Unbounded Sampling Research Articles

Effect of a surface polarized layer on the optical properties of a nematic cell

The optical properties of a cell of nematic liquid crystal presenting a tilted surface polarization submitted to an electric field are theoretically investigated. The origin of the surface polarization is assumed to be related to the interaction of the nematic molecules with the substrate and to the polar order due to the cell filling procedure. The analysis shows that the coupling of the surface polarization with the external field has different effects on the two surfaces limiting the sample. On one of them, the coupling gives rise, in an unbounded sample, to a continuous variation of the easy angle, whereas on the other one it is responsible for a first-order like transition of the easy axis orientation. For a sample of finite thickness our analysis shows that in the presence of a coupling between the two surfaces, operated by the elastic properties of the liquid crystal, the abrupt variation of the easy axis on one of the surfaces induces also on the other surface a discontinuity on the nematic surface orientation. The optical transmission of the cell versus the amplitude of the applied voltage, for an impinging monochromatic linearly polarized light, presents a discontinuity for the critical voltage at which the first-order transition of the surface tilt angles appears.

Error Analysis of Regularized Trigonometric Linear Regression With Unbounded Sampling: A Statistical Learning Viewpoint

Error Analysis of Regularized Trigonometric Linear Regression With Unbounded Sampling: A Statistical Learning Viewpoint

Sometimes Size Does Not Matter

Recently Díaz, Hössjer and Marks (DHM) presented a Bayesian framework to measure cosmological tuning (either fine or coarse) that uses maximum entropy (maxent) distributions on unbounded sample spaces as priors for the parameters of the physical models ( https://doi.org/10.1088/1475-7516/2021/07/020 ). The DHM framework stands in contrast to previous attempts to measure tuning that rely on a uniform prior assumption. However, since the parameters of the models often take values in spaces of infinite size, the uniformity assumption is unwarranted. This is known as the normalization problem. In this paper we explain why and how the DHM framework not only evades the normalization problem but also circumvents other objections to the tuning measurement like the so called weak anthropic principle, the selection of a single maxent distribution and, importantly, the lack of invariance of maxent distributions with respect to data transformations. We also propose to treat fine-tuning as an emergence problem to avoid infinite loops in the prior distribution of hyperparameters (common to all Bayesian analysis), and explain that previous attempts to measure tuning using uniform priors are particular cases of the DHM framework. Finally, we prove a theorem, explaining when tuning is fine or coarse for different families of distributions. The theorem is summarized in a table for ease of reference, and the tuning of three physical parameters is analyzed using the conclusions of the theorem.

Evolving anomaly detection for network streaming data

Network security has always been a concern because it remains to be an unresolved problem. Unlike signature-based methods, anomaly-based methods can detect novel attacks and thus have gained increasing attention over the past decades. However, as the huge and unbounded network data samples continuously arrive at an unprecedented rate and always evolve and change, building a precise network normal pattern has become extremely difficult. In this study, an evolving anomaly detection method for network streaming data is proposed. Clusters are incrementally updated as the new network samples arrive at the incremental updating phase. The outliers, which include not only the global outliers but also the local outliers, are detected using the local density and global density thresholds at the anomaly detection phase. Meanwhile, a buffer is used to store temporary outliers, which may subsequently become normal samples, to avoid normal network samples being deleted as outliers.Three prominent streaming data (packet-based KDDCUP’99, NSL_KDD, and flow-based CIDDS-001) are used to validate the proposed algorithm. The detection rate of the proposed algorithm can achieve the best result. The result is nearly 100% on KDDCUP’99 and CIDDS-001. The false positive rate and accuracy are 0.0125 and 0.9886 on CIDDS-001, respectively. Experimental results indicate that the proposed algorithm can process real-time network anomaly detection with a much lower time and memory computational cost, and it outperforms other unsupervised anomaly detection methods and most supervised anomaly detection methods reported in the literature in terms of detection rate, false-positive rate, and detection accuracy.

Time reversal of Markov processes with jumps under a finite entropy condition

Motivated by entropic optimal transport, time reversal of Markov jump processes in Rn is investigated. Relying on an abstract integration by parts formula for the carré du champ of a Markov process recently obtained in Cattiaux et al. (2021), and using an entropic improvement strategy discovered by Föllmer (1985, 1986), we compute the semimartingale characteristics of the time reversed process for a wide class of jump processes in Rn with possibly unbounded variation sample paths and singular intensities of jump.

Perturbative diagonalization for Maryland-type quasiperiodic operators with flat pieces

We consider quasiperiodic operators on Zd with unbounded monotone sampling functions (“Maryland-type”), which are not required to be strictly monotone and are allowed to have flat segments. Under several geometric conditions on the frequencies, lengths of the segments, and their positions, we show that these operators enjoy Anderson localization at large disorder.

