Relative Minimum Distance Research Articles

Comet P/2003 T12 (SOHO): A possible fragment of comet 169P/NEAT?

This work provides insights into the possible origin of comet P/2003 T12 (SOHO) and the dynamics of comet fragmentation events. We studied the hypothesis of the origin of the comet P/2003 T12 (SOHO) as a fragment of the Jupiter family comet 169P/NEAT. We studied the recent dynamical evolution of the comet pair and determined the epochs of relative minimum distance and velocity as well as the similarity between the orbits using different criteria following Rożek et al. (2011) and Kholshevnikov et al. (2016). We generated 6000 clones of both comets with orbital elements compatible with the observational uncertainties of the actual orbits and found that their evolution is stable for the past ∼ 5000 years. We found four epochs where the relative distance and velocity exhibit simultaneous minima. We studied possible fragmentation events in these epochs by applying a simple break-up model for the generation of fictitious fragments at different relative speeds. Analyzing the orbital distance between the fragments, we found some fragments that exhibit noticeable stable behavior at a very low mutual orbital distance according to several distance definitions, which suggest that those fragments evolve in orbits very similar to that of the P/2003 T12 (SOHO). We conclude that comet P/2003 T12 (SOHO) could be a fragment of comet 169P/NEAT and the most likely epoch for such fragmentation would be at least 2000 years ago (around 94 A.D.), given that the fragments that best resemblance comet P/2003 T12 (SOHO) are found in this epoch.

Milky Way globular clusters on cosmological timescales

Context. The present epoch of the Gaia success gives us a possibility to predict the dynamical evolution of our Solar System in the global Galactic framework with high precision. Aims. We statistically investigated the total interaction of globular clusters with the Solar System during six billion years of look-back time. We estimated the gravitational influence of globular clusters’ flyby onto the Oort cloud system. Methods. To perform the realistic orbital dynamical evolution for each individual cluster, we used our own high-order parallel dynamical N-body φ-GPU code that we developed. To reconstruct the orbital trajectories of clusters, we used five external dynamical time variable galactic potentials selected from the IllustrisTNG-100 cosmological database and one static potential. To detect a cluster’s close passages near the Solar System, we adopted a simple distance criteria of below 200 pc. To take into account a cluster’s measurement errors (based on Gaia DR3), we generated 1000 initial positions and velocity randomisations for each cluster in each potential. Results. We found 35 globular clusters that have had close passages near the Sun in all the six potentials during the whole lifetime of the Solar System. We can conclude that at a relative distance of 50 pc between a GC and the SolS, we obtain on average ∼15% of the close passage probability over all six billion years, and at dR = 100 pc, we get on average ∼35% of the close passage probability over all six billion years. The globular clusters BH 140, UKS 1, and Djorg 1 have a mean minimum relative distance to the Sun of 9, 19, and 17 pc, respectively. We analysed the gravitational energetic influence on the whole Oort cloud system from the closest selected globular cluster flyby. We generally found that a globular cluster with a typical mass above a few times 105 M⊙ and with deep close passages in a 1–2 pc immediately results in the ejection more than ∼30% of particles from the Oort cloud system. Conclusions. We can assume that a globular cluster with close passages near the Sun is not a frequent occurrence but also not an exceptional event in the Solar System’s lifetime.

Explicit Cyclic and Quasi-Cyclic Codes with Optimal, Best Known Parameters and Large Relative Minimum Distances

Explicit Cyclic and Quasi-Cyclic Codes with Optimal, Best Known Parameters and Large Relative Minimum Distances

Risk analysis of autonomous vehicle test scenarios using a novel analytic hierarchy process method

AbstractScenario‐based test methods are employed to assess the safety and performance of autonomous vehicles. The analytic hierarchy process (AHP) method is a common assessment method for determining the criticality of test scenarios. However, the AHP method is subjective and less reproducible when performed by different persons, as the elements of pairwise comparison values that are directly linked to the outcome must be assigned by the person involved. This paper proposes a novel AHP method that automatically generates pairwise comparison values by optimizing the correlation between performance metrics and risk of test scenarios by simulation. Performance metrics are defined as the minimum relative distances and corresponding relative velocities between vehicles, and the risk of the test scenario is determined by the pairwise comparison values of AHP. The novel AHP method was evaluated using a cut‐in scenario. The results showed that the minimum relative distance and the risk determined by the novel AHP method achieved a better correlation coefficient of −0.96, which is better than the conventional AHP of −0.828 and Fuzzy AHP of −0.824. These results suggest that the criticality of the test scenarios determined by the novel AHP method can more accurately reflect real‐world driving environments.

