Function-correcting codes with homogeneous distance

Place recognition is based on long-term memory codes providing local position information. We propose a Maximum-Likelihood model of place recognition taking into account stored and perceived landmark distances and bearings. Stored landmark distance is assumed to be based on triangulation and is therefore veridical. Landmark distance perceived during homing are assumed to be hyperbolically compressed (Gilinsky, 1951). We evaluate the model with experimental data which was collected from place recognition experiments in a virtual reality setup. Three groups of participants learned a goal location within three different configurations of four distinguishable landmarks (parallelogram, irregular with large distance variation between landmarks, irregular with homogeneous distances). In the following test phase the participants navigated to the goal location, but the environment was now covered by “ground fog” removing all environmental information except the landmarks themselves. Error ellipses were elongated towards the most distant landmark and, in the irregular conditions, showed a systematic bias in the same direction. The model reproduces the ellipse orientations if we assume that distance measurements are less noisy for near distances (from about 30 m) than bearing measurements; it also reproduces the systematic biases due to the hyperbolic compression of perceived distances (Gilinsky’s A = 90 m).

We present an updated version of the multicolor light-curve shape method to measure distances to Type Ia supernovae (SNe Ia), incorporating new procedures for K-correction and extinction corrections. We also develop a simple model to disentangle intrinsic color variations and reddening by dust and expand the method to incorporate U-band light curves and to more easily accommodate prior constraints on any of the model parameters. We apply this method to 133 nearby SNe Ia, including 95 objects in the Hubble flow (cz ≥ 2500 km s-1), which give an intrinsic dispersion of less than 7% in distance. The Hubble flow sample, which is of critical importance to all cosmological uses of SNe Ia, is the largest ever presented with homogeneous distances. We find that the Hubble flow SNe with H0dSN ≥ 7400 km s-1 yield an expansion rate that is 6.5% ± 1.8% lower than the rate determined from SNe within that distance, and this can have a large effect on measurements of the dark energy equation of state with SNe Ia. Peculiar velocities of SN Ia host galaxies in the rest frame of the Local Group are consistent with the dipole measured in the cosmic microwave background. Direct fits of SNe Ia that are significantly reddened by dust in their host galaxies suggest that their mean extinction law may be described by RV 2.7, but optical colors alone provide weak constraints on RV.

The emerging technologies and data centric applications have been becoming an integral part of business intelligence, decision process and numerous daily activities. To enable efficient pattern classification and data analysis, clustering has emerged as a potential mechanism that classifies data elements based on respective feature homogeneity. Although K-Means clustering has exhibited appreciable performance for data clustering, it suffers to enable optimal classification with high dimensional data sets. Numerous optimization efforts including genetic algorithm (GA) based clustering also require further optimization to avoid local minima issues. In this paper, an improved Canonical GA based Bisecting K-Means algorithm (CGABC) has been developed. The proposed model incorporates min-max normalization based feature normalization of the high dimensional data sets, which is followed by T-Test analysis that significantly reduces data dimensions based on feature similarity of the data elements. The fitness value has been assigned based on inter-cluster (heterogeneous distance) and within-cluster (homogeneous distance) distances. To enable optimal features and process parameter selection, particularly cluster centers information, the conventional GA has been modified by applying multistage reproduction process, enhanced crossover and mutation. By incorporating the optimized cluster center information the Bisecting K-Means clustering has been performed, which has exhibited optimal solution for highly accurate and efficient clustering with high dimensional data sets.

We present new accurate abundances for five neutron-capture (Y, La, Ce, Nd, Eu) elements in 73 classical Cepheids located across the Galactic thin disk. Individual abundances are based on high spectral resolution (R ~ 38,000) and high signal-to-noise ratio (S/N ~ 50-300) spectra collected with UVES at ESO VLT for the DIONYSOS project. Taking account for similar Cepheid abundances provided either by our group (111 stars) or available in the literature, we end up with a sample of 435 Cepheids covering a broad range in iron abundances (-1.6 < [Fe/H] < 0.6). We found, using homogeneous individual distances and abundance scales, well defined gradients for the above elements. However, the slope of the light s-process element (Y) is at least a factor of two steeper than the slopes of heavy s- (La, Ce, Nd) and r- (Eu) process elements. The s to r abundance ratio ([La/Eu]) of Cepheids shows a well defined anticorrelation with of both Eu and Fe. On the other hand, Galactic field stars attain an almost constant value and only when they approach solar iron abundance display a mild enhancement in La. The [Y/Eu] ratio shows a mild evidence of a correlation with Eu and, in particular, with iron abundance for field Galactic stars. We also investigated the s-process index - [hs/ls] - and we found a well defined anticorrelation, as expected, between [La/Y] and iron abundance. Moreover, we found a strong correlation between [La/Y] and [La/Fe] and, in particular, a clear separation between Galactic and Sagittarius red giants. Finally, the comparison between predictions for low-mass asymptotic giant branch stars and the observed [La/Y] ratio indicate a very good agreement over the entire metallicity range covered by Cepheids. However, the observed spread, at fixed iron content, is larger than predicted by current models.

