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We consider a system of two nonlocal and nonlinear partial differential equations that describe some aspects of yeast cell-cell communication. We study local and global existence and uniqueness of solutions. We consider mild solutions and we perform bilinear and trilinear fixed point arguments in suitable functional spaces. [ABSTRACT FROM AUTHOR]

In this article we study some problems related to the incompressible 3D Navier–Stokes equations from the point of view of Lebesgue spaces of variable exponent. These functional spaces present some particularities that make them quite different from the usual Lebesgue spaces: indeed, some of the most classical tools in analysis are not available in this framework. We will give here some ideas to overcome some of the difficulties that arise in this context in order to obtain different results related to the existence of mild solutions for this evolution problem. [ABSTRACT FROM AUTHOR]

Simple Summary: Breast cancer stands as the predominant form of cancer identified in women, underscoring the urgent demand for innovative targeted therapies. Engineered adoptive cell therapies represent a groundbreaking approach, empowering the immune cells of patients to precisely target their tumors through cancer-specific receptors. Encouragingly, preclinical studies have illuminated the immense promise of this strategy. Nonetheless, the translation of this technique into clinical practice hinges on the accumulation of additional robust clinical data. Within this review, we offer a comprehensive examination of the current landscape surrounding engineered cell therapies for breast cancer, delving into both their limitations and the compelling prospects for enhancement. Breast cancer remains a significant health challenge, and novel treatment approaches are critically needed. This review presents an in-depth analysis of engineered adoptive T-cell therapies (E-ACTs), an innovative frontier in cancer immunotherapy, focusing on their application in breast cancer. We explore the evolving landscape of chimeric antigen receptor (CAR) and T-cell receptor (TCR) T-cell therapies, highlighting their potential and challenges in targeting breast cancer. The review addresses key obstacles such as target antigen selection, the complex breast cancer tumor microenvironment, and the persistence of engineered T-cells. We discuss the advances in overcoming these barriers, including strategies to enhance T-cell efficacy. Finally, our comprehensive analysis of the current clinical trials in this area provides insights into the future possibilities and directions of E-ACTs in breast cancer treatment. [ABSTRACT FROM AUTHOR]

When p > 1 , using as base space classical Lorentz spaces associated to a weight from the Ariño–Muckenhoupt class B p , we will study Gagliardo–Nirenberg inequalities. As a by-product we will also consider Morrey–Sobolev inequalities. These arguments can be generalized to many different frameworks, in particular the proofs are given in the setting of stratified Lie groups. [ABSTRACT FROM AUTHOR]

Background: Epidermal growth factor receptor (EGFR) mutations (EGFRm) represent one of the most common genomic alterations identified among patients with non-small cell lung cancer (NSCLC). Several targeted agents for patients with EGFRm have been proven safe and effective, including the third-generation tyrosine kinase inhibitor (TKI) osimertinib. Nonetheless, some patients will present with or develop EGFR-TKI resistance mechanisms. Objective: We characterized the genomic landscape of primary resistance to osimertinib among Hispanic patients with EGFR-mutant NSCLC. Methods: An observational longitudinal cohort study was conducted with two groups of patients, those with intrinsic resistance (cohort A) and those with long-term survival (cohort B). All patients were treated and followed between January 2018 and May 2022. All patients were assessed for Programmed Cell Death Ligand 1 (PD-L1) expression and Bcl-2-like protein 11 (BIM)/AXL mRNA expression before starting TKI. After 8 weeks of treatment, a liquid biopsy was performed to determine the presence of circulating free DNA (cfDNA), and next-generation sequencing (NGS) was used to identify mutations at the time of progression. In both cohorts, overall response rate (ORR), progression-free survival (PFS), and overall survival (OS) were evaluated. Results: We found a homogeneous distribution of EGFR-sensitizing mutations in both cohorts. For cohort A, exon 21 mutations were more common than exon 19 deletions (ex19dels) for cohort B (P = 0.0001). The reported ORR for osimertinib was 6.3% and 100% for cohorts A and B, respectively (P = 0.0001). PFS was significantly higher in cohort B (27.4 months vs. 3.1 months; P = 0.0001) and ex19del patients versus L858R (24.5 months, 95% confidence interval [CI] 18.2–NR), vs. 7.6 months, 95% CI 4.8–21.1; P = 0.001). OS was considerably lower for cohort A (20.1 months vs. 36.0 months; P = 0.0001) and was better for patients with ex19del, no brain metastasis, and low tumor mutation burden. At the time of progression, more mutations were found in cohort A, identifying off-target alterations more frequently, including TP53, RAS, and RB1. Conclusion: EGFR-independent alterations are common among patients with primary resistance to osimertinib and significantly impact PFS and OS. Our results suggest that among Hispanic patients, other variables associated with intrinsic resistance include the number of commutations, high levels AXL mRNA, and low levels of BIM mRNA, T790M de novo, EGFR p.L858R presence, and a high tumoral mutational burden. [ABSTRACT FROM AUTHOR]

