Abstract:
We present an algorithm for reconstructing haplotypes (alleles for multiple SNPs on same chromosome) from pools of two individual DNAs, in which Hardy-Weinberg equilibrium conditions or other assumptions are not required. The program outputs, in addition to inferred haplotypes, a minimal number of haplotype-tagging SNPs that are identified after an exhaustive search procedure.Our method and algorithms lead to a significant reduction in genotyping effort, for example, in case-control disease association studies while maintaining the possibility of reconstructing haplotypes under very general conditions.While SNPs in many ways are highly useful genetic markers, it may only be the joint effect of multiple SNPs in a gene that provides much information about association to disease because, taken together, the SNPs represent a much more polymorphic system than each SNP by itself. The effects of these SNPs are perhaps best represented by their haplotypes. Ideally, a researcher would want to obtain genotypes on all SNPs in a gene but this effort tends to be expensive. Thus, several authors have proposed that pools of DNA from n individuals be genotyped, which reduces genotyping costs by a factor of n [1]. In case-control association studies, an extreme approach is to form one pool for case and one pool for control individuals [2,3]. Originally, pooling was introduced as a method for efficiently screening for a rare disease [4] and thus for identifying individuals. On the other hand, grouping was later used to protect confidentiality [5].Several methodological investigations of pooling efficiency have focused on marker allele frequency estimation [6,7] and on testing for association between markers and disease based on pooled data [8]. Extensions to two loci involve estimation of allele frequencies and the disequilibrium parameter based on pooled data [9].Clearly, DNA pools of large numbers of individuals will only allow investigating SNP alleles and will be unable to look a

Abstract:
From the equations of motion for baryons in the scalar strong interaction hadron theory (SSI), two coupled third order radial wave equations for baryon doublets have been derived and published in 1994. These equations are solved numerically here, using quark masses obtained from meson spectra and the masses of the neutron, ?0 and ?0 as input. Confined wave functions dependent upon the quark-diquark distance as well as the values of the four integration constants entering the quark-diquark interaction potential are found approximately. These approximative, zeroth order results are employed in a first order perturbational treatment of the equations of motion for baryons in SSI for free neutron decay. The predicted magnitude of neutron’s half life agrees with data. If the only free parameter is adjusted to produce the known A asymmetry coefficient, the predicted B asymmetry agrees well with data and vice versa. It is pointed out that angular momentum is not conserved in free neutron decay and that the weak coupling constant is detached from the much stronger fine structure constant of electromagnetic coupling.

Abstract:
It is shown that the gauge boson mass is natu-rally generated–without Higgs–in the pion beta decay using the scalar strong interaction had-ron theory. This mass generation is made pos-sible by the presence of relative time between quarks in the pion in a fully Lorentz covariant formalism.

Abstract:
CP conservation and violation in neutral kaon decay are considered from a first principles’ theory, recently published as “Scalar Strong Interaction Hadron Theory”. The arbitrary phase angle relating K^{0} and ^{0} in current phenomenology is identified to be related to the product of the relative energy to the relative time between the s and d quarks in these kaons. The argument of the CP violating parameter ? is predicted to be 45? without employing measured data. The K^{0}_{S} decay rate is twice the K^{0}_{L} -K^{0}_{S} masss difference, in near agreement with data, and both are proportional to the square of the relative energy 29.44 eV. Any pion from K^{0}_{L} decay will also have a mass shift of ≈1.28 × 10^{-5} eV. The present first principles’ theory is consistent with CP conservation. To achieve CP violation, the relative time cannot extend to both +∞ and -∞ but is bounded in at least one direction. The values of these bounds lie outside the present theory and it is unknown how they can be brought forth. -B^{0} mixing is also considered and the relative energy is 663.66 eV.

Abstract:
From the equations of motion for baryons in the scalar strong interaction hadron theory (SSI), two coupled third order radial wave equations for baryon doublets have been derived and published in 1994. These equations are solved numerically here, using quark masses obtained from meson spectra and the masses of the neutron, ?0 and ?0 as input. Confined wave functions dependent upon the quark-diquark distance as well as the values of the four integration constants entering the quark-diquark interaction potential are found approximately. These approximative, zeroth order results are employed in a first order perturbational treatment of the equations of motion for baryons in SSI for free neutron decay. The predicted magnitude of neutron’s half life agrees with data. If the only free parameter is adjusted to produce the known A asymmetry coefficient, the predicted B asymmetry agrees well with data and vice versa. It is pointed out that angular momentum is not conserved in free neutron decay and that the weak coupling constant is detached from the much stronger fine structure constant of electromagnetic coupling.

Abstract:
CP conservation and violation in neutral kaon decay are considered from a first principles’ theory, recently published as “Scalar Strong Interaction Hadron Theory”. The arbitrary phase angle relating K0 and 0 in current phenomenology is identified to be related to the product of the relative energy to the relative time between the s and d quarks in these kaons. The argument of the CP violating parameter ? is predicted to be 45? without employing measured data. The K0S decay rate is twice the K0L -K0S masss difference, in near agreement with data, and both are proportional to the square of the relative energy 29.44 eV. Any pion from K0L decay will also have a mass shift of ≈1.28 × 10-5 eV. The present first principles’ theory is consistent with CP conservation. To achieve CP violation, the relative time cannot extend to both +∞ and -∞ but is bounded in at least one direction. The values of these bounds lie outside the present theory and it is unknown how they can be brought forth. -B0 mixing is also considered and the relative energy is 663.66 eV.

This paper is an extension of the book of reference [1] below. QCD Lagrangian is derived from the same equations of motion for quarks used to construct the equations of motion for mesons and baryons in the scalar strong interaction hadron theory that accounts for many basic low energy data not covered by QCD. At high energies, the energetic quarks in a hadron can be far from each other and approximately free. Each quark is associated with a vector in an internal space characterizing its mass and charge. These spaces are interchangeable and provide a new symmetry equivalent to color symmetry in QCD. A quark in a meson has two “colors” and in a baryon three “colors”; the β function of QCD is 61%-92% greater in high energy interactions leading to baryons than that to mesons. This function enters themeasurable running coupling constant and this prediction is testable against experiment. QCD, successful at high energies, is thus reconciled with the scalar strong interaction hadron theory and both complement each other.

The magnetic moments of the baryon octet are derived from a first
principle’s theory, the scalar strong interaction hadron theory, and are in
approximate agreement with data. It is conjectured that this agreement may be
improved by including the “spin-orbit coupling” term not evaluated here.

Abstract:
The Higgs-like boson H(126) discovered in 2012 is tentatively assigned to a newly found bound state of two charged gauge bosons W^{+}W^{-}. Starting from the scalar strong interaction hadron theory, a first principles’ theory, a nonlinear, soliton-like differential equation dependent upon the distance between the two W bosons is derived. This equation is solved on a computer. A new, nonlinear confinement mechanism, not yet understood, binds the both bosons and gives a bound state mass E_{B} = 155.8 GeV. This E_{B}, derived at the quantum mechanical level, is estimated to reduce to E_{B} = 110 GeV when quantized field effects are included via coarse approximations and replacement of the bare constants by renormalized ones. These developments lead to a revised status of the standard model.

Abstract:
The Higgs-like boson discovered at CERN in 2012 is tentatively assigned to a newly found bound state of two charged gauge bosons W^{+}W^{-} with a mass of E_{B} ≈ 117 GeV, much closer to the measured 125 GeV than 110 GeV predicted in a paper with the same title earlier this year. The improvement is due to a shift from the earlier SU(2) representation assignment for the gauge bosons to the more realistic SU(3) one and that the computations are carried out with much greater accuracy.