Covariant hydrodynamics of Hamiltonian systems

The theory of hydrodynamic reduction of non-autonomous Hamiltonian mechanics (V. Kozlov, 1983) is presented in the geometric formalism of bundles over the time axis R. In this formalism, time is one of the coordinates, not a parameter; the connections describe reference frames and velocity fields of mechanical systems. The equations of the theory are presented in a form that is invariant with respect to time-dependent coordinate transformations and the choice of reference frames.

New possibilities of the PCA-Seq method in the analysis of time series (on the example of solar activity)

When analyzing a 1D time series, it is traditional to represent it as the sum of the trend, cyclical components and noise. The trend is seen as an external influence. However, the impact can be not only additive, but also multiplicative. In this case, not only the level changes, but also the amplitude of the cyclic components. In the PCA-Seq method, a generalization of SSA, it is possible to pre-standardize fragments of a time series to solve this problem. The algorithm is applied to the Anderson series – a sign alternating version of the well-known Wolf series, reflecting the 22-year Hale cycle. The existence of this cycle is not disputed at high solar activity, but there are doubts about the constancy of its period at this time, as well as its existence during the epoch of low solar activity. The processing of the series by the PCA-Seq method revealed clear oscillations fluctuations of almost constant amplitude with an average period of 21.9 years, and it was found that the correlation of these oscillations with the time axis for 300 years does not differ significantly from zero. This confirms the hypothesis of the existence of 22-year oscillations in solar activity even at its minima, like the Maunder minimum.

Ancestral sequences of a large promiscuous enzyme family correspond to bridges in sequence space in a network representation

Evolutionary relationships of protein families can be characterized either by networks or by trees. Whereas trees allow for hierarchical grouping and reconstruction of the most likely ancestral sequences, networks lack a time axis but allow for thresholds of pairwise sequence identity to be chosen and, therefore, the clustering of family members with presumably more similar functions. Here, we use the large family of arylsulfatases and phosphonate monoester hydrolases to investigate similarities, strengths and weaknesses in tree and network representations. For varying thresholds of pairwise sequence identity, values of betweenness centrality and clustering coefficients were derived for nodes of the reconstructed ancestors to measure the propensity to act as a bridge in a network. Based on these properties, ancestral protein sequences emerge as bridges in protein sequence networks. Interestingly, many ancestral protein sequences appear close to extant sequences. Therefore, reconstructed ancestor sequences might also be interpreted as yet-to-be-identified homologues. The concept of ancestor reconstruction is compared to consensus sequences, too. It was found that hub sequences in a network, e.g. reconstructed ancestral sequences that are connected to many neighbouring sequences, share closer similarity with derived consensus sequences. Therefore, some reconstructed ancestor sequences can also be interpreted as consensus sequences.

Violence Recognition Based on Auditory-Visual Fusion of Autoencoder Mapping

In the process of violence recognition, accuracy is reduced due to problems related to time axis misalignment and the semantic deviation of multimedia visual auditory information. Therefore, this paper proposes a method for auditory–visual information fusion based on autoencoder mapping. First, a feature extraction model based on the CNN–LSTM framework is established, and multimedia segments are used as whole input to solve the problem of time axis misalignment of visual and auditory information. Then, a shared semantic subspace is constructed based on an autoencoder mapping model and is optimized by semantic correspondence, which solves the problem of audiovisual semantic deviation and realizes the fusion of visual and auditory information on segment level features. Finally, the whole network is used to identify violence. The experimental results show that the method can make good use of the complementarity between modes. Compared with single-mode information, the multimodal method can achieve better results.

Time-Rescaling Regression Method for Exponential Decay Time Series Predictions

The exponential law has been discovered in various systems around the world. In this study, we introduce two existing and one proposed analytical method for exponential decay time-series predictions. The proposed method is given by a linear regression that is based on rescaling the time axis in terms of exponential decay laws. We confirm that the proposed method has a higher prediction accuracy than existing methods by performance evaluation using random numbers and verification using actual data. The proposed method can be used for analyzing real data modeled with exponential functions, which are ubiquitous in the world.

