A compact program code for simulations of quantum algorithms in classical computers

A general quantum simulation language on a classical computer provides the opportunity to compare an experiential result from the development of quantum computers with mathematical theory. The intention of this research is to develop a program language that is able to make simulations of all quantum algorithms in same framework. This study examines the simulation of quantum algorithms on a classical computer with a symbolic programming language. We use the language Mathematica to make simulations of well-known quantum algorithms. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. This gives us an uncomplicated and clear language for the implementations of algorithms. The computational language includes essential formulations such as quantum state, superposition and quantum operator. This symbolic programming language provides a universal framework for examining the existing as well as future quantum algorithms. This study contributes with an implementation of a quantum algorithm in a program code where the substance is applicable in other simulations of quantum algorithms.     

Physical layer secrecy of a cognitive radio with spatially correlated Alamouti OSTBC system

In this paper, an underlay spectrum-sharing system with Alamouti orthogonal space–time block coding (OSTBC) is considered to analyze and evaluate the physical layer security (PLS) performance of the cognitive radio system under a practical scenario with spatially correlated transmit antennas. It is assumed that there exists a passive eavesdropper and the cognitive channel and the wiretap channel follow Rayleigh fading distribution. To investigate and study the PLS performance of the cognitive system, first closed-form expressions are derived for three PLS metrics, namely: the probability of strictly-positive secrecy capacity (PSPSC), the secrecy outage probability (SOP), and the average secrecy capacity (ASC). Then numerical results obtained from the derived closed-form expressions are presented and validated by the computer simulations, to study the effects of spatial correlation on the PLS performance of the considered cognitive radio system under different parameters. It is shown that increasing the SNR of the cognitive system (Alice-to-Bob) channel yields an improvement in the PLS of the cognitive system. Moreover, a smaller value of the eavesdropping (Alice-to-Eve) channel SNR always leads to a better PLS for the cognitive system. It is also observed that the spatial correlation related to Alice-to-Bob channel degrades the PLS, and the spatial correlation related to Alice-to-Eve channel has less impact on the PLS performance.     

Correlated randomness and switching phenomena

One challenge of biology, medicine, and economics is that the systems treated by these serious scientific disciplines have no perfect metronome in time and no perfect spatial architecture—crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time and remarkably fine-tuned structures in space. Further, many of these processes and structures have the remarkable feature of “switching” from one behavior to another as if by magic. The past century has, philosophically, been concerned with placing aside the human tendency to see the universe as a fine-tuned machine. Here we will address the challenge of uncovering how, through randomness (albeit, as we shall see, strongly correlated randomness), one can arrive at some of the many spatial and temporal patterns in biology, medicine, and economics and even begin to characterize the switching phenomena that enables a system to pass from one state to another. Inspired by principles developed by A. Nihat Berker and scores of other statistical physicists in recent years, we discuss some applications of correlated randomness to understand switching phenomena in various fields. Specifically, we present evidence from experiments and from computer simulations supporting the hypothesis that water’s anomalies are related to a switching point (which is not unlike the “tipping point” immortalized by Malcolm Gladwell), and that the bubbles in economic phenomena that occur on all scales are not “outliers” (another Gladwell immortalization). Though more speculative, we support the idea of disease as arising from some kind of yet-to-be-understood complex switching phenomenon, by discussing data on selected examples, including heart disease and Alzheimer disease.     

Mathematical modeling of the heating of a fast ignition target by an ion beam

We develop a BIN computer code for simulating the interaction of a monochromatic ion beam with a plasma, which takes into account changes in the spatial distribution of the heated-plasma temperature. This enables us to calculate the heating of both homogeneous and inhomogeneous plasmas with parameters corresponding to their real spatial distributions at the time of maximum compression of the inertial confinement fusion (ICF) target. We present the results of a numerical simulation using the BIN code for the heating of a homogeneous deuterium–tritium plasma by a short pulse of monochromatic ions at various ion velocity and plasma–electron thermal velocity ratios. We also present the results of calculations for the heating of an inhomogeneous plasma of a non-cryogenic target formed as a beryllium deuteride–tritide shell by beams of light, medium, and heavy ions. As the initial distributions, we use the results of numerical simulations for such a target, precompressed by a laser pulse (carried out at the M. V. Keldysh Institute of Applied Mathematics using the DIANA code). We demonstrate the possibility of forming the central ignitor with the parameters sufficient for igniting the targets by beams of ions with energies E ~ 100 ? 400 MeV/u and specific energy densities of the beam Q ～ 5?20 GJ/cm². The required specific energy density drops with increase in the ion energy; however, due to the increased path length, larger-charge ions have to be used.     

