Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds

When analyzing complex networks, an important task is the identification of those nodes which play a leading role for the overall communicability of the network. In the context of modifying networks (or making them robust against targeted attacks or outages), it is also relevant to know how sensitive the network's communicability reacts to changes in certain nodes or edges. Recently, the concept of total network sensitivity was introduced in [O. De la Cruz Cabrera, J. Jin, S. Noschese, L. Reichel, Communication in complex networks, Appl. Numer. Math., 172, pp. 186-205, 2022], which allows to measure how sensitive the total communicability of a network is to the addition or removal of certain edges. One shortcoming of this concept is that sensitivities are extremely costly to compute when using a straight-forward approach (orders of magnitude more expensive than the corresponding communicability measures). In this work, we present computational procedures for estimating network sensitivity with a cost that is essentially linear in the number of nodes for many real-world complex networks. Additionally, we extend the sensitivity concept such that it also covers sensitivity of subgraph centrality and the Estrada index, and we discuss the case of node removal. We propose a priori bounds for these sensitivities which capture the qualitative behavior well and give insight into the general behavior of matrix function based network indices under perturbations. These bounds are based on decay results for Fr\'echet derivatives of matrix functions with structured, low-rank direction terms which might be of independent interest also for other applications than network analysis

Sketched and Truncated Polynomial Krylov Subspace Methods: Matrix Equations

Thanks to its great potential in reducing both computational cost and memory requirements, combining sketching and Krylov subspace techniques has attracted a lot of attention in the recent literature on projection methods for linear systems, matrix function approximations, and eigenvalue problems. Applying this appealing strategy in the context of linear matrix equations turns out to be far more involved than a straightforward generalization. These difficulties include establishing well-posedness of the projected problem and deriving possible error estimates depending on the sketching properties. Further computational complications include the lack of a natural residual norm estimate and of an explicit basis for the generated subspace. In this paper we propose a new sketched-and-truncated polynomial Krylov subspace method for Sylvester equations that aims to address all these issues. The potential of our novel approach, in terms of both computational time and storage demand, is illustrated with numerical experiments. Comparisons with a state-of-the-art projection scheme based on rational Krylov subspaces are also included

Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices

We consider the problem of estimating the trace of a matrix function $f(A)$. In certain situations, in particular if $f(A)$ cannot be well approximated by a low-rank matrix, combining probing methods based on graph colorings with stochastic trace estimation techniques can yield accurate approximations at moderate cost. So far, such methods have not been thoroughly analyzed, though, but were rather used as efficient heuristics by practitioners. In this manuscript, we perform a detailed analysis of stochastic probing methods and, in particular, expose conditions under which the expected approximation error in the stochastic probing method scales more favorably with the dimension of the matrix than the error in non-stochastic probing. Extending results from [E. Aune, D. P. Simpson, J. Eidsvik, Parameter estimation in high dimensional Gaussian distributions, Stat. Comput., 24, pp. 247--263, 2014], we also characterize situations in which using just one stochastic vector is always -- not only in expectation -- better than the deterministic probing method. Several numerical experiments illustrate our theory and compare with existing methods

Alzheimer's Risk Gene TREM2 Determines Functional Properties of New Type of Human iPSC-Derived Microglia

Microglia are key in the homeostatic well-being of the brain and microglial dysfunction has been implicated in neurodegenerative disorders such as Alzheimer's disease (AD). Due to the many limitations to study microglia in situ or isolated for large scale drug discovery applications, there is a high need to develop robust and scalable human cellular models of microglia with reliable translatability to the disease. Here, we describe the generation of microglia-like cells from human induced pluripotent stem cells (iPSC) with distinct phenotypes for mechanistic studies in AD. We started out from an established differentiation protocol to generate primitive macrophage precursors mimicking the yolk sac ontogeny of microglia. Subsequently, we tested 36 differentiation conditions for the cells in monoculture where we exposed them to various combinations of media, morphogens, and extracellular matrices. The optimized protocol generated robustly ramified cells expressing key microglial markers. Bulk mRNA sequencing expression profiles revealed that compared to cells obtained in co-culture with neurons, microglia-like cells derived from a monoculture condition upregulate mRNA levels for Triggering Receptor Expressed On Myeloid Cells 2 (TREM2), which is reminiscent to the previously described disease-associated microglia. TREM2 is a risk gene for AD and an important regulator of microglia. The regulatory function of TREM2 in these cells was confirmed by comparing wild type with isogenic TREM2 knock-out iPSC microglia. The TREM2-deficient cells presented with stronger increase in free cytosolic calcium upon stimulation with ATP and ADP, as well as stronger migration towards complement C5a, compared to TREM2 expressing cells. The functional differences were associated with gene expression modulation of key regulators of microglia. In conclusion, we have established and validated a work stream to generate functional human iPSC-derived microglia-like cells by applying a directed and neuronal co-culture independent differentiation towards functional phenotypes in the context of AD. These cells can now be applied to study AD-related disease settings and to perform compound screening and testing for drug discoverySG was supported by the Roche Postdoctoral Fellowship (RPF) program and IP by the Roche Internships for Scientific Exchange (RiSE) progra

