The geometry of fractal percolation

A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost every realization of fractal percolation. The extensions go in three directions: {itemize} the statements work for all directions, not almost all, the statements are true for more general projections, for example radial projections onto a circle, in the case $\dim_H >1$, each projection has not only positive Lebesgue measure but also has nonempty interior. {itemize}Comment: Survey submitted for AFRT2012 conferenc

How large dimension guarantees a given angle?

We study the following two problems: (1) Given $n\ge 2$ and \al, how large Hausdorff dimension can a compact set A\su\Rn have if $A$ does not contain three points that form an angle \al? (2) Given \al and \de, how large Hausdorff dimension can a %compact subset $A$ of a Euclidean space have if $A$ does not contain three points that form an angle in the \de-neighborhood of \al? An interesting phenomenon is that different angles show different behaviour in the above problems. Apart from the clearly special extreme angles 0 and $180^\circ$, the angles $60^\circ,90^\circ$ and $120^\circ$ also play special role in problem (2): the maximal dimension is smaller for these special angles than for the other angles. In problem (1) the angle $90^\circ$ seems to behave differently from other angles

The Lagrange and Markov spectra from the dynamical point of view

This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \& 19, 2016 during the research school "Applications of Ergodic Theory in Number Theory" -- an activity related to the Jean-Molet Chair project of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira).Comment: 27 pages, 6 figures. Survey articl

Self-similar sets: projections, sections and percolation

We survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets.Postprin

A computational evaluation of over-representation of regulatory motifs in the promoter regions of differentially expressed genes

BACKGROUND: Observed co-expression of a group of genes is frequently attributed to co-regulation by shared transcription factors. This assumption has led to the hypothesis that promoters of co-expressed genes should share common regulatory motifs, which forms the basis for numerous computational tools that search for these motifs. While frequently explored for yeast, the validity of the underlying hypothesis has not been assessed systematically in mammals. This demonstrates the need for a systematic and quantitative evaluation to what degree co-expressed genes share over-represented motifs for mammals. RESULTS: We identified 33 experiments for human and mouse in the ArrayExpress Database where transcription factors were manipulated and which exhibited a significant number of differentially expressed genes. We checked for over-representation of transcription factor binding sites in up- or down-regulated genes using the over-representation analysis tool oPOSSUM. In 25 out of 33 experiments, this procedure identified the binding matrices of the affected transcription factors. We also carried out de novo prediction of regulatory motifs shared by differentially expressed genes. Again, the detected motifs shared significant similarity with the matrices of the affected transcription factors. CONCLUSIONS: Our results support the claim that functional regulatory motifs are over-represented in sets of differentially expressed genes and that they can be detected with computational methods

Metabolic Network Topology Reveals Transcriptional Regulatory Signatures of Type 2 Diabetes

Type 2 diabetes mellitus (T2DM) is a disorder characterized by both insulin resistance and impaired insulin secretion. Recent transcriptomics studies related to T2DM have revealed changes in expression of a large number of metabolic genes in a variety of tissues. Identification of the molecular mechanisms underlying these transcriptional changes and their impact on the cellular metabolic phenotype is a challenging task due to the complexity of transcriptional regulation and the highly interconnected nature of the metabolic network. In this study we integrate skeletal muscle gene expression datasets with human metabolic network reconstructions to identify key metabolic regulatory features of T2DM. These features include reporter metabolites—metabolites with significant collective transcriptional response in the associated enzyme-coding genes, and transcription factors with significant enrichment of binding sites in the promoter regions of these genes. In addition to metabolites from TCA cycle, oxidative phosphorylation, and lipid metabolism (known to be associated with T2DM), we identified several reporter metabolites representing novel biomarker candidates. For example, the highly connected metabolites NAD+/NADH and ATP/ADP were also identified as reporter metabolites that are potentially contributing to the widespread gene expression changes observed in T2DM. An algorithm based on the analysis of the promoter regions of the genes associated with reporter metabolites revealed a transcription factor regulatory network connecting several parts of metabolism. The identified transcription factors include members of the CREB, NRF1 and PPAR family, among others, and represent regulatory targets for further experimental analysis. Overall, our results provide a holistic picture of key metabolic and regulatory nodes potentially involved in the pathogenesis of T2DM