We consider an n‐dimensional parabolic‐type PDE with a diffusion given by a fractional Laplace operator and with a quadratic nonlinearity of the "gradient" of the solution, convoluted with a term b$\mathfrak {b}$ which can be singular. Our first result is the well‐posedness for this problem: We show existence and uniqueness of a (local in time) mild solution. The main result is about blow‐up of said solution, and in particular we find sufficient conditions on the initial datum and on the term b$\mathfrak {b}$ to ensure blow‐up of the solution in finite time. [ABSTRACT FROM AUTHOR]

Objectives: To compare the rate disparity between outcomes (overall survival (OS), progression-free survival (PFS), and safety) of concurrent chemoradiation (cCRT) followed by durvalumab in two patient cohorts with locally advanced (LA) stage III non-small cell lung cancer (NSCLC), one non-Hispanic White (NHW), and the other Latin-American. Methods: A multicenter retrospective study was performed, including 80 Hispanic and 45 NHW LA stage III NSCLC patients treated with cCRT followed by durvalumab. Both cohorts were analyzed in terms of main outcomes (OS, PFS, and safety) and compared between them and with the PACIFIC trial population outcomes. The efficacyeffectiveness gap was assessed using an efficacy-effectiveness (EE) factor that was calculated by dividing each cohort median overall survival by the corresponding reference OS from the PACIFIC trial. In both cohorts, results of PD-L1 testing were recorded, and the main outcomes were compared according to PD-1 expression levels (=50%, 1-49%, and <1%). Results: For the entire population (N=125), the overall response rate (ORR) was 57.6% (N=72), and 18.4% (N=25) achieved stable disease. OS was 26.3 months (95%CI 23.9-28.6), and PFS was 20.5 months (95%CI 18.0-23.0). PFS assessed by ethnicity showed a median for the Hispanic population of 19.4 months (95%CI 16.4-22.5) and 21.2 months (95%CI 17.2-23.3; p=0.76) for the NHW group. OS by race showed a significant difference in favor of the NHW group, with a median OS of 27.7 months (95%CI 24.6-30.9) vs. 20.0 months (95%CI 16.4-23.5) for Hispanics. (P=0.032). Unadjusted 12-month and 24-month OS was 86.6% (95%CI 79.9-88.0) and 46.6% (95%CI 40.2-48.3) for NHW compared to 82.5% (95%CI 77.1-84.2) and 17.5% (95%CI 15.6-24.5) in Hispanics. NHW had an EE factor of 0.78 and Hispanics had 0.58, showing a reduction in survival versus NHW and PACIFIC of 20% and 42%, respectively. HR for the OS among NHWs and Hispanics was 1.53 (95%CI 1.12-1.71; P=0.052) and 2.31 (95%CI 1.76-2.49; P=0.004). Fifty-six patients (44.8%) had some degree of pneumonitis due to cCRT plus durvalumab. There was no difference in the proportion of pneumonitis according to race (P=0.95), and the severity of pneumonitis was not significantly different between Hispanics and NHWs (P=0.41). Conclusions: Among patients with LA stage III NSCLC, NHW had better survival outcomes when compared to Hispanics, with an OS that seems to favor the NHW population and with an EE factor that shows a shorter survival in Hispanics compared with NHW and with the PACIFIC trial group. [ABSTRACT FROM AUTHOR]

Immunotherapy has redefined the treatment of cancer patients and it is constantly generating new advances and approaches. Among the multiple options of immunotherapy, bispecific antibodies (bsAbs) represent a novel thoughtful approach. These drugs integrate the action of the immune system in a strategy to redirect the activation of innate and adaptive immunity toward specific antigens and specific tumor locations. Here we discussed some basic aspects of the design and function of bsAbs, their main challenges and the state-of-the-art of these molecules in the treatment of hematological and solid malignancies and future perspectives. [ABSTRACT FROM AUTHOR]