New Insights into Restless Genital Syndrome: Static Mechanical Hyperesthesia and Neuropathy of the Nervus Dorsalis Clitoridisj sm_1435 2778..2787 for Sexual Medicine

Introduction. Systematic study of dysesthetic and paresthetic regions contributing to persistent genital arousal in women with restless genital syndrome (ReGS) is needed for its clinical management. Aim. To investigate distinct localizations of ReGS. Methods. Twenty-three women, fulfilling all five criteria of persistent genital arousal disorder were included into the study. In-depth interviews, routine and hormonal investigations, electroencephalographs, and magnetic resonance imaging (MRI) of brain and pelvis were performed in all women. The localizations of genital sensations were investigated by physical examination of the ramus inferior of the pubic bone (RIPB) and by sensory testing of the skin of the genital area with a cotton swab (genital tactile mapping test or GTM test). Main Outcome Measures. Sensitivity of RIPB, GTM test. Results. Of 23 women included in the study, 18(78%), 16(69%), and 12(52%) reported restless legs syndrome, overactive bladder syndrome, and urethra hypersensitivity. Intolerance of tight clothes and underwear (allodynia or hyperpathia) was reported by 19 (83%) women. All women were diagnosed with ReGS. Sitting aggravated ReGS in 20(87%) women. In all women, MRI showed pelvic varices of different degree in the vagina (91%), labia minora and/or majora (35%), and uterus (30%). Finger touch investigation of the dorsal nerve of the clitoris (DNC) along the RIPB provoked ReGS in all women. Sensory testing showed unilateral and bilateral static mechanical Hyperesthesia on various trigger points in the dermatome of the pudendal nerve, particularly in the part innervated by DNC, including pelvic bone. In three women, sensory testing induced an uninhibited orgasm during physical examination. Conclusions. ReGS is highly associated with pelvic varices and with sensory neuropathy of the pudendal nerve and DNC, whose symptoms are suggestive for small fiber neuropathy (SFN). Physical examination for static mechanical Hyperesthesia is a diagnostic test for ReGS and is recommended for all individuals with complaints of persistent restless genital arousal in absence of sexual desire. Waldinger MD, Venema PL, van Gils APG, and Schweitzer DH. New insights into restless genital syndrome: Static mechanical hyperesthesia and neuropathy of the nervus dorsalis clitoridis. J Sex Med 2009;6:2778-2787

Richard Löwenherz im Museum : Menschen und Objekte in Bewegung

Irgendwo in unserem sogenannten Allgemeinwissen über das Mittelalter ist auch die Vorstellung verankert, dass das Leben früher ruhiger, gemütlicher und nicht so hektisch war wie heute. Früher, als die Welt noch ‚normal’ war, hatten die meisten Menschen einen festen Lebensmittelpunkt, waren fest verwurzelt in einer Gemeinschaft und verließen ihre Heimat nur dann, wenn es sich gar nicht vermeiden lies. Nur wenige – nämlich die besonders Überprivilegierten und die besonders Unterprivilegierten -, also die, die es sich leisten konnten oder die, die dazu gezwungen wurden, waren unterwegs. Alle anderen blieben ein Leben lang zuhause, an dem Ort, an dem sie ihren festen Lebensmittelpunkt hatten. Soweit unser intuitives Vorwissen darüber, wie es früher, also auch schon im Mittelalter, gewesen sein muss. Dieses mehr ‚gefühlte’ als wissenschaftlich erwiesene Vorwissen haben wir im Rahmen eines Hauptseminars zur Geschichte des Mittelalters im Herbst 2017 gründlich hinterfragt. Ausgangspunkt war die Ausstellung „Richard Löwenherz“, die im September am Historischen Museum der Pfalz in Speyer eröffnet wurde. Ein Seminar zum Thema führte uns auf die Spuren der im Museum gezeigten Objekte, von dort auf die Spuren der Menschen im Umfeld des berühmten Königs von England

The World Federation of ADHD International Consensus Statement:208 Evidence-based conclusions about the disorder

Background: Misconceptions about ADHD stigmatize affected people, reduce credibility of providers, and prevent/delay treatment. To challenge misconceptions, we curated findings with strong evidence base. Methods: We reviewed studies with more than 2000 participants or meta-analyses from five or more studies or 2000 or more participants. We excluded meta-analyses that did not assess publication bias, except for meta-analyses of prevalence. For network meta-analyses we required comparison adjusted funnel plots. We excluded treatment studies with waiting-list or treatment as usual controls. From this literature, we extracted evidence-based assertions about the disorder. Results: We generated 208 empirically supported statements about ADHD. The status of the included statements as empirically supported is approved by 80 authors from 27 countries and 6 continents. The contents of the manuscript are endorsed by 366 people who have read this document and agree with its contents. Conclusions: Many findings in ADHD are supported by meta-analysis. These allow for firm statements about the nature, course, outcome causes, and treatments for disorders that are useful for reducing misconceptions and stigma.</p