Hasil untuk "Neurosciences. Biological psychiatry. Neuropsychiatry"

Osamudiamen S. Ogbeide, Madeleine K. Nowak, Madeleine K. Nowak et al.

IntroductionThis study examines the capability of detecting neurological changes caused by subconcussive head impacts by analyzing the blink reflex of an individual when they encounter puffs of air as a stimulus.MethodsFollowing attrition and technical issues, 26 participants (15 females, 11 males: age ± SD; 21.3 ± 2.11 years) with at least 5 years of soccer heading experience were included in the final analysis. Participants performed 10 soccer headers with soccer balls projected at a speed of 30 mph. Parameters related to blink reflex, including blink latency, differential latency, number of oscillations, delta 30, and excursions, were assessed by the EyeStat device at pre-heading baseline, and 2-h and 24-h post-heading.ResultsSignificant declines in blink reflex parameters were observed at specific post-heading timepoints compared to baseline. At 24-h post-heading, significant reductions were detected in the overall blink latency (p = 0.0255), the blink latencies of the right eye (p = 0.0411), ipsilateral latency (p = 0.0314) and contralateral latency (p = 0.0434). At 2-h post-heading, significant declines were observed in the overall delta 30 value (p = 0.0053) and delta 30 of the right eye (p = 0.0260). Both delta 30 values returned to baseline by the 24-h post-heading timepoint. No significant changes in the differential latency, number of oscillations, and excursion of the eye were found.DiscussionThese findings suggest changes in the latency and delta 30 of a blink reflex is a viable measure of detection for neurological changes when monitoring subconcussive head impacts.

A. Ivanov, S. Shelyag

Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time periodic mixed coefficient and a nonlinear delayed negative feedback. The dynamics is studied analytically with supportive numerical simulation and justification of the theoretical outcomes. The principal nonlinearity involving the state variable is of the negative feedback type, the periodic multiplicative coefficient can change its sign, leading to equations with mixed positive-negative feedback. The existence of slowly oscillating periodic solutions of two different types is established. The theoretical analysis and derivation are based on the reduction of dynamics in the delay equations to that of interval maps. The theoretical outcomes are verified and supported by comprehensive numerical computations. The differential delay equations considered are generalisations of some well-known autonomous models from biological applications.

Eric W. Bridgeford, Brian S. Caffo, Maya B. Mathur et al.

Over the past two decades, considerable strides have been made in advancing neuroscientific techniques, yet challenges remain in attributing causality to observed associations. This review addresses a fundamental issue in observational neuroscience studies and advocates for incorporating causal inference frameworks into standard practice. We systematically introduce necessary definitions and concepts, emphasizing how causal assumptions underlie statistical analyses even when not explicitly stated. Through a running example on sleep quality and white matter integrity, we illustrate how persistent challenges, including confounding and selection biases, can be conceptualized and addressed using causal frameworks. We demonstrate practical approaches for making assumption violations transparent through hands-on examples: supplementary case studies using multi-site harmonization and head motion exclusion procedures provide step-by-step diagnostic techniques for checking covariate overlap and identifying selection bias through exclusion pattern analysis. We explore how these causal perspectives can inform both experimental design and analytical choices, particularly for observational studies where traditional randomization is infeasible. Together, we believe this framework offers concrete tools for strengthening causal interpretations and inspiring more robust approaches to problems in neuroscience.

Ohad Regev, Apurba Shil, Tal Bronshtein et al.

