Reduced resonance schemes and Chen ranks

The resonance varieties are cohomological invariants that are studied in a variety of topological, combinatorial, and geometric contexts. We discuss their scheme structure in a general algebraic setting and introduce various properties that ensure the reducedness of the associated projective resonance scheme. We prove an asymptotic formula for the Hilbert series of the associated Koszul module, then discuss applications to vector bundles on algebraic curves and to Chen ranks formulas for finitely generated groups, with special emphasis on K\"ahler and right-angled Artin groups.Comment: 34 page

Higher resonance schemes and Koszul modules of simplicial complexes

Each connected graded, graded-commutative algebra $A$ of finite type over a field $\Bbbk$ of characteristic zero defines a complex of finitely generated, graded modules over a symmetric algebra, whose homology graded modules are called the (higher) Koszul modules of $A$. In this note, we investigate the geometry of the support loci of these modules, called the resonance schemes of the algebra. When $A=\Bbbk\langle \Delta \rangle$ is the exterior Stanley-Reisner algebra associated to a finite simplicial complex $\Delta$, we show that the resonance schemes are reduced. We also compute the Hilbert series of the Koszul modules and give bounds on the regularity and projective dimension of these graded modules. This leads to a relationship between resonance and Hilbert series that generalizes a known formula for the Chen ranks of a right-angled Artin group.Comment: 16 page

Many-task computing on many-core architectures

Many-Task Computing (MTC) is a common scenario for multiple parallel systems, such as cluster, grids, cloud and supercomputers, but it is not so popular in shared memory parallel processors. In this sense and given the spectacular growth in performance and in number of cores integrated in many-core architectures, the study of MTC on such architectures is becoming more and more relevant. In this paper, authors present what are those programming mechanisms to take advantages of such massively parallel features for the particular target of MTC. Also, the hardware features of the two dominant many-core platforms (NVIDIA's GPUs and Intel Xeon Phi) are also analyzed for our specific framework. Given the important differences in terms of hardware and software in our two many-core platforms, we have considered different strategies based on CUDA (for GPUs) and OpenMP (for Intel Xeon Phi). We carried out several test cases based on an appropriate and widely studied problem for benchmarking as matrix multiplication. Essentially, this study consisted of comparing the time consumed for computing in parallel several tasks one by one (the whole computational resources are used just to compute one task at a time) with the time consumed for computing in parallel the same set of tasks simultaneously (the whole computational resources are used for computing the set of tasks at very same time). Finally, we compared both software-hardware scenarios to identify the most relevant computer features in each of our many-core architectures

Förster Resonance Energy Transfer (FRET) Correlates of Altered Subunit Stoichiometry in Cys-Loop Receptors, Exemplified by Nicotinic α4β2

We provide a theory for employing Förster resonance energy transfer (FRET) measurements to determine altered heteropentameric ion channel stoichiometries in intracellular compartments of living cells. We simulate FRET within nicotinic receptors (nAChRs) whose α4 and β2 subunits contain acceptor and donor fluorescent protein moieties, respectively, within the cytoplasmic loops. We predict FRET and normalized FRET (NFRET) for the two predominant stoichiometries, (α4)3(β2)2 vs. (α4)2(β2)3. Studying the ratio between FRET or NFRET for the two stoichiometries, minimizes distortions due to various photophysical uncertainties. Within a range of assumptions concerning the distance between fluorophores, deviations from plane pentameric geometry, and other asymmetries, the predicted FRET and NFRET for (α4)3(β2)2 exceeds that of (α4)2(β2)3. The simulations account for published data on transfected Neuro2a cells in which α4β2 stoichiometries were manipulated by varying fluorescent subunit cDNA ratios: NFRET decreased monotonically from (α4)3(β2)2 stoichiometry to mostly (α4)2(β2)3. The simulations also account for previous macroscopic and single-channel observations that pharmacological chaperoning by nicotine and cytisine increase the (α4)2(β2)3 and (α4)3(β2)2 populations, respectively. We also analyze sources of variability. NFRET-based monitoring of changes in subunit stoichiometry can contribute usefully to studies on Cys-loop receptors