Filtering homogeneous observers in control of integrator chains

SummaryAny homogeneous controller asymptotically stabilizing disturbed integrator chains can be coupled with the proposed robust homogeneous filtering observer. The type of convergence (in finite‐time, in fixed‐time to any ball or exponential) is determined by the sign of the system homogeneity degree (HD). Filtering high‐gain observers and sliding‐mode‐based observers/differentiators are important particular cases corresponding to zero and negative HDs, respectively. Stabilization accuracy is estimated in the presence of possibly unbounded sampling noises featuring locally bounded iterated integrals. Accurate stabilization and differentiation are demonstrated for extremely large noises.

Analysis of Regression Algorithms with Unbounded Sampling.

In this letter, we study a class of the regularized regression algorithms when the sampling process is unbounded. By choosing different loss functions, the learning algorithms can include a wide range of commonly used algorithms for regression. Unlike the prior work on theoretical analysis of unbounded sampling, no constraint on the output variables is specified in our setting. By an elegant error analysis, we prove consistency and finite sample bounds on the excess risk of the proposed algorithms under regular conditions.

Efficient exponential timestepping algorithm using control variate technique for simulating a functional of exit time of one-dimensional Brownian diffusion with applications in finance

The exponential timestepping Euler algorithm with a boundary test is adapted to simulate an expected of a function of exit time, such as the expected payoff of barrier options under the constant elasticity of variance (CEV) model. However, this method suffers from a high Monte Carlo (MC) statistical error due to its exponentially large exit times with unbounded samples. To reduce this kind of error efficiently and to speed up the MC simulation, we combine such an algorithm with an effective variance reduction technique called the control variate method. We call the resulting algorithm the improved Exp algorithm for abbreviation. In regard to the examples we consider in this paper for the restricted CEV process, we found that the variance of the improved Exp algorithm is about six times smaller than that of the Jansons and Lythe original method for the down-and-out call barrier option. It is also about eight times smaller for the up-and-out put barrier option, indicating that the gain in efficiency is significant without significant increase in simulation time.

CFOF

We present a novel notion of outlier, called the Concentration Free Outlier Factor, or CFOF. As a main contribution, we formalize the notion of concentration of outlier scores and theoretically prove that CFOF does not concentrate in the Euclidean space for any arbitrary large dimensionality. To the best of our knowledge, there are no other proposals of data analysis measures related to the Euclidean distance for which it has been provided theoretical evidence that they are immune to the concentration effect. We determine the closed form of the distribution of CFOF scores in arbitrarily large dimensionalities and show that the CFOF score of a point depends on its squared norm standard score and on the kurtosis of the data distribution, thus providing a clear and statistically founded characterization of this notion. Moreover, we leverage this closed form to provide evidence that the definition does not suffer of the hubness problem affecting other measures in high dimensions. We prove that the number of CFOF outliers coming from each cluster is proportional to cluster size and kurtosis, a property that we call semi-locality. We leverage theoretical findings to shed lights on properties of well-known outlier scores. Indeed, we determine that semi-locality characterizes existing reverse nearest neighbor-based outlier definitions, thus clarifying the exact nature of their observed local behavior. We also formally prove that classical distance-based and density-based outliers concentrate both for bounded and unbounded sample sizes and for fixed and variable values of the neighborhood parameter. We introduce the fast-CFOF algorithm for detecting outliers in large high-dimensional dataset. The algorithm has linear cost, supports multi-resolution analysis, and is embarrassingly parallel. Experiments highlight that the technique is able to efficiently process huge datasets and to deal even with large values of the neighborhood parameter, to avoid concentration, and to obtain excellent accuracy.

Penalty variable sample size method for solving optimization problems with equality constraints in a form of mathematical expectation

Equality-constrained optimization problems with deterministic objective function and constraints in the form of mathematical expectation are considered. The constraints are approximated by employing the sample average where the sample size varies throughout the iterations in an adaptive manner. The proposed method incorporates variable sample size scheme with cumulative and unbounded sample into the well- known quadratic penalty iterative procedure. Line search is used for globalization and the sample size is updated in a such way to preserve the balance between two types of errors—errors coming from the sample average approximation and the approximation of the optimal point. Moreover, the penalty parameter is also updated in an adaptive way. We prove that the proposed algorithm pushes the sample size and the penalty parameter to infinity which further allows us to prove the almost sure convergence towards a Karush-Kuhn-Tucker optimal point of the original problem under the rather standard assumptions. Numerical comparison on a set of relevant problems shows the advantage of the proposed adaptive scheme over the heuristic (predetermined) sample scheduling in terms of number of function evaluations as a measure of the optimization cost.

Online minimum error entropy algorithm with unbounded sampling

Minimum error entropy (MEE) criterion is an important optimization method in information theoretic learning (ITL) and has been widely used and studied in various practical scenarios. In this paper, we shall introduce the online MEE algorithm for dealing with big datasets, associated with reproducing kernel Hilbert spaces (RKHS) and unbounded sampling processes. Explicit convergence rate will be given under the conditions of regularity of the regression function and polynomially decaying step sizes. Besides its low complexity, we will also show that the learning ability of online MEE is superior to the previous work in the literature. Our main techniques depend on integral operators on RKHS and probability inequalities for random variables with values in a Hilbert space.

