Random Sign Research Articles

A new active learning surrogate model for time- and space-dependent system reliability analysis

This study introduces a novel method for time- and space-dependent system reliability analysis, integrating an active learning surrogate model with an innovative parallel updating strategy. A global Kriging model is developed to represent the signs of random samples using efficient global optimization. From a Bayesian perspective, the prediction probabilities of random sample signs within the time-space domain are calculated, and the sample with the lowest prediction probability is chosen to update the global Kriging model. The system extremum for each sample in the time-space domain is determined, and the corresponding random variables, time-space coordinates, and failure modes are selected. To further decrease iteration times, a parallel updating strategy that considers both the predicted probability and the correlation among candidate samples is proposed. Additionally, a new stopping criterion is introduced to balance accuracy and efficiency, terminating the updating process appropriately. The method's accuracy and efficiency are validated through three examples.

Orthogonal realizations of random sign patterns and other applications of the SIPP

A sign pattern is an array with entries in $\{+,-,0\}$. A real matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A. Curtis and B.L. Shader, Sign patterns of orthogonal matrices and the strong inner product property, Linear Algebra Appl. 592: 228-259, 2020], is an important tool when determining whether a sign pattern allows row orthogonality because it guarantees there is a nearby matrix with the same property, allowing zero entries to be perturbed to nonzero entries, while preserving the sign of every nonzero entry. This paper uses the SIPP to initiate the study of conditions under which random sign patterns allow row orthogonality with high probability. Building on prior work, $5\times n$ nowhere zero sign patterns that minimally allow orthogonality are determined. Conditions on zero entries in a sign pattern are established that guarantee any row orthogonal matrix with such a sign pattern has the SIPP.

A Bimodal Extension of the Log-Normal Distribution on the Real Line with an Application to DNA Microarray Data

A bimodal double log-normal distribution on the real line is proposed using the random sign mixture transform. Its associated statistical inferences are derived. Its parameters are estimated by the maximum likelihood method. The performance of the estimators and the corresponding confidence intervals is checked by simulation studies. Application of the proposed distribution to a real data set from a DNA microarray is presented.

Proof of Tomaszewski's conjecture on randomly signed sums

We prove the following conjecture, due to Tomaszewski (1986): Let X=∑i=1naixi, where ∑iai2=1 and each xi is a uniformly random sign. Then Pr⁡[|X|≤1]≥1/2.Our main novel tools are local concentration inequalities and an improved Berry-Esseen inequality for Rademacher sums.

Bounds on approximating Max kXOR with quantum and classical local algorithms

We consider the power of local algorithms for approximately solving Max kXOR, a generalization of two constraint satisfaction problems previously studied with classical and quantum algorithms (MaxCut and Max E3LIN2). In Max kXOR each constraint is the XOR of exactly k variables and a parity bit. On instances with either random signs (parities) or no overlapping clauses and D+1 clauses per variable, we calculate the expected satisfying fraction of the depth-1 QAOA from Farhi et al [arXiv:1411.4028] and compare with a generalization of the local threshold algorithm from Hirvonen et al [arXiv:1402.2543]. Notably, the quantum algorithm outperforms the threshold algorithm for k>4.On the other hand, we highlight potential difficulties for the QAOA to achieve computational quantum advantage on this problem. We first compute a tight upper bound on the maximum satisfying fraction of nearly all large random regular Max kXOR instances by numerically calculating the ground state energy density P(k) of a mean-field k-spin glass [arXiv:1606.02365]. The upper bound grows with k much faster than the performance of both one-local algorithms. We also identify a new obstruction result for low-depth quantum circuits (including the QAOA) when k=3, generalizing a result of Bravyi et al [arXiv:1910.08980] when k=2. We conjecture that a similar obstruction exists for all k.

