A rapid method for calculating maximal and minimal inter-satellite distances

In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its accuracy. The proposed algorithm searches for the optimal piecewise polynomial (OPP) with the minimum computational cost while ensuring that the error is below a specified threshold. This was accomplished by using smooth piecewise polynomials with optimal order and numbers of intervals. The computational cost only depended on polynomial complexity, i.e., the order and the number of intervals at runtime function call. In previous studies, the user had to decide one or all of the orders and the number of intervals. In contrast, the OPP approximation algorithm determines both of them. For the optimal approximation, computational costs for all the possible combinations of piecewise polynomials were calculated and tabulated in ascending order for the specific target CPU off-line. Each combination was optimized through constrained least squares and the random selection method for the given sample points. Afterward, whether the approximation error was below the predetermined value was examined. When the error was permissible, the combination was selected as the optimal approximation, or the next combination was examined. To verify the performance, several representative functions were examined and analyzed.

-An iterative procedure for deriving minimum-length phylogenetic trees from allele frequencies using Rogers' genetic distance as the measure of branch length is extended to include eight additional distances: a modified Rogers' distance; Nei's standard, maximum and minimum distances; Cavalli-Sforza and Edwards' chord and arc distances; and modified forms of the chord and arc distances. The derivation of such trees is defended as a parsimony procedure, and I conclude that any distance used in this procedure must be metric. The nine genetic distances are compared on the criteria of: metricity; ability to produce ancestral allele frequencies with heterozygosity approximating that of the terminal taxa; convergence to a stable solution; and computer time. The modified Cavalli-Sforza and Edwards' chord distance is equal or superior to the other distances on the first three criteria, but requires more computer time than most. Rogers' distance has the properties of metricity and convergence, and ranks below the modified chord distance on ancestral heterozygosity, but generally requires about one-half as much computer time as the modified chord distance. [Minimum-length trees; allele frequencies; parsimony; genetic distances.] In a recent paper (Rogers, 1984), I described a technique for deriving minimumlength phylogenetic trees from allele frequencies by estimating allele frequencies for the ancestral taxa that minimize total tree length as measured by Rogers' (1972) genetic distance. In the present paper, I show how the same procedure can be applied with: a modified Rogers' distance (Wright, 1978); Nei's (1972,1973) standard, minimum and maximum distances; Cavalli-Sforza and Edwards' (1967) arc and chord distances; and modified forms of the arc and chord distances (where the multilocus distances are simple arithmetic averages of the single-locus distances). The derivation of the equations for finding optimal ancestral allele frequencies will be found in the Appendix. I also attempt to justify the construction of minimum-length trees from allele frequencies as a parsimony method and evaluate the suitability of each genetic distance for constructing minimum-length trees using several theoretical and practical criteria. MINIMUM-LENGTH ALLELE-FREQUENCY TREES AND PARSIMONY The goal of the techniques described in this paper and the earlier paper (Rogers, 1984) is to produce from a class of continuous characters (i.e., allele frequencies) minimum-length phylogenetic trees that have the same parsimony property as the minimum-length trees for discrete characters produced by the character-Wagner method described by Kluge and Farris (1969) and Farris (1970). In the latter method, the length of a tree is the total number of independent origins of (discrete) character states required by the topology of the tree and the character states of the ancestral taxa (interior nodes) of the tree. Since, for any one character state, the number of homoplasious (convergent, parallel) origins is always one less than the total number of independent origins (Fig. la, b), minimizing total tree length for all characters minimizes the total number of homoplasious origins for the whole tree. Thus, the character-Wagner method is a parsimony method; it minimizes the number of ad hoc hypotheses of convergent or parallel evolution (Farris, 1983). Farris (1983) has implied that only those minimum-length methods that employ discrete characters qualify as parsimony methods. I believe that this is too restrictive. For example, two of the hypothetical trees (i.e., c and d) in Figure 1 differ only in the choice of allele-frequency character