Coefficient-based [formula omitted]-regularized regression with indefinite kernels and unbounded sampling

We consider the kernel-based coefficient least squares learning algorithm for regression with lq-regularizer, 1<q≤2. Our error analysis is carried out under more general conditions. The kernel function may be non-positive definite and the output sample values satisfy the moment hypothesis rather than the uniform boundedness. We derive the capacity dependent error bounds of the algorithm by constructing the stepping stone function for the indefinite kernels. When the output values are bounded, we obtain a learning rate that can be arbitrarily close to the best rate O(m−1) under some mild conditions of the regression function and the hypothesis space.

Support vector machines regression with unbounded sampling

ABSTRACTUniform boundedness of output variables is a standard assumption in most theoretical analysis of regression algorithms. This standard assumption has recently been weaken to a moment hypothesis in least square regression (LSR) setting. Although there has been a large literature on error analysis for LSR under the moment hypothesis, very little is known about the statistical properties of support vector machines regression with unbounded sampling. In this paper, we fill the gap in the literature. Without any restriction on the boundedness of the output sampling, we establish an ad hoc convergence analysis for support vector machines regression under very mild conditions.

Nanometric pitch in modulated structures of twist-bend nematic liquid crystals

The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulated structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase NTB is characterized by a heliconical structure with a pitch in the nanometric range, in agreement with experimental results. For a sample of finite thickness, we show that the wavevector of the stable periodic structure depends not only on the elastic parameters, but also on the anchoring energy, easy axis direction, and the thickness of the sample.

Intelligent Manufacturing: TCAD-Assisted Adaptive Weighting Neural Networks

Using machine intelligence on device and process performance prediction is an emerging methodology in the IC industry. While semiconductor technology computer-aided design (TCAD) has been researched and developed for over 30 years, it should contribute to or be used in conjunction with machine learning algorithms in solution finding procedure. Here, we propose an adaptive weighting neural network (AWNN) model that combines the advantages of statistical the machine learning model and the physical TCAD model. Using aspect ratio dependent etching as an example, our proposed AWNN outperforms conventional artificial neural network in terms of mean square errors in the test set where 5-10 times reduction is observed. The effectiveness of the TCAD AWNN model can be especially effective in the case of sampling over a vast sample space since the under-sampling problem can be compensated by the TCAD model. The large and nearly unbounded sample space is very common in IC technology, where cascaded and repeated process steps exist (~150 process steps and ~20 masks for 90-nm CMOS process).

Oscillations of the orientational structure of a ferronematic liquid crystal in an elliptically polarized rotating magnetic field

In the framework of the continuum approach we study the behavior of the orientational structure of a ferronematic liquid crystal with soft planar coupling between the liquid crystal matrix and magnetic particles in an elliptically polarized rotating magnetic field. We reveal synchronous and asynchronous oscillating regimes of orientational structure rotation for unbounded sample. We obtain the dependence of the critical angular velocity, which determines the boundary of regimes, on suspension parameters and the magnetic field for different values of its ellipticity. We show that transitions between the regimes are induced by the change in the coupling energy, the ellipticity parameter, the angular velocity, and the magnetic field. We find out that the critical angular velocity of an elliptically polarized magnetic field is always less than the critical velocity of a circularly polarized field. We analyze the stability thresholds of the orientational rotation regimes of a ferronematic liquid crystal and a nematic without magnetic admixture depending on the ellipticity of the magnetic field. We show that the presence of the magnetic particles increases the stability threshold of a synchronous oscillating regime of the suspension rotation.

Breakdown of nonlinear elasticity in stress-controlled thermal amorphous solids.

In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample-to-sample fluctuations that grow without bound with the system size. More relevant, however, for experiments are the conditions of stress control. In the present Rapid Communication we show that also under stress control the shear modulus exists, but higher-order moduli show unbounded sample-to-sample fluctuation. The unavoidable consequence is that the characterization of stress-strain curves in experiments should be done with a stress-dependent shear modulus rather than with nonlinear expansions.

Coefficient-based regularized regression with dependent and unbounded sampling

We consider the coefficient-based least squares regularized regression learning algorithm for the strongly and uniformly mixing samples. We obtain the capacity independent error bounds of the algorithm by means of the integral operator techniques. A standard assumption in theoretical study of learning algorithms for regression is the uniform boundedness of output sample values. We abandon this boundedness assumption and carry out the error analysis with output sample values satisfying a generalized moment hypothesis.

Error Analysis of ERM Algorithm with Unbounded and Non-Identical Sampling

A standard assumption in the literature of learning theory is the samples which are drawn independently from an identical distribution with a uniform bounded output. This excludes the common case with Gaussian distribution. In this paper we extend these assumptions to a general case. To be precise, samples are drawn from a sequence of unbounded and non-identical probability distributions. By drift error analysis and Bennett inequality for the unbounded random variables, we derive a satisfactory learning rate for the ERM algorithm.