Abstract Background Recent evidence suggests that certain fetal anomalies detected upon prenatal ultrasound screenings are associated with autism spectrum disorder (ASD). In this cross-sectional study, we aimed to identify genetic variants associated with fetal ultrasound anomalies (UFAs) in children with ASD. Methods The study included all children with ASD who are registered in the database of the Azrieli National Center of Autism and Neurodevelopment and for whom both prenatal ultrasound and whole exome sequencing (WES) data were available. We applied our in-house integrative bioinformatics pipeline, AutScore, to these WES data to prioritize rare, gene-disrupting variants (GDVs) probably contributing to ASD susceptibily. Univariate statistics and multivariable regression were used to assess the associations between UFAs and GDVs identified in these children. Results The study sample comprised 126 children, of whom 43 (34.1%) had at least one UFA detected in the prenatal ultrasound scan. A total of 87 candidate ASD genetic variants were detected in 60 children, with 24 (40%) children carrying multiple variants. Children with UFAs were more likely to have loss-of-function (LoF) mutations (aOR = 2.55, 95%CI: 1.13–5.80). This association was particularly noticeable when children with structural anomalies or children with UFAs in their head and brain scans were compared to children without UFAs (any mutation: aOR = 8.28, 95%CI: 2.29–30.01; LoF: aOR = 5.72, 95%CI: 2.08–15.71 and any mutation: aOR = 6.39, 95%CI: 1.34–30.47; LoF: aOR = 4.50, 95%CI: 1.32–15.35, respectively). GDVs associated with UFAs were enriched in genes highly expressed across all tissues (aOR = 2.76, 95%CI: 1.14–6.68). There was a weak, but significant, correlation between the number of mutations and the number of abnormalities detected in the same children (r = 0.21, P = 0.016). Conclusions The results provide valuable insights into the potential genetic basis of prenatal organogenesis abnormalities associated with ASD and shed light on the complex interplay between genetic factors and fetal development.

Zack Goldblum, Zhongchuan Xu, Haoer Shi et al.

The exponential growth of neuroscientific data necessitates platforms that facilitate data management and multidisciplinary collaboration. In this paper, we introduce Pennsieve - an open-source, cloud-based scientific data management platform built to meet these needs. Pennsieve supports complex multimodal datasets and provides tools for data visualization and analyses. It takes a comprehensive approach to data integration, enabling researchers to define custom metadata schemas and utilize advanced tools to filter and query their data. Pennsieve's modular architecture allows external applications to extend its capabilities, and collaborative workspaces with peer-reviewed data publishing mechanisms promote high-quality datasets optimized for downstream analysis, both in the cloud and on-premises. Pennsieve forms the core for major neuroscience research programs including NIH SPARC Initiative, NIH HEAL Initiative's PRECISION Human Pain Network, and NIH HEAL RE-JOIN Initiative. It serves more than 80 research groups worldwide, along with several large-scale, inter-institutional projects at clinical sites through the University of Pennsylvania. Underpinning the SPARC.Science, Epilepsy.Science, and Pennsieve Discover portals, Pennsieve stores over 125 TB of scientific data, with 35 TB of data publicly available across more than 350 high-impact datasets. It adheres to the findable, accessible, interoperable, and reusable (FAIR) principles of data sharing and is recognized as one of the NIH-approved Data Repositories. By facilitating scientific data management, discovery, and analysis, Pennsieve fosters a robust and collaborative research ecosystem for neuroscience and beyond.

Hannah Ihme, Philippe Courtet, Nathan Risch et al.

Abstract Background Childhood trauma (CT), depression, and psychological pain are known predictors of suicidal ideation. Recent literature additionally highlights the importance of the attachment system. Methods We aimed to predict suicidal ideation through CT, attachment, and psychological and social pain by using mediation models aiming to predict suicidal ideation through CT (predictor) and attachment (mediator). In the same models, we introduced psychological or social pain as a moderator of the relationship between attachment, CT, and suicidal ideation. We included 161 depressed patients and assessed depression, attachment, CT, suicidal ideation, psychological pain, and social pain. Results We found (1) a complete mediating effect of anxious attachment (a2b2 = 0.0035, CI95% = [0.0010; 0.0069]) on the relationship between CT on suicidal ideation, and (2) a significant complete conditional mediating effect of anxious attachment and psychological pain (index of moderated mediation VAS: 0.0014; CI95% = [0.0002; 0.0032]) but not social pain on the relationship between CT and suicidal ideation. Both models were controlled for history of suicidal attempt, depression severity, and sex. Conclusions Our results suggest a developmental profile of suicidal ideation in mood disorder that is characterized by the presence of CT and insecure attachment, especially anxious attachment, that is sensitive to experiences of psychological pain. Nevertheless, we cannot conclude that avoidantly attached individuals do not present the same mechanism, as they may not disclose those ideas.

Xiao-Xiao Han, Jia Qiao, Zhan-Ao Meng et al.

