The Role of Prescription Trends in the Opioid Epidemic and the Factors that Affect Physician Prescriptions

Every day, more than 90 Americans die as a result of opioid overdose (NIH, 2017a), and opioid overdoses have quadrupled since 1999 (CDC, 2016). Opioids are best described as a class of drug that includes synthetic versions, such as fentanyl, the commonly known illegal drug, heroin, and prescribed medications such as oxycodone (OxyContin®) and hydrocodone (Vicodin®; NIH, 2017b). Opioids directly activate the analgesia, or pain relieving portion of the brain as well as the reward region (Volkow & McLellan, 2016). This makes the drug effective for reducing pain as well as giving the body a sense of reward. However, the drug manipulates the reward system by building a learned association between taking the drug and the satisfactory effect received from the drug (Volkow & McLellan, 2016). This learned association puts the patient or user at risk for misuse of the drug, making opioid prescribing difficult for physicians. Other factors affecting opioid prescribing are racial disparities, patient-physician mistrust, pain perception, and the difference between acute and chronic pain (Mathur, Richeson, Paice, Muzyka, & Chiao 2014; Volkow & McLellan, 2016). The purpose of this article is to explore the factors that affect physicians’ decisions to prescribe opioids, and to examine how prescription trends influence the opioid epidemic

Deciding Finiteness for Matrix Groups Over Function Fields

Let S be any finite subset GLn(F(t)) where F is a field. In this paper we give algorithms to decide if the group generated by S is finite. In the case of characteristic zero, slight modifications of earlier work of Babai, Beals and Rockmore [1] give polynomial time deterministic algorithms to solve this problem. The case of positive characteristic turns out to be more subtle and our algorithms depend on a structure theorem proved here, generalizing a theorem of Weil. We also present a fairly detailed analysis of the size of finite subgroups in this case and give bounds which depend upon the number of generators. To this end we also introduce the notion of the diameter of a finitely generated algebra and derive some upper bounds related to this quantity. In positive characteristic the deterministic algorithms we present are exponential. A randomized algorithm based on ideas of the Meat-Axe is also given. While not provably efficient, the success of the Meat-Axe suggests the randomized algorithm will be useful

Effects of Carbohydrates on Landing Mechanics and Postural Stability During Intermittent High-Intensity Exercise to Fatigue

Please refer to the pdf version of the abstract located adjacent to the title

Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to a "string" type boundary value problem known from prior works

Neumark Operators and Sharp Reconstructions, the finite dimensional case

A commutative POV measure $F$ with real spectrum is characterized by the existence of a PV measure $E$ (the sharp reconstruction of $F$) with real spectrum such that $F$ can be interpreted as a randomization of $E$. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark's extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of $F$ and the sharp reconstruction of $F$. The relevance of this result to the theory of non-ideal quantum measurement and to the definition of unsharpness is analyzed.Comment: 37 page

Efficient quantum algorithms for simulating sparse Hamiltonians

We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and |H| is bounded by a constant, we may select any positive integer $k$ such that the simulation requires O((\log^*n)t^{1+1/2k}) accesses to matrix entries of H. We show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.Comment: 9 pages, 2 figures, substantial revision

On an inverse problem for anisotropic conductivity in the plane

Let $\hat \Omega \subset \mathbb R^2$ be a bounded domain with smooth boundary and $\hat \sigma$ a smooth anisotropic conductivity on $\hat \Omega$. Starting from the Dirichlet-to-Neumann operator $\Lambda_{\hat \sigma}$ on $\partial \hat \Omega$, we give an explicit procedure to find a unique domain $\Omega$, an isotropic conductivity $\sigma$ on $\Omega$ and the boundary values of a quasiconformal diffeomorphism $F:\hat \Omega \to \Omega$ which transforms $\hat \sigma$ into $\sigma$.Comment: 9 pages, no figur

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

Scalability of quantum computation with addressable optical lattices

We make a detailed analysis of error mechanisms, gate fidelity, and scalability of proposals for quantum computation with neutral atoms in addressable (large lattice constant) optical lattices. We have identified possible limits to the size of quantum computations, arising in 3D optical lattices from current limitations on the ability to perform single qubit gates in parallel and in 2D lattices from constraints on laser power. Our results suggest that 3D arrays as large as 100 x 100 x 100 sites (i.e., $\sim 10^6$ qubits) may be achievable, provided two-qubit gates can be performed with sufficiently high precision and degree of parallelizability. Parallelizability of long range interaction-based two-qubit gates is qualitatively compared to that of collisional gates. Different methods of performing single qubit gates are compared, and a lower bound of $1 \times 10^{-5}$ is determined on the error rate for the error mechanisms affecting $^{133}$Cs in a blue-detuned lattice with Raman transition-based single qubit gates, given reasonable limits on experimental parameters.Comment: 17 pages, 5 figures. Accepted for publication in Physical Review