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In this paper, the solution of the one-dimensional second-order unsteady nonlinear fuzzy partial differential Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite unconfined aquifer bordering a lake. In the examined problem, there is a sudden rise and subsequent stabilization of the lake's water level, thus the aquifer is recharging from the lake. The aquifer boundary conditions are considered fuzzy and, therefore, ambiguities are created to the solution of the overall physical problem. Then, the fuzzy problem is translated to a system of crisp boundary value problems. By using a Boltzmann transformation, the crisp problem is transformed into an integro-differential equation and solved with the help of a special numerical method. This method has a simple iterative procedure, which converges rapidly and is proven very accurate in comparison with other analytical methods. Additionally, the algebraic equation estimates very close to the storage coefficient, the flux at the stream-aquifer origin, and the water stored volume with respect to other exact solutions. This method is very useful for practical cases (artificial recharge problems, irrigation, and drainage projects), giving the possibility to decision-makers to take the right decision.

Introduction: Despite initial efficacy, most patients (pts) with HR+/HER2– advanced breast cancer (BC) eventually progress on endocrine therapy (ET) plus a CDK4/6 inhibitor (CDK4/6i). In preclinical models, resistance to ET + CDK4/6i can be overcome by concomitant inhibition of CDK2. Therefore, simultaneous inhibition of CDK2/4/6 may provide a new therapeutic strategy to prolong clinical benefit. This first-in-human dose escalation/expansion study (NCT03519178) is evaluating the safety, pharmacokinetics (PK), pharmacodynamics (PD) and preliminary antitumor activity of the first-in-class selective CDK2/4/6 inhibitor PF-06873600 (PF-3600) as monotherapy and combined with ET. The results of Part 1 monotherapy dose escalation and initial combination with ET are presented.Methods: This is a phase 1/2a, open-label, non-randomized, study of PF-3600 as monotherapy and combined with letrozole or fulvestrant (F). Pts with locally advanced/metastatic HR+/HER2– BC whose tumor progressed on previous ET + CDK4/6i and with ≤2 prior lines of chemotherapy (Cx), triple-negative breast cancer (TNBC) with ≤2 prior lines of Cx, and platinum-resistant ovarian cancer (OVCA) with ≤3 prior lines of treatment (Tx) were eligible for Part 1 dose escalation. Pts received escalating doses of PF-3600 (1–50 mg) BID orally. Dose escalation followed the modified toxicity probability interval method. Tx continued until disease progression, toxicity requiring discontinuation or pt withdrawal. Primary objectives for Part 1 were to evaluate safety including dose-limiting toxicities (DLTs) in the 1st 28-day cycle, adverse events (AEs), and laboratory abnormalities; and to select the recommended dose for expansion (RDE) in combination with ET. Results: As of 24 June 2021, 67 pts (HR+/HER2– BC, n=59; TNBC, n=2; OVCA, n=6) received PF-3600 (n=58) or PF-3600 + F (n=9). In the PF-3600 group, 22 (38%) and 36 (62%) pts had ECOG performance status (PS) 0 and 1, respectively. In the PF-3600 + F group, 6 (67%) and 3 (33%) pts had ECOG PS 0 and 1, respectively. The median (range) number of prior Tx in the metastatic setting was 4.0 (1, 8) for PF-3600 and 4.0 (3, 6) for PF-3600 + F. The most frequently reported treatment-related AEs (all grade/grade ≥3) for PF-3600 alone and PF-3600 + F, respectively, were nausea (50%/0% and 67%/0%), anemia (38%/14% and 44%/11%) and neutropenia (29%/16% and 22%/11%). Six (13%) of 48 DLT-evaluable pts treated with monotherapy had DLTs; all occurred at the highest doses (35 and 50 mg BID). At the RDE of 25 mg BID (PF-3600 alone, n=17; PF-3600 + F, n=9), there were no DLTs. PF-3600 exposure increased with dose, was not significantly impacted by F and at the RDE remained above the preclinical efficacious concentrations in most of the tested models for >70% of the dosing interval. The disease control rate was 48% (28/58, PF-3600) and 67% (6/9, PF-3600 + F) including 3 pts who remained stable for >13 mos with one ongoing for >28 mos. Three heavily pre-treated pts with HR+/HER2– BC (including prior ET + CDK4/6i and Cx) treated with PF-3600 alone had partial responses (2 confirmed), including 1 pt who remained on Tx for >13 mos. Modulation of cell cycle PD biomarkers (pRb and Ki-67) in paired tumor biopsies was observed. Data are not final and subject to change. Updated data will be presented.Conclusions: PF-3600 can be combined with ET with a manageable AE profile and demonstrates promising preliminary antitumor activity in heavily pretreated pts, including those with HR+/HER2– BC progressing on ET + CDK4/6i and Cx. Dose expansion in combination with ET in pts with HR+/HER2– BC with and without prior CDK4/6i Tx is ongoing. Citation Format: Timothy A. Yap, Cynthia Basu, Jonathan W. Goldman, Michael Gordon, Erika Hamilton, Adrianne Kelly, Feng Liu, Allison R. Moreau, Heather Neumann, Kyriakos Papadopoulos, Hope S. Rugo, Geoffrey I. Shapiro, Shaveta Vinayak, Li Zhou, Komal Jhaveri. A first-in-human phase 1/2a dose escalation/expansion study of the first-in-class CDK2/4/6 inhibitor PF-06873600 alone or with endocrine therapy in patients with breast or ovarian cancer [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P5-16-06.

Introduction: Many patients do not benefit from immunotherapies targeting immune checkpoints such as PD(L)-1 due to a variety of resistance mechanisms. The AhR pathway is downstream of the Trp-IDO/TDO-Kyn axis. High levels of immune-suppressive AhR-activating ligands, such as kynurenine derived from IDO1/TDO2-expressing tumors, have been implicated as a potential resistance mechanism and are associated with poor responses to PD-1 therapies. Compared with inhibition of IDO1/TDO2 alone, direct AhR inhibition can block the activation of this transcription factor and may better counteract immune suppression. BAY2416964 is a novel, oral AhR inhibitor currently in a Phase I clinical trial in patients with solid tumors. Preclinically, BAY2416964 can block the activation of AhR by kynurenine and relieve its immune-suppressive effects, thereby restoring anti-tumor T-cell activity, reducing the level of inhibitory myeloid-derived suppressor cells and regulatory T cells, and improving the effectiveness of PD-1 blockade. We have analyzed PK and biomarker data from the ongoing monotherapy dose-escalation study to explore a potential optimal dose and schedule for effective AhR inhibition. Methods: PK data were intensely sampled from patients in 10 different groups with different dosing regimens (once and twice daily) and various food-intake scenarios. AhR downstream target gene expression after ex vivo kynurenic acid stimulation of patients’ peripheral blood mononuclear cells (PBMCs) was assessed. A population PK (popPK) model was developed and calibrated to characterize the PK of BAY2416964 across treatment groups. This model accounts for the non-linear relationship between dose and bioavailability as well as the effect of food intake. Results: The preliminary popPK model identified a non-linear relationship between the BAY2416964 dose and its (relative) bioavailability which was dependent on the respective food condition. The popPK model was able to describe the clinical BAY2416964 plasma exposures from all dose groups, including the effect of food intake. Ex vivo analysis of PBMCs showed inhibition of kynurenic acid-induced AhR downstream gene expression (such as CYP1A1, CYP1B1), suggesting effective in vivo target engagement in the doses tested. Conclusion: This modeling-based PK analysis along with target engagement in peripheral blood informed the posology to be tested in the dose-expansion part of the ongoing clinical trial. Citation Format: Kyriakos Papadopoulos, Michael Cecchini, Juanita S. Lopez, Dirk Jäger, Ki Young Chung, Michael Platten, Florian Prinz, Yuko Ishii, David Schaer, Ilona Gutcher, Gabriele Leder, Radost Pencheva, Thomas Wagener, Christian Scheerans, Carsten Zieschang, Andrea Wagner, Spyros Stamatelos, Ecaterina Dumbrava. Preliminary analysis of pharmacokinetic (PK) and target engagement biomarkers from a first in human phase 1 study of immunomodulatory aryl hydrocarbon receptor (AhR) inhibitor BAY2416964 [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 2 (Clinical Trials and Late-Breaking Research); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(8_Suppl):Abstract nr CT276.

