Alternate Entropy Computations by Applying Recurrence Matrix Masking

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.

Study on the Universal Tapered Segmental Ring Assembly Simulation Algorithm and Deviation Assessment: A Case Study on Metro Line Tunnel

Universal tapered segmental ring system has been adopted to assemble tangent and curve line elements into the shield tunnels through the relative rotation of the adjacent front and rear rings, which simplifies the formwork design, demonstrates strong universality, and is easy for quality assurance. To evaluate the position deviation caused by the taper value and propose the assembly scheme for the contractor, this article developed the universal tapered segmental ring assembly simulation technology. Firstly, the assembly procedure of the universal tapered segmental ring system both in normal case and in special case is introduced, including the interval tunnel of special rings and actual engineering that needs deviation correction. Secondly, relevant core algorithms are introduced in detail, including the coordinate position algorithm of horizontal and vertical curves and computer graphic algorithm of spatial point rotating around any axis. Finally, this article takes a background metro line tunnel as a case to validate the algorithm and illustrate the assessment methodology of universal tapered segmental ring assembly accuracy. The sections with maximum deviation are found as an alert ahead of the shield advancing. In conclusion, the algorithms and methodology proposed in this article illustrate the excellent suitability and robustness in shield tunnels adopting a universal tapered segmental ring system in the stage of both design and construction.

Covariant Space-Time Line Elements in the Friedmann-Lemaitre-Robertson-Walker Geometry

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

Repeats Mimic Immunostimulatory Viral Features Across a Vast Evolutionary Landscape

An emerging hallmark across many human diseases – such as cancer, autoimmune and neurodegenerative disorders – is the aberrant transcription of typically silenced repetitive elements. Once transcribed they can mimic pathogen-associated molecular patterns and bind pattern recognition receptors, thereby engaging the innate immune system and triggering inflammation in a process known as viral mimicry. Yet how to quantify pathogen mimicry, and the degree to which it is shaped by natural selection, remains a gap in our understanding of both genome evolution and the immunological basis of disease. Here we propose a theoretical framework that combines recent biological observations with statistical physics and population genetics to quantify the selective forces on virus-like features generated by repeats and integrate these forces into predictive evolutionary models. We establish that many repeat families have evolutionarily maintained specific classes of viral mimicry. We show that for HSATII and intact LINE-1 selective forces maintain CpG motifs, while for a set of SINE and LINE elements the formation of long double-stranded RNA is more prevalent than expected from a neutral evolutionary model. We validate our models by showing predicted immunostimulatory inverted SINE elements bind the MDA5 receptor under conditions of epigenetic dysregulation and that they are disproportionately present during intron retention when RNA splicing is pharmacologically inhibited. We conclude viral mimicry is a general evolutionary mechanism whereby genomes co-opt features generated by repetitive sequences to trigger the immune system, acting as a quality control system to flag genome dysregulation. We demonstrate these evolutionary principles can be learned and applied to predictive models. Our work therefore serves as a resource to identify repeats with candidate immunostimulatory features and leverage them therapeutically.

Simplified Approach to Detect Satellite Maneuvers Using TLE Data and Simplified Perturbation Model Utilizing Orbital Element Variation

In this study, an algorithm to identify the maneuvers of a satellite is developed by comparing the Keplerian elements acquired from the two-line elements (TLEs) and Keplerian elements propagated from simplified perturbation models. TLEs contain a specific set of orbital elements, whereas the simplified perturbation models are used to propagate the state vectors at a given time. By comparing the corresponding Keplerian elements derived from both methods, a satellite’s maneuver is identified. This article provides an outline of the working methodology and efficacy of the method. The function of this approach is evaluated in two case studies, i.e., TOPEX/Poseidon and Envisat, whose maneuver histories are available. The same method is implemented to identify the station-keeping maneuvers for TDRS-3, whose maneuver history is not available. Results derived from the analysis indicate that maneuvers with a magnitude of even as low as cm/s are detected when the detection parameters are calibrated properly.

Covariant Space-Time Line Elements in the Friedmann-Lemaitre-Robertson-Walker Geometry

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

Tuning of NASA Standard Breakup Model for Fragmentation Events Modelling

The continuous growth of space debris motivates the development and the improvement of tools that support the monitoring of a more and more congested space environment. Satellite breakup models play a key role to predict and analyze orbital debris evolution, and the NASA Standard Breakup Model represents a widely used reference, with current activities relevant to its evolution and improvements especially towards fragmentation of small mass spacecraft. From an operational perspective, an important point for fragmentation modelling concerns the tuning of the breakup model to achieve consistency with orbital data of observed fragments. In this framework, this paper proposes an iterative approach to estimate the model inputs, and in particular, the parents’ masses involved in a collision event. The iterative logic exploits the knowledge of Two Line Elements (TLE) of the fragments at some time after the event to adjust the input parameters of the breakup model with the objective of obtaining the same number of real fragments within a certain tolerance. Atmospheric re-entry is accounted for. As a result, the breakup model outputs a set of fragments whose statistical distribution, in terms of number and size, is consistent with the catalogued ones. The iterative approach is demonstrated for two different scenarios (i.e., catastrophic collision and non-catastrophic collision) using numerical simulations. Then, it is also applied to a real collision event.