Noise considerations in the determination of diffusion tensor anisotropy

In this study the noise sensitivity of various anisotropy indices has been investigated by Monte-Carlo computer simulations and magnetic resonance imaging (MRI) measurements in a phantom and 5 healthy volunteers. Particularly, we compared the noise performance of indices defined solely in terms of eigenvalues and those based on both the eigenvalues and eigenvectors. It is found that anisotropy indices based on both eigenvalues and eigenvectors are less sensitive to noise, and spatial averaging with neighboring pixels can further reduce the standard deviation. To reduce the partial volume effect caused by the spatial averaging with neighboring voxels, an averaging method in the time domain based on the orientation coherence of eigenvectors in repeated experiments has been proposed.     

A Gabor subband decomposition ICA and MRF hybrid algorithm for infrared image reconstruction from subpixel shifted sequences

An image blind reconstruction, as a blind source separation problem, has been solved recently by independent component analysis (ICA). Based on ICA theory, in this paper, a high resolution image is reconstructed from low resolution and subpixel shifted sequences captured by infrared microscan imaging system. The algorithm has the attractive feature that neither the prior knowledge of the blur kernel nor the value of subpixel misregistrations between the input channels is required. The statistical independence in the image domain is improved by the multiscale Gabor subband decompositions, which are designed for the best ability to cover the whole spatial frequency and to avoid overlapping between the subbands. The mutual information is employed to locate a subband with the least dependent components. In terms of MAP estimator, we combine the super-Gaussian with Markov random field to form a hybrid image distribution. This strategy helps to estimate the separating matrix reasonable to extract the sources with the image properties, that is, sharp enough as well as correlative in local area. The proposed algorithm is capable of performing high resolution image sources which are not strictly independent, and its viability is proved by the computer simulations and real experiments.     

Fluctuation-dominated kinetics in the a+b→0 reaction between immobile particles

We consider the accumulation of immobile particles landing on a one-dimensional lattice and annihilating via the A + B 0 bimolecular reaction. Here we focus on short-range interactions with cutoff. We investigate through computer simulations both the kinetics of the particles' accumulation and also their spatial distribution. The relation between the exponents describing the growth of the particles' concentration and the correlation length of their distribution shows that the kinetics of accumulation is fluctuation-dominated.This work is dedicated to Prof. George H. Weiss.     

Effects of interpolation methods in spatial normalization of diffusion tensor imaging data on group comparison of fractional anisotropy

This study investigated the effects on the measurement of fractional anisotropy (FA) during interpolation of diffusion tensor images in spatial normalization, which is required for voxel-based statistics. Diffusion tensor imaging data were obtained from nine male patients with attention deficit/hyperactivity disorder and nine age-matched control subjects. Regions of interest were selected from the genu of corpus callosum (GCC) and the right anterior corona radiata (RACR), with FA values measured before and after spatial normalization using two interpolation algorithms: linear and rotationally linear. Computer simulations were performed to verify the experimental findings. Between-group difference in FA was observed in the GCC and RACR before spatial normalization (P<.00001). Interpolation reduced the measured FA values significantly (P<.00001 for both algorithms) but did not affect the group difference in the GCC. For the RACR, the between-group difference vanished (P=.968) after linear interpolation but was relatively unaffected by using rotationally linear interpolation (P=.00001). FA histogram analysis and computer simulations confirmed these findings. This work suggests that caution should be exercised in voxel-based group comparisons as spatial normalization may affect the FA value in nonnegligible degrees, particularly in brain areas with predominantly crossing fibers.     

Computer simulations of the growth of breath figures

We describe computer simulations of the growth of breath figures, the patterns formed when droplets condense on a cold surface. The focus is on the coalescence of droplets, which is an important growth mechanism, and the conditions for self-similar patterns, which are experimentally observed. It is assumed that individual droplets grow according to a power law; droplets that touch coalesce instantly and are replaced by a new droplet at the center of gravity of the coalescing pair. The average droplet radius, distribution of droplet sizes, surface coverage, and radial distribution function are determined as a function of the time for a variety of initial coverages and polydispersities. These quantities are compared to those determined by experiment, and our simple model is found to be in good accord with the observed behavior. It is observed that the process of coalescence induces spatial correlation between droplets.This paper is dedicated to Howard Reiss on his 66th birthday.     

Singularities in speckled speckle: Statistics

Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary points) using analytical theory and computer simulations. We find anomalous spatial arrangements of the critical points and orders of magnitude anomalies in their relative number densities, and in the densities of the associated zero crossings.     

Large scale simulations of two-species annihilation,A+B→0, with drift

We present results of computer simulations of the diffusion-limited reaction process A+B→0, on the line, under extreme drift conditions, for lattices of up to 2²⁷ sites, and where the process proceeds to completion (no particles left). These enormous simulations are made possible by the renormalized reaction-cell method (RRC). Our results allow us to resolve an existing controversy about the rate of growth of domain sizes, and about corrections to scaling of the concentration decay.     

