QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show the rather surprising structural result that a disjoint union of cycles is the complement of a disk graph if and only if at most one of those cycles is of odd length. From that, we derive the first QPTAS and subexponential algorithm running in time 2^{O~(n^{2/3})} for Maximum Clique on disk graphs. In stark contrast, Maximum Clique on intersection graphs of filled ellipses or filled triangles is unlikely to have such algorithms, even when the ellipses are close to unit disks. Indeed, we show that there is a constant ratio of approximation which cannot be attained even in time 2^{n^{1-epsilon}}, unless the Exponential Time Hypothesis fails

QPTAS and subexponential algorithm for maximum clique on disk graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for \textsc{Maximum Clique} on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show the rather surprising structural result that a disjoint union of cycles is the complement of a disk graph if and only if at most one of those cycles is of odd length. From that, we derive the first QPTAS and subexponential algorithm running in time $2^{\tilde{O}(n^{2/3})}$ for \textsc{Maximum Clique} on disk graphs. In stark contrast, \textsc{Maximum Clique} on intersection graphs of filled ellipses or filled triangles is unlikely to have such algorithms, even when the ellipses are close to unit disks. Indeed, we show that there is a constant ratio of approximation which cannot be attained even in time $2^{n^{1-\varepsilon}}$, unless the Exponential Time Hypothesis fails

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Adeno-associated virus-mediated brain delivery of 5-lipoxygenase modulates the AD-like phenotype of APP mice

<p>Abstract</p> <p>Background</p> <p>The 5-lipoxygenase (5LO) enzymatic pathway is widely distributed within the central nervous system. Previous works showed that this protein is up-regulated in Alzheimer's disease (AD), and that its genetic absence results in a reduction of Amyloid beta (Aβ) levels in the Tg2576 mice.</p> <p>Here by employing an adeno-associated viral (AAV) vector system to over-express 5LO in the same mouse model, we examined its contribution to their cognitive impairments and brain AD-like amyloid pathology.</p> <p>Results</p> <p>Our results showed that compared with controls, 5LO-targeted gene brain over-expression in Tg2576 mice results in significant memory deficits. On the other hand, brain tissues had a significant elevation in the levels of Aβ peptides and deposition, no change in the steady state levels of amyloid-β precursor protein (APP), BACE-1 or ADAM-10, but a significant increase in PS1, nicastrin, and Pen-2, three major components of the γ-secretase complex. Additional data indicate that the transcription factor CREB was elevated and so were the mRNA levels for PS1, nicastrin and Pen-2.</p> <p>Conclusions</p> <p>These data demonstrate that neuronal 5LO plays a functional role in the pathogenesis of AD-like amyloidotic phenotype by modulating the γ-secretase pathway. They support the hypothesis that this enzyme is a novel therapeutic target for the treatment and prevention of AD.</p

Acting rehearsal in collaborative multimodal mixed reality environments

This paper presents the use of our multimodal mixed reality telecommunication system to support remote acting rehearsal. The rehearsals involved two actors, located in London and Barcelona, and a director in another location in London. This triadic audiovisual telecommunication was performed in a spatial and multimodal collaborative mixed reality environment based on the 'destination-visitor' paradigm, which we define and put into use. We detail our heterogeneous system architecture, which spans the three distributed and technologically asymmetric sites, and features a range of capture, display, and transmission technologies. The actors' and director's experience of rehearsing a scene via the system are then discussed, exploring successes and failures of this heterogeneous form of telecollaboration. Overall, the common spatial frame of reference presented by the system to all parties was highly conducive to theatrical acting and directing, allowing blocking, gross gesture, and unambiguous instruction to be issued. The relative inexpressivity of the actors' embodiments was identified as the central limitation of the telecommunication, meaning that moments relying on performing and reacting to consequential facial expression and subtle gesture were less successful

Genetic variation at MECOM, TERT, JAK2 and HBS1L-MYB predisposes to myeloproliferative neoplasms