Integrating Secure Communications Into Frequency Hopping MIMO Radar With Improved Data Rate

Dual-function radar-communication (DFRC) based on frequency hopping (FH) MIMO radar (FH-MIMO DFRC) achieves symbol rate much higher than radar pulse repetition frequency. Such DFRC, however, is prone to eavesdropping due to the spatially uniform illumination of an FH-MIMO radar. In this paper, we reveal the potential of using permutations of hopping frequencies to achieve secure and high-speed FH-MIMO DFRC. Specifically, we identify the angle-dependent issue in detecting permutations and develop an element-wise phase compensation (EPC) to solve the issue for a legitimate user (Bob). EPC makes the demodulation at an eavesdropper (Eve) conditioned on knowing the angle-of-departure (AoD) of Bob. We also propose the random sign reversal (RSR) technique which randomly selects several antennas over hops and reverses their signs. Owing to EPC, there is a sign rule available for Bob. We employ the rule and develop a low-complexity algorithm for Bob to remove RSR. We further prove that, given the same signal-to-noise ratio, RSR plus EPC make the demodulation performance of Eve inferior to that of Bob in most angular regions. Confirmed by simulation, our design achieves substantially high physical layer security for FH-MIMO DFRC, improves demodulation performance compared with existing designs, and reduces mutual interference among radar targets.

SignDS-FL: Local Differentially Private Federated Learning with Sign-based Dimension Selection

Federated Learning (FL) [ 31 ] is a decentralized learning mechanism that has attracted increasing attention due to its achievements in computational efficiency and privacy preservation. However, recent research highlights that the original FL framework may still reveal sensitive information of clients’ local data from the exchanged local updates and the global model parameters. Local Differential Privacy (LDP), as a rigorous definition of privacy, has been applied to Federated Learning to provide formal privacy guarantees and prevent potential privacy leakage. However, previous LDP-FL solutions suffer from considerable utility loss with an increase of model dimensionality. Recent work [ 29 ] proposed a two-stage framework that mitigates the dimension-dependency problem by first selecting one “important” dimension for each local update and then perturbing the dimension value to construct the sparse privatized update. However, the framework may still suffer from utility loss because of the insufficient per-stage privacy budget and slow model convergence. In this article, we propose an improved framework, SignDS-FL , which shares the concept of dimension selection with Reference [ 29 ], but saves the privacy cost for the value perturbation stage by assigning random sign values to the selected dimensions. Besides using the single-dimension selection algorithms in Reference [ 29 ], we propose an Exponential Mechanism-based Multi-Dimension Selection algorithm that further improves model convergence and accuracy. We evaluate the framework on a number of real-world datasets with both simple logistic regression models and deep neural networks. For training logistic regression models on structured datasets, our framework yields only a \( \sim \) 1%–2% accuracy loss in comparison to a \( \sim \) 5%–15% decrease of accuracy for the baseline methods. For training deep neural networks on image datasets, the accuracy loss of our framework is less than \( 8\% \) and at best only \( 2\% \) . Extensive experimental results show that our framework significantly outperforms the previous LDP-FL solutions and enjoys an advanced utility-privacy balance.

The political economy of fiscal transparency and independent fiscal councils

This paper develops a theory of fiscal transparency aimed at highlighting the potential contribution of independent fiscal councils to fiscal responsibility. In a political economy model with electoral competition, voters care about the candidates’ competence to supply valuable public goods and about their congruence (subjective sense of proximity). Voters observe candidates’ congruence but must form views about their competence based on the expected amount of public goods they could provide, and on other random signs about competence, public debt and the state of the economy. More transparency reduces noise around these relevant considerations. The model exhibits a bias towards excessive public debt for both “partisan” (myopia) and “opportunistic” (signaling competence through additional spending) motives so that institutional arrangements mitigating the debt bias carry welfare gains. While transparency about public debt itself is irrelevant, clearer signals about competence raise public debt if the incumbent enjoys a sufficiently large electoral advantage but reduce debt otherwise. Increased transparency about the state of the economy raises debt and is less valued by voters and the incumbent than greater transparency about competence. The latter is preferred by all players if the incumbent does not hold too large an electoral advantage. Otherwise, the incumbent and the public may have diverging preferences regarding greater transparency. Our analysis reveals the ambiguity about the potential contribution of independent fiscal councils (IFCs) to fiscal responsibility through increased transparency, and points to the inherent fragility of the political backing for such institutions.