Background: Isocitrate dehydrogenase 1/2 (IDH1/2) is mutated in a subset of cholangiocarcinoma (CCA), gliomas, and other solid tumors. LY3410738 is a potent, selective, covalent, dual inhibitor of IDH1/2 mutations (IDH1/2m). LY3410738 binds covalently at a novel binding site, enabling continued potency in preclinical models in the setting of second site IDH resistance mutations. We present initial results from the first-in-human phase 1 study of oral LY3410738 in patients (pts) with IDH1/2m CCA, and IDH1m glioma or other solid tumors. Methods: Dose escalation (3+3 design) evaluated LY3410738 monotherapy in advanced IDHm CCA and other solid tumors (NCT04521686). Key objectives included determining the RP2D, safety, PK, PD (inhibition of plasma D-2-HG), and preliminary antitumor activity. Results: As of 28 July 2022, 80 pts including 42 with CCA (33 IDH1m, 9 IDH2m), 27 with glioma (IDH1m), and 11 other tumor types (IDH1m) received LY3410738 dosed at 25-600 mg QD or 300 mg BID. Pts were median 52 years of age (range, 23-80) with a median of 2 prior therapies (range, 1-7). 19% of CCA pts had received prior IDH1 inhibitor. Median time on treatment was 3.7 months (range, 0.1-19). No DLTs or treatment related deaths were observed; the MTD was not reached. Treatment emergent adverse events (TEAEs) ≥15% included nausea (35%), vomiting (21%), and decreased appetite (19%) and were mostly grade 1-2. Most frequent grade ≥3 TEAEs >2% were anemia (4%), cholangitis (3%), headache (3%), decreased lymphocyte count (3%), and hyponatremia (3%). LY3410738 exposure was dose proportional. In pts with IDH1m cancers, LY3410738 achieved sustained D-2-HG inhibition at all dose levels, including in pts who received prior IDH1 inhibitor. In pts with IDH2m cancers, a higher dose (≥150 mg daily dose) was required for D-2-HG inhibition. Among the 42 pts with R/R CCA, the best response included 1 PR and 22 SD. Of the 22 glioma pts with contrast enhancing tumors, best response included 3 PR and 9 SD. Conclusions: LY3410738 demonstrated a favorable safety profile with potent and sustained D-2-HG inhibition in pts with IDH1/2m advanced solid tumors. Consistent with the expectations for IDH inhibitor monotherapy in this setting, CCA and glioma pts exhibited prolonged stable disease. RP2D evaluation is ongoing. Updated data on LY3410738 monotherapy will be presented at the meeting. Citation Format: Jordi Rodon, Lipika Goyal, Teresa Macarulla Mercade, Masafumi Ikeda, Shunsuke Kondo, Do-Youn Oh, Li-Yuan Bai, Makoto Ueno, Antoine Italiano, Kyriakos Papadopoulos, David Spigel, Sani H. Kizilbash, Rasha Cosman, Joon Oh Park, Li-Tzong Chen, Tomoya Yokota, Anita A. Turk, Chih-Yi Liao, Rachna Shroff, Anthony El-Khoueiry, Taroh Satoh, Antoine Hollebecque, Mitesh J. Borad, Nilofer Azad, Kurt A. Jaeckle, Herbert H. Loong, Jorge Adeva, Wei Peng Yong, Junjie Zhao, Hui Liu, Anna M. Szpurka, Ivelina Gueorguieva, Kamnesh R. Pradhan, Xiaojian Xu, James J. Harding. A first-in-human phase 1 study of LY3410738, a covalent inhibitor of mutant IDH, in advanced IDH-mutant cholangiocarcinoma and other solid tumors [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 2 (Clinical Trials and Late-Breaking Research); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(8_Suppl):Abstract nr CT098.

Background: Mechanisms of resistance to CDK4/6 inhibitors (CDK4/6i) have been well studied and several alterations identified including RB loss and altered expression of related genes including CCNE1, E2F4 and CDK6. However, whether duration of clinical treatment might elicit specific mechanism(s) of CDK4/6i resistance is unclear. To better understand if duration of clinical treatment correlates with unique resistance mechanisms, we established, characterized, and compared a panel of ER+ breast XPDX models from patients who benefitted then progressed on a CDK4/6i. Patients were separated into two groups by time to progression (TTP): those who responded up to twelve months (RES12) and patients with clinical response greater than one year (RES13+). Methods: Seventeen breast cancer XPDX models were analyzed, including eight previously described (7xRES12; 1xRES13+: SABCS2021: T Hernandez et al). Nine new models were established from seven patients: six from fluid samples with three designated as ductal (ST3105B, ST3105C, STM001B) and three lobular carcinoma (STM182, STM229, STM229B); two from lymph node biopsies (ST5676, STM127) and one from a liver core biopsy (ST4887B), all reported as ductal carcinoma. STM182 was classified as RES12 and the remaining eight as RES13+. These models were passaged and challenged with CDK4/6i to confirm resistance. Receptor expression was determined by IHC and genomic analyses including WES and RNAseq, were performed to identify mechanisms of resistance. For in vivo studies, CDK4/6i were dosed PO once daily at 50 mg/kg; endpoints included tumor volume (TV) and time from treatment initiation (TTI) with %T/C values and tumor regression reported at study completion; a %T/C of ≤20 versus control was considered sensitive. Tumor regression (%T/C Results: Clinical TTP for RES12 (n=8) was four to twelve months and RES13+ (n=9) from thirteen to forty-two months. All models retained ER expression in evaluated passages with similar histology compared with archival clinical samples. Sequencing identified several variants including RB1 truncations or deletions and increased gene expression in CCND1, CCNE1 and the PIK3CA/AKT pathway. Interestingly, 5/8 RES12 models reported ESR1 mutations or fusions versus 1/9 RES13+ and PIK3CA mutations were reported in 1/8 RES12 versus 5/9 RES13+. Several RES13+ models also reported variants and increased amplification in the RICTOR/TORC2 pathway versus RES12. Conclusion: We have established, characterized, and compared a panel of seventeen breast XPDX models from fourteen female patients representing early or late acquired resistance to CDK4/6i therapy and identified potential differences in each set. These models and resulting data are useful in developing novel therapies for CDK4/6i-resistant patients. Citation Format: Alyssa Simonson, Johnnie Flores, Morgan Lynch, Emily Carpenter, Justine Hruzek, Jim Lund, Natalia Baños Herraiz, Kyriakos Papadopoulos, Amy Vander Woude, Gladys Rodriguez, Sreenivasa Chandana, Thomas Gribbin, Nehal Lakhani, Tatiana Hernandez, Maria Jose de Miguel, Amy Lang, Michael J. Wick. Short or long-term treatment with CDK4/6 inhibitors in patients with ER+ breast cancer: characterization and comparative analysis of resistance in seventeen XPDX models. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 3869.

