Random Sign Research Articles

Unbinding transition in semi-infinite two-dimensional localized systems

We consider a two-dimensional strongly localized system defined in a half-space and whose transfer integral in the edge can be different than in the bulk. We predict an unbinding transition, as the edge transfer integral is varied, from a phase where conduction paths are distributed across the bulk to a bound phase where propagation is mainly along the edge. At criticality the logarithm of the conductance follows the $F_1$ Tracy-Widom distribution. We verify numerically these predictions for both the Anderson and the Nguyen, Spivak and Shklovskii models. We also check that for a half-space, i.e., when the edge transfer integral is equal to the bulk transfer integral, the distribution of the conductance is the $F_4$ Tracy-Widom distribution. These findings are strong indications that random signs directed polymer models and their quantum extensions belong to the Kardar-Parisi- Zhang universality class. We have analyzed finite-size corrections at criticality and for a half-plane.

Amniocytes from aneuploidy embryos have enhanced random aneuploidy and signs of senescence — Can these findings be related to medical problems?

ObjectivesGenomic aneuploidy is a common cause of human genetic disorders. Individuals with aneuploidy tend to develop malignancies. Recent studies correlated aneuploidy with early aging, senescence and organ dysfunction. This study investigated potential explanations for these increased risks by evaluating random aneuploidy and senescence rates in amniocytes from fetuses with aneuploidy. MethodsThe rates of random aneuploidy in amniocytes from normal pregnancies were evaluated and compared to amniocytes from fetuses with trisomies 21, 18 and 47,XXY using a FISH technique with X+Y, 9 and 18 probes. Senescence was evaluated by calculating the percentage of amniocytes with fragmented nuclei: senescence associated heterochromatin foci (SAHF), using DAPI staining. ResultsSignificantly increased rates of cells with aneuploidy were observed in trisomies 18 and 21, and 47,XXY (p<0.001) compared to the control group for the somatic and sex chromosomes. Increased rates of amniocytes with SAHFs were observed among the trisomy samples compared to the control group. ConclusionsHigher incidence of random aneuploidy and senescence were observed in amniocytes from fetuses with trisomy. These findings might explain the greater lifetime tendency to develop malignancies and diseases related to early aging in these individuals.

Fast and RIP-Optimal Transforms

We study constructions of $$k \times n$$k×n matrices $$A$$A that both (1) satisfy the restricted isometry property (RIP) at sparsity $$s$$s with optimal parameters, and (2) are efficient in the sense that only $$O(n\log n)$$O(nlogn) operations are required to compute $$Ax$$Ax given a vector $$x$$x. Our construction is based on repeated application of independent transformations of the form $$DH$$DH, where $$H$$H is a Hadamard or Fourier transform and $$D$$D is a diagonal matrix with random $$\{+1,-1\}$${+1,-1} elements on the diagonal, followed by any $$k \times n$$k×n matrix of orthonormal rows (e.g. selection of $$k$$k coordinates). We provide guarantees (1) and (2) for a regime of parameters that is comparable with previous constructions, but using a construction that uses Fourier transforms and diagonal matrices only. Our main result can be interpreted as a rate of convergence to a random matrix of a random walk in the orthogonal group, in which each step is obtained by a Fourier transform $$H$$H followed by a random sign change matrix $$D$$D. After a few number of steps, the resulting matrix is random enough in the sense that any arbitrary selection of rows gives rise to an RIP matrix for, sparsity as high as slightly below $$s=\sqrt{n}$$s=n, with high probability. The proof uses a bootstrapping technique that, roughly speaking, says that if a matrix $$A$$A has some suboptimal RIP parameters, then the action of two steps in this random walk on this matrix has improved parameters. This idea is interesting in its own right, and may be used to strengthen other constructions.

Log-integrability of Rademacher Fourier series, with applications to random analytic functions

It is proved that any power of the logarithm of a Fourier series with random signs is integrable. This result has applications to the distribution of values of random Taylor series, one of which answers a long-standing question by J.-P. Kahane.

