A new method for identifying vertebrates using only their mitochondrial DNA

A new method for determining whether or not a mitrochondrial DNA (mtDNA) sequence belongs to a vertebrate is described and tested. This method only needs the mtDNA sequence of the organism in question, and unlike alignment based methods, it does not require it to be compared with anything else. The method is tested on all 1877 mtDNA sequences that were on NCBI's nucleotide database on August 12, 2009, and works in 94.57% of the cases. Furthermore, all organisms on which this method failed are closely related phylogenetically in comparison to all other organisms included in the study. A list of potential extensions to this method and open problems that emerge out of this study is presented at the end.Comment: 7 Pages, 6 Figure

Beryllium monohydride (BeH): Where we are now, after 86 years of spectroscopy

BeH is one of the most important benchmark systems for ab initio methods and for studying Born-Oppenheimer breakdown. However the best empirical potential and best ab initio potential for the ground electronic state to date give drastically different predictions in the long-range region beyond which measurements have been made, which is about \sim1000 cm^{-1} for ^{9} BeH, \sim3000 cm^{-1} for ^{9} BeD, and \sim13000 cm^{-1} for ^{9} BeT. Improved empirical potentials and Born-Oppenheimer breakdown corrections have now been built for the ground electronic states X(1^{2}\Sigma^{+}) of all three isotopologues. The predicted dissociation energy for ^{9} BeH from the new empirical potential is now closer to the current best ab initio prediction by more than 66% of the discrepancy between the latter and the previous best empirical potential. The previous best empirical potential predicted the existence of unobserved vibrational levels for all three isotopologues, and the current best ab initio study also predicted the existence of all of these levels, and four more. The present empirical potential agrees with the ab initio prediction of all of these extra levels not predicted by the earlier empirical potential. With one exception, all energy spacings between vibrational energy levels for which measurements have been made, are predicted with an agreement of better than 1 cm^{-1} between the new empirical potential and the current best ab initio potential, but some predictions for unobserved levels are still in great disagreement, and the equilibrium bond lengths are different by orders of magnitude.Comment: Feedback encouraged. 9 Pages, 4 Figures, 4 Tables. The author thanks JSPS for financial suppor

Numerical Feynman integrals for density operator dynamics using master equation interpolants: faster convergence and significant reduction of computational cost

The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an approximation of the density operator at a sparse grid of points in time. Instead of relying only on \textit{ad hoc} interpolation methods such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as 2 time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method.Comment: 5 pages, 4 figures. v2: no change in results, no change in figures, fixed formatting on page 3, some word changes, version of abstract appearing in paper has been shortene

Analytic potentials and vibrational energies for Li2_{2} states dissociating to \mbox{Li}\left(2S\right)+\mbox{Li}\left(3P\right). Part 1: The 2S+1Πu/g^{2S+1}\Pi_{u/g} states

Analytic potentials are built for all four $^{2S+1}\Pi_{u/g}$ states of Li$_{2}$ dissociating to Li$(2S)$ + Li$(3P)$: $3b(3^{3}\Pi_{u})$, $3B(3^{1}\Pi_{u})$, $3C(3^{1}\Pi_{g}),$ and $3d(3^{3}\Pi_{g})$. These potentials include the effect of spin-orbit coupling for large internuclear distances, and include state of the art long-range constants. This is the first successful demonstration of fully analytic diatomic potentials that capture features that are usually considered too difficult to capture without a point-wise potential, such as multiple minima, and shelves. Vibrational energies for each potential are presented for the isotopologues $^{6,6}$Li$_{2}$, $^{6,7}$Li$_{2}$, $^{7,7}$Li$_{2}$, and the elusive `halo nucleonic molecule' $^{11,11}$Li$_{2}$. These energies are claimed to be accurate enough for new high-precision experimental setups such as the one presented in {[}Sebastian \emph{et al.} Phys. Rev. A, \textbf{90}, 033417 (2014){]} to measure and assign energy levels of these electronic states, all of which have not yet been explored in the long-range region. Measuring energies in the long-range region of these electronic states may be significant for studying the \emph{ab initio} vs experiment discrepancy discussed in {[}Tang \emph{et al.} Phys. Rev. A, \textbf{84}, 052502 (2014){]} for the $C_{3}$ long-range constant of Lithium, which has significance for improving the SI definition of the second.Comment: Feedback encouraged. 19 pages, 4 figure

Simulating neurobiological localization of acoustic signals based on temporal and volumetric differentiations

The localization of sound sources by the human brain is computationally simulated from a neurobiological perspective. The simulation includes the neural representation of temporal differences in acoustic signals between the ipsilateral and contralateral ears for constant sound intensities (angular localization), and of volumetric differences in acoustic signals for constant azimuthal angles (radial localization). The transmission of the original acoustic signal from the environment, through each significant stage of intermediate neurons, to the primary auditory cortex, is also simulated. The errors that human brains make in attempting to localize sounds in evolutionarily uncommon environments (such as when one ear is in water and one ear is in air) are then mathematically predicted. A basic overview of the physiology behind sound localization in the brain is also provided.Comment: 26 pages, 18 figure