Race and sex were found to be the most salient parameters of friendship. Multivariate analyses revealed that blacks tend to have less homogeneous friendship networks than their white counterparts only in regard to marital status. How close respondents felt to their friends, on the average, was positively related to the level of age and sex homogeneity of the network. Respondent's education was positively related to all five types of homogeneity. It was found that the size theorem from Blau's primitive theory of social structure accounted for some of the findings. Exceptions were in race and education homogeneity, where discrimination and social distance figured into possible explanations.

Experimental and numerical investigation of the hetero-/homogeneous combustion of lean propane/air mixtures over platinum

Transformation of cubic molybdenum carbide into hexagonal β-Mo2C was found to follow the Avrami–Erofeev kinetic model with an n parameter of four indicating a slow nucleation step with a polyhedral growth of the transformed phase. The transformation not only occurred at 773 K under atmospheric H2 pressure, but also imperceptibly occurred under the employed hydrogenation reaction conditions (413 K and 70 psig of H2 pressure) when using toluene or 1-octene as reactants, not affecting the activity under the steady state. Our computational studies also revealed that both crystal structures share common atomic cluster arrangements with small differences in angles and interatomic distances. The transformation was triggered by local distortions which favored shorter and more homogeneous interatomic distances as present in the hexagonal phase. The prepared molybdenum carbide materials were selective to the hydrogenation of 1-octene under the mild hydrogenation conditions tested. Hydrogenation of 1-octene was preferential in a 50 wt% mixture of toluene and 1-octene with minimal toluene hydrogenation under the tested conditions.

Temporal distance, social distance and probabilistic distance are three basic dimensions of psychological distance. It has been proved that different kinds of psychological distance have similar effects on cognitive representations of events. In general, distant events are represented as high-level construals, whereas near events are represented as low-level construals. As events become more distant, the high-level construals become more influential in shaping preference whereas the low-level construals become less influential(Liberman, Trope, Stephan, 2007; Liberman, Trope, 2008; Trope, Liberman, 2010).This study investigates the effects of temporal, social and probabilistic distance on intertemporal choice and risky choice. We hypothesize that different kinds of distance have similar effects on intertemporal and risky choice, based on the assumptions that these three kinds of distance share the same nature as psychological distance, and that intertemporal choice and risky choice have common processes of option representation and weighting. When psychological distance increases, money magnitude as high-level construal becomes more influential while time and probability as low-level construals become less influential(Sagristano, Trope, Liberman, 2002; Trope Liberman, 2003). Therefore, participants in distant conditions would choose delayed and risky alternatives with larger monetary value.Experiment 1 investigated the effect of temporal distance on intertemporal and risky choices. Participants were told that they would participate in a visual experiment, but before that they needed to make an intertemporal choice as their rewards between "$50 immediately" and "$90 in 3 months"(experiment 1a), or between " $ 50 for sure" and " $ 200 with the probability of 20%"(experiment 1b). In near condition, the experiment would be conducted soon, and in distant condition the experiment would be conducted in 6 months.Experiment 2 investigated the effect of social distance. In near condition, participants would make choice for themselves, and in distant condition, for other people. Experiment 3 investigated the effect of probabilistic distance. In near condition, participants were told that they would participate in the experiment with 90%probability, and in distant condition, with 10% probability. The options of intertemporal choice and risky choice are similar to experiment 1. The results show that no matter what kind of distance was involved, there were more participants in distant condition who chose delayed or risky alternatives than those who did in near condition,which confirms the hypotheses.The similar effects of temporal, social and probabilistic distance on intertemporal and risky choices suggest that intermporal and risky choices share common psychological process, and these three kinds of distance are homogeneous psychological distance.