In this article, we examine the solution of the fuzzy linear vertical infiltration equation, which represents the water movement in porous media in that part which is called the vadose zone. This zone is very important for semi-arid areas, due to complex phenomena related to the moisture content in it. These phenomena concern the interchange of moisture content between the vadose zone and the atmosphere, groundwater and vegetation, transfer of moisture and vapor and retention of moisture. The equation describing the problem is a partial differential parabolic equation of second order. The calculation of water flow in the unsaturated zone requires the knowledge of the initial and boundary conditions as well as the various soil parameters. But these parameters are subject to different kinds of uncertainty due to human and machine imprecision. For that reason, fuzzy set theory was used here for facing imprecision or vagueness. As the problem concerns fuzzy differential equations, the generalized Hukuhara (gH) derivative was used for total derivatives, as well as the extension of this theory for partial derivatives. The results are the fuzzy moisture content, the fuzzy cumulative infiltration and the fuzzy infiltration rate versus time. These results allow researchers and engineers involved in Irrigation and Drainage Engineering to take into account the uncertainties involved in infiltration.

Very well-drained lands could have a positive impact in various soil health indicators such as soil erosion and soil texture. A drainage system is responsible for properly aerated soil. Until today, in order to design a drainage system, a big challenge remained to find the subsurface drain spacing because many of the soil and hydraulic parameters present significant uncertainties. This fact also creates uncertainties to the overall physical problem solution, which, if not included in the preliminary design studies and calculations, could have bad consequences for the cultivated lands and soils. Finding the drain spacing requires the knowledge of the unsteady groundwater movement, which is described by the linear Boussinesq equation (Glover-Dumm equation). In this paper, the Adomian solution to the second order unsteady linear fuzzy partial differential one-dimensional Boussinesq equation is presented. The physical problem concerns unsteady drain spacing in a semi-infinite unconfined aquifer. The boundary conditions, with an initially horizontal water table, are considered fuzzy and the overall problem is translated to a system of crisp boundary value problems. Consequently, the crisp problem is solved using an Adomian decomposition method (ADM) and useful practical results are presented. In addition, by application of the possibility theory, the fuzzy results are translated into a crisp space, enabling the decision maker to make correct decisions about both the drain spacing and the future soil health management practices, with a reliable degree of confidence.

In this article, we examine the solution to the fuzzy linear absorption equation, which represents the water movement in a horizontal column and describes the wetting up of the column under tension. The parameters of this problem are subject to different kinds of uncertainty due to human and machine imprecision. For that reason fuzzy set theory was used for facing imprecision or vagueness. As the problem concerns fuzzy differential equations, the Generalised Hukuhara (gH) derivative was used for total derivatives, as well as the extension of this theory for partial derivatives.

We first observe that the Path topology of Hawking, King and MacCarthy is an analogue, in curved space-times, of a topology that was suggested by Zeeman as an alternative topology to his so-called Fine topology in Minkowski space-time. We then review a result of a recent paper on spaces of paths and the Path topology, and see that there are at least five more topologies in the class $$\mathfrak{Z}-\mathfrak{G}$$ of Zeeman-Gobel topologies which admit a countable basis, incorporate the causal and conformal structures, but the Limit Curve Theorem (LCT) fails to hold. The “problem” that the LCT does not hold can be resolved by “adding back” the light cones in the basic-open sets of these topologies, and create new basic open sets for new topologies. But, the main question is: do we really need the LCT. to hold, and why? Why is the manifold topology, under which the group of homeomorphisms of a space-time is vast and of no physical significance (Zeeman), more preferable than an appropriate topology in the class $$\mathfrak{Z}-\mathfrak{G}$$ under which a homeomorphism is an isometry (Gobel)? Since topological conditions that come as a result of a causality requirement are key in the existence of singularities in general relativity, the global topological conditions that one will supply the space-time manifold might play an important role in describing the transition from a quantum nonlocal theory to a classical local theory.

Selected salicylidene imines were evaluated for their antioxidant and cytotoxic potentials. Several of them exerted potent scavenging capacity towards ABTS radical and hydrogen peroxide. The insight into the preferable antioxidative mechanism was reached employing density functional theory. In the absence of free radicals, the SPLET mechanism is dominant in polar surroundings, while HAT is prevailing in a non-polar environment. The results obtained for the reactions of the most active compounds with some medically relevant radicals pointed out competition between HAT and SPLET mechanisms. The assessment of their cytotoxic properties revealed inhibition of ER-a human breast adenocarcinoma cells or estrogen-independent prostate cancer cells. Molecular docking study with the cyclooxygenase (COX) 2 enzyme was performed to examine the most probable bioactive conformations and possible interactions between the tested derivatives and COX-2 binding pocket.

The optimal approach for Transcatheter aortic valve implantation (TAVI) is the transfemoral access but alternative TAVI approaches offer the possibility of valve replacement in patients who are not eligible to the transfemoral route. This review paper intends to compare the current available alternative approaches for TAVI in terms of their safety and efficacy, based on the current literature. The transapical, transaortic, transsubclavian, transcarotid, transcaval and suprasternal approaches have been analyzed. The choice of the alternative approach dependents on local Heart Team expertise, patient specific characteristics, access specific characteristics and the need or not for general anesthesia. More studies are needed to investigate the impact of each individual approach on long-term outcomes.

