Hilbert Space Representations of Probability Distributions

Many problems in unsupervised learning require the analysis of features of probability distributions. At the most fundamental level, we might wish to determine whether two distributions are the same, based on samples from each - this is known as the two-sample or homogeneity problem. We use kernel methods to address this problem, by mapping probability distributions to elements in a reproducing kernel Hilbert space (RKHS). Given a sufficiently rich RKHS, these representations are unique: thus comparing feature space representations allows us to compare distributions without ambiguity. Applications include testing whether cancer subtypes are distinguishable on the basis of DNA microarray data, and whether low frequency oscillations measured at an electrode in the cortex have a different distribution during a neural spike. A more difficult problem is to discover whether two random variables drawn from a joint distribution are independent. It turns out that any dependence between pairs of random variables can be encoded in a cross-covariance operator between appropriate RKHS representations of the variables, and we may test independence by looking at a norm of the operator. We demonstrate this independence test by establishing dependence between an English text and its French translation, as opposed to French text on the same topic but otherwise unrelated. Finally, we show that this operator norm is itself a difference in feature means

Injection Kinetics and Electronic Structure at the N719 TiO2 Interface Studied by Means of Ultrafast XUV Photoemission Spectroscopy

The method of transient XUV photoemission spectroscopy is developed to investigate the ultrafast dynamics of heterogeneous electron transfer at the interface between the N719 ruthenium dye complex and TiO2 nanoparticles. XUV light from high order harmonic generation is used to probe the electron density distribution among the ground and excited states at the interface after its exposure to a pump laser pulse of 530 nm wavelength. A spectral decomposition of the transient emission signal is used to follow the population and decay dynamics of the involved transient states individually. By comparing results obtained for the N719 TiO2 and N719 FTO interfaces, we can unambiguously reveal the kinetics of electrons injected to TiO2 from the singlet metal to ligand charge transfer MLCT excited state of the dye. With the developed approach, we characterize both the kinetic constants and the absolute binding energies of the singlet and triplet MLCT states of the dye and the state of electrons injected to the conduction band of TiO2. The energy levels of the singlet and triplet states are found to lie 0.7 eV above and 0.2 eV below the conduction band minimum, respectively. This energetic structure gives rise to a strong driving force for injection from the singlet state and a slow electron transfer from the triplet state, the latter being possible due to a partial overlap of the triplet state band of N719 and the conduction band of TiO

The effect of lysergic acid diethylamide (LSD) on whole-brain functional and effective connectivity

Psychedelics have emerged as promising candidate treatments for various psychiatric conditions, and given their clinical potential, there is a need to identify biomarkers that underlie their effects. Here, we investigate the neural mechanisms of lysergic acid diethylamide (LSD) using regression dynamic causal modelling (rDCM), a novel technique that assesses whole-brain effective connectivity (EC) during resting-state functional magnetic resonance imaging (fMRI). We modelled data from two randomised, placebo-controlled, double-blind, cross-over trials, in which 45 participants were administered 100 μg LSD and placebo in two resting-state fMRI sessions. We compared EC against whole-brain functional connectivity (FC) using classical statistics and machine learning methods. Multivariate analyses of EC parameters revealed predominantly stronger interregional connectivity and reduced self-inhibition under LSD compared to placebo, with the notable exception of weakened interregional connectivity and increased self-inhibition in occipital brain regions as well as subcortical regions. Together, these findings suggests that LSD perturbs the Excitation/Inhibition balance of the brain. Notably, whole-brain EC did not only provide additional mechanistic insight into the effects of LSD on the Excitation/Inhibition balance of the brain, but EC also correlated with global subjective effects of LSD and discriminated experimental conditions in a machine learning-based analysis with high accuracy (91.11%), highlighting the potential of using whole-brain EC to decode or predict subjective effects of LSD in the future

Multiscale Photon Based In Situ and Operando Spectroscopies in Time and Energy Landscapes

Following catalytic reactions, in situ and operando are now the focus of a number of dedicated experiments at light sources which have been developed to track the electronic and molecular structural dynamics of catalysts. The challenges for this goal are two fold first, the development of spectroscopic tools in the energy domain and time domain is required. The photocatalytic processes have early dynamics of tens of femtoseconds, while further reaction takes seconds, minutes, and even hours. Second, a combination of tools to probe processes not only in solids, but also in solutions and at interfaces, is now needed. In this special issue, we present recent developments at the synchrotron facility BESSY II using photon energy from the infrared and extreme ultraviolet up to the soft X ray regime for in situ and operando applications addressing these two major challenges. As this work is a result of contributions from several groups, each section will present the group s activities and related team members involve