Expanding and non-expanding layers of interstratified clay minerals have been examined by high-resolution transmission electron microscopy. Permanent expansion of swelling layers under the electron beam was achieved by intercalation ofn-alkylammonium ions, especially the octadecylammonium ion. Oriented flakes of clay minerals were prepared by embedding the expanded or non-expanded clay minerals in epoxy resin, followed by centrifugation before hardening of the resin. The minerals were then cut perpendicular to 001 using an ultramicrotome. Crystals ofmacroscopic trioctahedral vermiculitesshow homogeneous interplanar distances of 24 Å after intercalation of octadecylammonium ions. Crystals ofdioctahedral soil vermiculitesoften show a central zone with non-expanding 10 Å layers; the outer zone shows a disturbed layer sequence extensively expanded byn-alkylammonium ions. After embedding in epoxy resin, vermiculites show stable 9·2 Å interplanar spacings but smectites expand to 13 Å.Montmorillonitesof theWyoming typeshow curved stacks of layers. Most of the layer stacks ofmontmorillonitesof theCheto typeare split and disordered aggregates of single layers are formed. Crystals ofillitesandglauconitesare built up of aggregated small stacks of 10 Å layers, the layer stacks consisting of 10 layers. Mostly the boundaries of the layer stacks are parallel to their 001 planes; sometimes low-angle boundaries are found. The dimensions of the layer stacks, ∼ 100 Å thick and some hundreds of Å in plane, are equal to the dimensions of the domains of coherent scattering of X-rays. The border layers between the layer stacks are identical with those 5 to 10% of layers which swell with glycerol or ethylene glycol during X-ray analysis. Some of the layer stacks of illite and glauconite crystals are expanded by octadecylammonium ions within a fortnight. The other stacks show unchanged 10 Å spacings. The different expanding behaviour of different layer stacks reflects the heterogeneity of the layer-charge distribution in the mica clay minerals.K-bentonitesshow the same expanding behaviour as illites and glauconites but the number of layers expanding with octadecylammonium ions is greater in K-bentonites than in illite crystals. Expanded mixed-layered minerals of the illite-smectite type show a different layer stacking sequence from illites. Random irregular stacking of mica layers with expanded layers are recognized rather than coherent stacks of mica layers. The crystals have a stepped morphology, perhaps effected by translations along the 001 plane. After reaction of therectoritefromGarland Countywith octadecylammonium ions, the non-expanded mica layers and the expanded smectite-like layers can be distinguished. The heterogeneity of the interlayer charges of the smectite layers is documented by the formation of alkyl double-layers with 17 Å spacings and alkyl triple-layers with 21 Å spaces in irregular sequence. The ‘rectorite’ from theGoto Mineexpands nearly homogeneously in comparison with the rectorite from Garland County. After reaction with octadecylammonium ions, interplanar spacings of mostly 31 Å are observed but rarely spacings of 27 Å. The smectite layers of thecorrensitefromKaubenheimare expanded by tetradecyl-ammonium ions to 18 Å spacings by formation of alkyl double-layers. A regular 1 : 1 layer structure of 14 Å chlorite layers and expanded 18 Å smectite layers with total spacing of 32 Å can be observed.Muscoviteandpyrophylliteare not expandable byn-alkyl-ammonium ions within a fortnight. However, sporadic layers ofceladonitecrystals are expanded. Generally the 10 Å or 9·2 Å layers extend over the whole crystals of the three minerals. In celadonite crystals, disorder is caused sporadically by interrupted layers or slightly enlarged layer spacings.

We present an interior proximal method for solving constrained nonconvex optimization problems where the objective function is given by the difference of two convex function (DC function). To this end, we consider a linearized proximal method with a proximal distance as regularization. Convergence analysis of particular choices of the proximal distance as second-order homogeneous proximal distances and Bregman distances are considered. Finally, some academic numerical results are presented for a constrained DC problem and generalized Fermat–Weber location problems.

