Directory of Open Access Journals (Sweden)
A. Klemm
1999-01-01
Full Text Available Distributions of basic characteristics of random mappings with a single absorbing center are calculated. Results explain some phenomena occurring in computer simulations of the logistic mapping.
Efficient $\\chi ^{2}$ Kernel Linearization via Random Feature Maps.
Yuan, Xiao-Tong; Wang, Zhenzhen; Deng, Jiankang; Liu, Qingshan
2016-11-01
Explicit feature mapping is an appealing way to linearize additive kernels, such as χ2 kernel for training large-scale support vector machines (SVMs). Although accurate in approximation, feature mapping could pose computational challenges in high-dimensional settings as it expands the original features to a higher dimensional space. To handle this issue in the context of χ2 kernel SVMs learning, we introduce a simple yet efficient method to approximately linearize χ2 kernel through random feature maps. The main idea is to use sparse random projection to reduce the dimensionality of feature maps while preserving their approximation capability to the original kernel. We provide approximation error bound for the proposed method. Furthermore, we extend our method to χ2 multiple kernel SVMs learning. Extensive experiments on large-scale image classification tasks confirm that the proposed approach is able to significantly speed up the training process of the χ2 kernel SVMs at almost no cost of testing accuracy.
Neurodynamics in Randomly Coupled Circle Maps
Matsuno, Tetsuya; Toko, Kiyoshi; Yamafuji, Kaoru
1996-05-01
The dynamics of retrieval processes in a system composed of coupled circle maps is studied by means of a statistical method and numerical simulations. Phase patterns are embedded in coupling parameters so that the system may work as an associative memory system. A parameter, which is an amplification factor multiplied to all the coupling strengths, is introduced for investigating the effect of the strength of the coupling nonlinearity on the behavior of the system concerned. The statistical method provides a set of time evolution equations representing the macroscopic behavior. It is found that the storage capacity is considerably enhanced by the introduced amplification factor. It is also shown that the system exhibits macroscopic chaotic oscillations when the strength of the coupling is sufficiently large. Moreover, the clustering is observed, as in other types of the globally coupled nonlinear systems.
Random-breakage mapping method applied to human DNA sequences
Lobrich, M.; Rydberg, B.; Cooper, P. K.; Chatterjee, A. (Principal Investigator)
1996-01-01
The random-breakage mapping method [Game et al. (1990) Nucleic Acids Res., 18, 4453-4461] was applied to DNA sequences in human fibroblasts. The methodology involves NotI restriction endonuclease digestion of DNA from irradiated calls, followed by pulsed-field gel electrophoresis, Southern blotting and hybridization with DNA probes recognizing the single copy sequences of interest. The Southern blots show a band for the unbroken restriction fragments and a smear below this band due to radiation induced random breaks. This smear pattern contains two discontinuities in intensity at positions that correspond to the distance of the hybridization site to each end of the restriction fragment. By analyzing the positions of those discontinuities we confirmed the previously mapped position of the probe DXS1327 within a NotI fragment on the X chromosome, thus demonstrating the validity of the technique. We were also able to position the probes D21S1 and D21S15 with respect to the ends of their corresponding NotI fragments on chromosome 21. A third chromosome 21 probe, D21S11, has previously been reported to be close to D21S1, although an uncertainty about a second possible location existed. Since both probes D21S1 and D21S11 hybridized to a single NotI fragment and yielded a similar smear pattern, this uncertainty is removed by the random-breakage mapping method.
The Poincaré Map of Randomly Perturbed Periodic Motion
Hitczenko, Pawel; Medvedev, Georgi S.
2013-10-01
A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and analyze the Poincaré map of the randomly perturbed periodic motion. We show that the time of the first exit from a small neighborhood of the fixed point of the map, which corresponds to the unperturbed periodic orbit, is well approximated by the geometric distribution. The parameter of the geometric distribution tends to zero together with the noise intensity. Therefore, our result can be interpreted as an estimate of the stability of periodic motion to random perturbations. In addition, we show that the geometric distribution of the first exit times translates into statistical properties of solutions of important differential equation models in applications. To this end, we demonstrate three distinct examples from mathematical neuroscience featuring complex oscillatory patterns characterized by the geometric distribution. We show that in each of these models the statistical properties of emerging oscillations are fully explained by the general properties of randomly perturbed periodic motions identified in this paper.
Maps of random walks on complex networks reveal community structure.
Rosvall, Martin; Bergstrom, Carl T
2008-01-29
To comprehend the multipartite organization of large-scale biological and social systems, we introduce an information theoretic approach that reveals community structure in weighted and directed networks. We use the probability flow of random walks on a network as a proxy for information flows in the real system and decompose the network into modules by compressing a description of the probability flow. The result is a map that both simplifies and highlights the regularities in the structure and their relationships. We illustrate the method by making a map of scientific communication as captured in the citation patterns of >6,000 journals. We discover a multicentric organization with fields that vary dramatically in size and degree of integration into the network of science. Along the backbone of the network-including physics, chemistry, molecular biology, and medicine-information flows bidirectionally, but the map reveals a directional pattern of citation from the applied fields to the basic sciences.
Random Wandering Around Homoclinic-like Manifolds in Symplectic Map Chain
Goto, Shin-itiro; Nozaki, Kazuhiro; Yamada, Hiroyasu
2001-01-01
We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behaviour. It is found that the modulational instability in the reduced map triggers random wandering of orbits around some homoclinic-like manifolds, which is understood as the Bernoulli shifts.
Random Wandering around Homoclinic-Like Manifolds in a Symplectic Map Chain
Shin-itiro, GOTO; Kazuhiro, NOZAKI; Hiroyasu, YAMADA; Department of Physics, Nagoya University
2002-01-01
We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behavior. It is found that the modulational instability in the reduced map triggers random wandering of orbits around some homoclinic-like manifolds. This behavior is understood as Bernoulli shifts.
Edgington, Eugene
2007-01-01
Statistical Tests That Do Not Require Random Sampling Randomization Tests Numerical Examples Randomization Tests and Nonrandom Samples The Prevalence of Nonrandom Samples in Experiments The Irrelevance of Random Samples for the Typical Experiment Generalizing from Nonrandom Samples Intelligibility Respect for the Validity of Randomization Tests Versatility Practicality Precursors of Randomization Tests Other Applications of Permutation Tests Questions and Exercises Notes References Randomized Experiments Unique Benefits of Experiments Experimentation without Mani
DYNAMIC STRAIN MAPPING AND REAL-TIME DAMAGE STATE ESTIMATION UNDER BIAXIAL RANDOM FATIGUE LOADING
National Aeronautics and Space Administration — DYNAMIC STRAIN MAPPING AND REAL-TIME DAMAGE STATE ESTIMATION UNDER BIAXIAL RANDOM FATIGUE LOADING SUBHASISH MOHANTY*, ADITI CHATTOPADHYAY, JOHN N. RAJADAS, AND CLYDE...
Improving the pseudo-randomness properties of chaotic maps using deep-zoom.
Machicao, Jeaneth; Bruno, Odemir M
2017-05-01
A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a "deep-zoom" manner by using k-digits to the right from the decimal separator of a given point from the underlying chaotic map. Interesting phenomena have been identified. Rapid randomization was observed, i.e., chaotic patterns tend to become indistinguishable when compared to the original orbits of the underlying chaotic map. Our results were presented using different graphical analyses (i.e., time-evolution, bifurcation diagram, Lyapunov exponent, Poincaré diagram, and frequency distribution). Moreover, taking advantage of this randomization improvement, we propose a Pseudo-Random Number Generator (PRNG) based on the k-logistic map. The pseudo-random qualities of the proposed PRNG passed both tests successfully, i.e., DIEHARD and NIST, and were comparable with other traditional PRNGs such as the Mersenne Twister. The results suggest that simple maps such as the logistic map can be considered as good PRNG methods.
Complexity and properties of a multidimensional Cat-Hadamard map for pseudo random number generation
Kim Hue, Ta Thi; Hoang, Thang Manh
2017-07-01
This paper presents a novel method to extend the Cat map from 2-dimension to higher dimension using the fast pseudo Hadamard Transform, and the resulted maps are called Cat-Hadamard maps. The complexity and properties of Cat-Hadamard maps are investigated under the point of view for cryptographic applications. In addition, we propose a method for constructing a pseudo random number generator using a novel design concept of the high dimensional Cat map. The simulation results show that the proposed generator fulfilled all the statistic tests of the NIST SP 800-90 A.
Constructing Binomial Trees Via Random Maps for Analysis of Financial Assets
Directory of Open Access Journals (Sweden)
Antonio Airton Carneiro de Freitas
2010-04-01
Full Text Available Random maps can be constructed from a priori knowledge of the financial assets. It is also addressed the reverse problem, i.e. from a function of an empirical stationary probability density function we set up a random map that naturally leads to an implied binomial tree, allowing the adjustment of models, including the ability to incorporate jumps. An applica- tion related to the options market is presented. It is emphasized that the quality of the model to incorporate a priori knowledge of the financial asset may be affected, for example, by the skewed vision of the analyst.
A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps
Petters, A. O.; Rider, B.; Teguia, A. M.
2009-07-01
Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory of stochastic microlensing. Beginning with the random time delay function and associated lensing map, we determine exact expressions for the mean and variance of these transformations. In addition, we derive the probability density function (pdf) of a random point-mass potential, which form the constituent of a stochastic microlens potential. We characterize the exact pdf of a normalized random time delay function at the origin, showing that it is a shifted gamma distribution, which also holds at leading order in the limit of a large number of point masses if the normalized time delay function was at a general point of the lens plane. For the large number of point-mass limit, we also prove that the asymptotic pdf of the random lensing map under a specified scaling converges to a bivariate normal distribution. We show analytically that the pdf of the random scaled lensing map at leading order depends on the magnitude of the scaled bending angle due purely to point masses as well as demonstrate explicitly how this radial symmetry is broken at the next order. Interestingly, we found at leading order a formula linking the expectation and variance of the normalized random time delay function to the first Betti number of its domain. We also determine an asymptotic pdf for the random bending angle vector and find an integral expression for the probability of a lens plane point being near a fixed point. Lastly, we show explicitly how the results are affected by location in the lens plane. The results of this paper are relevant to the theory of random fields and provide a platform for further generalizations as well as analytical limits for checking astrophysical studies of stochastic microlensing.
A tale of two "forests": random forest machine learning AIDS tropical forest carbon mapping.
Directory of Open Access Journals (Sweden)
Joseph Mascaro
Full Text Available Accurate and spatially-explicit maps of tropical forest carbon stocks are needed to implement carbon offset mechanisms such as REDD+ (Reduced Deforestation and Degradation Plus. The Random Forest machine learning algorithm may aid carbon mapping applications using remotely-sensed data. However, Random Forest has never been compared to traditional and potentially more reliable techniques such as regionally stratified sampling and upscaling, and it has rarely been employed with spatial data. Here, we evaluated the performance of Random Forest in upscaling airborne LiDAR (Light Detection and Ranging-based carbon estimates compared to the stratification approach over a 16-million hectare focal area of the Western Amazon. We considered two runs of Random Forest, both with and without spatial contextual modeling by including--in the latter case--x, and y position directly in the model. In each case, we set aside 8 million hectares (i.e., half of the focal area for validation; this rigorous test of Random Forest went above and beyond the internal validation normally compiled by the algorithm (i.e., called "out-of-bag", which proved insufficient for this spatial application. In this heterogeneous region of Northern Peru, the model with spatial context was the best preforming run of Random Forest, and explained 59% of LiDAR-based carbon estimates within the validation area, compared to 37% for stratification or 43% by Random Forest without spatial context. With the 60% improvement in explained variation, RMSE against validation LiDAR samples improved from 33 to 26 Mg C ha(-1 when using Random Forest with spatial context. Our results suggest that spatial context should be considered when using Random Forest, and that doing so may result in substantially improved carbon stock modeling for purposes of climate change mitigation.
A tale of two "forests": random forest machine learning AIDS tropical forest carbon mapping.
Mascaro, Joseph; Asner, Gregory P; Knapp, David E; Kennedy-Bowdoin, Ty; Martin, Roberta E; Anderson, Christopher; Higgins, Mark; Chadwick, K Dana
2014-01-01
Accurate and spatially-explicit maps of tropical forest carbon stocks are needed to implement carbon offset mechanisms such as REDD+ (Reduced Deforestation and Degradation Plus). The Random Forest machine learning algorithm may aid carbon mapping applications using remotely-sensed data. However, Random Forest has never been compared to traditional and potentially more reliable techniques such as regionally stratified sampling and upscaling, and it has rarely been employed with spatial data. Here, we evaluated the performance of Random Forest in upscaling airborne LiDAR (Light Detection and Ranging)-based carbon estimates compared to the stratification approach over a 16-million hectare focal area of the Western Amazon. We considered two runs of Random Forest, both with and without spatial contextual modeling by including--in the latter case--x, and y position directly in the model. In each case, we set aside 8 million hectares (i.e., half of the focal area) for validation; this rigorous test of Random Forest went above and beyond the internal validation normally compiled by the algorithm (i.e., called "out-of-bag"), which proved insufficient for this spatial application. In this heterogeneous region of Northern Peru, the model with spatial context was the best preforming run of Random Forest, and explained 59% of LiDAR-based carbon estimates within the validation area, compared to 37% for stratification or 43% by Random Forest without spatial context. With the 60% improvement in explained variation, RMSE against validation LiDAR samples improved from 33 to 26 Mg C ha(-1) when using Random Forest with spatial context. Our results suggest that spatial context should be considered when using Random Forest, and that doing so may result in substantially improved carbon stock modeling for purposes of climate change mitigation.
Diffusion MRI noise mapping using random matrix theory
Veraart, Jelle; Fieremans, Els; Novikov, Dmitry S.
2016-01-01
Purpose To estimate the spatially varying noise map using a redundant magnitude MR series. Methods We exploit redundancy in non-Gaussian multi-directional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of PCA eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions. Results We present a model-independent local noise mapping method capable of estimating noise level down to about 1% error. In contrast to current state-of-the art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal. Conclusions Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the PCA eigenspectrum in terms of the Marchenko-Pastur distribution. PMID:26599599
Fractal generator for efficient production of random planar patterns and symbols in digital mapping
Chen, Qiyu; Liu, Gang; Ma, Xiaogang; Li, Xinchuan; He, Zhenwen
2017-08-01
In digital cartography, the automatic generation of random planar patterns and symbols is still an ongoing challenge. Those patterns and symbols of randomness have randomly variated configurations and boundaries, and their generating algorithms are constrained by the shape features, cartographic standards and many other conditions. The fractal geometry offers favorable solutions to simulate random boundaries and patterns. In the work presented in this paper, we used both fractal theory and random Iterated Function Systems (IFS) to develop a method for the automatic generation of random planar patterns and symbols. The marshland and the trough cross-bedding patterns were used as two case studies for the implementation of the method. We first analyzed the morphological characteristics of those two planar patterns. Then we designed algorithms and implementation schemes addressing the features of each pattern. Finally, we ran the algorithms to generate the patterns and symbols, and compared them with the requirements of a few digital cartographic standards. The method presented in this paper has already been deployed in a digital mapping system for practical uses. The flexibility of the method also allows it to be reused and/or adapted in various software platforms for digital mapping.
Selecting a phoneme-to-grapheme mapping: Random or weighted selection?
Directory of Open Access Journals (Sweden)
Binna Lee
2015-05-01
Our findings demonstrate that random selection underestimates MOA’s PG correspondences whereas weighted selection predicts higher PG correspondences than he produces. To explain his intermediate spelling performance on PPEs, we will test additional approaches to weighing the relative probability of PG mappings, including using log frequencies, separating consonant and vowel status, and considering the number of grapheme options in each phoneme.
Analysis of family-wise error rates in statistical parametric mapping using random field theory.
Flandin, Guillaume; Friston, Karl J
2017-11-01
This technical report revisits the analysis of family-wise error rates in statistical parametric mapping-using random field theory-reported in (Eklund et al. []: arXiv 1511.01863). Contrary to the understandable spin that these sorts of analyses attract, a review of their results suggests that they endorse the use of parametric assumptions-and random field theory-in the analysis of functional neuroimaging data. We briefly rehearse the advantages parametric analyses offer over nonparametric alternatives and then unpack the implications of (Eklund et al. []: arXiv 1511.01863) for parametric procedures. Hum Brain Mapp, 2017. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.
UAV Remote Sensing for Urban Vegetation Mapping Using Random Forest and Texture Analysis
Directory of Open Access Journals (Sweden)
Quanlong Feng
2015-01-01
Full Text Available Unmanned aerial vehicle (UAV remote sensing has great potential for vegetation mapping in complex urban landscapes due to the ultra-high resolution imagery acquired at low altitudes. Because of payload capacity restrictions, off-the-shelf digital cameras are widely used on medium and small sized UAVs. The limitation of low spectral resolution in digital cameras for vegetation mapping can be reduced by incorporating texture features and robust classifiers. Random Forest has been widely used in satellite remote sensing applications, but its usage in UAV image classification has not been well documented. The objectives of this paper were to propose a hybrid method using Random Forest and texture analysis to accurately differentiate land covers of urban vegetated areas, and analyze how classification accuracy changes with texture window size. Six least correlated second-order texture measures were calculated at nine different window sizes and added to original Red-Green-Blue (RGB images as ancillary data. A Random Forest classifier consisting of 200 decision trees was used for classification in the spectral-textural feature space. Results indicated the following: (1 Random Forest outperformed traditional Maximum Likelihood classifier and showed similar performance to object-based image analysis in urban vegetation classification; (2 the inclusion of texture features improved classification accuracy significantly; (3 classification accuracy followed an inverted U relationship with texture window size. The results demonstrate that UAV provides an efficient and ideal platform for urban vegetation mapping. The hybrid method proposed in this paper shows good performance in differentiating urban vegetation mapping. The drawbacks of off-the-shelf digital cameras can be reduced by adopting Random Forest and texture analysis at the same time.
Methods of Reverberation Mapping. I. Time-lag Determination by Measures of Randomness
Chelouche, Doron; Nuñez, Francisco Pozo; Zucker, Shay
2017-01-01
A class of methods for measuring time delays between astronomical time series is introduced in the context of quasar reverberation mapping, which is based on measures of randomness or complexity of the data. Several distinct statistical estimators are considered that do not rely on polynomial interpolations of the light curves nor on their stochastic modeling, and do not require binning in correlation space. Methods based on von Neumann's mean-square successive-difference estimator are found ...
Local random quantum circuits: Ensemble completely positive maps and swap algebras
Energy Technology Data Exchange (ETDEWEB)
Zanardi, Paolo [Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA and Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore)
2014-08-15
We define different classes of local random quantum circuits (L-RQC) and show that (a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and (b) average purity dynamics can be described by the action of these maps on operator algebras of permutations (swap algebras). An exactly solvable one-dimensional case is analyzed to illustrate the power of the swap algebra formalism. More in general, we prove short time area-law bounds on average purity for uncorrelated L-RQC and infinite time results for both the uncorrelated and correlated cases.
Local random quantum circuits: Ensemble completely positive maps and swap algebras
Zanardi, Paolo
2014-08-01
We define different classes of local random quantum circuits (L-RQC) and show that (a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and (b) average purity dynamics can be described by the action of these maps on operator algebras of permutations (swap algebras). An exactly solvable one-dimensional case is analyzed to illustrate the power of the swap algebra formalism. More in general, we prove short time area-law bounds on average purity for uncorrelated L-RQC and infinite time results for both the uncorrelated and correlated cases.
Rapid Land Cover Map Updates Using Change Detection and Robust Random Forest Classifiers
Directory of Open Access Journals (Sweden)
Konrad J. Wessels
2016-10-01
Full Text Available The paper evaluated the Landsat Automated Land Cover Update Mapping (LALCUM system designed to rapidly update a land cover map to a desired nominal year using a pre-existing reference land cover map. The system uses the Iteratively Reweighted Multivariate Alteration Detection (IRMAD to identify areas of change and no change. The system then automatically generates large amounts of training samples (n > 1 million in the no-change areas as input to an optimized Random Forest classifier. Experiments were conducted in the KwaZulu-Natal Province of South Africa using a reference land cover map from 2008, a change mask between 2008 and 2011 and Landsat ETM+ data for 2011. The entire system took 9.5 h to process. We expected that the use of the change mask would improve classification accuracy by reducing the number of mislabeled training data caused by land cover change between 2008 and 2011. However, this was not the case due to exceptional robustness of Random Forest classifier to mislabeled training samples. The system achieved an overall accuracy of 65%–67% using 22 detailed classes and 72%–74% using 12 aggregated national classes. “Water”, “Plantations”, “Plantations—clearfelled”, “Orchards—trees”, “Sugarcane”, “Built-up/dense settlement”, “Cultivation—Irrigated” and “Forest (indigenous” had user’s accuracies above 70%. Other detailed classes (e.g., “Low density settlements”, “Mines and Quarries”, and “Cultivation, subsistence, drylands” which are required for operational, provincial-scale land use planning and are usually mapped using manual image interpretation, could not be mapped using Landsat spectral data alone. However, the system was able to map the 12 national classes, at a sufficiently high level of accuracy for national scale land cover monitoring. This update approach and the highly automated, scalable LALCUM system can improve the efficiency and update rate of regional land
ajansen; kwhitefoot; panteltje1; edprochak; sudhakar, the
2014-07-01
In reply to the physicsworld.com news story “How to make a quantum random-number generator from a mobile phone” (16 May, http://ow.ly/xFiYc, see also p5), which describes a way of delivering random numbers by counting the number of photons that impinge on each of the individual pixels in the camera of a Nokia N9 smartphone.
Energy Technology Data Exchange (ETDEWEB)
Dotsenko, Viktor S [Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow (Russian Federation)
2011-03-31
In the last two decades, it has been established that a single universal probability distribution function, known as the Tracy-Widom (TW) distribution, in many cases provides a macroscopic-level description of the statistical properties of microscopically different systems, including both purely mathematical ones, such as increasing subsequences in random permutations, and quite physical ones, such as directed polymers in random media or polynuclear crystal growth. In the first part of this review, we use a number of models to examine this phenomenon at a simple qualitative level and then consider the exact solution for one-dimensional directed polymers in a random environment, showing that free energy fluctuations in such a system are described by the universal TW distribution. The second part provides detailed appendix material containing the necessary mathematical background for the first part. (reviews of topical problems)
A Joint Land Cover Mapping and Image Registration Algorithm Based on a Markov Random Field Model
Directory of Open Access Journals (Sweden)
Apisit Eiumnoh
2013-10-01
Full Text Available Traditionally, image registration of multi-modal and multi-temporal images is performed satisfactorily before land cover mapping. However, since multi-modal and multi-temporal images are likely to be obtained from different satellite platforms and/or acquired at different times, perfect alignment is very difficult to achieve. As a result, a proper land cover mapping algorithm must be able to correct registration errors as well as perform an accurate classification. In this paper, we propose a joint classification and registration technique based on a Markov random field (MRF model to simultaneously align two or more images and obtain a land cover map (LCM of the scene. The expectation maximization (EM algorithm is employed to solve the joint image classification and registration problem by iteratively estimating the map parameters and approximate posterior probabilities. Then, the maximum a posteriori (MAP criterion is used to produce an optimum land cover map. We conducted experiments on a set of four simulated images and one pair of remotely sensed images to investigate the effectiveness and robustness of the proposed algorithm. Our results show that, with proper selection of a critical MRF parameter, the resulting LCMs derived from an unregistered image pair can achieve an accuracy that is as high as when images are perfectly aligned. Furthermore, the registration error can be greatly reduced.
Matula, Dominik
2013-01-01
The author summarizes some previous results concerning random triangles. He describes the Gaussian triangle and random triangles whose vertices lie in a unit n-dimensional ball, in a rectangle or in a general bounded convex set. In the second part, the author deals with an inscribed triangle in a triangle - let ABC be an equilateral triangle and let M, N, O be three points, each laying on one side of the ABC. We call MNO inscribed triangle (in an equi- laterral triangle). The median triangle ...
Mehta, Madan Lal
1990-01-01
Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications. This book presents a coherent and detailed analytical treatment of random matrices, leading
Mapping Deforestation in North Korea Using Phenology-Based Multi-Index and Random Forest
Directory of Open Access Journals (Sweden)
Yihua Jin
2016-12-01
Full Text Available Phenology-based multi-index with the random forest (RF algorithm can be used to overcome the shortcomings of traditional deforestation mapping that involves pixel-based classification, such as ISODATA or decision trees, and single images. The purpose of this study was to investigate methods to identify specific types of deforestation in North Korea, and to increase the accuracy of classification, using phenological characteristics extracted with multi-index and random forest algorithms. The mapping of deforestation area based on RF was carried out by merging phenology-based multi-indices (i.e., normalized difference vegetation index (NDVI, normalized difference water index (NDWI, and normalized difference soil index (NDSI derived from MODIS (Moderate Resolution Imaging Spectroradiometer products and topographical variables. Our results showed overall classification accuracy of 89.38%, with corresponding kappa coefficients of 0.87. In particular, for forest and farm land categories with similar phenological characteristic (e.g., paddy, plateau vegetation, unstocked forest, hillside field, this approach improved the classification accuracy in comparison with pixel-based methods and other classes. The deforestation types were identified by incorporating point data from high-resolution imagery, outcomes of image classification, and slope data. Our study demonstrated that the proposed methodology could be used for deciding on the restoration priority and monitoring the expansion of deforestation areas.
Hengl, Tomislav; Heuvelink, Gerard B. M.; Kempen, Bas; Leenaars, Johan G. B.; Walsh, Markus G.; Shepherd, Keith D.; Sila, Andrew; MacMillan, Robert A.; Mendes de Jesus, Jorge; Tamene, Lulseged; Tondoh, Jérôme E.
2015-01-01
80% of arable land in Africa has low soil fertility and suffers from physical soil problems. Additionally, significant amounts of nutrients are lost every year due to unsustainable soil management practices. This is partially the result of insufficient use of soil management knowledge. To help bridge the soil information gap in Africa, the Africa Soil Information Service (AfSIS) project was established in 2008. Over the period 2008–2014, the AfSIS project compiled two point data sets: the Africa Soil Profiles (legacy) database and the AfSIS Sentinel Site database. These data sets contain over 28 thousand sampling locations and represent the most comprehensive soil sample data sets of the African continent to date. Utilizing these point data sets in combination with a large number of covariates, we have generated a series of spatial predictions of soil properties relevant to the agricultural management—organic carbon, pH, sand, silt and clay fractions, bulk density, cation-exchange capacity, total nitrogen, exchangeable acidity, Al content and exchangeable bases (Ca, K, Mg, Na). We specifically investigate differences between two predictive approaches: random forests and linear regression. Results of 5-fold cross-validation demonstrate that the random forests algorithm consistently outperforms the linear regression algorithm, with average decreases of 15–75% in Root Mean Squared Error (RMSE) across soil properties and depths. Fitting and running random forests models takes an order of magnitude more time and the modelling success is sensitive to artifacts in the input data, but as long as quality-controlled point data are provided, an increase in soil mapping accuracy can be expected. Results also indicate that globally predicted soil classes (USDA Soil Taxonomy, especially Alfisols and Mollisols) help improve continental scale soil property mapping, and are among the most important predictors. This indicates a promising potential for transferring pedological
Monte Carlo Random-Walk Experiments as a Test of Chaotic Orbits of Maps of the Interval
Arneodo, A.; Sornette, D.
1984-05-01
We have performed Monte Carlo random-walk experiments on a one-dimensional periodic lattice with a trapping site using the logistic map as a generator of pseudorandom numbers. Comparison with analytical results indicates that, when it has sensitive dependence to the initial conditions, this map provides a true pseudorandom generator.
Acosta, Juan; Penela, Diego; Andreu, David; Cabrera, Mario; Carlosena, Alicia; Vassanelli, Francesca; Alarcón, Francisco; Soto-Iglesias, David; Korshunov, Viatcheslav; Borras, Roger; Linhart, Markus; Martínez, Mikel; Fernández-Armenta, Juan; Mont, Lluis; Berruezo, Antonio
2017-01-08
Ventricular tachycardia (VT) substrate ablation is based on detailed electroanatomical maps (EAM). This study analyses whether high-density multielectrode mapping (MEM) is superior to conventional point-by-point mapping (PPM) in guiding VT substrate ablation procedures. This was a randomized controlled study (NCT02083016). Twenty consecutive ischemic patients undergoing VT substrate ablation were randomized to either group A [n = 10; substrate mapping performed first by PPM (Navistar) and secondly by MEM (PentaRay) ablation guided by PPM] or group B [n = 10; substrate mapping performed first by MEM and second by PPM ablation guided by MEM]. Ablation was performed according to the scar-dechanneling technique. Late potential (LP) pairs were defined as a Navistar-LP and a PentaRay-LP located within a three-dimensional distance of ≤ 3 mm. Data obtained from EAM, procedure time, radiofrequency time, and post-ablation VT inducibility were compared between groups. Larger bipolar scar areas were obtained with MEM (55.7±31.7 vs. 50.5±26.6 cm(2); P = 0.017). Substrate mapping time was similar with MEM (19.7±7.9 minutes) and PPM (25±9.2 minutes); P = 0.222. No differences were observed in the number of LPs identified within the scar by MEM vs. PPM (73±50 vs. 76±52 LPs per patient, respectively; P = 0.965). A total of 1104 LP pairs were analysed. Using PentaRay, far-field/LP ratio was significantly lower (0.58±0.4 vs. 1.64±1.1; P = 0.01) and radiofrequency time was shorter [median (interquartile range) 12 (7-20) vs. 22 (17-33) minutes; P = 0.023]. No differences were observed in VT inducibility after procedure. MEM with PentaRay catheter provided better discrimination of LPs due to a lower sensitivity for far-field signals. Ablation guided by MEM was associated with a shorter radiofrequency time. Published on behalf of the European Society of Cardiology. All rights reserved. © The Author 2017. For permissions, please email
Random walks in a random environment
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the 'quenched' and the 'averaged' case. Keywords. Large deviations; random walks in a random environment. 1. Introduction. A random walk on Zd is a stochastic ...
Eisavi, Vahid; Homayouni, Saeid; Yazdi, Ahmad Maleknezhad; Alimohammadi, Abbas
2015-05-01
Thematic mapping of complex landscapes, with various phenological patterns from satellite imagery, is a particularly challenging task. However, supplementary information, such as multitemporal data and/or land surface temperature (LST), has the potential to improve the land cover classification accuracy and efficiency. In this paper, in order to map land covers, we evaluated the potential of multitemporal Landsat 8's spectral and thermal imageries using a random forest (RF) classifier. We used a grid search approach based on the out-of-bag (OOB) estimate of error to optimize the RF parameters. Four different scenarios were considered in this research: (1) RF classification of multitemporal spectral images, (2) RF classification of multitemporal LST images, (3) RF classification of all multitemporal LST and spectral images, and (4) RF classification of selected important or optimum features. The study area in this research was Naghadeh city and its surrounding region, located in West Azerbaijan Province, northwest of Iran. The overall accuracies of first, second, third, and fourth scenarios were equal to 86.48, 82.26, 90.63, and 91.82%, respectively. The quantitative assessments of the results demonstrated that the most important or optimum features increase the class separability, while the spectral and thermal features produced a more moderate increase in the land cover mapping accuracy. In addition, the contribution of the multitemporal thermal information led to a considerable increase in the user and producer accuracies of classes with a rapid temporal change behavior, such as crops and vegetation.
A new fate mapping system reveals context-dependent random or clonal expansion of microglia.
Tay, Tuan Leng; Mai, Dominic; Dautzenberg, Jana; Fernández-Klett, Francisco; Lin, Gen; Sagar; Datta, Moumita; Drougard, Anne; Stempfl, Thomas; Ardura-Fabregat, Alberto; Staszewski, Ori; Margineanu, Anca; Sporbert, Anje; Steinmetz, Lars M; Pospisilik, J Andrew; Jung, Steffen; Priller, Josef; Grün, Dominic; Ronneberger, Olaf; Prinz, Marco
2017-06-01
Microglia constitute a highly specialized network of tissue-resident immune cells that is important for the control of tissue homeostasis and the resolution of diseases of the CNS. Little is known about how their spatial distribution is established and maintained in vivo. Here we establish a new multicolor fluorescence fate mapping system to monitor microglial dynamics during steady state and disease. Our findings suggest that microglia establish a dense network with regional differences, and the high regional turnover rates found challenge the universal concept of microglial longevity. Microglial self-renewal under steady state conditions constitutes a stochastic process. During pathology this randomness shifts to selected clonal microglial expansion. In the resolution phase, excess disease-associated microglia are removed by a dual mechanism of cell egress and apoptosis to re-establish the stable microglial network. This study unravels the dynamic yet discrete self-organization of mature microglia in the healthy and diseased CNS.
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Random functions and turbulence
Panchev, S
1971-01-01
International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical moments by characteristic functions; functional transformations of random variables; multidimensional random variables with spherical symmetry; and random variables and distribution functions. The book then discusses random processes and random fields, including stationarity and ergodicity of random
DEFF Research Database (Denmark)
Møller, Anders Bjørn; Malone, Brendan P.; Odgers, Nathan
algorithm were evaluated. The resulting maps were validated on 777 soil profiles situated in a grid covering Denmark. The experiments showed that the results obtained with Jacobsen’s map were more accurate than the results obtained with the CEC map, despite a nominally coarser scale of 1:2,000,000 vs. 1...... of European Communities (CEC, 1985) respectively, both using the FAO 1974 classification. Furthermore, the effects of implementing soil-landscape relationships, using area proportional sampling instead of per polygon sampling, and replacing the default C5.0 classification tree algorithm with a random forest......:1,000,000. This finding is probably related to the fact that Jacobsen’s map was more detailed with a larger number of polygons, soil map units and soil types, despite its coarser scale. The results showed that the implementation of soil-landscape relationships, area-proportional sampling and the random forest...
Directory of Open Access Journals (Sweden)
Pierre Dubeau
2017-10-01
Full Text Available The Dabus Wetland complex in the highlands of Ethiopia is within the headwaters of the Nile Basin and is home to significant ecological communities and rare or endangered species. Its many interrelated wetland types undergo seasonal and longer-term changes due to weather and climate variations as well as anthropogenic land use such as grazing and burning. Mapping and monitoring of these wetlands has not been previously undertaken due primarily to their relative isolation and lack of resources. This study investigated the potential of remote sensing based classification for mapping the primary vegetation groups in the Dabus Wetlands using a combination of dry and wet season data, including optical (Landsat spectral bands and derived vegetation and wetness indices, radar (ALOS PALSAR L-band backscatter, and elevation (SRTM derived DEM and other terrain metrics as inputs to the non-parametric Random Forest (RF classifier. Eight wetland types and three terrestrial/upland classes were mapped using field samples of observed plant community composition and structure groupings as reference information. Various tests to compare results using different RF input parameters and data types were conducted. A combination of multispectral optical, radar and topographic variables provided the best overall classification accuracy, 94.4% and 92.9% for the dry and wet season, respectively. Spectral and topographic data (radar data excluded performed nearly as well, while accuracies using only radar and topographic data were 82–89%. Relatively homogeneous classes such as Papyrus Swamps, Forested Wetland, and Wet Meadow yielded the highest accuracies while spatially complex classes such as Emergent Marsh were more difficult to accurately classify. The methods and results presented in this paper can serve as a basis for development of long-term mapping and monitoring of these and other non-forested wetlands in Ethiopia and other similar environmental settings.
Haron, Zaiton; Bakar, Suhaimi Abu; Dimon, Mohamad Ngasri
2015-01-01
Strategic noise mapping provides important information for noise impact assessment and noise abatement. However, producing reliable strategic noise mapping in a dynamic, complex working environment is difficult. This study proposes the implementation of the random walk approach as a new stochastic technique to simulate noise mapping and to predict the noise exposure level in a workplace. A stochastic simulation framework and software, namely RW-eNMS, were developed to facilitate the random walk approach in noise mapping prediction. This framework considers the randomness and complexity of machinery operation and noise emission levels. Also, it assesses the impact of noise on the workers and the surrounding environment. For data validation, three case studies were conducted to check the accuracy of the prediction data and to determine the efficiency and effectiveness of this approach. The results showed high accuracy of prediction results together with a majority of absolute differences of less than 2 dBA; also, the predicted noise doses were mostly in the range of measurement. Therefore, the random walk approach was effective in dealing with environmental noises. It could predict strategic noise mapping to facilitate noise monitoring and noise control in the workplaces. PMID:25875019
Random Numbers and Quantum Computers
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
The Utility of AISA Eagle Hyperspectral Data and Random Forest Classifier for Flower Mapping
Directory of Open Access Journals (Sweden)
Elfatih M. Abdel-Rahman
2015-10-01
Full Text Available Knowledge of the floral cycle and the spatial distribution and abundance of flowering plants is important for bee health studies to understand the relationship between landscape and bee hive productivity and honey flow. The key objective of this study was to show how AISA Eagle hyperspectral data and random forest (RF can be optimally utilized to produce flowering and spatially explicit land use/land cover (LULC maps for a study site in Kenya. AISA Eagle imagery was captured at the early flowering period (January 2014 and at the peak flowering season (February 2013. Data on white and yellow flowering trees as well as LULC classes in the study area were collected and used as ground-truth points. We utilized all 64 AISA Eagle bands and also used variable importance in RF to identify the most important bands in both AISA Eagle data sets. The results showed that flowering was most accurately mapped using the AISA Eagle data from the peak flowering period (85.71%–88.15% overall accuracy for the peak flowering season imagery versus 80.82%–83.67% for the early flowering season. The variable optimization (i.e., variable selection analysis showed that less than half of the AISA bands (n = 26 for the February 2013 data and n = 21 for the January 2014 data were important to attain relatively reliable classification accuracies. Our study is an important first step towards the development of operational flower mapping routines and for understanding the relationship between flowering and bees’ foraging behavior.
Random fixed points and random differential inclusions
Directory of Open Access Journals (Sweden)
Nikolaos S. Papageorgiou
1988-01-01
Full Text Available In this paper, first, we study random best approximations to random sets, using fixed point techniques, obtaining this way stochastic analogues of earlier deterministic results by Browder-Petryshyn, KyFan and Reich. Then we prove two fixed point theorems for random multifunctions with stochastic domain that satisfy certain tangential conditions. Finally we consider a random differential inclusion with upper semicontinuous orientor field and establish the existence of random solutions.
On the design of henon and logistic map-based random number generator
Magfirawaty; Suryadi, M. T.; Ramli, Kalamullah
2017-10-01
The key sequence is one of the main elements in the cryptosystem. True Random Number Generators (TRNG) method is one of the approaches to generating the key sequence. The randomness source of the TRNG divided into three main groups, i.e. electrical noise based, jitter based and chaos based. The chaos based utilizes a non-linear dynamic system (continuous time or discrete time) as an entropy source. In this study, a new design of TRNG based on discrete time chaotic system is proposed, which is then simulated in LabVIEW. The principle of the design consists of combining 2D and 1D chaotic systems. A mathematical model is implemented for numerical simulations. We used comparator process as a harvester method to obtain the series of random bits. Without any post processing, the proposed design generated random bit sequence with high entropy value and passed all NIST 800.22 statistical tests.