Background: Preclinical models of prostate cancer are challenging to develop and maintain, especially those that grow in a castrated setting while maintaining receptor and antigen expression. To this end, we have established and characterized a panel of XenoSTART patient-derived (XPDX) prostate models using both intact and castrated athymic nude mice. These models, designated ST1273, ST2347, ST4017, and ST4420, were characterized for receptor expression, genomic alterations, and in vivo drug sensitivity to relevant therapies. Methods: XPDX models representing prostate cancer were established from primary (ST1273) or metastatic (ST2347, ST4017, ST4420) biopsy samples implanted into intact athymic nude mice supplemented with exogenous testosterone. Resulting models were passaged and further developed in both intact and castrated athymic nudes until growth stabilization. Resulting models were characterized using genomic analysis, including WES and RNAseq, receptor expression, and in vivo drug sensitivity studies. Models found sensitive to enzalutamide were conditioned to resistance in vivo by chronic drug administration and resulting models (designated STxxxx/EZR) were characterized and compared with parent lines. For in vivo studies, activity of relevant treatments were benchmarked including enzalutamide administered once daily by oral gavage at 50 mg/kg and docetaxel administered by intravenous injection once weekly at 10 mg/kg. In vivo study endpoints included tumor volume and time from treatment initiation with %T/C values and tumor regression reported at study completion; a %T/C of ≤ 20 versus control was considered sensitive. Results: Each model developed in a castrate or conditioned setting retained similar receptor expression to the parent model including positive AR (2+/3+) and PSMA (2+/3+) staining. Genomic characterization identified a PIK3CA mutation in ST1273 models (PIK3CAE545A), AR mutations in ST2347 (ART878A) and ST4017 (ARH875Y), and a TMPRSS2:ERG fusion in ST4420. In vivo, the ST1273 parent model was found sensitive to enzalutamide (%T/C=11%) but insensitive in castrated mice (%T/C=76%) and the ST1273/EZR model was resistant to enzalutamide in intact (%T/C=56%) or castrated (%T/C=100%) mice. The ST2347 parent model was also found sensitive to enzalutamide (%T/C=19%) but insensitive in castrated mice (%T/C=50%). ST4017 and ST4420 studies in intact and castrated mice are currently underway. All models were sensitive to docetaxel. Conclusion: We have established and characterized a panel of prostate XPDX models using both intact and castrated athymic nude mice and conditioned resistance to enzalutamide by chronic drug administration. These models can be utilized as a valuable tool in better understanding castrate-resistant prostate cancer and in developing novel therapies for enzalutamide-resistant patients. Citation Format: Johnnie Flores, Alyssa Simonson, Dustin Kneifel, Alejandra Diaz, Morgan Harris, Kyriakos Papadopoulos, Amita Patnaik, Drew Rasco, Scott Ulmer, Michael J. Wick. Establishment and characterization of a panel of castrate-resistant prostate cancer XPDX models with differential enzalutamide response [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 3109.

Background: First-line treatment for some cancer types includes platinum-based therapy. While the rate of initial response to treatment is high, most patients develop platinum-resistant disease. Current salvage therapy provides benefit to some patients, demonstrating the need for additional effective therapies. To assist in identifying new therapies, we have established XenoSTART patient-derived xenograft (XPDX) models representing breast, ovary, uterine, and lung cancers. Each model was characterized by DNA/RNA analysis, sensitivity to platinum treatment, and annotated with donor patient treatment status at the time of sample collection. Methods: 210 XPDX models were evaluated in this screen including 66 breast, 56 ovary, 36 uterine, and 52 lung xenografts. WES and RNAseq were performed on each model and patient treatment history and outcome annotated. For in vivo studies, models were implanted into female nudes and administered (IP; q7dx3) 3 m/k cisplatin or 60 m/k carboplatin. Study endpoints included tumor volume and time from treatment initiation with %T/C values and tumor regression reported at study completion; a %T/C of ≤ 20 versus control was considered sensitive. Results: Study results are summarized below in Table 1: Sequencing identified several variants in resistant, chemo-naïve models including point mutations in RAS/RAF/MET/PIK3CA genes and others, while sensitive models lacked common driver mutations. Conclusion: We have characterized 210 XPDX models. Uterine models were most often resistant to platinum, while almost 1/2 of ovary and 1/3 of breast models were sensitive, regardless of treatment status. Only 15% of lung models were sensitive to platinum; cancer driver variants were found in several models. Overall, we report differential platinum sensitivity in a panel of diverse models useful in understanding mechanisms of resistance and for development of effective therapies in platinum-resistant cancers. Table 1. Type Breast Ovary Uterine Lung Total 66 56 36 52 # Sensitive 25 25 9 8 % 38% 45% 25% 15% Naïve 11 16 8 5 % 44% 64% 89% 63% P-1st 6 6 1 2 % 24% 24% 11% 25% P-2nd+ 6 3 0 1 % 24% 12% 0% 13% # Insensitive 41 31 27 44 % 62% 55% 75% 85% Naïve 11 9 20 21 % 27% 29% 74% 48% P-1st 14 10 5 13 % 34% 32% 19% 30% P-2nd+ 16 12 2 10 % 39% 39% 7% 23% Naïve=No Prior Treatment; P-1st=Post 1st Line Therapy; P-2nd=Post 2nd+ Line Therapy Citation Format: Alyssa Simonson, Johnnie Flores, Lizette Firova, Christian Hernandez, Morgan Harris, Kyriakos Papadopoulos, Drew Rasco, Amita Patnaik, Allan White, Lon Smith, Ronald Drengler, Amy Lang, Murali Beeram, Michael J. Wick. Correlation of platinum sensitivity with donor patient treatment status in a panel of breast, ovary, uterine, and lung XPDX models [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 1092.

Background: Neuregulin-1 (NRG1) rearrangements drive cancers by binding to ERBB3/ERBB2 heterodimers and activating downstream signaling. NRG1 fusion proteins have recently been identified in several cancer types including lung and ovary. To better understand the role of NRG1 fusions in cancer we established three XenoSTART patient-derived xenograft (XPDX) models driven by NRG1 rearrangements including two CD74-NRG1 lung models designated ST2891 and ST3204 and one SARAF-NRG1 ovary model designated ST2476. These models were established in athymic nude mice and characterized for receptor expression, genomic alterations, and in vivo drug sensitivity. Methods: ST2891 was established from an excision biopsy collected from a 68-year-old male with NSCLC following treatment with carboplatin/paclitaxel and carboplatin/pemetrexed. ST3204 was established from a lymph node biopsy collected from a 63-year-old female with NSCLC following treatment with cisplatin/pemetrexed. ST2476 was established from primary tissue collected from a chemo naïve 61-year-old female with ovarian cancer. The resulting models were passaged and characterized using immunohistochemical and genomic analysis including WES and RNAseq. In vivo studies were performed testing various chemotherapy and targeted agents; study endpoints included tumor volume and time from treatment initiation with %T/C values and tumor regression reported at study completion; a %T/C of ≤ 20 versus control was considered sensitive. Tumor regression (%T/C Results: All models reported ERBB2 and ERBB3 staining in evaluated passages with similar histology compared with archival clinical samples. WES analysis of the three models did not identify any variants in EGFR/ERBB2-4/RAS/RAF genes. RNA sequencing revealed CD74-NRG1 or SARAF-NRG1 gene fusions independently confirmed using molecular studies. In vivo, both lung models were resistant to weekly cisplatin or T-DM1 and daily palbociclib (50 mg/kg) or daily afatinib up to 10 mg/kg. ST3204 was found sensitive to weekly pertuzumab (1 mg/kg). Both lung models were resistant to trastuzumab (1 mg/kg). The ST2476 ovary XPDX was found resistant to endocrine therapies and reported some sensitivity to weekly cisplatin. Conclusion: We have established and characterized a panel of three XPDX models driven by NRG1 rearrangements including two CD74-NRG1 lung models and one SARAF-NRG1 ovary model. These models are valuable tools for further developing therapies targeting NRG1-driven cancers. Citation Format: Alyssa Simonson, Johnnie Flores, Crystal Moreno, Justine Hruzek, Kyriakos Papadopoulos, Drew Rasco, Amita Patnaik, Ronald Drengler, Allan White, Jun Ma, Michael J. Wick. Establishment and characterization of neuregulin-1 (NRG1) fusion driven XPDX models [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 353.

