On 22-cycles of graphs

Let $G=(V,E)$ be a finite undirected graph. Orient the edges of $G$ in an arbitrary way. A $2$-cycle on $G$ is a function $d : E^2\to \mathbb{Z}$ such for each edge $e$, $d(e, \cdot)$ and $d(\cdot, e)$ are circulations on $G$, and $d(e, f) = 0$ whenever $e$ and $f$ have a common vertex. We show that each $2$-cycle is a sum of three special types of $2$-cycles: cycle-pair $2$-cycles, Kuratowski $2$-cycles, and quad $2$-cycles. In case that the graph is Kuratowski connected, we show that each $2$-cycle is a sum of cycle-pair $2$-cycles and at most one Kuratowski $2$-cycle. Furthermore, if $G$ is Kuratowski connected, we characterize when every Kuratowski $2$-cycle is a sum of cycle-pair $2$-cycles. A $2$-cycles $d$ on $G$ is skew-symmetric if $d(e,f) = -d(f,e)$ for all edges $e,f\in E$. We show that each $2$-cycle is a sum of two special types of skew-symmetric $2$-cycles: skew-symmetric cycle-pair $2$-cycles and skew-symmetric quad $2$-cycles. In case that the graph is Kuratowski connected, we show that each skew-symmetric $2$-cycle is a sum of skew-symmetric cycle-pair $2$-cycles. Similar results like this had previously been obtained by one of the authors for symmetric $2$-cycles. Symmetric $2$-cycles are $2$-cycles $d$ such that $d(e,f)=d(f,e)$ for all edges $e,f\in E$

Visual semantics

Veel betekenisaspecten van taal liggen opgeslagen in het semantische geheugen. Het semantische geheugen is gebaseerd op onze ervaring met concrete objecten zoals planten, dieren en gereedschappen. Onderzoek met mensen die als gevolg van een hersenbeschadiging moeite hebben met het begrijpen van taal, heeft uitgewezen dat de betekenis van taal ook afhankelijk is van diverse sensorische en motorische gebieden van de hersenen, met name de visuele hersengebieden. Het ventrale pad is betrokken bij het herkennen van objecten, het dorsale pad maakt het mogelijk acties uit te voeren met objecten. Resultaten van experimenten die in dit proefschrift beschreven zijn geven aan dat het semantische geheugen een zeer nauwe relatie onderhoudt met het visuele systeem in onze hersenen. Dit ondersteunt ook de gedachte van een model van visuele semantiek waarin visueel-beschrijvende informatie eerst wordt opgehaald uit het lange-termijngeheugen en vervolgens wordt geactiveerd in het object-werkgeheugen. Het werkgeheugen is waarschijnlijk van belang in de koppeling tussen talige en visuele informatie. Visuele semantiek ligt dus eigenlijk op het kruispunt van semantische, visuele en talige processen Bron:Taaluniversum

Batch Reinforcement Learning on the Industrial Benchmark: First Experiences

The Particle Swarm Optimization Policy (PSO-P) has been recently introduced and proven to produce remarkable results on interacting with academic reinforcement learning benchmarks in an off-policy, batch-based setting. To further investigate the properties and feasibility on real-world applications, this paper investigates PSO-P on the so-called Industrial Benchmark (IB), a novel reinforcement learning (RL) benchmark that aims at being realistic by including a variety of aspects found in industrial applications, like continuous state and action spaces, a high dimensional, partially observable state space, delayed effects, and complex stochasticity. The experimental results of PSO-P on IB are compared to results of closed-form control policies derived from the model-based Recurrent Control Neural Network (RCNN) and the model-free Neural Fitted Q-Iteration (NFQ). Experiments show that PSO-P is not only of interest for academic benchmarks, but also for real-world industrial applications, since it also yielded the best performing policy in our IB setting. Compared to other well established RL techniques, PSO-P produced outstanding results in performance and robustness, requiring only a relatively low amount of effort in finding adequate parameters or making complex design decisions

State anxiety alters the neural oscillatory correlates of predictions and prediction errors during reward-based learning

Anxiety influences how the brain estimates and responds to uncertainty. The consequences of these processes on behaviour have been described in theoretical and empirical studies, yet the associated neural correlates remain unclear. Rhythm-based accounts of Bayesian predictive coding propose that predictions in generative models of perception are represented in alpha (8–12 Hz) and beta oscillations (13–30 Hz). Updates to predictions are driven by prediction errors weighted by precision (inverse variance), and are encoded in gamma oscillations (>30 Hz) and associated with suppression of beta activity. We tested whether state anxiety alters the neural oscillatory activity associated with predictions and precision-weighted prediction errors (pwPE) during learning. Healthy human participants performed a probabilistic reward-based learning task in a volatile environment. In our previous work, we described learning behaviour in this task using a hierarchical Bayesian model, revealing more precise (biased) beliefs about the tendency of the reward contingency in state anxiety, consistent with reduced learning in this group. The model provided trajectories of predictions and pwPEs for the current study, allowing us to assess their parametric effects on the time-frequency representations of EEG data. Using convolution modelling for oscillatory responses, we found that, relative to a control group, state anxiety increased beta activity in frontal and sensorimotor regions during processing of pwPE, and in fronto-parietal regions during encoding of predictions. No effects of state anxiety on gamma modulation were found. Our findings expand prior evidence on the oscillatory representations of predictions and pwPEs into the reward-based learning domain. The results suggest that state anxiety modulates beta-band oscillatory correlates of pwPE and predictions in generative models, providing insights into the neural processes associated with biased belief updating and poorer learning

A Benchmark Environment Motivated by Industrial Control Problems

In the research area of reinforcement learning (RL), frequently novel and promising methods are developed and introduced to the RL community. However, although many researchers are keen to apply their methods on real-world problems, implementing such methods in real industry environments often is a frustrating and tedious process. Generally, academic research groups have only limited access to real industrial data and applications. For this reason, new methods are usually developed, evaluated and compared by using artificial software benchmarks. On one hand, these benchmarks are designed to provide interpretable RL training scenarios and detailed insight into the learning process of the method on hand. On the other hand, they usually do not share much similarity with industrial real-world applications. For this reason we used our industry experience to design a benchmark which bridges the gap between freely available, documented, and motivated artificial benchmarks and properties of real industrial problems. The resulting industrial benchmark (IB) has been made publicly available to the RL community by publishing its Java and Python code, including an OpenAI Gym wrapper, on Github. In this paper we motivate and describe in detail the IB's dynamics and identify prototypic experimental settings that capture common situations in real-world industry control problems