Intravenous alteplase for stroke with unknown time of onset guided by advanced imaging: systematic review and meta-analysis of individual patient data

Background: Patients who have had a stroke with unknown time of onset have been previously excluded from thrombolysis. We aimed to establish whether intravenous alteplase is safe and effective in such patients when salvageable tissue has been identified with imaging biomarkers. Methods: We did a systematic review and meta-analysis of individual patient data for trials published before Sept 21, 2020. Randomised trials of intravenous alteplase versus standard of care or placebo in adults with stroke with unknown time of onset with perfusion-diffusion MRI, perfusion CT, or MRI with diffusion weighted imaging-fluid attenuated inversion recovery (DWI-FLAIR) mismatch were eligible. The primary outcome was favourable functional outcome (score of 0–1 on the modified Rankin Scale [mRS]) at 90 days indicating no disability using an unconditional mixed-effect logistic-regression model fitted to estimate the treatment effect. Secondary outcomes were mRS shift towards a better functional outcome and independent outcome (mRS 0–2) at 90 days. Safety outcomes included death, severe disability or death (mRS score 4–6), and symptomatic intracranial haemorrhage. This study is registered with PROSPERO, CRD42020166903. Findings: Of 249 identified abstracts, four trials met our eligibility criteria for inclusion: WAKE-UP, EXTEND, THAWS, and ECASS-4. The four trials provided individual patient data for 843 individuals, of whom 429 (51%) were assigned to alteplase and 414 (49%) to placebo or standard care. A favourable outcome occurred in 199 (47%) of 420 patients with alteplase and in 160 (39%) of 409 patients among controls (adjusted odds ratio [OR] 1·49 [95% CI 1·10–2·03]; p=0·011), with low heterogeneity across studies (I2=27%). Alteplase was associated with a significant shift towards better functional outcome (adjusted common OR 1·38 [95% CI 1·05–1·80]; p=0·019), and a higher odds of independent outcome (adjusted OR 1·50 [1·06–2·12]; p=0·022). In the alteplase group, 90 (21%) patients were severely disabled or died (mRS score 4–6), compared with 102 (25%) patients in the control group (adjusted OR 0·76 [0·52–1·11]; p=0·15). 27 (6%) patients died in the alteplase group and 14 (3%) patients died among controls (adjusted OR 2·06 [1·03–4·09]; p=0·040). The prevalence of symptomatic intracranial haemorrhage was higher in the alteplase group than among controls (11 [3%] vs two [<1%], adjusted OR 5·58 [1·22–25·50]; p=0·024). Interpretation: In patients who have had a stroke with unknown time of onset with a DWI-FLAIR or perfusion mismatch, intravenous alteplase resulted in better functional outcome at 90 days than placebo or standard care. A net benefit was observed for all functional outcomes despite an increased risk of symptomatic intracranial haemorrhage. Although there were more deaths with alteplase than placebo, there were fewer cases of severe disability or death. Funding: None

Patient-reported outcome measures for hip-related pain: A review of the available evidence and a consensus statement from the International Hip-related Pain Research Network, Zurich 2018

Hip-related pain is a well-recognised complaint among active young and middle-aged active adults. People experiencing hip-related disorders commonly report pain and reduced functional capacity, including difficulties in executing activities of daily living. Patient-reported outcome measures (PROMs) are essential to accurately examine and compare the effects of different treatments on disability in those with hip pain. In November 2018, 38 researchers and clinicians working in the field of hip-related pain met in Zurich, Switzerland for the first International Hip-related Pain Research Network meeting. Prior to the meeting, evidence summaries were developed relating to four prioritised themes. This paper discusses the available evidence and consensus process from which recommendations were made regarding the appropriate use of PROMs to assess disability in young and middle-aged active adults with hip-related pain. Our process to gain consensus had five steps: (1) systematic review of systematic reviews; (2) preliminary discussion within the working group; (3) update of the more recent high-quality systematic review and examination of the psychometric properties of PROMs according to established guidelines; (4) formulation of the recommendations considering the limitations of the PROMs derived from the examination of their quality; and (5