Joint Security and Resilience Control in IIoT-Based Virtual Control Train Sets Under Jamming Attacks

The virtually coupled train sets (VCTS) have been proposed to improve transportation efficiency, passenger satisfaction and operational capability for communication-based train control (CBTC) systems. Reliable and real-time trainto-train (T2T) wireless communications are quite desirable to ensure the stability of VCTS. Moreover, with the development of industrial Internet of Things (IIoT), an IIoT-based VCTS is proposed. Due to the physically exposed wireless environment, T2T wireless communications are vulnerable to jamming attacks (JAs), causing packets loss, time delay, and interference with the operation of VCTS systems. The distance between adjacent trains in the IIoT-based VCTS would be violate the minimum relative braking distance regulated by the traditional moving block (MB) principle if JAs were not mitigated. This is a severe safety events, which is intolerable for train control systems. In this study, we develop an event-triggered control (ETC) based resilience control method to mitigate the impact of JAs on the IIoT-based VCTS. A cooperative control approach, stable IIoT-based VCTS range and T2T communication cycle are jointly designed in the ETC-based model. The resilience control approach enables the communication cycle to be adjusted by sacrificing part of the system performance to ensure the safety and stability of VCTS systems when JAs occurs. Extensive simulation results demonstrate that the proposed ETC-based resilience control model can successfully defend against jamming attacks, and the transportation efficiency in urban rail transits can be significantly improved even under JAs.

A quick method for determining the relative minimum audible distance using sound images.

Auditory localization plays an essential role in various tasks, including spatial orientation, locomotion, attention and memory. Optimization of experimental routine is important for preliminary assessment of the subject's sound localization ability. In the present study, a new quick technique for estimating the relative minimum audible distance (RMAD) using sound images is introduced. Twenty adults with normal hearing took part in six RMAD measurements in free field. The reference RMAD values were obtained using a method of constant stimuli by physically positioning a real sound source. The same method was used with stationary sound images created by superposition of signals emitted by two loudspeakers. To optimize the measurements, the RMADs were determined for the sound images using two adaptive psychoacoustic procedures known as one-down, one-up and two-down, one-up staircases. The group-average RMADs obtained by the method of constant stimuli for both types of stimuli and by two adaptive procedures were similar, 7% (SD = 2%). The effect of whether subjects were sighted or blindfolded was not significant for measurements of RMAD to sound images. The average measurement times were 373 s (SD = 20 s) for the method of constant stimuli, 85 s (SD = 9 s) for the one-down, one-up, and 124 s (SD = 14 s) for the two-down, one-up procedure. The results are consistent with the previous studies and confirm the validity of the measurements of RMAD using adaptive procedures with stationary sound images as a quick method.

Forest-Fire-Risk Prediction Based on Random Forest and Backpropagation Neural Network of Heihe Area in Heilongjiang Province, China

Forest fires are important factors that influence and restrict the development of forest ecosystems. In this paper, forest-fire-risk prediction was studied based on random forest (RF) and backpropagation neural network (BPNN) algorithms. The Heihe area of Heilongjiang Province is one of the key forest areas and forest-fire-prone areas in China. Based on daily historical forest-fire data from 1995 to 2015, daily meteorological data, topographic data and basic geographic information data, the main forest-fire driving factors were first analyzed by using RF importance characteristic evaluation and logistic stepwise regression. Then, the prediction models were established by using the two machine learning methods. Furthermore, the goodness of fit of the models was tested using the receiver operating characteristic test method. Finally, the fire-risk grades were divided by applying the kriging method. The results showed that 11 driving factors were significantly correlated with forest-fire occurrence, and days after the last rain, daily average relative humidity, daily maximum temperature, daily average water vapor pressure, daily minimum relative humidity and distance to settlement had a high correlation with the risk of forest-fire occurrence. The prediction accuracy of the two algorithms in regard to fire points was higher than that for nonfire points. The overall prediction accuracy and goodness of fit of the RF and BPNN algorithms were similar. The two methods were both suitable for forest-fire occurrence prediction. The high-fire-risk zones were mainly concentrated in the northwestern and central parts of the Heihe area.