Curve Registration of Functional Data for Approximate Bayesian Computation

Approximate Bayesian computation is a likelihood-free inference method which relies on comparing model realisations to observed data with informative distance measures. We obtain functional data that are not only subject to noise along their y axis but also to a random warping along their x axis, which we refer to as the time axis. Conventional distances on functions, such as the L2 distance, are not informative under these conditions. The Fisher–Rao metric, previously generalised from the space of probability distributions to the space of functions, is an ideal objective function for aligning one function to another by warping the time axis. We assess the usefulness of alignment with the Fisher–Rao metric for approximate Bayesian computation with four examples: two simulation examples, an example about passenger flow at an international airport, and an example of hydrological flow modelling. We find that the Fisher–Rao metric works well as the objective function to minimise for alignment; however, once the functions are aligned, it is not necessarily the most informative distance for inference. This means that likelihood-free inference may require two distances: one for alignment and one for parameter inference.

Cigarette smoking trajectories in adolescent smokers: Does the time axis metric matter?

Introduction Most studies modeling adolescent cigarette smoking trajectories use age as the time axis, possibly obscuring depiction of the natural course of cigarette smoking. We used a simulated example and real data to contrast smoking trajectories obtained from models that used time since smoking onset or calendar time (age) as the time axis. Methods Data were drawn from a longitudinal investigation of 1293 grade 7 students (mean age 12.8 years) recruited from 10 high schools in Montreal, Canada in 1999-2000, who were followed into young adulthood. Cigarette consumption was measured every 3 months during high school, and again at mean age 20.4 and 24.0. Analyses using time since onset of smoking as the time metric was restricted to 307 incident smokers; analysis using calendar time included 645 prevalent and incident smokers. Smoking status and nicotine dependence (ND) were assessed at mean age 20.4 and 24.0. Simulated data mimicked the real study during high school. Results Use of different time metrics resulted in different numbers and shapes of trajectories in the simulated and real datasets. Participants in the calendar time analyses reported more ND in young adulthood, reflecting inclusion of 388 prevalent smokers who had smoked for longer durations. Conclusions Choosing the right time metric for trajectory analysis should be balanced against research intent. Trajectory analyses using the time since onset metric depict the natural course of smoking in incident smokers. Those using calendar time offer a snapshot of smoking across age during a given time period. Implications This study uses simulated and real data to show that trajectory analyses of cigarette smoking that use calendar time (e.g., age) versus time since onset as the time axis metric tell a different story. Trajectory analyses using the time since onset metric depict the natural course of smoking in incident smokers. Those using calendar time offer a snapshot of smoking across age during a given time period. Choosing the right time metric should be balanced against research intent.

Minimizing Curvature in Euclidean and Lorentz Geometry

In this paper, an interesting symmetry in Euclidean geometry, which is broken in Lorentz geometry, is studied. As it turns out, attempting to minimize the integral of the square of the scalar curvature leads to completely different results in these two cases. The main concern in this paper is about metrics in R3, which are close to being invariant under rotation. If we add a time-axis and let the metric start to rotate with time, it turns out that, in the case of (locally) Euclidean geometry, the (four-dimensional) scalar curvature will increase with the speed of rotation as expected. However, in the case of Lorentz geometry, the curvature will instead initially decrease. In other words, rotating metrics can, in this case, be said to be less curved than non-rotating ones. This phenomenon seems to be very general, but because of the enormous amount of computations required, it will only be proved for a class of metrics which are close to the flat one, and the main (symbolic) computations have been carried out on a computer. Although the results here are purely mathematical, there is also a connection to physics. In general, a deeper understanding of Lorentz geometry is of fundamental importance for many applied problems.

Secure and Guarantee QoS in a Video Sequence: a New Approach Based on TLS Protocol to Secure Data and RTP to Ensure Real-time Exchanges

The continued development of networks has significantly contributed to increasing the quantity of information available to replace old intelligence-gathering methods faster and more efficiently. For this, it is necessary to implement services that meet the consumers' requirements and measure precisely the factors that can generate obstacles to any communication, among these causes we can cite strong security and high quality of services. In this work, we implement a secure approach useful in continuous communications in a time axis (video sequence, VOIP call...), the process consists in establishing a well-secured connection between two interlocutors (the server that broadcasts the video sequence and a client) using an AES encryption key of size 256. A step of jitter check (latency variation) periodically is essential for the customer in order to make a decision: If the jitter is within the standards (compared to the tolerable value), we continue to encrypt with the AES256 key, if no, both ends must go through an automatic and uninterrupted fast renegotiation of the video to switch to a small AES key (192,128) to reduce the bandwidth on the channel, this operation must be repeated in an alternative way until the end of the communication.