In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of variable exponents and in the framework of Orlicz spaces. [ABSTRACT FROM AUTHOR]

We study here a new generalization of Caffarelli, Kohn and Nirenberg's partial regularity theory for weak solutions of the MagnetoHydroDynamic equations. Indeed, in this framework some hypotheses on the pressure P are usually asked (for example, P ∈ LtqLx¹ with q > 1) and then local Hölder regularity, in time and space variables, for weak solutions can be obtained over small neighborhoods. By introducing the notion of dissipative solutions, we weaken the hypothesis on the pressure (we will only assume that P ∈ D') and we will obtain H¨older regularity in the space variable for weak solutions. [ABSTRACT FROM AUTHOR]

We consider here the Navier–Stokes equations in R 3 with a stationary, divergence-free external force and with an additional damping term that depends on two parameters. We first study the well-posedness of weak solutions for these equations and then, for a particular set of the damping parameters, we will obtain an upper and lower control for the energy dissipation rate ε according to the Kolmogorov K41 theory. However, although the behavior of weak solutions corresponds to the K41 theory, we will show that in some specific cases the damping term introduced in the Navier–Stokes equations prevents the turbulent characterization of the Taylor scale even though the Grashof number (which is equivalent to the Reynolds numbers) is large. [ABSTRACT FROM AUTHOR]

Within the global setting of singular drifts in Morrey-Campanato spaces presented in Chamorro and Menozzi (Revista Matemática Iberoamericana 32(N∘4): 1445-1499 2016), we study now the Hölder regularity properties of the solutions of a transport-diffusion equation with nonlinear singular drifts that satisfy a Besov stability property. We will see how this Besov information is relevant and how it allows to improve previous results. Moreover, in some particular cases we show that as the nonlinear drift becomes more regular, in the sense of Morrey-Campanato spaces, the additional Besov stability property will be less useful. [ABSTRACT FROM AUTHOR]

We study the role of the pressure in the partial regularity theory for weak solutions of the Navier-Stokes equations. By introducing the notion of dissipative solutions, due to D uchon and R obert (Nonlinearity 13:249-255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin's local regularity criterion. [ABSTRACT FROM AUTHOR]

We investigate some smoothness properties for a linear transport-diffusion equation involving a class of non-degenerate Lévy type operators with singular drift. Our main argument is based on a duality method using the molecular decomposition of Hardy spaces through which we derive some Hölder continuity for the associated parabolic PDE. This property will be fulfilled as far as the singular drift belongs to a suitable Morrey-Campanato space for which the regularizing properties of the Lévy operator suffice to obtain global Hölder continuity. [ABSTRACT FROM AUTHOR]

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Copyright of Analítika: Journal of Statistical Analysis / Revista de Análisis Estadístico is the property of Analitika: Journal of Statistical Analysis / Revista de Analisis Estadistico and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The ability to accurately classify land cover in periods before appropriate training and validation data exist is a critical step towards understanding subtle long-term impacts of climate change. These trends cannot be properly understood and distinguished from individual disturbance events or decadal cycles using only a decade or less of data. Understanding these long-term changes in low lying coastal areas, home to a huge proportion of the global population, is of particular importance. Relatively simple deep learning models that extract representative spatiotemporal patterns can lead to major improvements in temporal generalizability. To provide insight into major changes in low lying coastal areas, our study (1) developed a recurrent convolutional neural network that incorporates spectral, spatial, and temporal contexts for predicting land cover class, (2) evaluated this model across time and space and compared this model to conventional Random Forest and Support Vector Machine methods as well as other deep learning approaches, and (3) applied this model to classify land cover across 20 years of Landsat 5 data in the low-lying coastal plain of North Carolina, USA. We observed striking changes related to sea level rise that support evidence on a smaller scale of agricultural land and forests transitioning into wetlands and "ghost forests". This work demonstrates that recurrent convolutional neural networks should be considered when a model is needed that can generalize across time and that they can help uncover important trends necessary for understanding and responding to climate change in vulnerable coastal regions. [ABSTRACT FROM AUTHOR]