Joint EANM/SIOPE/RAPNO practice guidelines/SNMMI procedure standards for imaging of paediatric gliomas using PET with radiolabelled amino acids and [¹⁸F]FDG: version 1.0

Positron emission tomography (PET) has been widely used in paediatric oncology. 2-Deoxy-2-[18F]fluoro-D-glucose ([18F]FDG) is the most commonly used radiopharmaceutical for PET imaging. For oncological brain imaging, different amino acid PET radiopharmaceuticals have been introduced in the last years. The purpose of this document is to provide imaging specialists and clinicians guidelines for indication, acquisition, and interpretation of [18F]FDG and radiolabelled amino acid PET in paediatric patients affected by brain gliomas. There is no high level of evidence for all recommendations suggested in this paper. These recommendations represent instead the consensus opinion of experienced leaders in the field. Further studies are needed to reach evidence-based recommendations for the applications of [18F]FDG and radiolabelled amino acid PET in paediatric neuro-oncology. These recommendations are not intended to be a substitute for national and international legal or regulatory provisions and should be considered in the context of good practice in nuclear medicine. The present guidelines/standards were developed collaboratively by the EANM and SNMMI with the European Society for Paediatric Oncology (SIOPE) Brain Tumour Group and the Response Assessment in Paediatric Neuro-Oncology (RAPNO) working group. They summarize also the views of the Neuroimaging and Oncology and Theranostics Committees of the EANM and reflect recommendations for which the EANM and other societies cannot be held responsible

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

General psychopathology links burden of recent life events and psychotic symptoms in a network approach

Recent life events have been implicated in the onset and progression of psychosis. However, psychological processes that account for the association are yet to be fully understood. Using a network approach, we aimed to identify pathways linking recent life events and symptoms observed in psychosis. Based on previous literature, we hypothesized that general symptoms would mediate between recent life events and psychotic symptoms. We analyzed baseline data of patients at clinical high risk for psychosis and with recent-onset psychosis (n = 547) from the Personalised Prognostic Tools for Early Psychosis Management (PRONIA) study. In a network analysis, we modeled links between the burden of recent life events and all individual symptoms of the Positive and Negative Syndrome Scale before and after controlling for childhood trauma. To investigate the longitudinal associations between burden of recent life events and symptoms, we analyzed multiwave panel data from seven timepoints up to month 18. Corroborating our hypothesis, burden of recent life events was connected to positive and negative symptoms through general psychopathology, specifically depression, guilt feelings, anxiety and tension, even after controlling for childhood trauma. Longitudinal modeling indicated that on average, burden of recent life events preceded general psychopathology in the individual. In line with the theory of an affective pathway to psychosis, recent life events may lead to psychotic symptoms via heightened emotional distress. Life events may be one driving force of unspecific, general psychopathology described as characteristic of early phases of the psychosis spectrum, offering promising avenues for interventions

Reduced parahippocampal cortical thickness in subjects at ultra-high risk for psychosis

Background Grey matter volume and cortical thickness represent two complementary aspects of brain structure. Several studies have described reductions in grey matter volume in people at ultra-high risk (UHR) of psychosis; however, little is known about cortical thickness in this group. The aim of the present study was to investigate cortical thickness alterations in UHR subjects and compare individuals who subsequently did and did not develop psychosis. Method We examined magnetic resonance imaging data collected at four different scanning sites. The UHR subjects were followed up for at least 2 years. Subsequent to scanning, 50 UHR subjects developed psychosis and 117 did not. Cortical thickness was examined in regions previously identified as sites of neuroanatomical alterations in UHR subjects, using voxel-based cortical thickness. Results At baseline UHR subjects, compared with controls, showed reduced cortical thickness in the right parahippocampal gyrus (p<0.05, familywise error corrected). There were no significant differences in cortical thickness between the UHR subjects who later developed psychosis and those who did not. Conclusions These data suggest that UHR symptomatology is characterized by alterations in the thickness of the medial temporal cortex. We did not find evidence that the later progression to psychosis was linked to additional alterations in cortical thickness, although we cannot exclude the possibility that the study lacked sufficient power to detect such difference