Entropy-driven phase transitions with influence of the field-dependent diffusion coefficient

We present a comprehensive study of phase transitions in a single-field reaction-diffusion stochastic systems with a field-dependent mobility of a power-law form and internal fluctuations. Using variational principles and mean-field theory we have shown that the noise can sustain spatial patterns and leads to phase transitions type of “order-disorder”. These phase transitions can be critical and non-critical in character. Our theoretical results are verified by computer simulations.     

Manifesting the Quantum World

In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. Being part of the Scientific Image of the world, the theory concerns the process by which (the physical aspect of) what Sellars called the Manifest Image of the world comes into being. This process consists in the progressive differentiation of an intrinsically undifferentiated entity. By entering into reflexive spatial relations, this entity gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified. If there is a distinctly quantum domain, it is a non-spatial and non-temporal dimension across which the transition from the unity of this entity to the multiplicity of the world takes place. Instead of being constituents of the physical world, subatomic particles, atoms, and molecules are instrumental in its manifestation. These conclusions are based on the following interpretive principle and its more direct consequences: whenever the calculation of probabilities calls for the addition of amplitudes, the distinctions we make between the alternatives lack objective reality. Applied to alternatives involving distinctions between regions of space, this principle implies that, owing to the indefiniteness of positions, the spatiotemporal differentiation of the physical world is incomplete: the existence of a real-valued spatiotemporal background is an unrealistic idealization. This guarantees the existence of observables whose values are real per se, as against “real by virtue of being indicated by the values of observables that are real per se.” Applied to alternatives involving distinctions between things, it implies that, intrinsically, all fundamental particles are numerically identical and thus identifiable with the aforementioned undifferentiated entity.     

Hopping behavior in the Kuramoto-Sivashinsky equation

We report the first observations of numerical "hopping" cellular flame patterns found in computer simulations of the Kuramoto-Sivashinsky equation. Hopping states are characterized by nonuniform rotations of a ring of cells, in which individual cells make abrupt changes in their angular positions while they rotate around the ring. Until now, these states have been observed only in experiments but not in truly two-dimensional computer simulations. A modal decomposition analysis of the simulated patterns, via the proper orthogonal decomposition, reveals spatio-temporal behavior in which the overall temporal dynamics is similar to that of equivalent experimental states but the spatial dynamics exhibits a few more features that are not seen in the experiments. Similarities in the temporal behavior and subtle differences in the spatial dynamics between numerical hopping states and their experimental counterparts are discussed in more detail.     

相对性区域创新指数与经济周期挖掘

提出了一类新的相对性区域创新指数,并采用世界专利申请数据对其进行了具体计算.基于区域创新同经济发展水平之间的超线性关系,该指数消除了经济发展水平对创新能力的影响,可以实现对不同发展水平的经济体之间进行有效的创新能力横纵对比.该创新指数尽管极其简单,却揭示出一系列迥异于传统认知的现象,例如中国大陆地区的技术创新能力在1980年代就已经位居世界前列.采用该指数,不但可以在较高水平上解释世界各国的经济增长,还发现它同经济增长率之间的相关性存在一个20年的经济周期.这些结果显示,该指数作为一个单一性指标,以极小的数据依赖就实现了较高程度的解释性,不但重新定位了世界各经济体的创新能力,对深入理解创新同经济发展之间的关系提供了新的角度,而且暗示着这类相对性经济指标的发展潜力与应用空间.     

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors.The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.     

Generation of quadratic spatial dark soliton in periodically poled lithium niobate

In this paper, we report the evolution of quadratic spatial dark soliton in periodically poled lithium niobate (PPLN). The generation of solitons pairs by wavefront modulation methods is investigated in both numerical simulations and experiments. We found that quadratic dark spatial solitons have analogue performances compared with that in χ⁽³⁾ defocusing Kerr media.     

On the efficiency of sovereign bond markets

The existence of memory in financial time series has been extensively studied for several stock markets around the world by means of different approaches. However, fixed income markets, i.e. those where corporate and sovereign bonds are traded, have been much less studied. We believe that, given the relevance of these markets, not only from the investors’, but also from the issuers’ point of view (government and firms), it is necessary to fill this gap in the literature. In this paper, we study the sovereign market efficiency of thirty bond indices of both developed and emerging countries, using an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This representation space allows us to establish an efficiency ranking of different markets and distinguish different bond market dynamics. We conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. Additionally, we find a correlation between permutation entropy, economic development and market size that could be of interest for policy makers and investors.