Introduction/Purpose: While hallux valgus (HV) is understood to be a triplanar deformity of the first metatarsal, less is known about the contribution of the sesamoid-metatarsal joint (SMJ) to pain and function. Osteoarthritis of the SMJ is frequently present in HV feet, with an incidence rate ranging from 32% to 81%. Following surgical correction, approximately 10% of HV patients remain dissatisfied, but factors affecting postoperative outcomes are poorly understood. The primary aim of our study was to describe the relationship between degenerative changes at the SMJ as measured on weightbearing CT (WBCT) scans and 1-year patient-reported outcome scores following a modified Lapidus procedure for correction of HV. We hypothesized that decreased joint space at the SMJ would affect postoperative patient-reported outcomes. Methods: This study included 48 consecutive patients who underwent a modified Lapidus procedure for HV, had preoperative and at least 5-month postoperative WBCT scans, and had preoperative PROMIS scores and at least 1-year postoperative PROMIS Physical Function (PF), Pain Interference, and Pain Intensity scores. For each patient, the first metatarsal and sesamoids on pre- and postoperative WBCT scans were segmented using Disior Bonelogic software and uploaded to Geomagic Design X to perform distancing mapping. The minimum and average distances between the first metatarsal head and medial sesamoid (medial-SMJ) for each patient pre- and postoperatively were calculated. Sesamoid subluxation was measured on WBCT scans using the grading system from 0 to 3 (Yildirim et al.). A simple linear regression model was used to investigate the correlations between minimum preoperative and postoperative medial-SMJ distances and 1-year postoperative PROMIS scores in patients with postoperative reduction of the sesamoids (grade 0). Results: Preoperatively, the mean minimum and average medial-SMJ distances were 0.76 ± 0.37 mm and 1.54 ± 0.33 mm, respectively. Postoperatively, the mean minimum and average medial-SMJ distances were 1.08 ± 0.25 mm and 1.73 ± 0.24 mm, respectively. Thirty-five of 48 patients had a complete reduction of the sesamoids. Lower preoperative minimum distances at the medial-SMJ were significantly correlated with worse 1-year PROMIS PF scores (r=0.405, P=0.016) (Figure 1). Similarly, lower preoperative minimum distances at the medial-SMJ were significantly correlated with worse 1-year PROMIS Pain Intensity scores (r=-0.350, P=0.039) but did not reach significance for 1-year PROMIS Pain Interference scores (r=-0.286, P=0.095). The postoperative minimum medial-SMJ distance was not correlated with 1-year PROMIS PF, Pain Interference, and Pain Intensity scores. Conclusion: In HV patients undergoing a modified Lapidus procedure with postoperatively reduced sesamoids, decreased joint space at the medial sesamoid-metatarsal head articulation was associated with worse 1-year postoperative function as measured by PROMIS PF scores and worse 1-year postoperative pain as measured by PROMIS Pain Intensity scores. In contrast, postoperative degenerative changes at the SMJ were not found to be associated with patient-reported outcomes. Our results suggest that pre-existing SMJ arthritic changes may affect postoperative outcomes and may be a source of dissatisfaction following HV surgery despite appropriate correction of the deformity. Figure 1. Preoperative medial sesamoid to the first metatarsal head minimum distance relative to 1-year PROMIS Physical Function, Pain Intensity, and Pain Interference scores. A simple linear regression demonstrates a significant association between preoperative medial sesamoid –metatarsal head minimum joint distance and 1-year PROMIS Physical Function (r=0.405, P=0.016) and Pain Intensity (r=‒0.305, P=0.039) scores.

Identification of polychaetes from the Vellar estuary mangroves is very essential to assess their diversity status. In this study, we have used sequences of the Cytochrome Oxidase I (COI) from 15 species belongs to eight families to barcode and investigate the molecular variation among the Vellar estuary polychaetes. Based on the sequence data, it was observed that the maximum A+T content (62.00%) was recorded in Diopatra neapolitana and minimum (55.00%) in Laonice cirrata. Similarly, the maximum C+G value of 45.00% was observed in Laonice cirrata and least content of 38.00% was estimated in Capitella capitata and Diopatra neapolitana. The maximum K2P distance (1.459) was found between Lubrineridae and Capitellidae family. Whereas, the minimum K2P distance of 0.270 was observed between Nereididae and Spionidae. However, the maximum K2P distance within family was observed in Lubrineridae (0.197) and the minimum value of 0.005 was recorded in Spionidae.The maximum K2P distance (1.459) was found between the genus Capitella and Lumbrineris whereas the minimum distance (0.230) was observed between Platynereis and Perinereis. However, the maximum K2P distance within genus was observed in Perinereis (0.211) whereas the minimum distance of 0.005 was perceived in Laonice. The intra genus K2P genetic distance in Marphysa, Naineris, Platynereis, Capitella, Diopatra was zero. The maximum likelihood tree clearly demonstrates the efficacy of COI gene in discriminating polychaete individuals both at conspecific and congeneric levels. Further molecular tools such as microsattelite, RAPD is needed to assess the population structure of the above identified species.