Directory of Open Access Journals (Sweden)
Wampler Peter J
2013-01-01
Full Text Available Abstract Background A remote sensing technique was developed which combines a Geographic Information System (GIS; Google Earth, and Microsoft Excel to identify home locations for a random sample of households in rural Haiti. The method was used to select homes for ethnographic and water quality research in a region of rural Haiti located within 9 km of a local hospital and source of health education in Deschapelles, Haiti. The technique does not require access to governmental records or ground based surveys to collect household location data and can be performed in a rapid, cost-effective manner. Methods The random selection of households and the location of these households during field surveys were accomplished using GIS, Google Earth, Microsoft Excel, and handheld Garmin GPSmap 76CSx GPS units. Homes were identified and mapped in Google Earth, exported to ArcMap 10.0, and a random list of homes was generated using Microsoft Excel which was then loaded onto handheld GPS units for field location. The development and use of a remote sensing method was essential to the selection and location of random households. Results A total of 537 homes initially were mapped and a randomized subset of 96 was identified as potential survey locations. Over 96% of the homes mapped using Google Earth imagery were correctly identified as occupied dwellings. Only 3.6% of the occupants of mapped homes visited declined to be interviewed. 16.4% of the homes visited were not occupied at the time of the visit due to work away from the home or market days. A total of 55 households were located using this method during the 10 days of fieldwork in May and June of 2012. Conclusions The method used to generate and field locate random homes for surveys and water sampling was an effective means of selecting random households in a rural environment lacking geolocation infrastructure. The success rate for locating households using a handheld GPS was excellent and only
Wampler, Peter J; Rediske, Richard R; Molla, Azizur R
2013-01-18
A remote sensing technique was developed which combines a Geographic Information System (GIS); Google Earth, and Microsoft Excel to identify home locations for a random sample of households in rural Haiti. The method was used to select homes for ethnographic and water quality research in a region of rural Haiti located within 9 km of a local hospital and source of health education in Deschapelles, Haiti. The technique does not require access to governmental records or ground based surveys to collect household location data and can be performed in a rapid, cost-effective manner. The random selection of households and the location of these households during field surveys were accomplished using GIS, Google Earth, Microsoft Excel, and handheld Garmin GPSmap 76CSx GPS units. Homes were identified and mapped in Google Earth, exported to ArcMap 10.0, and a random list of homes was generated using Microsoft Excel which was then loaded onto handheld GPS units for field location. The development and use of a remote sensing method was essential to the selection and location of random households. A total of 537 homes initially were mapped and a randomized subset of 96 was identified as potential survey locations. Over 96% of the homes mapped using Google Earth imagery were correctly identified as occupied dwellings. Only 3.6% of the occupants of mapped homes visited declined to be interviewed. 16.4% of the homes visited were not occupied at the time of the visit due to work away from the home or market days. A total of 55 households were located using this method during the 10 days of fieldwork in May and June of 2012. The method used to generate and field locate random homes for surveys and water sampling was an effective means of selecting random households in a rural environment lacking geolocation infrastructure. The success rate for locating households using a handheld GPS was excellent and only rarely was local knowledge required to identify and locate households. This
Methods of Reverberation Mapping. I. Time-lag Determination by Measures of Randomness
Energy Technology Data Exchange (ETDEWEB)
Chelouche, Doron; Pozo-Nuñez, Francisco [Department of Physics, Faculty of Natural Sciences, University of Haifa, Haifa 3498838 (Israel); Zucker, Shay, E-mail: doron@sci.haifa.ac.il, E-mail: francisco.pozon@gmail.com, E-mail: shayz@post.tau.ac.il [Department of Geosciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801 (Israel)
2017-08-01
A class of methods for measuring time delays between astronomical time series is introduced in the context of quasar reverberation mapping, which is based on measures of randomness or complexity of the data. Several distinct statistical estimators are considered that do not rely on polynomial interpolations of the light curves nor on their stochastic modeling, and do not require binning in correlation space. Methods based on von Neumann’s mean-square successive-difference estimator are found to be superior to those using other estimators. An optimized von Neumann scheme is formulated, which better handles sparsely sampled data and outperforms current implementations of discrete correlation function methods. This scheme is applied to existing reverberation data of varying quality, and consistency with previously reported time delays is found. In particular, the size–luminosity relation of the broad-line region in quasars is recovered with a scatter comparable to that obtained by other works, yet with fewer assumptions made concerning the process underlying the variability. The proposed method for time-lag determination is particularly relevant for irregularly sampled time series, and in cases where the process underlying the variability cannot be adequately modeled.
Methods of Reverberation Mapping. I. Time-lag Determination by Measures of Randomness
Chelouche, Doron; Pozo-Nuñez, Francisco; Zucker, Shay
2017-08-01
A class of methods for measuring time delays between astronomical time series is introduced in the context of quasar reverberation mapping, which is based on measures of randomness or complexity of the data. Several distinct statistical estimators are considered that do not rely on polynomial interpolations of the light curves nor on their stochastic modeling, and do not require binning in correlation space. Methods based on von Neumann’s mean-square successive-difference estimator are found to be superior to those using other estimators. An optimized von Neumann scheme is formulated, which better handles sparsely sampled data and outperforms current implementations of discrete correlation function methods. This scheme is applied to existing reverberation data of varying quality, and consistency with previously reported time delays is found. In particular, the size-luminosity relation of the broad-line region in quasars is recovered with a scatter comparable to that obtained by other works, yet with fewer assumptions made concerning the process underlying the variability. The proposed method for time-lag determination is particularly relevant for irregularly sampled time series, and in cases where the process underlying the variability cannot be adequately modeled.
Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry
Mayer, Volker; Skorulski, Bartlomiej
2011-01-01
The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic syst...
DEFF Research Database (Denmark)
Paolini, Enrico; Stefanovic, Cedomir; Liva, Gianluigi
2015-01-01
, in which the structure of the access protocol can be mapped to a structure of an erasure-correcting code defined on graph. This opens the possibility to use coding theory and tools for designing efficient random access protocols, offering markedly better performance than ALOHA. Several instances of coded......The rise of machine-to-machine communications has rekindled the interest in random access protocols as a support for a massive number of uncoordinatedly transmitting devices. The legacy ALOHA approach is developed under a collision model, where slots containing collided packets are considered...... as waste. However, if the common receiver (e.g., base station) is capable to store the collision slots and use them in a transmission recovery process based on successive interference cancellation, the design space for access protocols is radically expanded. We present the paradigm of coded random access...
Polymer Dynamics in Random Media, Replica Theory, Ternary Systems: Mappings and Equivalences
U. Ebert (Ute); L. Schäfer
1994-01-01
htmlabstractFor polymer dynamics in quenched random media a renormalizability proof is lacking and calculations are lengthy. We here propose and define the static and the ergodic limit of the dynamic theory, and show, that these limits are equivalent to well-known renormalizable static polymer
Random broadcast on random geometric graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
Ergodicity of Random Walks on Random DFA
Balle, Borja
2013-01-01
Given a DFA we consider the random walk that starts at the initial state and at each time step moves to a new state by taking a random transition from the current state. This paper shows that for typical DFA this random walk induces an ergodic Markov chain. The notion of typical DFA is formalized by showing that ergodicity holds with high probability when a DFA is sampled uniformly at random from the set of all automata with a fixed number of states. We also show the same result applies to DF...
Random fractional Fourier transform.
Liu, Zhengjun; Liu, Shutian
2007-08-01
We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers.
Random walks in a random environment
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 114; Issue 4. Random Walks in a Random Environment. S R S Varadhan. Invited Articles Volume 114 Issue ... Author Affiliations. S R S Varadhan1. Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, NY 10012, USA ...
Random walks on random Koch curves
Energy Technology Data Exchange (ETDEWEB)
Seeger, S; Hoffmann, K H [Institut fuer Physik, Technische Universitaet, D-09107 Chemnitz (Germany); Essex, C [Department of Applied Mathematics, University of Western Ontario, London, ON N6A 5B7 (Canada)
2009-06-05
Diffusion processes in porous materials are often modeled as random walks on fractals. In order to capture the randomness of the materials random fractals are employed, which no longer show the deterministic self-similarity of regular fractals. Finding a continuum differential equation describing the diffusion on such fractals has been a long-standing goal, and we address the question of whether the concepts developed for regular fractals are still applicable. We use the random Koch curve as a convenient example as it provides certain technical advantages by its separation of time and space features. While some of the concepts developed for regular fractals can be used unaltered, others have to be modified. Based on the concept of fibers, we introduce ensemble-averaged density functions which produce a differentiable estimate of probability explicitly and compare it to random walk data.
Directory of Open Access Journals (Sweden)
Quanlong Feng
2015-03-01
Full Text Available Flooding is a severe natural hazard, which poses a great threat to human life and property, especially in densely-populated urban areas. As one of the fastest developing fields in remote sensing applications, an unmanned aerial vehicle (UAV can provide high-resolution data with a great potential for fast and accurate detection of inundated areas under complex urban landscapes. In this research, optical imagery was acquired by a mini-UAV to monitor the serious urban waterlogging in Yuyao, China. Texture features derived from gray-level co-occurrence matrix were included to increase the separability of different ground objects. A Random Forest classifier, consisting of 200 decision trees, was used to extract flooded areas in the spectral-textural feature space. Confusion matrix was used to assess the accuracy of the proposed method. Results indicated the following: (1 Random Forest showed good performance in urban flood mapping with an overall accuracy of 87.3% and a Kappa coefficient of 0.746; (2 the inclusion of texture features improved classification accuracy significantly; (3 Random Forest outperformed maximum likelihood and artificial neural network, and showed a similar performance to support vector machine. The results demonstrate that UAV can provide an ideal platform for urban flood monitoring and the proposed method shows great capability for the accurate extraction of inundated areas.
Vogels, M. F. A.; de Jong, S. M.; Sterk, G.; Addink, E. A.
2017-02-01
Land-use and land-cover (LULC) conversions have an important impact on land degradation, erosion and water availability. Information on historical land cover (change) is crucial for studying and modelling land- and ecosystem degradation. During the past decades major LULC conversions occurred in Africa, Southeast Asia and South America as a consequence of a growing population and economy. Most distinct is the conversion of natural vegetation into cropland. Historical LULC information can be derived from satellite imagery, but these only date back until approximately 1972. Before the emergence of satellite imagery, landscapes were monitored by black-and-white (B&W) aerial photography. This photography is often visually interpreted, which is a very time-consuming approach. This study presents an innovative, semi-automated method to map cropland acreage from B&W photography. Cropland acreage was mapped on two study sites in Ethiopia and in The Netherlands. For this purpose we used Geographic Object-Based Image Analysis (GEOBIA) and a Random Forest classification on a set of variables comprising texture, shape, slope, neighbour and spectral information. Overall mapping accuracies attained are 90% and 96% for the two study areas respectively. This mapping method increases the timeline at which historical cropland expansion can be mapped purely from brightness information in B&W photography up to the 1930s, which is beneficial for regions where historical land-use statistics are mostly absent.
Giabbanelli, Philippe J; Crutzen, Rik
2014-12-12
Controlling bias is key to successful randomized controlled trials for behaviour change. Bias can be generated at multiple points during a study, for example, when participants are allocated to different groups. Several methods of allocations exist to randomly distribute participants over the groups such that their prognostic factors (e.g., socio-demographic variables) are similar, in an effort to keep participants' outcomes comparable at baseline. Since it is challenging to create such groups when all prognostic factors are taken together, these factors are often balanced in isolation or only the ones deemed most relevant are balanced. However, the complex interactions among prognostic factors may lead to a poor estimate of behaviour, causing unbalanced groups at baseline, which may introduce accidental bias. We present a novel computational approach for allocating participants to different groups. Our approach automatically uses participants' experiences to model (the interactions among) their prognostic factors and infer how their behaviour is expected to change under a given intervention. Participants are then allocated based on their inferred behaviour rather than on selected prognostic factors. In order to assess the potential of our approach, we collected two datasets regarding the behaviour of participants (n = 430 and n = 187). The potential of the approach on larger sample sizes was examined using synthetic data. All three datasets highlighted that our approach could lead to groups with similar expected behavioural changes. The computational approach proposed here can complement existing statistical approaches when behaviours involve numerous complex relationships, and quantitative data is not readily available to model these relationships. The software implementing our approach and commonly used alternatives is provided at no charge to assist practitioners in the design of their own studies and to compare participants' allocations.
Ahmed, Sara; Ernst, Pierre; Bartlett, Susan J; Valois, Marie-France; Zaihra, Tasneem; Paré, Guy; Grad, Roland; Eilayyan, Owis; Perreault, Robert; Tamblyn, Robyn
2016-12-01
Whether Web-based technologies can improve disease self-management is uncertain. My Asthma Portal (MAP) is a Web-based self-management support system that couples evidence-based behavioral change components (self-monitoring of symptoms, physical activity, and medication adherence) with real-time monitoring, feedback, and support from a nurse case manager. The aim of this study was to compare the impact of access to a Web-based asthma self-management patient portal linked to a case-management system (MAP) over 6 months compared with usual care on asthma control and quality of life. A multicenter, parallel, 2-arm, pilot, randomized controlled trial was conducted with 100 adults with confirmed diagnosis of asthma from 2 specialty clinics. Asthma control was measured using an algorithm based on overuse of fast-acting bronchodilators and emergency department visits, and asthma-related quality of life was assessed using the Mini-Asthma Quality of Life Questionnaire (MAQLQ). Secondary mediating outcomes included asthma symptoms, depressive symptoms, self-efficacy, and beliefs about medication. Process evaluations were also included. A total of 49 individuals were randomized to MAP and 51 to usual care. Compared with usual care, participants in the intervention group reported significantly higher asthma quality of life (mean change 0.61, 95% CI 0.03 to 1.19), and the change in asthma quality of life for the intervention group between baseline and 3 months (mean change 0.66, 95% CI 0.35 to 0.98) was not seen in the control group. No significant differences in asthma quality of life were found between the intervention and control groups at 6 (mean change 0.46, 95% CI -0.12 to 1.05) and 9 months (mean change 0.39, 95% CI -0.2 to 0.98). For poor control status, there was no significant effect of group, time, or group by time. For all self-reported measures, the intervention group had a significantly higher proportion of individuals, demonstrating a minimal clinically
Pseudo-random number generator based on asymptotic deterministic randomness
Energy Technology Data Exchange (ETDEWEB)
Wang Kai [Department of Radio Engineering, Southeast University, Nanjing (China)], E-mail: kaiwang@seu.edu.cn; Pei Wenjiang; Xia Haishan [Department of Radio Engineering, Southeast University, Nanjing (China); Cheung Yiuming [Department of Computer Science, Hong Kong Baptist University, Hong Kong (China)
2008-06-09
A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.
Kistler, Peter M; Rajappan, Kim; Harris, Stuart; Earley, Mark J; Richmond, Laura; Sporton, Simon C; Schilling, Richard J
2008-12-01
A detailed appreciation of the left atrial/pulmonary venous (LA/PV) anatomy may be important in improving the safety and success of catheter ablation for AF. The aim of this randomized study was to determine the impact of computed tomographic (CT) integration into an electroanatomic mapping (EAM) system on clinical outcome in patients undergoing catheter ablation for atrial fibrillation (AF). Eighty patients with AF were randomized to undergo first-time wide encirclement of ipsilateral PV pairs using EAM alone (40 patients) or with CT (40 patients, Cartomerge). Wide encirclement of the pulmonary veins was performed using irrigated radiofrequency ablation with the electrophysiological endpoint of electrical isolation (EI). The primary endpoint was single-procedure success at 6 month follow up. Acute and long-term procedural outcomes were also determined. There was no significant difference in single procedure success between EAM (56%) and cavotricuspid isthmus image (CTI) (50%) groups (P = 0.9). Acute procedural outcomes (EI, PV reconnection, sinus rhythm restored by ablation in persistent AF), fluoroscopy, and procedure durations (EI of right PVs, EI of left PVs, total) did not differ significantly between EAM and CTI groups. Image integration to guide catheter ablation for AF did not significantly improve the clinical outcome. Achieving PV EI is the critical determinant of procedural success rather than the mapping tools used to achieve it.
Directory of Open Access Journals (Sweden)
Heiko Balzter
2015-11-01
Full Text Available The European CORINE land cover mapping scheme is a standardized classification system with 44 land cover and land use classes. It is used by the European Environment Agency to report large-scale land cover change with a minimum mapping unit of 5 ha every six years and operationally mapped by its member states. The most commonly applied method to map CORINE land cover change is by visual interpretation of optical/near-infrared satellite imagery. The Sentinel-1A satellite carries a C-band Synthetic Aperture Radar (SAR and was launched in 2014 by the European Space Agency as the first operational Copernicus mission. This study is the first investigation of Sentinel-1A for CORINE land cover mapping. Two of the first Sentinel-1A images acquired during its ramp-up phase in May and December 2014 over Thuringia in Germany are analysed. 27 hybrid level 2/3 CORINE classes are defined. 17 of these were present at the study site and classified based on a stratified random sample of training pixels from the polygon-eroded CORINE 2006 map. Sentinel-1A logarithmic radar backscatter at HH and HV polarisation (May acquisition, VV and VH polarisation (December acquisition, and the HH image texture are used as input bands to the classification. In addition, a Digital Terrain Model (DTM, a Canopy Height Model (CHM and slope and aspect maps from the Shuttle Radar Topography Mission (SRTM are used as input bands to account for geomorphological features of the landscape. In future, elevation data will be delivered for areas with sufficiently high coherence from the Sentinel-1A Interferometric Wide-Swath Mode itself. When augmented by elevation data from radar interferometry, Sentinel-1A is able to discriminate several CORINE land cover classes, making it useful for monitoring of cloud-covered regions. A bistatic Sentinel-1 Convoy mission would enable single-pass interferometric acquisitions without temporal decorrelation.
Random matrices, random processes and integrable systems
2011-01-01
This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random ma...
Directory of Open Access Journals (Sweden)
He Yong
2012-09-01
Full Text Available Abstract Background A33 is a type II integral membrane protein expressed on the extracellular enveloped form of vaccinia virus (VACV. Passive transfer of A33-directed monoclonal antibodies or vaccination with an A33 subunit vaccine confers protection against lethal poxvirus challenge in animal models. Homologs of A33 are highly conserved among members of the Orthopoxvirus genus and are potential candidates for inclusion in vaccines or assays targeting extracellular enveloped virus activity. One monoclonal antibody directed against VACV A33, MAb-1G10, has been shown to target a conformation-dependent epitope. Interestingly, while it recognizes VACV A33 as well as the corresponding variola homolog, it does not bind to the monkeypox homolog. In this study, we utilized a random phage display library to investigate the epitope recognized by MAb-1G10 that is critical for facilitating cell-to-cell spread of the vaccinia virus. Results By screening with linear or conformational random phage libraries, we found that phages binding to MAb-1G10 display the consensus motif CEPLC, with a disulfide bond formed between two cysteine residues required for MAb-1G10 binding. Although the phage motif contained no linear sequences homologous to VACV A33, structure modeling and analysis suggested that residue D115 is important to form the minimal epitope core. A panel of point mutants expressing the ectodomain of A33 protein was generated and analyzed by either binding assays such as ELISA and immunoprecipitation or a functional assessment by blocking MAb-1G10 mediated comet inhibition in cell culture. Conclusions These results confirm L118 as a component of the MAb-1G10 binding epitope, and further identify D115 as an essential residue. By defining the minimum conformational structure, as well as the conformational arrangement of a short peptide sequence recognized by MAb-1G10, these results introduce the possibility of designing small molecule mimetics that may
Odindi, John; Adam, Elhadi; Ngubane, Zinhle; Mutanga, Onisimo; Slotow, Rob
2014-01-01
Plant species invasion is known to be a major threat to socioeconomic and ecological systems. Due to high cost and limited extents of urban green spaces, high mapping accuracy is necessary to optimize the management of such spaces. We compare the performance of the new-generation WorldView-2 (WV-2) and SPOT-5 images in mapping the bracken fern [Pteridium aquilinum (L) kuhn] in a conserved urban landscape. Using the random forest algorithm, grid-search approaches based on out-of-bag estimate error were used to determine the optimal ntree and mtry combinations. The variable importance and backward feature elimination techniques were further used to determine the influence of the image bands on mapping accuracy. Additionally, the value of the commonly used vegetation indices in enhancing the classification accuracy was tested on the better performing image data. Results show that the performance of the new WV-2 bands was better than that of the traditional bands. Overall classification accuracies of 84.72 and 72.22% were achieved for the WV-2 and SPOT images, respectively. Use of selected indices from the WV-2 bands increased the overall classification accuracy to 91.67%. The findings in this study show the suitability of the new generation in mapping the bracken fern within the often vulnerable urban natural vegetation cover types.
DEFF Research Database (Denmark)
Liu, Jianping; Kjaergard, Lise Lotte; Gluud, Christian
2002-01-01
The quality of randomization of Chinese randomized trials on herbal medicines for hepatitis B was assessed. Search strategy and inclusion criteria were based on the published protocol. One hundred and seventy-six randomized clinical trials (RCTs) involving 20,452 patients with chronic hepatitis B....../150) of the studies were imbalanced at the 0.05 level of probability for the two treatments and 13.3% (20/150) imbalanced at the 0.01 level in the randomization. It is suggested that there may exist misunderstanding of the concept and the misuse of randomization based on the review....
Rapid land cover map updates using change detection and robust random forest classifiers
CSIR Research Space (South Africa)
Wessels, Konrad J
2016-01-01
Full Text Available The paper evaluated the Landsat Automated Land Cover Update Mapping (LALCUM) system designed to rapidly update a land cover map to a desired nominal year using a pre-existing reference land cover map. The system uses the Iteratively Reweighted...
Blocked Randomization with Randomly Selected Block Sizes
Directory of Open Access Journals (Sweden)
Jimmy Efird
2010-12-01
Full Text Available When planning a randomized clinical trial, careful consideration must be given to how participants are selected for various arms of a study. Selection and accidental bias may occur when participants are not assigned to study groups with equal probability. A simple random allocation scheme is a process by which each participant has equal likelihood of being assigned to treatment versus referent groups. However, by chance an unequal number of individuals may be assigned to each arm of the study and thus decrease the power to detect statistically significant differences between groups. Block randomization is a commonly used technique in clinical trial design to reduce bias and achieve balance in the allocation of participants to treatment arms, especially when the sample size is small. This method increases the probability that each arm will contain an equal number of individuals by sequencing participant assignments by block. Yet still, the allocation process may be predictable, for example, when the investigator is not blind and the block size is fixed. This paper provides an overview of blocked randomization and illustrates how to avoid selection bias by using random block sizes.
Blocked randomization with randomly selected block sizes.
Efird, Jimmy
2011-01-01
When planning a randomized clinical trial, careful consideration must be given to how participants are selected for various arms of a study. Selection and accidental bias may occur when participants are not assigned to study groups with equal probability. A simple random allocation scheme is a process by which each participant has equal likelihood of being assigned to treatment versus referent groups. However, by chance an unequal number of individuals may be assigned to each arm of the study and thus decrease the power to detect statistically significant differences between groups. Block randomization is a commonly used technique in clinical trial design to reduce bias and achieve balance in the allocation of participants to treatment arms, especially when the sample size is small. This method increases the probability that each arm will contain an equal number of individuals by sequencing participant assignments by block. Yet still, the allocation process may be predictable, for example, when the investigator is not blind and the block size is fixed. This paper provides an overview of blocked randomization and illustrates how to avoid selection bias by using random block sizes.
Knotters, M.; Brus, D.J.
2013-01-01
The quality of ecotope maps of five districts of main water courses in the Netherlands was assessed on the basis of independent validation samples of field observations. The overall proportion of area correctly classified, and user's and producer's accuracy for each map unit were estimated. In four
Hsu, Li-Ling; Pan, Hui-Ching; Hsieh, Suh-Ing
2016-02-01
Pre-registration programs have been found to insufficiently prepare nurses for working in the neurosciences specialism. Effective approaches to neurology education are important, not only to enhance motivation to learn, but also for learners to develop basic competence in handling patients with neurological problems. To demonstrate that outcome-based course design using concept mapping would bring about significant differences in the nursing students' competency, cognitive load, and learning satisfaction with the neurological care course. A two-group pretest and post-test experimental study was administered. Two of the four clusters of participants were randomly assigned to the experimental group for experiencing an outcome-based course design using concept mapping, and the rest were designated the control group to be given objective-based lectures only. The Competency Inventory of Nursing Students, Cognitive Load Scale of Neurological Nursing, and Learning Satisfaction Scale of Neurological Nursing were used in this study for the students to rate their own performance. In addition, The Concept Map Scoring Scale was used in the experimental group for examining students' concept mapping ability. Significant increases of mean nursing competency scores in both groups from pre-test to post-test were found. There was no statistically significant difference in mean nursing competency score between the experimental group and the control groups at post-test. The mean cognitive load score of the experimental group was lower than the control group at post-test. The mean learning satisfaction scores of the experimental group were higher than the control group. This article provides that outcome-based concept mapping as educational method could encourage a group of nursing students to take a bio-psycho-social approach to medicine, which might ultimately result in better nursing care quality. Copyright © 2015 Elsevier Ltd. All rights reserved.
Random walks, random fields, and disordered systems
Černý, Jiří; Kotecký, Roman
2015-01-01
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a mod...
DEFF Research Database (Denmark)
Andersen, Allan T.; Nielsen, Bo Friis
2000-01-01
. The implications for the correlation structure when shuffling an exactly second-order self-similar process are examined. We apply the Markovian arrival process (MAP) as a tool to investigate whether general conclusions can be made with regard to the statistical implications of the shuffling experiments......In this paper, we examine the implications of certain random permutations in an arrival process that have gained considerable interest in recent literature. The so-called internal and external shuffling have been used to explain phenomena observed in traffic traces from LANs. Loosely, the internal...... shuffling can be viewed as a way of performing local permutations in the arrival stream, while the external shuffling is a way of performing global permutations. We derive formulas for the correlation structures of the shuffled processes in terms of the original arrival process in great generality...
Quantum random number generators
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos
2017-01-01
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. This review discusses the different technologies in quantum random number generation from the early devices based on radioactive decay to the multiple ways to use the quantum states of light to gather entropy from a quantum origin. Randomness extraction and amplification and the notable possibility of generating trusted random numbers even with untrusted hardware using device-independent generation protocols are also discussed.
Hall, Rob; Rinaldo, Alessandro; Wasserman, Larry
2011-01-01
We propose a relaxed privacy definition called {\\em random differential privacy} (RDP). Differential privacy requires that adding any new observation to a database will have small effect on the output of the data-release procedure. Random differential privacy requires that adding a {\\em randomly drawn new observation} to a database will have small effect on the output. We show an analog of the composition property of differentially private procedures which applies to our new definition. We sh...
Masoumi, Feizollah; Eslamkish, Taymour; Abkar, Ali Akbar; Honarmand, Mehdi; Harris, Jeff R.
2017-05-01
The ensemble classifier, Random Forests (RF), is assessed for mapping lithology using the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) imagery over an area in southern Iran. The study area in the northern part of Rabor in the Kerman's Cenozoic magmatic arc (KCMA) is well exposed and contains some copper mineralization occurrences. In this research, the following six groups of ASTER datasets were used for RF classification: nine spectral bands in the VNIR and SWIR, five thermal bands in TIR, all 14 bands (including VNIR, SWIR, and TIR), band ratios, texture features, and principal components (PCs). The results showed that band ratios and all ASTER bands were able to more efficiently discriminate rock units than PC and texture images. The overall classification accuracies achieved were 62.58%, 55.40%, 65.04%, 67.12%, 54.54%, and 53.99% for the nine VNIR/SWIR bands, five TIR bands, all ASTER bands, band ratios, textural, and PCs datasets, respectively. Four datasets including all ASTER bands, band ratios, textural, and PCs datasets (37 bands) were combined as one group and applied in second RF classification which led to increase overall accuracy (up to 81.52%). Based on the four classified maps, an uncertainty map was produced to identify areas of variable (uncertain) classification results, which revealed that approximately 21.43% of all pixels on the classified map were highly uncertain. The RF algorithm found that 12 of the predictors were more important in the classification process. These predictors were used in a third RF classification, which resulted in an overall classification accuracy of 77.21%. Thus, the third RF classification decreases the accuracy. Field observations were used to validate our classification results.
Quantifying randomness in real networks
Orsini, Chiara; Dankulov, Marija M.; Colomer-de-Simón, Pol; Jamakovic, Almerima; Mahadevan, Priya; Vahdat, Amin; Bassler, Kevin E.; Toroczkai, Zoltán; Boguñá, Marián; Caldarelli, Guido; Fortunato, Santo; Krioukov, Dmitri
2015-10-01
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks--the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain--and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.
Synchronous slowing down in coupled logistic maps via random network topology
Wang, Sheng-Jun; Du, Ru-Hai; Jin, Tao; Wu, Xing-Sen; Qu, Shi-Xian
2016-03-01
The speed and paths of synchronization play a key role in the function of a system, which has not received enough attention up to now. In this work, we study the synchronization process of coupled logistic maps that reveals the common features of low-dimensional dissipative systems. A slowing down of synchronization process is observed, which is a novel phenomenon. The result shows that there are two typical kinds of transient process before the system reaches complete synchronization, which is demonstrated by both the coupled multiple-period maps and the coupled multiple-band chaotic maps. When the coupling is weak, the evolution of the system is governed mainly by the local dynamic, i.e., the node states are attracted by the stable orbits or chaotic attractors of the single map and evolve toward the synchronized orbit in a less coherent way. When the coupling is strong, the node states evolve in a high coherent way toward the stable orbit on the synchronized manifold, where the collective dynamics dominates the evolution. In a mediate coupling strength, the interplay between the two paths is responsible for the slowing down. The existence of different synchronization paths is also proven by the finite-time Lyapunov exponent and its distribution.
DEFF Research Database (Denmark)
Jacobsen, Finn
2000-01-01
the random errors of estimates of the sound intensity in, say, one-third octave bands from the power and cross power spectra of the signals from an intensity probe determined with a dual channel FFT analyser. This is not very practical, though. In this paper it is demonstrated that one can predict the random...
a randomized controlled trial.
African Journals Online (AJOL)
milk, only an estimated one -fourth of neonates in India were breastfed within ... standard of care in India and mothers are informed about. 6 months of ... weeks postpartum. A random number sequence was generated using a com- puter program. Block randomization was used with a fixed block size of four. Concealment of ...
Hashing, Randomness and Dictionaries
DEFF Research Database (Denmark)
Pagh, Rasmus
time and memory space. To some extent we also consider lower bounds, i.e., we attempt to show limitations on how efficient algorithms are possible. A central theme in the thesis is randomness. Randomized algorithms play an important role, in particular through the key technique of hashing. Additionally...
Directory of Open Access Journals (Sweden)
Shi Zhan
2011-03-01
Full Text Available These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to the main part, Section 3, where branching random walks are studied from a deeper point of view, and are connected to the model of directed polymers on a tree. Tree-related random processes form a rich and exciting research subject. These notes cover only special topics. For a general account, we refer to the St-Flour lecture notes of Peres [47] and to the forthcoming book of Lyons and Peres [42], as well as to Duquesne and Le Gall [23] and Le Gall [37] for continuous random trees.
Autonomous Byte Stream Randomizer
Paloulian, George K.; Woo, Simon S.; Chow, Edward T.
2013-01-01
Net-centric networking environments are often faced with limited resources and must utilize bandwidth as efficiently as possible. In networking environments that span wide areas, the data transmission has to be efficient without any redundant or exuberant metadata. The Autonomous Byte Stream Randomizer software provides an extra level of security on top of existing data encryption methods. Randomizing the data s byte stream adds an extra layer to existing data protection methods, thus making it harder for an attacker to decrypt protected data. Based on a generated crypto-graphically secure random seed, a random sequence of numbers is used to intelligently and efficiently swap the organization of bytes in data using the unbiased and memory-efficient in-place Fisher-Yates shuffle method. Swapping bytes and reorganizing the crucial structure of the byte data renders the data file unreadable and leaves the data in a deconstructed state. This deconstruction adds an extra level of security requiring the byte stream to be reconstructed with the random seed in order to be readable. Once the data byte stream has been randomized, the software enables the data to be distributed to N nodes in an environment. Each piece of the data in randomized and distributed form is a separate entity unreadable on its own right, but when combined with all N pieces, is able to be reconstructed back to one. Reconstruction requires possession of the key used for randomizing the bytes, leading to the generation of the same cryptographically secure random sequence of numbers used to randomize the data. This software is a cornerstone capability possessing the ability to generate the same cryptographically secure sequence on different machines and time intervals, thus allowing this software to be used more heavily in net-centric environments where data transfer bandwidth is limited.
Liu, Ying; Cao, Guofeng; Zhao, Naizhuo; Mulligan, Kevin; Ye, Xinyue
2018-01-04
Accurate measurements of ground-level PM 2.5 (particulate matter with aerodynamic diameters equal to or less than 2.5 μm) concentrations are critically important to human and environmental health studies. In this regard, satellite-derived gridded PM 2.5 datasets, particularly those datasets derived from chemical transport models (CTM), have demonstrated unique attractiveness in terms of their geographic and temporal coverage. The CTM-based approaches, however, often yield results with a coarse spatial resolution (typically at 0.1° of spatial resolution) and tend to ignore or simplify the impact of geographic and socioeconomic factors on PM 2.5 concentrations. In this study, with a focus on the long-term PM 2.5 distribution in the contiguous United States, we adopt a random forests-based geostatistical (regression kriging) approach to improve one of the most commonly used satellite-derived, gridded PM 2.5 datasets with a refined spatial resolution (0.01°) and enhanced accuracy. By combining the random forests machine learning method and the kriging family of methods, the geostatistical approach effectively integrates ground-based PM 2.5 measurements and related geographic variables while accounting for the non-linear interactions and the complex spatial dependence. The accuracy and advantages of the proposed approach are demonstrated by comparing the results with existing PM 2.5 datasets. This manuscript also highlights the effectiveness of the geographical variables in long-term PM 2.5 mapping, including brightness of nighttime lights, normalized difference vegetation index and elevation, and discusses the contribution of each of these variables to the spatial distribution of PM 2.5 concentrations. Copyright © 2017 Elsevier Ltd. All rights reserved.
L.R. Iverson; A.M. Prasad; A. Liaw
2004-01-01
More and better machine learning tools are becoming available for landscape ecologists to aid in understanding species-environment relationships and to map probable species occurrence now and potentially into the future. To thal end, we evaluated three statistical models: Regression Tree Analybib (RTA), Bagging Trees (BT) and Random Forest (RF) for their utility in...
Nakagawa, Toshio
2014-01-01
Exploring random maintenance models, this book provides an introduction to the implementation of random maintenance, and it is one of the first books to be written on this subject. It aims to help readers learn new techniques for applying random policies to actual reliability models, and it provides new theoretical analyses of various models including classical replacement, preventive maintenance and inspection policies. These policies are applied to scheduling problems, backup policies of database systems, maintenance policies of cumulative damage models, and reliability of random redundant systems. Reliability theory is a major concern for engineers and managers, and in light of Japan’s recent earthquake, the reliability of large-scale systems has increased in importance. This also highlights the need for a new notion of maintenance and reliability theory, and how this can practically be applied to systems. Providing an essential guide for engineers and managers specializing in reliability maintenance a...
DEFF Research Database (Denmark)
Wanscher, Jørgen Bundgaard; Sørensen, Majken Vildrik
2006-01-01
highly uniform multidimensional draws, which are highly relevant for todays traffic models. This paper shows among others combined shuffling and scrambling seems needless, that scrambling gives the lowest correlation and that there are detectable differences between random numbers, dependent...
Molchanov, Ilya
2017-01-01
This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integ...
Shukla, Gaurav; Garg, Rahul Dev; Srivastava, Hari Shanker; Garg, Pradeep Kumar
2017-04-01
The purpose of this study is to effectively implement random forest algorithm for crop classification of large areas and to check the classification capability of different variables. To incorporate dependency of crops in different variables namely, texture, phenological, parent material and soil, soil moisture, topographic, vegetation, and climate, 35 digital layers are prepared using different satellite data (ALOS DEM, Landsat-8, MODIS NDVI, RISAT-1, and Sentinel-1A) and climatic data (precipitation and temperature). The importance of variables is also calculated based on mean decrease in accuracy and mean decrease in Gini score. Importance and capabilities of variables for crop mapping have been discussed. Variables associated with spectral responses have shown greater importance in comparison to topographic and climate variables. The spectral range (0.85 to 0.88 μm) of the near-infrared band is the most useful variable with the highest scores. The topographic variable and elevation have secured the second place rank in the both scores. This indicates the importance of spectral responses as well as of topography in model development. Climate variables have not shown as much importance as others, but in association with others, they cause a decrease in the out of bag (OOB) error rate. In addition to the OOB data, a 20% independent dataset of training samples is used to evaluate RF model. Results show that RF has good capability for crop classification.
Quasiclassical Random Matrix Theory
Prange, R. E.
1996-01-01
We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry, [as with Dyson's circular unitary ensemble], we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, th...
Quantum randomness and unpredictability
Energy Technology Data Exchange (ETDEWEB)
Jaeger, Gregg [Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA (United States)
2017-06-15
Quantum mechanics is a physical theory supplying probabilities corresponding to expectation values for measurement outcomes. Indeed, its formalism can be constructed with measurement as a fundamental process, as was done by Schwinger, provided that individual measurements outcomes occur in a random way. The randomness appearing in quantum mechanics, as with other forms of randomness, has often been considered equivalent to a form of indeterminism. Here, it is argued that quantum randomness should instead be understood as a form of unpredictability because, amongst other things, indeterminism is not a necessary condition for randomness. For concreteness, an explication of the randomness of quantum mechanics as the unpredictability of quantum measurement outcomes is provided. Finally, it is shown how this view can be combined with the recently introduced view that the very appearance of individual quantum measurement outcomes can be grounded in the Plenitude principle of Leibniz, a principle variants of which have been utilized in physics by Dirac and Gell-Mann in relation to the fundamental processes. This move provides further support to Schwinger's ''symbolic'' derivation of quantum mechanics from measurement. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Bandiera, R.; Petruk, O.
2016-06-01
The maps of intensity and polarization of the radio synchrotron emission from shell-type supernova remnants (SNRs) contain a considerable amount of information, although of not easy interpretation. With the aim of deriving constraints on the 3D spatial distribution of the emissivity, as well as on the structure of both ordered and random magnetic fields (MFs), we present here a scheme to model maps of the emission and polarization in SNRs. We first generalize the classical treatment of the synchrotron emission to the case in which the MF is composed of an ordered MF plus an isotropic random component, with arbitrary relative strengths. For a power-law particle energy distribution, we derive analytic formulae that formally resemble those for the classical case. We also treat the shock compression of a fully random upstream field and we predict that the polarization fraction in this case should be higher than typically measured in SNRs. We implement the above treatment into a code, which simulates the observed polarized emission of an emitting shell, taking into account also the effect of the internal Faraday rotation. Finally, we show simulated maps for different orientations with respect to the observer, levels of the turbulent MF component, Faraday rotation levels, distributions of the emissivity (either barrel-shaped or limited to polar caps) and geometries for the ordered MF component (either tangential to the shell or radial). Their analysis allows us to outline properties useful for the interpretation of radio intensity and polarization maps.