Complex-valued sparse reconstruction via arctangent regularization

Complex-valued sparse reconstruction is conventionally solved by transforming it into real-valued problems. However, this method might not work efficiently and correctly, especially when the size of the problem is large, or the mutual coherence is high. In this paper, we present a novel algorithm called the arctangent regularization (ATANR), which can handle the complex-valued problems of large size and high mutual coherence directly. The ATANR is implemented with the iterative least squares (IRLS) framework, and accelerated by the dimension reduction and active set selection steps. Further, we summarize and analyze the common properties of a penalty kernel which is suitable for sparse reconstruction. The analyses show that the key difference, between the arctangent kernel and the ℓ1 norm, is that the first order derivative of ATANR is close to zero for a nonzero variable. This will make ATANR less sensitive to the regularization parameter λ than ℓ1 regularization methods. Finally, lots of numerical experiments validate that ATANR usually has better performance than the conventional ℓ1 regularization methods, not only for the random signs ensemble, but also for the sensing matrix with high mutual coherence, such as the resolution enhancement case.

Giant magnetoresistance in the variable-range hopping regime

We predict the universal power law dependence of localization length on magnetic field in the strongly localized regime. This effect is due to the orbital quantum interference. Physically, this dependence shows up in an anomalously large negative magnetoresistance in the hopping regime. The reason for the universality is that the problem of the electron tunneling in a random media belongs to the same universality class as directed polymer problem even in the case of wave functions of random sign. We present numerical simulations which prove this conjecture. We discuss the existing experiments that show anomalously large magnetoresistance. We also discuss the role of localized spins in real materials and the spin polarizing effect of magnetic field.

Conformists and Contrarians in a Kuramoto Model with Uniformly Distributed Natural Frequencies

A generalization of the Kuramoto model in which oscillators are coupled to the mean field with random signs is investigated in this work. We focus on a situation in which the natural frequencies of oscillators follow a uniform probability density. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already reported π state and travelling wave state in the one with natural frequencies following Lorenztian probability density or a delta function. The dependence of the observed dynamics on the parameters of the model is explored and we find that the onset of synchronization in the model displays a non-monotonic dependence on both positive and negative coupling strength.

Lattice Gauge Theory for the Classical XY Model of Spin Glasses

A simple cubic lattice of planar rotators coupled via nearest neighbor bonds with random sign has been investigated on the basis of the lattice gauge theory. At low temperatures this spin glass problem is transformed into a simpler problem of random distribution of monopoles over the dual lattice sites. A rigorous expression for the Edward-Anderson's q has been obtained in this monopole formalism. It is concluded that q is very small, if not vanishing, as compared with 1 even in the low temperature limit. This means that the susceptibility diverges as Χ ∝1/T.

Generalized Random Sign and Alert Delay models for imperfect maintenance

This paper considers the modelling of the process of Corrective and condition-based Preventive Maintenance, for complex repairable systems. In order to take into account the dependency between both types of maintenance and the possibility of imperfect maintenance, Generalized Competing Risks models have been introduced in "Doyen and Gaudoin (J Appl Probab 43:825-839, 2006)". In this paper, we study two classes of these models, the Generalized Random Sign and Generalized Alert Delay models. A Generalized Competing Risks model can be built as a generalization of a particular Usual Competing Risks model, either by using a virtual age framework or not. The models properties are studied and their parameterizations are discussed. Finally, simulation results and an application to real data are presented.

Area-dependence of spin-triplet supercurrent in ferromagnetic Josephson junctions

In 2010, several experimental groups obtained compelling evidence for spin-triplet supercurrent in Josephson junctions containing strong ferromagnetic materials. Our own best results were obtained from large-area junctions containing a thick central Co/Ru/Co “synthetic antiferromagnet” and two thin outer layers made of Ni or PdNi alloy. Because the ferromagnetic layers in our samples are multi-domain, one would expect the sign of the local current-phase relation inside the junctions to vary randomly as a function of lateral position. Here we report measurements of the area dependence of the critical current in several samples, where we find some evidence for those random sign variations. When the samples are magnetized, however, the critical current becomes clearly proportional to the area, indicating that the current-phase relation has the same sign across the entire area of the junctions.

