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The geometric Lie algebra SU(3) isotropic vector matrix realization of the periodic table reported at PIRT 2017 has now been broken up to a disjoint-set modular R3SO(3) building kit, exactly sufficing to stage the Big Bang and ensuing nucleosynthesis events: First the ultrashort radiation/plasma inflation of the Big Bang phase transition moment with release of photons, neutrinos and module precursors, which in next seconds recombine to the Protium proton/electron compound and its neutron conversion to continue separately or in fusion of the two get on to Deuterium and from there to Tritium, Helium in isotope and form, and traces of Lithium and possibly Beryllium. That is, literally the whole primordial start-gas delivered within a few minutes to billion-year wait for sufficiently energetic perturbations with itself for astrophysical/cosmogenic/experimental nucleosynthesis of the full periodic table and likewise replicable by systematic space-filling assembly/disassembly of the here disclosed neutrino and photon lattice vector, particle, wave-packet and neutron building bricks, providing clues also on isotope/neutron excess, shell/subshell, spectroscopy, and chemical bond structural make-up and disposition. Furthermore, the absolute trigonometric sharpness of the nucleosynthesis phase transition burst and expansion is reciprocal to the absolute speed of light and hence a specific test and verification of the relativity theory.

More recently, motivated by extensively technical applications of carbon nanostructures, there is a growing interest in exploring novel non-carbon nanostructures. As the nearest neighbor of carbon in the periodic table, boron has exceptional properties of low volatility and high melting point and is stronger than steel, harder than corundum, and lighter than aluminum. Boron nanostructures thus are expected to have broad applications in various circumstances. In this contribution, we have performed a systematical study of the stability and electronic and magnetic properties of boron nanowires using the spin-polarized density functional calculations. Our calculations have revealed that there are six stable configurations of boron nanowires obtained by growing along different base vectors from the unit cell of the bulk -rhombohedral boron (-B) and -rhombohedral boron (-B). Well known, the boron bulk is usually metallic without magnetism. However, theoretical results about the magnetic and electronic properties showed that, whether for the -B-based or the -B-based nanowires, their magnetism is dependent on the growing direction. When the boron nanowires grow along the base vector [001], they exhibit ferromagnetism and have the magnetic moments of 1.98 and 2.62 B, respectively, for the -c [001] and -c [001] directions. Electronically, when the boron nanowire grows along the -c [001] direction, it shows semiconducting and has the direct bandgap of 0.19 eV. These results showed that boron nanowires possess the unique direction dependence of the magnetic and semiconducting behaviors, which are distinctly different from that of the bulk boron. Therefore, these theoretical findings would bring boron nanowires to have many promising applications that are novel for the boron bulk.

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Here, in our CA model, each cell of the CA lattice is occupied by one individual of the host population and in each cell there may be an amount of vectors. At each time step t, each individual is in one of three states: susceptible (S), infected (I), or recovered (R). The state transitions between the time steps t and t + 1 of this SIR-type epidemic model are driven by probabilistic rules. The goal is to examine the influence on the infected host group of distinct spatial distributions and time variations of the vector abundance, by running computer simulations.

Inspired by the mosquito theorem, another set of simulations was run to determine the critical number of vectors Vcritical below which the disease disappears. For values of V below the ones shown in Table 2, the infection was naturally eradicated in 10 consecutive simulations. These critical values were numerically found by varying V with a step size of 100. Observe that these two tables lead to a surprising conclusion: the prevalence in clustered distributions is lower than in homogeneous distributions; however, clustered distributions impair disease eradication. That is, clustered distributions require a greater effort to eliminate the disease than homogeneous distributions, in which the prevalence is higher! This result should be taken into account in the planning of public-health interventions.

The prediction of the lattice constant of binary body centered cubic crystals is performed in terms of first principle calculations and machine learning. In particular, 1541 binary body centered cubic crystals are calculated using density functional theory. Results from first principle calculations, corresponding information from periodic table, and mathematically tailored data are stored as a dataset. Data mining reveals seven descriptors which are key to determining the lattice constant where the contribution of descriptors is also discussed and visualized. Support vector regression (SVR) technique is implemented to train the data where the predicted lattice constants have the mean score of 83.6% accuracy via cross-validation and maximum error of 4% when compared to experimentally determined lattice constants. In addition, trained SVR is successful in predicting material combinations from a desired lattice constant. Thus, a set of descriptors for determining the lattice constant is identified and can be used as a base descriptor for lattice constants of further complex crystals. This would allow for the acceleration of the search for lattice constants of desired atomic compositions as well as the prediction of new materials based on a specified lattice constant.