Axial slicing versus bivalving in the pathological examination of pancreatoduodenectomy specimens (APOLLO): a multicentre randomized controlled trial

Background: In pancreatoduodenectomy specimens, dissection method may affect the assessment of primary tumour origin (i.e. pancreatic, distal bile duct or ampullary adenocarcinoma), which is primarily determined macroscopically. This is the first study to prospectively compare the two commonly used techniques, i.e. axial slicing and bivalving. Methods: In four centres, a randomized controlled trial was performed in specimens of patients with a suspected (pre)malignant tumour in the pancreatic head. Primary outcome measure was the level of certainty (scale 0–100) regarding tumour origin by four independent gastrointestinal pathologists based on macroscopic assessment. Secondary outcomes were inter-observer agreement and R1 rate. Results: In total, 128 pancreatoduodenectomy specimens were randomized. The level of certainty in determining the primary tumour origin did not differ between axial slicing and bivalving (mean score 72 [sd 13] vs. 68 [sd 16], p = 0.21), nor did inter-observer agreement, both being moderate (kappa 0.45 vs. 0.47). In pancreatic cancer specimens, R1 rate (60% vs. 55%, p = 0.71) and the number of harvested lymph nodes (median 16 vs. 17, p = 0.58) were similar. Conclusion: This study demonstrated no differences in determining the tumour origin between axial slicing and bivalving. Both techniques performed similarly regarding inter-observer agreement, R1 rate, and lymph node harvest

Efficacy of dose-escalated chemoradiation on complete tumour response in patients with locally advanced rectal cancer (RECTAL-BOOST); a phase 2 randomised controlled trial

Purpose Pathological complete tumour response following chemoradiation in patients with locally advanced rectal cancer (LARC) is associated with favourable prognosis and allows organ-sparing treatment strategies. We aimed to investigate the effect of an external radiation boost to the tumour prior to chemoradiation on pathological or sustained clinical complete tumour response in LARC. Methods and materials This multicentre, non-blinded, phase 2, randomised controlled trial followed the trials within cohorts-design, which is a pragmatic trial design allowing cohort participants to be randomized for an experimental intervention. Patients in the intervention group are offered the intervention (and can accept or refuse this), whereas patients in the control group are not notified about the randomisation. Participants of a colorectal cancer cohort referred for chemoradiation of LARC to either of two radiotherapy centres were eligible. Patients were randomised to no boost or an external radiation boost (5 x 3 Gy) without concurrent chemotherapy directly followed by standard pelvic chemoradiation (25 x 2 Gy with concurrent capecitabine). The primary outcome was pathological complete response (pCR, i.e. ypT0N0) in patients with planned surgery at 12 weeks or, as surrogate for pCR, a 2-year sustained clinical complete response for patients treated with an organ preservation strategy. Analyses were intention to treat. The study was registered with ClinicalTrials.gov, number NCTXXXXXX. Results Between Sept 2014 and July 2018, 128 patients were randomised. Fifty-one of the 64 (79.7%) patients in the intervention group accepted and received a boost. Compared with the control group, fewer patients in the intervention group had a cT4-stage and a low rectal tumour (31.3% versus 17.2% and 56.3% versus 45.3% respectively), and more patients had a cN2-stage (59.4% versus 70.3% respectively). Rate of pathological or sustained clinical complete tumour response was similar between the groups: 23 of 64 (35.9%, 95%CI 24.3-48.9) in the intervention group versus 24 of 64 (37.5%, 95%CI 25.7-50.5) in the control group (OR=0.94 95%CI 0.46-1.92). Near-complete or complete tumour regression was more common in the intervention group: 34 of 49 (69.4%) versus 24 of 53 (45.3%) in the control group (OR=2.74, 95%CI 1.21-6.18). Grade >3 acute toxicity was comparable: 6 of 64 (9.4%) in the intervention group versus 5 of 64 (7.8%) in the control group (OR=1.22 95%CI 0.35-4.22). Conclusion Dose escalation with an external radiotherapy boost to the tumour prior to neoadjuvant chemoradiation did not increase the pathological or sustained clinical complete tumour response rate in LARC