Golkarian, Ali; Naghibi, Seyed Amir; Kalantar, Bahareh; Pradhan, Biswajeet
2018-02-17
Ever increasing demand for water resources for different purposes makes it essential to have better understanding and knowledge about water resources. As known, groundwater resources are one of the main water resources especially in countries with arid climatic condition. Thus, this study seeks to provide groundwater potential maps (GPMs) employing new algorithms. Accordingly, this study aims to validate the performance of C5.0, random forest (RF), and multivariate adaptive regression splines (MARS) algorithms for generating GPMs in the eastern part of Mashhad Plain, Iran. For this purpose, a dataset was produced consisting of spring locations as indicator and groundwater-conditioning factors (GCFs) as input. In this research, 13 GCFs were selected including altitude, slope aspect, slope angle, plan curvature, profile curvature, topographic wetness index (TWI), slope length, distance from rivers and faults, rivers and faults density, land use, and lithology. The mentioned dataset was divided into two classes of training and validation with 70 and 30% of the springs, respectively. Then, C5.0, RF, and MARS algorithms were employed using R statistical software, and the final values were transformed into GPMs. Finally, two evaluation criteria including Kappa and area under receiver operating characteristics curve (AUC-ROC) were calculated. According to the findings of this research, MARS had the best performance with AUC-ROC of 84.2%, followed by RF and C5.0 algorithms with AUC-ROC values of 79.7 and 77.3%, respectively. The results indicated that AUC-ROC values for the employed models are more than 70% which shows their acceptable performance. As a conclusion, the produced methodology could be used in other geographical areas. GPMs could be used by water resource managers and related organizations to accelerate and facilitate water resource exploitation.
A discrete fractional random transform
Liu, Zhengjun; Zhao, Haifa; Liu, Shutian
2006-01-01
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption.
Directory of Open Access Journals (Sweden)
B. S. Daya Sagar
2001-01-01
Full Text Available This letter presents a brief framework based on nonlinear morphological transformations to generate a self organized critical connectivity network map (SOCCNM in 2-dimensional space. This simple and elegant framework is implemented on a section that contains a few simulated water bodies to generate SOCCNM. This is based on a postulate that the randomly situated surface water bodies of various sizes and shapes self organize during flooding process.
African Journals Online (AJOL)
zlukovi
modelled as a quadratic regression, nested within parity. The previous lactation length was ... This proportion was mainly covered by linear and quadratic coefficients. Results suggest that RRM could .... The multiple trait models in scalar notation are presented by equations (1, 2), while equation. (3) represents the random ...
van der Heijden, P.G.M.; Cruyff, Maarten; Bockenholt, U.
2014-01-01
In survey research it is often problematic to ask people sensitive questions because they may refuse to answer or they may provide a socially desirable answer that does not reveal their true status on the sensitive question. To solve this problem Warner (1965) proposed randomized response (RR). Here
Random eigenvalue problems revisited
Indian Academy of Sciences (India)
The description of real-life engineering structural systems is associated with some amount of uncertainty in specifying material properties, geometric parameters, boundary conditions and applied loads. In the context of structural dynamics it is necessary to consider random eigenvalue problems in order to account for these ...
absolutely regular random sequences
Directory of Open Access Journals (Sweden)
Michel Harel
1996-01-01
Full Text Available In this paper, the central limit theorems for the density estimator and for the integrated square error are proved for the case when the underlying sequence of random variables is nonstationary. Applications to Markov processes and ARMA processes are provided.
Indian Academy of Sciences (India)
chaos to galaxies. We demonstrate the applicability of random matrix theory for networks by pro- viding a new dimension to complex systems research. We show that in spite of huge differences ... as mentioned earlier, different types of networks can be constructed based on the nature of connections. For example,.
Random eigenvalue problems revisited
Indian Academy of Sciences (India)
Several studies have been conducted on this topic since the mid-sixties. The. A list of .... Random eigenvalue problems revisited. 297 and various elements of Hij ,i ≤ j are statistically independent and Gaussian. The pdf of H can be expressed as, ...... Generality of this result however remains to be verified in future studies.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 2. On Randomness and Probability How to Mathematically Model Uncertain Events ... Author Affiliations. Rajeeva L Karandikar1. Statistics and Mathematics Unit, Indian Statistical Institute, 7 S J S Sansanwal Marg, New Delhi 110 016, India.
Odagaki, Takashi; Kasuya, Keisuke
2017-09-01
Using the Monte Carlo simulation, we investigate a memory-impaired self-avoiding walk on a square lattice in which a random walker marks each of sites visited with a given probability p and makes a random walk avoiding the marked sites. Namely, p = 0 and p = 1 correspond to the simple random walk and the self-avoiding walk, respectively. When p> 0, there is a finite probability that the walker is trapped. We show that the trap time distribution can well be fitted by Stacy's Weibull distribution b(a/b){a+1}/{b}[Γ({a+1}/{b})]-1x^a\\exp(-a/bx^b)} where a and b are fitting parameters depending on p. We also find that the mean trap time diverges at p = 0 as p- α with α = 1.89. In order to produce sufficient number of long walks, we exploit the pivot algorithm and obtain the mean square displacement and its Flory exponent ν(p) as functions of p. We find that the exponent determined for 1000 step walks interpolates both limits ν(0) for the simple random walk and ν(1) for the self-avoiding walk as [ ν(p) - ν(0) ] / [ ν(1) - ν(0) ] = pβ with β = 0.388 when p ≪ 0.1 and β = 0.0822 when p ≫ 0.1. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Evolution of random catalytic networks
Energy Technology Data Exchange (ETDEWEB)
Fraser, S.M. [Santa Fe Inst., NM (United States); Reidys, C.M. [Santa Fe Inst., NM (United States)]|[Los Alamos National Lab., NM (United States)
1997-06-01
In this paper the authors investigate the evolution of populations of sequences on a random catalytic network. Sequences are mapped into structures, between which are catalytic interactions that determine their instantaneous fitness. The catalytic network is constructed as a random directed graph. They prove that at certain parameter values, the probability of some relevant subgraphs of this graph, for example cycles without outgoing edges, is maximized. Populations evolving under point mutations realize a comparatively small induced subgraph of the complete catalytic network. They present results which show that populations reliably discover and persist on directed cycles in the catalytic graph, though these may be lost because of stochastic effects, and study the effect of population size on this behavior.
Random vibrations theory and practice
Wirsching, Paul H; Ortiz, Keith
1995-01-01
Random Vibrations: Theory and Practice covers the theory and analysis of mechanical and structural systems undergoing random oscillations due to any number of phenomena— from engine noise, turbulent flow, and acoustic noise to wind, ocean waves, earthquakes, and rough pavement. For systems operating in such environments, a random vibration analysis is essential to the safety and reliability of the system. By far the most comprehensive text available on random vibrations, Random Vibrations: Theory and Practice is designed for readers who are new to the subject as well as those who are familiar with the fundamentals and wish to study a particular topic or use the text as an authoritative reference. It is divided into three major sections: fundamental background, random vibration development and applications to design, and random signal analysis. Introductory chapters cover topics in probability, statistics, and random processes that prepare the reader for the development of the theory of random vibrations a...
Hokr, Brett H; Mason, John D; Beier, Hope T; Rockwll, Benjamin A; Thomas, Robert J; Noojin, Gary D; Petrov, Georgi I; Golovan, Leonid A; Yakovlev, Vladislav V
2013-01-01
Propagation of light in a highly scattering medium is among the most fascinating optical effect that everyone experiences on an everyday basis and possesses a number of fundamental problems which have yet to be solved. Conventional wisdom suggests that non-linear effects do not play a significant role because the diffusive nature of scattering acts to spread the intensity, dramatically weakening these effects. We demonstrate the first experimental evidence of lasing on a Raman transition in a bulk three-dimensional random media. From a practical standpoint, Raman transitions allow for spectroscopic analysis of the chemical makeup of the sample. A random Raman laser could serve as a bright Raman source allowing for remote, chemically specific, identification of powders and aerosols. Fundamentally, the first demonstration of this new light source opens up an entire new field of study into non-linear light propagation in turbid media, with the most notable application related to non-invasive biomedical imaging.
DEFF Research Database (Denmark)
Jaeger, Manfred
2009-01-01
We investigate the relation between the behavior of non-deterministic systems under fairness constraints, and the behavior of probabilistic systems. To this end, first a framework based on computable stopping strategies is developed that provides a common foundation for describing both fair...... and probabilistic behavior. On the basis of stopping strategies it is then shown that fair behavior corresponds in a precise sense to random behavior in the sense of Martin-Löf's definition of randomness. We view probabilistic systems as concrete implementations of more abstract non-deterministic systems. Under...... this perspective the question is investigated what probabilistic properties are needed in such an implementation to guarantee (with probability one) certain required fairness properties in the behavior of the probabilistic system. Generalizing earlier concepts of ε -bounded transition probabilities, we introduce...
Voiculescu, Dan; Nica, Alexandru
1992-01-01
This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.
Intravaginal stimulation randomized trial.
Smith, J J
1996-01-01
The effectiveness of intravaginal electrical stimulation was compared to standard therapy in the treatment of genuine stress urinary incontinence and detrusor instability. A total of 57 women with urinary incontinence was evaluated with video urodynamics and voiding diaries before and after treatment. Of the women 18 with stress urinary incontinence were randomized to electrical stimulation or Kegel exercise and 38 with detrusor instability were randomized to anticholinergic therapy or electrical stimulation. Of patients using electrical stimulation in the stress urinary incontinence group 66% improved and 72% of the patients with detrusor instability treated with electrical stimulation improved. These rates were not statistically significant when compared to traditional therapy. Electrical stimulation is safe and at least as effective as properly performed Kegel and anticholinergic therapy in the treatment of stress urinary incontinence and detrusor instability.
Certified randomness in quantum physics.
Acín, Antonio; Masanes, Lluis
2016-12-07
The concept of randomness plays an important part in many disciplines. On the one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other, randomness is a resource for cryptography, algorithms and simulations. Standard methods for generating randomness rely on assumptions about the devices that are often not valid in practice. However, quantum technologies enable new methods for generating certified randomness, based on the violation of Bell inequalities. These methods are referred to as device-independent because they do not rely on any modelling of the devices. Here we review efforts to design device-independent randomness generators and the associated challenges.
Certified randomness in quantum physics
Acín, Antonio; Masanes, Lluis
2016-12-01
The concept of randomness plays an important part in many disciplines. On the one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other, randomness is a resource for cryptography, algorithms and simulations. Standard methods for generating randomness rely on assumptions about the devices that are often not valid in practice. However, quantum technologies enable new methods for generating certified randomness, based on the violation of Bell inequalities. These methods are referred to as device-independent because they do not rely on any modelling of the devices. Here we review efforts to design device-independent randomness generators and the associated challenges.
Random Quantum Dynamics: From Random Quantum Circuits to Quantum Chaos
Brown, Winton G.
Quantum circuits consisting of single and two-qubit gates selected at random from a universal gate set are examined. Specifically, the asymptotic rate for large numbers of qubits n and large circuit depth k at which t-order statistical moments of the matrix elements of the resulting random unitary transformation converge to their values with respect to the invariant Haar measure on U(2 n) are determined. The asymptotic convergence rate is obtained from the spectral gap of a superoperator describing the action of the circuit on t-copies of the system Hilbert space. For a class of random quantum circuits that are reversible and invariant under permutation of the qubit labels, the gap and hence the asymptotic convergence rate is shown to scale as ˜ 1/n for sufficiently large n, with a coefficient that may in general depend on t. Bounds are derived between the convergence rates for a broader class of reversible random quantum circuits and the convergence rates of second order moments of irreversible random quantum circuits are examined through a mapping to a Markov chain. Weak constraints are constructed for finite moments of matrix elements of local observables with respect to the eigenvectors of general many-body Hamiltonians in the thermodynamic limit. This is accomplished by means of an expansion in terms of polynomials which are orthogonal with respect to the density of states. The way in which such constraints are satisfied is explored in connection to non-integrability and is argued to provide a general framework for analyzing many-body quantum chaos. Hamiltonians consisting of the XX-interaction between spin-1/2 particles (qubits) which are nearest neighbors on a 3-regular random graph (non-integrable), and an open chain (integrable), are diagonalized numerically to illustrate how the weak constraints can be satisfied. The entanglement content of the eigenvectors of chaotic many-body Hamiltonians is discussed as well as the connection between quantum chaos and
Random recursive trees and the elephant random walk
Kürsten, Rüdiger
2016-03-01
One class of random walks with infinite memory, so-called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We use a coupling between the two models to translate results from elephant random walks to the percolation process. We calculate, besides other quantities, exact expressions for the first and the second moment of the root cluster size and of the number of nodes in child clusters of the first generation. We further introduce another model, the skew elephant random walk, and calculate the first and second moment of this process.
Strong Decomposition of Random Variables
DEFF Research Database (Denmark)
Hoffmann-Jørgensen, Jørgen; Kagan, Abram M.; Pitt, Loren D.
2007-01-01
A random variable X is stongly decomposable if X=Y+Z where Y=Φ(X) and Z=X-Φ(X) are independent non-degenerated random variables (called the components). It is shown that at least one of the components is singular, and we derive a necessary and sufficient condition for strong decomposability...... of a discrete random variable....
Investigating the Randomness of Numbers
Pendleton, Kenn L.
2009-01-01
The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…
Dynamic randomization and a randomization model for clinical trials data.
Kaiser, Lee D
2012-12-20
Randomization models are useful in supporting the validity of linear model analyses applied to data from a clinical trial that employed randomization via permuted blocks. Here, a randomization model for clinical trials data with arbitrary randomization methodology is developed, with treatment effect estimators and standard error estimators valid from a randomization perspective. A central limit theorem for the treatment effect estimator is also derived. As with permuted-blocks randomization, a typical linear model analysis provides results similar to the randomization model results when, roughly, unit effects display no pattern over time. A key requirement for the randomization inference is that the unconditional probability that any patient receives active treatment is constant across patients; when this probability condition is violated, the treatment effect estimator is biased from a randomization perspective. Most randomization methods for balanced, 1 to 1, treatment allocation satisfy this condition. However, many dynamic randomization methods for planned unbalanced treatment allocation, like 2 to 1, do not satisfy this constant probability condition, and these methods should be avoided. Copyright © 2012 John Wiley & Sons, Ltd.
Random Projection Trees Revisited
Dhesi, Aman; Kar, Purushottam
2010-01-01
The Random Projection Tree structures proposed in [Freund-Dasgupta STOC08] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTreeMax and the RPTreeMean data structures. Our result for RPTreeMax gives a near-optimal bound on the number of levels required by this data structure to reduce the size of its cells by a factor $s \\geq 2$. We also prove a packing lemma for this data structure. Our...
Deift, Percy
2009-01-01
This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derive
Random Cell Identifiers Assignment
Directory of Open Access Journals (Sweden)
Robert Bestak
2012-01-01
Full Text Available Despite integration of advanced functions that enable Femto Access Points (FAPs to be deployed in a plug-and-play manner, the femtocell concept still cause several opened issues to be resolved. One of them represents an assignment of Physical Cell Identifiers (PCIs to FAPs. This paper analyses a random based assignment algorithm in LTE systems operating in diverse femtocell scenarios. The performance of the algorithm is evaluated by comparing the number of confusions for various femtocell densities, PCI ranges and knowledge of vicinity. Simulation results show that better knowledge of vicinity can significantly reduce the number of confusions events.
Random Constraint Satisfaction Problems
Directory of Open Access Journals (Sweden)
Amin Coja-Oghlan
2009-11-01
Full Text Available Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with probability close to one due to non-constructive arguments. However, no algorithms are known to find solutions efficiently with a non-vanishing probability at even much lower densities. This fact appears to be related to a phase transition in the set of all solutions. The goal of this extended abstract is to provide a perspective on this phenomenon, and on the computational challenge that it poses.
Fiechtner, Lauren; Puente, Gabriella C; Sharifi, Mona; Block, Jason P; Price, Sarah; Marshall, Richard; Blossom, Jeff; Gerber, Monica W; Taveras, Elsie M
2017-07-06
Novel approaches to health care delivery that leverage community resources could improve outcomes for children at high risk for obesity. We describe the process by which we created an online interactive community resources map for use in the Connect for Health randomized controlled trial. The trial was conducted in the 6 pediatric practices that cared for the highest percentage of children with overweight or obesity within a large multi-specialty group practice in eastern Massachusetts. By using semistructured interviews with parents and community partners and geographic information systems (GIS), we created and validated a community resource map for use in a randomized controlled trial for childhood obesity. We conducted semistructured interviews with 11 parents and received stakeholder feedback from 5 community partners, 2 pediatricians, and 3 obesity-built environment experts to identify community resources that could support behavior change. We used GIS databases to identify the location of resources. After the resources were validated, we created an online, interactive searchable map. We evaluated parent resource empowerment at baseline and follow-up, examined if the participant families went to new locations for physical activity and food shopping, and evaluated how satisfied the families were with the information they received. Parents, community partners, and experts identified several resources to be included in the map, including farmers markets, supermarkets, parks, and fitness centers. Parents expressed the need for affordable activities. Parent resource empowerment increased by 0.25 units (95% confidence interval, 0.21-0.30) over the 1-year intervention period; 76.2% of participants were physically active at new places, 57.1% of participant families shopped at new locations; and 71.8% reported they were very satisfied with the information they received. Parents and community partners identified several community resources that could help support
Enhancing superconducting critical current by randomness
Wang, Y. L.; Thoutam, L. R.; Xiao, Z. L.; Shen, B.; Pearson, J. E.; Divan, R.; Ocola, L. E.; Crabtree, G. W.; Kwok, W. K.
2016-01-01
The key ingredient of high critical currents in a type-II superconductor is defect sites that pin vortices. Contrary to earlier understanding on nanopatterned artificial pinning, here we show unequivocally the advantages of a random pinscape over an ordered array in a wide magnetic field range. We reveal that the better performance of a random pinscape is due to the variation of its local density of pinning sites (LDOPS), which mitigates the motion of vortices. This is confirmed by achieving even higher enhancement of the critical current through a conformally mapped random pinscape, where the distribution of the LDOPS is further enlarged. The demonstrated key role of LDOPS in enhancing superconducting critical currents gets at the heart of random versus commensurate pinning. Our findings highlight the importance of random pinscapes in enhancing the superconducting critical currents of applied superconductors.
Pradillo, Gerardo; Heintz, Aneesh; Vlahovska, Petia
2017-11-01
The spontaneous rotation of a sphere in an applied uniform DC electric field (Quincke effect) has been utilized to engineer self-propelled particles: if the sphere is initially resting on a surface, it rolls. The Quincke rollers have been widely used as a model system to study collective behavior in ``active'' suspensions. If the applied field is DC, an isolated Quincke roller follows a straight line trajectory. In this talk, we discuss the design of a Quincke roller that executes a random-walk-like behavior. We utilize AC field - upon reversal of the field direction a fluctuation in the axis of rotation (which is degenerate in the plane perpendicular to the field and parallel to the surface) introduces randomness in the direction of motion. The MSD of an isolated Quincke walker depends on frequency, amplitude, and waveform of the electric field. Experiment and theory are compared. We also investigate the collective behavior of Quincke walkers,the transport of inert particles in a bath of Quincke walkers, and the spontaneous motion of a drop containing Quincke active particle. supported by NSF Grant CBET 1437545.
Funaki, Tadahisa
2016-01-01
Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book. Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ∇φ-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hyd...
Mak, Chi H.; Pham, Phuong; Afif, Samir A.; Goodman, Myron F.
2015-09-01
Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C →U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.
Noginov, Mikhail A
2005-01-01
Random lasers are the simplest sources of stimulated emission without cavity, with the feedback provided by scattering in a gain medium. First proposed in the late 60’s, random lasers have grown to a large research field. This book reviews the history and the state of the art of random lasers, provides an outline of the basic models describing their behavior, and describes the recent advances in the field. The major focus of the book is on solid-state random lasers. However, it also briefly describes random lasers based on liquid dyes with scatterers. The chapters of the book are almost independent of each other. So, the scientists or engineers interested in any particular aspect of random lasers can read directly the relevant section. Researchers entering the field of random lasers will find in the book an overview of the field of study. Scientists working in the field can use the book as a reference source.
Malarz, K.; Szvetelszky, Z.; Szekf, B.; Kulakowski, K.
2006-11-01
We consider the average probability X of being informed on a gossip in a given social network. The network is modeled within the random graph theory of Erd{õ}s and Rényi. In this theory, a network is characterized by two parameters: the size N and the link probability p. Our experimental data suggest three levels of social inclusion of friendship. The critical value pc, for which half of agents are informed, scales with the system size as N-gamma with gamma approx 0.68. Computer simulations show that the probability X varies with p as a sigmoidal curve. Influence of the correlations between neighbors is also evaluated: with increasing clustering coefficient C, X decreases.
Investments in random environments
Navarro-Barrientos, Jesús Emeterio; Cantero-Álvarez, Rubén; Matias Rodrigues, João F.; Schweitzer, Frank
2008-03-01
We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, x(t) , depends on the stochasticity of the return on investment, r(t) , for which different model assumptions are discussed. The fat-tail distribution of the budget is investigated and compared with theoretical predictions. We are mainly interested in the most probable value xmp of the budget that reaches a constant value over time. Based on an analytical investigation of the dynamics, we are able to predict xmpstat . We find a scaling law that relates the most probable value to the characteristic parameters describing the stochastic process. Our analytical results are confirmed by stochastic computer simulations that show a very good agreement with the predictions.
Tailored Random Graph Ensembles
Roberts, E. S.; Annibale, A.; Coolen, A. C. C.
2013-02-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Vempala, Santosh S
2005-01-01
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neig...
Huang, Yu-Chuan; Chen, Hsing-Hsia; Yeh, Mei-Ling; Chung, Yu-Chu
2012-06-01
Critical thinking (CT) is essential to the exercise of professional judgment. As nurses face increasingly complex health-care situations, critical thinking can promote appropriate clinical decision-making and improve the quality of nursing care. This study aimed to evaluate the effects of a program of case studies, alone (CS) or combined with concept maps (CSCM), on improving CT in clinical nurses. The study was a randomized controlled trial. The experimental group participated in a 16-week CSCM program, whereas the control group participated in a CS program of equal duration. A randomized-controlled trial with a multistage randomization process was used to select and to assign participants, ultimately resulting in 67 nurses in each group. Data were collected before and after the program using the California Critical Thinking Skill Test (CCTST) and the California Critical Thinking Disposition Inventory (CCTDI). After the programs, there were significant differences between the two groups in the critical thinking skills of analysis, evaluation, inference, deduction, and induction. There was also an overall significant difference, and a significant difference in the specific disposition of open-mindedness. This study supports the application of case studies combined with concept maps as a hospital-based teaching strategy to promote development of critical thinking skills and encourage dispositions for nurses. The CSCM resulted in greater improvements in all critical thinking skills of as well as the overall and open-minded affective dispositions toward critical thinking, compared with the case studies alone. An obvious improvement in the CSCM participants was the analytic skill and disposition. Further longitudinal studies and data collection from multisite evaluations in a range of geographic locales are warranted. Copyright © 2012 Elsevier Ltd. All rights reserved.
Random discrete Schroedinger operators from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Breuer, Jonathan [Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Forrester, Peter J [Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic 3010 (Australia); Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute, Rehovot 76100 (Israel)
2007-02-02
We investigate random, discrete Schroedinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature {beta}. They are similar to the class of 'critical' random Schroedinger operators with random potentials which diminish as vertical bar x vertical bar{sup -1/2}. We show that as a function of {beta} they undergo a transition from a regime of (power-law) localized eigenstates with a pure point spectrum for {beta} < 2 to a regime of extended states with a singular continuous spectrum for {beta} {>=} 2. (fast track communication)
Hagensieker, Ron; Roscher, Ribana; Rosentreter, Johannes; Jakimow, Benjamin; Waske, Björn
2017-12-01
Remote sensing satellite data offer the unique possibility to map land use land cover transformations by providing spatially explicit information. However, detection of short-term processes and land use patterns of high spatial-temporal variability is a challenging task. We present a novel framework using multi-temporal TerraSAR-X data and machine learning techniques, namely discriminative Markov random fields with spatio-temporal priors, and import vector machines, in order to advance the mapping of land cover characterized by short-term changes. Our study region covers a current deforestation frontier in the Brazilian state Pará with land cover dominated by primary forests, different types of pasture land and secondary vegetation, and land use dominated by short-term processes such as slash-and-burn activities. The data set comprises multi-temporal TerraSAR-X imagery acquired over the course of the 2014 dry season, as well as optical data (RapidEye, Landsat) for reference. Results show that land use land cover is reliably mapped, resulting in spatially adjusted overall accuracies of up to 79% in a five class setting, yet limitations for the differentiation of different pasture types remain. The proposed method is applicable on multi-temporal data sets, and constitutes a feasible approach to map land use land cover in regions that are affected by high-frequent temporal changes.
Directory of Open Access Journals (Sweden)
Kim André Vanselow
2014-07-01
Full Text Available In many arid mountains, dwarf shrubs represent the most important fodder and firewood resources; therefore, they are intensely used. For the Eastern Pamirs (Tajikistan, they are assumed to be overused. However, empirical evidence on this issue is lacking. We aim to provide a method capable of mapping vegetation in this mountain desert. We used random forest models based on remote sensing data (RapidEye, ASTER GDEM and 359 plots to predictively map total vegetative cover and the distribution of the most important firewood plants, K. ceratoides and A. leucotricha. These species were mapped as present in 33.8% of the study area (accuracy 90.6%. The total cover of the dwarf shrub communities ranged from 0.5% to 51% (per pixel. Areas with very low cover were limited to the vicinity of roads and settlements. The model could explain 80.2% of the total variance. The most important predictor across the models was MSAVI2 (a spectral vegetation index particularly invented for low-cover areas. We conclude that the combination of statistical models and remote sensing data worked well to map vegetation in an arid mountainous environment. With this approach, we were able to provide tangible data on dwarf shrub resources in the Eastern Pamirs and to relativize previous reports about their extensive depletion.
When are cellular automata random?
Coe, J. B.; Ahnert, S. E.; Fink, T. M. A.
2008-12-01
A random cellular automaton is one in which a cell's behaviour is independent of its previous states. We derive analytical conditions which must be satisfied by random cellular automata and find deterministic and probabilistic cellular automata that satisfy these conditions. Many random cellular automata are seen to have a flow as they are updated through time. We define a correlation current that describes this flow and develop an analytical expression for its size. We compare results from this analytical expression with those from simulation. The randomness in a cell comes from randomness in adjacent cells or from the stochastic nature of update rules. We give an expression for how much randomness comes from each of these two sources.
Methods and analysis of realizing randomized grouping.
Hu, Liang-Ping; Bao, Xiao-Lei; Wang, Qi
2011-07-01
Randomization is one of the four basic principles of research design. The meaning of randomization includes two aspects: one is to randomly select samples from the population, which is known as random sampling; the other is to randomly group all the samples, which is called randomized grouping. Randomized grouping can be subdivided into three categories: completely, stratified and dynamically randomized grouping. This article mainly introduces the steps of complete randomization, the definition of dynamic randomization and the realization of random sampling and grouping by SAS software.
[Controlled randomized clinical trials].
Jaillon, Patrice
2007-01-01
It is generally agreed that the first comparative clinical trial in history was done by James Lind in 1747, in the treatment of scurvy. The general bases of modern experimental medicine were published by Claude Bernard in 1865. However, it is the development of new drugs and the evolution of methodological concepts that led to the first randomized controlled clinical trial, in 1948, which showed that the effects of streptomycin on pulmonary tuberculosis were significantly different from those of a placebo. Today, "evidence-based" medicine aims to rationalize the medical decision-making process by taking into account, first and foremost, the results of controlled randomized clinical trials, which provide the highest level of evidence. In the second half of the 20th century it became clear that different kinds of clinical trials might not provide the same level of evidence. Practitioners' intimate convictions must be challenged by the results of controlled clinical trials. Take the CAST trial for example, which, in 1989, tested antiarrhythmic drugs versus placebo in patients with myocardial infarction. It was well known that ventricular arrhythmias were a factor of poor prognosis in coronary heart disease, and it was therefore considered self-evident that drug suppression of these ventricular arrhythmias would reduce the mortality rate. In the event, the CAST trial showed the exact opposite, with an almost 3-fold increase in total mortality among patients with coronary heart disease who were treated with antiarrhythmic drugs. These results had a profound impact on the use of antiarrythmic drugs, which became contraindicated after myocardial infarction. A clinical trial has to fulfill certain methodological standards to be accepted as evidence-based medicine. First, a working hypothesis has to be formulated, and then the primary outcome measure must be chosen before beginning the study. An appropriate major endpoint for efficacy must be selected, in keeping with the
Fractional random walk lattice dynamics
Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.
2017-02-01
We analyze time-discrete and time-continuous ‘fractional’ random walks on undirected regular networks with special focus on cubic periodic lattices in n = 1, 2, 3,.. dimensions. The fractional random walk dynamics is governed by a master equation involving fractional powers of Laplacian matrices {{L}\\fracα{2}}} where α =2 recovers the normal walk. First we demonstrate that the interval 0<α ≤slant 2 is admissible for the fractional random walk. We derive analytical expressions for the transition matrix of the fractional random walk and closely related the average return probabilities. We further obtain the fundamental matrix {{Z}(α )} , and the mean relaxation time (Kemeny constant) for the fractional random walk. The representation for the fundamental matrix {{Z}(α )} relates fractional random walks with normal random walks. We show that the matrix elements of the transition matrix of the fractional random walk exihibit for large cubic n-dimensional lattices a power law decay of an n-dimensional infinite space Riesz fractional derivative type indicating emergence of Lévy flights. As a further footprint of Lévy flights in the n-dimensional space, the transition matrix and return probabilities of the fractional random walk are dominated for large times t by slowly relaxing long-wave modes leading to a characteristic {{t}-\\frac{n{α}} -decay. It can be concluded that, due to long range moves of fractional random walk, a small world property is emerging increasing the efficiency to explore the lattice when instead of a normal random walk a fractional random walk is chosen.
Octonions in random matrix theory
Forrester, Peter J.
2016-01-01
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random by symmetry considerations. Only for $N=2$ is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for $N...
Random Numbers from Astronomical Imaging
Pimbblet, Kevin A.; Bulmer, Michael
2004-01-01
This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined.
Monocular Road Detection Using Structured Random Forest
Directory of Open Access Journals (Sweden)
Liang Xiao
2016-05-01
Full Text Available Road detection is a key task for autonomous land vehicles. Monocular vision-based road-detection algorithms are mostly based on machine learning approaches and are usually cast as classification problems. However, the pixel-wise classifiers are faced with the ambiguity caused by changes in road appearance, illumination and weather. An effective way to reduce the ambiguity is to model the contextual information with structured learning and prediction. Currently, the widely used structured prediction model in road detection is the Markov random field or conditional random field. However, the random field-based methods require additional complex optimization after pixel-wise classification, making them unsuitable for real-time applications. In this paper, we present a structured random forest-based road-detection algorithm which is capable of modelling the contextual information efficiently. By mapping the structured label space to a discrete label space, the test function of each split node can be trained in a similar way to that of the classical random forests. Structured random forests make use of the contextual information of image patches as well as the structural information of the labels to get more consistent results. Besides this benefit, by predicting a batch of pixels in a single classification, the structured random forest-based road detection can be much more efficient than the conventional pixel-wise random forest. Experimental results tested on the KITTI-ROAD dataset and data collected in typical unstructured environments show that structured random forest-based road detection outperforms the classical pixel-wise random forest both in accuracy and efficiency.
Importance of randomness in biological networks: A random matrix ...
Indian Academy of Sciences (India)
2015-01-29
Jan 29, 2015 ... We show that in spite of huge differences these interaction networks, representing real-world systems, posses from random matrix models, the spectral properties of the underlying matrices of these networks follow random matrix theory bringing them into the same universality class. We further demonstrate ...
Asymmetric evolving random networks
Coulomb, S.; Bauer, M.
2003-10-01
We generalize the Poissonian evolving random graph model of M. Bauer and D. Bernard (2003), to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non Poissonian degree distributions. A node is added at each time step and is connected to the rest of the graph by oriented edges emerging from older nodes. This leads to a statistical asymmetry between incoming and outgoing edges. The law for the number of new edges at each time step is fixed but arbitrary. Thermodynamical behavior is expected when this law has a large time limit. Although (by construction) the incoming degree distributions depend on this law, this is not the case for most qualitative features concerning the size distribution of connected components, as long as the law has a finite variance. As the variance grows above 1/4, the average being < 1/2, a giant component emerges, which connects a finite fraction of the vertices. Below this threshold, the distribution of component sizes decreases algebraically with a continuously varying exponent. The transition is of infinite order, in sharp contrast with the case of static graphs. The local-in-time profiles for the components of finite size allow to give a refined description of the system.
Directory of Open Access Journals (Sweden)
Sidovar MF
2016-02-01
Full Text Available Matthew F Sidovar,1 Brendan L Limone,2 Craig I Coleman2 1Clinical Development and Medical Affairs, Acorda Therapeutics, Ardsley, NY, 2Department of Pharmacy Practice, University of Connecticut School of Pharmacy, Storrs, CT, USA Background: Mapping of patient-reported outcomes to the five-dimension EuroQol (EQ-5D health index is increasingly being used for understanding the relationship of outcomes to health states and for predicting utilities that have application in economic evaluations. The 12-item Multiple Sclerosis Walking Scale (MSWS-12 is a patient-reported outcome that assesses the impact of walking impairment in people with MS. An equation for mapping the MSWS-12 to the EQ-5D was previously developed and validated using a North American Research Committee on MS (NARCOMS registry cohort. Materials and methods: This analysis retested the validity of the equation mapping the MSWS-12 to the three-level EQ-5D (EQ-5D-3L by using an independent cohort of patients with MS enrolled in a randomized controlled trial. Mapping was evaluated at two separate time points (baseline and week 4 during the clinical trial. The mapping equation’s performance was subsequently assessed with mean absolute error (MAE and root-mean-square error (RMSE by comparing equation-based estimates to values elicited in the trial using the actual EQ-5D-3L questionnaire. Results: The mapping equation predicted EQ-5D-3L values in this external cohort with reasonable precision at both time points (MAE 0.116 and RMSE 0.155 at baseline; MAE 0.105 and RMSE 0.138 at week 4, and was similar to that reported in the original NARCOMS cohort (MAE 0.109 and RMSE 0.145. Also as observed in the original NARCOMS cohort, the mapping equation performed best in patients with EQ-5D-3L values between 0.50 and 0.75, and poorly in patients with values <0.50.Conclusion: The mapping equation performed similarly in this external cohort as in the original derivation cohort, including a poorer
Random selection of Borel sets
Directory of Open Access Journals (Sweden)
Bernd Günther
2010-10-01
Full Text Available A theory of random Borel sets is presented, based on dyadic resolutions of compact metric spaces. The conditional expectation of the intersection of two independent random Borel sets is investigated. An example based on an embedding of Sierpinski’s universal curve into the space of Borel sets is given.
Students' Misconceptions about Random Variables
Kachapova, Farida; Kachapov, Ilias
2012-01-01
This article describes some misconceptions about random variables and related counter-examples, and makes suggestions about teaching initial topics on random variables in general form instead of doing it separately for discrete and continuous cases. The focus is on post-calculus probability courses. (Contains 2 figures.)
Forecasting Using Random Subspace Methods
T. Boot (Tom); D. Nibbering (Didier)
2016-01-01
textabstractRandom subspace methods are a novel approach to obtain accurate forecasts in high-dimensional regression settings. We provide a theoretical justification of the use of random subspace methods and show their usefulness when forecasting monthly macroeconomic variables. We focus on two
Developments in Random Matrix Theory
Snaith, N. C.; Forrester, P. J.; Verbaarschot, J. J. M.
2003-01-01
In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given.
Energy Technology Data Exchange (ETDEWEB)
Jackson, A.D. [Niels Bohr Inst., Copenhagen (Denmark)
1998-08-10
Chiral random matrix theory has recently been shown to provide a tool useful for both modeling chiral symmetry restoration in QCD and for providing analytic descriptions of the microscopic spectral content of lattice gauge simulations. The basic ideas of chiral random matrix theory and some recent results are discussed. (orig.) 24 refs.
Directory of Open Access Journals (Sweden)
MS Yıldırım
2016-02-01
Full Text Available The aim of this study was to compare the effects of static stretching, proprioceptive neuromuscular facilitation (PNF stretching and Mulligan technique on hip flexion range of motion (ROM in subjects with bilateral hamstring tightness. A total of 40 students (mean age: 21.5±1.3 years, mean body height: 172.8±8.2 cm, mean body mass index: 21.9±3.0 kg • m-2 with bilateral hamstring tightness were enrolled in this randomized trial, of whom 26 completed the study. Subjects were divided into 4 groups performing (I typical static stretching, (II PNF stretching, (III Mulligan traction straight leg raise (TSLR technique, (IV no intervention. Hip flexion ROM was measured using a digital goniometer with the passive straight leg raise test before and after 4 weeks by two physiotherapists blinded to the groups. 52 extremities of 26 subjects were analyzed. Hip flexion ROM increased in all three intervention groups (p<0.05 but not in the no-intervention group after 4 weeks. A statistically significant change in initial–final assessment differences of hip flexion ROM was found between groups (p<0.001 in favour of PNF stretching and Mulligan TSLR technique in comparison to typical static stretching (p=0.016 and p=0.02, respectively. No significant difference was found between Mulligan TSLR technique and PNF stretching (p=0.920. The initial–final assessment difference of hip flexion ROM was similar in typical static stretching and no intervention (p=0.491. A 4-week stretching intervention is beneficial for increasing hip flexion ROM in bilateral hamstring tightness. However, PNF stretching and Mulligan TSLR technique are superior to typical static stretching. These two interventions can be alternatively used for stretching in hamstring tightness.
Quasi-Random Rumor Spreading: Reducing Randomness Can Be Costly
Doerr, Benjamin; Fouz, Mahmoud
2010-01-01
We give a time-randomness tradeoff for the quasi-random rumor spreading protocol proposed by Doerr, Friedrich and Sauerwald [SODA 2008] on complete graphs. In this protocol, the goal is to spread a piece of information originating from one vertex throughout the network. Each vertex is assumed to have a (cyclic) list of its neighbors. Once a vertex is informed by one of its neighbors, it chooses a position in its list uniformly at random and then informs its neighbors starting from that positi...
