canonical or regular. In particular, we show that wild canonical del Pezzo surfaces exist only in characteristic $2$ . As an application, we deduce that canonical del Pezzo surfaces form a bounded family over $\mathbb {Z}$ , generalising work of Tanaka. More generally, we prove the BAB conjecture on the boundedness of $\varepsilon $ -klt del Pezzo surfaces over arbitrary fields of characteristic different from $2, 3$ and $5$ .

Boundedness in families with applications to arithmetic hyperbolicity

AbstractMotivated by conjectures of Demailly, Green–Griffiths, Lang and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the persistence of arithmetic hyperbolicity along field extensions for projective normal surfaces with non‐zero irregularity. These results rely on the mild boundedness of semi‐abelian varieties. We also introduce and study the notion of pseudo‐algebraic hyperbolicity which extends Demailly's notion of algebraic hyperbolicity for projective schemes.

Singularities of normal quartic surfaces, III : char = 2, nonsupersingular

Singularities of normal quartic surfaces, III : char = 2, nonsupersingular