Thirty genotypes of wheat were grown in an Alpha Lattice Design with three replications for evaluation and divergence analysis. Seeds were sown on 24 November 2011 at Regional Wheat Research Centre, Bangladesh Agricultural Research Institute, Shyampur, Rajshahi. Significant variation was observed among the genotypes and these are grouped into six clusters. Clusters III and VI were comprised of maximum number of genotypes (6) followed by clusters I, IV, and V with 5 genotypes and the minimum genotypes (3) were in cluster II. The maximum inter-cluster distance was recorded between the Cluster VI and Cluster II followed by cluster III and Cluster II, which indicates that genotypes belonging to these distant clusters could be used in hybridization programme for getting a wide spectrum of variation among the segregates. The minimum intercluster distance was found between the Cluster IV and Cluster I followed by that of Cluster V and Cluster IV. The maximum intra-cluster distance was recorded in Cluster II, consisted of three genotypes of diverse origin followed by Cluster V consisting of five genotypes which indicated that the genotypes of these clusters might have considerable diversity among themselves. While the minimum distance was computed in Cluster I composed of five genotypes which indicated that these genotypes were genetically very close to each other. Considering the eigenvalues of all principal component analysis the PC1, PC2, PC3, PC4, and PC5 with values contributed 30.78%, 20.11%, 17.75%, 10.93%, and 7.63%, respectively, of the total variation. The results revealed from the present study that the first principal component had high positive component loading from grains/spike and high negative loading from grain yield. Considering the clusters mean value, the genotype of Cluster II and VI are most divergent and maximum heterosis and wide variability in genetic architecture may be expected from the crosses between the genotypes belonged to these clusters. More specifically the cluster II could be selected for dwarf in nature, early heading and maturity and bold grain size. The genotypes from the cluster IV could be selected for maximum spikes/m2 and maximum grain yield. The positive value of both vectors for days to heading and spikes/m2 indicated that these traits had the highest contribution towards divergence among the 30 drought tolerant wheat genotypes. DOI: http://dx.doi.org/10.3329/bjar.v39i3.21982 Bangladesh J. Agril. Res. 39(3): 385-396, September 2014

Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears a geometric structure known as Poisson Voronoi tessellation. These tessellations find applications in various fields such as biology, material science, and communications, where the statistical properties of the Voronoi cells reveal patterns and structures that hold key insights into the underlying processes generating the observed phenomena. In this paper, we investigate a distance measure of Poisson Voronoi tessellations that is emerging in the literature, yet for which its statistical and geometrical properties remain explored only in the asymptotic case when the density of seed points approaches infinity. Our work, specifically focused on homogeneous Poisson point processes, characterizes the cumulative distribution functions governing the maximum and minimum distances between the points generating the Voronoi regions and their respective vertices for an arbitrary density of points in R 2 . For that, we conduct a Monte-Carlo type simulation with 1 0 8 Voronoi cells and fit the resulting empirical cumulative distribution functions to the Generalized Gamma, Gamma, Log-normal, Rayleigh, and Weibull distributions. Our analysis compares these fits in terms of root mean-squared error and maximum absolute variation, revealing the Generalized Gamma distribution as the best-fit model for characterizing these distances in homogeneous Poisson Voronoi tessellations. Furthermore, we provide the maximum likelihood estimates and the 95% confidence intervals of the parameters of the Generalized Gamma distribution along with the algorithm implemented to calculate the maximum and minimum distances. • Generator-vertex distances studied in finite Poisson Voronoi tessellations. • Empirical CDFs of max/min distances obtained via Monte Carlo simulation. • Generalized Gamma provides best fit across multiple error metrics • Maximum likelihood estimates and confidence intervals provided for all parameters.

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. Quantum maximal distance separable (MDS) codes are optimal in the sense they attain maximal minimum distance. Recently, constructing quantum MDS codes has received much attention and seems to become more and more difficult. In this paper, based on classical constacyclic codes, we construct some new quantum MDS codes by employing the Hermitian construction. Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.

Phenotypic Distance and Yield Potential of Six Arecanut Accessions from Jambi Province Phenotype distance of six arecanut accessions from Jambi Province have been calculated using D2 Mahalanobis Statistical Method. Its purposes was to get mother palm with far phenotype distance to use as in breeding program of arecanut in Jambi Province. Result of analysis showed that six of arecanut accession is classified in three group. First group had the maximum distance within cluster, while second group and third group have minimum distance within group. Maximum distance between group is shown between first group and third group ( D = 2076,5365). Biggest contributor to phenotype distance between six arecanut accession from Jambi is weight of nut character (80%), followed by number of fruits/bunch and fruit equatorial section with percentage of contribution each 13.33 % and 6.67%. Betara-1 and Sakernan accession have high potential production and potential for mother palm source of seed.