Thermodynamics of random number generation
Aghamohammadi, Cina; Crutchfield, James P.
2017-06-01
We analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced Information Processing Second Law. Given access to a specified source of randomness, a random number generator (RNG) produces samples from a desired target probability distribution. This differs from pseudorandom number generators (PRNGs) that use wholly deterministic algorithms and from true random number generators (TRNGs) in which the randomness source is a physical system. For each class, we analyze the thermodynamics of generators based on algorithms implemented as finite-state machines, as these allow for direct bounds on the required physical resources. This establishes bounds on heat dissipation and work consumption during the operation of three main classes of RNG algorithms—including those of von Neumann, Knuth, and Yao and Roche and Hoshi—and for PRNG methods. We introduce a general TRNG and determine its thermodynamic costs exactly for arbitrary target distributions. The results highlight the significant differences between the three main approaches to random number generation: One is work producing, one is work consuming, and the other is potentially dissipation neutral. Notably, TRNGs can both generate random numbers and convert thermal energy to stored work. These thermodynamic costs on information creation complement Landauer's limit on the irreducible costs of information destruction.
An introduction to random sets
Nguyen, Hung T
2006-01-01
The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that in science and engineering, and even in the statistics community, the topic is not well known and much of the enormous potential of random sets remains untapped.An Introduction to Random Sets provides a friendly but solid initiation into the theory of random sets. It builds the foundation for studying random set data, which, viewed as imprecise or incomplete observations, are ubiquitous in today''s technological society. The author, widely known for his best-selling A First Course in Fuzzy Logic text as well as his pioneering work in random sets, explores motivations, such as coarse data analysis and uncertainty analysis in intelligent systems, for studying random s...
Papakonstantinou, Periklis A.; Woodruff, David P.; Yang, Guang
2016-09-01
Generating random bits is a difficult task, which is important for physical systems simulation, cryptography, and many applications that rely on high-quality random bits. Our contribution is to show how to generate provably random bits from uncertain events whose outcomes are routinely recorded in the form of massive data sets. These include scientific data sets, such as in astronomics, genomics, as well as data produced by individuals, such as internet search logs, sensor networks, and social network feeds. We view the generation of such data as the sampling process from a big source, which is a random variable of size at least a few gigabytes. Our view initiates the study of big sources in the randomness extraction literature. Previous approaches for big sources rely on statistical assumptions about the samples. We introduce a general method that provably extracts almost-uniform random bits from big sources and extensively validate it empirically on real data sets. The experimental findings indicate that our method is efficient enough to handle large enough sources, while previous extractor constructions are not efficient enough to be practical. Quality-wise, our method at least matches quantum randomness expanders and classical world empirical extractors as measured by standardized tests.
Random matrix theory and symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Caselle, M.; Magnea, U
2004-05-01
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero-Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.
Random processes in nuclear reactors
Williams, M M R
1974-01-01
Random Processes in Nuclear Reactors describes the problems that a nuclear engineer may meet which involve random fluctuations and sets out in detail how they may be interpreted in terms of various models of the reactor system. Chapters set out to discuss topics on the origins of random processes and sources; the general technique to zero-power problems and bring out the basic effect of fission, and fluctuations in the lifetime of neutrons, on the measured response; the interpretation of power reactor noise; and associated problems connected with mechanical, hydraulic and thermal noise sources
Characterization of nonstationary random processes
Energy Technology Data Exchange (ETDEWEB)
Paez, T.L.
1985-01-01
Current methods for shock test specification and shock testing treat the shock environment as a deterministic source. The present study proposes to treat shock sources as nonstationary random processes. A model for a realistic nonstationary random process shock source is specified, and the effect of variation of parameters in the shock source is shown. A method for estimating the parameters of the random process is established, and some numerical examples show that the method yields reasonable results. The use of this model in shock testing is discussed.
Symmetrization of binary random variables
Kagan, Abram; Mallows, Colin L.; Shepp, Larry A.; Vanderbei, Robert J.; Vardi, Yehuda
1999-01-01
A random variable [math] is called an independent symmetrizer of a given random variable [math] if (a) it is independent of [math] and (b) the distribution of [math] is symmetric about [math] . In cases where the distribution of [math] is symmetric about its mean, it is easy to see that the constant random variable [math] is a minimum-variance independent symmetrizer. Taking [math] to have the same distribution as [math] clearly produces a symmetric sum, but it may not be of minimum variance....
Electromagnetic scattering from random media
Field, Timothy R
2009-01-01
- ;The book develops the dynamical theory of scattering from random media from first principles. Its key findings are to characterize the time evolution of the scattered field in terms of stochastic differential equations, and to illustrate this framework
Random walks on reductive groups
Benoist, Yves
2016-01-01
The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Octonions in random matrix theory
Forrester, Peter J.
2017-04-01
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random matrices by symmetry considerations. Only for N=2 is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for N=3. We then proceed to consider the matrix structure X†X, when X has random octonion entries. Analytic results are obtained from N=2, but are observed to break down in the 3×3 case.
Cluster randomization and political philosophy.
Chwang, Eric
2012-11-01
In this paper, I will argue that, while the ethical issues raised by cluster randomization can be challenging, they are not new. My thesis divides neatly into two parts. In the first, easier part I argue that many of the ethical challenges posed by cluster randomized human subjects research are clearly present in other types of human subjects research, and so are not novel. In the second, more difficult part I discuss the thorniest ethical challenge for cluster randomized research--cases where consent is genuinely impractical to obtain. I argue that once again these cases require no new analytic insight; instead, we should look to political philosophy for guidance. In other words, the most serious ethical problem that arises in cluster randomized research also arises in political philosophy. © 2011 Blackwell Publishing Ltd.
Random sequential adsorption of cubes.
Cieśla, Michał; Kubala, Piotr
2018-01-14
Random packings built of cubes are studied numerically using a random sequential adsorption algorithm. To compare the obtained results with previous reports, three different models of cube orientation sampling were used. Also, three different cube-cube intersection algorithms were tested to find the most efficient one. The study focuses on the mean saturated packing fraction as well as kinetics of packing growth. Microstructural properties of packings were analyzed using density autocorrelation function.
Growing random networks with fitness
Ergun, G.; Rodgers, GJ
2001-01-01
Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes of connectivity $k$ and random additive fitness $\\eta$, with rate $(k-1)+ \\eta $. For $\\eta >0$ we find the connectivity distribution is power law with exponent $\\gamma=+2$. In the second model (B), the network is built by connecting nodes to nodes of conn...
Large Deviations for Random Trees.
Bakhtin, Yuri; Heitsch, Christine
2008-08-01
We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.
Randomness in Contemporary Graphic Art
Zavřelová, Veronika
2016-01-01
Veronika Zavřelová Bachelor thesis Charles University in Prague, Faculty of Education, Department of Art Education Randomness in contemporary graphic art imaginative picture card game ANNOTATION This (bachelor) thesis concerns itself with a connection between verbal and visual character system within the topic of Randomness in contemporary graphic art - imaginative picture card game. The thesis is mainly based on the practical part - exclusively created card game Piktim. The card game uses as...
Yan, Dong; de Beurs, Kirsten M.
2016-05-01
The objective of this paper is to demonstrate a new method to map the distributions of C3 and C4 grasses at 30 m resolution and over a 25-year period of time (1988-2013) by combining the Random Forest (RF) classification algorithm and patch stable areas identified using the spatial pattern analysis software FRAGSTATS. Predictor variables for RF classifications consisted of ten spectral variables, four soil edaphic variables and three topographic variables. We provided a confidence score in terms of obtaining pure land cover at each pixel location by retrieving the classification tree votes. Classification accuracy assessments and predictor variable importance evaluations were conducted based on a repeated stratified sampling approach. Results show that patch stable areas obtained from larger patches are more appropriate to be used as sample data pools to train and validate RF classifiers for historical land cover mapping purposes and it is more reasonable to use patch stable areas as sample pools to map land cover in a year closer to the present rather than years further back in time. The percentage of obtained high confidence prediction pixels across the study area ranges from 71.18% in 1988 to 73.48% in 2013. The repeated stratified sampling approach is necessary in terms of reducing the positive bias in the estimated classification accuracy caused by the possible selections of training and validation pixels from the same patch stable areas. The RF classification algorithm was able to identify the important environmental factors affecting the distributions of C3 and C4 grasses in our study area such as elevation, soil pH, soil organic matter and soil texture.
Supersymmetry in random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kieburg, Mario
2010-05-04
I study the applications of supersymmetry in random matrix theory. I generalize the supersymmetry method and develop three new approaches to calculate eigenvalue correlation functions. These correlation functions are averages over ratios of characteristic polynomials. In the first part of this thesis, I derive a relation between integrals over anti-commuting variables (Grassmann variables) and differential operators with respect to commuting variables. With this relation I rederive Cauchy- like integral theorems. As a new application I trace the supermatrix Bessel function back to a product of two ordinary matrix Bessel functions. In the second part, I apply the generalized Hubbard-Stratonovich transformation to arbitrary rotation invariant ensembles of real symmetric and Hermitian self-dual matrices. This extends the approach for unitarily rotation invariant matrix ensembles. For the k-point correlation functions I derive supersymmetric integral expressions in a unifying way. I prove the equivalence between the generalized Hubbard-Stratonovich transformation and the superbosonization formula. Moreover, I develop an alternative mapping from ordinary space to superspace. After comparing the results of this approach with the other two supersymmetry methods, I obtain explicit functional expressions for the probability densities in superspace. If the probability density of the matrix ensemble factorizes, then the generating functions exhibit determinantal and Pfaffian structures. For some matrix ensembles this was already shown with help of other approaches. I show that these structures appear by a purely algebraic manipulation. In this new approach I use structures naturally appearing in superspace. I derive determinantal and Pfaffian structures for three types of integrals without actually mapping onto superspace. These three types of integrals are quite general and, thus, they are applicable to a broad class of matrix ensembles. (orig.)
Random integral equations on time scales
Directory of Open Access Journals (Sweden)
Vasile Lupulescu
2013-01-01
Full Text Available In this paper, we present the existence and uniqueness of random solution of a random integral equation of Volterra type on time scales. We also study the asymptotic properties of the unique random solution.
Phase Transitions on Random Lattices: How Random is Topological Disorder?
Barghathi, Hatem; Vojta, Thomas
2015-03-01
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω = (d - 1) / (2 d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d + 1) ν > 2 rather than the usual Harris criterion dν > 2 , making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d > 1 . These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices. This work was supported by the NSF under Grant Nos. DMR-1205803 and PHYS-1066293. We acknowledge the hospitality of the Aspen Center for Physics.
Mondrian Forests: Efficient Online Random Forests
Lakshminarayanan, Balaji; Roy, Daniel M.; Teh, Yee Whye
2014-01-01
Ensembles of randomized decision trees, usually referred to as random forests, are widely used for classification and regression tasks in machine learning and statistics. Random forests achieve competitive predictive performance and are computationally efficient to train and test, making them excellent candidates for real-world prediction tasks. The most popular random forest variants (such as Breiman's random forest and extremely randomized trees) operate on batches of training data. Online ...
Wave propagation and scattering in random media
Ishimaru, Akira
1978-01-01
Wave Propagation and Scattering in Random Media, Volume 2, presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner. The topics covered in this book may be grouped into three categories: waves in random scatterers, waves in random continua, and rough surface scattering. Random scatterers are random distributions of many particles. Examples are rain, fog, smog, hail, ocean particles, red blood cells, polymers, and other particles in a state of Brownian motion. Random continua are the media whose characteristics vary randomly an
Random operator equations in mathematical physics. I
Adomian, G.
1970-01-01
Stochastic differential equations objectives, limitations and restrictive assumptions in physical problems, discussing electromagnetic wave propagation in random continuum or random dAlembertian operator
The parabolic Anderson model random walk in random potential
König, Wolfgang
2016-01-01
This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
Localization transition of biased random walks on random networks.
Sood, Vishal; Grassberger, Peter
2007-08-31
We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength bc exists such that most walks find the target within a finite time when b > bc. For b infinity before hitting the target. The phase transition at b=bc is a critical point in the sense that quantities such as the return probability P(t) show power laws, but finite-size behavior is complex and does not obey the usual finite-size scaling ansatz. By extending rigorous results for biased walks on Galton-Watson trees, we give the exact analytical value for bc and verify it by large scale simulations.
Advances in randomized parallel computing
Rajasekaran, Sanguthevar
1999-01-01
The technique of randomization has been employed to solve numerous prob lems of computing both sequentially and in parallel. Examples of randomized algorithms that are asymptotically better than their deterministic counterparts in solving various fundamental problems abound. Randomized algorithms have the advantages of simplicity and better performance both in theory and often in practice. This book is a collection of articles written by renowned experts in the area of randomized parallel computing. A brief introduction to randomized algorithms In the aflalysis of algorithms, at least three different measures of performance can be used: the best case, the worst case, and the average case. Often, the average case run time of an algorithm is much smaller than the worst case. 2 For instance, the worst case run time of Hoare's quicksort is O(n ), whereas its average case run time is only O( n log n). The average case analysis is conducted with an assumption on the input space. The assumption made to arrive at t...
Directory of Open Access Journals (Sweden)
Tian Gao
2015-02-01
Full Text Available The knowledge about spatial distribution of plantation forests is critical for forest management, monitoring programs and functional assessment. This study demonstrates the potential of multi-seasonal (spring, summer, autumn and winter Landsat-8 Operational Land Imager imageries with random forests (RF modeling to map larch plantations (LP in a typical plantation forest landscape in North China. The spectral bands and two types of textures were applied for creating 675 input variables of RF. An accuracy of 92.7% for LP, with a Kappa coefficient of 0.834, was attained using the RF model. A RF-based importance assessment reveals that the spectral bands and bivariate textural features calculated by pseudo-cross variogram (PC strongly promoted forest class-separability, whereas the univariate textural features influenced weakly. A feature selection strategy eliminated 93% of variables, and then a subset of the 47 most essential variables was generated. In this subset, PC texture derived from summer and winter appeared the most frequently, suggesting that this variability in growing peak season and non-growing season can effectively enhance forest class-separability. A RF classifier applied to the subset led to 91.9% accuracy for LP, with a Kappa coefficient of 0.829. This study provides an insight into approaches for discriminating plantation forests with phenological behaviors.
Triangulation in Random Refractive Distortions.
Alterman, Marina; Schechner, Yoav Y; Swirski, Yohay
2017-03-01
Random refraction occurs in turbulence and through a wavy water-air interface. It creates distortion that changes in space, time and with viewpoint. Localizing objects in three dimensions (3D) despite this random distortion is important to some predators and also to submariners avoiding the salient use of periscopes. We take a multiview approach to this task. Refracted distortion statistics induce a probabilistic relation between any pixel location and a line of sight in space. Measurements of an object's random projection from multiple views and times lead to a likelihood function of the object's 3D location. The likelihood leads to estimates of the 3D location and its uncertainty. Furthermore, multiview images acquired simultaneously in a wide stereo baseline have uncorrelated distortions. This helps reduce the acquisition time needed for localization. The method is demonstrated in stereoscopic video sequences, both in a lab and a swimming pool.
Black holes and random matrices
Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori; Polchinski, Joseph; Saad, Phil; Shenker, Stephen H.; Stanford, Douglas; Streicher, Alexandre; Tezuka, Masaki
2017-05-01
We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function | Z( β + it)|2 as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Free probability and random matrices
Mingo, James A
2017-01-01
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Quantum random walks and their convergence to Evans–Hudson ...
Indian Academy of Sciences (India)
Using coordinate-free basic operators on toy Fock spaces, quantum random walks are defined following the ideas of Attal and Pautrat. Extending the result for one dimensional noise, strong convergence of quantum random walks associated with bounded structure maps to Evans–Hudson flow is proved under suitable ...
Cross over of recurrence networks to random graphs and random ...
Indian Academy of Sciences (India)
2017-01-27
Jan 27, 2017 ... analysis based on net theoretic measures has developed into a major field, .... with the value of the scaling index γ falling between 2 and 3. To compute the network measures, we first construct an ensemble of synthetic networks, both random and ... higher k values are present to maintain the same γ. In both.
Bose condensation in (random traps
Directory of Open Access Journals (Sweden)
V.A. Zagrebnov
2009-01-01
Full Text Available We study a non-interacting (perfect Bose-gas in random external potentials (traps. It is shown that a generalized Bose-Einstein condensation in the random eigenstates manifests if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose-gas. Moreover, we prove that the amounts of both condensate densities are equal. This statement is relevant for justification of the Bogoliubov approximation} in the theory of disordered boson systems.
Random organization and plastic depinning
Energy Technology Data Exchange (ETDEWEB)
Reichhardt, Charles [Los Alamos National Laboratory; Reichhardt, Cynthia [Los Alamos National Laboratory
2008-01-01
We provide evidence that the general phenomenon of plastic depinning can be described as an absorbing phase transition, and shows the same features as the random organization which was recently studied in periodically driven particle systems [L. Corte, Nature Phys. 4, 420 (2008)]. In the plastic flow system, the pinned regime corresponds to the absorbing state and the moving state corresponds to the fluctuating state. When an external force is suddenly applied, the system eventually organizes into one of these two states with a time scale that diverges as a power law at a nonequilibrium transition. We propose a simple experiment to test for this transition in systems with random disorder.
Neutron transport in random media
Energy Technology Data Exchange (ETDEWEB)
Makai, M. [KFKI Atomic Energy Research Institute, Budapest (Hungary)
1996-08-01
The survey reviews the methods available in the literature which allow a discussion of corium recriticality after a severe accident and a characterization of the corium. It appears that to date no one has considered the eigenvalue problem, though for the source problem several approaches have been proposed. The mathematical formulation of a random medium may be approached in different ways. Based on the review of the literature, we can draw three basic conclusions. The problem of static, random perturbations has been solved. The static case is tractable by the Monte Carlo method. There is a specific time dependent case for which the average flux is given as a series expansion.
Algebraic polynomials with random coefficients
Directory of Open Access Journals (Sweden)
K. Farahmand
2002-01-01
Full Text Available This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω+a1(ω(n11/2x+a2(ω(n21/2x2+…an(ω(nn1/2xn when n is large. The coefficients {aj(w}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr. A special case of dependent coefficients is also studied.
Composite continuous time random walks
Hilfer, Rudolf
2017-12-01
Random walks in composite continuous time are introduced. Composite time flow is the product of translational time flow and fractional time flow [see Chem. Phys. 84, 399 (2002)]. The continuum limit of composite continuous time random walks gives a diffusion equation where the infinitesimal generator of time flow is the sum of a first order and a fractional time derivative. The latter is specified as a generalized Riemann-Liouville derivative. Generalized and binomial Mittag-Leffler functions are found as the exact results for waiting time density and mean square displacement.
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
Ambainis, Andris; Harrow, Aram W.; Hastings, Matthew B.
2012-02-01
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in {(mathbb {C}^d)^{⊗ k}}, where k and p/ d k are fixed while d → ∞. When k = 1, the Marčenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ({(1+sqrt{p/d^k})^2}) but the smallest eigenvalue {(min(0,1-sqrt{p/d^k})^2)} and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately {(1+sqrt{p/d^k})^2} and the spectral density approaches that of the Marčenko-Pastur law, generalizing the random matrix theory result to the random tensor case. Our bound on the largest eigenvalue has implications both for sampling from a particular heavy-tailed distribution and for a recently proposed quantum data-hiding and correlation-locking scheme due to Leung and Winter. Since the matrices we consider have neither independent entries nor unitary invariance, we need to develop new techniques for their analysis. The main contribution of this paper is to give three different methods for analyzing mixtures of random product states: a diagrammatic approach based on Gaussian integrals, a combinatorial method that looks at the cycle decompositions of permutations and a recursive method that uses a variant of the Schwinger-Dyson equations.
Directory of Open Access Journals (Sweden)
Williams Hywel C
2011-05-01
Full Text Available Abstract Background Massive duplication of effort occurs when researchers all over the world undertake extensive searches for randomized controlled trials when preparing systematic reviews, when developing evidence-based guidelines and when applying for research funding for eczema treatments. Such duplication wastes valuable resources. Searching for randomized controlled trials of eczema is a laborious task involving scrutiny of thousands of individual references from diverse electronic databases in order to obtain a few papers of interest. Clinicians and patients who wish to find out more about a particular treatment are at risk of missing the relevant evidence if they are not trained in electronic bibliographic searching. Systematic reviews cannot be relied upon to comprehensively inform current optimal eczema treatments due to incomplete coverage and because many may be out of date. An international, publically available and comprehensive resource which brings together all randomized controlled trials on eczema treatment using a highly sensitive search has the potential to release more filtered knowledge about patient care to those who need it most and to significantly shorten the duration and costs of many clinical eczema research and guideline projects. Description The Global Resource of EczemA Trials brings together information on all randomized controlled trials of eczema treatments published from the beginning of 2000 up to the end of 2010 and will be updated every month. We searched the Cochrane Central Register of Controlled Trials in The Cochrane Library and the Cochrane Skin Group Specialised Register, MEDLINE, EMBASE, LILACS, AMED and CINHAL databases. We included 268 RCTs (24th March 2011 covering over 70 different treatment interventions. The structure of the Global Resource of Eczema Trials allows the user as much, or as little, specificity when retrieving information on trials as they wish, in an easy to use format. For each
A Mixed Effects Randomized Item Response Model
Fox, J.-P.; Wyrick, Cheryl
2008-01-01
The randomized response technique ensures that individual item responses, denoted as true item responses, are randomized before observing them and so-called randomized item responses are observed. A relationship is specified between randomized item response data and true item response data. True item response data are modeled with a (non)linear…
Nobile, Fabio
2015-01-07
We consider a general problem F(u, y) = 0 where u is the unknown solution, possibly Hilbert space valued, and y a set of uncertain parameters. We specifically address the situation in which the parameterto-solution map u(y) is smooth, however y could be very high (or even infinite) dimensional. In particular, we are interested in cases in which F is a differential operator, u a Hilbert space valued function and y a distributed, space and/or time varying, random field. We aim at reconstructing the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial expansions, for the output of computer experiments. In the case of PDEs with random parameters, the metamodel is then used to approximate statistics of the output quantity. We discuss the stability of discrete least squares on random points show convergence estimates both in expectation and probability. We also present possible strategies to select, either a-priori or by adaptive algorithms, sequences of approximating polynomial spaces that allow to reduce, and in some cases break, the curse of dimensionality
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral...
Privacy preserving randomized gossip algorithms
Hanzely, Filip
2017-06-23
In this work we present three different randomized gossip algorithms for solving the average consensus problem while at the same time protecting the information about the initial private values stored at the nodes. We give iteration complexity bounds for all methods, and perform extensive numerical experiments.
Common Randomness Principles of Secrecy
Tyagi, Himanshu
2013-01-01
This dissertation concerns the secure processing of distributed data by multiple terminals, using interactive public communication among themselves, in order to accomplish a given computational task. In the setting of a probabilistic multiterminal source model in which several terminals observe correlated random signals, we analyze secure…
Supersymmetry in Random Matrix Theory
Guhr, Thomas
2010-01-01
Supersymmetry is nowadays indispensable for many problems in Random Matrix Theory. It is presented here with an emphasis on conceptual and structural issues. An introduction to supermathematics is given. The Hubbard-Stratonovich transformation as well as its generalization and superbosonization are explained. The supersymmetric non-linear sigma model, Brownian motion in superspace and the color-flavor transformation are discussed.
Chaos, complexity, and random matrices
Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni
2017-11-01
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.
Fatigue Reliability under Random Loads
DEFF Research Database (Denmark)
Talreja, R.
1979-01-01
We consider the problem of estimating the probability of survival (non-failure) and the probability of safe operation (strength greater than a limiting value) of structures subjected to random loads. These probabilities are formulated in terms of the probability distributions of the loads and the...... propagation stage. The consequences of this behaviour on the fatigue reliability are discussed....
Stalled ERP at Random Textiles
Brumberg, Robert; Kops, Eric; Little, Elizabeth; Gamble, George; Underbakke, Jesse; Havelka, Douglas
2016-01-01
Andre Raymond, Executive Vice President of Sales and Marketing for Random Textiles Co. Inc. (RTC), stood in front of the podium to address his team of 70 sales consultants in Las Vegas, NV. The organization had increased market share and achieved record sales over the past three years; however, in the shadow of this success lurked an obstacle that…
Randomized Item Response Theory Models
Fox, Gerardus J.A.
2005-01-01
The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR technique is the probability of the true response modeled by
Random matrix theory and multivariate statistics
Diaz-Garcia, Jose A.; Jáimez, Ramon Gutiérrez
2009-01-01
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases the classical random matrix ensembles, are proposed. Some properties of these classes of ensemble are analysed. In addition, the random matrix ensemble approach is extended and a unified theory proposed for the study of distributions for real normed divisio...
Random scalar fields and hyperuniformity
Ma, Zheng; Torquato, Salvatore
2017-06-01
Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize two-phase media, scalar fields, and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. Specifically, we analyze spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-Bénard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that they are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding (level-cutting) a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology, and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.
Directory of Open Access Journals (Sweden)
Valentine Lebourgeois
2017-03-01
Full Text Available Sentinel-2 images are expected to improve global crop monitoring even in challenging tropical small agricultural systems that are characterized by high intra- and inter-field spatial variability and where satellite observations are disturbed by the presence of clouds. To overcome these constraints, we analyzed and optimized the performance of a combined Random Forest (RF classifier/object-based approach and applied it to multisource satellite data to produce land use maps of a smallholder agricultural zone in Madagascar at five different nomenclature levels. The RF classifier was first optimized by reducing the number of input variables. Experiments were then carried out to (i test cropland masking prior to the classification of more detailed nomenclature levels, (ii analyze the importance of each data source (a high spatial resolution (HSR time series, a very high spatial resolution (VHSR coverage and a digital elevation model (DEM and data type (spectral, textural or other, and (iii quantify their contributions to classification accuracy levels. The results show that RF classifier optimization allowed for a reduction in the number of variables by 1.5- to 6-fold (depending on the classification level and thus a reduction in the data processing time. Classification results were improved via the hierarchical approach at all classification levels, achieving an overall accuracy of 91.7% and 64.4% for the cropland and crop subclass levels, respectively. Spectral variables derived from an HSR time series were shown to be the most discriminating, with a better score for spectral indices over the reflectances. VHSR data were only found to be essential when implementing the segmentation of the area into objects and not for the spectral or textural features they can provide during classification.
Directory of Open Access Journals (Sweden)
Gray Fiona C
2009-08-01
Full Text Available Abstract Background DNA polymerase δ plays an essential role in chromosomal DNA replication in eukaryotic cells, being responsible for synthesising the bulk of the lagging strand. In fission yeast, Pol δ is a heterotetrameric enzyme comprising four evolutionarily well-conserved proteins: the catalytic subunit Pol3 and three smaller subunits Cdc1, Cdc27 and Cdm1. Pol3 binds directly to the B-subunit, Cdc1, which in turn binds the C-subunit, Cdc27. Human Pol δ comprises the same four subunits, and the crystal structure was recently reported of a complex of human p50 and the N-terminal domain of p66, the human orthologues of Cdc1 and Cdc27, respectively. Results To gain insights into the structure and function of Cdc1, random and directed mutagenesis techniques were used to create a collection of thirty alleles encoding mutant Cdc1 proteins. Each allele was tested for function in fission yeast and for binding of the altered protein to Pol3 and Cdc27 using the two-hybrid system. Additionally, the locations of the amino acid changes in each protein were mapped onto the three-dimensional structure of human p50. The results obtained from these studies identify amino acid residues and regions within the Cdc1 protein that are essential for interaction with Pol3 and Cdc27 and for in vivo function. Mutations specifically defective in Pol3-Cdc1 interactions allow the identification of a possible Pol3 binding surface on Cdc1. Conclusion In the absence of a three-dimensional structure of the entire Pol δ complex, the results of this study highlight regions in Cdc1 that are vital for protein function in vivo and provide valuable clues to possible protein-protein interaction surfaces on the Cdc1 protein that will be important targets for further study.
Bipartite quantum states and random complex networks
Garnerone, Silvano; Giorda, Paolo; Zanardi, Paolo
2012-01-01
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of random graphs known as complex networks. In the case of classical random graphs, we derive an analytic expression for the averaged entanglement entropy \\bar S while for general complex networks we rely on numerics. For a large number of nodes n we find a scaling \\bar {S} \\sim c log n +g_{ {e}} where both the prefactor c and the sub-leading O(1) term ge are characteristic of the different classes of complex networks. In particular, ge encodes topological features of the graphs and is named network topological entropy. Our results suggest that quantum entanglement may provide a powerful tool for the analysis of large complex networks with non-trivial topological properties.
Quantum Entanglement Growth under Random Unitary Dynamics
Directory of Open Access Journals (Sweden)
Adam Nahum
2017-07-01
Full Text Available Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ equation. The mean entanglement grows linearly in time, while fluctuations grow like (time^{1/3} and are spatially correlated over a distance ∝(time^{2/3}. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i a stochastic model of a growing surface, (ii a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.
Registration of randomized clinical trials
DEFF Research Database (Denmark)
Østervig, R M; Sonne, A; Rasmussen, L S
2015-01-01
starting enrolment before 2010 to 63.2% after 2010 (24/38, P clinical trials were registered at clinicaltrials.gov. CONCLUSION: Many published randomized controlled trials from Acta Anaesthesiologica Scandinavica were not adequately registered but the requirement of trial registration has...... the proportion of correctly registered randomized controlled trials (RCTs) published in Acta from 2009 to 2014. METHODS: We manually searched all Acta issues from 2009 to 2014 for RCTs. Information about timing of data collection and registration in trial registries was extracted. We classified RCTs as correctly...... registered when it could be verified that patient enrolment was started after registration in a trial registry. RESULTS: We identified 200 RCTs. Dates for patient enrolment were not specified in 51 (25.5%). The proportion of correctly registered trials increased significantly from 17.1% (19/111) for trials...
Conservation constraints on random matrices
Ma Wen Jong; Hsieh, J
2003-01-01
We study the random matrices constrained by the summation rules that are present in the Hessian of the potential energy surface in the instantaneous normal mode calculations, as a result of momentum conservation. In this paper, we analyse the properties related to such conservation constraints in two classes of real symmetric matrices: one with purely row-wise summation rules and the other with the constraints on the blocks of each matrix, which underscores partially the spatial dimension. We show explicitly that the constraints are removable by separating the degrees of freedom of the zero-eigenvalue modes. The non-spectral degrees of freedom under the constraints can be realized in terms of the ordinary constraint-free orthogonal symmetry but with the rank deducted by the block dimension. We propose that the ensemble of real symmetric matrices with full randomness, constrained by the summation rules, is equivalent to the Gaussian orthogonal ensemble (GOE) with lowered rank. Independent of the joint probabil...
Logical independence and quantum randomness
Energy Technology Data Exchange (ETDEWEB)
Paterek, T; Kofler, J; Aspelmeyer, M; Zeilinger, A; Brukner, C [Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna (Austria); Prevedel, R; Klimek, P [Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)], E-mail: tomasz.paterek@univie.ac.at
2010-01-15
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.
Optimal randomized scheduling by replacement
Energy Technology Data Exchange (ETDEWEB)
Saias, I.
1996-05-01
In the replacement scheduling problem, a system is composed of n processors drawn from a pool of p. The processors can become faulty while in operation and faulty processors never recover. A report is issued whenever a fault occurs. This report states only the existence of a fault but does not indicate its location. Based on this report, the scheduler can reconfigure the system and choose another set of n processors. The system operates satisfactorily as long as, upon report of a fault, the scheduler chooses n non-faulty processors. We provide a randomized protocol maximizing the expected number of faults the system can sustain before the occurrence of a crash. The optimality of the protocol is established by considering a closely related dual optimization problem. The game-theoretic technical difficulties that we solve in this paper are very general and encountered whenever proving the optimality of a randomized algorithm in parallel and distributed computation.
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
The weighted random graph model
Garlaschelli, Diego
2009-07-01
We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is characterized by a geometric weight distribution, a binomial degree distribution and a negative binomial strength distribution. We also characterize exactly the percolation phase transitions associated with edge removal and with the appearance of weighted subgraphs of any order and intensity. We find that even this completely null model displays a percolation behaviour similar to what is observed in real weighted networks, implying that edge removal cannot be used to detect community structure empirically. By contrast, the analysis of clustering successfully reveals different patterns between the WRG and real networks.
Systematic Differences and Random Rates
DEFF Research Database (Denmark)
Knudsen, Thorbjørn; Levinthal, Daniel A.; Winter, Sidney G.
2017-01-01
of quantity in the face of a downward sloping demand curve and recognition of their impact on the market price. If firms are subject to random firm-specific shocks, then in this equilibrium setting a population of such firms would generate a pattern of growth consistent with Gibrat’s law. However, if broader......A fundamental premise of the strategy field is the existence of persistent firm level differences in resources and capabilities. This property of heterogeneity should express itself in a variety of empirical “signatures,” such as firm performance and arguably systematic and persistent differences...... component, but for much of an industry’s and firm’s history should have a random pattern consistent with the Gibrat property. The intuition is as follows. In a Cournot equilibrium, firms of better “type” (i.e., lower cost) realize a larger market share, but act with some restraint on their choice...
Scanning of Markov Random Processes
Directory of Open Access Journals (Sweden)
Gustav Cepciansky
2003-01-01
Full Text Available Function of most electronic devices is based on the microprocessor control. A microprocessor must scan and evaluate function of many controlled equipment that can be transformed into 2 statuses - "free" or "busy". Microprocessors in a digital exchange are the typical example of that. It can be said the microprocessors are in a discrete dialogue with the controlled parts. They ascertain in regular time intervals whether the status of the controlled equipment has changed. 1 or more "busy" statuses may exist in the same time. As the changes from "free" to "busy" and from "busy" to "free" occur randomly, the state of i busy statuses lasts for a random period too. If the changes have pro-perties of Markov process, the probability which each change will be detected with and hence the scanning rate needed can be derived.
Random matrix improved subspace clustering
Couillet, Romain
2017-03-06
This article introduces a spectral method for statistical subspace clustering. The method is built upon standard kernel spectral clustering techniques, however carefully tuned by theoretical understanding arising from random matrix findings. We show in particular that our method provides high clustering performance while standard kernel choices provably fail. An application to user grouping based on vector channel observations in the context of massive MIMO wireless communication networks is provided.
Random matrix theory within superstatistics
Abul-Magd, A. Y.
2005-01-01
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions and the two-level co...
Staggered chiral random matrix theory
Osborn, James C.
2010-01-01
We present a random matrix theory (RMT) for the staggered lattice QCD Dirac operator. The staggered RMT is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.
Superstatistics in Random Matrix Theory
Abul-Magd, A. Y.
2011-01-01
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented other versions of the theory that keep...
Analyzing Walksat on random formulas
Coja-Oghlan, Amin; Frieze, Alan
2011-01-01
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from Papadimitriou (FOCS 1991)/Schoning (FOCS 1999) finds a satisfying assignment of F in polynomial time w.h.p. if m/n0. This is an improvement by a factor of $\\Theta(k)$ over the best previous analysis of Walksat from Coja-Oghlan, Feige, Frieze, Krivelevich, Vilenchik (SODA 2009).
Permutation Entropy for Random Binary Sequences
Directory of Open Access Journals (Sweden)
Lingfeng Liu
2015-12-01
Full Text Available In this paper, we generalize the permutation entropy (PE measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.
Human action analysis with randomized trees
Yu, Gang; Liu, Zicheng
2014-01-01
This book will provide a comprehensive overview on human action analysis with randomized trees. It will cover both the supervised random trees and the unsupervised random trees. When there are sufficient amount of labeled data available, supervised random trees provides a fast method for space-time interest point matching. When labeled data is minimal as in the case of example-based action search, unsupervised random trees is used to leverage the unlabelled data. We describe how the randomized trees can be used for action classification, action detection, action search, and action prediction.
Manyfield inflation in random potentials
Bjorkmo, Theodor; Marsh, M. C. David
2018-02-01
We construct models of inflation with many randomly interacting fields and use these to study the generation of cosmological observables. We model the potentials as multi-dimensional Gaussian random fields (GRFs) and identify powerful algebraic simplifications that, for the first time, make it possible to access the manyfield limit of inflation in GRF potentials. Focussing on small-field, slow-roll, approximate saddle-point inflation in potentials with structure on sub-Planckian scales, we construct explicit examples involving up to 100 fields and generate statistical ensembles comprising of 164,000 models involving 5 to 50 fields. For the subset of these that support at least sixty e-folds of inflation, we use the 'transport method' and δ N formalism to determine the predictions for cosmological observables at the end of inflation, including the power spectrum and the local non-Gaussianities of the primordial perturbations. We find three key results: i) Planck compatibility is not rare, but future experiments may rule out this class of models; ii) In the manyfield limit, the predictions from these models agree well with, but are sharper than, previous results derived using potentials constructed through non-equilibrium Random Matrix Theory; iii) Despite substantial multifield effects, non-Gaussianities are typically very small: fNLloc ll 1. We conclude that many of the 'generic predictions' of single-field inflation can be emergent features of complex inflation models.
MUSCLE MRI SEGMENTATION USING RANDOM WALKER METHOD
Directory of Open Access Journals (Sweden)
A. V. Shukelovich
2013-01-01
Full Text Available A technique of marker set construction for muscle MRI segmentation using random walker approach is introduced. The possibility of clinician’s manual labor amount reduction and random walker algorithm optimization is studied.
Self-correcting random number generator
Energy Technology Data Exchange (ETDEWEB)
Humble, Travis S.; Pooser, Raphael C.
2016-09-06
A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.
Optical physics: Clear directions for random lasers
Wiersma, Diederik S.
2016-11-01
Random lasers use disordered structures to produce light, which is usually emitted in many directions. A random laser that can produce a collimated beam offers a wide range of applications, from imaging to security scanning.
Process of random distributions : classification and prediction ...
African Journals Online (AJOL)
Dirichlet random distribution. The parameter of this process can be the distribution of any usual such as the (multifractional) Brownian motion. We also extend Kraft random distribution to the continuous time case. We give an application in ...
On the randomness of pulsar nulls
Redman, Stephen L.; Rankin, Joanna M.
2009-05-01
Pulsar nulling is not always a random process; most pulsars, in fact, null non-randomly. The Wald-Wolfowitz statistical runs test is a simple diagnostic that pulsar astronomers can use to identify pulsars that have non-random nulls. It is not clear at this point how the dichotomy in pulsar nulling randomness is related to the underlying nulling phenomenon, but its nature suggests that there are at least two distinct reasons that pulsars null.
Analysis of android random number generator
Sarıtaş, Serkan
2013-01-01
Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013. Thesis (Master's) -- Bilkent University, 2013. Includes bibliographical references leaves 61-65. Randomness is a crucial resource for cryptography, and random number generators are critical building blocks of almost all cryptographic systems. Therefore, random number generation is one of the key parts of secure communication. Random number generatio...