Developing the Dead: Spirit Photography, Mormonism, and Noise

Developing the Dead: Spirit Photography, Mormonism, and Noise

Parity and time-reversal invariance violation in neutron-nucleus scattering

Parity violating (PV) as well as parity and time-reversal invariance violating (PTRIV) effects are enhanced a million times in neutron reactions near $p$-wave compound resonances. We present the calculation of such effects using a statistical theory based on the properties of chaotic eigenstates and discuss a possibility to extract the strength constants of PTRIV interactions from the experimental data, including nucleon-nucleon and pion-nucleon CP-violating interactions, the QCD $\ensuremath{\theta}$-term, and the quark chromo-EDM. PV effects have random signs for all target nuclei except for $^{232}\mathrm{Th}$, where PV effects of a positive sign have been observed for ten statistically significant $p$-wave resonances, with energy smaller than 250 eV. This may be an indication of a possible regular (nonchaotic) contribution to PV effects. We link this regular effect to the doublets of opposite parity states in the rotation spectra of nuclei with an octupole deformation and suggest other target nuclei where this hypothesis may be tested. We also discuss a permanent sign contribution produced by doorway states. An estimate of the ratio of PTRIV effects to PV effects is presented. Although a polarized target is not needed for the measurement of PV effects, for the interpretation of the results, it may be convenient to do both PV and PTRIV experiments with a polarized target.

Sharp Khinchin-type inequalities for symmetric discrete uniform random variables

We establish several optimal moment comparison inequalities (Khinchin-type inequalities) for weighted sums of independent identically distributed symmetric discrete random variables which are uniform on sets of consecutive integers. Specifically, we obtain sharp constants for the second moment and any moment of order at least 3 (using convex dominance by Gaussian random variables). In the case of only 3 atoms, we also establish a Schur-convexity result. For moments of order less than 2, we get sharp constants in two cases by exploiting Haagerup’s arguments for random signs.

Pinning of interfaces in a random medium with zero mean

We consider two related models for the propagation of a curvature sensitive interface in a time independent random medium. In both cases we suppose that the medium contains obstacles that act on the propagation of the interface with an inhibitory or an acceleratory force. We show that the interface remains bounded for all times even when a small constant external driving force is applied. This phenomenon has already been known when only inhibitory obstacles are present. In this work we extend this result to the case of – for example – a random medium of random zero mean forcing. The first model we study is discrete with a random forcing on each lattice site. In this case we construct a supersolution employing a local path optimization procedure. In the second, continuous, model we consider a random heterogenous medium consisting of localized small obstacles of random sign. To construct a stationary supersolution here, we need to pass through sufficiently many blocking obstacles while avoiding any obstacles of the other sign. This is done by employing a custom percolation argument.

A Littlewood-Type Theorem for Random Bergman Functions

AbstractLet $f(z)=\sum _{n=0}^{\infty }a_n z^n$ be a formal power series with complex coefficients. Let $({\mathcal{R}} f)(z)= \sum _{n=0}^{\infty }\pm a_n z^n$ be the randomization of $f$ by choosing independently a random sign for each coefficient. Let $H^p({\mathbb{D}})$ and $L^p_a({\mathbb{D}})$ $(p>0)$ denote the Hardy space and the Bergman space, respectively, over the unit disk in the complex plane. In 1930, Littlewood proved that if $f \in H^2({\mathbb{D}})$, then ${\mathcal{R}} f \in H^p({\mathbb{D}})$ for any $p \in (0, \infty )$ almost surely, and if $f \notin H^2({\mathbb{D}})$, then ${\mathcal{R}} f \notin H^p({\mathbb{D}})$ for any $p \in (0, \infty )$ almost surely. In this paper, we obtain a characterization of the pairs $(p, q) \in (0, \infty )^2$ such that ${\mathcal{R}} f$ is almost surely in $L^q_a({\mathbb{D}})$ whenever $f \in L^p_a({\mathbb{D}})$, including counterexamples to show the optimality of the embedding. In contrast to Littlewood’s theorem, random Bergman functions exhibit no improvement of regularity for any $p>0$, but the loss of regularity for $p<2$ is not as drastic as the Hardy case; there is indeed a nontrivial boundary curve given by $\frac{1}{q}-\frac{2}{p}+\frac{1}{2}=0$. Several other results about random Bergman functions are established along the way. The technical difficulties, especially when $p<1$, are different from the Hardy space and we devise a different route of proof. The Dirichlet space follows as a corollary. An improvement of the original Littlewood theorem is obtained.