Objectives: Investigate the biomechanical characteristics in tracheostomized patients with aspiration following acquired brain injury (ABI) and further explore the relationship between the biomechanical characteristics and aspiration. Methods: This is a single-center cross-sectional study. The tracheostomized patients with aspiration following ABI and age-matched healthy controls were recruited. The biomechanical characteristics, including velopharynx (VP) maximal pressure, tongue base (TB) maximal pressure, upper esophageal sphincter (UES) residual pressure, UES relaxation duration, and subglottic pressure, were examined by high-resolution manometry and computational fluid dynamics simulation analysis. The penetration–aspiration scale (PAS) score was evaluated by a videofluoroscopic swallowing study. Results: Fifteen healthy subjects and fifteen tracheostomized patients with aspiration following ABI were included. The decreased VP maximal pressure, increased UES residual pressure, and shortened UES relaxation duration were found in the patient group compared with the control group (<i>p</i> < 0.05). Furthermore, the subglottic pressure significantly decreased in patients (<i>p</i> < 0.05), while no significant difference was found in TB maximal pressure between groups (<i>p</i> > 0.05). In addition, in the patient group, VP maximal pressure (<i>r</i>_s = −0.439; <i>p</i> = 0.015), UES relaxation duration (<i>r</i>_s = −0.532; <i>p</i> = 0.002), and the subglottic pressure (<i>r</i>_s = −0.775; <i>p</i> < 0.001) were negatively correlated with the PAS score, while UES residual pressure (<i>r</i>_s = 0.807; <i>p</i> < 0.001) was positively correlated with the PAS score (<i>p</i> < 0.05), the correlation between TB maximal pressure and PAS score (<i>r</i>_s = −0.315; <i>p</i> = 0.090) did not reach statistical significance. Conclusions: The biomechanical characteristics in tracheostomized patients with aspiration following ABI might manifest as decreased VP maximal pressure and subglottic pressure, increased UES residual pressure, and shortened UES relaxation duration, in which VP maximal pressure, UES relaxation duration, subglottic pressure, and UES residual pressure were correlated with aspiration.

Wei Zheng, Xin-Hu Yang, Li-Mei Gu et al.

ObjectivesMelancholic depression may respond differently to certain treatments. The aim of this study was to compare the antianhedonic effects of six intravenous injections of 0.5 mg/kg ketamine in patients with melancholic and non-melancholic depression, which remain largely unknown.MethodsIndividuals experiencing melancholic (n = 30) and non-melancholic (n = 105) depression were recruited and assessed for anhedonic symptoms using the Montgomery–Åsberg Depression Rating Scale (MADRS). The presence of melancholic depression was measured with the depression scale items at baseline based on DSM-5 criteria.ResultsA total of 30 (22.2%) patients with depression fulfilled the DSM-5 criteria for melancholic depression. Patients with melancholic depression had a non-significant lower antianhedonic response (43.3 vs. 50.5%, t = 0.5, p &gt; 0.05) and remission (20.0 vs. 21.0%, t = 0.01, p &gt; 0.05) to repeated-dose ketamine infusions than those with non-melancholic depression. The melancholic group had significantly lower MADRS anhedonia subscale scores than the non-melancholic group at day 26 (p &lt; 0.05).ConclusionAfter six ketamine infusions, the improvement of anhedonic symptoms was found in both patients with melancholic and non-melancholic depression, and the efficacy was similar in both groups.

Seyedmehdi Orouji, Vincent Taschereau-Dumouchel, Aurelio Cortese et al.

In human neuroscience, machine learning can help reveal lower-dimensional neural representations relevant to subjects' behavior. However, state-of-the-art models typically require large datasets to train, so are prone to overfitting on human neuroimaging data that often possess few samples but many input dimensions. Here, we capitalized on the fact that the features we seek in human neuroscience are precisely those relevant to subjects' behavior. We thus developed a Task-Relevant Autoencoder via Classifier Enhancement (TRACE), and tested its ability to extract behaviorally-relevant, separable representations compared to a standard autoencoder, a variational autoencoder, and principal component analysis for two severely truncated machine learning datasets. We then evaluated all models on fMRI data from 59 subjects who observed animals and objects. TRACE outperformed all models nearly unilaterally, showing up to 12% increased classification accuracy and up to 56% improvement in discovering "cleaner", task-relevant representations. These results showcase TRACE's potential for a wide variety of data related to human behavior.

Arthur Lefevre, Diego Benusiglio, Diego Benusiglio et al.

