Large Fourier transforms never exactly realized by braiding conformal blocks

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set \{\U(2), \textrm{CNOT}\}, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1, \omega=e^{\frac{2\pi i}{N}}$, can be realized exactly by quantum circuits of size $O(n^2), n=\textrm{log}N$, and so can the discrete sine/cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine/cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that approximation is unavoidable to implement the Fourier transforms by braiding conformal blocks

Convergence of the Magnus series

The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a sufficient condition for convergence, which improves on several earlier results.Comment: 11 pages; v2: added justification for conjecture, minor clarifications and correction

Changes in electrophysiological static and dynamic human brain functional architecture from childhood to late adulthood

Published: 04 November 2020This magnetoencephalography study aimed at characterizing age-related changes in resting-state functional brain organization from mid-childhood to late adulthood. We investigated neuromagnetic brain activity at rest in 105 participants divided into three age groups: children (6–9 years), young adults (18–34 years) and healthy elders (53–78 years). The effects of age on static resting-state functional brain integration were assessed using band-limited power envelope correlation, whereas those on transient functional brain dynamics were disclosed using hidden Markov modeling of power envelope activity. Brain development from childhood to adulthood came with (1) a strengthening of functional integration within and between resting-state networks and (2) an increased temporal stability of transient (100–300 ms lifetime) and recurrent states of network activation or deactivation mainly encompassing lateral or medial associative neocortical areas. Healthy aging was characterized by decreased static resting-state functional integration and dynamic stability within the primary visual network. These results based on electrophysiological measurements free of neurovascular biases suggest that functional brain integration mainly evolves during brain development, with limited changes in healthy aging. These novel electrophysiological insights into human brain functional architecture across the lifespan pave the way for future clinical studies investigating how brain disorders affect brain development or healthy aging.This study was supported by the Action de Recherche Concertée Consolidation (ARCC, “Characterizing the spatio-temporal dynamics and the electrophysiological bases of resting state networks”, ULB, Brussels, Belgium), the Fonds Erasme (Research Convention “Les Voies du Savoir”,Brussels, Belgium) and the Fonds de la Recherche Scientifique (Research Convention: T.0109.13, FRS-FNRS, Brussels, Belgium). Nicolas Coquelet has been supported by the ARCC, by the Fonds Erasme (Research Convention “Les Voies du Savoir”, Brussels, Belgium) and is supported by the FRS-FNRS (Research Convention: Excellence of Science EOS “MEMODYN”). Alison Mary is Postdoctoral Researcher at the FRS-FNRS. Maxime Niesen and Marc Vander Ghinst have been supported by the Fonds Erasme. Mariagrazia Ranzini is supported by the Marie Sklodowska-Curie European Union’s Horizon 2020 research and innovation program (Research Grant: 839394). Mathieu Bourguignon is supported by the program Attract of Innoviris (Research Grant 2015-BB2B-10, Brussels, Belgium), the Marie Sklodowska-Curie Action of the European Commission (Research Grant: 743562) and by the Spanish Ministery of Economy and Competitiveness (Research Grant: PSI2016-77175-P). Xavier De Tiège is Postdoctorate Clinical Master Specialist at the FRS-FNRS. The MEG project at the CUB Hôpital Erasme is financially supported by the Fonds Erasme

Dirofilaria repens Infection and Concomitant Meningoencephalitis

Dirofilaria repens, a filarial nematode of dogs and other carnivores, can accidentally infect humans. Clinical symptoms are usually restricted to a subcutaneous nodule containing a single infertile parasite. Here, we report a case of D. repens infection with a subcutaneous gravid worm and the patient’s concomitant meningoencephalitis and aphasia

Diophantine Approximation and applications in Interference Alignment

This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R n. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1]

Sufficient conditions for the convergence of the Magnus expansion

Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation $Y' = A(t) Y$. The first one provides a bound on the convergence domain based on the norm of the operator $A(t)$. The second condition links the convergence of the expansion with the structure of the spectrum of $Y(t)$, thus yielding a more precise characterization. Several examples are proposed to illustrate the main issues involved and the information on the convergence domain provided by both conditions.Comment: 20 page

Molybdenum solar neutrino experiment

The goal of the molybdenum solar neutrino experiment is to deduce the /sup 8/B solar neutrino flux, averaged over the past several million years, from the concentration of /sup 98/Tc in a deeply buried molybdenum deposit. The experiment is important to an understanding of stellar processes because it will shed light on the reason for the discrepancy between theory and observation of the chlorine solar neutrino experiment. Possible reasons for the discrepancy may lie in the properties of neutrinos (neutrino oscillations or massive neutrinos) or in deficiencies of the standard solar model. The chlorine experiment only measures the /sup 8/B neutrino flux in current times and does not address possible temporal variations in the interior of the sun, which are also not considered in the standard model. In the molybdenum experiment, we plan to measure /sup 98/Tc (4.2 Myr), also produced by /sup 8/B neutrinos, and possibly /sup 97/Tc (2.6 Myr), produced by lower energy neutrinos

