Computing the Hessenberg matrix associated with a self-similar measure

We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures. Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix

True and intentionally fabricated memories

The aim of the experiment reported here was to investigate the processes underlying the construction of truthful and deliberately fabricated memories. Properties of memories created to be intentionally false - fabricated memories - were compared to properties of memories believed to be true - true memories. Participants recalled and then wrote or spoke true memories and fabricated memories of everyday events. It was found that true memories were reliably more vivid than fabricated memories and were nearly always recalled from a first person perspective. In contrast, fabricated differed from true memories in that they were judged to be reliably older, were more frequently recalled from a third person perspective, and linguistic analysis revealed that they required more cognitive effort to generate. No notable differences were found across modality of reporting. Finally, it was found that, intentionally fabricated memories were created by recalling and then ‘editing’ true memories. Overall, these findings show that true and fabricated memories systematically differ, despite the fact that both are based on true memories

Switching memory perspective

The perspective in which memories were spontaneously recalled, field (original perspective) or observer (see oneself in the memory), was examined for both recent and remote memories. Recent memories were dominated by field perspective whilst remote memories were dominated by observer perspective. Further, field memories contained reliably more episodic detail than observer memories. After a 1-week interval, the same memories were recalled again but with a switched memory perspective. Switching from an observer to a field perspective did not reliably increase the amount of episodic details in a memory. Switching from field to observer perspective did, however, reliably reduce the number of episodic details. These findings suggest that memories may be represented in long-term memory with a fixed perspective, either field or observer, which can be temporarily altered sometimes changing the nature of a memory, i.e. how much detail remains accessible

The influence of central neuropathic pain in paraplegic patients on performance of a motor imagery based brain computer interface

The aim of this study was to test how the presence of central neuropathic pain (CNP) influences the performance of a motor imagery based Brain Computer Interface (BCI). In this electroencephalography (EEG) based study, we tested BCI classification accuracy and analysed event related desynchronisation (ERD) in 3 groups of volunteers during imagined movements of their arms and legs. The groups comprised of nine able-bodied people, ten paraplegic patients with CNP (lower abdomen and legs) and nine paraplegic patients without CNP. We tested two types of classifiers: a 3 channel bipolar montage and classifiers based on common spatial patterns (CSPs), with varying number of channels and CSPs. Paraplegic patients with CNP achieved higher classification accuracy and had stronger ERD than paraplegic patients with no pain for all classifier configurations. Highest 2-class classification accuracy was achieved for CSP classifier covering wider cortical area: 82 ± 7% for patients with CNP, 82 ± 4% for able-bodied and 78 ± 5% for patients with no pain. Presence of CNP improves BCI classification accuracy due to stronger and more distinct ERD. Results of the study show that CNP is an important confounding factor influencing the performance of motor imagery based BCI based on ERD

Fictional first memories

YesIn a large-scale survey, 6,641 respondents provided descriptions of their first memory and their age when they encoded that memory, and they completed various memory judgments and ratings. In good agreement with many other studies, where mean age at encoding of earliest memories is usually found to fall somewhere in the first half of the 3rd year of life, the mean age at encoding here was 3.2 years. The established view is that the distribution around mean age at encoding is truncated, with very few or no memories dating to the preverbal period, that is, below about 2 years of age. However, we found that 2,487 first memories (nearly 40% of the entire sample) dated to an age at encoding of 2 years and younger, with 893 dating to 1 year and younger. We discuss how such improbable, fictional first memories could have arisen and contrast them with more probable first memories, those with an age at encoding of 3 years and older

Percolation and epidemics in a two-dimensional small world

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of "shortcuts" in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.Comment: 7 pages, 3 figures, 2 table

Valence-quark distributions in the pion

We calculate the pion's valence-quark momentum-fraction probability distribution using a Dyson-Schwinger equation model. Valence-quarks with an active mass of 0.30 GeV carry 71% of the pion's momentum at a resolving scale q_0=0.54 GeV = 1/(0.37 fm). The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from q_0 to q=2 GeV, it yields first, second and third moments in agreement with lattice and phenomenological estimates, and valence-quarks carrying 49% of the pion's momentum. However, pointwise there is a discrepancy between our calculated distribution and that hitherto inferred from parametrisations of extant pion-nucleon Drell-Yan data.Comment: 8 pages, 3 figures, REVTEX, aps.sty, epsfig.sty, minor corrections, version to appear in PR

Information decomposition of symbolic sequences

We developed a non-parametric method of Information Decomposition (ID) of a content of any symbolical sequence. The method is based on the calculation of Shannon mutual information between analyzed and artificial symbolical sequences, and allows the revealing of latent periodicity in any symbolical sequence. We show the stability of the ID method in the case of a large number of random letter changes in an analyzed symbolic sequence. We demonstrate the possibilities of the method, analyzing both poems, and DNA and protein sequences. In DNA and protein sequences we show the existence of many DNA and amino acid sequences with different types and lengths of latent periodicity. The possible origin of latent periodicity for different symbolical sequences is discussed.Comment: 18 pages, 8 figure

Achievable rates for the Gaussian quantum channel

We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in the phase space of 2N canonical variables. From the existence of symplectically integral lattices with suitable properties, we infer a lower bound on the quantum capacity of the Gaussian quantum channel that matches the one-shot coherent information optimized over Gaussian input states.Comment: 12 pages, 4 eps figures, REVTe

Solution of the Kwiecinski evolution equations for unintegrated parton distributions using the Mellin transform

The Kwiecinski equations for the QCD evolution of the unintegrated parton distributions in the transverse-coordinate space (b) are analyzed with the help of the Mellin-transform method. The equations are solved numerically in the general case, as well as in a small-b expansion which converges fast for b Lambda_QCD sufficiently small. We also discuss the asymptotic limit of large bQ and show that the distributions generated by the evolution decrease with b according to a power law. Numerical results are presented for the pion distributions with a simple valence-like initial condition at the low scale, following from chiral large-N_c quark models. We use two models: the Spectral Quark Model and the Nambu--Jona-Lasinio model. Formal aspects of the equations, such as the analytic form of the b-dependent anomalous dimensions, their analytic structure, as well as the limits of unintegrated parton densities at x -> 0, x -> 1, and at large b, are discussed in detail. The effect of spreading of the transverse momentum with the increasing scale is confirmed, with growing asymptotically as Q^2 alpha(Q^2). Approximate formulas for for each parton species is given, which may be used in practical applications.Comment: 18 pages, 6 figures, RevTe