Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

Effects of expectation and caffeine on arousal, well-being, and reaction time

The objective of this study is to determine the impact of expectation associated with placebo and caffeine ingestion. We used a three-armed, randomized, double-blind design. Two three-armed experiments varying instruction (true, false, control) investigated the role of expectations of changes in arousal (blood pressure, heart rate), subjective well-being, and reaction time (RT). In Experiment 1 (N = 45), decaffeinated coffee was administered, and expectations were produced in one group by making them believe they had ingested caffeinated coffee. In Experiment 2 (N = 45), caffeinated orange juice was given in both experimental groups, but only one was informed about the true content. In Experiment 1, a significant effect for subjective alertness was found in the placebo treatment compared to the control group. However, for RT and well-being no significant effects were found. In Experiment 2, no significant expectancy effects were found. Caffeine produced large effects for blood pressure in both treatments compared to the control group, but the effects were larger for the false information group. For subjective well-being (alertness, calmness), considerable but nonsignificant changes were found for correctly informed participants, indicating possible additivity of pharmacologic effect and expectations. The results tentatively indicate that placebo and expectancy effects primarily show through introspection.

Modulating the granularity of category formation by global cortical states

The unsupervised categorization of sensory stimuli is typically attributed to feedforward processing in a hierarchy of cortical areas. This purely sensory-driven view of cortical processing, however, ignores any internal modulation, e.g., by top-down attentional signals or neuromodulator release. To isolate the role of internal signaling on category formation, we consider an unbroken continuum of stimuli without intrinsic category boundaries. We show that a competitive network, shaped by recurrent inhibition and endowed with Hebbian and homeostatic synaptic plasticity, can enforce stimulus categorization. The degree of competition is internally controlled by the neuronal gain and the strength of inhibition. Strong competition leads to the formation of many attracting network states, each being evoked by a distinct subset of stimuli and representing a category. Weak competition allows more neurons to be co-active, resulting in fewer but larger categories. We conclude that the granularity of cortical category formation, i.e., the number and size of emerging categories, is not simply determined by the richness of the stimulus environment, but rather by some global internal signal modulating the network dynamics. The model also explains the salient non-additivity of visual object representation observed in the monkey inferotemporal (IT) cortex. Furthermore, it offers an explanation of a previously observed, demand-dependent modulation of IT activity on a stimulus categorization task and of categorization-related cognitive deficits in schizophrenic patients.

Response surface modeling of the interaction between propofol and sevoflurane

BACKGROUND: Propofol and sevoflurane display additivity for gamma-aminobutyric acid receptor activation, loss of consciousness, and tolerance of skin incision. Information about their interaction regarding electroencephalographic suppression is unavailable. This study examined this interaction as well as the interaction on the probability of tolerance of shake and shout and three noxious stimulations by using a response surface methodology. METHODS: Sixty patients preoperatively received different combined concentrations of propofol (0-12 microg/ml) and sevoflurane (0-3.5 vol.%) according to a crisscross design (274 concentration pairs, 3 to 6 per patient). After having reached pseudo-steady state, the authors recorded bispectral index, state and response entropy and the response to shake and shout, tetanic stimulation, laryngeal mask airway insertion, and laryngoscopy. For the analysis of the probability of tolerance by logistic regression, a Greco interaction model was used. For the separate analysis of bispectral index, state and response entropy suppression, a fractional Emax Greco model was used. All calculations were performed with NONMEM V (GloboMax LLC, Hanover, MD). RESULTS: Additivity was found for all endpoints, the Ce(50, PROP)/Ce(50, SEVO) for bispectral index suppression was 3.68 microg. ml(-1)/ 1.53 vol.%, for tolerance of shake and shout 2.34 microg . ml(-1)/ 1.03 vol.%, tetanic stimulation 5.34 microg . ml(-1)/ 2.11 vol.%, laryngeal mask airway insertion 5.92 microg. ml(-1) / 2.55 vol.%, and laryngoscopy 6.55 microg. ml(-1)/2.83 vol.%. CONCLUSION: For both electroencephalographic suppression and tolerance to stimulation, the interaction of propofol and sevoflurane was identified as additive. The response surface data can be used for more rational dose finding in case of sequential and coadministration of propofol and sevoflurane.

Elicitable distortion risk measures: A concise proof

Elicitability has recently been discussed as a desirable property for risk measures. Kou and Peng (2014) showed that an elicitable distortion risk measure is either a Value-at-Risk or the mean. We give a concise alternative proof of this result, and discuss the conflict between comonotonic additivity and elicitability.