Linear Multistep Numerical Methods for Ordinary Differential Equations

A review of the most popular Linear Multistep (LM) Methods for solving Ordinary Differential Equations numerically is presented. These methods are first derived from first principles, and are discussed in terms of their order, consistency, and various types of stability. Particular varieties of stability that may not be familiar, are briefly defined first. The methods that are included are the Adams-Bashforth Methods, Adams-Moulton Methods, and Backwards Differentiation Formulas. Advantages and disadvantages of these methods are also described. Not much prior knowledge of numerical methods or ordinary differential equations is required, although knowledge of basic topics from calculus is assumed.Comment: A general review that does not require much prior knowledge in numerical ODEs. 10 page

State of the art for ab initio vs empirical potentials for predicting 6e−^{-} excited state molecular energies: Application to Li2(b,13Πu)_{2}\left(b,1^{3}\Pi_{u}\right)

We build the first analytic empirical potential for the most deeply bound \mbox{Li}_{2} state: $b\left(1^{3}\Pi_{u}\right)$. Our potential is based on experimental energy transitions covering $v=0-34$, and very high precision theoretical long-range constants. It provides high accuracy predictions up to $v=100$ which pave the way for high-precision long-range measurements, and hopefully an eventual resolution of the age old discrepancy between experiment and theory for the \mbox{Li}\left(2^{2}S\right)+\mbox{Li}\left(2^{2}P\right) $C_{3}$ value. State of the art ab initio calculations predict vibrational energy spacings that are all in at most 0.8 cm$^{-1}$ disagreement with the empirical potential.Comment: Feedback encouraged. 16 pages, 3 figure

Crushing runtimes in adiabatic quantum computation with Energy Landscape Manipulation (ELM): Application to Quantum Factoring

We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonian's density of states away from the ground state, so that fewer states occupy the low-lying energies near the minimum, hence allowing for faster adiabatic passages to find the ground state with less risk of getting caught in an undesired low-lying excited state during the passage. Even more generally, our methods can be used to transform a discrete optimization problem into a new one whose unique minimum still encodes the desired answer, but with the objective function's values forming a different landscape. Aspects of the landscape such as the objective function's range, or the values of certain coefficients, or how many different inputs lead to a given output value, can be decreased *or* increased. One of the many examples for which these methods are useful is in finding the ground state of a Hamiltonian using NMR: If it is difficult to find a molecule such that the distances between the spins match the interactions in the Hamiltonian, the interactions in the Hamiltonian can be changed without at all changing the ground state. We apply our methods to an AQC algorithm for integer factorization, and the first method reduces the maximum runtime in our example by up to 754%, and the second method reduces the maximum runtime of another example by up to 250%. These two methods may also be combined.Comment: Feedback Encourage

Quantum factorization of 56153 with only 4 qubits

The largest number factored on a quantum device reported until now was 143. That quantum computation, which used only 4 qubits at 300K, actually also factored much larger numbers such as 3599, 11663, and 56153, without the awareness of the authors of that work. Furthermore, unlike the implementations of Shor's algorithm performed thus far, these 4-qubit factorizations do not need to use prior knowledge of the answer. However, because they only use 4 qubits, these factorizations can also be performed trivially on classical computers. We discover a class of numbers for which the power of quantum information actually comes into play. We then demonstrate a 3-qubit factorization of 175, which would be the first quantum factorization of a triprime.Comment: Replaced 44929 with larger number (56153) that results in same Hamiltonian as 143, edited corresponding table and equations. Similarly replaced 13081 with 11663. Fixed typo in equations 14, 15, 19-2

On the empirical dipole polarizability of He from spectroscopy of HeH+^{+}

Using a long-range polarization potential for HeH$^{+}$, we can obtain an empirical value for the Boltzmann constant $k_{B}$ with an order of magnitude greater precision than the previous best experimental value based on the dipole polarizability of $^{4}$He. We find that relativistic and QED effects of order $\alpha_{{\rm FS}}^{3}$ in the fine structure constant are crucial in the quadrupole polarizability in order to fit the dipole polarizbility with this precision using the polarization potential. By calculating finite-mass corrections for $^{3}$He, we also present theoretical values for the dipole and quadrupole polarizabilities of $^{3}$He with 9 and 7 digits of precision respectively.Comment: We thank Krzystof Pachucki, Z-C. Yan, Stephen Lundeen, Richard Drachman, Anand Bhatia, Robert Le Roy, Grzegorz Lach, and Jim Mitroy for helpful discussion