Universality and the circular law for sparse random matrices

The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the eigenvalues of a random sign matrix, where each entry is +1 or -1 with equal probability, looks the same as an analogous plot of the eigenvalues of a random matrix where each entry is complex Gaussian with zero mean and unit variance. In the current paper, we prove a universality result for sparse random n by n matrices where each entry is nonzero with probability $1/n^{1-\alpha}$ where $0<\alpha\le1$ is any constant. One consequence of the sparse universality principle is that the circular law holds for sparse random matrices so long as the entries have zero mean and unit variance, which is the most general result for sparse random matrices to date.

Simple bounds for recovering low-complexity models

This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in \({\mathbb{R}^n}\) can be efficiently recovered from 2s log n measurements with high probability and a rank r, n × n matrix can be efficiently recovered from r(6n − 5r) measurements with high probability. For sparse vectors, this is within an additive factor of the best known nonasymptotic bounds. For low-rank matrices, this matches the best known bounds. We present a parallel analysis for block-sparse vectors obtaining similarly tight bounds. In the case of sparse and block-sparse signals, we additionally demonstrate that our bounds are only slightly weakened when the measurement map is a random sign matrix. Our results are based on analyzing a particular dual point which certifies optimality conditions of the respective convex programming problem. Our calculations rely only on standard large deviation inequalities and our analysis is self-contained.

Random projection method for ultra wideband signal acquisition

High-speed high-resolution analog-to-digital (A/D) conversion demanded by ultra wideband (UWB) signal processing is a very challenging problem. This paper proposes a parallel random projection method for UWB signal acquisition. The proposed method can achieve high sampling rate, high resolution and technical feasibility of hardware implementation. In the proposed method, an analog UWB signal is projected over a set of random sign functions. Then the low-rate high-resolution analog-to-digital convertors (ADCs) are used to sample the projection coefficients. The signal can be reconstructed by simple linear calculation with the sampling matrix, without complying with optimization algorithm and prior knowledge. In other aspects, unlike other approaches that need to utilize an accurate time-shift at extremely high frequency, or design a hybrid filter bank, or generate specific basis functions or work for signals with prior knowledge, the proposed method is a universal sampling approach and easy to apply. The simulation results of signal to noise ratio (SNR) and spurious-free dynamic range (SFDR) validate the efficiency of the proposed method for UWB signal acquisition.

Transport Properties of a Chain of Anharmonic Oscillators with Random Flip of Velocities

We consider the stationary states of a chain of $n$ anharmonic coupled oscillators, whose deterministic hamiltonian dynamics is perturbed by random independent sign change of the velocities (a random mechanism that conserve energy). The extremities are coupled to thermostats at different temperature $T_\ell$ and $T_r$ and subject to constant forces $\tau_\ell$ and $\tau_r$. If the forces differ $\tau_\ell \neq \tau_r$ the center of mass of the system will move of a speed $V_s$ inducing a tension gradient inside the system. Our aim is to see the influence of the tension gradient on the thermal conductivity. We investigate the entropy production properties of the stationary states, and we prove the existence of the Onsager matrix defined by Green-kubo formulas (linear response). We also prove some explicit bounds on the thermal conductivity, depending on the temperature.

Kuramoto Model of Coupled Oscillators with Positive and Negative Coupling Parameters: An Example of Conformist and Contrarian Oscillators

We consider a generalization of the Kuramoto model in which the oscillators are coupled to the mean field with random signs. Oscillators with positive coupling are "conformists"; they are attracted to the mean field and tend to synchronize with it. Oscillators with negative coupling are "contrarians"; they are repelled by the mean field and prefer a phase diametrically opposed to it. The model is simple and exactly solvable, yet some of its behavior is surprising. Along with the stationary states one might have expected (a desynchronized state, and a partially-synchronized state, with conformists and contrarians locked in antiphase), it also displays a traveling wave, in which the mean field oscillates at a frequency different from the population's mean natural frequency.