Background: We previously reported (RAS AACR 2022) a preclinical screen testing KRASG12C-inhibitors (KRASG12C-i) in 13 colorectal and 13 lung KRASG12C XPDX models; all tested models were from patients naïve to KRASG12C-i. To better understand mechanisms of resistance in this agent class, we established three lung XPDX models designated ST5185B, ST5431B, and ST5489 from patients before therapy with a KRASG12C-i. We also established one colorectal XPDX, designated ST4859, post therapy. Once established these models were molecularly characterized, in vivo sensitivity to sotorasib and adagrasib determined, and results compared with clinical response. Ex vivo cultures and 3D-XPDX࣪ studies were also performed evaluating both compounds comparing drug sensitivity. Methods: Lung: ST5185B was established from a pretreated 68-year-old male; ST5431B was established from a chemo-naïve 67-year-old male; additional samples were collected during and after progression on KRASG12C-i and are currently in development. ST5489 was established from a pretreated 64-year-old female. CRC: ST4859 was established from a 57-year-old female pretreated with a KRASG12C-i; all patients received at least one cycle of KRASG12C-i therapy. Models were WES and RNA sequenced and sotorasib and adagrasib sensitivity determined. For each study, agents were dosed PO once daily at 100 mg/kg; study endpoints included tumor volume and time from treatment initiation with %T/C values reported at study completion; a %T/C of ≤ 20% was considered sensitive. Results: In all models sequencing confirmed KRASG12C and other variants previously identified with clinical studies. In vivo studies identified ST5185B as resistant to sotorasib (%T/C=70%) and adagrasib (%T/C=86%); this donor patient progressed after six weeks on KRASG12C-i therapy. ST5431B reported sensitivity to both therapies; this donor patient had a partial response (50% decrease) for six months prior to progression. ST5489 reported sensitivity to sotorasib (%T/C=14%) and adagrasib (%T/C=8%); this donor patient interrupted dosing due to KRASG12C-i intolerance and discontinued therapy, with disease progression after five weeks. ST4859 reported resistance to both drugs; this donor patient had stable disease on KRASG12C-i therapy for approximately seven months prior to progression. Ex vivo cultures and 3D-XPDX࣪ studies from all models reported sensitivity to both agents similar to in vivo studies. Summary: We developed, evaluated, and correlated in vivo sensitivity of sotorasib and adagrasib in a panel of four XPDX models established from patients receiving KRASG12C-i therapy. Studies are underway to generate drug-resistant clones of sensitive models and to elucidate mechanisms of drug resistance in ST4859. Citation Format: Johnnie Flores, Alyssa Simonson, Peter Forofontov, Anna Stackpole, Drew Rasco, Amita Patnaik, Kyriakos Papadopoulos, Teresa DesRochers, Natalie Williams, Ronald Drengler, Lon Smith, Michael J. Wick. Correlation of drug sensitivity to clinical response in XPDX models established from patients treated with KRAS-G12C-inhibitor therapy [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 412.

Consider a set M equipped with a structure ∗. We call a natural topology T∗, on (M, ∗), the topology induced by ∗. For example, a natural topology for a metric space (X, d) is a topology Td induced by the metric d, and for a linearly ordered set (X

Background: 15-20% of metastatic breast cancers are characterized by overexpression or amplification of human epidermal growth factor receptor 2 (HER2). First-line treatment for HER2-positive metastatic breast cancer includes the anti-HER2 monoclonal antibodies trastuzumab and pertuzumab in combination with chemotherapy. Second-line therapy includes T-DM1, an antibody-drug conjugate (ADC) consisting of trastuzumab conjugated to maytansinoid (DM1). Until recently, patients who progress on T-DM1 were left with few treatment options. Trastuzumab deruxtecan (DS-8201a) is an antibody-drug conjugate (ADC) consisting of an anti-HER2 (human epidermal growth factor receptor 2) antibody linked to a novel topoisomerase I inhibitor payload using a cleavable tetrapeptide-based linker and was recently approved for unresectable or T-DM1-refractory HER2+ breast cancer. In addition, DS-8201a is currently being evaluated as a treatment in breast cancers with low and medium expression of HER2. To better understand the potential for DS-8201a as a treatment in these cancer types, we evaluated this therapy in a panel of ER+/- XPDX models with differential HER2 expression. In addition, we compared DS-8201a activity to T-DM1 and benchmarked efficacy of the topoisomerase I inhibitor irinotecan in all tested models. Methods: One hundred (50ER+/50ER-) breast XPDX models were evaluated in this study. Models were established and characterized for estrogen receptor and HER2 expression by IHC and profiled using WES and RNAseq. For in vivo studies, DS-8201a and T-DM1 were administered IV at 3 mg/kg and irinotecan IP at 100 mg/kg on a weeklyx3 schedule. In vivo study endpoints included tumor volume and time from treatment initiation with %T/C values and tumor regression reported at study completion; a %T/C of ≤ 20 versus control was considered sensitive. Results: Models were grouped by ER positivity (+/-) and model HER2 score and designated as null (0), low (1+), medium (2+) or high (3+); models established from clinically HER2+ patients were also noted. In the ER+ group, HER2 low and medium expressing models accounted for over 80% of the total, while 15% were categorized as high and less than 5% as null. All models with high and 30% with medium HER2 staining were from clinically HER2+ patients, no low or null models were established from breast cancer assigned HER2+ clinically. In the ER- group, HER2 low and medium expressing models accounted for 75% of the total, while 12% were categorized as high and 13% as null. All models with high and 13% with medium HER2 staining were from clinically HER2+ patients; 5% of low or null models were established from breast cancer assigned HER2+ clinically. In vivo, 65% of the ER+ group reported sensitivity to DS-8201a versus 25% to T-DM1; 10% of DS-8201a, and 40% of T-DM1 sensitive models were high expression models and the remaining low and medium with no null models reporting sensitivity to either agent. 35% of tested ER+ models were sensitive to both HER2 therapies and 50% of models sensitive to DS-8201a were also sensitive to irinotecan. In the ER- group, 70% reported sensitivity to DS-8201a versus 25% to T-DM1; 20% of DS-8201a and 25% of T-DM1 sensitive models were high expression models and the remaining low and medium with one null model (ST069) sensitive to both agents. 25% of tested ER- models were sensitive to both HER2 therapies and 40% of models sensitive to DS-8201a were also sensitive to irinotecan. Conclusion: We have compared activity of DS-8201a, T-DM1 and irinotecan in a panel of ER+/- XPDX models and correlated activity based on HER2 expression. This data and panel can be utilized as a valuable tool in better understanding the potential for DS-8201a and other HER2-targeting therapies as a treatment in cancers driven by HER2 expression. Citation Format: Alyssa Simonson, Peter Forofontov, Johnnie R Flores, Kimberly Hernandez, April Cabang, Amy Lang, Gladys Rodriguez, Kyriakos Papadopoulos, Murali Beeram, Arthur Rosenthal, Brittany DeBerry, Lon Smith, Ronald Drengler, Amita Patnaik, Drew Rasco, Luis Rodriguez, Steven Abbate, Scott Ulmer, Michael Wick. Correlation of HER2 receptor expression and in vivo activity of the HER2-targeting therapies trastuzumab deruxtecan (DS-8201a) and T-DM1 activity in a panel of breast XPDX models [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P5-01-04.

