Parton distribution functions on the lattice and in the continuum

Ioffe-time distributions, which are functions of the Ioffe-time $\nu$, are the Fourier transforms of parton distribution functions with respect to the momentum fraction variable $x$. These distributions can be obtained from suitable equal time, quark bilinear hadronic matrix elements which can be calculated from first principles in lattice QCD, as it has been recently argued. In this talk I present the first numerical calculation of the Ioffe-time distributions of the nucleon in the quenched approximation.Comment: 8 pages, 10 figures. arXiv admin note: text overlap with arXiv:1706.0537

Progress on Complex Langevin simulations of a finite density matrix model for QCD

We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.Comment: 8 pages, 7 figures, Proceedings of the 35th International Symposium on Lattice Field Theory, Granada, Spai

Random Matrix Models for Dirac Operators at finite Lattice Spacing

We study discretization effects of the Wilson and staggered Dirac operator with $N_{\rm c}>2$ using chiral random matrix theory (chRMT). We obtain analytical results for the joint probability density of Wilson-chRMT in terms of a determinantal expression over complex pairs of eigenvalues, and real eigenvalues corresponding to eigenvectors of positive or negative chirality as well as for the eigenvalue densities. The explicit dependence on the lattice spacing can be readily read off from our results which are compared to numerical simulations of Wilson-chRMT. For the staggered Dirac operator we have studied random matrices modeling the transition from non-degenerate eigenvalues at non-zero lattice spacing to degenerate ones in the continuum limit.Comment: 7 pages, 6 figures, Proceedings for the XXIX International Symposium on Lattice Field Theory, July 10 -- 16 2011, Squaw Valley, Lake Tahoe, California, PACS: 12.38.Gc, 05.50.+q, 02.10.Yn, 11.15.H

Neonatal seizure detection based on single-channel EEG: instrumentation and algorithms

Seizure activity in the perinatal period, which constitutes the most common neurological emergency in the neonate, can cause brain disorders later in life or even death depending on their severity. This issue remains unsolved to date, despite the several attempts in tackling it using numerous methods. Therefore, a method is still needed that can enable neonatal cerebral activity monitoring to identify those at risk. Currently, electroencephalography (EEG) and amplitude-integrated EEG (aEEG) have been exploited for the identification of seizures in neonates, however both lack automation. EEG and aEEG are mainly visually analysed, requiring a specific skill set and as a result the presence of an expert on a 24/7 basis, which is not feasible. Additionally, EEG devices employed in neonatal intensive care units (NICU) are mainly designed around adults, meaning that their design specifications are not neonate specific, including their size due to multi-channel requirement in adults - adults minimum requirement is ≥ 32 channels, while gold standard in neonatal is equal to 10; they are bulky and occupy significant space in NICU. This thesis addresses the challenge of reliably, efficiently and effectively detecting seizures in the neonatal brain in a fully automated manner. Two novel instruments and two novel neonatal seizure detection algorithms (SDAs) are presented. The first instrument, named PANACEA, is a high-performance, wireless, wearable and portable multi-instrument, able to record neonatal EEG, as well as a plethora of (bio)signals. This device despite its high-performance characteristics and ability to record EEG, is mostly suggested to be used for the concurrent monitoring of other vital biosignals, such as electrocardiogram (ECG) and respiration, which provide vital information about a neonate's medical condition. The two aforementioned biosignals constitute two of the most important artefacts in the EEG and their concurrent acquisition benefit the SDA by providing information to an artefact removal algorithm. The second instrument, called neoEEG Board, is an ultra-low noise, wireless, portable and high precision neonatal EEG recording instrument. It is able to detect and record minute signals (< 10 nVp) enabling cerebral activity monitoring even from lower layers in the cortex. The neoEEG Board accommodates 8 inputs each one equipped with a patent-pending tunable filter topology, which allows passband formation based on the application. Both the PANACEA and the neoEEG Board are able to host low- to middle-complexity SDAs and they can operate continuously for at least 8 hours on 3-AA batteries. Along with PANACEA and the neoEEG Board, two novel neonatal SDAs have been developed. The first one, termed G prime-smoothed (G ́_s), is an on-line, automated, patient-specific, single-feature and single-channel EEG based SDA. The G ́_s SDA, is enabled by the invention of a novel feature, termed G prime (G ́) and can be characterised as an energy operator. The trace that the G ́_s creates, can also be used as a visualisation tool because of its distinct change at a presence of a seizure. Finally, the second SDA is machine learning (ML)-based and uses numerous features and a support vector machine (SVM) classifier. It can be characterised as automated, on-line and patient-independent, and similarly to G ́_s it makes use of a single-channel EEG. The proposed neonatal SDA introduces the use of the Hilbert-Huang transforms (HHT) in the field of neonatal seizure detection. The HHT analyses the non-linear and non-stationary EEG signal providing information for the signal as it evolves. Through the use of HHT novel features, such as the per intrinsic mode function (IMF) (0-3 Hz) sub-band power, were also employed. Detection rates of this novel neonatal SDA is comparable to multi-channel SDAs.Open Acces