Protecting points from operator pencils

We classify all sets of the form $\bigcup_{t\in\mathbb{R}}\mathrm{spec}(A+tB)$ where $A$ and $B$ are self-adjoint operators and $B$ is bounded, non-negative, and non-zero. We show that these sets are exactly the complements of discrete subsets of $\mathbb{R}$, that is, of at most countable subsets of $\mathbb{R}$ that contain none of their accumulation points.Comment: 6 pages; a counterexample for sign-indefinite perturbations and some references have been added, some editorial change

Active inference on discrete state-spaces: A synthesis

Active inference is a normative principle underwriting perception, action, planning, decision-making and learning in biological or artificial agents. From its inception, its associated process theory has grown to incorporate complex generative models, enabling simulation of a wide range of complex behaviours. Due to successive developments in active inference, it is often difficult to see how its underlying principle relates to process theories and practical implementation. In this paper, we try to bridge this gap by providing a complete mathematical synthesis of active inference on discrete state-space models. This technical summary provides an overview of the theory, derives neuronal dynamics from first principles and relates this dynamics to biological processes. Furthermore, this paper provides a fundamental building block needed to understand active inference for mixed generative models; allowing continuous sensations to inform discrete representations. This paper may be used as follows: to guide research towards outstanding challenges, a practical guide on how to implement active inference to simulate experimental behaviour, or a pointer towards various in-silico neurophysiological responses that may be used to make empirical predictions

Neurocognitive basis of model-based decision making and its metacontrol in childhood

Human behavior is supported by both goal-directed (model-based) and habitual (model-free) decision-making, each differing in its flexibility, accuracy, and computational cost. The arbitration between habitual and goal-directed systems is thought to be regulated by a process known as metacontrol. However, how these systems emerge and develop remains poorly understood. Recently, we found that while children between 5 and 11 years displayed robust signatures of model-based decision-making, which increased during this developmental period, there were substantial individual differences in the display of metacontrol. Here, we inspect the neurocognitive basis of model-based decision-making and metacontrol in childhood and focus this investigation on executive functions, fluid reasoning, and brain structure. A total of 69 participants between the ages of 6-13 completed a two-step decision-making task and an extensive behavioral test battery. A subset of 44 participants also completed a structural magnetic resonance imaging scan. We find that individual differences in metacontrol are specifically associated with performance on an inhibition task and individual differences in thickness of dorsolateral prefrontal, temporal, and superior-parietal cortices. These brain regions likely reflect the involvement of cognitive processes crucial to metacontrol, such as cognitive control and contextual processing

D'Alembert sums for vibrating bar with viscous ends

We describe a new method for finding analytic solutions to some initial-boundary problems for partial differential equations with constant coefficients. The method is based on expanding the denominator of the Laplace transformed Green's function of the problem into a convergent geometric series. If the denominator is a linear combination of exponents with real powers one obtains a closed form solution as a sum with finite but time dependent number of terms. We call it a d'Alembert sum. This representation is computationally most effective for small evolution times, but it remains valid even when the system of eigenmodes is incomplete and the eigenmode expansion is unavailable. Moreover, it simplifies in such cases. In vibratory problems d'Alembert sums represent superpositions of original and partially reflected traveling waves. They generalize the d'Alembert type formulas for the wave equation, and reduce to them when original waves can undergo only finitely many reflections in the entire course of evolution. The method is applied to vibrations of a bar with dampers at each end and at some internal point. The results are illustrated by computer simulations and comparisons to modal and FEM solutions.Comment: 18 pages, 8 figure

Rapid KRAS, EGFR, BRAF and PIK3CA Mutation Analysis of Fine Needle Aspirates from Non-Small-Cell Lung Cancer Using Allele-Specific qPCR

Endobronchial Ultrasound Guided Transbronchial Needle Aspiration (EBUS-TBNA) and Trans-esophageal Ultrasound Scanning with Fine Needle Aspiration (EUS-FNA) are important, novel techniques for the diagnosis and staging of non-small cell lung cancer (NSCLC) that have been incorporated into lung cancer staging guidelines. To guide and optimize treatment decisions, especially for NSCLC patients in stage III and IV, EGFR and KRAS mutation status is often required. The concordance rate of the mutation analysis between these cytological aspirates and histological samples obtained by surgical staging is unknown. Therefore, we studied the extent to which allele-specific quantitative real-time PCR with hydrolysis probes could be reliably performed on EBUS and EUS fine needle aspirates by comparing the results with histological material from the same patient. We analyzed a series of 43 NSCLC patients for whom cytological and histological material was available. We demonstrated that these standard molecular techniques can be accurately applied on fine needle cytological aspirates from NSCLC patients. Importantly, we show that all mutations detected in the histological material of primary tumor were also identified in the cytological samples. We conclude that molecular profiling can be reliably performed on fine needle cytology aspirates from NSCLC patients

National records of 3000 European bee and hoverfly species: A contribution to pollinator conservation

Pollinators play a crucial role in ecosystems globally, ensuring the seed production of most flowering plants. They are threatened by global changes and knowledge of their distribution at the national and continental levels is needed to implement efficient conservation actions, but this knowledge is still fragmented and/or difficult to access. As a step forward, we provide an updated list of around 3000 European bee and hoverfly species, reflecting their current distributional status at the national level (in the form of present, absent, regionally extinct, possibly extinct or non-native). This work was attainable by incorporating both published and unpublished data, as well as knowledge from a large set of taxonomists and ecologists in both groups. After providing the first National species lists for bees and hoverflies for many countries, we examine the current distributional patterns of these species and designate the countries with highest levels of species richness. We also show that many species are recorded in a single European country, highlighting the importance of articulating European and national conservation strategies. Finally, we discuss how the data provided here can be combined with future trait and Red List data to implement research that will further advance pollinator conservation

Estimating the Operator Exponential

We obtain some new spectral norm and trace norm estimates for the decay of the operator exponential by means of the solution of the underlying Ljapunov equation