Forests, cumulants, martingales

This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a "broken exponential martingale" expansion that generalizes and unifies the exponentiation result of Al{\`o}s, Gatheral, and Radoi\v{c}i\'c and the cumulant recursion formula of Lacoin, Rhodes, and Vargas. Specifically, we exhibit the two previous results as lower dimensional projections of the same generalized forest expansion, subsequently related by forest reordering. Our approach also leads to sharp integrability conditions for validity of the cumulant formula, as required by many of our examples, including iterated stochastic integrals, L\'evy area, Bessel processes, KPZ with smooth noise, Wiener-It\^o chaos and "rough" stochastic (forward) variance models.Comment: 25 pages. Additional applications. Analytic proof of forest reordering. Relation to Al\`os et al. (SSRN'17, Quant. Finance '20) and Lacoin et al. (arXiv'19) discussed in detai

S-Adenosylhomocysteine hydrolase deficiency: A second patient, the younger brother of the index patient, and outcomes during therapy

S-Adenosylhomocysteine (AdoHcy) hydrolase deficiency has been proven in a human only once, in a recently described Croatian boy. Here we report the clinical course and biochemical abnormalities of the younger brother of this proband. This younger brother has the same two mutations in the gene encoding AdoHcy hydrolase, and has been monitored since birth. We report, as well, outcomes during therapy for both patients. The information obtained suggests that the disease starts in utero and is characterized primarily by neuromuscular symptomatology (hypotonia, sluggishness, psychomotor delay, absent tendon reflexes, delayed myelination). The laboratory abnormalities are markedly increased creatine kinase and elevated aminotransferases, as well as specific amino acid aberrations that pinpoint the aetiology. The latter include, most importantly, markedly elevated plasma AdoHcy. Plasma S-adenosylmethionine (AdoMet) is also elevated, as is methionine (although the hypermethioninaemia may be absent or nonsignificant in the first weeks of life). The disease seems to be at least to some extent treatable, as shown by improved myelination and psychomotor development during dietary methionine restriction and supplementation with creatine and phosphatidylcholine

Individual participant data meta-analysis to compare EPDS accuracy to detect major depression with and without the self-harm item

Item 10 of the Edinburgh Postnatal Depression Scale (EPDS) is intended to assess thoughts of intentional self-harm but may also elicit concerns about accidental self-harm. It does not specifically address suicide ideation but, nonetheless, is sometimes used as an indicator of suicidality. The 9-item version of the EPDS (EPDS-9), which omits item 10, is sometimes used in research due to concern about positive endorsements of item 10 and necessary follow-up. We assessed the equivalence of total score correlations and screening accuracy to detect major depression using the EPDS-9 versus full EPDS among pregnant and postpartum women. We searched Medline, Medline In-Process and Other Non-Indexed Citations, PsycINFO, and Web of Science from database inception to October 3, 2018 for studies that administered the EPDS and conducted diagnostic classification for major depression based on a validated semi-structured or fully structured interview among women aged 18 or older during pregnancy or within 12 months of giving birth. We conducted an individual participant data meta-analysis. We calculated Pearson correlations with 95% prediction interval (PI) between EPDS-9 and full EPDS total scores using a random effects model. Bivariate random-effects models were fitted to assess screening accuracy. Equivalence tests were done by comparing the confidence intervals (CIs) around the pooled sensitivity and specificity differences to the equivalence margin of δ = 0.05. Individual participant data were obtained from 41 eligible studies (10,906 participants, 1407 major depression cases). The correlation between EPDS-9 and full EPDS scores was 0.998 (95% PI 0.991, 0.999). For sensitivity, the EPDS-9 and full EPDS were equivalent for cut-offs 7–12 (difference range − 0.02, 0.01) and the equivalence was indeterminate for cut-offs 13–15 (all differences − 0.04). For specificity, the EPDS-9 and full EPDS were equivalent for all cut-offs (difference range 0.00, 0.01). The EPDS-9 performs similarly to the full EPDS and can be used when there are concerns about the implications of administering EPDS item 10. Trial registration: The original IPDMA was registered in PROSPERO (CRD42015024785)

Interactive histogenesis of axonal strata and proliferative zones in the human fetal cerebral wall

Development of the cerebral wall is characterized by partially overlapping histogenetic events. However, little is known with regards to when, where, and how growing axonal pathways interact with progenitor cell lineages in the proliferative zones of the human fetal cerebrum. We analyzed the developmental continuity and spatial distribution of the axonal sagittal strata (SS) and their relationship with proliferative zones in a series of human brains (8-40 post-conceptional weeks; PCW) by comparing histological, histochemical, and immunocytochemical data with magnetic resonance imaging (MRI). Between 8.5 and 11 PCW, thalamocortical fibers from the intermediate zone (IZ) were initially dispersed throughout the subventricular zone (SVZ), while sizeable axonal "invasion" occurred between 12.5 and 15 PCW followed by callosal fibers which "delaminated" the ventricular zone-inner SVZ from the outer SVZ (OSVZ). During midgestation, the SS extensively invaded the OSVZ, separating cell bands, and a new multilaminar axonal-cellular compartment (MACC) was formed. Preterm period reveals increased complexity of the MACC in terms of glial architecture and the thinning of proliferative bands. The addition of associative fibers and the formation of the centrum semiovale separated the SS from the subplate. In vivo MRI of the occipital SS indicates a "triplet" structure of alternating hypointense and hyperintense bands. Our results highlighted the developmental continuity of sagittally oriented "corridors" of projection, commissural and associative fibers, and histogenetic interaction with progenitors, neurons, and glia. Histogenetical changes in the MACC, and consequently, delineation of the SS on MRI, may serve as a relevant indicator of white matter microstructural integrity in the developing brain

Availability Analysis of Different PON Models

Due to the increasing demands of individual users, Passive Optical Networks (PON) are a promising technology for future broadband access networks. Reliable access to network services is a very important feature, so the availability of the connection is becoming one of the most important requirements. Failure of the optical fiber occurring between the Optical Line Terminal (OLT) and the passive optical splitter can cause the services becoming unavailable for a large number of users, so it is necessary to prevent such an occurrence by providing backup resources – in this case a spare optical fiber. When constructing the spare path (protection fiber), it is important to keep in mind that, if possible, the working and the spare fiber should not be positioned within the same cable. Failure of the optical fiber between the passive splitter and the individual user also means a loss of service for that user. In that case, protection may be offered by adding spare fibers. The question is, however, whether such a solution is cost-effective, as it would lead to a significant cost increase in the construction of the access network. This paper presents the availability analysis conducted for different PON models

Forests, cumulants, martingales

This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a "broken exponential martingale" expansion that generalizes and unifies the exponentiation result of Al{ò}s, Gatheral, and Radoičić and the cumulant recursion formula of Lacoin, Rhodes, and Vargas. Specifically, we exhibit the two previous results as lower dimensional projections of the same generalized forest expansion, subsequently related by forest reordering. Our approach also leads to sharp integrability conditions for validity of the cumulant formula, as required by many of our examples, including iterated stochastic integrals, Lévy area, Bessel processes, KPZ with smooth noise, Wiener-Itô chaos and "rough" stochastic (forward) variance models