Energy Technology Data Exchange (ETDEWEB)
Stipčević, Mario, E-mail: mario.stipcevic@irb.hr [Photonics and Quantum Optics Research Unit, Center of Excellence for Advanced Materials and Sensing Devices, Ruđer Bošković Institute, Bijenička 54, 10000 Zagreb (Croatia)
2016-03-15
In this work, a new type of elementary logic circuit, named random flip-flop (RFF), is proposed, experimentally realized, and studied. Unlike conventional Boolean logic circuits whose action is deterministic and highly reproducible, the action of a RFF is intentionally made maximally unpredictable and, in the proposed realization, derived from a fundamentally random process of emission and detection of light quanta. We demonstrate novel applications of RFF in randomness preserving frequency division, random frequency synthesis, and random number generation. Possible usages of these applications in the information and communication technology, cryptographic hardware, and testing equipment are discussed.
Random packing of colloids and granular matter
Wouterse, A.
2008-01-01
This thesis deals with the random packing of colloids and granular matter. A random packing is a stable disordered collection of touching particles, without long-range positional and orientational order. Experimental random packings of particles with the same shape but made of different materials
49 CFR 382.305 - Random testing.
2010-10-01
... 49 Transportation 5 2010-10-01 2010-10-01 false Random testing. 382.305 Section 382.305... ALCOHOL USE AND TESTING Tests Required § 382.305 Random testing. (a) Every employer shall comply with the requirements of this section. Every driver shall submit to random alcohol and controlled substance testing as...
49 CFR 655.45 - Random testing.
2010-10-01
... 49 Transportation 7 2010-10-01 2010-10-01 false Random testing. 655.45 Section 655.45... of Testing § 655.45 Random testing. (a) Except as provided in paragraphs (b) through (d) of this section, the minimum annual percentage rate for random drug testing shall be 50 percent of covered...
Source-Independent Quantum Random Number Generation
Cao, Zhu; Zhou, Hongyi; Yuan, Xiao; Ma, Xiongfeng
2016-01-01
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts—a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness. However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output. To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted. In our randomness analysis, we make no assumptions about the dimension of the source. For instance, multiphoton emissions are allowed in optical implementations. Our analysis takes into account the finite-key effect with the composable security definition. In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit. In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 ×103 bit /s .
Variational Infinite Hidden Conditional Random Fields
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja; Ghahramani, Zoubin
2015-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An Infinite hidden conditional random field is a hidden conditional random field with a countably infinite number of
Randomness and the Madness of Crowds
Weitzel, Utz|info:eu-repo/dai/nl/276323394; Rosenkranz, Stephanie|info:eu-repo/dai/nl/157222241
2016-01-01
Human interaction often appears to be random and at times even chaotic. We use game theory, the mathematical study of interactive decision making, to explain the role of rationality and randomness in strategic behavior. In many of these situations, humans deliberately create randomness as a best
Wave Propagation inside Random Media
Cheng, Xiaojun
This thesis presents results of studies of wave scattering within and transmission through random and periodic systems. The main focus is on energy profiles inside quasi-1D and 1D random media. The connection between transport and the states of the medium is manifested in the equivalence of the dimensionless conductance, g, and the Thouless number which is the ratio of the average linewidth and spacing of energy levels. This equivalence and theories regarding the energy profiles inside random media are based on the assumption that LDOS is uniform throughout the samples. We have conducted microwave measurements of the longitudinal energy profiles within disordered samples contained in a copper tube supporting multiple waveguide channels with an antenna moving along a slit on the tube. These measurements allow us to determine the local density of states (LDOS) at a location which is the sum of energy from all incoming channels on both sides. For diffusive samples, the LDOS is uniform and the energy profile decays linearly as expected. However, for localized samples, we find that the LDOS drops sharply towards the middle of the sample and the energy profile does not follow the result of the local diffusion theory where the LDOS is assumed to be uniform. We analyze the field spectra into quasi-normal modes and found that the mode linewidth and the number of modes saturates as the sample length increases. Thus the Thouless number saturates while the dimensionless conductance g continues to fall with increasing length, indicating that the modes are localized near the boundaries. This is in contrast to the general believing that g and Thouless number follow the same scaling behavior. Previous measurements show that single parameter scaling (SPS) still holds in the same sample where the LDOS is suppressed te{shi2014microwave}. We explore the extension of SPS to the interior of the sample by analyzing statistics of the logrithm of the energy density ln W(x) and found that
Random roots and lineage sorting.
Rosenfeld, Jeffrey A; Payne, Ansel; DeSalle, Rob
2012-07-01
Lineage sorting has been suggested as a major force in generating incongruent phylogenetic signal when multiple gene partitions are examined. The degree of lineage sorting can be estimated using the coalescent process and simulation studies have also pointed to a major role for incomplete lineage sorting as a factor in phylogenetic inference. Some recent empirical studies point to an extreme role for this phenomenon with up to 50-60% of all informative genes showing incongruence as a result of lineage sorting. Here, we examine seven large multi-partition genome level data sets over a large range of taxonomic representation. We took the approach of examining outgroup choice and its impact on tree topology, by swapping outgroups into analyses with successively larger genetics distances to the ingroup. Our results indicate a linear relationship of outgroup distance with incongruence in the data sets we examined suggesting a strong random rooting effect. In addition, we attempted to estimate the degree of lineage sorting in several large genome level data sets by examining triads of very closely related taxa. This exercise resulted in much lower estimates of incongruent genes that could be the result of lineage sorting, with an overall estimate of around 10% of the total number of genes in a genome showing incongruence as a result of true lineage sorting. Finally we examined the behavior of likelihood and parsimony approaches on the random rooting phenomenon. Likelihood tends to stabilize incongruence as outgroups get further and further away from the ingroup. In one extreme case, likelihood overcompensates for sequence divergence but increases random rooting causing long branch repulsion. Copyright © 2012 Elsevier Inc. All rights reserved.
Microscopy using randomized speckle illumination
Perinchery, Sandeep M.; Shinde, Anant; Murukeshan, V. M.
2017-06-01
It is well known for structured illumination microscopy (SIM) that the lateral resolution by a factor of two beyond the classical diffraction limit is achieved using spatially structured illumination in wide-field fluorescence microscope. In the state of art SIM systems, grating patterns are generally generated by physical gratings or by spatial light modulators such as digital micro mirrors (DMD), liquid crystal displays (LCD). In this study, using a combination of LCD and ground glasses, size controlled randomized speckle patterns are generated as an illumination source for the microscope. Proof of concept of using speckle illumination in SIM configuration is tested by imaging fixed BPAE cells.
Randomized selection on the GPU
Energy Technology Data Exchange (ETDEWEB)
Monroe, Laura Marie [Los Alamos National Laboratory; Wendelberger, Joanne R [Los Alamos National Laboratory; Michalak, Sarah E [Los Alamos National Laboratory
2011-01-13
We implement here a fast and memory-sparing probabilistic top N selection algorithm on the GPU. To our knowledge, this is the first direct selection in the literature for the GPU. The algorithm proceeds via a probabilistic-guess-and-chcck process searching for the Nth element. It always gives a correct result and always terminates. The use of randomization reduces the amount of data that needs heavy processing, and so reduces the average time required for the algorithm. Probabilistic Las Vegas algorithms of this kind are a form of stochastic optimization and can be well suited to more general parallel processors with limited amounts of fast memory.
Random measures, theory and applications
Kallenberg, Olav
2017-01-01
Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.
a randomized, placebo- controlled study
Hall, Franziska van
2012-01-01
Introduction: Repetitive transcranial magnetic stimulation (rTMS) is a well-tolerated non-invasive method, which has also been proved to have mild antidepressant effects and is used as “add-on“-therapy in treating pharmaco-resistant major depression. Objective: The efficacy of an escitalopram plus rTMS-combination-treatment was evaluated and compared to escitalopram plus sham rTMS. Methods: We designed a four week-, randomized, rater-blinded, and controlled add-on study with two trea...
Transport properties on a random comb
Balakrishnan, V.; Van den Broeck, C.
1995-02-01
We study the random walk of a particle in a random comb structure, both in the presence of a biasing field and an the field-free case. We show that the mean-field treatment of the quenched disorder can be exactly mapped on to a continuous time random walk (CTRW) on the backbone of the comb, with a definite waiting time density. We find an exact expression for this central quantity. The Green function for the CTRW is then obtained. Its first and second moments determine the drift and diffusion at all times. We show that the drift velocity v vanishes asymptotically for power-law and stretched-exponential distributions of branch lengths on the comb, whatever be the biasing field strength. For an exponential branch-length distribution, v is a nonmonotonic function of the bias, increasing initially to a maximum and then decreasing to zero at a critical value. In the field-free case, anomalous diffusion occurs for a range of power-law distributions of the branch length. The corresponding exponent for the mean square displacement is obtained, as is the asymptotic form of the positional probability distribution for the random walk. We show that normal diffusion occurs whenever the mean branch length is finite, and present a simple formula for the effective diffusion constant; these results are extended to regular (nonrandom) combs as well. The physical reason for anomalous drift or diffusion is traced to the properties of the distribution of a first passage time (on a finite chain) that controls the effective waiting time density of the CTRW.
Holographic coherent states from random tensor networks
Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang
2017-08-01
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we generalize the random tensor network approach to allow quantum superposition of different spatial geometries. We setup a framework in which all possible bulk spatial geometries, characterized by weighted adjacient matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded in this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around classical geometries define "code subspaces" which are mapped to the boundary Hilbert space isometrically with quantum error correction properties. In addition, we also show that the overlap between different geometries is suppressed exponentially as a function of the geometrical difference between the two geometries. The geometrical difference is measured in an area law fashion, which is a manifestation of the holographic nature of the states considered.
Decompounding random sums: A nonparametric approach
DEFF Research Database (Denmark)
Hansen, Martin Bøgsted; Pitts, Susan M.
Observations from sums of random variables with a random number of summands, known as random, compound or stopped sums arise within many areas of engineering and science. Quite often it is desirable to infer properties of the distribution of the terms in the random sum. In the present paper we...... review a number of applications and consider the nonlinear inverse problem of inferring the cumulative distribution function of the components in the random sum. We review the existing literature on non-parametric approaches to the problem. The models amenable to the analysis are generalized considerably...
Random matrix techniques in quantum information theory
Collins, Benoît; Nechita, Ion
2016-01-01
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Random matrix techniques in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Collins, Benoît, E-mail: collins@math.kyoto-u.ac.jp [Department of Mathematics, Kyoto University, Kyoto 606-8502 (Japan); Département de Mathématique et Statistique, Université d’Ottawa, 585 King Edward, Ottawa, Ontario K1N6N5 (Canada); CNRS, Lyon (France); Nechita, Ion, E-mail: nechita@irsamc.ups-tlse.fr [Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching (Germany); Laboratoire de Physique Théorique, CNRS, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France)
2016-01-15
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Random number datasets generated from statistical analysis of randomly sampled GSM recharge cards.
Okagbue, Hilary I; Opanuga, Abiodun A; Oguntunde, Pelumi E; Ugwoke, Paulinus O
2017-02-01
In this article, a random number of datasets was generated from random samples of used GSM (Global Systems for Mobile Communications) recharge cards. Statistical analyses were performed to refine the raw data to random number datasets arranged in table. A detailed description of the method and relevant tests of randomness were also discussed.
Randomized Block Cubic Newton Method
Doikov, Nikita
2018-02-12
We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN) method, which in each iteration builds a model of the objective function formed as the sum of the natural models of its three components: a linear model with a quadratic regularizer for the differentiable term, a quadratic model with a cubic regularizer for the twice differentiable term, and perfect (proximal) model for the nonsmooth term. Our method in each iteration minimizes the model over a random subset of blocks of the search variable. RBCN is the first algorithm with these properties, generalizing several existing methods, matching the best known bounds in all special cases. We establish ${\\\\cal O}(1/\\\\epsilon)$, ${\\\\cal O}(1/\\\\sqrt{\\\\epsilon})$ and ${\\\\cal O}(\\\\log (1/\\\\epsilon))$ rates under different assumptions on the component functions. Lastly, we show numerically that our method outperforms the state-of-the-art on a variety of machine learning problems, including cubically regularized least-squares, logistic regression with constraints, and Poisson regression.
Chromatic polynomials of random graphs
Energy Technology Data Exchange (ETDEWEB)
Van Bussel, Frank; Fliegner, Denny; Timme, Marc [Max Planck Institute for Dynamics and Self-Organization (MPIDS), Goettingen (Germany); Ehrlich, Christoph [Department of Physics, Technical University of Dresden, Dresden (Germany); Stolzenberg, Sebastian, E-mail: fvb@nld.ds.mpg.d, E-mail: timme@nld.ds.mpg.d [Department of Physics, Ithaca and Weill Cornell Medical College, New York City, Cornell University, NY (United States)
2010-04-30
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Chromatic polynomials of random graphs
Van Bussel, Frank; Ehrlich, Christoph; Fliegner, Denny; Stolzenberg, Sebastian; Timme, Marc
2010-04-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Entanglement dynamics in random media
Menezes, G.; Svaiter, N. F.; Zarro, C. A. D.
2017-12-01
We study how the entanglement dynamics between two-level atoms is impacted by random fluctuations of the light cone. In our model the two-atom system is envisaged as an open system coupled with an electromagnetic field in the vacuum state. We employ the quantum master equation in the Born-Markov approximation in order to describe the completely positive time evolution of the atomic system. We restrict our investigations to the situation in which the atoms are coupled individually to two spatially separated cavities, one of which displays the emergence of light-cone fluctuations. In such a disordered cavity, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that disorder has the effect of slowing down the entanglement decay. We conjecture that in a strong-disorder environment the mean life of entangled states can be enhanced in such a way as to almost completely suppress quantum nonlocal decoherence.
Drop Spreading with Random Viscosity
Xu, Feng; Jensen, Oliver
2016-11-01
Airway mucus acts as a barrier to protect the lung. However as a biological material, its physical properties are known imperfectly and can be spatially heterogeneous. In this study we assess the impact of these uncertainties on the rate of spreading of a drop (representing an inhaled aerosol) over a mucus film. We model the film as Newtonian, having a viscosity that depends linearly on the concentration of a passive solute (a crude proxy for mucin proteins). Given an initial random solute (and hence viscosity) distribution, described as a Gaussian random field with a given correlation structure, we seek to quantify the uncertainties in outcomes as the drop spreads. Using lubrication theory, we describe the spreading of the drop in terms of a system of coupled nonlinear PDEs governing the evolution of film height and the vertically-averaged solute concentration. We perform Monte Carlo simulations to predict the variability in the drop centre location and width (1D) or area (2D). We show how simulation results are well described (at much lower computational cost) by a low-order model using a weak disorder expansion. Our results show for example how variability in the drop location is a non-monotonic function of the solute correlation length increases. Engineering and Physical Sciences Research Council.
What Randomized Benchmarking Actually Measures
Proctor, Timothy; Rudinger, Kenneth; Young, Kevin; Sarovar, Mohan; Blume-Kohout, Robin
2017-09-01
Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r . For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not a well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. These theories allow explicit computation of the error rate that RB measures (r ), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.
Xu, Ganggang
2016-07-15
We propose a new class of trans-Gaussian random fields named Tukey g-and-h (TGH) random fields to model non-Gaussian spatial data. The proposed TGH random fields have extremely flexible marginal distributions, possibly skewed and/or heavy-tailed, and, therefore, have a wide range of applications. The special formulation of the TGH random field enables an automatic search for the most suitable transformation for the dataset of interest while estimating model parameters. Asymptotic properties of the maximum likelihood estimator and the probabilistic properties of the TGH random fields are investigated. An efficient estimation procedure, based on maximum approximated likelihood, is proposed and an extreme spatial outlier detection algorithm is formulated. Kriging and probabilistic prediction with TGH random fields are developed along with prediction confidence intervals. The predictive performance of TGH random fields is demonstrated through extensive simulation studies and an application to a dataset of total precipitation in the south east of the United States.
Probability, random variables, and random processes theory and signal processing applications
Shynk, John J
2012-01-01
Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several app
Robust Extraction of Tomographic Information via Randomized Benchmarking
Directory of Open Access Journals (Sweden)
Shelby Kimmel
2014-03-01
Full Text Available We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution or, more generally, any unital trace-preserving evolution. This approach inherits randomized benchmarking’s robustness to preparation, measurement, and gate imperfections, thereby avoiding systematic errors caused by these imperfections. We also extend these techniques to efficiently estimate the average fidelity of a quantum map to unitary maps outside of the Clifford group. The unitaries we consider correspond to large circuits commonly used as building blocks to achieve scalable, universal, and fault-tolerant quantum computation. Hence, we can efficiently verify all such subcomponents of a circuit-based universal quantum computer. In addition, we rigorously bound the time and sampling complexities of randomized benchmarking procedures, proving that the required nonlinear estimation problem can be solved efficiently.
Randomized clinical trials in HEPATOLOGY
DEFF Research Database (Denmark)
Kjaergard, L L; Nikolova, D; Gluud, C
1999-01-01
Evidence shows that the quality of randomized clinical trials (RCTs) affects estimates of intervention efficacy, which is significantly exaggerated in low-quality trials. The present study examines the quality of all 235 RCTs published in HEPATOLOGY from the initiation in 1981 through August 1998......-blinding. The median quality score of all trials was 3 points (range, 1-5 points). Multiple logistic regression analysis explored the association between quality and therapeutic areas, number of centers, external funding, year of publication, and country of origin. High-quality trials were most likely to investigate......, single-center trials, and trials with no external funding. Quality did not improve with time and was not associated with country of origin. The main conclusions are that the quality of RCTs in HEPATOLOGY needs improvement and that the probability of high quality increased with the number of centers...
The Random Quadratic Assignment Problem
Paul, Gerald; Shao, Jia; Stanley, H. Eugene
2011-11-01
The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.
Lower bounds for randomized Exclusive Write PRAMs
Energy Technology Data Exchange (ETDEWEB)
MacKenzie, P.D.
1995-05-02
In this paper we study the question: How useful is randomization in speeding up Exclusive Write PRAM computations? Our results give further evidence that randomization is of limited use in these types of computations. First we examine a compaction problem on both the CREW and EREW PRAM models, and we present randomized lower bounds which match the best deterministic lower bounds known. (For the CREW PRAM model, the lower bound is asymptotically optimal.) These are the first non-trivial randomized lower bounds known for the compaction problem on these models. We show that our lower bounds also apply to the problem of approximate compaction. Next we examine the problem of computing boolean functions on the CREW PRAM model, and we present a randomized lower bound, which improves on the previous best randomized lower bound for many boolean functions, including the OR function. (The previous lower bounds for these functions were asymptotically optimal, but we improve the constant multiplicative factor.) We also give an alternate proof for the randomized lower bound on PARITY, which was already optimal to within a constant additive factor. Lastly, we give a randomized lower bound for integer merging on an EREW PRAM which matches the best deterministic lower bound known. In all our proofs, we use the Random Adversary method, which has previously only been used for proving lower bounds on models with Concurrent Write capabilities. Thus this paper also serves to illustrate the power and generality of this method for proving parallel randomized lower bounds.
Random-Field Model of a Cooper Pair Insulator
Proctor, Thomas; Chudnovsky, Eugene; Garanin, Dmitry
2013-03-01
The model of a disordered superconducting film with quantum phase fluctuations is mapped on a random-field XY spin model in 2+1 dimensions. Analytical studies within continuum field theory, supported by our recent numerical calculations on discrete lattices, show the onset of the low-temperature Cooper pair insulator phase. The constant external field in the random-field spin model maps on the Josephson coupling between the disordered film and a bulk superconductor. Such a coupling, if sufficiently strong, restores superconductivity in the film. This provides an experimental test for the quantum fluctuation model of a superinsulator.
Randomness in retrospect: exploring the interactions between memory and randomness cognition.
Olivola, Christopher Y; Oppenheimer, Daniel M
2008-10-01
People tend to believe that sequences of random events produce fewer and shorter streaks than is actually the case. Although this error has been demonstrated repeatedly and in many forms, nearly all studies of randomness cognition have focused on how people think about random events occurring in the present or future. This article examines how our biased beliefs about randomness interact with properties of memory to influence our judgments about and memory for past random events. We explore this interaction by examining how beliefs about randomness affect our memory for random events and how certain properties of memory alter our tendency to categorize events as random. Across three experiments, we demonstrate an interaction between randomness cognition and three well-established but distinct properties of memory: (1) the reconstructive nature of memory, (2) primacy and recency effects, and (3) duration neglect. Theoretical and practical implications are discussed.
Pseudo random signal processing theory and application
Zepernick, Hans-Jurgen
2013-01-01
In recent years, pseudo random signal processing has proven to be a critical enabler of modern communication, information, security and measurement systems. The signal's pseudo random, noise-like properties make it vitally important as a tool for protecting against interference, alleviating multipath propagation and allowing the potential of sharing bandwidth with other users. Taking a practical approach to the topic, this text provides a comprehensive and systematic guide to understanding and using pseudo random signals. Covering theoretical principles, design methodologies and applications
Dynamic monopolies with randomized starting configuration
Kulich, Tomas
2010-01-01
Properties of systems with majority voting rules have been exhaustingly studied. In this work we focus on the randomized case - where the system is initialized by randomized initial set of seeds. Our main aim is to give an asymptotic estimate for sampling probability, such that the initial set of seeds is (is not) a dynamic monopoly almost surely. After presenting some trivial examples, we present exhaustive results for toroidal mesh and random 4-regular graph under simple majority scenario.
Randomized Clinical Trials in Stroke Research
Ahn, Chul; Ahn, Daniel
2010-01-01
A randomized clinical trial (RCT) is widely regarded as the most rigorous study design to determine the efficacy of intervention since spurious causality and bias associated with other experimental designs can be avoided. The purpose of this article is to provide clinicians and clinical researchers with the types of randomized clinical trials used in stroke studies and to discuss the advantages and limitations in each type of randomized stroke clinical trials.
Private randomness expansion with untrusted devices
Energy Technology Data Exchange (ETDEWEB)
Colbeck, Roger; Kent, Adrian, E-mail: rcolbeck@perimeterinstitute.ca, E-mail: a.p.a.kent@damtp.cam.ac.uk [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada)
2011-03-04
Randomness is an important resource for many applications, from gambling to secure communication. However, guaranteeing that the output from a candidate random source could not have been predicted by an outside party is a challenging task, and many supposedly random sources used today provide no such guarantee. Quantum solutions to this problem exist, for example a device which internally sends a photon through a beamsplitter and observes on which side it emerges, but, presently, such solutions require the user to trust the internal workings of the device. Here, we seek to go beyond this limitation by asking whether randomness can be generated using untrusted devices-even ones created by an adversarial agent-while providing a guarantee that no outside party (including the agent) can predict it. Since this is easily seen to be impossible unless the user has an initially private random string, the task we investigate here is private randomness expansion. We introduce a protocol for private randomness expansion with untrusted devices which is designed to take as input an initially private random string and produce as output a longer private random string. We point out that private randomness expansion protocols are generally vulnerable to attacks that can render the initial string partially insecure, even though that string is used only inside a secure laboratory; our protocol is designed to remove this previously unconsidered vulnerability by privacy amplification. We also discuss extensions of our protocol designed to generate an arbitrarily long random string from a finite initially private random string. The security of these protocols against the most general attacks is left as an open question.
Quantum random walks with history dependence
Flitney, Adrian P.; Abbott, Derek; Johnson, Neil F.
2003-01-01
We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased random walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.
Fatigue durability under random cyclic loading
Volkov, S. S.; Struzhanov, V. V.
2017-12-01
Methods for predicting the durability of metals have been developed while taking into account the effect of random loads acting during the service life of structures. Methods of the theory of functions of random variables are applied. Normal distribution and the Rayleigh distribution are used to estimate the random loads from the experimental histogram. A numerical example illustrates the influence of the statistical parameters of the load distribution on the predicted number of cycles before failure.
A discrete random walk on the hypercube
Zhang, Jingyuan; Xiang, Yonghong; Sun, Weigang
2018-03-01
In this paper, we study the scaling for mean first-passage time (MFPT) of random walks on the hypercube and obtain a closed-form formula for the MFPT over all node pairs. We also determine the exponent of scaling efficiency characterizing the random walks and compare it with those of the existing networks. Finally we study the random walks on the hypercube with a located trap and provide a solution of the Kirchhoff index of the hypercube.
A New Perspective on Randomized Gossip Algorithms
Loizou, Nicolas; Richtárik, Peter
2016-01-01
In this short note we propose a new approach for the design and analysis of randomized gossip algorithms which can be used to solve the average consensus problem. We show how that Randomized Block Kaczmarz (RBK) method - a method for solving linear systems - works as gossip algorithm when applied to a special system encoding the underlying network. The famous pairwise gossip algorithm arises as a special case. Subsequently, we reveal a hidden duality of randomized gossip algorithms, with the ...
Negative probability of random multiplier in turbulence
Bai, Xuan; Su, Weidong
2017-11-01
The random multiplicative process (RMP), which has been proposed for over 50 years, is a convenient phenomenological ansatz of turbulence cascade. In the RMP, the fluctuation in a large scale is statistically mapped to the one in a small scale by the linear action of an independent random multiplier (RM). Simple as it is, the RMP is powerful enough since all of the known scaling laws can be included in this model. So far as we know, however, a direct extraction for the probability density function (PDF) of RM has been absent yet. The reason is the deconvolution during the process is ill-posed. Nevertheless, with the progress in the studies of inverse problems, the situation can be changed. By using some new regularization techniques, for the first time we recover the PDFs of the RMs in some turbulent flows. All the consistent results from various methods point to an amazing observation-the PDFs can attain negative values in some intervals; and this can also be justified by some properties of infinitely divisible distributions. Despite the conceptual unconventionality, the present study illustrates the implications of negative probability in turbulence in several aspects, with emphasis on its role in describing the interaction between fluctuations at different scales. This work is supported by the NSFC (No. 11221062 and No. 11521091).
Randomized, interventional, prospective, comparative study to ...
African Journals Online (AJOL)
Randomized, interventional, prospective, comparative study to evaluate the antihypertensive efficacy and tolerability of ramipril versus telmisartan in stage 1 hypertensive patients with diabetes mellitus.
A signal theoretic introduction to random processes
Howard, Roy M
2015-01-01
A fresh introduction to random processes utilizing signal theory By incorporating a signal theory basis, A Signal Theoretic Introduction to Random Processes presents a unique introduction to random processes with an emphasis on the important random phenomena encountered in the electronic and communications engineering field. The strong mathematical and signal theory basis provides clarity and precision in the statement of results. The book also features: A coherent account of the mathematical fundamentals and signal theory that underpin the presented material Unique, in-depth coverage of
Optimal codon randomization via mathematical programming.
Nov, Yuval; Segev, Danny
2013-10-21
Codon randomization via degenerate oligonucleotides is a widely used approach for generating protein libraries. We use integer programming methodology to model and solve the problem of computing the minimal mixture of oligonucleotides required to induce an arbitrary target probability over the 20 standard amino acids. We consider both randomization via conventional degenerate oligonucleotides, which incorporate at each position of the randomized codon certain nucleotides in equal probabilities, and randomization via spiked oligonucleotides, which admit arbitrary nucleotide distribution at each of the codon's positions. Existing methods for computing such mixtures rely on various heuristics. © 2013 Elsevier Ltd. All rights reserved.
QUASI-RANDOM TESTING OF COMPUTER SYSTEMS
Directory of Open Access Journals (Sweden)
S. V. Yarmolik
2013-01-01
Full Text Available Various modified random testing approaches have been proposed for computer system testing in the black box environment. Their effectiveness has been evaluated on the typical failure patterns by employing three measures, namely, P-measure, E-measure and F-measure. A quasi-random testing, being a modified version of the random testing, has been proposed and analyzed. The quasi-random Sobol sequences and modified Sobol sequences are used as the test patterns. Some new methods for Sobol sequence generation have been proposed and analyzed.
RANDOM WALK HYPOTHESIS IN FINANCIAL MARKETS
Directory of Open Access Journals (Sweden)
Nicolae-Marius JULA
2017-05-01
Full Text Available Random walk hypothesis states that the stock market prices do not follow a predictable trajectory, but are simply random. If you are trying to predict a random set of data, one should test for randomness, because, despite the power and complexity of the used models, the results cannot be trustworthy. There are several methods for testing these hypotheses and the use of computational power provided by the R environment makes the work of the researcher easier and with a cost-effective approach. The increasing power of computing and the continuous development of econometric tests should give the potential investors new tools in selecting commodities and investing in efficient markets.
Action correlations and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Smilansky, Uzy; Verdene, Basile [Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100 (Israel)
2003-03-28
The correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin, and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical systems. We review this duality and the semiclassical theory which brings it about. The conjecture that the quantum spectral statistics are described in terms of random matrix theory, leads to the proposition that the classical two-point correlation function is also given in terms of a universal function. We study in detail the spectrum of actions of the Baker map, and use it to illustrate the steps needed to reveal the classical correlations, their origin and their relation to symbolic dynamics00.
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid
2016-01-13
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Inflation with a graceful exit in a random landscape
Energy Technology Data Exchange (ETDEWEB)
Pedro, F.G. [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica y Inst. de Fisica Teorica UAM/CSIC; Westphal, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2016-11-15
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N<<10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Quantum Chaos and Random Matrix Theory Some New Results
Smilansky, U
1996-01-01
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which are the quantum versions of area preserving maps. The relevant Random Matrix ensembles are the Circular ensembles. The resulting semiclassical expressions depend on the symmetry of the system with respect to time reversal, and on a classical parameter $\\mu = tr U -1$ where U is the classical 1-step evolution operator. For system without time reversal symmetry, we are able to reproduce the exact Random Matrix predictions in the limit $\\mu \\to 0$. For systems with time reversal symmetry we can reproduce only some of the features of Random Matrix Theory. For both classes we obtain the leading corrections in $\\mu$. The semiclassical theory for integrable systems is also developed, resulting in expressions which reproduce the theory for the Poissonian ensemble to leading order i...
Aggregated Recommendation through Random Forests
Directory of Open Access Journals (Sweden)
Heng-Ru Zhang
2014-01-01
Full Text Available Aggregated recommendation refers to the process of suggesting one kind of items to a group of users. Compared to user-oriented or item-oriented approaches, it is more general and, therefore, more appropriate for cold-start recommendation. In this paper, we propose a random forest approach to create aggregated recommender systems. The approach is used to predict the rating of a group of users to a kind of items. In the preprocessing stage, we merge user, item, and rating information to construct an aggregated decision table, where rating information serves as the decision attribute. We also model the data conversion process corresponding to the new user, new item, and both new problems. In the training stage, a forest is built for the aggregated training set, where each leaf is assigned a distribution of discrete rating. In the testing stage, we present four predicting approaches to compute evaluation values based on the distribution of each tree. Experiments results on the well-known MovieLens dataset show that the aggregated approach maintains an acceptable level of accuracy.
Dynamic computing random access memory
Traversa, F. L.; Bonani, F.; Pershin, Y. V.; Di Ventra, M.
2014-07-01
The present von Neumann computing paradigm involves a significant amount of information transfer between a central processing unit and memory, with concomitant limitations in the actual execution speed. However, it has been recently argued that a different form of computation, dubbed memcomputing (Di Ventra and Pershin 2013 Nat. Phys. 9 200-2) and inspired by the operation of our brain, can resolve the intrinsic limitations of present day architectures by allowing for computing and storing of information on the same physical platform. Here we show a simple and practical realization of memcomputing that utilizes easy-to-build memcapacitive systems. We name this architecture dynamic computing random access memory (DCRAM). We show that DCRAM provides massively-parallel and polymorphic digital logic, namely it allows for different logic operations with the same architecture, by varying only the control signals. In addition, by taking into account realistic parameters, its energy expenditures can be as low as a few fJ per operation. DCRAM is fully compatible with CMOS technology, can be realized with current fabrication facilities, and therefore can really serve as an alternative to the present computing technology.
Organization of growing random networks
Energy Technology Data Exchange (ETDEWEB)
Krapivsky, P. L.; Redner, S.
2001-06-01
The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively, and linking each to an earlier node of degree k with an attachment probability A{sub k}. When A{sub k} grows more slowly than linearly with k, the number of nodes with k links, N{sub k}(t), decays faster than a power law in k, while for A{sub k} growing faster than linearly in k, a single node emerges which connects to nearly all other nodes. When A{sub k} is asymptotically linear, N{sub k}(t){similar_to}tk{sup {minus}{nu}}, with {nu} dependent on details of the attachment probability, but in the range 2{lt}{nu}{lt}{infinity}. The combined age and degree distribution of nodes shows that old nodes typically have a large degree. There is also a significant correlation in the degrees of neighboring nodes, so that nodes of similar degree are more likely to be connected. The size distributions of the in and out components of the network with respect to a given node{emdash}namely, its {open_quotes}descendants{close_quotes} and {open_quotes}ancestors{close_quotes}{emdash}are also determined. The in component exhibits a robust s{sup {minus}2} power-law tail, where s is the component size. The out component has a typical size of order lnt, and it provides basic insights into the genealogy of the network.
Superstatistics in Random Matrix Theory
Directory of Open Access Journals (Sweden)
A.Y. Abul-Magd
2012-12-01
Full Text Available Random matrix theory (RMT provides a successful model for quantum systems, whose classical counterpart has chaotic dynamics. It is based on two assumptions: (1 matrix-element independence, and (2 base invariance. The last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors have presented other versions of the theory that keep base invariance at the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or by following the basic prescription of the recently suggested concept of superstatistics. The latter concept was introduced as a generalization of equilibrium thermodynamics to describe non-equilibrium systems by allowing the temperature to fluctuate. We here review the superstatistical generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments on billiards modeling systems in transition from order to chaos.
Persistent random walk with exclusion
Galanti, Marta; Fanelli, Duccio; Piazza, Francesco
2013-11-01
Modelling the propagation of a pulse in a dense milieu poses fundamental challenges at the theoretical and applied levels. To this aim, in this paper we generalize the telegraph equation to non-ideal conditions by extending the concept of persistent random walk to account for spatial exclusion effects. This is achieved by introducing an explicit constraint in the hopping rates, that weights the occupancy of the target sites. We derive the mean-field equations, which display nonlinear terms that are important at high density. We compute the evolution of the mean square displacement (MSD) for pulses belonging to a specific class of spatially symmetric initial conditions. The MSD still displays a transition from ballistic to diffusive behaviour. We derive an analytical formula for the effective velocity of the ballistic stage, which is shown to depend in a nontrivial fashion upon both the density (area) and the shape of the initial pulse. After a density-dependent crossover time, nonlinear terms become negligible and normal diffusive behaviour is recovered at long times.
Cryptographic pseudo-random sequences from the chaotic Hénon ...
Indian Academy of Sciences (India)
Pseudo-random number sequences are useful in many applications including Monte-Carlo simulation, spread spectrum ... a pseudo-random binary sequence from the two-dimensional chaotic Hénon map is explored. ... is the Hénon map, a two-dimensional discrete-time nonlinear dynamical system represented by the state ...
DEFF Research Database (Denmark)
Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.
1994-01-01
The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order perturbat......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... for multi-degree-of-freedom (MDOF) systems and the method is illustrated for a single-degree-of-freedom (SDOF) oscillator. The results are compared to those of exact results for a random oscillator subject to white noise excitation with random intensity....
Some common random fixed point theorems for contractive type conditions in cone random metric spaces
Directory of Open Access Journals (Sweden)
Saluja Gurucharan S.
2016-08-01
Full Text Available In this paper, we establish some common random fixed point theorems for contractive type conditions in the setting of cone random metric spaces. Our results unify, extend and generalize many known results from the current existing literature.
Random walk models of large-scale structure
Indian Academy of Sciences (India)
Abstract. This paper describes the insights gained from the excursion set approach, in which vari- ous questions about the phenomenology of large-scale structure formation can be mapped to problems associated with the first crossing distribution of appropriately defined barriers by random walks. Much of this is ...
Coverage of space by random sets
Indian Academy of Sciences (India)
Consider the non-negative integer line. For each integer point we toss a coin. If the toss at location i is a. Heads we place an interval (of random length) there and move to location i + 1,. Tails we move to location i + 1. Coverage of space by random sets – p. 2/29 ...
Critical Properties of Pure and Random Antiferromagnets
DEFF Research Database (Denmark)
Cowley, R. A.; Carneiro, K.
1980-01-01
Neutron scattering techniques have been used to study the critical properties of CoF2 and the randomly mixed systems: Co/ZnF2 and KMn/NiF3. The results for CoF2 are in excellent accord with the critical properties of the three-dimensional Ising model. In all of the random crystals studied the tra...
Topological properties of random wireless networks
Indian Academy of Sciences (India)
Wireless networks in which the node locations are random are best modelled as random geometric graphs (RGGs). In addition to their extensive application in the modelling of wireless networks, RGGs ﬁnd many new applications and are being studied in their own right. In this paper we ﬁrst provide a brief introduction to the ...
Random Network Coding over Composite Fields
DEFF Research Database (Denmark)
Geil, Olav; Lucani Rötter, Daniel Enrique
2017-01-01
Random network coding is a method that achieves multicast capacity asymptotically for general networks [1, 7]. In this approach, vertices in the network randomly and linearly combine incoming information in a distributed manner before forwarding it through their outgoing edges. To ensure success...
Random queues and risk averse users
DEFF Research Database (Denmark)
de Palma, André; Fosgerau, Mogens
2013-01-01
We analyze Nash equilibrium in time of use of a congested facility. Users are risk averse with general concave utility. Queues are subject to varying degrees of random sorting, ranging from strict queue priority to a completely random queue. We define the key “no residual queue” property, which...
Random matrix model for disordered conductors
Indian Academy of Sciences (India)
Keywords. Disordered conductors; random matrix theory; Dyson's Coulomb gas model. ... An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson's Coulomb gas analogy ...
Spatial Extent of Random Laser Modes
van der Molen, K.L.; Tjerkstra, R.W.; Mosk, Allard; Lagendijk, Aart
2007-01-01
We have experimentally studied the distribution of the spatial extent of modes and the crossover from essentially single-mode to distinctly multimode behavior inside a porous gallium phosphide random laser. This system serves as a paragon for random lasers due to its exemplary high index contrast.
Perfectly Secure Oblivious RAM without Random Oracles
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Meldgaard, Sigurd Torkel; Nielsen, Jesper Buus
2011-01-01
We present an algorithm for implementing a secure oblivious RAM where the access pattern is perfectly hidden in the information theoretic sense, without assuming that the CPU has access to a random oracle. In addition we prove a lower bound on the amount of randomness needed for implementing...
Aspects of insertion in random trees
Bagchi, Arunabha; Reingold, E.M.
1982-01-01
A method formulated by Yao and used by Brown has yielded bounds on the fraction of nodes with specified properties in trees bult by a sequence of random internal nodes in a random tree built by binary search and insertion, and show that in such a tree about bounds better than those now known. We
Decoding Algorithms for Random Linear Network Codes
DEFF Research Database (Denmark)
Heide, Janus; Pedersen, Morten Videbæk; Fitzek, Frank
2011-01-01
We consider the problem of efficient decoding of a random linear code over a finite field. In particular we are interested in the case where the code is random, relatively sparse, and use the binary finite field as an example. The goal is to decode the data using fewer operations to potentially a...