On Three Competing Maintenance Actions and the Related Condition Control

This paper considers three competing maintenance actions: corrective after failure, condition‐based preventive to avoid failure, and scheduled. A stochastic model is set for the time relationship between corrective and preventive maintenance. This model defines a version of the so‐called random signs censoring, and it leads to natural goodness measures for condition control. The effect of condition control on important observable and unobservable indicators is studied. The latter half of the paper considers static Weibull models for the time to failure and the effect of condition control; the main contribution is a calculation method that derives the four model parameters from four figures of input data. Corresponding parameter experimentation is demonstrated on maintenance cost analysis and condition control design.

Utility based maintenance analysis using a Random Sign censoring model

Industrial systems subject to failures are usually inspected when there are evident signs of an imminent failure. Maintenance is therefore performed at a random time, somehow dependent on the failure mechanism. A competing risk model, namely a Random Sign model, is considered to relate failure and maintenance times. We propose a novel Bayesian analysis of the model and apply it to actual data from a water pump in an oil refinery. The design of an optimal maintenance policy is then discussed under a formal decision theoretic approach, analyzing the goodness of the current maintenance policy and making decisions about the optimal maintenance time.

Decay laws, anisotropy and cyclone–anticyclone asymmetry in decaying rotating turbulence

The effect of a background rotation on the decay of grid-generated turbulence is investigated from experiments using the large-scale ‘Coriolis’ rotating platform. A first transition occurs at 0.4 tank rotation (instantaneous Rossby number Ro ≃ 0.25), characterized by a t−6/5 → t−3/5 transition of the energy-decay law. After this transition, anisotropy develops in the form of vertical layers, where the initial vertical velocity fluctuations remain trapped. The vertical vorticity field develops a cyclone–anticyclone asymmetry, reproducing the growth law of the vorticity skewness, Sω(t) ≃ (Ωt)0.7, reported by Morize, Moisy &amp; Rabaud (Phys. Fluids, vol. 17 (9), 2005, 095105). A second transition is observed at larger time, characterized by a return to vorticity symmetry. In this regime, the layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, and eventually become unstable. The present results indicate that the shear instability of the vertical layers contributes significantly to the re-symmetrization of the vertical vorticity at large time, by re-injecting vorticity fluctuations of random sign at small scales. These results emphasize the importance of the nature of the initial conditions in the decay of rotating turbulence.

Student understanding of the direction of the magnetic force on a charged particle

We study student understanding of the direction of the magnetic force experienced by a charged particle moving through a homogeneous magnetic field in both the magnetic pole and field line representations of the magnetic field. In five studies, we administer a series of simple questions in either written or interview format. Our results indicate that although students begin at the same low level of performance in both representations, they answer correctly more often in the field line representation than in the pole representation after instruction. This difference is due in part to more students believing that charges are attracted to magnetic poles than believing that charges are pushed along magnetic field lines. Although traditional instruction is fairly effective in teaching students to answer correctly up to a few weeks following instruction, especially for the field line representation, some students revert to their initial misconceptions several months after instruction. The responses reveal persistent and largely random sign errors in the direction of the force. The sign errors are largely nonsystematic and due to confusion about the direction of the magnetic field and the execution and choice of the right-hand rule and lack of recognition of the noncommutativity of the cross product.

Scaling Limit of the Prudent Walk

We describe the scaling limit of the nearest neighbour prudent walk on $Z^2$, which performs steps uniformly in directions in which it does not see sites already visited. We show that the scaling limit is given by the process $Z_u = \int_0^{3u/7} ( \sigma_1 1_{W(s)\geq 0}\vec{e}_1 + \sigma_2 1_{W(s)\geq 0}\vec{e}_2 ) ds$, $u \in [0,1]$, where $W$ is the one-dimensional Brownian motion and $\sigma_1, \sigma_2$ two random signs. In particular, the asymptotic speed of the walk is well-defined in the $L^1$-norm and equals 3/7.