Oxytocin (OT) is a neuropeptide produced by hypothalamic neurons and is known to modulate social behavior among other functions. Several experiments have shown that OT modulates neuronal activity in many brain areas, including sensory cortices. OT neurons thus project axons to various cortical and subcortical structures and activate neuronal subpopulations to increase the signal-to-noise ratio, and in turn, increases the saliency of social stimuli. Less is known about the origin of inputs to OT neurons, but recent studies show that cells projecting to OT neurons are often located in regions where the OT receptor (OTR) is expressed. Thus, we propose the existence of reciprocal connectivity between OT neurons and extrahypothalamic OTR neurons to tune OT neuron activity depending on the behavioral context. Furthermore, the latest studies have shown that OTR-expressing neurons located in social brain regions also project to other social brain regions containing OTR-expressing neurons. We hypothesize that OTR-expressing neurons across the brain constitute a common network coordinated by OT.

Gokben Hizli Sayar, Mesut Cetin

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Hakan Demirci, Yildirim Cinar, Nazan Bilgel

Background: The possible association between depressive symptoms and metabolic syndrome (MetS) has recently become an important topic of discussion. There is some limited and inconsistent evidence in the literature concerning whether or not depression and metabolic syndrome are associated. The aim of this study was to examine the association between depressive symptoms and metabolic syndrome. Methods: This is a cross-sectional community-based study. The setting is a family practice unit in an urban area which serves about 3,600 people. The participants were 250 individuals aged 18 and over, selected randomly from all enrolled patients in this family practice unit. National Cholesterol Education Program (NCEP- ATP-III) criteria were used for the classification of metabolic myndrome (MetS). The Beck Depression Inventory was filled out by the participants for the evaluation of depressive symptoms. Results: The prevalence of MetS was similar for men (48.8%) and women (48.1%) and increased with age in both sexes. Participants with only primary education were found to be 2.2 times more at risk of developing MetS than participants with a higher education. The prevalence of depressive symptoms was higher among women (31.0%) than men (9.9%). Statistical analyses revealed no statistically significant association between MetS and depressive symptoms. Conclusion: The prevalence of MetS was found to be high in both sexes. Women had a 3.8 times higher risk of developing depressive symptoms than men. We found no association of depressive symptoms with MetS or with any of the MetS criteria. Türkiye’de bir aile hekimliği ünitesinde depresyon ve metabolik sendrom ilişkisinin araştırılması Giriş: Depresif semptomlar ve metabolik sendrom (MetS) arasındaki muhtemel ilişki son dönemde önemli bir tartışma konusudur. Bu ilişkinin varlığı konusunda sınırlı veri vardır. Bu çalışmanın amacı depresyon ve MetS arasındaki ilişkiyi incelemektir. Yöntem: Bu çalışma toplum kökenli kesitsel bir çalışmadır. Çalışma 3600 kişiden sorumlu kentsel bir aile hekimliği biriminde yürütülmüştür. Çalışmaya katılanlar bu aile hekimliği ünitesine başvuran 18 yaş ve üzeri 250 kişiden oluşmuştur. MetS (MetS) sınışaması NCEP-ATPIII kriterleri kullanılarak yapılmıştır. Beck Depresyon Ölçeği depresyon değerlendirmesi için tüm katılımcılar tarafından doldurulmuştur. Bulgular: MetS prevalansı her iki cinsiyet için benzerdi (%48.8 erkek ve %48.1 bayan) ve yaş ilerledikçe artmaktaydı. İlkokul mezunları yüksekokul mezunlarına göre 2.2 kez daha fazla MetS riskine sahipti. Depresif şikayet prevalansı kadınlarda (%31) erkeklere (%9.9) oranla daha fazlaydı. İstatistik analizlerle MetS ve depresif semptomlar arasında anlamlı bir ilişki tespit edilemedi. Sonuç: MetS prevalansı her iki cinsiyet içinde yüksek bulundu. Depresif semptomlar açısından kadınlar erkeklere kıyasla 3.8 kat daha fazla risk altındaydı. Depresyon semptomları ile hem MetS hemde MetS kriterleri arasında ilişki bulamadık.

Pei-Lun Kuo, Ann Zenobia Moore, Frank R. Lin et al.