Functional single nucleotide polymorphisms within the cyclin-dependent kinase inhibitor 2A/2B region affect pancreatic cancer risk

The CDKN2A (p16) gene plays a key role in pancreatic cancer etiology. It is one of the most commonly somatically mutated genes in pancreatic cancer, rare germline mutations have been found to be associated with increased risk of developing familiar pancreatic cancer and CDKN2A promoter hyper-methylation has been suggested to play a critical role both in pancreatic cancer onset and prognosis. In addition several unrelated SNPs in the 9p21.3 region, that includes the CDNK2A, CDNK2B and the CDNK2B-AS1 genes, are associated with the development of cancer in various organs. However, association between the common genetic variability in this region and pancreatic cancer risk is not clearly understood. We sought to fill this gap in a case-control study genotyping 13 single nucleotide polymorphisms (SNPs) in 2,857 pancreatic ductal adenocarcinoma (PDAC) patients and 6,111 controls in the context of the Pancreatic Disease Research (PANDoRA) consortium. We found that the A allele of the rs3217992 SNP was associated with an increased pancreatic cancer risk (ORhet=1.14, 95% CI 1.01-1.27, p=0.026, ORhom=1.30, 95% CI 1.12-1.51, p=0.00049). This pleiotropic variant is reported to be a mir-SNP that, by changing the binding site of one or more miRNAs, could influence the normal cell cycle progression and in turn increase PDAC risk. In conclusion, we observed a novel association in a pleiotropic region that has been found to be of key relevance in the susceptibility to various types of cancer and diabetes suggesting that the CDKN2A/B locus could represent a genetic link between diabetes and pancreatic cancer risk

Convenient method for resolving degeneracies due to symmetry of the magnetic susceptibility tensor and its application to pseudo contact shift-based protein–protein complex structure determination

Pseudo contact shifts (PCSs) induced by paramagnetic lanthanide ions fixed in a protein frame provide long-range distance and angular information, and are valuable for the structure determination of protein–protein and protein–ligand complexes. We have been developing a lanthanide-binding peptide tag (hereafter LBT) anchored at two points via a peptide bond and a disulfide bond to the target proteins. However, the magnetic susceptibility tensor displays symmetry, which can cause multiple degenerated solutions in a structure calculation based solely on PCSs. Here we show a convenient method for resolving this degeneracy by changing the spacer length between the LBT and target protein. We applied this approach to PCS-based rigid body docking between the FKBP12-rapamycin complex and the mTOR FRB domain, and demonstrated that degeneracy could be resolved using the PCS restraints obtained from two-point anchored LBT with two different spacer lengths. The present strategy will markedly increase the usefulness of two-point anchored LBT for protein complex structure determination

Thermodynamics of Aryl-Dihydroxyphenyl-Thiadiazole Binding to Human Hsp90

The design of specific inhibitors against the Hsp90 chaperone and other enzyme relies on the detailed and correct understanding of both the thermodynamics of inhibitor binding and the structural features of the protein-inhibitor complex. Here we present a detailed thermodynamic study of binding of aryl-dihydroxyphenyl-thiadiazole inhibitor series to recombinant human Hsp90 alpha isozyme. The inhibitors are highly potent, with the intrinsic Kd approximately equal to 1 nM as determined by isothermal titration calorimetry (ITC) and thermal shift assay (TSA). Dissection of protonation contributions yielded the intrinsic thermodynamic parameters of binding, such as enthalpy, entropy, Gibbs free energy, and the heat capacity. The differences in binding thermodynamic parameters between the series of inhibitors revealed contributions of the functional groups, thus providing insight into molecular reasons for improved or diminished binding efficiency. The inhibitor binding to Hsp90 alpha primarily depended on a large favorable enthalpic contribution combined with the smaller favorable entropic contribution, thus suggesting that their binding was both enthalpically and entropically optimized. The enthalpy-entropy compensation phenomenon was highly evident when comparing the inhibitor binding enthalpies and entropies. This study illustrates how detailed thermodynamic analysis helps to understand energetic reasons for the binding efficiency and develop more potent inhibitors that could be applied for therapeutic use as Hsp90 inhibitors