Criteria of efficiency for conformal prediction

We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.Comment: 31 page

Rough paths in idealized financial markets

This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume that the price path is positive and right-continuous. The qualification "typical" means that there is a trading strategy (constructed explicitly in the proof) that risks only one monetary unit but brings infinite capital when the variation index of the realized price path exceeds 2. The paper also reviews some known results for continuous price paths and lists several open problems.Comment: 21 pages, this version adds (in Appendix C) a reference to new results in the foundations of game-theoretic probability based on Hardin and Taylor's work on hat puzzle

Discharge Identity of Medullary Inspiratory Neurons is Altered during Repetitive Fictive Cough

This study investigated the stability of the discharge identity of inspiratory decrementing (I-Dec) and augmenting (I-Aug) neurons in the caudal (cVRC) and rostral (rVRC) ventral respiratory column during repetitive fictive cough in the cat. Inspiratory neurons in the cVRC (n = 23) and rVRC (n = 17) were recorded with microelectrodes. Fictive cough was elicited by mechanical stimulation of the intrathoracic trachea. Approximately 43% (10 of 23) of I-Dec neurons shifted to an augmenting discharge pattern during the first cough cycle (C1). By the second cough cycle (C2), half of these returned to a decrementing pattern. Approximately 94% (16 of 17) of I-Aug neurons retained an augmenting pattern during C1 of a multi-cough response episode. Phrenic burst amplitude and inspiratory duration increased during C1, but decreased with each subsequent cough in a series of repetitive coughs. As a step in evaluating the model-driven hypothesis that VRC I-Dec neurons contribute to the augmentation of inspiratory drive during cough via inhibition of VRC tonic expiratory neurons that inhibit premotor inspiratory neurons, cross-correlation analysis was used to assess relationships of tonic expiratory cells with simultaneously recorded inspiratory neurons. Our results suggest that reconfiguration of inspiratory-related sub-networks of the respiratory pattern generator occurs on a cycle-by-cycle basis during repetitive coughing

Conformal Predictive Distributions with Kernels

This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine learning, whose early development was so deeply influenced by two remarkable groups at the Institute of Automation and Remote Control. The second development is combining predictive distributions with kernel methods, which were originated by one of those groups, including Emmanuel Braverman.Comment: 20 pages, 3 figures, prepared for the Proceedings of the Braverman Readings (Boston, 28-30 April 2017

Investigating the peculiar emission from the new VHE gamma-ray source H1722+119

The MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) telescopes observed the BL Lac object H1722+119 (redshift unknown) for six consecutive nights between 2013 May 17 and 22, for a total of 12.5 h. The observations were triggered by high activity in the optical band measured by the KVA (Kungliga Vetenskapsakademien) telescope. The source was for the first time detected in the very high energy (VHE, $E > 100$ GeV) $\gamma$-ray band with a statistical significance of 5.9 $\sigma$. The integral flux above 150 GeV is estimated to be $(2.0\pm 0.5)$ per cent of the Crab Nebula flux. We used contemporaneous high energy (HE, 100 MeV $< E < 100$ GeV) $\gamma$-ray observations from Fermi-LAT (Large Area Telescope) to estimate the redshift of the source. Within the framework of the current extragalactic background light models, we estimate the redshift to be $z = 0.34 \pm 0.15$. Additionally, we used contemporaneous X-ray to radio data collected by the instruments on board the Swift satellite, the KVA, and the OVRO (Owens Valley Radio Observatory) telescope to study multifrequency characteristics of the source. We found no significant temporal variability of the flux in the HE and VHE bands. The flux in the optical and radio wavebands, on the other hand, did vary with different patterns. The spectral energy distribution (SED) of H1722+119 shows surprising behaviour in the $\sim 3\times10^{14} - 10^{18}$ Hz frequency range. It can be modelled using an inhomogeneous helical jet synchrotron self-Compton model.Comment: 12 pages, 5 figures, 2 table

Multi-Wavelength Observations of the Blazar 1ES 1011+496 in Spring 2008

The BL Lac object 1ES 1011+496 was discovered at Very High Energy gamma-rays by MAGIC in spring 2007. Before that the source was little studied in different wavelengths. Therefore a multi-wavelength (MWL) campaign was organized in spring 2008. Along MAGIC, the MWL campaign included the Metsahovi radio observatory, Bell and KVA optical telescopes and the Swift and AGILE satellites. MAGIC observations span from March to May, 2008 for a total of 27.9 hours, of which 19.4 hours remained after quality cuts. The light curve showed no significant variability. The differential VHE spectrum could be described with a power-law function. Both results were similar to those obtained during the discovery. Swift XRT observations revealed an X-ray flare, characterized by a harder when brighter trend, as is typical for high synchrotron peak BL Lac objects (HBL). Strong optical variability was found during the campaign, but no conclusion on the connection between the optical and VHE gamma-ray bands could be drawn. The contemporaneous SED shows a synchrotron dominated source, unlike concluded in previous work based on nonsimultaneous data, and is well described by a standard one zone synchrotron self Compton model. We also performed a study on the source classification. While the optical and X-ray data taken during our campaign show typical characteristics of an HBL, we suggest, based on archival data, that 1ES 1011+496 is actually a borderline case between intermediate and high synchrotron peak frequency BL Lac objects.Comment: 13 pages, accepted for publication in MNRA