Background: Trastuzumab deruxtecan (DS-8201a) is an antibody-drug conjugate (ADC) consisting of an anti-HER2 (human epidermal growth factor receptor 2) antibody linked to a topoisomerase I inhibitor payload using a cleavable tetrapeptide-based linker and was recently approved for unresectable or T-DM1-refractory HER2+ breast cancer. While some mechanisms for clinical T-DM1 resistance have been identified, less is known about acquired or innate resistance to DS-8201a. We established two XPDX models of ER+/HER2+ breast cancer from tissue and fluid samples collected simultaneously from the same patient. These models designated ST4480B and ST4480C were developed and characterized for receptor expression, genomic alterations, and in vivo drug sensitivities toward multiple chemotherapies and targeted agents including DS-8201a and T-DM1. Methods: ST4480B and ST4480C were established from a 70-year-old Caucasian female with ER+/HER2+ metastatic breast cancer pretreated with chemotherapy and targeted agents including T-DM1 for nine months followed by capecitabine/trastuzumab/tucatinib combination for one year prior to sample collections. ST4480B was established from a lymph node biopsy and ST4480C from a fluid sample collected the same day; both were grown subcutaneously in female athymic nude mice supplemented with estradiol. The resulting models were passaged and receptor expression confirmed immunohistochemically; genomic analysis, including WES and RNAseq, was performed to further characterize models. For in vivo studies, both models were evaluated with several chemotherapy and targeted agents alone and in combination including: trastuzumab, pertuzumab, T-DM1, DS-8201a, neratinib, tucatinib, alpelisib, everolimus, and irinotecan. In vivo study endpoints included tumor volume and time from treatment initiation with %T/C values and tumor regression reported at study completion; a %T/C of ≤ 20 versus control was considered sensitive. Tumor regression (%T/C=— Citation Format: Johnnie R Flores, Anna Stackpole, Abimael Garza, Alexandra Ulmer, Alyssa Simonson, Kyriakos Papadopoulos, April Cabang, Jun Ma, Amita Patnaik, Drew Rasco, Amy Lang, Gladys Rodriguez, Murali Beeram, Michael J Wick. Establishment and characterization of two simultaneously developed T-DM1-resistant, ER+/HER2+ XPDX models from the same patient with differential in vivo sensitivity to trastuzumab deruxtecan (DS-8201a) [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P5-01-09.

Background: Fulvestrant is a selective estrogen receptor modulator (SERM) approved as a single agent for estrogen receptor positive, HER2 negative breast cancer patients at various stages of disease and in combination with CDK4/6 inhibitors following endocrine therapy failure. Although this agent requires intramuscular injection, it has demonstrated superior activity and fewer side effects versus some oral endocrine treatments however, resistance to fulvestrant often develops. To better understand fulvestrant resistance and its utility in patients who have failed other endocrine therapies, we evaluated the agent in a panel of ER+ breast models established from patients at various stages of disease representing endocrine-sensitive and -resistant disease. Methods: Sixty-five previously developed ER+ breast XPDX models were evaluated in this study. Models were grown subcutaneously in female athymic nude mice supplemented with estradiol in drinking water when necessary. All models were characterized at early and late passages for estrogen receptor expression by immunohistochemistry and profiled using WES and RNAseq. For in vivo studies, fulvestrant was administered by subcutaneous injection at 2.5 or 5 mg per dose once weekly until study completion. In vivo study endpoints included tumor volume and time from treatment initiation with %T/C values and tumor regression reported at study completion; a %T/C of ≤ 20 versus control was considered sensitive. Tumor regression (%T/C Citation Format: April Cabang, Crystal Moreno, Johnnie R Flores, Jenna Boedeker, Alyssa Simonson, Jun Ma, Amy Lang, Gladys Rodriguez, Arthur Rosenthal, Kyriakos Papadopoulos, Amita Patnaik, Drew Rasco, Lon Smith, Murali Beeram, Ronald Drengler, Luis Rodriguez, Steven Abbate, Scott Ulmer, Michael J Wick. Nonclinical activity of fulvestrant in a panel of ER+ breast XPDX models representing clinically acquired and innate resistance to endocrine therapies [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P5-01-11.

Background: Several CDK 4/6 inhibitors have recently been approved in combination with letrozole or fulvestrant in hormone receptor-positive breast cancer. Although this combination therapy has been found effective in some patients, resistance often develops. To aid in developing new therapies for CDK4/6 inhibitor-resistant breast cancer and better understand potential resistance mechanisms, we established a panel of nine XPDX models from eight female patients with luminal A breast cancer at time of progression following acquired resistance to CDK4/6 inhibitor therapy. These models, designated ST940C, ST2056, ST3164B, ST3164B/PBR, ST3932, ST4316B, ST4378, STF160, and STM001B were developed in athymic nude mice and characterized for receptor expression, genomic alterations, and in vivo drug sensitivity. Methods: STF160 was established from a primary biopsy and ST3932 from a metastatic soft tissue lesion; the remaining models were established from malignant fluid samples collected at various stages of treatment post CDK4/6 inhibitor response and progression. The resulting models were passaged and challenged with CDK4/6 inhibitors to confirm resistance and fulvestrant to assess sensitivity. Receptor expression was determined immunohistochemically. Genomic analysis, including WES and RNAseq, were performed to characterize models and identify mechanisms of resistance. For in vivo studies, palbociclib and abemaciclib were dosed by oral administration once daily at 50 mg/kg and fulvestrant by subcutaneous administration once weekly at 2.5 mg. In vivo study endpoints included tumor volume and time from treatment initiation with %T/C values and tumor regression reported at study completion; a %T/C of ≤ 20 versus control was considered sensitive. Tumor regression (%T/C20) to palbociclib or abemaciclib and single agent fulvestrant. ST940C and ST2056 were sensitive (%T/C≤20) to tested CDK4/6 inhibitors but resistant to fulvestrant. Conclusion: We have established and characterized a panel of nine XPDX models from eight female patients with luminal A breast cancer at time of progression following acquired resistance to CDK4/6 inhibitor therapy, seven of which were found resistant to single agent palbociclib and abemaciclib and all nine to fulvestrant. This panel can be utilized as a valuable tool in better understanding CDK4/6 inhibitor resistance and in developing novel therapies for CDK4/6 inhibitor-resistant patients. Citation Format: Tatiana Hernandez, Dustin Kneifel, Alyssa Simonson, Johnnie R Flores, Sarah Quick, April Cabang, Alexandra Ulmer, Kyriakos Papadopoulos, Amy Lang, Gladys Rodriguez, Murali Beeram, Drew Rasco, Amita Patnaik, Scott Ulmer, Michael J Wick. Establishment and characterization of luminal A breast XPDX models from patients with acquired resistance to CDK 4/6 inhibitors [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P5-01-06.