Asymptotically good $ \mathbb{Z}_{p}\mathbb{Z}_{p}[u]/\langle u^{t}\rangle $-additive cyclic codes

$ \mathbb{Z}_{2}(\mathbb{Z}_{2}+u\mathbb{Z}_{2}) $-additive cyclic codes were proved to be asymptotically good in 2020 by Yao et al., where $ u^{2} = 0 $. We extend the study to the double cyclic codes over two finite commutative chain rings. Let $ R_{t} = \mathbb{Z}_{p}[u]/\langle u^{t}\rangle = \mathbb{Z}_{p}+u\mathbb{Z}_{p}+u^{2}\mathbb{Z}_{p}+\ldots+u^{t-1}\mathbb{Z}_{p} $ be a chain ring, where $ u^{t} = 0 $. We construct a class of $ \mathbb{Z}_{p}R_{t} $-additive cyclic codes generated by pairs of polynomials, where $ p $ is a prime number. By using probabilistic methods, we study the asymptotic behaviour of the rates and relative minimum distances of a certain class of the codes. We show that there exists an asymptotically good infinite sequence of $ \mathbb{Z}_{p}R_{t} $-additive cyclic codes with the relative minimum distance of the code is convergent to $ \delta $, and the rate is convergent to $ \frac{1}{1+p^{t-1}} $ for $ 0< \delta< \frac{1}{1+p^{t-1}} $, and $ t\geq1 $.

An Adaptive Two-Stage Kriging-Based Infilling Strategy for Efficient Multi-Objective Global Optimization

Abstract Most practical multi-objective optimization problems are often characterized by two or more expensive and conflicting objectives, which require time-consuming simulations. Commonly used algorithms construct a surrogate model of each objective function from a few high-fidelity solutions. In order to further decrease the computational burden, adaptive infilling strategies for multi-objective problems are developed to guide the next infilling design for expensive evaluation and update the surrogate model as well as the Pareto front in an iterative manner. In this paper, a multi-objective infilling strategy integrating the Kriging model with a two-stage infilling framework is proposed, termed as ATKIS. This method allows exploitation and exploration alternately to pinpoint the infilling solution for improving the Pareto set and avoiding local over-exploitation simultaneously. At the local exploitation stage, Kriging-based prediction and uncertainty estimation are combined with Non-dominant Ranking and Minimum Relative Distance theories for determining a new design solution, which has maximum improvement relative to the current Pareto set. At the global exploration stage, Voronoi tessellation theory is employed to search for the sparsest position in the design space for a new evaluation. The proposed method is compared with five recent infilling strategies to investigate the performance of infilling ability using several numerical benchmarks. The experimental results show that the proposed method outperforms the other three strategies in improving both effectiveness and robustness using the improvement of hypervolume as the evaluating indicator. In addition, a lightweight optimization design of hoist sheaves shows that the proposed method can deal with real engineering problems, while significantly reducing the computational time and the number of expensive simulations of samples.

Asymptotic Bounds on the Rate of Locally Repairable Codes

New asymptotic upper bounds are presented on the rate of sequences of locally repairable codes (LRCs) with a prescribed relative minimum distance and locality over a finite field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> . The bounds apply to LRCs in which the recovery functions are linear; in particular, the bounds apply to linear LRCs over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> . The new bounds are shown to improve on previously published results, especially when the repair groups are disjoint, namely, they form a partition of the set of coordinates.

On matrices potentially useful for tree codes

Motivated by a concept studied in [1], we consider a property of matrices over finite fields that generalizes triangular totally nonsingular matrices to block matrices. We show that (1) matrices with this property suffice to construct asymptotically good tree codes and (2) a random block-triangular matrix over a field of quadratic size satisfies this property. We will also show that a generalization of this randomized construction yields codes over quadratic size fields for which the sum of the rate and minimum relative distance gets arbitrarily close to 1.