In a previous work we used a popular bio-inspired algorithm; particle swam optimization (PSO) to improve the performance of a well-known representation method of time series data which is the symbolic aggregate approximation (SAX), where PSO was used to propose a new weighted minimum distance WMD for SAX to recover some of the information loss resulting from the original minimum distance MINDIST on which SAX is based. WMD sets different weights to different segments of the time series according to their information content, where these weights are determined using PSO. We showed how SAX in conjunction with WMD can give better results in times series classification than the original SAX which uses MINDIST. In this paper we revisit this problem and propose optimizing WMD by using a hybrid of PSO and another bio-inspired optimization method which is Bacterial Foraging (BF); an effective bio-inspired optimization algorithm in solving difficult optimization problems. We show experimentally how by using this hybrid to set the weights of WMD we can obtain better classification results than those obtained when using PSO to set these weights.KeywordsBacterial ForagingParticle Swarm OptimizationSymbolic Aggregate ApproximationTime Series Data MiningWeighted Minimum Distance

We consider the non-orthogonal multiple access (NOMA) design for a classical two-user multiple access channel (MAC) with finite-alphabet inputs. In contrast to the majority of existing NOMA schemes using continuous Gaussian distributed inputs, we consider practical quadrature amplitude modulation (QAM) constellations at both transmitters, whose sizes are not necessarily the same. By adjusting the scaling factors (i.e., instantaneous transmitting powers) of both users, we aim to maximize the minimum Euclidean distance of the received sum-constellation for a maximum likelihood (ML) receiver. The formulated problem is a mixed continuous-discrete optimization problem and in general it is nontrivial to resolve. By carefully examining the structure of the objective function, we discover that Farey sequence can be employed to tackle the formulated problem. However, the existing Farey sequence is not applicable when the constellation sizes of the two users are different. To address this challenge, we define a new type of Farey sequence, termed punched Farey sequence. Based on this new definition and its properties, we manage to attain a closed-form optimal solution to the original problem by first dividing the entire feasible region into a finite number of Farey intervals and then taking the maximum over all the subintervals. Finally, computer simulations are carried out to verify our theoretical analysis, and to demonstrate the advantages of the proposed NOMA over known orthogonal and non-orthogonal designs.

Data stored in non-volatile memories may be destructed due to crosstalk and radiation but we can restore their data by using error-correcting codes. However, non-volatile memories consume a large amount of energy in writing. How to reduce writing bits even using error-correcting codes is one of the challenges in non-volatile memory design. In this paper, we propose a new write-reducing and error-correcting code, called Doughnut code. Doughnut code is based on state encoding limiting maximum and minimum Hamming distances. After that, we propose a code expansion method, which improves minimum and maximum Hamming distances by expanding a write-reducing code. When we apply our code expansion method to Doughnut code, we can obtain a write-reducing code whose error-correcting ability is equal to Hamming code. Experimental results show that the proposed write-reducing code reduces the number of writing bits by up to 36% compared to Hamming code.

In this paper a novel Ray Tracing 3D indoor propagation simulator at frequencies of 10-20 GHz using GPU is presented. To carry out the simulation, software tools as Nvidia CUDA 10.0, CMake 3.19.4, Nvidia OPTIX 6.5, Microsoft Visual Studio Community 2017 and Unity 2018.4.21f1 was used. Two indoor with line-of-sight (LOS) scenarios were defined within the Faculty of Informatics and Electronics al the Escuela Superior Politécnica de Chimborazo (ESPOCH), one in the Microwave Laboratory, with minimum and maximum distances between Transmitter and Receiver of 0.34m (far field) and 7m, respectively; and the second stage is located in the hall on the ground floor of the FIE building with minimum and maximum distances of 6 and 12m, respectively. In those scenarios, both, real and simulated measurements were made with frequency hops of 1GHz. For the simulation, a ray tracing propagation technique under GPU using NVIDEA-Optix was used. By comparing simulated and measurement power, it was observed a difference of 10 dB approximately.

Closed-loop distance-keeping for long-term satellite cluster flight

Maximum rank distance codes are the equivalent in rank-metric of Reed-Solomon codes whose subcodes have been widely studied. In this paper we characterize subspace subcodes of MRD codes and we show that it is possible to construct efficient polynomial-time encoding-decoding procedures for these subcodes. In a second part we show that subfield subcodes of maximum rank distance codes can be represented in some sense by the direct sum of maximum rank distance codes of smaller length and same minimum distance. We then derive an algorithm correcting some error-patterns beyond the error-correcting capability of the codes

Computing the extreme distances between two convex polygons