The spectra of the laplacians of fractal graphs not satisfying spectral decimation

We consider the spectra of the Laplacians of two sequences of fractal graphs in the context of the general theory introduced by Sabot in 2003. For the sequence of graphs associated with the pentagasket, we give a description of the eigenvalues in terms of the iteration of a map from (C-2)(3) to itself. For the sequence of graphs introduced in a previous paper by the author, we show that the results found therein can be related to Sabot's theory

Randomized phase III KEYNOTE-045 trial of pembrolizumab versus paclitaxel, docetaxel, or vinflunine in recurrent advanced urothelial cancer: results of >2 years of follow-up.

BackgroundNovel second-line treatments are needed for patients with advanced urothelial cancer (UC). Interim analysis of the phase III KEYNOTE-045 study showed a superior overall survival (OS) benefit of pembrolizumab, a programmed death 1 inhibitor, versus chemotherapy in patients with advanced UC that progressed on platinum-based chemotherapy. Here we report the long-term safety and efficacy outcomes of KEYNOTE-045.Patients and methodsAdult patients with histologically/cytologically confirmed UC whose disease progressed after first-line, platinum-containing chemotherapy were enrolled. Patients were randomly assigned 1 : 1 to receive pembrolizumab [200 mg every 3 weeks (Q3W)] or investigator's choice of paclitaxel (175 mg/m2 Q3W), docetaxel (75 mg/m2 Q3W), or vinflunine (320 mg/m2 Q3W). Primary end points were OS and progression-free survival (PFS) per Response Evaluation Criteria in Solid Tumors, version 1.1 (RECIST v1.1) by blinded independent central radiology review (BICR). A key secondary end point was objective response rate per RECIST v1.1 by BICR.ResultsA total of 542 patients were enrolled (pembrolizumab, n = 270; chemotherapy, n = 272). Median follow-up as of 26 October 2017 was 27.7 months. Median 1- and 2-year OS rates were higher with pembrolizumab (44.2% and 26.9%, respectively) than chemotherapy (29.8% and 14.3%, respectively). PFS rates did not differ between treatment arms; however, 1- and 2-year PFS rates were higher with pembrolizumab. The objective response rate was also higher with pembrolizumab (21.1% versus 11.0%). Median duration of response to pembrolizumab was not reached (range 1.6+ to 30.0+ months) versus chemotherapy (4.4 months; range 1.4+ to 29.9+ months). Pembrolizumab had lower rates of any grade (62.0% versus 90.6%) and grade ≥3 (16.5% versus 50.2%) treatment-related adverse events than chemotherapy.ConclusionsLong-term results (>2 years' follow-up) were consistent with those of previously reported analyses, demonstrating continued clinical benefit of pembrolizumab over chemotherapy for efficacy and safety for treatment of locally advanced/metastatic, platinum-refractory UC.Trial registrationClinicalTrials.gov: NCT02256436

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket

Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

Spectral analysis on infinite Sierpinski fractafolds

A fractafold, a space that is locally modeled on a specified fractal, is the fractal equivalent of a manifold. For compact fractafolds based on the Sierpinski gasket, it was shown by the first author how to compute the discrete spectrum of the Laplacian in terms of the spectrum of a finite graph Laplacian. A similar problem was solved by the second author for the case of infinite blowups of a Sierpinski gasket, where spectrum is pure point of infinite multiplicity. Both works used the method of spectral decimations to obtain explicit description of the eigenvalues and eigenfunctions. In this paper we combine the ideas from these earlier works to obtain a description of the spectral resolution of the Laplacian for noncompact fractafolds. Our main abstract results enable us to obtain a completely explicit description of the spectral resolution of the fractafold Laplacian. For some specific examples we turn the spectral resolution into a "Plancherel formula". We also present such a formula for the graph Laplacian on the 3-regular tree, which appears to be a new result of independent interest. In the end we discuss periodic fractafolds and fractal fields

Recent progress in genetics of aging, senescence and longevity: focusing on cancer-related genes

It is widely believed that aging results from the accumulation of molecular damage, including damage of DNA and mitochondria and accumulation of molecular garbage both inside and outside of the cell. Recently, this paradigm is being replaced by the “hyperfunction theory�, which postulates that aging is caused by activation of signal transduction pathways such as TOR (Target of Rapamycin). These pathways consist of different enzymes, mostly kinases, but also phosphatases, deacetylases, GTPases, and some other molecules that cause overactivation of normal cellular functions. Overactivation of these sensory signal transduction pathways can cause cellular senescence, age-related diseases, including cancer, and shorten life span. Here we review some of the numerous very recent publications on the role of signal transduction molecules in aging and age-related diseases. As was emphasized by the author of the “hyperfunction model�, many (or actually all) of them also play roles in cancer. So these “participants� in pro-aging signaling pathways are actually very well acquainted to cancer researchers. A cancer-related journal such as Oncotarget is the perfect place for publication of such experimental studies, reviews and perspectives, as it can bridge the gap between cancer and aging researchers

Identification of a novel susceptibility locus at 13q34 and refinement of the 20p12.2 region as a multi-signal locus associated with bladder cancer risk in individuals of European ancestry

Candidate gene and genome-wide association studies (GWAS) have identified 15 independent genomic regions associated with bladder cancer risk. In search for additional susceptibility variants, we followed up on four promising single-nucleotide polymorphisms (SNPs) that had not achieved genome-wide significance in 6911 cases and 11 814 controls (rs6104690, rs4510656, rs5003154 and rs4907479, P < 1 × 10−6), using additional data from existing GWAS datasets and targeted genotyping for studies that did not have GWAS data. In a combined analysis, which included data on up to 15 058 cases and 286 270 controls, two SNPs achieved genome-wide statistical significance: rs6104690 in a gene desert at 20p12.2 (P = 2.19 × 10−11) and rs4907479 within the MCF2L gene at 13q34 (P = 3.3 × 10−10). Imputation and fine-mapping analyses were performed in these two regions for a subset of 5551 bladder cancer cases and 10 242 controls. Analyses at the 13q34 region suggest a single signal marked by rs4907479. In contrast, we detected two signals in the 20p12.2 region—the first signal is marked by rs6104690, and the second signal is marked by two moderately correlated SNPs (r2 = 0.53), rs6108803 and the previously reported rs62185668. The second 20p12.2 signal is more strongly associated with the risk of muscle-invasive (T2-T4 stage) compared with non-muscle-invasive (Ta, T1 stage) bladder cancer (case–case P ≤ 0.02 for both rs62185668 and rs6108803). Functional analyses are needed to explore the biological mechanisms underlying these novel genetic associations with risk for bladder cancer