Basic properties of Sobolev's spaces on time scales

We study the theory of Sobolev's spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolev's spaces of functions defined on an arbitrary open interval of the real numbers are derived.This research is partially supported by D.G.I. and F.E.D.E.R. project MTM 2004-06652- C03-01, and by Xunta of Galicia and F.E.D.E.R. project PGIDIT05PXIC20702PN, SpainS

Multiple positive solutions in the sense of distributions of singular BVPs on time scales and an application to Emden-Fowler equations

This paper is devoted to using perturbation and variational techniques to derive some sufficient conditions for the existence of multiple positive solutions in the sense of distributions to a singular second-order dynamic equation with homogeneous Dirichlet boundary conditions, which includes those problems related to the negative exponent Emden-Fowler equationThis research is partially supported by MEC and F.E.D.E.R. Project MTM2007-61724, and by Xunta of Galicia and F.E.D.E.R. Project PGIDIT05PXIC20702PN, SpainS

Eight pruning deep learning models for low storage and high-speed COVID-19 computed tomography lung segmentation and heatmap-based lesion localization: A multicenter study using COVLIAS 2.0.

COVLIAS 1.0: an automated lung segmentation was designed for COVID-19 diagnosis. It has issues related to storage space and speed. This study shows that COVLIAS 2.0 uses pruned AI (PAI) networks for improving both storage and speed, wiliest high performance on lung segmentation and lesion localization.ology: The proposed study uses multicenter ∼9,000 CT slices from two different nations, namely, CroMed from Croatia (80 patients, experimental data), and NovMed from Italy (72 patients, validation data). We hypothesize that by using pruning and evolutionary optimization algorithms, the size of the AI models can be reduced significantly, ensuring optimal performance. Eight different pruning techniques (i) differential evolution (DE), (ii) genetic algorithm (GA), (iii) particle swarm optimization algorithm (PSO), and (iv) whale optimization algorithm (WO) in two deep learning frameworks (i) Fully connected network (FCN) and (ii) SegNet were designed. COVLIAS 2.0 was validated using "Unseen NovMed" and benchmarked against MedSeg. Statistical tests for stability and reliability were also conducted.Pruning algorithms (i) FCN-DE, (ii) FCN-GA, (iii) FCN-PSO, and (iv) FCN-WO showed improvement in storage by 92.4%, 95.3%, 98.7%, and 99.8% respectively when compared against solo FCN, and (v) SegNet-DE, (vi) SegNet-GA, (vii) SegNet-PSO, and (viii) SegNet-WO showed improvement by 97.1%, 97.9%, 98.8%, and 99.2% respectively when compared against solo SegNet. AUC > 0.94 (p 0.86 (p < 0.0001) on NovMed data set for all eight EA model. PAI <0.25 s per image. DenseNet-121-based Grad-CAM heatmaps showed validation on glass ground opacity lesions.Eight PAI networks that were successfully validated are five times faster, storage efficient, and could be used in clinical settings

Mitosis Phase Enrichment with Identification of Mitotic Centromere-Associated Kinesin As a Therapeutic Target in Castration-Resistant Prostate Cancer

The recently described transcriptomic switch to a mitosis program in castration-resistant prostate cancer (CRPC) suggests that mitotic proteins may be rationally targeted at this lethal stage of the disease. In this study, we showed upregulation of the mitosis-phase at the protein level in our cohort of 51 clinical CRPC cases and found centrosomal aberrations to also occur preferentially in CRPC compared with untreated, high Gleason–grade hormone-sensitive prostate cancer (P<0.0001). Expression profiling of chemotherapy-resistant CRPC samples (n = 25) was performed, and the results were compared with data from primary chemotherapy-naïve CRPC (n = 10) and hormone-sensitive prostate cancer cases (n = 108). Our results showed enrichment of mitosis-phase genes and pathways, with progression to both castration-resistant and chemotherapy-resistant disease. The mitotic centromere-associated kinesin (MCAK) was identified as a novel mitosis-phase target in prostate cancer that was overexpressed in multiple CRPC gene-expression datasets. We found concordant gene expression of MCAK between our parent and murine CRPC xenograft pairs and increased MCAK protein expression with clinical progression of prostate cancer to a castration-resistant disease stage. Knockdown of MCAK arrested the growth of prostate cancer cells suggesting its utility as a potential therapeutic target

Multiple positive solutions of singular discrete p-laplacian problems via variational methods

We obtain multiple positive solutions of singular discrete p-Laplacian problems using variational methods