Determining Principal Component Cardinality through the Principle of Minimum Description Length

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives objective compression-based criteria for model selection, but it is difficult to analytically applyits modern definition - NML (Normalized Maximum Likelihood) - to theproblem of PCA. This work shows a general reduction of NML prob-lems to lower-dimension problems. Applying this reduction, it boundsthe NML of PCA, by terms of the NML of linear regression, which areknown.Comment: LOD 201

MDL Convergence Speed for Bernoulli Sequences

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is finitely bounded, implying convergence with probability one, and (b) it additionally specifies the convergence speed. For MDL, in general one can only have loss bounds which are finite but exponentially larger than those for Bayes mixtures. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound (comparable to the one for Bayes mixtures) for certain important model classes. We discuss the application to Machine Learning tasks such as classification and hypothesis testing, and generalization to countable classes of i.i.d. models.Comment: 28 page

Mutual Information of Population Codes and Distance Measures in Probability Space

We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system size. A theory of the rate of saturation of the MI is developed. We show that this rate is controlled by a distance function between the response probabilities induced by different stimuli. This function, which we term the {\it Confusion Distance} between two probabilities, is related to the Renyi $\alpha$-Information.Comment: 11 pages, 3 figures, accepted to PR

Challenges of Religious Literacy in Education : Islam and the Governance of Religious Diversity in Multi-faith Schools

This chapter seeks take part in an emerging research where religion is approached as a whole school endeavor. Previous research and policy recommendations typically focused on teaching about religion in school, but the accommodation of religious diversity in the wider school culture merits more attention. Based on observations in our multiple case studies, we discuss the multi-level governance of religious diversity in Finnish multi-faith schools with a particular focus on the challenges of religious literacy for educators. The three examples we present focus on the inclusion of Muslims in Finnish schools and in particular on the challenges for educator (1) in interpreting the distinction between religion and culture, (2) in recognizing and handling intra-religious diversity, and (3) in being aware of Protestant conceptions of religion and culture. A theme cutting across these examples is how they reflect the tendencies either to see different situations merely through the lens of religion (religionisation), or not to recognize the importance of religion at all (religion-blindness). We argue that religious literacy should be recognized and developed as a vital part of the intercultural competencies of educators.Peer reviewe

Does antibacterial treatment for urinary tract infection contribute to the risk of breast cancer?

Low lignan status has been reported to be related to an elevated risk of breast cancer. Since lignan status is reduced by antibacterial medications, it is plausible to hypothesize that repeated use of antibiotics may also be a risk factor for breast cancer. History of treatment for urinary tract infection was studied for its prediction of breast cancer among 9461 Finnish women 19–89 years of age and initially cancer-free. During a follow-up in 1973–1991, a total of 157 breast cancer cases were diagnosed. Women reporting previous or present medication for urinary tract infection at baseline showed an elevated breast cancer risk in comparison with other women. The age-adjusted relative risk was 1.34 (95% confidence interval (CI) = 0.98–1.83). The association was concentrated to women under 50 years of age. The relative risk for these women was 1.74 (95% CI 1.13–2.68), whereas it was 0.97 (95% CI 0.59–1.58) for older women. The relative risk in the younger age-group was 1.47 (95% CI 0.73–2.97) during the first 10 years of follow-up, and 1.93 (95% CI 1.11–3.37) for follow-up times longer than 10 years. These data suggest that premenopausal women using long-term medication for urinary tract infections show a possible elevated risk of future breast cancer. The results are, however, still inconclusive and the hypothesis needs to be tested by other studies. © 2000 Cancer ResearchCampaig

Q_EC values of the Superallowed beta-Emitters 10-C, 34-Ar, 38-Ca and 46-V

The Q_EC values of the superallowed beta+ emitters 10-C, 34-Ar, 38-Ca and 46-V have been measured with a Penning-trap mass spectrometer to be 3648.12(8), 6061.83(8), 6612.12(7) and 7052.44(10) keV, respectively. All four values are substantially improved in precision over previous results.Comment: 9 pages, 7 figures, 5 table

An aldehyde as a rapid source of secondary aerosol precursors: theoretical and experimental study of hexanal autoxidation

Aldehydes are common constituents of natural and polluted atmospheres, and their gas-phase oxidation has recently been reported to yield highly oxygenated organic molecules (HOMs) that are key players in the formation of atmospheric aerosol. However, insights into the molecular-level mechanism of this oxidation reaction have been scarce. While OH initiated oxidation of small aldehydes, with two to five carbon atoms, under high-NOx conditions generally leads to fragmentation products, longer-chain aldehydes involving an initial non-aldehydic hydrogen abstraction can be a path to molecular functionalization and growth. In this work, we conduct a joint theoretical–experimental analysis of the autoxidation chain reaction of a common aldehyde, hexanal. We computationally study the initial steps of OH oxidation at the RHF-RCCSD(T)-F12a/VDZ-F12//ωB97X-D/aug-cc-pVTZ level and show that both aldehydic (on C1) and non-aldehydic (on C4) H-abstraction channels contribute to HOMs via autoxidation. The oxidation products predominantly form through the H abstraction from C1 and C4, followed by fast unimolecular 1,6 H-shifts with rate coefficients of 1.7×10-1 and 8.6×10-1 s−1, respectively. Experimental flow reactor measurements at variable reaction times show that hexanal oxidation products including HOM monomers up to C6H11O7 and accretion products C12H22O9−10 form within 3 s reaction time. Kinetic modeling simulations including atmospherically relevant precursor concentrations agree with the experimental results and the expected timescales. Finally, we estimate the hexanal HOM yields up to seven O atoms with mechanistic details through both C1 and C4 channels.</p

FingerReader: A Wearable Device to Support Text Reading on the Go

Visually impaired people report numerous difficulties with accessing printed text using existing technology, including problems with alignment, focus, accuracy, mobility and efficiency. We present a finger worn device that assists the visually impaired with effectively and efficiently reading paper-printed text. We introduce a novel, local-sequential manner for scanning text which enables reading single lines, blocks of text or skimming the text for important sections while providing real-time auditory and tactile feedback. The design is motivated by preliminary studies with visually impaired people, and it is small-scale and mobile, which enables a more manageable operation with little setup