Arbitrary Correlation Research Articles

Fallback tests for co-primary endpoints.

When efficacy of a treatment is measured by co‐primary endpoints, efficacy is claimed only if for each endpoint an individual statistical test is significant at level α. While such a strategy controls the family‐wise type I error rate (FWER), it is often strictly conservative and allows for no inference if not all null hypotheses can be rejected. In this paper, we investigate fallback tests, which are defined as uniform improvements of the classical test for co‐primary endpoints. They reject whenever the classical test rejects but allow for inference also in settings where only a subset of endpoints show a significant effect. Similarly to the fallback tests for hierarchical testing procedures, these fallback tests for co‐primary endpoints allow one to continue testing even if the primary objective of the trial was not met. We propose examples of fallback tests for two and three co‐primary endpoints that control the FWER in the strong sense under the assumption of multivariate normal test statistics with arbitrary correlation matrix and investigate their power in a simulation study. The fallback procedures for co‐primary endpoints are illustrated with a clinical trial in a rare disease and a diagnostic trial. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Mössbauer forward scattering: time-domain spectra

The transmission of the Mossbauer radiation through an absorber being in the acoustic oscillation mode under forward scattering (FS) conditions has been analyzed. The modification of the existing models of the FS spectra (frequency and time) formation to the case of the arbitrary phase correlation of nuclear oscillations in the sample has been proposed. An adequate description of the time delayed experiments with the 57Fe Mossbauer resonance using the modulation of the single-photon wave packet by acoustic field has been obtained. One has been done in the frame of the Raman scattering of Mossbauer photons. The models extended this way can be used to control the degree of phase correlation of nuclear oscillations (or other processes) induced in the sample by external fields.

Efficient Simulation of the Multi Asset Heston Model

This paper describes a procedure for efficiently simulating a multi asset Heston model with an arbitrary correlation structure. Very little literature can be found on the topic (e.g. Wadman (2010) and Dimitroff et al. (2011)), the latter being very restrictive on correlation assumptions. The scheme proposed in this text is based on Andersen's Quadratic Exponential (QE) scheme (2008) and operates with an arbitrary input correlation structure, which is partially decorrelated via a Gaussian copula approach to fit the single asset QE prerequisites. Given a long term horizon, it is shown numerically that, in the multi asset QE (MQE) scheme, all combinations of terminal correlations converge quickly to the true terminal correlations for decreasing Monte Carlo time step size, if the input correlation matrix is interpreted as the system's instantaneous correlation matrix. Convergence of vanilla and spread option prices is investigated, in order to verify the appropriate behaviour for higher moments of the marginal and the joint distribution under MQE. Finally, the superiority of MQE vs. Taylor based schemes is shown by comparing convergence of the empirical PDF, calculated with Monte Carlo, to the exact function calculated via Fourier inversion.

A method for analyzing multiple continuous phenotypes in rare variant association studies allowing for flexible correlations in variant effects.

For region-based sequencing data, power to detect genetic associations can be improved through analysis of multiple related phenotypes. With this motivation, we propose a novel test to detect association simultaneously between a set of rare variants, such as those obtained by sequencing in a small genomic region, and multiple continuous phenotypes. We allow arbitrary correlations among the phenotypes and build on a linear mixed model by assuming the effects of the variants follow a multivariate normal distribution with a zero mean and a specific covariance matrix structure. In order to account for the unknown correlation parameter in the covariance matrix of the variant effects, a data-adaptive variance component test based on score-type statistics is derived. As our approach can calculate the P-value analytically, the proposed test procedure is computationally efficient. Broad simulations and an application to the UK10K project show that our proposed multivariate test is generally more powerful than univariate tests, especially when there are pleiotropic effects or highly correlated phenotypes.