Clonal proliferation in myeloproliferative neoplasms (MPN) is driven by somatic mutations in JAK2, CALR or MPL, but the contribution of inherited factors is poorly characterized. Using a three-stage genome-wide association study of 3,437 MPN cases and 10,083 controls, we identify two SNPs with genome-wide significance in JAK2V617F-negative MPN: rs12339666 (JAK2; meta-analysis P=1.27 × 10−10) and rs2201862 (MECOM; meta-analysis P=1.96 × 10−9). Two additional SNPs, rs2736100 (TERT) and rs9376092 (HBS1L/MYB), achieve genome-wide significance when including JAK2V617F-positive cases. rs9376092 has a stronger effect in JAK2V617F-negative cases with CALR and/or MPL mutations (Breslow–Day P=4.5 × 10−7), whereas in JAK2V617F-positive cases rs9376092 associates with essential thrombocythemia (ET) rather than polycythemia vera (allelic χ2 P=7.3 × 10−7). Reduced MYB expression, previously linked to development of an ET-like disease in model systems, associates with rs9376092 in normal myeloid cells. These findings demonstrate that multiple germline variants predispose to MPN and link constitutional differences in MYB expression to disease phenotype

Duration of adenosine-induced myocardial hyperemia - Insights from quantitative 13N-ammonia positron emission tomography myocardial perfusion imaging

AIMS To assess the impact of adenosine on quantitative myocardial blood flow (MBF) in a rapid stress-rest protocol compared to a rest-stress protocol using 13N-ammonia positron emission tomography (PET) myocardial perfusion imaging (MPI) and to gain insights into the time dependency of such effects. METHODS AND RESULTS Quantitative MBF at rest (rMBF), during adenosine-induced stress (sMBF) and myocardial flow reserve (MFR) were obtained from 331 retrospectively identified patients who underwent 13N-ammonia PET-MPI for suspected chronic coronary syndrome and who all exhibited no perfusion defects. Of these, 146 (44.1%) underwent a rapid stress-rest protocol with a time interval (Δtstress-rest) of 20 ± 4 minutes between adenosine infusion offset and rest-imaging, as per clinical routine. The remaining 185 (55.9%) patients underwent a rest-stress protocol and served as the reference. Groups did not differ regarding demographics, risk factors, medication, left ventricular function, and calcium scores. rMBF was significantly higher in the stress-rest vs. the rest-stress group (0.80 [IQR 0.66-1.00] vs. 0.70 [0.58-0.83] ml·min-1·g-1, p < 0.001) and, as sMBF was identical between groups (2.52 [2.20-2.96] vs. 2.50 [1.96-3.11], p = 0.347), MFR was significantly lower in the stress-rest group (3.07 [2.43-3.88] vs. 3.50 [2.63-4.10], p < 0.001). There was a weak correlation between Δtstress-rest and rMBF (r = -0.259, p = 0.002) and between Δtstress-rest and MFR (r = 0.163, p = 0.049), and the proportion of patients with abnormally high rMBF was significantly decreasing with increasing Δtstress-rest. CONCLUSIONS Intravenously applied adenosine induces a long-lasting hyperemic effect on the myocardium. Consequently, rapid stress-rest protocols could lead to an overestimation of rMBF and an underestimation of MFR

EPTAS and Subexponential Algorithm for Maximum Clique on Disk and Unit Ball Graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Cliqe on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics ’90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show that the disjoint union of two odd cycles is never the complement of a disk graph nor of a unit (3-dimensional) ball graph. From that fact and existing results, we derive a simple QPTAS and a subexponential algorithm running in time 2O˜(n2/3) for Maximum Cliqe on disk and unit ball graphs. We then obtain a randomized EPTAS for computing the independence number on graphs having no disjoint union of two odd cycles as an induced subgraph, bounded VC-dimension, and linear independence number. This, in combination with our structural results, yields a randomized EPTAS for Max Cliqe on disk and unit ball graphs. Max Cliqe on unit ball graphs is equivalent to finding, given a collection of points in R3, a maximum subset of points with diameter at most some fixed value. In stark contrast, Maximum Cliqe on ball graphs and unit 4-dimensional ball graphs, as well as intersection graphs of filled ellipses (even close to unit disks) or filled triangles is unlikely to have such algorithms. Indeed, we show that, for all those problems, there is a constant ratio of approximation which cannot be attained even in time 2n1−ε, unless the Exponential Time Hypothesis fails