Moment inversion problem for piecewise D-finite functions

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial coefficients on each continuity interval. Therefore, they may be specified by a finite amount of information. This reconstruction problem has practical importance in Signal Processing and other applications. It is somewhat of a ``folklore'' that the sequence of the moments of such ``piecewise D-finite''functions satisfies a linear recurrence relation of bounded order and degree. We derive this recurrence relation explicitly. It turns out that the coefficients of the differential operator which annihilates every piece of the function, as well as the locations of the discontinuities, appear in this recurrence in a precisely controlled manner. This leads to the formulation of a generic algorithm for reconstructing a piecewise D-finite function from its moments. We investigate the conditions for solvability of the resulting linear systems in the general case, as well as analyze a few particular examples. We provide results of numerical simulations for several types of signals, which test the sensitivity of the proposed algorithm to noise

Effect of Crystal Quality on HCP-BCC Phase Transition in Solid 4He

The kinetics of HCP-BCC structure phase transition is studied by precise pressure measurement technique in 4He crystals of different quality. An anomalous pressure behavior in bad quality crystals under constant volume conditions is detected just after HCP-BCC structure phase transition. A sharp pressure drop of 0.2 bar was observed at constant temperature. The subsequent pressure kinetics is a non-monotonic temperature function. The effect observed can be explained if we suppose that microscopic liquid droplets appear on the HCP-BCC interphase region in bad quality crystals. After the interphase region disappearance, these droplets are crystallized with pressure reduction. It is shown that this effect is absent in high quality thermal-treated crystals.Comment: 4 pages, 4 figure

Local modes, phonons, and mass transport in solid 4^4He

We propose a model to treat the local motion of atoms in solid $^{4}$He as a local mode. In this model, the solid is assumed to be described by the Self Consistent Harmonic approximation, combined with an array of local modes. We show that in the bcc phase the atomic local motion is highly directional and correlated, while in the hcp phase there is no such correlation. The correlated motion in the bcc phase leads to a strong hybridization of the local modes with the T$_{1}(110)$ phonon branch, which becomes much softer than that obtained through a Self Consistent Harmonic calculation, in agreement with experiment. In addition we predict a high energy excitation branch which is important for self-diffusion. Both the hybridization and the presence of a high energy branch are a consequence of the correlation, and appear only in the bcc phase. We suggest that the local modes can play the role in mass transport usually attributed to point defects (vacancies). Our approach offers a more overall consistent picture than obtained using vacancies as the predominant point defect. In particular, we show that our approach resolves the long standing controversy regarding the contribution of point defects to the specific heat of solid $^{4}$He.Comment: 10 pages, 10 figure

Comparing phoneme frequency, age of acquisition, and loss in aphasia:Implications for phonological universals

Phonological complexity may be central to the nature of human language. It may shape the distribution of phonemes and phoneme sequences within languages, but also determine age of acquisition and susceptibility to loss in aphasia. We evaluated this claim using frequency statistics derived from a corpus of phonologically transcribed Italian words (phonitalia, available at phonitalia,org), rankings of phoneme age of acquisition (AoA) and rate of phoneme errors in patients with apraxia of speech (AoS) as an indication of articulatory complexity. These measures were related to cross-linguistically derived markedness rankings. We found strong correspondences. AoA, however, was predicted by both apraxic errors and frequency, suggesting independent contributions of these variables. Our results support the reality of universal principles of complexity. In addition they suggest that these complexity principles have articulatory underpinnings since they modulate the production of patients with AoS, but not the production of patients with more central phonological difficulties

Inner Speech during Silent Reading Reflects the Reader's Regional Accent

While reading silently, we often have the subjective experience of inner speech. However, there is currently little evidence regarding whether this inner voice resembles our own voice while we are speaking out loud. To investigate this issue, we compared reading behaviour of Northern and Southern English participants who have differing pronunciations for words like ‘glass’, in which the vowel duration is short in a Northern accent and long in a Southern accent. Participants' eye movements were monitored while they silently read limericks in which the end words of the first two lines (e.g., glass/class) would be pronounced differently by Northern and Southern participants. The final word of the limerick (e.g., mass/sparse) then either did or did not rhyme, depending on the reader's accent. Results showed disruption to eye movement behaviour when the final word did not rhyme, determined by the reader's accent, suggesting that inner speech resembles our own voice

Gender gap in parental leave intentions: Evidence from 37 countries

This is the final version. Available from Wiley via the DOI in this record. Despite global commitments and efforts, a gender-based division of paid and unpaid work persists. To identify how psychological factors, national policies, and the broader sociocultural context contribute to this inequality, we assessed parental-leave intentions in young adults (18–30years old) planning to have children (N = 13,942; 8,880 identified as women; 5,062 identified as men) across 37 countries that varied in parental-leave policies and societal gender equality. In all countries, women intended to take longer leave than men. National parental-leave policies and women’s political representation partially explained cross-national variations in the gender gap. Gender gaps in leave intentions were paradoxically larger in countries with more gender-egalitarian parental-leave policies (i.e., longer leave available to both fathers and mothers). Interestingly, this cross-national variation in the gender gap was driven by cross-national variations in women’s (rather than men’s) leave intentions. Financially generous leave and gender-egalitarian policies (linked to men’s higher uptake in prior research) were not associated with leave intentions in men. Rather, men’s leave intentions were related to their individual gender attitudes. Leave intentions were inversely related to career ambitions. The potential for existing policies to foster gender equality in paid and unpaid work is discussed.SSHRC Insight Development GrantSSHRC Insight GrantEconomic and Social Research CouncilState Research AgencyGuangdong 13th-five Philosophy and Social Science Planning ProjectNational Natural Science Foundation of ChinaSwiss National Science FoundationSwiss National Science FoundationCenter for Social Conflict and Cohesion StudiesCenter for Intercultural and Indigenous ResearchSSHRC Postdoctoral FellowshipSlovak Research and Development AgencySwiss National Science FoundationCanada Research ChairsSocial Sciences and Humanities Research Council of CanadaOntario Ministry of Research and InnovationHSE University, RFFaculty of Arts, Masaryk Universit