Symmetric Jump Processes and their Heat Kernel Estimates

We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently, a class of symmetric integro-differential operators). We focus on the sharp two-sided estimates for the transition density functions (or heat kernels) of the processes, a priori Holder estimate and parabolic Harnack inequalities for their parabolic functions. In contrast to the second order elliptic differential operator case, the methods to establish these properties for symmetric integro-differential operators are mainly probabilistic.Comment: To appear in Science in China Series A: Mathematic

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

Search for Higgs bosons produced via vector-boson fusion and decaying into bottom quark pairs in √s =13 TeV pp collisions with the ATLAS detector

A search for the bb ¯ decay of the Standard Model Higgs boson produced through vector-boson fusion is presented. Three mutually exclusive channels are considered: two all-hadronic channels and a photon-associated channel. Results are reported from the analysis of up to 30.6 fb −1 of pp data at s √ =13 TeV collected with the ATLAS detector at the LHC. The measured signal strength relative to the Standard Model prediction from the combined analysis is 2.5 +1.4 −1.3 for inclusive Higgs boson production and 3.0 +1.7 −1.6 for vector-boson fusion production only

Chromosome Painting Reveals Asynaptic Full Alignment of Homologs and HIM-8–Dependent Remodeling of X Chromosome Territories during Caenorhabditis elegans Meiosis

During early meiotic prophase, a nucleus-wide reorganization leads to sorting of chromosomes into homologous pairs and to establishing associations between homologous chromosomes along their entire lengths. Here, we investigate global features of chromosome organization during this process, using a chromosome painting method in whole-mount Caenorhabditis elegans gonads that enables visualization of whole chromosomes along their entire lengths in the context of preserved 3D nuclear architecture. First, we show that neither spatial proximity of premeiotic chromosome territories nor chromosome-specific timing is a major factor driving homolog pairing. Second, we show that synaptonemal complex-independent associations can support full lengthwise juxtaposition of homologous chromosomes. Third, we reveal a prominent elongation of chromosome territories during meiotic prophase that initiates prior to homolog association and alignment. Mutant analysis indicates that chromosome movement mediated by association of chromosome pairing centers (PCs) with mobile patches of the nuclear envelope (NE)–spanning SUN-1/ZYG-12 protein complexes is not the primary driver of territory elongation. Moreover, we identify new roles for the X chromosome PC (X-PC) and X-PC binding protein HIM-8 in promoting elongation of X chromosome territories, separable from their role(s) in mediating local stabilization of pairing and association of X chromosomes with mobile SUN-1/ZYG-12 patches. Further, we present evidence that HIM-8 functions both at and outside of PCs to mediate chromosome territory elongation. These and other data support a model in which synapsis-independent elongation of chromosome territories, driven by PC binding proteins, enables lengthwise juxtaposition of chromosomes, thereby facilitating assessment of their suitability as potential pairing partners

Increasing the dose intensity of chemotherapy by more frequent administration or sequential scheduling: a patient-level meta-analysis of 37 298 women with early breast cancer in 26 randomised trials