A comparison between Suzuki invariant code and one-point Hermitian code

In this paper we compare the performance of two algebraic geometry codes (Suzuki and Hermitian codes) constructed using maximal algebraic curves over [Formula: see text] with large automorphism groups by choosing specific divisors. We discuss their parameters, compare the rate of these codes as well as their relative minimum distances, and we show that both codes are asymptotically good in terms of the rate which is in contrast to their behavior in terms of the relative minimum distance.

An Automatic Emergency Braking Model considering Driver’s Intention Recognition of the Front Vehicle

Driver’s intention of the front vehicle plays an important role in the automatic emergency braking (AEB) system. If the front vehicle brakes suddenly, there is potential collision risk for following vehicle. Therefore, we propose a driver’s intention recognition model for the front vehicle, which is based on the backpropagation (BP) neural network and hidden Markov model (HMM). The brake pedal, accelerator pedal, and vehicle speed data are used as the input of the proposed BP-HMM model to recognize the driver’s intention, which includes uniform driving, normal braking, and emergency braking. According to the recognized driver’s intention transmitted by Internet of vehicles, an AEB model for the following vehicle is proposed, which can dynamically change the critical braking distance under different driving conditions to avoid rear-end collision. In order to verify the performance of the proposed models, we conducted driver’s intention recognition and AEB simulation tests in the cosimulation environment of Simulink and PreScan. The simulation test results show that the average recognition accuracy of the proposed BP-HMM model was 98%, which was better than that of the BP and HMM models. In the Car to Car Rear moving (CCRm) and Car to Car Rear braking (CCRb) tests, the minimum relative distance between the following vehicle and the front vehicle was within the range of 1.5 m–2.7 m and 2.63 m–5.28 m, respectively. The proposed AEB model has better collision avoidance performance than the traditional AEB model and can adapt to individual drivers.

$${\pmb {{\mathbb {Z}}}}_p{\pmb {{\mathbb {Z}}}}_p[v]$$-additive cyclic codes are asymptotically good

We construct a class of $${\mathbb {Z}}_p{\mathbb {Z}}_p[v]$$ -additive cyclic codes, where p is a prime number and $$v^2=v$$ . We determine the asymptotic properties of the relative minimum distance and rate of this class of codes. We prove that, for any positive real number $$0<\delta <1$$ such that the p-ary entropy at $$\frac{k+l}{2}\delta $$ is less than $$\frac{1}{2}$$ , the relative minimum distance of the random code is convergent to $$\delta $$ and the rate of the random code is convergent to $$\frac{1}{k+l}$$ , where p, k, l are pairwise coprime positive integers.

RELATIONSHIP OF SCR, CME AND CORONAL SHOCK WAVES WITH THE PARAMETERS OF TYPE IV AND II SOLAR RADIO BURSTS

ABSTRACT. This paper presents the results of a comparative analysis of the relationship between solar cosmic rays (SCR), coronal mass ejections (CME), and coronal shock waves (CSW) with the parameters of solar continual type IV radio bursts, as well as with the parame- ters of type II radio bursts. The sample under study con- tains 147 proton events accompanied by type IV continu- um radio bursts in the 25-15400 MHz range, type II radio bursts in the 25-180 MHz range, as well as CME and cor- onal shock waves. For the analysis, we used original rec- ords of solar radio emission at 8 fixed frequencies in the range 245-15400 MHz according to data from RSTN (Ra- dio Solar Telescope Network), original records of dynam- ic spectra from SRS (Solar Radio Spectrograph) in the range of 25-180 MHz, as well as original records intensity of the flux of SCR protons with proton energies in the range> 1-100 MeV according to data from the GOES spacecraft. A comparative analysis showed that the rela- tionship between the intensity of the SCR proton flux and the CME velocity is, on average, much stronger with the parameters of type IV radio bursts than with the parame- ters of type II radio bursts, which indicates the dominant role of the SCR acceleration process in the flare region, rather than shock waves. However, detailed studies of the fine structure of type II radio bursts have shown that there is a fairly strong relationship between the intensity of the flux of mean-relativistic protons I p and the frequency f min,1 at the fundamental harmonic (at the 1-st harmonic) at the time t min corresponding to the minimum relative distance b min between the harmonics of type II radio bursts. De- tailed studies of the fine structure of type II radio bursts have also shown that there is a strong relationship between the intensity of the SCR proton flux I p and parameter V II , which characterizes the displacement of the shock front with time t i in a narrow frequency range of 25-60 MHz.