The class of Zeeman topologies on spacetimes in the frame of relativity theory is considered to be of powerful intuitive justification, satisfying a sequence of properties with physical meaning, such as the group of homeomorphisms under such a topology is isomorphic to the Lorentz group and dilatations, in Minkowski spacetime, and to the group of homothetic symmetries in any curved spacetime. In this article we focus on two distinct topologies that were suggested by Zeeman as alternatives to his Fine topology, showing their connection with two orders: a timelike and a (non-causal) spacelike one. For the (non-causal) spacelike order, we introduce a partition of the null cone which gives the desired topology invariantly from the choice of the hyperplane of partition. In particular, we observe that these two orders induce topologies within the class of Zeeman topologies, while the two suggested topologies by Zeeman himself are intersection topologies of these two order topologies (respectively) with the manifold topology. We end up with a list of open questions and a discussion, comparing the topologies with bounded against those with unbounded open sets and their possible physical interpretation.

In this article we show that a contra second countable bitopological space is a $p_1$-Lindelof space, but the converse is not true in general. We provide suitable example with the help of concepts of nest and interlocking from LOTS. The relation between pairwise regular spaces and $p_1$-normal spaces is studied. At the end, we propose some open questions which may enrich various concepts related to Lindelofness in a bitopological space and other areas of mathematical ideas.

We report on the novel series of (CH3)3SPbI3−xBrx and (CH3)3SPbI3−xClx (x = 0, 1, 2, 3) perovskite compounds. X-ray diffraction analysis shows that the solid solutions of (CH3)3SPbI3−xBrx (x = 0, 1, 2, 3) and (CH3)3SPbI3−xClx (x = 0, 1, 2) crystallize in hexagonal symmetry (space group P63mc, No. 186) with 1D columns of face-sharing [PbX6] octahedra. (CH3)3SPbCl3 crystallizes in orthorhombic symmetry (space group Pnma, No. 62) forming 3D network of vertex- and face-sharing [PbCl6] octahedra. Optical and vibrational properties were investigated using UV–vis reflectance, photoluminescence and Raman spectroscopy at room temperature. The compounds show high chemical stability in ambient air at temperatures up to 80 °C and under solar simulator, in contrast to the hygroscopic CH3NH3PbI3 or CH(NH2)2PbI3 that are commonly used in perovskite solar cells. First principles theoretical ab initio and efficient semiempirical extended Huckel calculations were performed to evaluate the energy band gap values, whose results are in good agreement with the experimentally determined values.

Bigeneralized topology was introduced in 2010. In this paper, we aim to contribute in the development of this area by proving results with respect to the hereditary class that defines two types of Lindelöf spaces in a bigeneralized topological space (BGTS). Some results on strong BGTS (briefly SBGTS) are proved by defining a [Formula: see text]-perfect mapping. We also prove some equivalent conditions with respect to the hereditary class.

5',8-Cyclo-2'-deoxyadenosine (cdA) and 5',8-cyclo-2'-deoxyguanosine (cdG) in their two diastereomeric forms, 5'S and 5'R, are tandem lesions produced by the attack of hydroxyl radicals to the purine moieties of DNA. Their formation has been found to challenge the cells' repair machinery, initiating the nucleotide excision repair (NER) for restoring the genome integrity. The involvement of oxidatively induced DNA damage in carcinogenesis and the reduced capacity of some cancer cell lines to repair oxidised DNA base lesions, intrigued us to investigate the implication of these lesions in breast cancer, the most frequently occurring cancer in women. Using liquid chromatography tandem mass spectrometry (LC-MS/MS), we measured the levels of diastereomeric cdA's and cdG's in estrogen receptor-alpha positive (ER-alpha) MCF-7 and triple negative MDA-MB-231 breast cancer cell lines before and after exposure to two different conditions: ionising radiations and hydrogen peroxide, followed by an interval period to allow DNA repair. An increase at the measured levels of all four lesions, i.e. 5'S-cdA, 5'R-cdA, 5'S-cdG and 5'R-cdG, was observed either after gamma-irradiation (5Gy dose) or hydrogen peroxide treatment (300muM) compared to the untreated cells (control), independently from the length of the interval period for repair. For comparison reasons, we also measured the levels of 8-oxo-2'-deoxyadenosine (8-oxo-dA), a well-known oxidatively induced DNA damage lesion and base excision repair (BER) substrate. The collected data indicate that MCF-7 and MDA-MB-231 breast cancer cells are highly susceptible to radiation-induced DNA damage, being mainly defective in the repair of these lesions.

In this article, we examine the solution to the second order unsteady partial differential equation (Boussinesq equation), in case of an aquifer recharging from a lake. To this end, the generalized Hukuhara (gH) derivative was used for total derivatives, as well as the extension of this theory concerning partial derivatives. The case studies proved to follow the generalized Hukuhara (gH) derivative conditions and offer a unique solution. The development of the aquifer water profile was examined, as well as the calculation of the recharging fuzzy water movement profiles, and the results were depicted in diagrams.

Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime: a topology sufficient for the description of spacetime singularities or a topology which incorporates the causal structure? Or both? Is it more preferable to consider a topology with as many physical properties as possible, whose description might be complicated and counterintuitive, or a topology which can be described via a countable basis but misses some important information? These are just a few from the questions that we ask in this chapter, which serves as a critical review of the terrain and contains a survey with remarks, corrections and open questions.

We clarify and discuss a misunderstanding between uniform completeness and metric completeness that has appeared in the literature in a study on the Alexandrov topology for a spacetime.

