An elementary representation of the higher-order Jacobi-type differential equation

We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order equations was introduced by J. and R. Koekoek in 1999 essentially by using special function methods. In this paper, a completely elementary representation of the Jacobi-type differential operator of any even order is given. This enables us to trace the orthogonality relation of the Jacobi-type polynomials back to their differential equation. Moreover, we establish a new factorization of the Jacobi-type operator which gives rise to a recurrence relation with respect to the order of the equation.Comment: 17 page

A task-based connectome study

This article was supported by the German Research Foundation (DFG) and the Open Access Publication Fund of Humboldt-Universität zu Berlin.The functional connectome is organized into several separable intrinsic connectivity networks (ICNs) that are thought to be the building blocks of the mind. However, it is currently not well understood how these networks are engaged by emotionally salient information, and how such engagement fits into emotion theories. The current study assessed how ICNs respond during the processing of angry and fearful faces in a large sample (N = 843) and examined how connectivity changes relate to the ICNs. All ICNs were modulated by emotional faces and showed functional interactions, a finding which is in line with the “theory of constructed emotions” that assumes that basic emotion do not arise from separable ICNs but from their interplay. We further identified a set of brain regions whose connectivity changes during the tasks suggest a special role as “affective hubs” in the brain. While hubs were located in all ICNs, we observed high selectivity for the amygdala within the subcortical network, a finding which also fits into “primary emotion” theory. The topology of hubs corresponded closely to a set of brain regions that has been implicated in anxiety disorders, pointing towards a clinical relevance of the present findings. The present data are the most comprehensive mapping of connectome-wide changes in functionally connectivity evoked by an affective processing task thus far and support two competing views on how emotions are represented in the brain, suggesting that the connectome paradigm might help with unifying the two ideas.Peer Reviewe

Attention networks and the intrinsic network structure of the human brain

Attention network theory distinguishes three independent systems, each supported by its own distributed network: an alerting network to deploy attentional resources in anticipation, an orienting network to direct attention to a cued location, and a control network to select relevant information at the expense of concurrently available information. Ample behavioral and neuroimaging evidence supports the dissociation of the three attention domains. The strong assumption that each attentional system is realized through a separable network, however, raises the question how these networks relate to the intrinsic network structure of the brain. Our understanding of brain networks has advanced majorly in the past years due to the increasing focus on brain connectivity. The brain is intrinsically organized into several large-scale networks whose modular structure persists across task states. Existing proposals on how the presumed attention networks relate to intrinsic networks rely mostly on anecdotal and partly contradictory arguments. We addressed this issue by mapping different attention networks at the level of cifti-grayordinates. Resulting group maps were compared to the group-level topology of 23 intrinsic networks, which we reconstructed from the same participants' resting state fMRI data. We found that all attention domains recruited multiple and partly overlapping intrinsic networks and converged in the dorsal fronto-parietal and midcingulo-insular network. While we observed a preference of each attentional domain for its own set of intrinsic networks, implicated networks did not match well to those proposed in the literature. Our results indicate a necessary refinement of the attention network theory.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659We acknowledge support by the Open Access Publication Fund of Humboldt‐Universität zu Berlin.Peer Reviewe

Characterizing functional modules in the human thalamus: coactivation-based parcellation and systems-level functional decoding

The human thalamus relays sensory signals to the cortex and facilitates brain-wide communication. The thalamus is also more directly involved in sensorimotor and various cognitive functions but a full characterization of its functional repertoire, particularly in regard to its internal anatomical structure, is still outstanding. As a putative hub in the human connectome, the thalamus might reveal its functional profile only in conjunction with interconnected brain areas. We therefore developed a novel systems-level Bayesian reverse inference decoding that complements the traditional neuroinformatics approach towards a network account of thalamic function. The systems-level decoding considers the functional repertoire (i.e., the terms associated with a brain region) of all regions showing co-activations with a predefined seed region in a brain-wide fashion. Here, we used task-constrained meta-analytic connectivity-based parcellation (MACM-CBP) to identify thalamic subregions as seed regions and applied the systems-level decoding to these subregions in conjunction with functionally connected cortical regions. Our results confirm thalamic structure–function relationships known from animal and clinical studies and revealed further associations with language, memory, and locomotion that have not been detailed in the cognitive neuroscience literature before. The systems-level decoding further uncovered large systems engaged in autobiographical memory and nociception. We propose this novel decoding approach as a useful tool to detect previously unknown structure–function relationships at the brain network level, and to build viable starting points for future studies.Peer Reviewe

The Grayson spectral sequence for hermitian K-theory

Let R be a regular ring such that 2 is invertible. We construct a spectral sequence converging to the hermitian K-theory, alias the Grothendieck-Witt theory, of R. In particular, we construct a tower for the hermitian K-groups in even shifts, whose terms are given by the hermitian K-theory of automorphisms. The spectral sequence arises as the homotopy spectral sequence of this tower and is analogous to Grayson’s version of the motivic spectral sequence [Gra95]. Further, we construct similar towers for the hermitian K-theory in odd shifts if R is a field of characteristic different from 2. We show by a counter example that the arising spectral sequence does not behave as desired. We proceed by proposing an alternative version for the tower and verify its correctness in weight 1. Finally we give a geometric representation of the (hermitian) K-theory of automorphisms in terms of the general linear group, the orthogonal group, or in terms of e-symmetric matrices, respectively. The K-theory of automorphisms can be identified with motivic cohomology if R is local and of finite type over a field. Therefore the hermitian K-theory of automorphisms as presented in this thesis is a candidate for the analogue of motivic cohomology in the hermitian world

Лингвистические и культурологические аспекты современного инженерного образования : сборник материалов Международной научно-практической конференции, Томск, 10-12 ноября 2020 г.

В сборнике материалов представлены тезисы докладов студентов, начинающих и опытных исследователей, принявших участие в Международной научно-практической конференции «Лингвистические и культурологические аспекты современного инженерного образования», проведённой 10-12 ноября 2020 года на базе Национального исследовательского Томского политехнического университета. Сборник предназначен для студентов, молодых учёных, переводчиков и всех интересующихся проблемами современного языкознания, переводоведения и лингводидактики

The Big Five Personality Traits and Brain Arousal in the Resting State

Based on Eysenck’s biopsychological trait theory, brain arousal has long been considered to explain individual differences in human personality. Yet, results from empirical studies remained inconclusive. However, most published results have been derived from small samples and, despite inherent limitations, EEG alpha power has usually served as an exclusive indicator for brain arousal. To overcome these problems, we here selected N = 468 individuals of the LIFE-Adult cohort and investigated the associations between the Big Five personality traits and brain arousal by using the validated EEG- and EOG-based analysis tool VIGALL. Our analyses revealed that participants who reported higher levels of extraversion and openness to experience, respectively, exhibited lower levels of brain arousal in the resting state. Bayesian and frequentist analysis results were especially convincing for openness to experience. Among the lower-order personality traits, we obtained the strongest evidence for neuroticism facet ‘impulsivity’ and reduced brain arousal. In line with this, both impulsivity and openness have previously been conceptualized as aspects of extraversion. We regard our findings as well in line with the postulations of Eysenck and consistent with the recently proposed ‘arousal regulation model’. Our results also agree with meta-analytically derived effect sizes in the field of individual differences research, highlighting the need for large (collaborative) studies.Peer Reviewe