Удельная активность радионуклидов и их взаимосвязь с валовым химическим составом почв

The total heavy metal content and activity concentration of natural radionuclides were obtained in native and anthropogenically transformed soil of the Rostov agglomeration (south of the Russia). The specific activity of natural radionuclides in soils of the has been comparable with indicators typical for chernozems of the Rostov region. Increased activity of 40K, 232Th is observed in the upper horizons, which is due to the origin of the radionuclides themselves and fertilization in the agrogenic period of soils, before the specified areas were included in the urban area. The correlation between activity concentration of radionuclide and total content of heavy metals were derived by Spearman's Rank-Order Correlation. The study was revealed that the activity concentration of thorium and radium doesn’t provide significant correlation with the total content of heavy metals. The group of buried horizons have shown a positive correlation with naturally occurring 40K in contrast with humus horizon (AU). The carbonates-accumulating group of horizons (BCA, [BCA]) have random correlation sign by each of metals. The most significant correlation was observed for the B horizons group.

Generalized Notions of Sparsity and Restricted Isometry Property. Part II: Applications

Restricted isometry property (RIP) provides a near isometric map for sparse signals. RIP of structured random matrices has played a key role for dimensionality reduction and recovery from compressive measurements. In a companion paper, we have developed a unified theory for RIP of group structured measurement operators on generalized sparsity models. The implication of the extended result will be further discussed in this paper in terms of its pros and cons over the conventional theory. We first show that the extended RIP theory enables the optimization of sample complexity over various relaxations of the canonical sparsity model. Meanwhile, the generalized sparsity model is no longer described as a union of subspaces. Thus the sparsity level is not sub-additive. This incurs that RIP of double the sparsity level does not imply RIP on the Minkowski difference of the sparsity model with itself, which is crucial for dimensionality reduction. We show that a group structured measurement operator provides an RIP-like property with additive distortion for non-sub-additive models. This weaker result can be useful for applications like locality-sensitive hashing. Moreover, we also present that the group structured measurements with random sign enables near isometric sketching on any set similar to the Gaussian measurements. Lastly, an extension of theory to infinite dimension is derived and illustrated over selected examples given by Lebesgue measure of support and Sobolev seminorms.

Brownian Loops, Layering Fields and Imaginary Gaussian Multiplicative Chaos

We study fields reminiscent of vertex operators built from the Brownian loop soup in the limit as the loop soup intensity tends to infinity. More precisely, following Camia et al. (Nucl Phys B 902:483–507, 2016), we take a (massless or massive) Brownian loop soup in a planar domain and assign a random sign to each loop. We then consider random fields defined by taking, at every point of the domain, the exponential of a purely imaginary constant times the sum of the signs associated to the loops that wind around that point. For domains conformally equivalent to a disk, the sum diverges logarithmically due to the small loops, but we show that a suitable renormalization procedure allows to define the fields in an appropriate Sobolev space. Subsequently, we let the intensity of the loop soup tend to infinity and prove that these vertex-like fields tend to a conformally covariant random field which can be expressed as an explicit functional of the imaginary Gaussian multiplicative chaos with covariance kernel given by the Brownian loop measure. Besides using properties of the Brownian loop soup and the Brownian loop measure, a main tool in our analysis is an explicit Wiener–Itô chaos expansion of linear functionals of vertex-like fields. Our methods apply to other variants of the model in which, for example, Brownian loops are replaced by disks.

One Bit is All It Takes: A Devastating Timing Attack on BLISS’s Non-Constant Time Sign Flips

Abstract As one of the most efficient lattice-based signature schemes, and one of the only ones to have seen deployment beyond an academic setting (e.g., as part of the VPN software suite strongSwan), BLISS has attracted a significant amount of attention in terms of its implementation security, and side-channel vulnerabilities of several parts of its signing algorithm have been identified in previous works. In this paper, we present an even simpler timing attack against it. The bimodal Gaussian distribution that BLISS is named after is achieved using a random sign flip during signature generation, and neither the original implementation of BLISS nor strongSwan ensure that this sign flip is carried out in constant time. It is therefore possible to recover the corresponding sign through side-channel leakage (using, e.g., cache attacks or branch tracing). We show that obtaining this single bit of leakage (for a moderate number of signatures) is in fact sufficient for a full key recovery attack. The recovery is carried out using a maximum likelihood estimation on the space of parameters, which can be seen as a statistical manifold. The analysis of the attack thus reduces to the computation of the Fisher information metric.

Decompensation in Critical Care: Early Prediction of Acute Heart Failure Onset.