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.
Concentration inequalities for random fields via coupling
Chazottes, J. R.; Collet, P.; Kuelske, C.; Redig, F.
We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the coupling, one obtains exponential concentration
Individual Differences Methods for Randomized Experiments
Tucker-Drob, Elliot M.
2011-01-01
Experiments allow researchers to randomly vary the key manipulation, the instruments of measurement, and the sequences of the measurements and manipulations across participants. To date, however, the advantages of randomized experiments to manipulate both the aspects of interest and the aspects that threaten internal validity have been primarily…
Theory of amplitude quantization of random signals
Knyshev, I. P.
2008-01-01
Conditions of ideal amplitude quantization of random signal with exact restoration of two-dimension probability density distribution function are defined. Interrelation of time discretization interval and amplitude quantization is shown. As an example transformation of normal random process is considered.
k-Means: Random Sampling Procedure
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. k-Means: Random Sampling Procedure. Optimal 1-Mean is. Approximation of Centroid (Inaba et al). S = random sample of size O(1/ ); Centroid of S is a (1+ )-approx centroid of P with constant probability.
Pseudocontinuation and cyclicity for random power series
Abakumov, Evgeny; Poltoratski, Alexei
2007-01-01
We prove that a random function in the Hardy space $H^2$ is a non-cyclic vector for the backward shift operator almost surely. The question of existence of a local pseudocontinuation for a random analytic function is also studied.
Overlap Synchronisation in Multipartite Random Energy Models
Genovese, Giuseppe; Tantari, Daniele
2017-12-01
In a multipartite random energy model, made of a number of coupled generalised random energy models (GREMs), we determine the joint law of the overlaps in terms of the ones of the single GREMs. This provides the simplest example of the so-called overlap synchronisation.
Color Charts, Esthetics, and Subjective Randomness
Sanderson, Yasmine B.
2012-01-01
Color charts, or grids of evenly spaced multicolored dots or squares, appear in the work of modern artists and designers. Often the artist/designer distributes the many colors in a way that could be described as "random," that is, without an obvious pattern. We conduct a statistical analysis of 125 "random-looking" art and design color charts and…
Cluster Randomized Trials with Treatment Noncompliance
Jo, Booil; Asparouhov, Tihomir; Muthen, Bengt O.; Ialongo, Nicholas S.; Brown, C. Hendricks
2008-01-01
Cluster randomized trials (CRTs) have been widely used in field experiments treating a cluster of individuals as the unit of randomization. This study focused particularly on situations where CRTs are accompanied by a common complication, namely, treatment noncompliance or, more generally, intervention nonadherence. In CRTs, compliance may be…
The design of cluster randomized crossover trials
Rietbergen, C.; Moerbeek, M.
2011-01-01
The inefficiency induced by between-cluster variation in cluster randomized (CR) trials can be reduced by implementing a crossover (CO) design. In a simple CO trial, each subject receives each treatment in random order. A powerful characteristic of this design is that each subject serves as its own
Bizhani, Golnoosh; Paczuski, Maya; Grassberger, Peter
2012-07-01
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and nonequilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first-order behaviors in two different classes of models: The first are generalized epidemic processes that describe in their spatially embedded version—either on or off a regular lattice—compact or fractal cluster growth in random media at zero temperature. A random graph version of these processes is mapped onto a model previously proposed for complex social contagion. We compute detailed phase diagrams and compare our numerical results at the tricritical point in d=3 with field theory predictions of Janssen [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.70.026114 70, 026114 (2004)]. The second class consists of exponential (“Hamiltonian,” i.e., formally equilibrium) random graph models and includes the Strauss and the two-star model, where “chemical potentials” control the densities of links, triangles, or two-stars. When the chemical potentials in either graph model are O(logN), the percolation transition can coincide with a first-order phase transition in the density of links, making the former also discontinuous. Hysteresis loops can then be of mixed order, with second-order behavior for decreasing link fugacity, and a jump (first order) when it increases.
Random point sets and their diffraction
Baake, Michael; Kösters, Holger
2011-07-01
The diffraction of various random subsets of the integer lattice ℤ d , such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in ℝ d . We present several systems with an effective stochastic interaction that still allow for explicit calculations of the autocorrelation and the diffraction measure. We concentrate on one-dimensional examples for illustrative purposes, and briefly indicate possible generalisations to higher dimensions. In particular, we discuss the stationary Poisson process in ℝ d and the renewal process on the line. The latter permits a unified approach to a rather large class of one-dimensional structures, including random tilings. Moreover, we present some stationary point processes that are derived from the classical random matrix ensembles as introduced in the pioneering work of Dyson and Ginibre. Their reconsideration from the diffraction point of view improves the intuition on systems with randomness and mixed spectra.
Random Number Generators in Secure Disk Drives
Directory of Open Access Journals (Sweden)
Hars Laszlo
2009-01-01
Full Text Available Abstract Cryptographic random number generators seeded by physical entropy sources are employed in many embedded security systems, including self-encrypting disk drives, being manufactured by the millions every year. Random numbers are used for generating encryption keys and for facilitating secure communication, and they are also provided to users for their applications. We discuss common randomness requirements, techniques for estimating the entropy of physical sources, investigate specific nonrandom physical properties, estimate the autocorrelation, then mix reduce the data until all common randomness tests pass. This method is applied to a randomness source in disk drives: the always changing coefficients of an adaptive filter for the read channel equalization. These coefficients, affected by many kinds of physical noise, are used in the reseeding process of a cryptographic pseudorandom number generator in a family of self encrypting disk drives currently in the market.
Random dynamical systems, entropies and information
Serva, M
1999-01-01
Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is general consensus on what should be the correct indicator for complexity is still not reached. In particular, this characterization is still lacking for systems whose time evolution is influenced by factors which are not under control and appear as random parameters or random noise. We show in this paper how to find the correct indicators for complexity in the information theory context. The crucial point is that the answer is twofold depending on the fact that the random parameters are measurable or not. The content of this apparently trivial observation has been often ignored in literature leading to paradoxical results. Predictability is obviously larger when the random parameters are measurable, nevertheless, in the contrary case, predictability improves when the unknown random parameters are time correlated.
Application of Vector Triggering Random Decrement
DEFF Research Database (Denmark)
Asmussen, J. C.; Ibrahim, S. R.; Brincker, Rune
1997-01-01
result is a Random Decrement function from each measurement. In traditional Random Decrement estimation the triggering condition is a scalar condition, which should only be fulfilled in a single measurement. In vector triggering Random Decrement the triggering condition is a vector condition....... The advantage of this new approach should be a reduction in estimation time without a significant loss of accuracy, since the vector triggering conditions ensure cross information between the measurements in the Random Decrement functions. The different problems with this technique is highlighted in two......This paper deals with applications of the vector triggering Random Decrement technique. This technique is new and developed with the aim of minimizing estimation time and identification errors. The theory behind the technique is discussed in an accompanying paper. The results presented...
Application of Vector Triggering Random Decrement
DEFF Research Database (Denmark)
Asmussen, J. C.; Ibrahim, S. R.; Brincker, Rune
result is a Random Decrement function from each measurement. In traditional Random Decrement estimation the triggering condition is a scalar condition, which should only be fulfilled in a single measurement. In vector triggering Random Decrement the triggering condition is a vector condition....... The advantage of this new approach should be a reduction in estimation time without a significant loss of accuracy, since the vector triggering conditions ensure cross information between the measurements in the Random Decrement functions. The different problems with this technique is highlighted in two......This paper deals with applications of the vector triggering Random Decrement technique. This technique is new and developed with the aim of minimizing estimation time and identification errors. The theory behind the technique is discussed in an accompanying paper. The results presented...
A random matrix approach to language acquisition
Nicolaidis, A.; Kosmidis, Kosmas; Argyrakis, Panos
2009-12-01
Since language is tied to cognition, we expect the linguistic structures to reflect patterns that we encounter in nature and are analyzed by physics. Within this realm we investigate the process of lexicon acquisition, using analytical and tractable methods developed within physics. A lexicon is a mapping between sounds and referents of the perceived world. This mapping is represented by a matrix and the linguistic interaction among individuals is described by a random matrix model. There are two essential parameters in our approach. The strength of the linguistic interaction β, which is considered as a genetically determined ability, and the number N of sounds employed (the lexicon size). Our model of linguistic interaction is analytically studied using methods of statistical physics and simulated by Monte Carlo techniques. The analysis reveals an intricate relationship between the innate propensity for language acquisition β and the lexicon size N, N~exp(β). Thus a small increase of the genetically determined β may lead to an incredible lexical explosion. Our approximate scheme offers an explanation for the biological affinity of different species and their simultaneous linguistic disparity.
Directory of Open Access Journals (Sweden)
Shuiqing Yu
2013-01-01
Full Text Available This paper investigates the dynamic output feedback control for nonlinear networked control systems with both random packet dropout and random delay. Random packet dropout and random delay are modeled as two independent random variables. An observer-based dynamic output feedback controller is designed based upon the Lyapunov theory. The quantitative relationship of the dropout rate, transition probability matrix, and nonlinear level is derived by solving a set of linear matrix inequalities. Finally, an example is presented to illustrate the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Hyontai Sug
2012-01-01
Full Text Available Random forests are known to be good for data mining of classification tasks, because random forests are robust for datasets having insufficient information possibly with some errors. But applying random forests blindly may not produce good results, and a dataset in the domain of rotogravure printing is one of such datasets. Hence, in this paper, some best classification accuracy based on clever application of random forests to predict the occurrence of cylinder bands in rotogravure printing is investigated. Since random forests could generate good results with an appropriate combination of parameters like the number of randomly selected attributes for each split and the number of trees in the forests, an effective data mining procedure considering the property of the target dataset by way of trial random forests is investigated. The effectiveness of the suggested procedure is shown by experiments with very good results.
Solution Methods for Structures with Random Properties Subject to Random Excitation
DEFF Research Database (Denmark)
Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.
This paper deals with the lower order statistical moments of the response of structures with random stiffness and random damping properties subject to random excitation. The arising stochastic differential equations (SDE) with random coefficients are solved by two methods, a second order...... perturbation approach and a Markovian method. The second order perturbation approach is grounded on the total probability theorem and can be compactly written. Moreover, the problem to be solved is independent of the dimension of the random variables involved. The Markovian approach suggests transforming...... the SDE with random coefficients with deterministic initial conditions to an equivalent nonlinear SDE with deterministic coefficient and random initial conditions. In both methods, the statistical moment equations are used. Hierarchy of statistical moments in the markovian approach is closed...
Non-diffractive beam in random media
Shiina, Tatsuo
2017-09-01
Beam propagation has been given important attention in a variety of applications in medicine, remote sensing and information science. Especially, the beam propagation in highly scattering media, which is called random media, is important. In general, the multiple scattering gets rid of beam characteristics, e.g., intensity distribution, phase front, and polarization. In this study, self-converging effect of annular beam was applied in random media. Diluted milk was used as random media, and the transmitted light was detected with a narrow view angle of 5.5mrad. The collimated annular beam of a few tens millimeters takes a few hundred meters to transform its beam shape into the non-diffractive beam in free space, while this transformation was shorten only to 20 cm in random media, that is, the collimated annular beam caused its transformation at only 20 cm in random media. The transformed beam kept its optical characteristics of ;non-diffractive beam;. Such transformation of the annular beam needs the appropriate condition of random media. Media concentration and propagation distance control the generation of the center peak intensity of the transformed beam. This study indicates the generation of the non-diffractive beam in random media and reveals its appropriate condition.
True randomness from an incoherent source
Qi, Bing
2017-11-01
Quantum random number generators (QRNGs) harness the intrinsic randomness in measurement processes: the measurement outputs are truly random, given the input state is a superposition of the eigenstates of the measurement operators. In the case of trusted devices, true randomness could be generated from a mixed state ρ so long as the system entangled with ρ is well protected. We propose a random number generation scheme based on measuring the quadrature fluctuations of a single mode thermal state using an optical homodyne detector. By mixing the output of a broadband amplified spontaneous emission (ASE) source with a single mode local oscillator (LO) at a beam splitter and performing differential photo-detection, we can selectively detect the quadrature fluctuation of a single mode output of the ASE source, thanks to the filtering function of the LO. Experimentally, a quadrature variance about three orders of magnitude larger than the vacuum noise has been observed, suggesting this scheme can tolerate much higher detector noise in comparison with QRNGs based on measuring the vacuum noise. The high quality of this entropy source is evidenced by the small correlation coefficients of the acquired data. A Toeplitz-hashing extractor is applied to generate unbiased random bits from the Gaussian distributed raw data, achieving an efficiency of 5.12 bits per sample. The output of the Toeplitz extractor successfully passes all the NIST statistical tests for random numbers.
Phase transitions for information diffusion in random clustered networks
Lim, Sungsu; Shin, Joongbo; Kwak, Namju; Jung, Kyomin
2016-09-01
We study the conditions for the phase transitions of information diffusion in complex networks. Using the random clustered network model, a generalisation of the Chung-Lu random network model incorporating clustering, we examine the effect of clustering under the Susceptible-Infected-Recovered (SIR) epidemic diffusion model with heterogeneous contact rates. For this purpose, we exploit the branching process to analyse information diffusion in random unclustered networks with arbitrary contact rates, and provide novel iterative algorithms for estimating the conditions and sizes of global cascades, respectively. Showing that a random clustered network can be mapped into a factor graph, which is a locally tree-like structure, we successfully extend our analysis to random clustered networks with heterogeneous contact rates. We then identify the conditions for phase transitions of information diffusion using our method. Interestingly, for various contact rates, we prove that random clustered networks with higher clustering coefficients have strictly lower phase transition points for any given degree sequence. Finally, we confirm our analytical results with numerical simulations of both synthetically-generated and real-world networks.
Random signals and noise a mathematical introduction
Engelberg, Shlomo
2011-01-01
Understanding the nature of random signals and noise is critically important for detecting signals and for reducing and minimizing the effects of noise in applications such as communications and control systems. Outlining a variety of techniques and explaining when and how to use them, Random Signals and Noise: A Mathematical Introduction focuses on applications and practical problem solving rather than probability theory.A Firm FoundationBefore launching into the particulars of random signals and noise, the author outlines the elements of probability that are used throughout the book and incl
Nonparametric estimation in random sum models
Directory of Open Access Journals (Sweden)
Hassan S. Bakouch
2013-05-01
Full Text Available Let X1,X2,…,XN be independent, identically distributed, non-negative, integervalued random variables and let N be a non-negative, integer-valued random variable independent of X1,X2,…,XN . In this paper, we consider two nonparametric estimation problems for the random sum variable. The first is the estimation of the means of Xi and N based on the second-moment assumptions on distributions of Xi and N . The second is the nonparametric estimation of the distribution of Xi given a parametric model for the distribution of N . Some asymptotic properties of the proposed estimators are discussed.
Randomly interacting bosons on two spin levels
Mulhall, D.
2017-12-01
The problem of random interactions leading to regular spectra in shell model type simulations is described. The key results are reviewed alnog with a selection of the explanations. A model system of N particles on 2 spin levels having random 2-body collisions that conserve angular momentum is examined. Preliminary results are described, including the ground state spin distributions peaked at extreme values of angular momentum, signatures of rotational bands, and smooth parabolic yrast lines. A simple random matrix theory analysis shows signatures of quantum chaos in the level spacing distribution and the Δ3 statistic.
A Random Walk to Economic Freedom?
Directory of Open Access Journals (Sweden)
Witte, Mark David
2013-04-01
Full Text Available Given the wide use of economic freedom in economic literature it is imperative to understand how economic freedom evolves. Results suggest that levels of economic freedom are dominated by random shocks. Using a test for stationarity devised by Westerlund and Larsson (2012 we are unable to reject the null hypothesis of a random walk. The changes to economic freedom also are mostly driven by random shocks with only a minor role played by country specific characteristics. Additionally, changes to economic freedom are partially reversed as increases (decreases in one year are partially offset by decreases (increases in the next year.
Modelling complex networks by random hierarchical graphs
Directory of Open Access Journals (Sweden)
M.Wróbel
2008-06-01
Full Text Available Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of Erdős-Rényi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpiński gasket-based graphs with random "decorations". We calculate the important characteristics of these graphs - average degree, average shortest path length, small-world graph family characteristics. They depend on probability of decorations. We analyze the Ising model on our graphs and describe its critical properties using a renormalization-group technique.
Elements of random walk and diffusion processes
Ibe, Oliver C
2013-01-01
Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic
Randomized Prediction Games for Adversarial Machine Learning.
Rota Bulo, Samuel; Biggio, Battista; Pillai, Ignazio; Pelillo, Marcello; Roli, Fabio
In spam and malware detection, attackers exploit randomization to obfuscate malicious data and increase their chances of evading detection at test time, e.g., malware code is typically obfuscated using random strings or byte sequences to hide known exploits. Interestingly, randomization has also been proposed to improve security of learning algorithms against evasion attacks, as it results in hiding information about the classifier to the attacker. Recent work has proposed game-theoretical formulations to learn secure classifiers, by simulating different evasion attacks and modifying the classification function accordingly. However, both the classification function and the simulated data manipulations have been modeled in a deterministic manner, without accounting for any form of randomization. In this paper, we overcome this limitation by proposing a randomized prediction game, namely, a noncooperative game-theoretic formulation in which the classifier and the attacker make randomized strategy selections according to some probability distribution defined over the respective strategy set. We show that our approach allows one to improve the tradeoff between attack detection and false alarms with respect to the state-of-the-art secure classifiers, even against attacks that are different from those hypothesized during design, on application examples including handwritten digit recognition, spam, and malware detection.In spam and malware detection, attackers exploit randomization to obfuscate malicious data and increase their chances of evading detection at test time, e.g., malware code is typically obfuscated using random strings or byte sequences to hide known exploits. Interestingly, randomization has also been proposed to improve security of learning algorithms against evasion attacks, as it results in hiding information about the classifier to the attacker. Recent work has proposed game-theoretical formulations to learn secure classifiers, by simulating different
A random matrix theory of decoherence
Energy Technology Data Exchange (ETDEWEB)
Gorin, T [Departamento de FIsica, Universidad de Guadalajara, Blvd Marcelino GarcIa Barragan y Calzada OlImpica, Guadalajara CP 44840, JalIsco (Mexico); Pineda, C [Institut fuer Physik und Astronomie, University of Potsdam, 14476 Potsdam (Germany); Kohler, H [Fachbereich Physik, Universitaet Duisburg-Essen, D-47057 Duisburg (Germany); Seligman, T H [Instituto de Ciencias FIsicas, Universidad Nacional Autonoma de Mexico (Mexico)], E-mail: thomas.gorin@red.cucei.udg.mx, E-mail: carlospgmat03@gmail.com
2008-11-15
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence and entropy were considered; we further discuss when one or the other approach is relevant. The two approaches agree in the limit of large environments. Analytic results for the average density matrix and its purity are presented in linear response approximation. The two-qubit system is analysed, mainly numerically, in more detail.
Randomness as a resource for design
DEFF Research Database (Denmark)
Leong, T.; Vetere, F.; Howard, Steve
2006-01-01
is used to engender certain affective responses (such as feeling refreshed) by using various constraining techniques (such as playlists) whilst engaging in everyday activities (such as driving a car). The paper argues that randomness can be used as an innovative design resource for supporting rich...... examining the influence of randomness on the user experience of music listening. 113 instances of self-reporting were collected and analysed according to four themes: listening mode, content organisation, activities during listening, and affective outcomes. The analysis provides insights into how randomness...
A New Substitution Cipher - Random-X
Directory of Open Access Journals (Sweden)
Falguni Patel
2015-08-01
Full Text Available Ciphers are the encryption methods to prepare the algorithm for encryption and decryption. The currently known ciphers are not strong enough to protect the data. A new substitution cipher Random-X that we introduce in this paper can be used for password encryption and data encryption. Random-X cipher is a unique substitution cipher which replaces the units of plaintext with triplets of letters. The beauty of this cipher is that the encrypted string of the same plain text is not always same. This makes it strong and difficult to crack. This paper covers the principle the implementation ideas and testing of Random-X cipher.
Comments on the random Thirring model
Berkooz, Micha; Narayan, Prithvi; Rozali, Moshe; Simón, Joan
2017-09-01
The Thirring model with random couplings is a translationally invariant generalisation of the SYK model to 1+1 dimensions, which is tractable in the large N limit. We compute its two point function, at large distances, for any strength of the random coupling. For a given realisation, the couplings contain both irrelevant and relevant marginal operators, but statistically, in the large N limit, the random couplings are overall always marginally irrelevant, in sharp distinction to the usual Thirring model. We show the leading term to the β function in conformal perturbation theory, which is quadratic in the couplings, vanishes, while its usually subleading cubic term matches our RG flow.
Evolving Random Forest for Preference Learning
DEFF Research Database (Denmark)
Abou-Zleikha, Mohamed; Shaker, Noor
2015-01-01
This paper introduces a novel approach for pairwise preference learning through a combination of an evolutionary method and random forest. Grammatical evolution is used to describe the structure of the trees in the Random Forest (RF) and to handle the process of evolution. Evolved random forests ...... obtained for predicting pairwise self-reports of users for the three emotional states engagement, frustration and challenge show very promising results that are comparable and in some cases superior to those obtained from state-of-the-art methods....
Kooistra, L.; Kuilder, E.T.; Mucher, C.A.
2017-01-01
Very high resolution aerial images and LiDAR (AHN2) datasets with a national coverage provide opportunities to produce vegetation maps automatically. As such the entire area of the river floodplains in the Netherlands may be mapped with high accuracy and regular updates, capturing the dynamic
Votino, C; Kacem, Y; Dobrescu, O; Dessy, H; Cos, T; Foulon, W; Jani, J
2012-02-01
To prospectively assess the contribution of a high-frequency linear transducer and of moving target indicator (MTI) filtered color flow mapping in the visualization of cardiac fetal anatomy at the routine 11 to 13 + 6-week scan. This was a cross-sectional prospective study, including 300 singleton fetuses at 11 to 13 + 6 weeks' gestation. Patients were randomized into four groups and a detailed fetal cardiac examination was conducted transabdominally using either a conventional curvilinear transducer, a conventional curvilinear transducer and MTI filtered color flow mapping, a high-frequency linear transducer or a high-frequency linear transducer and MTI filtered color flow mapping. Regression analysis was used to investigate the effect on the ability to visualize different cardiac structures of the following parameters: gestational age at ultrasound examination; fetal crown-rump length (CRL); maternal body mass index (BMI); transducer-heart distance; the technique used at ultrasound; and the position of the placenta. The four-chamber view was visualized in 89.0% of fetuses and regression analysis showed this rate was correlated with CRL and the use of MTI filtered color flow mapping during ultrasonography, and inversely correlated with BMI and transducer-heart distance. Use of a conventional curvilinear transducer and MTI filtered color flow mapping allowed visualization of the four-chamber view in 97.3% of fetuses, while this was only possible in 84.0% of fetuses using a high-frequency linear transducer. The left and right outflow tracts were visualized in 62.3 and 57.7% of fetuses, respectively. Regression analysis showed that the ability to visualize the left or the right outflow tract was correlated with the use of MTI filtered color flow mapping during scanning and was inversely correlated with transducer-heart distance. The use of a conventional curvilinear transducer and MTI filtered color flow mapping allowed visualization of the left and right outflow
Pseudo-random tool paths for CNC sub-aperture polishing and other applications.
Dunn, Christina R; Walker, David D
2008-11-10
In this paper we first contrast classical and CNC polishing techniques in regard to the repetitiveness of the machine motions. We then present a pseudo-random tool path for use with CNC sub-aperture polishing techniques and report polishing results from equivalent random and raster tool-paths. The random tool-path used - the unicursal random tool-path - employs a random seed to generate a pattern which never crosses itself. Because of this property, this tool-path is directly compatible with dwell time maps for corrective polishing. The tool-path can be used to polish any continuous area of any boundary shape, including surfaces with interior perforations.
Li, Yanbin; Mulani, Sameer B.; Kapania, Rakesh K.; Fei, Qingguo; Wu, Shaoqing
2017-07-01
An algorithm that integrates Karhunen-Loeve expansion (KLE) and the finite element method (FEM) is proposed to perform non-stationary random vibration analysis of structures under excitations, represented by multiple random processes that are correlated in both time and spatial domains. In KLE, the auto-covariance functions of random excitations are discretized using orthogonal basis functions. The KLE for multiple correlated random excitations relies on expansions in terms of correlated sets of random variables reflecting the cross-covariance of the random processes. During the response calculations, the eigenfunctions of KLE used to represent excitations are applied as forcing functions to the structure. The proposed algorithm is applied to a 2DOF system, a 2D cantilever beam and a 3D aircraft wing under both stationary and non-stationary correlated random excitations. Two methods are adopted to obtain the structural responses: a) the modal method and b) the direct method. Both the methods provide the statistics of the dynamic response with sufficient accuracy. The structural responses under the same type of correlated random excitations are bounded by the response obtained by perfectly correlated and uncorrelated random excitations. The structural response increases with a decrease in the correlation length and with an increase in the correlation magnitude. The proposed methodology can be applied for the analysis of any complex structure under any type of random excitation.
Handbook of Large-Scale Random Networks
Bollobas, Bela; Miklos, Dezso
2008-01-01
Covers various aspects of large-scale networks, including mathematical foundations and rigorous results of random graph theory, modeling and computational aspects of large-scale networks, as well as areas in physics, biology, neuroscience, sociology and technical areas
Turbulence hierarchy in a random fibre laser.
González, Iván R Roa; Lima, Bismarck C; Pincheira, Pablo I R; Brum, Arthur A; Macêdo, Antônio M S; Vasconcelos, Giovani L; de S Menezes, Leonardo; Raposo, Ernesto P; Gomes, Anderson S L; Kashyap, Raman
2017-05-31
Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers. The distribution of intensity fluctuations in an extensive data set exhibits three qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture of two distributions with exponentially decaying tails near the threshold and a mixture of distributions with stretched-exponential tails above threshold. All distributions are well described by a hierarchical stochastic model that incorporates Kolmogorov's theory of turbulence, which includes energy cascade and the intermittence phenomenon. Our findings have implications for explaining the remarkably challenging turbulent behaviour in photonics, using a random fibre laser as the experimental platform.
Introduction to Random Signals and Noise
van Etten, Wim
Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding,
Deterministic extraction from weak random sources
Gabizon, Ariel
2011-01-01
In this research monograph, the author constructs deterministic extractors for several types of sources, using a methodology of recycling randomness which enables increasing the output length of deterministic extractors to near optimal length.
Random Life Curves for Common Engineering Materials
Hu, T.
1983-01-01
Program incorporates non-Rayleigh effects in evaluating structure life. RMS2 computer program converts constant amplitude fatigue allowables to random-loading allowables, with influence of peak distribution and mean stress considered. RMS2 written in FORTRAN IV.
Speech Recognition Using Randomized Relational Decision Trees
National Research Council Canada - National Science Library
Amit, Yali
1999-01-01
.... This implies that we recognize words as units, without recognizing their subcomponents. Multiple randomized decision trees are used to access the large pool of acoustic events in a systematic manner and are aggregated to produce the classifier.
Blinding in randomized clinical trials: imposed impartiality
DEFF Research Database (Denmark)
Hróbjartsson, A; Boutron, I
2011-01-01
Blinding, or "masking," is a crucial method for reducing bias in randomized clinical trials. In this paper, we review important methodological aspects of blinding, emphasizing terminology, reporting, bias mechanisms, empirical evidence, and the risk of unblinding. Theoretical considerations...
Supersymmetric SYK model and random matrix theory
Li, Tianlin; Liu, Junyu; Xin, Yuan; Zhou, Yehao
2017-06-01
In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the N=1 supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the spectral form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic hamiltonian with supersymmetry.
Field Induced Memory Effects in Random Nematics
Directory of Open Access Journals (Sweden)
Amid Ranjkesh
2014-01-01
Full Text Available We studied numerically external field induced memory effects in randomly perturbed nematic liquid crystals. Random anisotropy nematic-type lattice model was used. The impurities imposing orientational disorder were randomly spatially distributed with the concentration p below the percolation threshold. Simulations were carried for finite temperatures, where we varied p, interaction strength between LC molecules, and impurities and external field B. In the {B,T} plane we determined lines separating short range—quasi long range and quasi long range—long range order. Furthermore, crossover regime separating external field and random field dominated regime was estimated. We calculated remanent nematic ordering in samples at B=0 as a function of the previously experienced external field strength B.
Anomaly detection and reconstruction from random projections.
Fowler, James E; Du, Qian
2012-01-01
Compressed-sensing methodology typically employs random projections simultaneously with signal acquisition to accomplish dimensionality reduction within a sensor device. The effect of such random projections on the preservation of anomalous data is investigated. The popular RX anomaly detector is derived for the case in which global anomalies are to be identified directly in the random-projection domain, and it is determined via both random simulation, as well as empirical observation that strongly anomalous vectors are likely to be identifiable by the projection-domain RX detector even in low-dimensional projections. Finally, a reconstruction procedure for hyperspectral imagery is developed wherein projection-domain anomaly detection is employed to partition the data set, permitting anomaly and normal pixel classes to be separately reconstructed in order to improve the representation of the anomaly pixels.
Quantum random walks circuits with photonic waveguides
Peruzzo, Alberto; Matthews, Jonathan; Politi, Alberto; Lobino, Mirko; Zhou, Xiao-Qi; Thompson, Mark G.; O'Brien, Jeremy; Matsuda, Nobuyuki; Ismail, N.; Worhoff, Kerstin; Bromberg, Yaron; Lahini, Yoav; Silberberg, Yaron
2010-01-01
Arrays of 21 evanescently coupled waveguides are fabricated to implement quantum random walks and a generalised form of two-photon non-classical interference, which observed via two photon correlation.
Palm theory for random time changes
Directory of Open Access Journals (Sweden)
Masakiyo Miyazawa
2001-01-01
Full Text Available Palm distributions are basic tools when studying stationarity in the context of point processes, queueing systems, fluid queues or random measures. The framework varies with the random phenomenon of interest, but usually a one-dimensional group of measure-preserving shifts is the starting point. In the present paper, by alternatively using a framework involving random time changes (RTCs and a two-dimensional family of shifts, we are able to characterize all of the above systems in a single framework. Moreover, this leads to what we call the detailed Palm distribution (DPD which is stationary with respect to a certain group of shifts. The DPD has a very natural interpretation as the distribution seen at a randomly chosen position on the extended graph of the RTC, and satisfies a general duality criterion: the DPD of the DPD gives the underlying probability P in return.
Generating Realistic Labelled, Weighted Random Graphs
Davis, Michael Charles; Liu, Weiru; Miller, Paul; Hunter, Ruth; Kee, Frank
2015-01-01
Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels a...
Directory of Open Access Journals (Sweden)
Hong Wang
2015-07-01
Full Text Available The textural and spatial information extracted from very high resolution (VHR remote sensing imagery provides complementary information for applications in which the spectral information is not sufficient for identification of spectrally similar landscape features. In this study grey-level co-occurrence matrix (GLCM textures and a local statistical analysis Getis statistic (Gi, computed from IKONOS multispectral (MS imagery acquired from the Yellow River Delta in China, along with a random forest (RF classifier, were used to discriminate Robina pseudoacacia tree health levels. Specifically, eight GLCM texture features (mean, variance, homogeneity, dissimilarity, contrast, entropy, angular second moment, and correlation were first calculated from IKONOS NIR band (Band 4 to determine an optimal window size (13 × 13 and an optimal direction (45°. Then, the optimal window size and direction were applied to the three other IKONOS MS bands (blue, green, and red for calculating the eight GLCM textures. Next, an optimal distance value (5 and an optimal neighborhood rule (Queen’s case were determined for calculating the four Gi features from the four IKONOS MS bands. Finally, different RF classification results of the three forest health conditions were created: (1 an overall accuracy (OA of 79.5% produced using the four MS band reflectances only; (2 an OA of 97.1% created with the eight GLCM features calculated from IKONOS Band 4 with the optimal window size of 13 × 13 and direction 45°; (3 an OA of 93.3% created with the all 32 GLCM features calculated from the four IKONOS MS bands with a window size of 13 × 13 and direction of 45°; (4 an OA of 94.0% created using the four Gi features calculated from the four IKONOS MS bands with the optimal distance value of 5 and Queen’s neighborhood rule; and (5 an OA of 96.9% created with the combined 16 spectral (four, spatial (four, and textural (eight features. The most important feature ranked by RF
Entropy Characterization of Random Network Models
Directory of Open Access Journals (Sweden)
Pedro J. Zufiria
2017-06-01
Full Text Available This paper elaborates on the Random Network Model (RNM as a mathematical framework for modelling and analyzing the generation of complex networks. Such framework allows the analysis of the relationship between several network characterizing features (link density, clustering coefficient, degree distribution, connectivity, etc. and entropy-based complexity measures, providing new insight on the generation and characterization of random networks. Some theoretical and computational results illustrate the utility of the proposed framework.
Random Sets Lotteries and Decision Theory
Marc-Arthur Diaye; Gleb Koshevoy
2011-01-01
Even if its roots are much older, random sets theory has been considered as an academic area, part of stochastic geometry, since Matheron [7]. Random sets theory was first applied in some fields related to engineering sciences like geology, image analysis and expert systems (see Goutsias et al. [4]), and recently in non-parametric statistics (Koshevoy et al. [5]) or also (see Molchanov [9]) in economic theory (for instance in finance and game the- ory) and in econometrics (for instance in lin...
Random Young diagrams in a Rectangular Box
DEFF Research Database (Denmark)
Beltoft, Dan; Boutillier, Cédric; Enriquez, Nathanaël
We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.......We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape....
Astronomical random numbers for quantum foundations experiments
Leung, Calvin; Brown, Amy; Nguyen, Hien; Friedman, Andrew S.; Kaiser, David I.; Gallicchio, Jason
2017-01-01
Photons from distant astronomical sources can be used as a classical source of randomness to improve fundamental tests of quantum nonlocality, wave-particle duality, and local realism through Bell's inequality and delayed-choice quantum eraser tests inspired by Wheeler's cosmic-scale Mach-Zehnder interferometer gedankenexperiment. Such sources of random numbers may also be useful for information-theoretic applications such as key distribution for quantum cryptography. Building on the design o...
Mathematical Problems in Imaging in Random Media
2015-01-15
random media but flat boundaries. 2 distribution to a random Markov diffusion P whose generator can be computed explicitly in terms of the...Note how the numerically computed weights (blue line) match those computed analytically (red). Note also that the algorithm estimates that only the first...source electromagnetic inversion. We analyzed theoretically the algorithm and assesed its performance using numerical simulations. • The solicited article
Probabilistic Signal Recovery and Random Matrices
2016-12-08
is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources , gathering and...a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION...proved a sharp invertibility result for sparse random matrices, showed how to improve the norm of a general random matrix by removing a small submatrix
Diffusion in a weakly random Hamiltonian flow
Komorowski, T.; Ryzhik, L.
2005-01-01
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion. We also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves...
Contextuality in canonical systems of random variables.
Dzhafarov, Ehtibar N; Cervantes, Víctor H; Kujala, Janne V
2017-11-13
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions of the context-sharing random variables. We propose to represent any system of measurements in a canonical form and to consider the system contextual if and only if its canonical representation is contextual. As an illustration, we establish a criterion for contextuality of the canonical system consisting of all dichotomizations of a single pair of content-sharing categorical random variables.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).
The Theory of Random Laser Systems
Xun Ya Jian
2002-01-01
Studies of random laser systems are a new direction with promising potential applications and theoretical interest. The research is based on the theories of localization and laser physics. So far, the research shows that there are random lasing modes inside the systems which is quite different from the common laser systems. From the properties of the random lasing modes, they can understand the phenomena observed in the experiments, such as multi-peak and anisotropic spectrum, lasing mode number saturation, mode competition and dynamic processes, etc. To summarize, this dissertation has contributed the following in the study of random laser systems: (1) by comparing the Lamb theory with the Letokhov theory, the general formulas of the threshold length or gain of random laser systems were obtained; (2) they pointed out the vital weakness of previous time-independent methods in random laser research; (3) a new model which includes the FDTD method and the semi-classical laser theory. The solutions of this model ...
Contextuality in canonical systems of random variables
Dzhafarov, Ehtibar N.; Cervantes, Víctor H.; Kujala, Janne V.
2017-10-01
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions of the context-sharing random variables. We propose to represent any system of measurements in a canonical form and to consider the system contextual if and only if its canonical representation is contextual. As an illustration, we establish a criterion for contextuality of the canonical system consisting of all dichotomizations of a single pair of content-sharing categorical random variables. This article is part of the themed issue `Second quantum revolution: foundational questions'.
Sunspot random walk and 22-year variation
Love, Jeffrey J.; Rigler, E. Joshua
2012-01-01
We examine two stochastic models for consistency with observed long-term secular trends in sunspot number and a faint, but semi-persistent, 22-yr signal: (1) a null hypothesis, a simple one-parameter random-walk model of sunspot-number cycle-to-cycle change, and, (2) an alternative hypothesis, a two-parameter random-walk model with an imposed 22-yr alternating amplitude. The observed secular trend in sunspots, seen from solar cycle 5 to 23, would not be an unlikely result of the accumulation of multiple random-walk steps. Statistical tests show that a 22-yr signal can be resolved in historical sunspot data; that is, the probability is low that it would be realized from random data. On the other hand, the 22-yr signal has a small amplitude compared to random variation, and so it has a relatively small effect on sunspot predictions. Many published predictions for cycle 24 sunspots fall within the dispersion of previous cycle-to-cycle sunspot differences. The probability is low that the Sun will, with the accumulation of random steps over the next few cycles, walk down to a Dalton-like minimum. Our models support published interpretations of sunspot secular variation and 22-yr variation resulting from cycle-to-cycle accumulation of dynamo-generated magnetic energy.
Randomization Does Not Help Much, Comparability Does.
Directory of Open Access Journals (Sweden)
Uwe Saint-Mont
Full Text Available According to R.A. Fisher, randomization "relieves the experimenter from the anxiety of considering innumerable causes by which the data may be disturbed." Since, in particular, it is said to control for known and unknown nuisance factors that may considerably challenge the validity of a result, it has become very popular. This contribution challenges the received view. First, looking for quantitative support, we study a number of straightforward, mathematically simple models. They all demonstrate that the optimism surrounding randomization is questionable: In small to medium-sized samples, random allocation of units to treatments typically yields a considerable imbalance between the groups, i.e., confounding due to randomization is the rule rather than the exception. In the second part of this contribution, the reasoning is extended to a number of traditional arguments in favour of randomization. This discussion is rather non-technical, and sometimes touches on the rather fundamental Frequentist/Bayesian debate. However, the result of this analysis turns out to be quite similar: While the contribution of randomization remains doubtful, comparability contributes much to a compelling conclusion. Summing up, classical experimentation based on sound background theory and the systematic construction of exchangeable groups seems to be advisable.