PriceTbl = ret2price(ReturnTbl) returns the table or timetable of price series PriceTbl computed from converting each variable in the table or timetable of continuously compounded return series ReturnTbl. To select different variables in Tbl from which to compute prices, use the DataVariables name-value argument.

[___] = ret2price(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in previous syntaxes. ret2price returns the output argument combination for the corresponding input arguments. For example, ret2price(Tbl,Method="periodic",DataVariables=1:5) computes prices from the simple periodic returns in the first five variables in the input table Tbl.

prices is a 1657-by-1 vector of monthly NYSE prices from the continuously compounded returns. ret2price sets the starting price to 1 by default; specify the StartPrice name-value argument to set an appropriate starting price.

Because DTM is a table, PriceTbl is a table. PriceTbl contains the price series computed from the continuously compounded returns (variable names match the input variable names), observation times Tick, and time intervals Interval.

Because TT is a timetable, PriceTT is a timetable. PriceTT contains only those requested price series. Because the input data is time aware, the time-related variables in PriceTT contain more information about the observation times than returned when the input data is a matrix or table. For example, rather than tick times, the output timetable contains observation dates for the prices and the interval is in days.

Time series of returns, specified as a table or timetable with numObs rows. Each row of Tbl is a sampling time. For a table, the optional Ticks name-value argument specifies sampling times. For a timetable, ReturnTbl.Time specifies sampling times and it must be a datetime vector.

When the input return series are in a timetable, ret2price computes time intervals from the start time StartTime and the row times in ReturnTbl.Time, and ignores Intervals. ReturnTbl.Time must be a datetime vector.

Variables in ReturnTbl, from which ret2price computes prices, specified as a string vector or cell vector of character vectors containing variable names in ReturnTbl.Properties.VariableNames, or an integer or logical vector representing the indices of names. The selected variables must be numeric.

Observation times of the Price series, returned as a length numObs + 1 numeric vector, beginning with the value of the StartTime name-value argument. ret2price returns ticks when you supply the input Returns.

The radial tree for the vector properties (cf. Figure 8) separates the same two classes as PCA loadings plot and dendrogram (Figure 6 and Figure 7). Splits graph for properties (cf. Figure 9) reveals conflicting relation between classes because of interdependences. It is in agreement with PCA loadings plot and binary/radial trees (Figure 6, Figure 7 and Figure 8).

Property P variation of vector (cf. Figure 11) is expressed in decimal system, P = 105i1 + 104i2 + 103i3 + 102i4 + 10i5 + i6, vs. structural parameters {i1,i2,i3,i4,i5,i6} for the pesticides. Most points and lines i3/i5 collapse. For instance, for molecule 1 (methamidophos) , vector property P = 1050 + 1040 + 1031 + 1020 + 101 + 0 = 1010 where the structural parameters are 0 and 1, and the corresponding points are (i1 = i2 = i4 = i6 = 0, P = 1010) and (i3 = i5 = 1, P = 1010). The results show parameters hierarchy: i1 > i2 > i3 > i4 > i5 > i6 in agreement with PT of properties (Table 6) with vertical groups defined by {i1,i2,i3,i4,i5} and horizontal periods described by {i6}. The property was not used in PT development and validates it.

Property P change of vector in base 10 (cf. Figure 12) is represented vs. number of group in PT, for pesticides (Table 1 subset of Table 6). It reveals minima corresponding to compounds with ca. (group g00101) and maxima with ca. (group g11111). For group 6, period 2 is superimposed on 1. For instance, for group g001010 and period p0, molecule 1 (methamidophos) lies in the first group in the subset with P = 1010 and the point is (group = 1, P = 1010). Periods p0 and p1 represent rows 1 and 2, respectively, in Table 6. Function P(i1,i2,i3,i4,i5,i6) denotes two periodic waves clearly limited by two maxima, which suggest a periodic behaviour that recalls form of a trigonometric function. For , a maximum is shown. Distance in units between each pair of consecutive maxima is six, which coincides with pesticide sets in successive periods. The maxima occupy analogous positions and are in phase. The representative points in phase should correspond to elements in the same group in PT. For both maxima, some coherence exists between two representations; however, the consistency is not general. Waves comparison shows two differences: period 1 is somewhat step-like and period 2 is incomplete. The most characteristic points are maxima, which lie about group g11111. The values of are repeated as the periodic law (PL) states. ff782bc1db