Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.Comment: 28 pages, LaTeX. This is an expanded version of a paper that appeared in the Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, Nov. 20--22, 1994. Minor revisions made January, 199

Thermal transport in granular metals

We study the electron thermal transport in granular metals at large tunnel conductance between the grains, $g_T \gg 1$ and not too low a temperature $T > g_T\delta$, where $\delta$ is the mean energy level spacing for a single grain. Taking into account the electron-electron interaction effects we calculate the thermal conductivity and show that the Wiedemann-Franz law is violated for granular metals. We find that interaction effects suppress the thermal conductivity less than the electrical conductivity.Comment: Replaced with published versio

Consequences of converting graded to action potentials upon neural information coding and energy efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ~50% in generator potentials, to ~3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation

Long term (5 Year) safety of bronchial thermoplasty: Asthma Intervention Research (AIR) trial

<b>Background:</b> Bronchial thermoplasty (BT) is a bronchoscopic procedure that improves asthma control by reducing excess airway smooth muscle. Treated patients have been followed out to 5 years to evaluate long-term safety of this procedure. <br></br> <br></br> <b>Methods:</b> Patients enrolled in the Asthma Intervention Research Trial were on inhaled corticosteroids ≥200 μg beclomethasone or equivalent + long-acting-beta2-agonists and demonstrated worsening of asthma on long-acting-β2-agonist withdrawal. Following initial evaluation at 1 year, subjects were invited to participate in a 4 year safety study. Adverse events (AEs) and spirometry data were used to assess long-term safety out to 5 years post-BT. <br></br> <br></br> <b>Results:</b> 45 of 52 treated and 24 of 49 control group subjects participated in long-term follow-up of 5 years and 3 years respectively. The rate of respiratory adverse events (AEs/subject) was stable in years 2 to 5 following BT (1.2, 1.3, 1.2, and 1.1, respectively,). There was no increase in hospitalizations or emergency room visits for respiratory symptoms in Years 2, 3, 4, and 5 compared to Year 1. The FVC and FEV1 values showed no deterioration over the 5 year period in the BT group. Similar results were obtained for the Control group. <br></br><br></br> <b>Conclusions:</b> The absence of clinical complications (based on AE reporting) and the maintenance of stable lung function (no deterioration of FVC and FEV1) over a 5-year period post-BT in this group of patients with moderate to severe asthma support the long-term safety of the procedure out to 5 years

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M

Growing smooth interfaces with inhomogeneous, moving external fields: dynamical transitions, devil's staircases and self-assembled ripples

We study the steady state structure and dynamics of an interface in a pure Ising system on a square lattice placed in an inhomogeneous external field. The field has a profile with a fixed shape designed to stabilize a flat interface, and is translated with velocity v_e. For small v_e, the interface is stuck to the profile, is macroscopically smooth, and is rippled with a periodicity in general incommensurate with the lattice parameter. For arbitrary orientations of the profile, the local slope of the interface locks in to one of infinitely many rational values (devil's staircase) which most closely approximates the profile. These ``lock-in'' structures and ripples dissappear as v_e increases. For still larger v_e the profile detaches from the interface which is now characterized by standard Kardar-Parisi-Zhang (KPZ) exponents.Comment: 4 pages, 4 figures, published version, minor change

Scheduling periodic tasks in a hard real-time environment

We consider a real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks $au_i=(c_i,p_i)$ on a minimum number of identical machines and to compute offsets $a_i$ for the tasks such that no collision occurs. A task $au_i$ releases a job of running time $c_i$ at each time $a_i + kcdot p_i,k in mathbb{N}_0$ and a collision occurs if two jobs are simultaneously active on the same machine. We shed some light on the complexity and approximability landscape of this problem. Although the problem cannot be approximated within a factor of $n^{1-varepsilon}$ for any $varepsilon>0$, an interesting restriction is much more tractable: If the periods are dividing (for each $i,j$ one has $p_i | p_j$ or $p_j | p_i$), the problem allows for a better structured representation of solutions, which leads to a 2-approximation. This result is tight, even asymptotically

Plasmon oscillations in ellipsoid nanoparticles: beyond dipole approximation

The plasmon oscillations of a metallic triaxial ellipsoid nanoparticle have been studied within the framework of the quasistatic approximation. A general method has been proposed for finding the analytical expressions describing the potential and frequencies of the plasmon oscillations of an arbitrary multipolarity order. The analytical expressions have been derived for an electric potential and plasmon oscillation frequencies of the first 24 modes. Other higher orders plasmon modes are investigated numerically.Comment: 33 pages, 12 figure

Theory and Computation of the Spheroidal Wave Functions

In this paper we report on a package, written in the Mathematica computer algebra system, which has been developed to compute the spheroidal wave functions of Meixner [J. Meixner and R.W. Schaefke, Mathieusche Funktionen und Sphaeroidfunktionen, 1954] and is available online (www.physics.uwa.edu.au/~falloon/spheroidal/spheroidal.html). This package represents a substantial contribution to the existing software, since it computes the spheroidal wave functions to arbitrary precision for general complex parameters mu, nu, gamma and argument z; existing software can only handle integer mu, nu and does not give arbitrary precision. The package also incorporates various special cases and computes analytic power series and asymptotic expansions in the parameter gamma. The spheroidal wave functions of Flammer [C. Flammer, Spheroidal Wave Functions, 1957] are included as a special case of Meixner's more general functions. This paper presents a concise review of the general theory of spheroidal wave functions and a description of the formulas and algorithms used in their computation, and gives high-precision numerical examples.Comment: 26 pages, 4 Appendices, 5 Table

Mathematica tools for quaternionic polynomials

In this paper we revisit the ring of (left) one-sided quaternionic polynomials with special focus on its zero structure. This area of research has attracted the attention of several authors and therefore it is natural to develop computational tools for working in this setting. The main contribution of this paper is a Mathematica collection of functions QPolynomial for solving polynomial problems that we frequently find in applications.(undefined)info:eu-repo/semantics/publishedVersio