On nested code pairs from the Hermitian curve

Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [15] and in the CSS construction of quantum codes [14]. The important parameters are (1) the codimension, (2) the relative minimum distance of the codes, and (3) the relative minimum distance of the dual set of codes. Given values for two of them, one aims at finding a set of nested codes having parameters with these values and with the remaining parameter being as large as possible. In this work we study nested codes from the Hermitian curve. For not too small codimension, we present improved constructions and provide closed formula estimates on their performance. For small codimension we show how to choose pairs of one-point algebraic geometric codes in such a way that one of the relative minimum distances is larger than the corresponding non-relative minimum distance.

Analysis of close approach and collision probability between operational satellites and/ or space debris

In recent years, the number of space debris has increased significantly, which can threaten the safety of operational satellites. In this paper we developed an accurate model for active satellite protection from collision in order to determine close approaches between two objects (satellites and /or debris) using the Hoot's method and the time of close approach. We calculate the minimum relative distance considering J2 and atmospheric drag perturbations, and compared it to the close approach distance. The Collision probability between two closed objects is calculated using Chan model and analyzed in a given time-scale to avoid any dangerous collision. We applied our models on the cataloged debris (more than 1000) resulted from the crash between Iridium 33 and Cosmos 2251; in addition, ten satellites from the Iridium satellites list at the same altitudes of the debris crowdie region are considered. The numerical results have shown one real case of close approach with high probability of collision that may threaten one of those active satellites.

A modified Gilbert-Varshamov bound for self-dual quasi-twisted codes of index four

In this work, we study a family of self-dual four circulant codes and a family of self-dual four negacirculant codes, and the exact counting formula is derived for these families of codes. In addition, we prove that asymptotically good self-dual four circulant codes and negacirculant codes over finite fields exist, and both of them satisfy a modified Gilbert-Varshamov bound on the relative minimum distance with asymptotic rate 12.

Alphabet-Dependent Bounds for Linear Locally Repairable Codes Based on Residual Codes

Locally repairable codes (LRCs) have gained significant interest for the design of large distributed storage systems as they allow a small number of erased nodes to be recovered by accessing only a few others. Several works have thus been carried out to understand the optimal rate-distance tradeoff, but only recently the size of the alphabet has been taken into account. In this paper, a novel definition of locality is proposed to keep track of the precise number of nodes required for a local repair when the repair sets do not yield MDS codes. Then, a new alphabet-dependent bound is derived, which applies both to the new definition and the initial definition of locality. The new bound is based on consecutive residual codes and intrinsically uses the Griesmer bound. A special case of the bound yields both the extension of the Cadambe-Mazumdar bound and the Singleton-type bound for codes with locality $(r, {\delta})$, implying that the new bound is at least as good as these bounds. Furthermore, an upper bound on the asymptotic rate-distance tradeoff of LRCs is derived, and yields the tightest known upper bound for large relative minimum distances. Achievability results are also provided by deriving the locality of the family of Simplex codes together with a few examples of optimal codes.

Asymptotic bounds for spherical codes

The set of all error-correcting codes over a fixed finite alphabet of cardinality determines the set of code points in the unit square with coordinates := (relative transmission rate, relative minimal distance). The central problem of the theory of such codes consists in maximising simultaneously the transmission rate of the code and the relative minimum Hamming distance between two different code words. The classical approach to this problem explored in vast literature consists in inventing explicit constructions of “good codes” and comparing new classes of codes with earlier ones. A less classical approach studies the geometry of the whole set of code points (with fixed), at first independently of its computability properties, and only afterwards turning to problems of computability, analogies with statistical physics, and so on. The main purpose of this article consists in extending this latter strategy to the domain of spherical codes.