The main focus in this thesis is linear codes over rings. In the first part, we look at linear codes over Galois rings, and using the homogeneous weight, we improve upon Wilson's results about the prime power that divides the coefficients of the homogeneous weight enumerators of these codes. We also prove that our results are best possible. Our results about homogeneous weight enumerators of linear codes over Galois rings generalize the results that we have for the Lee weight enumerators of linear codes over the ring of integers modulo 4. We also consider other weight enumerators, in particular the complete weight enumerators of linear codes and we obtain MacWilliams-like identities for these weight enumerators considering different rings. These MacWilliams-like identities lead to MacWilliams identities for the Hamming weight enumerators of linear codes over rings. We also give a counter-example to show that we cannot have MacWilliams-like identities for the Euclidean weight enumerators of linear codes over the ring of integers modulo 4. We also look at Gray maps from Galois rings to the finite field of prime size. We first give an application of the distance preserving Gray maps to obtain good ternary codes, and then we give an inductive algebraic construction of a distance preserving Gray map from Galois rings with the homogeneous distance to the field of prime size with the Hamming distance as well as a combinatorial construction. By using the Gray maps, we obtain some results about the weight enumerators of linear codes over the ring of dual numbers. In the last part of this work, we consider the permutation invariance of binary codes and the connection with linearity over certain rings. Among the rings considered, we have different variations and extensions of the ring of dual numbers. In this context we consider the Reed-Muller codes and answer questions about permutation invariance of Reed-Muller codes under certain permutation groups and the linearity of Reed-Muller codes over these aforementioned rings.

We present the Milky Way Star Clusters (MWSC) survey based on 470 million stars extracted from the all-sky catalogues PPMXL and 2mass. The target list comprises 3784 entries and includes all open and globular clusters, as well as all cluster candidates, known at present. By means of a combined photometric/astrometric pipeline process, we determine individual membership probabilities for cluster stars and provide fundamental cluster parameters such as cluster centre coordinates, mean proper motions, radial velocity, distance, reddening, age and tidal radius. This sample includes ~ 700 clusters with fundamental parameters based on optical data and offers a good opportunity for a comparison of the near-infrared (NIR) and optical cluster distance scales. We find that distances and reddening values obtained from the colour–magnitude diagrams (CMDs) in the NIR agree well with earlier distance estimates based on optical CMDs. These newly obtained homogeneous distances, together with the other cluster parameters, allow us to study the properties of the open cluster population in the Galactic disk.

This contribution reflects a detailed overall survey of the Carina Spiral Feature based on uvbyβ photometry of O- and B-type stars. New observations are combined with all data currently available, to collate a complete homogeneous magnitude-limited uvbyβ database. A uniform procedure is applied to obtain the photometry-derived stellar parameters. A homogeneous distance scale is established to the most prominent young structures in the field and the distribution of the visual extinction is analyzed.

In this work, we aimed to derive the gri-band period–luminosity (PL) and period–luminosity–color (PLC) relations for late-type contact binaries, for the first time, located in globular clusters, using the homogeneous light curves collected by the Zwicky Transient Factory (ZTF). We started with 79 contact binaries in 15 globular clusters, and retained 30 contact binaries in 10 globular clusters that have adequate numbers of data points in the ZTF light curves and are unaffected by blending. Magnitudes at mean and maximum light of these contact binaries were determined using a fourth-order Fourier expansion, while extinction corrections were done using the Bayerstar2019 3D reddening map together with adopting the homogeneous distances to their host globular clusters. After removing early-type and “anomaly” contact binaries, our derived gri-band PL and period–Wesenheit (PW) relations exhibited a much larger dispersion with large errors on the fitted coefficients. Nevertheless, the gr-band PL and PW relations based on this small sample of contact binaries in globular clusters were consistent with those based on a larger sample of nearby contact binaries. Good agreements of the PL and PW relations suggested both samples of contact binaries in the local Solar neighborhood and in the distant globular clusters can be combined and used to derive and calibrate the PL, PW, and PLC relations. The final derived gr-band PL, PW, and PLC relations were much improved over those based on the limited sample of contact binaries in the globular clusters.

Let p &#x2260; 3 be any prime. The structures of all &#x03BB;-constacyclic codes of length 3p^s over the finite commutative chain ring Fp^m + uFp^m (u² = 0) are established in the term of their generator polynomials. As an application, Hamming and homogeneous distance of a class of such codes and RT distances of all are given. Among such &#x03BB;-constacyclic codes, the unique maximum-distance-separable (briefly, MDS) code with respect to the RT distance is obtained. Moreover, when &#x03BB; is not a cube in Fpm, the necessary and sufficient condition for the &#x03BB;-constacyclic code of length 3p^s over Fp^m + uFp^m (u² = 0) be an MDS constacyclic code with respect to Hamming distance is provided.