Objectives: Age-related hearing loss (ARHL) is highly prevalent among older adults, but the potential mechanisms and predictive markers for ARHL are lacking. Epigenetic age acceleration has been shown to be predictive of many age-associated diseases and mortality. However, the association between epigenetic age acceleration and hearing remains unknown. Our study aims to investigate the relationship between epigenetic age acceleration and audiometric hearing in the Baltimore Longitudinal Study of Aging (BLSA).Methods: Participants with both DNA methylation and audiometric hearing measurements were included. The main independent variables are epigenetic age acceleration measures, including intrinsic epigenetic age acceleration—“IEAA,” Hannum age acceleration—“AgeAccelerationResidualHannum,” PhenoAge acceleration—“AgeAccelPheno,” GrimAge acceleration—“AgeAccelGrim,” and methylation-based pace of aging estimation—“DunedinPoAm.” The main dependent variable is speech-frequency pure tone average. Linear regression was used to assess the association between epigenetic age acceleration and hearing.Results: Among the 236 participants (52.5% female), after adjusting for age, sex, race, time difference between measurements, cardiovascular factors, and smoking history, the effect sizes were 0.11 995% CI: (–0.00, 0.23), p = 0.054] for Hannum’s clock, 0.08 [95% CI: (–0.03, 0.19), p = 0.143] for Horvath’s clock, 0.10 [95% CI: (–0.01, 0.21), p = 0.089] for PhenoAge, 0.20 [95% CI: (0.06, 0.33), p = 0.004] for GrimAge, and 0.21 [95% CI: (0.09, 0.33), p = 0.001] for DunedinPoAm.Discussion: The present study suggests that some epigenetic age acceleration measurements are associated with hearing. Future research is needed to study the potential subclinical cardiovascular causes of hearing and to investigate the longitudinal relationship between DNA methylation and hearing.

Malinda L. S. Tantirigama, Timothy Zolnik, Benjamin Judkewitz et al.

In this review article, we highlight several disparate ideas that are linked to changes in brain state (i.e., sleep to arousal, Down to Up, synchronized to de-synchronized). In any discussion of the brain state, we propose that the cortical pyramidal neuron has a central position. EEG recordings, which typically assess brain state, predominantly reflect the activity of cortical pyramidal neurons. This means that the dominant rhythmic activity that characterizes a particular brain state ultimately has to manifest globally across the pyramidal neuron population. During state transitions, it is the long-range connectivity of these neurons that broadcast the resultant changes in activity to many subcortical targets. Structures like the thalamus, brainstem/hypothalamic neuromodulatory systems, and respiratory systems can also strongly influence brain state, and for many decades we have been uncovering bidirectional pathways that link these structures to state changes in the cerebral cortex. More recently, movement and active behaviors have emerged as powerful drivers of state changes. Each of these systems involve different circuits distributed across the brain. Yet, for a system-wide change in brain state, there must be a collaboration between these circuits that reflects and perhaps triggers the transition between brain states. As we expand our understanding of how brain state changes, our current challenge is to understand how these diverse sets of circuits and pathways interact to produce the changes observed in cortical pyramidal neurons.

Paul Y. Wang, Sandalika Sapra, Vivek Kurien George et al.

Although a number of studies have explored deep learning in neuroscience, the application of these algorithms to neural systems on a microscopic scale, i.e. parameters relevant to lower scales of organization, remains relatively novel. Motivated by advances in whole-brain imaging, we examined the performance of deep learning models on microscopic neural dynamics and resulting emergent behaviors using calcium imaging data from the nematode C. elegans. We show that neural networks perform remarkably well on both neuron-level dynamics prediction, and behavioral state classification. In addition, we compared the performance of structure agnostic neural networks and graph neural networks to investigate if graph structure can be exploited as a favorable inductive bias. To perform this experiment, we designed a graph neural network which explicitly infers relations between neurons from neural activity and leverages the inferred graph structure during computations. In our experiments, we found that graph neural networks generally outperformed structure agnostic models and excel in generalization on unseen organisms, implying a potential path to generalizable machine learning in neuroscience.

