An analytic technique for statistically modeling random atomic clock errors in estimation

Minimum variance estimation requires that the statistics of random observation errors be modeled properly. If measurements are derived through the use of atomic frequency standards, then one source of error affecting the observable is random fluctuation in frequency. This is the case, for example, with range and integrated Doppler measurements from satellites of the Global Positioning and baseline determination for geodynamic applications. An analytic method is presented which approximates the statistics of this random process. The procedure starts with a model of the Allan variance for a particular oscillator and develops the statistics of range and integrated Doppler measurements. A series of five first order Markov processes is used to approximate the power spectral density obtained from the Allan variance

Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

Differences in Acute:Chronic Workload Ratio Preceding Injury Occurrence in United Soccer League Players

Professional soccer players are prone to injuries. Training loads (TL), including games, are associated with injury occurrence. Acute:Chronic workload ratio (ACWR), an index of TL, is considered an accurate injury rate metric. In respect to the relationship between injury occurrence and ACWR load obtained using global positioning systems (GPS), little evidence exists in United Soccer League (USL) teams. It is possible high ACWR during the season to lead to injuries. PURPOSE: To investigate the interaction effect of players’ injury status with ACWR of professional soccer players of a USL team. METHODS: In 2019-20, in-season data were gathered from 20 players (Age 26.3 ± 2.7) across six 3-week microcycles. Players’ TL was monitored over 133 training sessions and 40 regular season games using 10-Hz GPS and 400-Hz accelerometer (PlayerTek, Catapult Innovations). All physical, technical, and tactical overload/underload activities consisted of soccer-specific exercises (utilizing possession, small-sided games: 3v3-11v11) and tactical drills (based on coaches’ desired style of play and game-specific situations). ACWR for players’ total load accumulation was calculated for the week’s acute TL prior to injury week by the mean chronic 4-week TL prior to injury week. Injury group include 11 players who got injured during the in-season and 9 that remained healthy. A factorial repeated design in SPSS for injury group (2) and ACWR injury occurrence time (7) was used to examine the interaction effect. RESULTS: Injury group*ACWR injury time was not significant F6,66= .81, p=.56, η2 = .07. CONCLUSION: There was no difference in ACWR index between injured and non-injured players. For every ACWR injury week the injured ones had higher but non-significant ACWR values ranged from .17 to 1.7 than non-injured besides the cycle2/week2 and cycle3/week2. Our findings warrant further investigation with more participants. Possible limitations may include sample size and convenience sample

Heterogeneous profiles of coupled sleep oscillations in human hippocampus

Cross-frequency coupling of sleep oscillations is thought to mediate memory consolidation. While the hippocampus is deemed central to this process, detailed knowledge of which oscillatory rhythms interact in the sleeping human hippocampus is lacking. Combining intracranial hippocampal and non-invasive electroencephalography from twelve neurosurgical patients, we characterized spectral power and coupling during non-rapid eye movement (NREM) and rapid eye movement (REM) sleep. Hippocampal coupling was extensive, with the majority of channels expressing spectral interactions. NREM consistently showed delta–ripple coupling, but ripples were also modulated by slow oscillations (SOs) and sleep spindles. SO–delta and SO–theta coupling, as well as interactions between delta/theta and spindle/beta frequencies also occurred. During REM, limited interactions between delta/theta and beta frequencies emerged. Moreover, oscillatory organization differed substantially between i) hippocampus and scalp, ii) sites along the anterior-posterior hippocampal axis, and iii) individuals. Overall, these results extend and refine our understanding of hippocampal sleep oscillations

Radical news? Immigrants’ television use, acculturation challenges, and support for terrorism

