Reliable recovery of hierarchically sparse signals for Gaussian and Kronecker product measurements

We propose and analyze a solution to the problem of recovering a block sparse signal with sparse blocks from linear measurements. Such problems naturally emerge inter alia in the context of mobile communication, in order to meet the scalability and low complexity requirements of massive antenna systems and massive machine-type communication. We introduce a new variant of the Hard Thresholding Pursuit (HTP) algorithm referred to as HiHTP. We provide both a proof of convergence and a recovery guarantee for noisy Gaussian measurements that exhibit an improved asymptotic scaling in terms of the sampling complexity in comparison with the usual HTP algorithm. Furthermore, hierarchically sparse signals and Kronecker product structured measurements naturally arise together in a variety of applications. We establish the efficient reconstruction of hierarchically sparse signals from Kronecker product measurements using the HiHTP algorithm. Additionally, we provide analytical results that connect our recovery conditions to generalized coherence measures. Again, our recovery results exhibit substantial improvement in the asymptotic sampling complexity scaling over the standard setting. Finally, we validate in numerical experiments that for hierarchically sparse signals, HiHTP performs significantly better compared to HTP.Comment: 11+4 pages, 5 figures. V3: Incomplete funding information corrected and minor typos corrected. V4: Change of title and additional author Axel Flinth. Included new results on Kronecker product measurements and relations of HiRIP to hierarchical coherence measures. Improved presentation of general hierarchically sparse signals and correction of minor typo

How is your mind-set? Proof of concept for the measurement of the level of emotional development

Background In persons with intellectual and developmental disabilities, not only cognitive brain functions, but also socio-emotional processing networks may be impaired. This study aims to validate the Scale of Emotional Development—Short (SED-S) to provide an instrument for the assessment of socio-emotional brain functions. Method The SED-S was applied in 160 children aged 0–12 years. Criterion validity was investigated at item and scale level in terms of the agreement between the scale classification and the child’s chronological age. Additionally, interrater reliability and internal consistency were assessed. Results For the majority of items, the expected response pattern emerged, showing the highest response probabilities in the respective target age groups. Agreement between the classification of the different SED-S domains and chronological age was high (κw = 0.95; exact agreement = 80.6%). Interrater reliability at domain level ranged from κw = .98 to 1.00 and internal consistency was high (α = .99). Conclusion The study normed the SED-S in a sample of typically developing children and provides evidence for criterion validity on item, domain and scale level

The “Material” and the “Mental” as Brain Constructs

Abstract: For most philosophers it is “inconceivable” that neural states could give rise to mind. However, as Nannini demonstrates, this argument is very weak, because modern physics is full of aspects that are radically opposed to conventional thinking. Furthermore, the qualia problem represents a pseudo-problem which arises, whenever we confound events in our phenomenal world (“actuality”) with events in the consciousness-independent world (“reality”). Everything we identify and measure as “material” brain structures and functions is a mental construct of a “real” brain inaccessible to us, and as such a mental construct it cannot be the true origin of mind. We have to accept that the alleged fundamental property differences of the material and the mental world are conventions of our mind. At the same time, we may hypothesize that “in reality” mind and consciousness are mental fields as emergent properties of cortical electromagnetic fields.Keywords: Brain-mind Relationship; Qualia Problem; Actual and Real World; Electromagnetic Fields; Mental Fields. Il “materiale” e il “mentale” come costrutti cerebraliRiassunto: Per molti filosofi è inconcepibile che gli stati neurali diano origine alla mente. Tuttavia, come Nannini dimostra, l’argomento cui fanno appello è molto debole poiché la fisica moderna contempla numerosi aspetti che contraddicono il modo di pensare convenzionale. Il problema dei qualia rappresenta inoltre uno pseudo-problema riconducibile al fatto di confondere gli eventi nel nostro mondo fenomenico (l’attualità) con gli eventi di un mondo indipendente dalla coscienza (la realtà). Tutto ciò che identifichiamo e misuriamo come strutture “materiali” e funzioni del cervello è un costrutto mentale di un cervello “reale” che è a noi inaccessibile. Come tale un costrutto mentale non può essere la vera origine della mente. Dobbiamo accettare che le supposte differenze nelle proprietà fondamentali del mondo materiale e del mondo mentale siano convenzioni della nostra mente. Allo stesso tempo, possiamo ipotizzare che in realtà la mente e la coscienza siano campi mentali che si danno quali proprietà emergenti di campi elettromagnetici corticali.Parole chiave: Rapporto mente-corpo; Problema dei qualia; Mondo reale e mondo attuale; Campi elettromagnetici; Campi mentali

Die (innere) Logik des Entscheidens: Zur neurobiologischen Fundierung ökonomischer Entscheidungen

Ziel des Beitrages ist es, die neueren Erkenntnisse der Neurobiologie zum Entscheidungsverhalten von Menschen für die Entwicklung eines idealtypischen Ablaufplans ökonomischer Entscheidungsvorgänge einzusetzen, indem die Logik deutlich gemacht wird, die den Aufbau des menschlichen Gehirns bestimmt. Ein solcher Ablaufplan kann dazu beitragen, ökonomische Modelle realitätsnäher als bisher formulieren zu können, und ökonomische Modelle, die bisher eher getrennt voneinander gesehen wurden, als Teil eines größeren Ganzen einzuordnen. Es zeigt sich, dass wesentliche Komponenten einiger viel verwendeter Mo-delle der Ökonomik Parallelen in der neurobiologischen und physiologischen Arbeitsweise des Gehirns finden. Dies kann einen Beitrag dazu leisten, Modelle zielgerichteter als bisher zur Lösung ökonomischer Probleme einzusetzen. --Neuroeeconomics,Behavioural Economics,Entscheidungsverhalten,Validierung ökonomischer Modelle

Hierarchical compressed sensing

Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become clear that a similar methodology would also carry over to a wealth of other classes of structured signals. In this work, we provide an overview over the theory of compressed sensing for a particularly rich family of such signals, namely those of hierarchically structured signals. Examples of such signals are constituted by blocked vectors, with only few non-vanishing sparse blocks. We present recovery algorithms based on efficient hierarchical hard-thresholding. The algorithms are guaranteed to converge, in a stable fashion both with respect to measurement noise as well as to model mismatches, to the correct solution provided the measurement map acts isometrically restricted to the signal class. We then provide a series of results establishing the required condition for large classes of measurement ensembles. Building upon this machinery, we sketch practical applications of this framework in machine-type communications and quantum tomography.Comment: This book chapter is a report on findings within the DFG-funded priority program `Compressed Sensing in Information Processing' (CoSIP