I. V. Pozhidaev, A. S. Boiko, E. G. Kornetova

The use of atypical antipsychotic drugs has made metabolic disorders one of the most common side effect of pharmacotherapy for schizophrenic patients. The aim of this study was to assess the contribution of polymorphic variants of genes of the P450 cytochrome system to changes in body mass index in patients with schizophrenia. As a result of the study, we did not identify significant associations of genotypes and alleles of the studied polymorphic variants of the CYP2D6, CYP1A2, CYP2C19 genes with weight gain in patients with schizophrenia of Russian nationality of the Siberian region receiving antipsychotic therapy and can revealed neither protective nor predisposing effects. Metabolic syndrome and, increase in body weight especially, are complex side effect, and further studies is needed to increase successful exploration and identification of the genetic component and assess contribution.

Adham Fani Maleki, Serge Rivest

The immune system provides protection in the CNS via resident microglial cells and those that traffic into it in the course of pathological challenges. These populations of cells are key players in modulating immune functions that are involved in disease outcomes. In this review, we briefly summarize and highlight the current state of knowledge of the differential contributions of microglia and monocytes in Alzheimer’s disease and multiple sclerosis. The role of innate immunity is frequently seen as a Yin and Yang in both diseases, but this depends on the environment, pre-clinical disease models and the type of cells involved.

Carmen Simonsen, Sofie R. Aminoff, Anja Vaskinn et al.

Objectives: Perceived/experienced stigma and its relationship with clinical outcome were investigated across the first year of treatment in a large sample with first-episode psychosis (FEP). Methods: FEP participants (n = 112) in the TOP study were investigated at baseline and 1-year follow-up. Perceived/experienced stigma was measured with items from the World Health Organization Disability Assessment Schedule 2.0 (WHODAS 2.0), assessing problems because of barriers and hindrances, and living with dignity because of attitudes and actions of others. Clinical outcome included: symptoms, global functioning, self-rated disability and self-rated life satisfaction. Results: In the total sample, 46% perceived/experienced stigma at baseline, which decreased significantly to 32% at 1-year follow-up. Perceived/experienced stigma was present in 1/5 at both time-points (Sustained stigma), in 2/5 at only one time-point (Transient stigma), and in 2/5 it was not present at either time-point (No stigma). Compared to the No stigma group, the Sustained stigma group had significantly higher levels of positive, excited and depressive symptoms and self-rated disability, as well as lower levels of global functioning and life satisfaction at 1 year follow-up, while the Transient stigma group only had poorer functioning and higher self-rated disability. Yet the outcome variables improved across the first year of treatment in all three stigma groups. Conclusion: Perceived/experienced stigma was common in FEP, yet the rate decreased across the first year of treatment. Although there was some clinical improvement across the first year of treatment irrespective of stigma, stigma was related to poorer clinical outcome in a bidirectional manner. This suggests that perceived/experienced stigma is an important target in the early stages of treatment. Keywords: Perceived stigma, Experienced stigma, First-Episode psychosis, Life satisfaction, Symptomatology

Justas Dauparas, Haobo Wang, Avi Swartz et al.

Revealing the functional sites of biological sequences, such as evolutionary conserved, structurally interacting or co-evolving protein sites, is a fundamental, and yet challenging task. Different frameworks and models were developed to approach this challenge, including Position-Specific Scoring Matrices, Markov Random Fields, Multivariate Gaussian models and most recently Autoencoders. Each of these methods has certain advantages, and while they have generated a set of insights for better biological predictions, these have been restricted to the corresponding methods and were difficult to translate to the complementary domains. Here we propose a unified framework for the above-mentioned models, that allows for interpretable transformations between the different methods and naturally incorporates the advantages and insight gained individually in the different communities. We show how, by using the unified framework, we are able to achieve state-of-the-art performance for protein structure prediction, while enhancing interpretability of the prediction process.

Alessandro Betti, Marco Gori

The Backpropagation algorithm relies on the abstraction of using a neural model that gets rid of the notion of time, since the input is mapped instantaneously to the output. In this paper, we claim that this abstraction of ignoring time, along with the abrupt input changes that occur when feeding the training set, are in fact the reasons why, in some papers, Backprop biological plausibility is regarded as an arguable issue. We show that as soon as a deep feedforward network operates with neurons with time-delayed response, the backprop weight update turns out to be the basic equation of a biologically plausible diffusion process based on forward-backward waves. We also show that such a process very well approximates the gradient for inputs that are not too fast with respect to the depth of the network. These remarks somewhat disclose the diffusion process behind the backprop equation and leads us to interpret the corresponding algorithm as a degeneration of a more general diffusion process that takes place also in neural networks with cyclic connections.