Panov's theorem for weak Hopf algebras

Panov proved necessary and sufficient conditions to extend the Hopf algebra structure of an algebra R to an Ore extension R[x; sigma, delta] with x being a skew-primitive element. In this paper we extend Panov's result to Ore extensions over weak Hopf algebras. As an application we study Ore extensions of connected groupoid algebras

Irreducible actions and compressible modules

Any finite set of linear operators on an algebra $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a critically compressible left $B$-module, then the dimension of its self-injective hull $A$ over the ring of fractions of $A^B$ is bounded by the uniform dimension of $A$ and the number of linear operators generating $B$. This extends a known result on irreducible Hopf actions and applies in particular to weak Hopf action. Furthermore we prove necessary and sufficient conditions for an algebra A to be critically compressible in the case of group actions, group gradings and Lie actions

A neural integrator model for planning and value-based decision making of a robotics assistant

Modern manufacturing and assembly environments are characterized by a high variability in the built process which challenges human–robot cooperation. To reduce the cognitive workload of the operator, the robot should not only be able to learn from experience but also to plan and decide autonomously. Here, we present an approach based on Dynamic Neural Fields that apply brain-like computations to endow a robot with these cognitive functions. A neural integrator is used to model the gradual accumulation of sensory and other evidence as time-varying persistent activity of neural populations. The decision to act is modeled by a competitive dynamics between neural populations linked to different motor behaviors. They receive the persistent activation pattern of the integrators as input. In the first experiment, a robot learns rapidly by observation the sequential order of object transfers between an assistant and an operator to subsequently substitute the assistant in the joint task. The results show that the robot is able to proactively plan the series of handovers in the correct order. In the second experiment, a mobile robot searches at two different workbenches for a specific object to deliver it to an operator. The object may appear at the two locations in a certain time period with independent probabilities unknown to the robot. The trial-by-trial decision under uncertainty is biased by the accumulated evidence of past successes and choices. The choice behavior over a longer period reveals that the robot achieves a high search efficiency in stationary as well as dynamic environments.The work received financial support from FCT through the PhD fellowships PD/BD/128183/2016 and SFRH/BD/124912/2016, the project “Neurofield” (PTDC/MAT-APL/31393/2017) and the research centre CMAT within the project UID/MAT/00013/2013

Paradoxical tuberculosis associated immune reconstitution inflammatory syndrome presenting with chylous ascites and chylothorax in a HIV-1 infected child

We present a case of tuberculosis (TB) paradoxical immune reconstitution inflammatory syndrome (IRIS) complicated by chylous ascites and chylothorax in a HIV-infected child. There are few descriptions of TB IRIS in children. This case extends the clinical spectrum of TB IRIS. © The Author [2010]. Published by Oxford University Press. All rights reserved.Articl