Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs

This paper studies the problem of forecasting general stochastic processes using an extension of the Neural Jump ODE (NJ-ODE) framework. While NJ-ODE was the first framework to establish convergence guarantees for the prediction of irregularly observed time series, these results were limited to data stemming from It\^o-diffusions with complete observations, in particular Markov processes where all coordinates are observed simultaneously. In this work, we generalise these results to generic, possibly non-Markovian or discontinuous, stochastic processes with incomplete observations, by utilising the reconstruction properties of the signature transform. These theoretical results are supported by empirical studies, where it is shown that the path-dependent NJ-ODE outperforms the original NJ-ODE framework in the case of non-Markovian data. Moreover, we show that PD-NJ-ODE can be applied successfully to limit order book (LOB) data

Musterbildung auf Si- und Ge-Oberflächen durch niederenergetische Ionenstrahlerosion: Musterbildung auf Si- und Ge-Oberflächen durch niederenergetische Ionenstrahlerosion

Die vorliegende Arbeit beschäftigt sich mit der Oberflächenglättung und selbstorganisierten Musterbildung auf Si(100) und Ge(100) durch Beschuss mit niederenergetischen Edelgasionen (Ne, Ar, Kr, Xe). Die Untersuchungen wurden für Ionenenergien zwischen 400 eV und 2000 eV für Ioneneinfallswinkel von 0° bis 85° durchgeführt. Zudem wurde die zeitliche Entwicklung spezifischer Erosionsformen durch die Variation der Fluenz über zwei Größenordnungen analysiert. In den Experimenten finden sich deutliche Anzeichen einer Facettierung sowie einer Vergröberung der Strukturen mit zunehmender Erosionszeit. Diese Beobachtungen deuten darauf hin, dass von Beginn an gradientenabhängiges Zerstäuben und die Reflexion von Primärionen einen wesentlichen Einfluss auf die Strukturentwicklung haben. Die Ergebnisse werden im Kontext bestehender Musterbildungsmodelle diskutiert

Another proof for the equivalence between invariance of closed sets with respect to stochastic and deterministic systems☆☆The authors gratefully acknowledge the support from the RTN network HPRN-CT-2002-00281 (European Union) and from the FWF-grant Y 328 (Austrian Science Funds).

AbstractWe provide a short and elementary proof for the recently proved result by G. da Prato and H. Frankowska that – under minimal assumptions – a closed set is invariant with respect to a stochastic control system if and only if it is invariant with respect to the (associated) deterministic control system

Ripple coarsening on ion beam-eroded surfaces

The temporal evolution of ripple pattern on Ge, Si, Al(2)O(3), and SiO(2) by low-energy ion beam erosion with Xe (+) ions is studied. The experiments focus on the ripple dynamics in a fluence range from 1.1 × 10(17) cm(-2) to 1.3 × 10(19) cm(-2) at ion incidence angles of 65° and 75° and ion energies of 600 and 1,200 eV. At low fluences a short-wavelength ripple structure emerges on the surface that is superimposed and later on dominated by long wavelength structures for increasing fluences. The coarsening of short wavelength ripples depends on the material system and angle of incidence. These observations are associated with the influence of reflected primary ions and gradient-dependent sputtering. The investigations reveal that coarsening of the pattern is a universal behavior for all investigated materials, just at the earliest accessible stage of surface evolution

Single Cell RNA-Sequencing of Pluripotent States Unlocks Modular Transcriptional Variation

SummaryEmbryonic stem cell (ESC) culture conditions are important for maintaining long-term self-renewal, and they influence cellular pluripotency state. Here, we report single cell RNA-sequencing of mESCs cultured in three different conditions: serum, 2i, and the alternative ground state a2i. We find that the cellular transcriptomes of cells grown in these conditions are distinct, with 2i being the most similar to blastocyst cells and including a subpopulation resembling the two-cell embryo state. Overall levels of intercellular gene expression heterogeneity are comparable across the three conditions. However, this masks variable expression of pluripotency genes in serum cells and homogeneous expression in 2i and a2i cells. Additionally, genes related to the cell cycle are more variably expressed in the 2i and a2i conditions. Mining of our dataset for correlations in gene expression allowed us to identify additional components of the pluripotency network, including Ptma and Zfp640, illustrating its value as a resource for future discovery

Accuracy of MRI Classification Algorithms in a Tertiary Memory Center Clinical Routine Cohort

BACKGROUND:Automated volumetry software (AVS) has recently become widely available to neuroradiologists. MRI volumetry with AVS may support the diagnosis of dementias by identifying regional atrophy. Moreover, automatic classifiers using machine learning techniques have recently emerged as promising approaches to assist diagnosis. However, the performance of both AVS and automatic classifiers has been evaluated mostly in the artificial setting of research datasets.OBJECTIVE:Our aim was to evaluate the performance of two AVS and an automatic classifier in the clinical routine condition of a memory clinic.METHODS:We studied 239 patients with cognitive troubles from a single memory center cohort. Using clinical routine T1-weighted MRI, we evaluated the classification performance of: 1) univariate volumetry using two AVS (volBrain and Neuroreader$^{TM}$); 2) Support Vector Machine (SVM) automatic classifier, using either the AVS volumes (SVM-AVS), or whole gray matter (SVM-WGM); 3) reading by two neuroradiologists. The performance measure was the balanced diagnostic accuracy. The reference standard was consensus diagnosis by three neurologists using clinical, biological (cerebrospinal fluid) and imaging data and following international criteria.RESULTS:Univariate AVS volumetry provided only moderate accuracies (46% to 71% with hippocampal volume). The accuracy improved when using SVM-AVS classifier (52% to 85%), becoming close to that of SVM-WGM (52 to 90%). Visual classification by neuroradiologists ranged between SVM-AVS and SVM-WGM.CONCLUSION:In the routine practice of a memory clinic, the use of volumetric measures provided by AVS yields only moderate accuracy. Automatic classifiers can improve accuracy and could be a useful tool to assist diagnosis

In vitro characterisation of the anti-intravasative properties of the marine product heteronemin

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An Automated Pipeline for the Analysis of PET Data on the Cortical Surface

We present a fully automatic pipeline for the analysis of PET data on the cortical surface. Our pipeline combines tools from FreeSurfer and PETPVC, and consists of (i) co-registration of PET and T1-w MRI (T1) images, (ii) intensity normalization, (iii) partial volume correction, (iv) robust projection of the PET signal onto the subject's cortical surface, (v) spatial normalization to a template, and (vi) atlas statistics. We evaluated the performance of the proposed workflow by performing group comparisons and showed that the approach was able to identify the areas of hypometabolism characteristic of different dementia syndromes: Alzheimer's disease (AD) and both the semantic and logopenic variants of primary progressive aphasia. We also showed that these results were comparable to those obtained with a standard volume-based approach. We then performed individual classifications and showed that vertices can be used as features to differentiate cognitively normal and AD subjects. This pipeline is integrated into Clinica, an open-source software platform for neuroscience studies available at www.clinica.run