A Data Mining Method For Improving the Prediction Of Bioinformatics Data

The composition of proteins nearly correlated with its function. Therefore, it is very ungently important to discuss a method that can automatically forecast protein structure. The fusion encoding method of PseAA and DC was adopted to describe the protein features. Using this encoding method to express protein sequences will produce higher dimensional feature vectors. This paper uses the algorithm of predigesting the characteristic dimension of proteins. By extracting significant feature vectors from the primitive feature vectors, eigenvectors with high dimensions are changed to eigenvectors with low dimensions. The experimental method of jackknife test is adopted. The consequences indicate that the arithmetic put forwarded here is appropriate for identifying whether the given protein is a homo-oligomer or a hetero-oligomer.

Phase fluctuations in conventional superconductors

Within the Bardeen-Cooper-Schrieffer (BCS) theory, superconductivity is entirely governed by the pairing energy scale, which gives rise to the superconducting energy gap, Δ. However, another important energy scale, the superfluid phase stiffness, J, which determines the resilience of the superconductor to phase-fluctuations is normally ignored. The spectacular success of BCS theory owes to the fact that in conventional superconductors J is normally several orders of magnitude larger than Δ and thus an irrelevant energy scale. However, in certain situations such as in the presence of low carrier density, strong disorder, at low-dimensions or in granular superconductors, J can drastically come down and even become smaller than Δ. In such situations, the temperature and magnetic field evolution of superconducting properties is governed by phase fluctuations, which gives rise to novel electronic states where signatures of electronic pairing continue to exist even when the zero resistance state is destroyed. In this article, we will review the recent experimental developments on the study of phase fluctuations in conventional superconductors.

Blowing-up Solutions for 2nd-Order Critical Elliptic Equations: The Impact of the Scalar Curvature

Given a closed manifold $(M^n,g)$, $n\geq 3$, Druet [5, 7] proved that a necessary condition for the existence of energy-bounded blowing-up solutions to perturbations of the equation $$ \begin{align*} &\Delta_gu+h_0u=u^{\frac{n+2}{n-2}},\ u>0 \ \textrm{in }M\end{align*}$$is that $h_0\in C^1(M)$ touches the Yamabe potential somewhere when $n\geq 4$ (the condition is different for $n=6$). In this paper, we prove that Druet’s condition is also sufficient provided we add its natural differentiable version. For $n\geq 6$, our arguments are local. For the low dimensions $n\in \{4,5\}$, our proof requires to introduce a suitable mass that is defined only where Druet’s condition holds. This mass carries global information both on $h_0$ and $(M,g)$.

O010 The role of dysfunctional beliefs and attitudes about sleep in the association between daily sleep and affect in adolescents and emerging adults

Introduction Sleep and affect are closely related. Late adolescence and emerging adulthood are associated with unique sleep patterns and risk for mood disturbances. This daily study examined whether dysfunctional beliefs and attitudes about sleep (DBAS), a modifiable cognitive vulnerability factor, moderated daily sleep-affect associations. Methods 421 community adolescents (n=205, 54.1% females, M±SDage=16.9±0.87) and emerging adults (n=216, 73.1% females, M±SDage=21.31±1.73) self-reported sleep and affect (adapted 12-item PANAS) and wore an actigraphy device for 7–28 days, providing >5000 daily observations. Linear mixed models tested whether DBAS moderated daily associations between self-reported and actigraphic sleep duration (total sleep time), sleep efficiency, and next-day affect on between and within-person levels. Both valence (positive/negative) and arousal (high/low) dimensions of affect were examined. Covariates included age, gender, ethnicity, day of week, and previous-day affect. Results DBAS significantly moderated associations between average sleep and next-day positive, but not negative, affect. Individuals with higher DBAS had significantly lower high arousal positive affect as average sleep duration (actigraphic: p=.002; self-reported: p=.014) and efficiency (actigraphic: p=.014) decreased. Similar moderation was found for average self-reported sleep duration and low arousal positive affect (p=.032). No significant results emerged on the within-person level. Previous-day affect significantly predicted next-day affect across models and outcomes (all p<.001). Discussion Adolescents and emerging adults with more negative views about sleep may experience dampened positive affect in shorter, or poorer, sleep periods. DBAS may constitute a modifiable factor increasing affective vulnerability on a global but not day-to-day level, and a therapeutic target for sleep-related affect disturbances in youths.

Lie Symmetry Analysis of C 1 m , a , b Partial Differential Equations

In this article, we discussed the Lie symmetry analysis of C 1 m , a , b fractional and integer order differential equations. The symmetry algebra of both differential equations is obtained and utilized to find the similarity reductions, invariant solutions, and conservation laws. In both cases, the symmetry algebra is of low dimensions.

WDVV equations and invariant bi-Hamiltonian formalism

The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. The invariance of the bi-Hamiltonian formalism is proved for N = 3. More examples in higher dimensions show that the result might hold in general. The invariance group of the bi-Hamiltonian pairs that we find for WDVV equations is the group of projective transformations. The significance of projective invariance of WDVV equations is discussed in detail. The computer algebra programs that were used for calculations throughout the paper are provided in a GitHub repository.

Gated Recurrent Units Viewed Through the Lens of Continuous Time Dynamical Systems

Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network. As a result, it is both difficult to know a priori how successful a GRU network will perform on a given task, and also their capacity to mimic the underlying behavior of their biological counterparts. Using a continuous time analysis, we gain intuition on the inner workings of GRU networks. We restrict our presentation to low dimensions, allowing for a comprehensive visualization. We found a surprisingly rich repertoire of dynamical features that includes stable limit cycles (nonlinear oscillations), multi-stable dynamics with various topologies, and homoclinic bifurcations. At the same time we were unable to train GRU networks to produce continuous attractors, which are hypothesized to exist in biological neural networks. We contextualize the usefulness of different kinds of observed dynamics and support our claims experimentally.