Having their position gained among the smallest bulky DNA lesions recognized by the nucleotide excision repair (NER) enzyme, purine 5′,8-cyclo-2′-deoxynucleosides (5′,8-cPu) are increasingly attracting the interest in the field of genome integrity in health and diseases. Exclusively generated by one of the most harmful of the reactive oxygen species, the hydroxyl radical, 5′,8-cPu can be utilized also for highly valuable information regarding the oxidative status nearby the area where the genetic information is stored. Herein, we have collected the most recently reported biological studies, focusing on the repair mechanism of these lesions and their biological significance particularly in transcription. The LC-MS/MS quantification protocols that appeared in the literature are discussed in details, along with the reported values for the four 5′,8-cPu produced by in vitro γ-radiolysis experiments with calf thymus DNA. Mechanistic insights in the formation of the purine 5′,8-cyclo-2′-deoxynucleosides and their chemical stability are also given in the light of their potential to be utilized as DNA biomarkers of oxidative stress.

The motion planning problem is a fundamental problem in robotics, so that every autonomous robot should be able to deal with it. A number of solutions have been proposed and a probabilistic one seems to be quite reasonable. However, here we propose a more adoptive solution that uses fuzzy set theory and we expose this solution next to a sort survey on the recent theory of soft robots, for a future qualitative comparison between the two.

Let $Y$ and $Z$ be two fixed topological spaces and $C(Y,Z)$ the set of all continuous maps from $Y$ into $Z$. We construct and study topologies on $C(Y,Z)$ that we call ${\cal F}_n(\tau_n)$-family-open topologies. Furthermore, we find necessary and sufficient conditions such that these topologies to be splitting and jointly continuous. Finally, we present questions concerning a further study on this area., Comment: Quaestiones Mathematicae, Volume 39, 2016 - Issue 3, pages 363-379

The antioxidant activity of oils is an important parameter that determines oils' nutritional value and quality. To date, the methods for the determination of the antioxidant activity of oils are performed under batch conditions, therefore, they have large turnaround times and are labor-intensive. In this work, we describe the first automated method for the determination of the antioxidant activity of edible oils by resorting to the benefits of Flow Injection Analysis (FIA) and the high sensitivity of chemiluminescence (CL) detection. In the developed method, we used the chemiluminescent reaction of bis(2,4, 6-trichlorophenyl) oxalate with the reactive oxygen species produced by the catalytic decomposition of H2O2 by Mn(II) ions. The antioxidants present in the sample scavenge the reactive oxygen species and inhibit the light reaction. 1-Amino-pyrene was used as fluorophore and 1-methyl-imidazole as base catalyst in the reaction. Method validation and application to real samples showed that the analytical features of the method are very satisfactory in terms of linearity of response-lines of standard antioxidant compounds (R2 = 0.98–0.999), precision (%RSD = 0.85–1.9%) and accuracy (%recovery = 91–109%), suggesting that the developed assay could serve as an efficient tool to the routine screening of antioxidant properties in edible oils.

The order horismos induces the Zeeman [Formula: see text] topology, which is coarser than the Fine Zeeman Topology [Formula: see text]. The causal curves in a spacetime under [Formula: see text] are piecewise null. [Formula: see text] is considered to be the most physical topology in a spacetime manifold [Formula: see text], as the group of homeomorphisms of [Formula: see text] is isomorphic to the group of homothetic transformations of [Formula: see text]. [Formula: see text] was used in the a ambient boundary-ambient space cosmological model, in order to show that there is no possibility of formation of spacetime singularities. In this paper, we question this result, by reviewing the corresponding papers, and we propose new questions toward the improvement of this model.

The lipophilicity of untreated edible oils narrows the application of most published methods for the determination of antioxidant activity to hydrophilic extracts of oils. This research addresses the issue of the estimation of the total antioxidant properties of untreated edible oils by modifying two widely applied analytical methods, the Fe-Phenanthroline and the CUPRAC assays, to be used in untreated oils. The modifications pertain to the selection of mixture of solvents (ethanol-butanol in 3:1 v/v ratio), and the optimization of the reaction conditions (reagents concentration and reaction time). The developed methods were applied to a number of hydrophilic and lipophilic standard compounds and different types of commercial edible oils, as well as their corresponding aqueous or organic extracts. This implementation elucidated the differences in the antioxidant content of edible oils. All the results were compared to those of the DPPH and Folin-Ciocalteu methods and the analytical figures of merit for the methods have been estimated. Lastly, it was concluded that the modified CUPRAC assay has higher sensitivity compared to the Fe-Phenanthroline assay.

This research dwells on two widely used spectrophotometric methods, 2,2-diphenyl-1-picrylhydrazyl (DPPH) and 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) assays, which assess the free radical scavenging activity (RSA) of natural samples and standard compounds. In particular, these assays were modified in order to simplify the evaluation of RSA of untreated edible oils, as well as to assess the antioxidant profile of oils’ hydrophilic and lipophilic extracts with the same analytical procedure. A thorough study highlighted the effect of solvents on the DPPH and ABTS methods and resulted in selecting 2-propanol and an ethanol/1-butanol solvent mixture as the reaction solvent for the DPPH method and the ABTS method, respectively. The developed methods were used to evaluate the RSA of 12 antioxidant compounds and 8 edible oils. Then, the contribution of lipophilic and hydrophilic extracts to the total RSA of oils was estimated. The obtained results demonstrate the applicability of the method to routine edible oil analysis.

The group of homothetic symmetries in the conformal infinity (the $4$-dimensional "ambient boundary") of a $5$-dimensional spacetime restricts the choice of topology to a topology under which the group of homeomorphisms of a spacetime manifold is the group of homothetic transformations. Since there are such spacetime topologies in the class of Zeeman-G\"obel, under which the formation of basic contradiction present in proofs of singularity theorems is impossible, an important question is raised: why should one construct a $5$-dimensional metric, in order to return back such a topology to its $4$-dimensional conformal boundary, while such topologies, like those ones in the Zeeman-G\"obel class, are already considered as more "natural" topologies for a spacetime, rather than the artificial (according to Zeeman) manifold topology?

The anticancer activity of acridone derivatives has attracted increasing interest, therefore, a variety of substituted analogs belonging to this family have been developed and evaluated for their anti-cancer properties. A series of N-alkyl-acridones 1&ndash, 6 and N,N&prime, dialkyl-9,9&prime, biacridylidenes 7&ndash, 12 with variable alkyl chains were examined for their topoisomerase I activity at neutral and acidic conditions as well as for their binding capacity to calf thymus and possible radical trapping antioxidant activity. It was found that at a neutral pH, topoisomerase I activity of both classes of compounds was similar, while under acidic conditions, enhanced intercalation was observed. N-alkyl-acridone derivatives 1&ndash, 6 exhibited stronger, dose-dependent, cytotoxic activity against MCF-7 human breast epithelial cancer cells than N,N&prime, 12, revealing that conjugation of the heteroaromatic system plays a significant role on the effective distribution of the compound in the intracellular environment. Cellular investigation of long alkyl derivatives against cell migration exhibited 40&ndash, 50% wound healing effects and cytoplasm diffusion, while compounds with shorter alkyl chains were accumulated both in the nucleus and cytoplasm. All N,N&prime, biacridylidenes showed unexpected high scavenging activity towards DPPH or ABTS radicals which may be explained by higher stabilization of radical cations by the extended conjugation of heteroaromatic ring system.