Previous research shows that acculturation challenges predict immigrants’ support for terrorism. Here, we acknowledge the central role of mass media use in the acculturation process. We investigate whether immigrants who infrequently use ethnic and host country media, a possible indicator or driver of marginalisation, report higher sympathy with terrorism than frequent media users. We further examine if those who prefer ethnic over host country media, which might reflect or facilitate disengagement from the host society, support terrorism more strongly. To address these research questions, we conducted secondary analyses of a public opinion poll of Muslim immigrants resident in the United Kingdom (N = 880). Focusing on immigrants’ use of ethnic and host country television channels, latent class analysis identified four groups: Frequent and Infrequent Media Users as well as Ethnic and Host Country Media Users. Overall sympathy with terrorism was low. Contesting our hypothesis, Frequent Media Users supported terrorist action more than Infrequent Media Users. Ethnic Media Users also expressed higher sympathy with terrorism than Host Country Media Users. Findings emphasise the dynamic interplay between media use and acculturation challenges; they further suggest strategies to reduce immigrants’ support for terrorism

Scale-invariance of human EEG signals in sleep

We investigate the dynamical properties of electroencephalogram (EEG) signals of human in sleep. By using a modified random walk method, We demonstrate that the scale-invariance is embedded in EEG signals after a detrending procedure. Further more, we study the dynamical evolution of probability density function (PDF) of the detrended EEG signals by nonextensive statistical modeling. It displays scale-independent property, which is markedly different from the turbulent-like scale-dependent PDF evolution.Comment: 4 pages and 6 figure

The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach

We compare two influential ways of defining a generalized notion of space. The first, inspired by Gelfand duality, states that the category of 'noncommutative spaces' is the opposite of the category of C*-algebras. The second, loosely generalizing Stone duality, maintains that the category of 'pointfree spaces' is the opposite of the category of frames (i.e., complete lattices in which the meet distributes over arbitrary joins). One possible relationship between these two notions of space was unearthed by Banaschewski and Mulvey, who proved a constructive version of Gelfand duality in which the Gelfand spectrum of a commutative C*-algebra comes out as a pointfree space. Being constructive, this result applies in arbitrary toposes (with natural numbers objects, so that internal C*-algebras can be defined). Earlier work by the first three authors, shows how a noncommutative C*-algebra gives rise to a commutative one internal to a certain sheaf topos. The latter, then, has a constructive Gelfand spectrum, also internal to the topos in question. After a brief review of this work, we compute the so-called external description of this internal spectrum, which in principle is a fibered pointfree space in the familiar topos Sets of sets and functions. However, we obtain the external spectrum as a fibered topological space in the usual sense. This leads to an explicit Gelfand transform, as well as to a topological reinterpretation of the Kochen-Specker Theorem of quantum mechanics, which supplements the remarkable topos-theoretic version of this theorem due to Butterfield and Isham.Comment: 12 page

Noncommutative Lattices and Their Continuum Limits

We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra \cc(M) of continuous functions on $M$. We show how to recover the space $M$ and the algebra \cc(M) from a projective system of noncommutative lattices and an inductive system of noncommutative $C^*$-algebras, respectively.Comment: 22 pages, 8 Figures included in the LaTeX Source New version, minor modifications (typos corrected) and a correction in the list of author

Language processing within the human medial temporal lobe

Although the hippocampal formation is essential for verbal memory, it is not fully understood how it contributes to language comprehension. We recorded event-related potentials (ERPs) directly from two substructures of the medial temporal lobe (MTL), the rhinal cortex and the hippocampus proper, while epilepsy patients listened to sentences that either were correct or contained semantic or syntactic violations. Semantic violations elicited a large negative ERP response peaking at approximately 400 ms in the rhinal cortex. In contrast, syntactically incorrect sentences elicited a negative deflection of 500-800 ms in the hippocampus proper. The results suggest that functionally distinct aspects of integration in language comprehension are supported by different MTL structures: the rhinal cortex is involved in semantic integration, whereas the hippocampus proper subserves processes of syntactic integration. An analysis of phase synchronization within the gamma band between rhinal and hippocampal recording sites showed that both of the above-mentioned ERP components were preceded by an increase of phase synchronization. In contrast to these short phasic increases of phase synchronization in both violation conditions, correct sentences were associated with a long-lasting synchronization in a late time window, possibly reflecting the integration of semantic and syntactic information as required for normal comprehension