Background Increasing the dose intensity of cytotoxic therapy by shortening the intervals between cycles, or by giving individual drugs sequentially at full dose rather than in lower-dose concurrent treatment schedules, might enhance efficacy. Methods To clarify the relative benefits and risks of dose-intense and standard-schedule chemotherapy in early breast cancer, we did an individual patient-level meta-analysis of trials comparing 2-weekly versus standard 3-weekly schedules, and of trials comparing sequential versus concurrent administration of anthracycline and taxane chemotherapy. The primary outcomes were recurrence and breast cancer mortality. Standard intention-to-treat log-rank analyses, stratified by age, nodal status, and trial, yielded dose-intense versus standard-schedule first-event rate ratios (RRs). Findings Individual patient data were provided for 26 of 33 relevant trials identified, comprising 37 298 (93%) of 40 070 women randomised. Most women were aged younger than 70 years and had node-positive disease. Total cytotoxic drug usage was broadly comparable in the two treatment arms; colony-stimulating factor was generally used in the more dose-intense arm. Combining data from all 26 trials, fewer breast cancer recurrences were seen with dose-intense than with standard-schedule chemotherapy (10-year recurrence risk 28·0% vs 31·4%; RR 0·86, 95% CI 0·82–0·89; p<0·0001). 10-year breast cancer mortality was similarly reduced (18·9% vs 21·3%; RR 0·87, 95% CI 0·83–0·92; p<0·0001), as was all-cause mortality (22·1% vs 24·8%; RR 0·87, 95% CI 0·83–0·91; p<0·0001). Death without recurrence was, if anything, lower with dose-intense than with standard-schedule chemotherapy (10-year risk 4·1% vs 4·6%; RR 0·88, 95% CI 0·78–0·99; p=0·034). Recurrence reductions were similar in the seven trials (n=10 004) that compared 2-weekly chemotherapy with the same chemotherapy given 3-weekly (10-year risk 24·0% vs 28·3%; RR 0·83, 95% CI 0·76–0·91; p<0·0001), in the six trials (n=11 028) of sequential versus concurrent anthracycline plus taxane chemotherapy (28·1% vs 31·3%; RR 0·87, 95% CI 0·80–0·94; p=0·0006), and in the six trials (n=6532) testing both shorter intervals and sequential administration (30·4% vs 35·0%; RR 0·82, 95% CI 0·74–0·90; p<0·0001). The proportional reductions in recurrence with dose-intense chemotherapy were similar and highly significant (p<0·0001) in oestrogen receptor (ER)-positive and ER-negative disease and did not differ significantly by other patient or tumour characteristics. Interpretation Increasing the dose intensity of adjuvant chemotherapy by shortening the interval between treatment cycles, or by giving individual drugs sequentially rather than giving the same drugs concurrently, moderately reduces the 10-year risk of recurrence and death from breast cancer without increasing mortality from other causes. Funding Cancer Research UK, Medical Research Council

20-Year Risks of Breast-Cancer Recurrence after Stopping Endocrine Therapy at 5 Years

The administration of endocrine therapy for 5 years substantially reduces recurrence rates during and after treatment in women with early-stage, estrogen-receptor (ER)-positive breast cancer. Extending such therapy beyond 5 years offers further protection but has additional side effects. Obtaining data on the absolute risk of subsequent distant recurrence if therapy stops at 5 years could help determine whether to extend treatment

The impact of surgical delay on resectability of colorectal cancer: An international prospective cohort study

AIM: The SARS-CoV-2 pandemic has provided a unique opportunity to explore the impact of surgical delays on cancer resectability. This study aimed to compare resectability for colorectal cancer patients undergoing delayed versus non-delayed surgery. METHODS: This was an international prospective cohort study of consecutive colorectal cancer patients with a decision for curative surgery (January-April 2020). Surgical delay was defined as an operation taking place more than 4 weeks after treatment decision, in a patient who did not receive neoadjuvant therapy. A subgroup analysis explored the effects of delay in elective patients only. The impact of longer delays was explored in a sensitivity analysis. The primary outcome was complete resection, defined as curative resection with an R0 margin. RESULTS: Overall, 5453 patients from 304 hospitals in 47 countries were included, of whom 6.6% (358/5453) did not receive their planned operation. Of the 4304 operated patients without neoadjuvant therapy, 40.5% (1744/4304) were delayed beyond 4 weeks. Delayed patients were more likely to be older, men, more comorbid, have higher body mass index and have rectal cancer and early stage disease. Delayed patients had higher unadjusted rates of complete resection (93.7% vs. 91.9%, P = 0.032) and lower rates of emergency surgery (4.5% vs. 22.5%, P < 0.001). After adjustment, delay was not associated with a lower rate of complete resection (OR 1.18, 95% CI 0.90-1.55, P = 0.224), which was consistent in elective patients only (OR 0.94, 95% CI 0.69-1.27, P = 0.672). Longer delays were not associated with poorer outcomes. CONCLUSION: One in 15 colorectal cancer patients did not receive their planned operation during the first wave of COVID-19. Surgical delay did not appear to compromise resectability, raising the hypothesis that any reduction in long-term survival attributable to delays is likely to be due to micro-metastatic disease