Small union with large set of centers

Let $T\subset{\mathbb R}^n$ be a fixed set. By a scaled copy of $T$ around $x\in{\mathbb R}^n$ we mean a set of the form $x+rT$ for some $r>0$. In this survey paper we study results about the following type of problems: How small can a set be if it contains a scaled copy of $T$ around every point of a set of given size? We will consider the cases when $T$ is circle or sphere centered at the origin, Cantor set in ${\mathbb R}$, the boundary of a square centered at the origin, or more generally the $k$-skeleton ($0\le k<n$) of an $n$-dimensional cube centered at the origin or the $k$-skeleton of a more general polytope of ${\mathbb R}^n$. We also study the case when we allow not only scaled copies but also scaled and rotated copies and also the case when we allow only rotated copies

Lines Missing Every Random Point

We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.Comment: Added a section: "Betting in Doubly Exponential Time.

Sixty Years of Fractal Projections

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Comment: Submitted to proceedings of Fractals and Stochastics

Radioimmunotherapy of B-cell lymphoma with radiolabelled anti-CD20 monoclonal antibodies

CD20 has proven to be an excellent target for the treatment of B-cell lymphoma, first for the chimeric monoclonal antibody rituximab (Rituxan™), and more recently for the radiolabelled antibodies Y-90 ibritumomab tiuxetan (Zevalin™) and I-131 tositumomab (Bexxar™). Radiation therapy effects are due to beta emissions with path lengths of 1–5 mm; gamma radiation emitted by I-131 is the only radiation safety issue for either product. Dose-limiting toxicity for both radiolabelled antibodies is reversible bone marrow suppression. They produce response rates of 70%–90% in low-grade and follicular lymphoma and 40%–50% in transformed low-grade or intermediate-grade lymphomas. Both products produce higher response rates than related unlabelled antibodies, and both are highly active in patients who are relatively resistant to rituximab-based therapy. Median duration of response to a single course of treatment is about 1 year with complete remission rates that last 2 years or longer in about 25% of patients. Clinical trials suggest that anti- CD20 radioimmunotherapy is superior to total body irradiation in patients undergoing stem cell supported therapy for B-cell lymphoma, and that it is a safe and efficacious modality when used as consolidation therapy following chemotherapy. Among cytotoxic treatment options, current evidence suggests that one course of anti-CD20 radioimmunotherapy is as efficacious as six to eight cycles of combination chemotherapy. A major question that persists is how effective these agents are in the setting of rituximab- refractory lymphoma. These products have been underutilised because of the complexity of treatment coordination and concerns regarding reimbursement

Characteristics of Early-Onset vs Late-Onset Colorectal Cancer: A Review.

The incidence of early-onset colorectal cancer (younger than 50 years) is rising globally, the reasons for which are unclear. It appears to represent a unique disease process with different clinical, pathological, and molecular characteristics compared with late-onset colorectal cancer. Data on oncological outcomes are limited, and sensitivity to conventional neoadjuvant and adjuvant therapy regimens appear to be unknown. The purpose of this review is to summarize the available literature on early-onset colorectal cancer. Within the next decade, it is estimated that 1 in 10 colon cancers and 1 in 4 rectal cancers will be diagnosed in adults younger than 50 years. Potential risk factors include a Westernized diet, obesity, antibiotic usage, and alterations in the gut microbiome. Although genetic predisposition plays a role, most cases are sporadic. The full spectrum of germline and somatic sequence variations implicated remains unknown. Younger patients typically present with descending colonic or rectal cancer, advanced disease stage, and unfavorable histopathological features. Despite being more likely to receive neoadjuvant and adjuvant therapy, patients with early-onset disease demonstrate comparable oncological outcomes with their older counterparts. The clinicopathological features, underlying molecular profiles, and drivers of early-onset colorectal cancer differ from those of late-onset disease. Standardized, age-specific preventive, screening, diagnostic, and therapeutic strategies are required to optimize outcomes

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

Search for jet extinction in the inclusive jet-pT spectrum from proton-proton collisions at s=8 TeV

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published articles title, journal citation, and DOI.The first search at the LHC for the extinction of QCD jet production is presented, using data collected with the CMS detector corresponding to an integrated luminosity of 10.7  fb−1 of proton-proton collisions at a center-of-mass energy of 8 TeV. The extinction model studied in this analysis is motivated by the search for signatures of strong gravity at the TeV scale (terascale gravity) and assumes the existence of string couplings in the strong-coupling limit. In this limit, the string model predicts the suppression of all high-transverse-momentum standard model processes, including jet production, beyond a certain energy scale. To test this prediction, the measured transverse-momentum spectrum is compared to the theoretical prediction of the standard model. No significant deficit of events is found at high transverse momentum. A 95% confidence level lower limit of 3.3 TeV is set on the extinction mass scale