Methodological Investigation for Hydrogen Addition to Small Cage Carbon Fullerenes

Hydrogenated small fullerenes (Cn, n<60) are of interest as potential astrochemical species, and as intermediates in hydrogen catalysed fullerene growth. However computational identification of key stable species is difficult due to the vast combinatorial space of structures. In this study we explore routes to predict stable hydrogenated small fullerenes. We show that neither local fullerene geometry nor local electronic structure analysis are able to correctly predict subsequent low energy hydrogenation sites, and indeed sequential stable addition searches also sometimes fail to identify most stable hydrogenated fullerene isomers. Of the empirical and semi-empirical methods tested, GFN2-xTB consistently gives highly accurate energy correlation (r>0.99) to full DFT-LDA calculations at a fraction of the computational cost. This allows identification of the most stable hydrogenated fullerenes up to 4H for four fullerenes, namely two isomers of C28 and C40, via “brute force” systematic testing of all symmetry inequivalent combinations. The approach shows promise for wider systematic studies of smaller hydrogenated fullerenes.

The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL′

We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N3LO) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation — the jet function — from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at N3LO. We combine the newly obtained N3LO jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at N3LL′ accuracy, resulting in a factor of ∼ 4 reduction of uncertainties in the peak region compared to N3LL predictions.

Wavelet Transform for IoT – A Signal Processing Perspective

<div>Denoising of signals in an Internet-of-Things (IoT) network is critically challenging owing to the diverse nature of the nodes generating them, environments through which they travel, characteristics of noise plaguing the signals and the applications they cater to. In order to address the abovementioned challenges, we conceptualize a generalized framework combining wavelet packet transform (WPT) and energy correlation analysis. WPT decomposes both the low-frequency and high-frequency components of the received signals in different time scales and wavelet spaces. Noise components are identified, removed through filtering and the signal components are predicted back after filtering using inverse wavelet packet transform (IWPT). Next energy of the reconstructed signal components are compared with that of the original transmitted signal to modify the characteristics of the decomposed signal components. Using the modified details, the signal components are reconstructed back again and the noise components are filtered out. This process is repeated until noise is completely removed. Initial results suggest that, our proposed framework offers improvement in error probability performance of a medium-scale IoT network over traditional discrete wavelet transform (DWT) and WPT based techniques by around 3 dB and 7 dB respectively.</div>

Wavelet Transform for IoT – A Signal Processing Perspective

<div>Denoising of signals in an Internet-of-Things (IoT) network is critically challenging owing to the diverse nature of the nodes generating them, environments through which they travel, characteristics of noise plaguing the signals and the applications they cater to. In order to address the abovementioned challenges, we conceptualize a generalized framework combining wavelet packet transform (WPT) and energy correlation analysis. WPT decomposes both the low-frequency and high-frequency components of the received signals in different time scales and wavelet spaces. Noise components are identified, removed through filtering and the signal components are predicted back after filtering using inverse wavelet packet transform (IWPT). Next energy of the reconstructed signal components are compared with that of the original transmitted signal to modify the characteristics of the decomposed signal components. Using the modified details, the signal components are reconstructed back again and the noise components are filtered out. This process is repeated until noise is completely removed. Initial results suggest that, our proposed framework offers improvement in error probability performance of a medium-scale IoT network over traditional discrete wavelet transform (DWT) and WPT based techniques by around 3 dB and 7 dB respectively.</div>

Energy-energy correlation in hadronic Higgs decays: analytic results and phenomenology at NLO

In this work we complete the investigation of the recently introduced energy-energy correlation (EEC) function in hadronic Higgs decays at next-to-leading order (NLO) in fixed-order perturbation theory in the limit of vanishing light quark masses. The full analytic NLO result for the previously unknown EEC in the H → $$ q\overline{q} $$ q q ¯ + X channel is given in terms of classical polylogarithms and cross-checked against a numerical calculation. In addition to that, we discuss further corrections to predictions of the Higgs EEC event shape variable, including quark mass corrections, effects of parton shower and hadronization. We also estimate the statistical error on the measurements of the Higgs EEC at future Higgs factories and compare with the current perturbative uncertainty.