Clustering Brain Signals: A Robust Approach Using Functional Data Ranking

In this paper, we analyze electroencephalograms (EEG) which are recordings of brain electrical activity. We develop new clustering methods for identifying synchronized brain regions, where the EEGs show similar oscillations or waveforms according to their spectral densities. We treat the estimated spectral densities from many epochs or trials as functional data and develop clustering algorithms based on functional data ranking. The two proposed clustering algorithms use different dissimilarity measures: distance of the functional medians and the area of the central region. The performance of the proposed algorithms is examined by simulation studies. We show that, when contaminations are present, the proposed methods for clustering spectral densities are more robust than the mean-based methods. The developed methods are applied to two stages of resting state EEG data from a male college student, corresponding to early exploration of functional connectivity in the human brain

Role of sea quarks in the nucleon transverse spin

We present a phenomenological extraction of transversity distribution functions and Collins fragmentation functions by simultaneously fitting to semi-inclusive deep inelastic scattering and electron-positron annihilation data. The analysis is performed within the transverse momentum dependent factorization formalism, and sea quark transversity distributions are taken into account for the first time. We find the $\bar u$ quark favors a negative transversity distribution while that of the $\bar d$ quark is consistent with zero according to the current accuracy. In addition, based on a combined analysis of world data and simulated data, we quantitatively demonstrate the impact of the proposed Electron-ion Collider in China on precise determinations of the transversity distributions, especially for sea quarks, and the Collins fragmentation functions

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate the uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.Comment: 11 pages, 3 figures, published on Physics Letters

Spatially-coded Fourier ptychography: flexible and detachable coded thin films for quantitative phase imaging with uniform phase transfer characteristics

Fourier ptychography (FP) is an enabling imaging technique that produces high-resolution complex-valued images with extended field coverages. However, when FP images a phase object with any specific spatial frequency, the captured images contain only constant values, rendering the recovery of the corresponding linear phase ramp impossible. This challenge is not unique to FP but also affects other common microscopy techniques -- a rather counterintuitive outcome given their widespread use in phase imaging. The underlying issue originates from the non-uniform phase transfer characteristic inherent in microscope systems, which impedes the conversion of object wavefields into discernible intensity variations. To address this challenge, we present spatially-coded Fourier ptychography (scFP), a new method that synergizes FP with spatial-domain coded detection for true quantitative phase imaging. In scFP, a flexible and detachable coded thin film is attached atop the image sensor in a regular FP setup. The spatial modulation of this thin film ensures a uniform phase response across the entire synthetic bandwidth. It improves reconstruction quality and corrects refractive index underestimation issues prevalent in conventional FP and related tomographic implementations. The inclusion of the coded thin film further adds a new dimension of measurement diversity in the spatial domain. The development of scFP is expected to catalyse new research directions and applications for phase imaging, emphasizing the need for true quantitative accuracy with uniform frequency response

Role of Protein Charge Density on Hepatitis B Virus Capsid Formation

The role of electrostatic interactions in the viral capsid assembly process was studied by comparing the assembly process of a truncated hepatitis B virus capsid protein Cp149 with its mutant protein D2N/D4N, which has the same conformational structure but four fewer charges per dimer. The capsid protein self-assembly was investigated under a wide range of protein surface charge densities by changing the protein concentration, buffer pH, and solution ionic strength. Lowering the protein charge density favored the capsid formation. However, lowering charge beyond a certain point resulted in capsid aggregation and precipitation. Interestingly, both the wild-type and D2N/D4N mutant displayed identical assembly profiles when their charge densities matched each other. These results indicated that the charge density was optimized by nature to ensure an efficient and effective capsid proliferation under the physiological pH and ionic strength