Convergence rates for arbitrary statistical moments of random quantum circuits.
Brown, Winton G; Viola, Lorenza
2010-06-25
We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the resulting unitary converge to Haar measure averages. This is accomplished by mapping the superoperator that describes t order moments on n qubits to a multilevel SU(4^{t}) Lipkin-Meshkov-Glick Hamiltonian. We show that, for arbitrary fixed t, the ground-state manifold is exactly spanned by factorized eigenstates and, under the assumption that a mean-field ansatz accurately describes the low-lying excitations, the spectral gap scales as 1/n in the thermodynamic limit. Our results imply that random quantum circuits yield an efficient implementation of ϵ approximate unitary t designs.
Stochastic finite element method with simple random elements
Starkloff, Hans-Jörg
2008-01-01
We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.
Beentjes, Titus A A; van Gaal, Betsie G I; Goossens, Peter J J; Schoonhoven, Lisette
2016-01-19
E-mental health is a promising medium to keep mental health affordable and accessible. For consumers with severe mental illness the evidence of the effectiveness of e-health is limited. A number of difficulties and barriers have to be addressed concerning e-health for consumers with severe mental illness. One possible solution might be to blend e-health with face-to-face delivery of a recovery-oriented treatment, like the Illness Management & Recovery (IMR) programme. This paper describes the development of an e-health application for the IMR programme and the design of an early clustered randomized controlled trial. We developed the e-IMR intervention according to the six-step protocol of Intervention Mapping. Consumers joined the development group to address important and relevant issues for the target group. Decisions during the six-step development process were based on qualitative evaluations of the Illness Management & Recovery programme, structured interviews, discussion in the development group, and literature reviews on qualitative papers concerning consumers with severe mental illness, theoretical models, behavioural change techniques, and telemedicine for consumers with severe mental illness. The aim of the e-IMR intervention is to help consumers with severe mental illness to involve others, manage achieving goals, and prevent relapse. The e-IMR intervention consists of face-to-face delivery of the Illness Management & Recovery programme and an e-health application containing peer-testimonials on videos, follow up on goals and coping strategies, monitoring symptoms, solving problems, and communication opportunities. We designed an early cluster randomized controlled trial that will evaluate the e-IMR intervention. In the control condition the Illness Management & Recovery programme is provided. The main effect-study parameters are: illness management, recovery, psychiatric symptoms severity, self-management, quality of life, and general health. The
Interpreting parameters in the logistic regression model with random effects
DEFF Research Database (Denmark)
Larsen, Klaus; Petersen, Jørgen Holm; Budtz-Jørgensen, Esben
2000-01-01
interpretation, interval odds ratio, logistic regression, median odds ratio, normally distributed random effects......interpretation, interval odds ratio, logistic regression, median odds ratio, normally distributed random effects...
Random numbers spring from alpha decay
Energy Technology Data Exchange (ETDEWEB)
Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.
1980-05-01
Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a /sup 235/U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables.
Random walk centrality for temporal networks
Rocha, Luis E. C.; Masuda, Naoki
2014-06-01
Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included.
NAFASS in action: How to control randomness?
Nigmatullin, R. R.; Zhang, Wei
2013-03-01
In this paper the original method of transformation of one random function to another one is suggested. The problem of transformation of one random function to another one is based on the NAFASS approach suggested previously by one of the authors (RRN) in paper [1]. The problem can be formulated as follows: is it possible to transform one random function to another one (the functional forms of the both functions are not known) during the fixed segment of time t1? The solution of this problem shown in this paper gives a chance to manage with random functions that describe many complex systems, where the adequate model pretending on their functional or analytical description is not known. This transformation based on the successful solution of the Prony's problem gives unique chances to manage with some chemical processes, technological processes and understand better the general behavior of the different complex systems which cannot be managed by the human being. Besides this solution another solution of this problem related to control of detrended random sequences is considered also.
Random Bosonic States for Robust Quantum Metrology
Directory of Open Access Journals (Sweden)
M. Oszmaniec
2016-12-01
Full Text Available We study how useful random states are for quantum metrology, i.e., whether they surpass the classical limits imposed on precision in the canonical phase sensing scenario. First, we prove that random pure states drawn from the Hilbert space of distinguishable particles typically do not lead to superclassical scaling of precision even when allowing for local unitary optimization. Conversely, we show that random pure states from the symmetric subspace typically achieve the optimal Heisenberg scaling without the need for local unitary optimization. Surprisingly, the Heisenberg scaling is observed for random isospectral states of arbitrarily low purity and preserved under loss of a fixed number of particles. Moreover, we prove that for pure states, a standard photon-counting interferometric measurement suffices to typically achieve resolution following the Heisenberg scaling for all values of the phase at the same time. Finally, we demonstrate that metrologically useful states can be prepared with short random optical circuits generated from three types of beam splitters and a single nonlinear (Kerr-like transformation.
Improving randomness characterization through Bayesian model selection.
Díaz Hernández Rojas, Rafael; Solís, Aldo; Angulo Martínez, Alí M; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Pérez Castillo, Isaac
2017-06-08
Random number generation plays an essential role in technology with important applications in areas ranging from cryptography to Monte Carlo methods, and other probabilistic algorithms. All such applications require high-quality sources of random numbers, yet effective methods for assessing whether a source produce truly random sequences are still missing. Current methods either do not rely on a formal description of randomness (NIST test suite) on the one hand, or are inapplicable in principle (the characterization derived from the Algorithmic Theory of Information), on the other, for they require testing all the possible computer programs that could produce the sequence to be analysed. Here we present a rigorous method that overcomes these problems based on Bayesian model selection. We derive analytic expressions for a model's likelihood which is then used to compute its posterior distribution. Our method proves to be more rigorous than NIST's suite and Borel-Normality criterion and its implementation is straightforward. We applied our method to an experimental device based on the process of spontaneous parametric downconversion to confirm it behaves as a genuine quantum random number generator. As our approach relies on Bayesian inference our scheme transcends individual sequence analysis, leading to a characterization of the source itself.
Exploring complex networks through random walks.
Costa, Luciano da Fontoura; Travieso, Gonzalo
2007-01-01
Most real complex networks--such as protein interactions, social contacts, and the Internet--are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key issue to investigate and characterize how effectively the nodes and edges of such networks can be covered by different strategies. At the same time, it is critically important to infer how well can topological measurements such as the average node degree and average clustering coefficient be estimated during such network explorations. The present article addresses these problems by considering random, Barabási-Albert (BA), and geographical network models with varying connectivity explored by three types of random walks: traditional, preferential to untracked edges, and preferential to unvisited nodes. A series of relevant results are obtained, including the fact that networks of the three studied models with the same size and average node degree allow similar node and edge coverage efficiency, the identification of linear scaling with the size of the network of the random walk step at which a given percentage of the nodes/edges is covered, and the critical result that the estimation of the averaged node degree and clustering coefficient by random walks on BA networks often leads to heavily biased results. Many are the theoretical and practical implications of such results.
Programmable disorder in random DNA tilings
Tikhomirov, Grigory; Petersen, Philip; Qian, Lulu
2017-03-01
Scaling up the complexity and diversity of synthetic molecular structures will require strategies that exploit the inherent stochasticity of molecular systems in a controlled fashion. Here we demonstrate a framework for programming random DNA tilings and show how to control the properties of global patterns through simple, local rules. We constructed three general forms of planar network—random loops, mazes and trees—on the surface of self-assembled DNA origami arrays on the micrometre scale with nanometre resolution. Using simple molecular building blocks and robust experimental conditions, we demonstrate control of a wide range of properties of the random networks, including the branching rules, the growth directions, the proximity between adjacent networks and the size distribution. Much as combinatorial approaches for generating random one-dimensional chains of polymers have been used to revolutionize chemical synthesis and the selection of functional nucleic acids, our strategy extends these principles to random two-dimensional networks of molecules and creates new opportunities for fabricating more complex molecular devices that are organized by DNA nanostructures.
From quenched disorder to continuous time random walk
Burov, Stanislav
2017-11-01
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation, t →t /Λ1 /α , for a transient process in the subdiffusive regime is sufficient for asymptotic mapping. An exact form of the constant Λ1 /α is established. A disorder averaged position probability density function for a quenched trap model is obtained, and analytic expressions for the diffusion coefficient and drift are provided.
Pinsoneault, Terry B.
2005-01-01
The ability of the Minnesota Multiphasic Personality Inventory-Adolescent (MMPI-A; J. N. Butcher et al., 1992) validity scales to detect random, partially random, and nonrandom MMPI-A protocols was investigated. Investigations included the Variable Response Inconsistency scale (VRIN), F, several potentially useful new F and VRIN subscales, and…
Randomly weighted sums of subexponential random variables with application to ruin theory
Tang, Q.; Tsitsiashvili, G.
2003-01-01
Let {X k , 1 k n} be n independent and real-valued random variables with common subexponential distribution function, and let {k, 1 k n} be other n random variables independent of {X k , 1 k n} and satisfying a k b for some 0 < a b < for all 1 k n. This paper proves that the asymptotic relations P
Pseudo cluster randomization: balancing the disadvantages of cluster and individual randomization
Melis, R.J.F.; Teerenstra, S.; Olde Rikkert, M.G.M.; Borm, G.F.
2011-01-01
While designing a trial to evaluate a complex intervention, one may be confronted with the dilemma that randomization at the level of the individual patient risks contamination bias, whereas cluster randomization risks incomparability of study arms and recruitment problems. Literature provides only
The resistance of randomly grown trees
Colman, E. R.; Rodgers, G. J.
2011-12-01
An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability p or two edges with probability 1 - p. With each edge having a resistance equal to 1Ω, the total resistance Rn between the root vertex and a busbar connecting all the vertices at the nth level is considered. A dynamical system is presented which approximates Rn, it is shown that the mean value for this system approaches (1 + p)/(1 - p) as n → ∞, the distribution of Rn at large n is also examined. Additionally, a random sequence construction akin to a random Fibonacci sequence is used to approximate Rn; this sequence is shown to be related to the Legendre polynomials and its mean is shown to converge with | - (1 + p)/(1 - p)| ˜ n-1/2.
Probabilistic graphs using coupled random variables
Nelson, Kenric P.; Barbu, Madalina; Scannell, Brian J.
2014-05-01
Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic reasoning, but the restrictions reduce the expressive capability of each node making network designs complex. The ability to model coupled random variables using the calculus of nonextensive statistical mechanics provides a neural node design incorporating nonlinear coupling between input states while maintaining the rigor of probabilistic reasoning. A generalization of Bayes rule using the coupled product enables a single node to model correlation between hundreds of random variables. A coupled Markov random field is designed for the inferencing and classification of UCI's MLR `Multiple Features Data Set' such that thousands of linear correlation parameters can be replaced with a single coupling parameter with just a (3%, 4%) reduction in (classification, inference) performance.
A random walk model to evaluate autism
Moura, T. R. S.; Fulco, U. L.; Albuquerque, E. L.
2018-02-01
A common test administered during neurological examination in children is the analysis of their social communication and interaction across multiple contexts, including repetitive patterns of behavior. Poor performance may be associated with neurological conditions characterized by impairments in executive function, such as the so-called pervasive developmental disorders (PDDs), a particular condition of the autism spectrum disorders (ASDs). Inspired in these diagnosis tools, mainly those related to repetitive movements and behaviors, we studied here how the diffusion regimes of two discrete-time random walkers, mimicking the lack of social interaction and restricted interests developed for children with PDDs, are affected. Our model, which is based on the so-called elephant random walk (ERW) approach, consider that one of the random walker can learn and imitate the microscopic behavior of the other with probability f (1 - f otherwise). The diffusion regimes, measured by the Hurst exponent (H), is then obtained, whose changes may indicate a different degree of autism.
Embedded random matrix ensembles in quantum physics
Kota, V K B
2014-01-01
Although used with increasing frequency in many branches of physics, random matrix ensembles are not always sufficiently specific to account for important features of the physical system at hand. One refinement which retains the basic stochastic approach but allows for such features consists in the use of embedded ensembles. The present text is an exhaustive introduction to and survey of this important field. Starting with an easy-to-read introduction to general random matrix theory, the text then develops the necessary concepts from the beginning, accompanying the reader to the frontiers of present-day research. With some notable exceptions, to date these ensembles have primarily been applied in nuclear spectroscopy. A characteristic example is the use of a random two-body interaction in the framework of the nuclear shell model. Yet, topics in atomic physics, mesoscopic physics, quantum information science and statistical mechanics of isolated finite quantum systems can also be addressed using these ensemb...
Social patterns revealed through random matrix theory
Sarkar, Camellia; Jalan, Sarika
2014-11-01
Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real-world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remains the same throughout all datasets, random matrix theory provides insight into the interaction pattern of individuals of the society in situations of crisis. It has also been contemplated that individual accountability in terms of weighted interactions remains as a key to success unless segregation of tasks comes into play.
Effective Lagrangians and chiral random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Halasz, M.A.; Verbaarschot, J.J.M. [Department of Physics, State University of New York, Stony Brook, New York 11794 (United States)
1995-08-15
Recently, sum rules were derived for the inverse eigenvalues of the Dirac operator. They were obtained in two different ways: (i) starting from the low-energy effective Lagrangian and (ii) starting from a random matrix theory with the symmetries of the Dirac operator. This suggests that the effective theory can be obtained directly from the random matrix theory. Previously, this was shown for three or more colors with fundamental fermions. In this paper we construct the effective theory from a random matrix theory for two colors in the fundamental representation and for an arbitrary number of colors in the adjoint representation. We construct a fermionic partition function for Majorana fermions in Euclidean spacetime. Their reality condition is formulated in terms of complex conjugation of the second kind.
Random matrix theory for underwater sound propagation
Hegewisch, K. C.; Tomsovic, S.
2012-02-01
Ocean acoustic propagation can be formulated as a wave guide with a weakly random medium generating multiple scattering. Twenty years ago, this was recognized as a quantum chaos problem, and yet random matrix theory, one pillar of quantum or wave chaos studies, has never been introduced into the subject. The modes of the wave guide provide a representation for the propagation, which in the parabolic approximation is unitary. Scattering induced by the ocean's internal waves leads to a power-law random banded unitary matrix ensemble for long-range deep-ocean acoustic propagation. The ensemble has similarities, but differs, from those introduced for studying the Anderson metal-insulator transition. The resulting long-range propagation ensemble statistics agree well with those of full wave propagation using the parabolic equation.
Logarithmic universality in random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Splittorff, K. E-mail: split@alf.nbi.dk
1999-05-24
Universality in unitary invariant random matrix ensembles with complex matrix elements is considered. We treat two general ensembles which have a determinant factor in the weight. These ensembles are relevant, e.g., for spectra of the Dirac operator in QCD. In addition to the well established universality with respect to the choice of potential, we prove that microscopic spectral correlators are unaffected when the matrix in the determinant is replaced by an expansion in powers of the matrix. We refer to this invariance as logarithmic universality. The result is used in proving that a simple random matrix model with Ginsparg-Wilson symmetry has the same microscopic spectral correlators as chiral random matrix theory.
Random matrix theory with an external source
Brézin, Edouard
2016-01-01
This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.
Statistical properties of random clique networks
Ding, Yi-Min; Meng, Jun; Fan, Jing-Fang; Ye, Fang-Fu; Chen, Xiao-Song
2017-10-01
In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is introduced by combining the random selection rule of the Erdös and Rényi (ER) model and the concept of cliques. We find that random clique networks having a small average degree differ from the ER network in that they have a large clustering coefficient and a power law clustering spectrum, while networks having a high average degree have similar properties as the ER model. In addition, we find that the relation between the clustering coefficient and the average degree shows a non-monotonic behavior and that the degree distributions can be fit by multiple Poisson curves; we explain the origin of such novel behaviors and degree distributions.
Efficient broadcast on random geometric graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [INTERNATIONAL COMPUTER SCI.; Sauerwald, Thomas [INTERNATIONAL COMPUTER SCI.
2009-01-01
A Randon Geometric Graph (RGG) is constructed by distributing n nodes uniformly at random in the unit square and connecting two nodes if their Euclidean distance is at most r, for some prescribed r. They analyze the following randomized broadcast algorithm on RGGs. At the beginning, there is only one informed node. Then in each round, each informed node chooses a neighbor uniformly at random and informs it. They prove that this algorithm informs every node in the largest component of a RGG in {Omicron}({radical}n/r) rounds with high probability. This holds for any value of r larger than the critical value for the emergence of a giant component. In particular, the result implies that the diameter of the giant component is {Theta}({radical}n/r).
Random field estimation approach to robot dynamics
Rodriguez, Guillermo
1990-01-01
The difference equations of Kalman filtering and smoothing recursively factor and invert the covariance of the output of a linear state-space system driven by a white-noise process. Here it is shown that similar recursive techniques factor and invert the inertia matrix of a multibody robot system. The random field models are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. They are easier to describe than the models based on classical mechanics, which typically require extensive derivation and manipulation of equations of motion for complex mechanical systems. With the spatially random models, more primitive locally specified computations result in a global collective system behavior equivalent to that obtained with deterministic models. The primary goal of applying random field estimation is to provide a concise analytical foundation for solving robot control and motion planning problems.
Introduction to random matrices theory and practice
Livan, Giacomo; Vivo, Pierpaolo
2018-01-01
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum. The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory). Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
An Anderson-localized random nanolaser
Liu, Jin; Ek, Sara; Gregersen, Niels; Suhr, Troels; Schubert, Martin; Mørk, Jesper; Stobbe, Søren; Lodahl, Peter
2012-01-01
Precision is a virtue throughout science in general and in optics in particular where carefully fabricated nanometer-scale devices hold great promise for both classical and quantum photonics [1-6]. In such nanostructures, unavoidable imperfections often impose severe performance limits but, in certain cases, disorder may enable new functionalities [7]. Here we demonstrate on-chip random nanolasers where the cavity feedback is provided by the intrinsic disorder in a semiconductor photonic-crystal waveguide, leading to Anderson localization of light [8]. This enables highly e?cient and broadband tunable lasers with very small mode volumes. We observe an intriguing interplay between gain, dispersion-controlled slow light, and disorder, which determines the cross-over from ballistic transport to Anderson localization. Such a behavior is a unique feature of non-conservative random media that enables the demonstration of all-optical control of random lasing. Our statistical analysis shows a way towards ultimate thr...
Competitive Facility Location with Fuzzy Random Demands
Uno, Takeshi; Katagiri, Hideki; Kato, Kosuke
2010-10-01
This paper proposes a new location problem of competitive facilities, e.g. shops, with uncertainty and vagueness including demands for the facilities in a plane. By representing the demands for facilities as fuzzy random variables, the location problem can be formulated as a fuzzy random programming problem. For solving the fuzzy random programming problem, first the α-level sets for fuzzy numbers are used for transforming it to a stochastic programming problem, and secondly, by using their expectations and variances, it can be reformulated to a deterministic programming problem. After showing that one of their optimal solutions can be found by solving 0-1 programming problems, their solution method is proposed by improving the tabu search algorithm with strategic oscillation. The efficiency of the proposed method is shown by applying it to numerical examples of the facility location problems.
Preasymptotic convergence of randomized Kaczmarz method
Jiao, Yuling; Jin, Bangti; Lu, Xiliang
2017-12-01
Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the initial error is smooth (e.g. sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.
Cooperation evolution in random multiplicative environments
Yaari, G.; Solomon, S.
2010-02-01
Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature. The special properties of multiplicative noise as opposed to additive noise have been noticed for a long while. Even though apparently and formally the difference between free additive vs. multiplicative random walks consists in just a move from normal to log-normal distributions, in practice the implications are much more far reaching. While in an additive context the emergence and survival of cooperation requires special conditions (especially some level of reward, punishment, reciprocity), we find that in the multiplicative random context the emergence of cooperation is much more natural and effective. We study the various implications of this observation and its applications in various contexts.
The Continuous Spin Random Field Model : Ferromagnetic Ordering in d ≥ 3
Külske, Christof
1999-01-01
We investigate the Gibbs-measures of ferromagnetically coupled continuous spins in double-well potentials subjected to a random field (our specific example being the φ4 theory), showing ferromagnetic ordering in d ≥ 3 dimensions for weak disorder and large energy barriers. We map the random
Di Biase, Luigi; Tung, Roderick; Szili-Torok, Tamás; Burkhardt, J David; Weiss, Peter; Tavernier, Rene; Berman, Adam E; Wissner, Erik; Spear, William; Chen, Xu; Neužil, Petr; Skoda, Jan; Lakkireddy, Dhanunjaya; Schwagten, Bruno; Lock, Ken; Natale, Andrea
2017-04-01
Patients with ischemic cardiomyopathy (ICM) are prone to scar-related ventricular tachycardia (VT). The success of VT ablation depends on accurate arrhythmogenic substrate localization, followed by optimal delivery of energy provided by constant electrode-tissue contact. Current manual and remote magnetic navigation (RMN)-guided ablation strategies aim to identify a reentry circuit and to target a critical isthmus through activation and entrainment mapping during ongoing tachycardia. The MAGNETIC VT trial will assess if VT ablation using the Niobe™ ES magnetic navigation system results in superior outcomes compared to a manual approach in subjects with ischemic scar VT and low ejection fraction. This is a randomized, single-blind, prospective, multicenter post-market study. A total of 386 subjects (193 per group) will be enrolled and randomized 1:1 between treatment with the Niobe ES system and treatment via a manual procedure at up to 20 sites. The study population will consist of patients with ischemic cardiomyopathy with left ventricular ejection fraction (LVEF) of ≤35% and implantable cardioverter defibrillator (ICD) who have sustained monomorphic VT. The primary study endpoint is freedom from any recurrence of VT through 12 months. The secondary endpoints are acute success; freedom from any VT at 1 year in a large-scar subpopulation; procedure-related major adverse events; and mortality rate through 12-month follow-up. Follow-up will consist of visits at 3, 6, 9, and 12 months, all of which will include ICD interrogation. The MAGNETIC VT trial will help determine whether substrate-based ablation of VT with RMN has clinical advantages over manual catheter manipulation. Clinicaltrials.gov identifier: NCT02637947.
Yang, Qing; Fang, Ping
2016-10-01
Diabetes is one of the leading causes of morbidity and mortality worldwide, and type 2 diabetes is the most common type accounting for 90% of all diabetes cases. Health education is considered as the first choice to control blood glucose levels. We conducted a meta-analysis to assess the effect of health education tool "Conversation Map" in diabetes patients to control blood glucose. We searched PubMed, Embase, Cochrane Central Register of Controlled Trials, China Knowledge Resource Integrated Database, and China Science Periodical Database up to December, 2015. We assessed the results using the inverse variance method to pool diabetes relative indicators, and assessed the heterogeneity of the results using I-square. We collected 22 trials in our meta-analysis, which included 3360 patients. The results showed that the fasting blood-glucose level was significantly reduced in the type 2 diabetes group patients educated with "Conversation Map" when compared to their respective control groups (weighted mean difference [WMD]: -2.23, 95% confidence interval [CI]: -2.70 to -1.76, P levels (WMD: -0.63, 95% CI: -1.08 to -0.17, P diabetes, and significantly reduced patients' blood glucose related index.
A Random Matrix Approach to Credit Risk
Guhr, Thomas
2014-01-01
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided. PMID:24853864
Electromagnetic Wave Propagation in Random Media
DEFF Research Database (Denmark)
Pécseli, Hans
1984-01-01
The propagation of a narrow frequency band beam of electromagnetic waves in a medium with randomly varying index of refraction is considered. A novel formulation of the governing equation is proposed. An equation for the average Green function (or transition probability) can then be derived....... A Fokker-Planck type equation is contained as a limiting case. The results are readily generalized to include the features of the random coupling model and it is argued that the present problem is particularly suited for an analysis of this type....
Quantum optics in multiple scattering random media
DEFF Research Database (Denmark)
Lodahl, Peter
Quantum Optics in Multiple Scattering Random Media Peter Lodahl Research Center COM, Technical University of Denmark, Dk-2800 Lyngby, Denmark. Coherent transport of light in a disordered random medium has attracted enormous attention both from a fundamental and application point of view. Coherent...... quantum optics in multiple scattering media and novel fundamental phenomena have been predicted when examining quantum fluctuations instead of merely the intensity of the light [1]. Here I will present the first experimental study of the propagation of quantum noise through an elastic, multiple scattering...
A random matrix approach to credit risk.
Directory of Open Access Journals (Sweden)
Michael C Münnix
Full Text Available We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.
Quark Spectra, Topology, and Random Matrix Theory
Energy Technology Data Exchange (ETDEWEB)
Edwards, R.G.; Heller, U.M. [SCRI, Florida State University, Tallahassee, Florida 32306-4130 (United States); Kiskis, J. [Department of Physics, University of California, Davis, California 95616 (United States); Narayanan, R. [Department of Physics, Building 510A, Brookhaven National Laboratory, P.O. Box 5000, Upton, New York 11973 (United States)
1999-05-01
Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice overlap Dirac operator provides a nonperturbative, ultraviolet-regularized description of quarks with the correct chiral symmetry. Properties of the spectrum of this operator and their relation to random matrix theory are studied here. In particular, the predictions from chiral random matrix theory in topologically nontrivial gauge field sectors are tested for the first time. {copyright} {ital 1999} {ital The American Physical Society}
Intrinsic Dispersivity of Randomly Packed Monodisperse Spheres
Scheven, U. M.; Harris, R.; Johns, M. L.
2007-08-01
We determine the intrinsic longitudinal dispersivity ld of randomly packed monodisperse spheres by separating the intrinsic stochastic dispersivity ld from dispersion by unavoidable sample dependent flow heterogeneities. The measured ld, scaled by the hydrodynamic radius rh, coincide with theoretical predictions [Saffman, J. Fluid Mech. 7, 194 (1960)JFLSA70022-112010.1017/S0022112060001432] for dispersion in an isotropic random network of identical capillaries of length l and radius a, for l/a=3.82, and with rescaled simulation results [Maier et al., Phys. FluidsPHFLE61070-6631 12, 2065 (2000)10.1063/1.870452].
Random forest ensemble classification based fuzzy logic
Ben Ayed, Abdelkarim; Benhammouda, Marwa; Ben Halima, Mohamed; Alimi, Adel M.
2017-03-01
In this paper, we treat the supervised data classification, while using the fuzzy random forests that combine the hardiness of the decision trees, the power of the random selection that increases the diversity of the trees in the forest as well as the flexibility of the fuzzy logic for noise. We will be interested in the construction of a forest of fuzzy decision trees. Our system is validated on nine standard classification benchmarks from UCI repository and have the specificity to control some data, to reduce the rate of mistakes and to put in evidence more of hardiness and more of interoperability.
On testing the missing at random assumption
DEFF Research Database (Denmark)
Jaeger, Manfred
2006-01-01
Most approaches to learning from incomplete data are based on the assumption that unobserved values are missing at random (mar). While the mar assumption, as such, is not testable, it can become testable in the context of other distributional assumptions, e.g. the naive Bayes assumption. In this ......Most approaches to learning from incomplete data are based on the assumption that unobserved values are missing at random (mar). While the mar assumption, as such, is not testable, it can become testable in the context of other distributional assumptions, e.g. the naive Bayes assumption...
Random walk term weighting for information retrieval
DEFF Research Database (Denmark)
Blanco, R.; Lioma, Christina
2007-01-01
We present a way of estimating term weights for Information Retrieval (IR), using term co-occurrence as a measure of dependency between terms.We use the random walk graph-based ranking algorithm on a graph that encodes terms and co-occurrence dependencies in text, from which we derive term weights...... that represent a quantification of how a term contributes to its context. Evaluation on two TREC collections and 350 topics shows that the random walk-based term weights perform at least comparably to the traditional tf-idf term weighting, while they outperform it when the distance between co-occurring terms...
Investigation on random vibration of a drillstring
Qiu, Hongyuan; Yang, Jianming; Butt, Stephen; Zhong, Jinghan
2017-10-01
This paper investigates the axial-torsional coupled vibration of a drill-string under combined deterministic and random excitations. Finite element method (FEM) is used to model the system. The random excitation at the bit-rock interaction, which is considered in the bit axial direction, is treated as Gaussian white noise. Statistic linearization is first applied to find a equivalent linear dynamic system which is then solved with stochastic Newmark algorithm. The statistics of the responses, including the means and standard deviations of the bit axial displacement and rotational velocity are obtained and analyzed.
SDE based regression for random PDEs
Bayer, Christian
2016-01-06
A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to an approximation of the global solution of the random PDE. We provide an initial error and complexity analysis of the proposed method along with numerical examples illustrating its behaviour.
Enhancing superconducting critical current by randomness
Wang, Y. L.; Thoutam, L. R.; Xiao, Z. L.; Shen, B.; Pearson, J. E.; Divan, R.; Ocola, L. E.; Crabtree, G. W.; Kwok, W. K.
2015-01-01
The key ingredient of high critical currents in a type-II superconductor is defect sites that 'pin' vortices. Contrary to earlier understanding on nano-patterned artificial pinning, here we show unequivocally the advantages of a random pinscape over an ordered array in a wide magnetic field range. We reveal that the better performance of a random pinscape is due to the variation of its local-density-of-pinning-sites (LDOPS), which mitigates the motion of vortices. This is confirmed by achievi...
Random Circles and Fields on Circles.
1986-05-01
p is on the true circle C ; X is the corresponding radius of the random circle -5- Examples and comments Let W be a Wiener process on 3+, let a > 0 be...properties on C when M = W, it is expected that X be the analog of the Ornstein-Uhlenbeck process on the circle C . Indeed, the representation (2.12) shows this...evolution in time of a random field on the circle C . -35- The message of the following theorem is that the sections of X are all stationary and Markov
Infinite Random Graphs as Statistical Mechanical Models
DEFF Research Database (Denmark)
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe...... a relation to the so-called uniform infinite tree and results on the Hausdorff and spectral dimension of two-dimensional space-time obtained in B. Durhuus, T. Jonsson, J.F. Wheater, J. Stat. Phys. 139, 859 (2010) are briefly outlined. For the latter we discuss results on the absence of spontaneous...
Mathematical conversations multicolor problems, problems in the theory of numbers, and random walks
Dynkin, E B
2006-01-01
Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.
Animated Randomness, Avatars, Movement, and Personalization in Risk Graphics
Fuhrel-Forbis, Andrea; Wijeysundera, Harindra C; Exe, Nicole; Dickson, Mark; Holtzman, Lisa; Kahn, Valerie C; Zikmund-Fisher, Brian J
2014-01-01
effects on recall, but animated randomness was associated with better recall for those at lower risk and worse recall for those at higher risk (F 1,3544=7.06, P=.01). Conclusions Animated randomness may help people better understand the random nature of risk. However, in the context of cardiovascular risk, such understanding may result in lower healthy lifestyle intentions. Therefore, whether or not to display randomness may depend on whether one’s goal is to persuade or to inform. Avatars show promise for helping people grasp how population-based statistics map to an individual case. PMID:24642037
Animated randomness, avatars, movement, and personalization in risk graphics.
Witteman, Holly O; Fuhrel-Forbis, Andrea; Wijeysundera, Harindra C; Exe, Nicole; Dickson, Mark; Holtzman, Lisa; Kahn, Valerie C; Zikmund-Fisher, Brian J
2014-03-18
randomness was associated with better recall for those at lower risk and worse recall for those at higher risk (F1,3544=7.06, P=.01). Animated randomness may help people better understand the random nature of risk. However, in the context of cardiovascular risk, such understanding may result in lower healthy lifestyle intentions. Therefore, whether or not to display randomness may depend on whether one's goal is to persuade or to inform. Avatars show promise for helping people grasp how population-based statistics map to an individual case.
Construction of random perfect phylogeny matrix
Directory of Open Access Journals (Sweden)
Mehdi Sadeghi
2010-11-01
Full Text Available Mehdi Sadeghi1,2, Hamid Pezeshk4, Changiz Eslahchi3,5, Sara Ahmadian6, Sepideh Mah Abadi61National Institute of Genetic Engineering and Biotechnology, Tehran, Iran; 2School of Computer Science, 3School of Mathematics, Institute for Research in Fundamental Sciences (IPM, Tehran, Iran; 4School of Mathematics, Statistics and Computer Sciences, Center of Excellence in Biomathematics, College of Science, University of Tehran, Tehran, Iran; 5Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran; 6Department of Computer Engineering, Sharif University of Technology, Tehran, IranPurpose: Interest in developing methods appropriate for mapping increasing amounts of genome-wide molecular data are increasing rapidly. There is also an increasing need for methods that are able to efficiently simulate such data.Patients and methods: In this article, we provide a graph-theory approach to find the necessary and sufficient conditions for the existence of a phylogeny matrix with k nonidentical haplotypes, n single nucleotide polymorphisms (SNPs, and a population size of m for which the minimum allele frequency of each SNP is between two specific numbers a and b.Results: We introduce an O(max(n2, nm algorithm for the random construction of such a phylogeny matrix. The running time of any algorithm for solving this problem would be Ω (nm.Conclusion: We have developed software, RAPPER, based on this algorithm, which is available at http://bioinf.cs.ipm.ir/softwares/RAPPER.Keywords: perfect phylogeny, minimum allele frequency (MAF, tree, recursive algorithm
Slope failure analysis using the random material point method
Wang, B.; Hicks, M.A.; Vardon, P.J.
2016-01-01
The random material point method (RMPM), which combines random field theory and the material point method (MPM), is proposed. It differs from the random finite-element method (RFEM), by assigning random field (cell) values to material points that are free to move relative to the computational grid
Random-phase metasurfaces at optical wavelengths
DEFF Research Database (Denmark)
Pors, Anders; Ding, Fei; Chen, Yiting
2016-01-01
of an optically thick gold film overlaid by a subwavelength thin glass spacer and an array of gold nanobricks, we design and realize random-phase metasurfaces at a wavelength of 800 nm. Optical characterisation of the fabricated samples convincingly demonstrates the diffuse scattering of reflected light...
Hypnotherapy in radiotherapy patients: A randomized trial
Stalpers, Lukas J. A.; da Costa, Hanna C.; Merbis, Merijn A. E.; Fortuin, Andries A.; Muller, Martin J.; van Dam, Frits S. A. M.
2005-01-01
Purpose: To determine whether hypnotherapy reduces anxiety and improves the quality of life in cancer patients undergoing curative radiotherapy (RT). Methods and Materials: After providing written informed consent, 69 patients were randomized between standard curative RT alone (36 controls) and RT
Pollen Grains, Random Walks and Einstein
Indian Academy of Sciences (India)
wnian motion show us how the most profound physics and mathematics can emerge from simple, direct obser- vation of natural phenomena. Ideas related to Brownian motion and random walks appear today in mathematics, all the natural sciences, engineering, linguistics, finance, economics, and even the social sciences.
Malicet, Dominique
2017-09-01
In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo (S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν} . We prove that under the only condition that there is no probability measure invariant by {ν} -almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk (g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.
ASSISTments Dataset from Multiple Randomized Controlled Experiments
Selent, Douglas; Patikorn, Thanaporn; Heffernan, Neil
2016-01-01
In this paper, we present a dataset consisting of data generated from 22 previously and currently running randomized controlled experiments inside the ASSISTments online learning platform. This dataset provides data mining opportunities for researchers to analyze ASSISTments data in a convenient format across multiple experiments at the same time.…
Sign-compute-resolve for random access
Goseling, Jasper; Stefanovic, Cedomir; Popovski, Petar
2014-01-01
We present an approach to random access that is based on three elements: physical-layer network coding, signature codes and tree splitting. Upon occurrence of a collision, physical-layer network coding enables the receiver to decode the sum of the information that was transmitted by the individual
Causal random geometry from stochastic quantization
DEFF Research Database (Denmark)
Ambjørn, Jan; Loll, R.; Westra, W.
2010-01-01
in this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative quantum Hamiltonian of the random surface model including...... the sum over topologies. Interestingly, the generally fictitious stochastic time corresponds to proper time on the geometries...
Causal random geometry from stochastic quantization
Ambjørn, J.; Loll, R.|info:eu-repo/dai/nl/304830720; Westra, W.|info:eu-repo/dai/nl/304832073; Zohren, S.
2010-01-01
In this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative quantum Hamiltonian of the random surface model including the sum
Discrete optimization problems with random cost elements
Ghosh, D.; Das, S.
2000-01-01
In a general class of discrete optimization problems, some of the elements mayhave random costs associated with them. In such a situation, the notion of optimalityneeds to be suitably modified. In this work we define an optimal solutionto be a feasible solution with the minimum risk. We focus on the
A Randomized controlled trial of intramuscular pentazocine ...
African Journals Online (AJOL)
pain perception was assessed using visual analog scale (VAS) scores at presentation and after delivery while maternal ... Randomized controlled trial of intramuscular pentazocine compared to intravenous paracetamol for pain relief in labour. 117. Tropical Journal of Obstetrics .... An envelope was opened by a nurse and.
RMBNToolbox: random models for biochemical networks
Directory of Open Access Journals (Sweden)
Niemi Jari
2007-05-01
Full Text Available Abstract Background There is an increasing interest to model biochemical and cell biological networks, as well as to the computational analysis of these models. The development of analysis methodologies and related software is rapid in the field. However, the number of available models is still relatively small and the model sizes remain limited. The lack of kinetic information is usually the limiting factor for the construction of detailed simulation models. Results We present a computational toolbox for generating random biochemical network models which mimic real biochemical networks. The toolbox is called Random Models for Biochemical Networks. The toolbox works in the Matlab environment, and it makes it possible to generate various network structures, stoichiometries, kinetic laws for reactions, and parameters therein. The generation can be based on statistical rules and distributions, and more detailed information of real biochemical networks can be used in situations where it is known. The toolbox can be easily extended. The resulting network models can be exported in the format of Systems Biology Markup Language. Conclusion While more information is accumulating on biochemical networks, random networks can be used as an intermediate step towards their better understanding. Random networks make it possible to study the effects of various network characteristics to the overall behavior of the network. Moreover, the construction of artificial network models provides the ground truth data needed in the validation of various computational methods in the fields of parameter estimation and data analysis.
Random Access to Grammar-Compressed Strings
DEFF Research Database (Denmark)
Bille, Philip; Landau, Gad M.; Raman, Rajeev
2011-01-01
(n) is the inverse of the kth row of Ackermann's function. Our representations also efficiently support decompression of any substring in S: we can decompress any substring of length m in the same complexity as a single random access query and ad- ditional O(m) time. Combining these results with fast algorithms...
K-Median: Random Sampling Procedure
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. K-Median: Random Sampling Procedure. Sample a set of 1/ + 1 points from P. Let Q = first 1/ points, p = last point. Let T = Avg. 1-Median cost of P, c=1-Median. Let B1 = B(c,T/ 2), B2 = B(p, T). Let P' = points in B1.
New specifications for exponential random graph models
Snijders, Tom A. B.; Pattison, Philippa E.; Robins, Garry L.; Handcock, Mark S.; Stolzenberg, RM
2006-01-01
The most promising class of statistical models for expressing structural properties of social networks observed atone moment in time is the class of exponential random graph models (ERGMs), also known as p* models. The strong point of these models is that they can represent a variety of structural
Using optimized random amplified polymorphic DNA (RAPD ...