BackgroundHeart failure is a leading cause of mortality and morbidity worldwide. Acute heart failure, broadly defined as rapid onset of new or worsening signs and symptoms of heart failure, often requires hospitalization and admission to the intensive care unit (ICU). This acute condition is highly heterogeneous and less well-understood as compared to chronic heart failure. The ICU, through detailed and continuously monitored patient data, provides an opportunity to retrospectively analyze decompensation and heart failure to evaluate physiological states and patient outcomes.ObjectiveThe goal of this study is to examine the prevalence of cardiovascular risk factors among those admitted to ICUs and to evaluate combinations of clinical features that are predictive of decompensation events, such as the onset of acute heart failure, using machine learning techniques. To accomplish this objective, we leveraged tele-ICU data from over 200 hospitals across the United States.MethodsWe evaluated the feasibility of predicting decompensation soon after ICU admission for 26,534 patients admitted without a history of heart failure with specific heart failure risk factors (ie, coronary artery disease, hypertension, and myocardial infarction) and 96,350 patients admitted without risk factors using remotely monitored laboratory, vital signs, and discrete physiological measurements. Multivariate logistic regression and random forest models were applied to predict decompensation and highlight important features from combinations of model inputs from dissimilar data.ResultsThe most prevalent risk factor in our data set was hypertension, although most patients diagnosed with heart failure were admitted to the ICU without a risk factor. The highest heart failure prediction accuracy was 0.951, and the highest area under the receiver operating characteristic curve was 0.9503 with random forest and combined vital signs, laboratory values, and discrete physiological measurements. Random forest feature importance also highlighted combinations of several discrete physiological features and laboratory measures as most indicative of decompensation. Timeline analysis of aggregate vital signs revealed a point of diminishing returns where additional vital signs data did not continue to improve results.ConclusionsHeart failure risk factors are common in tele-ICU data, although most patients that are diagnosed with heart failure later in an ICU stay presented without risk factors making a prediction of decompensation critical. Decompensation was predicted with reasonable accuracy using tele-ICU data, and optimal data extraction for time series vital signs data was identified near a 200-minute window size. Overall, results suggest combinations of laboratory measurements and vital signs are viable for early and continuous prediction of patient decompensation.

On oracle-type local recovery guarantees in compressed sensing

Abstract We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on $\ell ^1$ minimization encompasses the case where (i) the measurements are block-structured samples in order to reflect the structured acquisition that is often encountered in applications and (ii) the signal has an arbitrary structured sparsity, by results depending on its support $S$. Within this framework and under a random sign assumption, the number of measurements needed by $\ell ^1$ minimization can be shown to be of the same order than the one required by an oracle least-squares estimator. Moreover, these bounds can be minimized by adapting the variable density sampling to a given prior on the signal support and to the coherence of the measurements. We illustrate both numerically and analytically that our results can be successfully applied to recover Haar wavelet coefficients that are sparse in levels from random Fourier measurements in dimension one and two, which can be of particular interest in imaging problems. Finally, a preliminary numerical investigation shows the potential of this theory for devising adaptive sampling strategies in sparse polynomial approximation.

Enhanced ENSO Prediction via Augmentation of Multimodel Ensembles with Initial Thermocline Perturbations

AbstractRecent studies have shown that regardless of model configuration, skill in predicting El Niño–Southern Oscillation (ENSO), in terms of target month and forecast lead time, remains largely dependent on the temporal characteristics of the boreal spring predictability barrier. Continuing the 2019 study by O’Kane et al., we compare multiyear ensemble ENSO forecasts from the Climate Analysis Forecast Ensemble (CAFE) to ensemble forecasts from state-of-the-art dynamical coupled models in the North American Multimodel Ensemble (NMME) project. The CAFE initial perturbations are targeted such that they are specific to tropical Pacific thermocline variability. With respect to individual NMME forecasts and multimodel ensemble averages, the CAFE forecasts reveal improvements in skill when predicting ENSO at lead times greater than 6 months, in particular when predictability is most strongly limited by the boreal spring barrier. Initial forecast perturbations generated exclusively as disturbances in the equatorial Pacific thermocline are shown to improve the forecast skill at longer lead times in terms of anomaly correlation and the random walk sign test. Our results indicate that augmenting current initialization methods with initial perturbations targeting instabilities specific to the tropical Pacific thermocline may improve long-range ENSO prediction.