African Journals Online (AJOL)
Citrus nobilis Lour. Gonggan is an excellent fruit variety which is widely planted in South China. The origin of Gonggan is not clear. It is conjectured that its origin is from a cross between tangerine and orange; however, there is no direct evidence to confirm this. Here, we applied the optimized random amplified polymorphic ...
Markov random fields on triangle meshes
DEFF Research Database (Denmark)
Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas
2010-01-01
In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process label...
Markov Random Fields on Triangle Meshes
DEFF Research Database (Denmark)
Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas
2010-01-01
In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process label...
The randomized complexity of maintaining the minimum
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Chaudhuri, Shiva; Radhakrishnan, Jaikumar
1996-01-01
The complexity of maintaining a set under the operations Insert, Delete and FindMin is considered. In the comparison model it is shown that any randomized algorithm with expected amortized cost t comparisons per Insert and Delete has expected cost at least n/(e22t)-1 comparisons for FindMin. If F...
Dynamics of excitable nodes on random graphs
Indian Academy of Sciences (India)
ogy and dynamics of excitable nodes on Erd˝os–Rényi (ER) [16] random graphs. Our focus is on rhythmic dynamics, namely periodic solutions, in this representative model. Since the network topology plays an important role, the question of how different growth rules. DOI: 10.1007/s12043-011-0180-6; ePublication: 31 ...
Ellipsometry with randomly varying polarization states
Liu, Fenz; Lee, Christopher James; Chen, Juequan; Chen, J.; Louis, Eric; van der Slot, Petrus J.M.; Boller, Klaus J.; Bijkerk, Frederik
2012-01-01
We show that, under the right conditions, one can make highly accurate polarization-based measurements without knowing the absolute polarization state of the probing light field. It is shown that light, passed through a randomly varying birefringent material has a well-defined orbit on the Poincar
Ellipsometry with random varying polarization state
Liu, Fenz; van Albada, B.; Lee, c; Bijkerk, Frederik
2012-01-01
We show that, under the right conditions, one can make highly accurate polarization-based measurements without knowing the absolute polarization state of the probing light field. It is shown that light, passed through a randomly varying birefringent material has a well-defined orbit on the Poincar
Random error in cardiovascular meta-analyses
DEFF Research Database (Denmark)
Albalawi, Zaina; McAlister, Finlay A; Thorlund, Kristian
2013-01-01
BACKGROUND: Cochrane reviews are viewed as the gold standard in meta-analyses given their efforts to identify and limit systematic error which could cause spurious conclusions. The potential for random error to cause spurious conclusions in meta-analyses is less well appreciated. METHODS: We...
Maximizing scientific knowledge from randomized clinical trials
DEFF Research Database (Denmark)
Gustafsson, Finn; Atar, Dan; Pitt, Bertram
2010-01-01
Trialists have an ethical and financial responsibility to plan and conduct clinical trials in a manner that will maximize the scientific knowledge gained from the trial. However, the amount of scientific information generated by randomized clinical trials in cardiovascular medicine is highly...
A new model of Random Regret Minimization
Chorus, C.G.
2010-01-01
A new choice model is derived, rooted in the framework of Random Regret Minimization (RRM). The proposed model postulates that when choosing, people anticipate and aim to minimize regret. Whereas previous regret-based discrete choice-models assume that regret is experienced with respect to only the
Probability of Failure in Random Vibration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Sørensen, John Dalsgaard
1988-01-01
Close approximations to the first-passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first-passage probability density function and the distribution function for the time interval spent below a barrier before out...
Eliciting illegal migration rates through list randomization
McKenzie, D.; Siegel, M.
2013-01-01
Most migration surveys do not ask about the legal status of migrants due to concerns about the sensitivity of this question. List randomization is a technique that has been used in a number of other social science applications to elicit sensitive information. We trial this technique by adding it to
Spectral Estimation by the Random DEC Technique
DEFF Research Database (Denmark)
Brincker, Rune; Jensen, J. Laigaard; Krenk, S.
This paper contains an empirical study of the accuracy of the Random Dec (RDD) technique. Realizations of the response from a single-degree-of-freedom system loaded by white noise are simulated using an ARMA model. The Autocorrelation function is estimated using the RDD technique and the estimated...
A Dexterous Optional Randomized Response Model
Tarray, Tanveer A.; Singh, Housila P.; Yan, Zaizai
2017-01-01
This article addresses the problem of estimating the proportion Pi[subscript S] of the population belonging to a sensitive group using optional randomized response technique in stratified sampling based on Mangat model that has proportional and Neyman allocation and larger gain in efficiency. Numerically, it is found that the suggested model is…
Optimal Allocation in Stratified Randomized Response Model
Directory of Open Access Journals (Sweden)
Javid Shabbir
2005-07-01
Full Text Available A Warner (1965 randomized response model based on stratification is used to determine the allocation of samples. Both linear and log-linear cost functions are discussed under uni and double stratification. It observed that by using a log-linear cost function, one can get better allocations.
Pollen Grains, Random Walks and Einstein
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 12. Pollen Grains, Random Walks and Einstein. Sriram Ramaswamy. Volume 10 Issue 12 December 2005 pp 106-124. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/010/12/0106-0124 ...
Pollen Grains, Random Walks and Einstein
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 5; Issue 3. Pollen Grains, Random Walks and Einstein. Sriram Ramaswamy. General Article Volume 5 Issue 3 March 2000 pp 16-34. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/005/03/0016-0034 ...
Brownian Motion Problem: Random Walk and Beyond
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 8. Brownian Motion Problem: Random Walk and Beyond. Shama Sharma Vishwamittar. General Article Volume 10 Issue 8 August 2005 pp 49-66. Fulltext. Click here to view fulltext PDF. Permanent link:
A Generalized Random Regret Minimization Model
Chorus, C.G.
2013-01-01
This paper presents, discusses and tests a generalized Random Regret Minimization (G-RRM) model. The G-RRM model is created by replacing a fixed constant in the attribute-specific regret functions of the RRM model, by a regret-weight variable. Depending on the value of the regret-weights, the G-RRM
A random approach to the Lebesgue integral
Grahl, Jack
2008-04-01
We construct an integral of a measurable real function using randomly chosen Riemann sums and show that it converges in probability to the Lebesgue integral where this exists. We then prove some conditions for the almost sure convergence of this integral.
Random effect selection in generalised linear models
DEFF Research Database (Denmark)
Denwood, Matt; Houe, Hans; Forkman, Björn
We analysed abattoir recordings of meat inspection codes with possible relevance to onfarm animal welfare in cattle. Random effects logistic regression models were used to describe individual-level data obtained from 461,406 cattle slaughtered in Denmark. Our results demonstrate that the largest ...
Prospective Randomized Controlled Comparison of Caudal ...
African Journals Online (AJOL)
controlled trial (RCT) and to compare the motor blockade and hemodynamic effects caused by them. ... Subjects and Methods: This was a prospective randomized controlled study including 50 consecutive patients in the ... decrease of SBP or HR by >30% was defined as hypotension or bradycardia, respectively and was ...
Random amplified polymorphic DNA (RAPD) marker associated ...
African Journals Online (AJOL)
Jane
2011-06-29
Jun 29, 2011 ... between the studied provenances were less than 39%. Key words: Acacia Senegal, provenance variation, random amplified polymorphic DNA (RAPD) marker, salt tolerance, seed germination, seedling growth. INTRODUCTION. Salinity is the major factor limiting plants growth, widely spread and has more ...
Random amplified polymorphic DNA (RAPD) marker associated ...
African Journals Online (AJOL)
Jane
2011-06-29
Jun 29, 2011 ... bands detected were polymorphic for the provenances of A. senegal and the dissimilarity indices between the studied provenances were less than 39%. Key words: Acacia Senegal, provenance variation, random amplified polymorphic DNA (RAPD) marker, salt tolerance, seed germination, seedling growth ...
Species selection and random drift in macroevolution.
Chevin, Luis-Miguel
2016-03-01
Species selection resulting from trait-dependent speciation and extinction is increasingly recognized as an important mechanism of phenotypic macroevolution. However, the recent bloom in statistical methods quantifying this process faces a scarcity of dynamical theory for their interpretation, notably regarding the relative contributions of deterministic versus stochastic evolutionary forces. I use simple diffusion approximations of birth-death processes to investigate how the expected and random components of macroevolutionary change depend on phenotype-dependent speciation and extinction rates, as can be estimated empirically. I show that the species selection coefficient for a binary trait, and selection differential for a quantitative trait, depend not only on differences in net diversification rates (speciation minus extinction), but also on differences in species turnover rates (speciation plus extinction), especially in small clades. The randomness in speciation and extinction events also produces a species-level equivalent to random genetic drift, which is stronger for higher turnover rates. I then show how microevolutionary processes including mutation, organismic selection, and random genetic drift cause state transitions at the species level, allowing comparison of evolutionary forces across levels. A key parameter that would be needed to apply this theory is the distribution and rate of origination of new optimum phenotypes along a phylogeny. © 2016 The Author(s). Evolution © 2016 The Society for the Study of Evolution.
Random Oracles in a Quantum World
D. Boneh; O. Dagdelen; M. Fischlin; D. Lehmann; C. Schaffner (Christian); M. Zhandry
2012-01-01
htmlabstractThe interest in post-quantum cryptography - classical systems that remain secure in the presence of a quantum adversary - has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that
The Home Office and Random Allocation Experiments.
Nuttall, Christopher
2003-01-01
Describes the history of the random experiment in the Home Office in the United Kingdom and demonstrates that research and the conduct of research is not an altogether rational process and that fashion, personality, and politics play a role in research policy and methodology choice. (SLD)
Reducing financial avalanches by random investments
Biondo, Alessio Emanuele; Pluchino, Alessandro; Rapisarda, Andrea; Helbing, Dirk
2013-12-01
Building on similarities between earthquakes and extreme financial events, we use a self-organized criticality-generating model to study herding and avalanche dynamics in financial markets. We consider a community of interacting investors, distributed in a small-world network, who bet on the bullish (increasing) or bearish (decreasing) behavior of the market which has been specified according to the S&P 500 historical time series. Remarkably, we find that the size of herding-related avalanches in the community can be strongly reduced by the presence of a relatively small percentage of traders, randomly distributed inside the network, who adopt a random investment strategy. Our findings suggest a promising strategy to limit the size of financial bubbles and crashes. We also obtain that the resulting wealth distribution of all traders corresponds to the well-known Pareto power law, while that of random traders is exponential. In other words, for technical traders, the risk of losses is much greater than the probability of gains compared to those of random traders.
Generating Realistic Labelled, Weighted Random Graphs
Directory of Open Access Journals (Sweden)
Michael Charles Davis
2015-12-01
Full Text Available Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs. Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.
On the Robustness and Efficiency of Some Randomized Designs
Wu, Chien-Fu
1981-01-01
A concept of model-robustness is defined in terms of the performance of the design in the presence of model violations. The robustness problem is discussed for several randomization procedures commonly used in experimental design situations. Among them, the balanced completely randomized design, the randomized complete block design and the randomized Latin square design are shown to be model-robust in their own settings. To compare different randomization procedures, we define a concept of ef...
Cremer, Marion; Schmid, Volker J; Kraus, Felix; Markaki, Yolanda; Hellmann, Ines; Maiser, Andreas; Leonhardt, Heinrich; John, Sam; Stamatoyannopoulos, John; Cremer, Thomas
2017-08-07
The association of active transcription regulatory elements (TREs) with DNAse I hypersensitivity (DHS[+]) and an 'open' local chromatin configuration has long been known. However, the 3D topography of TREs within the nuclear landscape of individual cells in relation to their active or inactive status has remained elusive. Here, we explored the 3D nuclear topography of active and inactive TREs in the context of a recently proposed model for a functionally defined nuclear architecture, where an active and an inactive nuclear compartment (ANC-INC) form two spatially co-aligned and functionally interacting networks. Using 3D structured illumination microscopy, we performed 3D FISH with differently labeled DNA probe sets targeting either sites with DHS[+], apparently active TREs, or DHS[-] sites harboring inactive TREs. Using an in-house image analysis tool, DNA targets were quantitatively mapped on chromatin compaction shaped 3D nuclear landscapes. Our analyses present evidence for a radial 3D organization of chromatin domain clusters (CDCs) with layers of increasing chromatin compaction from the periphery to the CDC core. Segments harboring active TREs are significantly enriched at the decondensed periphery of CDCs with loops penetrating into interchromatin compartment channels, constituting the ANC. In contrast, segments lacking active TREs (DHS[-]) are enriched toward the compacted interior of CDCs (INC). Our results add further evidence in support of the ANC-INC network model. The different 3D topographies of DHS[+] and DHS[-] sites suggest positional changes of TREs between the ANC and INC depending on their functional state, which might provide additional protection against an inappropriate activation. Our finding of a structural organization of CDCs based on radially arranged layers of different chromatin compaction levels indicates a complex higher-order chromatin organization beyond a dichotomic classification of chromatin into an 'open,' active and 'closed
Moyer, Steve; Uhl, Elizabeth R.
2015-05-01
For more than 50 years, the U.S. Army RDECOM CERDEC Night Vision and Electronic Sensors Directorate (NVESD) has been studying and modeling the human visual discrimination process as it pertains to military imaging systems. In order to develop sensor performance models, human observers are trained to expert levels in the identification of military vehicles. From 1998 until 2006, the experimental stimuli were block randomized, meaning that stimuli with similar difficulty levels (for example, in terms of distance from target, blur, noise, etc.) were presented together in blocks of approximately 24 images but the order of images within the block was random. Starting in 2006, complete randomization came into vogue, meaning that difficulty could change image to image. It was thought that this would provide a more statistically robust result. In this study we investigated the impact of the two types of randomization on performance in two groups of observers matched for skill to create equivalent groups. It is hypothesized that Soldiers in the Complete Randomized condition will have to shift their decision criterion more frequently than Soldiers in the Block Randomization group and this shifting is expected to impede performance so that Soldiers in the Block Randomized group perform better.
Random Graph Construction for Cryptographic Applications
Directory of Open Access Journals (Sweden)
P. G. Klyucharev
2017-01-01
Full Text Available The author in a number of his previous papers proposed methods to construct symmetric cryptographic algorithms based on the generalized cellular automata. To possess good cryptographic properties, graphs of such automata must meet a number of requirements. To construct such graphs both the deterministic methods and the randomized ones can be used. The paper deals with the randomized method of their construction.Briefly describing the generalized cellular automata it gives the requirements for graphs of such automata, including the following: the graph must have properties close to those of a randomly chosen graph; the graph diameter should be as small as possible; the graph must be regular; the graph should not be bipartite; the graph should have as minimum number of loops and multiple edges as possible; the graph degree should be (to reduce the communication complexity of the cellular automata four, at least.In the family of graphs there must be a sufficiently large number of graphs with the number of vertices from several tens to several thousand.The expanding graphs, in particular, the so-called Ramanujan graphs meet these requirements. To build small Ramanujan graphs two methods are known, namely constructing a random regular graph with subsequent verification of spectral characteristics and constructing a graph by using a certain known deterministic algorithm. The paper considers the first method and gives an algorithm for generating such graphs.For practical purposes, it is important to know what characteristics random regular graphs have. In order to find this, a computer experiment was carried out. For each N of the set {256,512,1024,2048,4096} and each d of the set {3,4,5,6,7,8,9,10,11,12,13,14,15,16} was generated a large number of random d-regular graphs on N vertices. A total of 448 thousand graphs were generated. The paper presents graphs of the density distribution of λ parameters and diameters of these graphs. It can be seen from
Robustness of Dengue Complex Network under Targeted versus Random Attack
Directory of Open Access Journals (Sweden)
Hafiz Abid Mahmood Malik
2017-01-01
Full Text Available Dengue virus infection is one of those epidemic diseases that require much consideration in order to save the humankind from its unsafe impacts. According to the World Health Organization (WHO, 3.6 billion individuals are at risk because of the dengue virus sickness. Researchers are striving to comprehend the dengue threat. This study is a little commitment to those endeavors. To observe the robustness of the dengue network, we uprooted the links between nodes randomly and targeted by utilizing different centrality measures. The outcomes demonstrated that 5% targeted attack is equivalent to the result of 65% random assault, which showed the topology of this complex network validated a scale-free network instead of random network. Four centrality measures (Degree, Closeness, Betweenness, and Eigenvector have been ascertained to look for focal hubs. It has been observed through the results in this study that robustness of a node and links depends on topology of the network. The dengue epidemic network presented robust behaviour under random attack, and this network turned out to be more vulnerable when the hubs of higher degree have higher probability to fail. Moreover, representation of this network has been projected, and hub removal impact has been shown on the real map of Gombak (Malaysia.
Inflation with a graceful exit in a random landscape
Energy Technology Data Exchange (ETDEWEB)
Pedro, F.G. [Departamento de Física Teórica and Instituto de Física Teórica UAM/CSIC,Universidad Autónoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Westphal, A. [Deutsches Elektronen-Synchrotron DESY, Theory Group,D-22603 Hamburg (Germany)
2017-03-30
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N≪10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Random fluctuation leads to forbidden escape of particles.
Rodrigues, Christian S; de Moura, Alessandro P S; Grebogi, Celso
2010-08-01
A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Kolmogorov-Arnold-Moser (KAM) islands escape within finite time. The nonhyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperboliclike time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate these phenomena with a numerical study applying random maps.
Inflation with a graceful exit in a random landscape
Pedro, F. G.; Westphal, A.
2017-03-01
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N ≪ 10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Molecular motors: thermodynamics and the random walk.
Thomas, N; Imafuku, Y; Tawada, K
2001-10-22
The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysis and u(0) is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D-v(2)tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining tau. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force-velocity relation and the random motion of molecular motors.
Cluster randomized trials for pharmacy practice research.
Gums, Tyler; Carter, Barry; Foster, Eric
2016-06-01
Introduction Cluster randomized trials (CRTs) are now the gold standard in health services research, including pharmacy-based interventions. Studies of behaviour, epidemiology, lifestyle modifications, educational programs, and health care models are utilizing the strengths of cluster randomized analyses. Methodology The key property of CRTs is the unit of randomization (clusters), which may be different from the unit of analysis (individual). Subject sample size and, ideally, the number of clusters is determined by the relationship of between-cluster and within-cluster variability. The correlation among participants recruited from the same cluster is known as the intraclass correlation coefficient (ICC). Generally, having more clusters with smaller ICC values will lead to smaller sample sizes. When selecting clusters, stratification before randomization may be useful in decreasing imbalances between study arms. Participant recruitment methods can differ from other types of randomized trials, as blinding a behavioural intervention cannot always be done. When to use CRTs can yield results that are relevant for making "real world" decisions. CRTs are often used in non-therapeutic intervention studies (e.g. change in practice guidelines). The advantages of CRT design in pharmacy research have been avoiding contamination and the generalizability of the results. A large CRT that studied physician-pharmacist collaborative management of hypertension is used in this manuscript as a CRT example. The trial, entitled Collaboration Among Pharmacists and physicians To Improve Outcomes Now (CAPTION), was implemented in primary care offices in the United States for hypertensive patients. Limitations CRT design limitations include the need for a large number of clusters, high costs, increased training, increased monitoring, and statistical complexity.
Directory of Open Access Journals (Sweden)
Gabriel Recchia
2015-01-01
Full Text Available Circular convolution and random permutation have each been proposed as neurally plausible binding operators capable of encoding sequential information in semantic memory. We perform several controlled comparisons of circular convolution and random permutation as means of encoding paired associates as well as encoding sequential information. Random permutations outperformed convolution with respect to the number of paired associates that can be reliably stored in a single memory trace. Performance was equal on semantic tasks when using a small corpus, but random permutations were ultimately capable of achieving superior performance due to their higher scalability to large corpora. Finally, “noisy” permutations in which units are mapped to other units arbitrarily (no one-to-one mapping perform nearly as well as true permutations. These findings increase the neurological plausibility of random permutations and highlight their utility in vector space models of semantics.
Recchia, Gabriel; Sahlgren, Magnus; Kanerva, Pentti; Jones, Michael N
2015-01-01
Circular convolution and random permutation have each been proposed as neurally plausible binding operators capable of encoding sequential information in semantic memory. We perform several controlled comparisons of circular convolution and random permutation as means of encoding paired associates as well as encoding sequential information. Random permutations outperformed convolution with respect to the number of paired associates that can be reliably stored in a single memory trace. Performance was equal on semantic tasks when using a small corpus, but random permutations were ultimately capable of achieving superior performance due to their higher scalability to large corpora. Finally, "noisy" permutations in which units are mapped to other units arbitrarily (no one-to-one mapping) perform nearly as well as true permutations. These findings increase the neurological plausibility of random permutations and highlight their utility in vector space models of semantics.
Miszczak, Jarosław Adam
2013-01-01
The presented package for the Mathematica computing system allows the harnessing of quantum random number generators (QRNG) for investigating the statistical properties of quantum states. The described package implements a number of functions for generating random states. The new version of the package adds the ability to use the on-line quantum random number generator service and implements new functions for retrieving lists of random numbers. Thanks to the introduced improvements, the new version provides faster access to high-quality sources of random numbers and can be used in simulations requiring large amount of random data. New version program summaryProgram title: TRQS Catalogue identifier: AEKA_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKA_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 18 134 No. of bytes in distributed program, including test data, etc.: 2 520 49 Distribution format: tar.gz Programming language: Mathematica, C. Computer: Any supporting Mathematica in version 7 or higher. Operating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit). RAM: Case-dependent Supplementary material: Fig. 1 mentioned below can be downloaded. Classification: 4.15. External routines: Quantis software library (http://www.idquantique.com/support/quantis-trng.html) Catalogue identifier of previous version: AEKA_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183(2012)118 Does the new version supersede the previous version?: Yes Nature of problem: Generation of random density matrices and utilization of high-quality random numbers for the purpose of computer simulation. Solution method: Use of a physical quantum random number generator and an on-line service providing access to the source of true random
Sparse Maximum-Entropy Random Graphs with a Given Power-Law Degree Distribution
van der Hoorn, Pim; Lippner, Gabor; Krioukov, Dmitri
2017-10-01
Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical requirements of realism is still lacking. These requirements are: sparsity, exchangeability, projectivity, and unbiasedness. The last requirement states that entropy of the graph ensemble must be maximized under the degree distribution constraints. Here we prove that the hypersoft configuration model, belonging to the class of random graphs with latent hyperparameters, also known as inhomogeneous random graphs or W-random graphs, is an ensemble of random power-law graphs that are sparse, unbiased, and either exchangeable or projective. The proof of their unbiasedness relies on generalized graphons, and on mapping the problem of maximization of the normalized Gibbs entropy of a random graph ensemble, to the graphon entropy maximization problem, showing that the two entropies converge to each other in the large-graph limit.
Jack, Darby W.; Asante, Kwaku Poku; Blair J. Wylie; Chillrud, Steve N.; Whyatt, Robin M.; Ae-Ngibise, Kenneth A.; Quinn, Ashlinn K.; Yawson, Abena Konadu; Boamah, Ellen Abrafi; Agyei, Oscar; Mujtaba, Mohammed; Kaali, Seyram; Kinney, Patrick; Owusu-Agyei, Seth
2015-01-01
Background: Household air pollution exposure is a major health risk, but validated interventions remain elusive. Methods/Design The Ghana Randomized Air Pollution and Health Study (GRAPHS) is a cluster-randomized trial that evaluates the efficacy of clean fuels (liquefied petroleum gas, or LPG) and efficient biomass cookstoves in the Brong-Ahafo region of central Ghana. We recruit pregnant women into LPG, efficient cookstove, and control arms and track birth weight and physician-assessed seve...
Pinsoneault, Terry B
2005-12-01
The ability of the Minnesota Multiphasic Personality Inventory-Adolescent (MMPI-A; J. N. Butcher et al., 1992) validity scales to detect random, partially random, and nonrandom MMPI-A protocols was investigated. Investigations included the Variable Response Inconsistency scale (VRIN), F, several potentially useful new F and VRIN subscales, and formulas F-sub-2 - F-sub-1 and F + F-sub-2 + |F - F-sub-2|. Protocols completed by 150 adolescents at a juvenile court setting, screened for randomness with a matched-pair Millon Adolescent Clinical Inventory (MACI) or Jesness Inventory, were compared with 100 computer-generated, all-random protocols, and with 5 levels of partially random protocols. VRIN was the most effective scale in detecting all-random protocols; however, the optimum cutoff of >or= 75 failed to identify 1/3 of them. Using the new scales, a decision algorithm was described that correctly classified 94%-95% of protocols as interpretable, partially interpretable, or uninterpretable.
Yavorska, Olena O; Burgess, Stephen
2017-12-01
MendelianRandomization is a software package for the R open-source software environment that performs Mendelian randomization analyses using summarized data. The core functionality is to implement the inverse-variance weighted, MR-Egger and weighted median methods for multiple genetic variants. Several options are available to the user, such as the use of robust regression, fixed- or random-effects models and the penalization of weights for genetic variants with heterogeneous causal estimates. Extensions to these methods, such as allowing for variants to be correlated, can be chosen if appropriate. Graphical commands allow summarized data to be displayed in an interactive graph, or the plotting of causal estimates from multiple methods, for comparison. Although the main method of data entry is directly by the user, there is also an option for allowing summarized data to be incorporated from the PhenoScanner database of genotype-phenotype associations. We hope to develop this feature in future versions of the package. The R software environment is available for download from [https://www.r-project.org/]. The MendelianRandomization package can be downloaded from the Comprehensive R Archive Network (CRAN) within R, or directly from [https://cran.r-project.org/web/packages/MendelianRandomization/]. Both R and the MendelianRandomization package are released under GNU General Public Licenses (GPL-2|GPL-3). © The Author 2017. Published by Oxford University Press on behalf of the International Epidemiological Association.
Sign Compute Resolve for Random Access
DEFF Research Database (Denmark)
Goseling, Jasper; Stefanovic, Cedomir; Popovski, Petar
2014-01-01
We present an approach to random access that is based on three elements: physical-layer network coding, signature codes and tree splitting. Upon occurrence of a collision, physical-layer network coding enables the receiver to decode the sum of the information that was transmitted by the individual...... users. For each user this information consists of the data that the user wants to communicate as well as the user's signature. As long as no more than K users collide, their identities can be recovered from the sum of their signatures. A splitting protocol is used to deal with the case that more than K...... users collide. We measure the performance of the proposed method in terms of user resolution rate as well as overall throughput of the system. The results show that our approach significantly increases the performance of the system even compared to coded random access, where collisions are not wasted...
Randomized Clinical Trials With Biomarkers: Design Issues
McShane, Lisa M.; Korn, Edward L.
2010-01-01
Clinical biomarker tests that aid in making treatment decisions will play an important role in achieving personalized medicine for cancer patients. Definitive evaluation of the clinical utility of these biomarkers requires conducting large randomized clinical trials (RCTs). Efficient RCT design is therefore crucial for timely introduction of these medical advances into clinical practice, and a variety of designs have been proposed for this purpose. To guide design and interpretation of RCTs evaluating biomarkers, we present an in-depth comparison of advantages and disadvantages of the commonly used designs. Key aspects of the discussion include efficiency comparisons and special interim monitoring issues that arise because of the complexity of these RCTs. Important ongoing and completed trials are used as examples. We conclude that, in most settings, randomized biomarker-stratified designs (ie, designs that use the biomarker to guide analysis but not treatment assignment) should be used to obtain a rigorous assessment of biomarker clinical utility. PMID:20075367
Piezoelectric energy harvesting from broadband random vibrations
Adhikari, S.; Friswell, M. I.; Inman, D. J.
2009-11-01
Energy harvesting for the purpose of powering low power electronic sensor systems has received explosive attention in the last few years. Most works using deterministic approaches focusing on using the piezoelectric effect to harvest ambient vibration energy have concentrated on cantilever beams at resonance using harmonic excitation. Here, using a stochastic approach, we focus on using a stack configuration and harvesting broadband vibration energy, a more practically available ambient source. It is assumed that the ambient base excitation is stationary Gaussian white noise, which has a constant power-spectral density across the frequency range considered. The mean power acquired from a piezoelectric vibration-based energy harvester subjected to random base excitation is derived using the theory of random vibrations. Two cases, namely the harvesting circuit with and without an inductor, have been considered. Exact closed-form expressions involving non-dimensional parameters of the electromechanical system have been given and illustrated using numerical examples.
Quantum Criticality of Hot Random Spin Chains
Vasseur, R.; Potter, A. C.; Parameswaran, S. A.
2015-05-01
We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit nonergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU (2 )k anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them "quantum critical glasses." We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit k →∞. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel nonequilibrium critical phases of matter.
Random phase textures: theory and synthesis.
Galerne, Bruno; Gousseau, Yann; Morel, Jean-Michel
2011-01-01
This paper explores the mathematical and algorithmic properties of two sample-based texture models: random phase noise (RPN) and asymptotic discrete spot noise (ADSN). These models permit to synthesize random phase textures. They arguably derive from linearized versions of two early Julesz texture discrimination theories. The ensuing mathematical analysis shows that, contrarily to some statements in the literature, RPN and ADSN are different stochastic processes. Nevertheless, numerous experiments also suggest that the textures obtained by these algorithms from identical samples are perceptually similar. The relevance of this study is enhanced by three technical contributions providing solutions to obstacles that prevented the use of RPN or ADSN to emulate textures. First, RPN and ADSN algorithms are extended to color images. Second, a preprocessing is proposed to avoid artifacts due to the nonperiodicity of real-world texture samples. Finally, the method is extended to synthesize textures with arbitrary size from a given sample.
Random Walk Picture of Basketball Scoring
Gabel, Alan
2011-01-01
We present evidence, based on play-by-play data from all 6087 games from the 2006/07--2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between different scoring intervals. Using this random-walk picture that is augmented by features idiosyncratic to basketball, we account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead. By further including the heterogeneity of team strengths, we build a computational model that accounts for essentially all statistical features of game scoring data and season win/loss records of each team.
Aspects of randomness in neural graph structures
Rudolph-Lilith, Michelle
2013-01-01
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural systems, however, a few moderately robust experimental reconstructions do exist, and these have long served as fundamental prototypes for studying connectivity patterns in the nervous system. In this paper, we provide a comparative analysis of these "historical" graphs, both in (unmodified) directed and (often symmetrized) undirected forms, and focus on simple structural characterizations of their connectivity. We find that in most measures the networks studied are captured by simple random graph models; in a few key measures, however, we observe a marked departure from the random graph prediction. Our results suggest that the mechanism of graph formation in th...
Interface mobility from interface random walk
Trautt, Zachary; Upmanyu, Moneesh; Karma, Alain
2007-03-01
Computational studies aimed at extracting interface mobilities require driving forces orders of magnitude higher than those occurring experimentally. We present a computational methodology that extracts the absolute interface mobility in the zero driving force limit by monitoring the one-dimensional random walk of the mean interface position along the interface normal. The method exploits a fluctuation-dissipation relation similar to the Stokes-Einstein relation, which relates the diffusion coefficient of this Brownian-like random walk to the interface mobility. Atomic-scale simulations of grain boundaries in model crystalline systems validate the theoretical predictions, and also highlight the profound effect of impurities. The generality of this technique combined with its inherent spatial-temporal efficiency should allow computational studies to effectively complement experiments in understanding interface kinetics in diverse material systems.
A Hybrid Random Number Generator(HRNG
Directory of Open Access Journals (Sweden)
Osvaldo Skliar
2011-07-01
Full Text Available The purpose of this paper is to present a novel Hybrid Random Number Generator (HRNG. Here “hybrid” refers to the fact that to construct this generator it is necessary to use 1physical components – texts – and a physical process, and 2 a mathematical procedure. This HRNG makes it possible to generate genuine random numbers which may be used both for computer simulation of probabilistic systems and in the field of cryptography. The results of a comparative study of the binary strings generated by this HRNG and of those generated by two highly used implementations of a congruential algorithm designed to generate pseudorandom numbers are given here. One of the latter is the implementation incorporated into the Java 2 platform (version 1.6, and the other is the implementation incorporated into the runtime library of Microsoft’s Visual C++ 2008 compiler.
Particle filters for random set models
Ristic, Branko
2013-01-01
“Particle Filters for Random Set Models” presents coverage of state estimation of stochastic dynamic systems from noisy measurements, specifically sequential Bayesian estimation and nonlinear or stochastic filtering. The class of solutions presented in this book is based on the Monte Carlo statistical method. The resulting algorithms, known as particle filters, in the last decade have become one of the essential tools for stochastic filtering, with applications ranging from navigation and autonomous vehicles to bio-informatics and finance. While particle filters have been around for more than a decade, the recent theoretical developments of sequential Bayesian estimation in the framework of random set theory have provided new opportunities which are not widely known and are covered in this book. These recent developments have dramatically widened the scope of applications, from single to multiple appearing/disappearing objects, from precise to imprecise measurements and measurement models. This book...
Random reward priming is task-contingent
DEFF Research Database (Denmark)
Ásgeirsson, Árni Gunnar; Kristjánsson, Árni
2014-01-01
Consistent financial reward of particular features influences the allocation of visual attention in many ways. More surprising are 1-trial reward priming effects on attention where reward schedules are random and reward on one trial influences attentional allocation on the next. Those findings...... are thought to reflect that rewarded features become more salient than unrewarded ones on the subsequent trial. Here we attempt to conceptually replicate this effect, testing its generalizability. In three versions of an analogous paradigm to the additional singleton paradigm involving singleton search...... for a Gabor patch of odd spatial frequency we found no evidence of reward priming, while we only partially replicate the reward priming in the exact original paradigm tested by Hickey and colleagues. The results cast doubt on the proposal that random reward enhances salience, suggested in the original papers...
Provable quantum advantage in randomness processing.
Dale, Howard; Jennings, David; Rudolph, Terry
2015-09-18
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics exactly coincides with the class computable quantum mechanically. It is strongly believed, but not proven, that quantum computing provides exponential speed-up for a range of problems, such as factoring. Here we address a computational scenario of randomness processing in which quantum theory provably yields, not only resource reduction over classical stochastic physics, but a strictly larger class of problems which can be solved. Beyond new foundational insights into the nature and malleability of randomness, and the distinction between quantum and classical information, these results also offer the potential of developing classically intractable simulations with currently accessible quantum technologies.
Statistical properties of random matrix product states
Garnerone, Silvano; de Oliveira, Thiago R.; Haas, Stephan; Zanardi, Paolo
2010-11-01
We study the set of random matrix product states (RMPS) introduced by Garnerone, de Oliveira, and Zanardi [S. Garnerone, T. R. de Oliveira, and P. Zanardi, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.81.032336 81, 032336 (2010)] as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical investigation of the properties of RMPS. We calculate the average state of the ensemble in the nonhomogeneous case, and numerically check the validity of this result. We also suggest using RMPS as a tool to approximate properties of general quantum random states. The numerical simulations presented here support the accuracy and efficiency of this approximation. These results suggest that any generalized canonical state can be approximated with high probability by the reduced density matrix of a RMPS, if the average matrix product states coincide with the associated microcanonical ensemble.
Random walk centrality in interconnected multilayer networks
Solé-Ribalta, Albert; Gómez, Sergio; Arenas, Alex
2015-01-01
Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in many fields, from economics to biology and from urban planning to social sciences, to identify the most (or the less) influential nodes in a network using centrality measures. However, defining the centrality of actors in interconnected complex networks is not trivial. In this paper, we rely on the tensorial formalism recently proposed to characterize and investigate this kind of complex topologies, and extend two well known random walk centrality measures, the random walk betweenness and closeness centrality, to interconnected multilayer networks. For each of the measures we provide analytical expressions that completely agree with numerically results.
The subtle nature of financial random walks.
Bouchaud, Jean-Philippe
2005-06-01
We first review the most important "stylized facts" of financial time series, that turn out to be, to a large extent, universal. We then recall how the multifractal random walk of Bacry, Muzy, and Delour generalizes the standard model of financial price changes and accounts in an elegant way for many of their empirical properties. In a second part, we provide empirical evidence for a very subtle compensation mechanism that underlies the random nature of price changes. This compensation drives the market close to a critical point, that may explain the sensitivity of financial markets to small perturbations, and their propensity to enter bubbles and crashes. We argue that the resulting unpredictability of price changes is very far from the neoclassical view that markets are informationally efficient.
The subtle nature of financial random walks
Bouchaud, Jean-Philippe
2005-06-01
We first review the most important "stylized facts" of financial time series, that turn out to be, to a large extent, universal. We then recall how the multifractal random walk of Bacry, Muzy, and Delour generalizes the standard model of financial price changes and accounts in an elegant way for many of their empirical properties. In a second part, we provide empirical evidence for a very subtle compensation mechanism that underlies the random nature of price changes. This compensation drives the market close to a critical point, that may explain the sensitivity of financial markets to small perturbations, and their propensity to enter bubbles and crashes. We argue that the resulting unpredictability of price changes is very far from the neoclassical view that markets are informationally efficient.
Maximal Inequalities for Dependent Random Variables
DEFF Research Database (Denmark)
Hoffmann-Jorgensen, Jorgen
2016-01-01
Maximal inequalities play a crucial role in many probabilistic limit theorem; for instance, the law of large numbers, the law of the iterated logarithm, the martingale limit theorem and the central limit theorem. Let X-1, X-2,... be random variables with partial sums S-k = X-1 + ... + X......-k. Then a maximal inequality gives conditions ensuring that the maximal partial sum M-n = max(1) (...
Systems with randomly failing repairable components
DEFF Research Database (Denmark)
Der Kiureghian, Armen; Ditlevsen, Ove Dalager; Song, Junho
2005-01-01
Closed-form expressions are derived for the steady-state availability, mean rate of failure, mean duration of downtime and reliability of a general system with randomly and independently failing repairable components. Component failures are assumed to be homogeneous Poisson events in time and rep......, or reducing the mean duration of system downtime. Example applications to an electrical substation system demonstrate the use of the formulas developed in the paper....
Entropy estimates for simple random fields
DEFF Research Database (Denmark)
Forchhammer, Søren; Justesen, Jørn
1995-01-01
We consider the problem of determining the maximum entropy of a discrete random field on a lattice subject to certain local constraints on symbol configurations. The results are expected to be of interest in the analysis of digitized images and two dimensional codes. We shall present some examples...... of binary and ternary fields with simple constraints. Exact results on the entropies are known only in a few cases, but we shall present close bounds and estimates that are computationally efficient...
Symmetry Breaking in a random passive scalar
Kilic, Zeliha; McLaughlin, Richard; Camassa, Roberto
2017-11-01
We consider the evolution of a decaying passive scalar in the presence of a gaussian white noise fluctuating shear flow. We focus on deterministic initial data and establish the short, intermediate, and long time symmetry properties of the evolving point wise probability measure for the random passive scalar. Analytical results are compared directly to Monte Carlo simulations. Time permitting we will compare the predictions to experimental observations.