An efficient bi-objective optimization framework for statistical chip-level yield analysis under parameter variations

With shrinking technology, the increase in variability of process, voltage, and temperature (PVT) parameters significantly impacts the yield analysis and optimization for chip designs. Previous yield estimation algorithms have been limited to predicting either timing or power yield. However, neglecting the correlation between power and delay will result in significant yield loss. Most of these approaches also suffer from high computational complexity and long runtime. We suggest a novel bi-objective optimization framework based on Chebyshev affine arithmetic (CAA) and the adaptive weighted sum (AWS) method. Both power and timing yield are set as objective functions in this framework. The two objectives are optimized simultaneously to maintain the correlation between them. The proposed method first predicts the guaranteed probability bounds for leakage and delay distributions under the assumption of arbitrary correlations. Then a power-delay bi-objective optimization model is formulated by computation of cumulative distribution function (CDF) bounds. Finally, the AWS method is applied for power-delay optimization to generate a well-distributed set of Pareto-optimal solutions. Experimental results on ISCAS benchmark circuits show that the proposed bi-objective framework is capable of providing sufficient trade-off information between power and timing yield.

Suppression of Dephasing by Qubit Motion in Superconducting Circuits.

We suggest and demonstrate a protocol which suppresses the low-frequency dephasing by qubit motion, i.e., transfer of the logical qubit of information in a system of n≥2 physical qubits. The protocol requires only the nearest-neighbor coupling and is applicable to different qubit structures. Our analysis of its effectiveness against noises with arbitrary correlations, together with experiments using up to three superconducting qubits, shows that for the realistic uncorrelated noises, qubit motion increases the dephasing time of the logical qubit as √n. In general, the protocol provides a diagnostic tool for measurements of the noise correlations.

Physical Layer Security for Multiple-Antenna Systems: A Unified Approach

Secrecy capacity is a fundamental information-theoretic performance metric to predict the maximum data rate of reliable communication, while the intended message is not revealed to the eavesdropper. Motivated by this consideration in this paper, a unified communication-theoretic framework for the analysis of the probability of nonzero secrecy capacity, the secrecy outage probability, and the secrecy capacity of multiple-antenna systems over fading channels is proposed. Specifically, a powerful frequency-domain approach is first developed in which the integrals involved in the evaluation of the probability of nonzero secrecy capacity and secrecy outage probability are transformed into the frequency domain, by employing Parseval’s theorem. A generic approach for the evaluation of the asymptotic secrecy outage probability at high signal-to-noise ratio (SNR) region is also introduced, thus providing useful insight as to the parameters affecting the secrecy performance. Finally, a unified numerical approach for computing the average secrecy capacity of multiple-antenna systems under arbitrary fading environments is developed. The proposed framework is general enough to accommodate any well-known multiantenna transmission technique and fading model. Finally, the secrecy performance of several multiple-antenna system setups is assessed, in the presence of generalized fading conditions and arbitrary antenna correlation, while various numerical and computer simulation results are shown and compared to substantiate the proposed mathematical analysis.

Software Reliability Growth Model with Partial Differential Equation for Various Debugging Processes

Most Software Reliability Growth Models (SRGMs) based on the Nonhomogeneous Poisson Process (NHPP) generally assume perfect or imperfect debugging. However, environmental factors introduce great uncertainty for SRGMs in the development and testing phase. We propose a novel NHPP model based on partial differential equation (PDE), to quantify the uncertainties associated with perfect or imperfect debugging process. We represent the environmental uncertainties collectively as a noise of arbitrary correlation. Under the new stochastic framework, one could compute the full statistical information of the debugging process, for example, its probabilistic density function (PDF). Through a number of comparisons with historical data and existing methods, such as the classic NHPP model, the proposed model exhibits a closer fitting to observation. In addition to conventional focus on the mean value of fault detection, the newly derived full statistical information could further help software developers make decisions on system maintenance and risk assessment.

''DOUBLE-HUMPED EFFECT'' IN THE TURBULENT COLLISION MAGNETIZED PLASMA

Statistical moments of the spatial power spectrum of multiple scattered ordinary and extraordinary waves in the turbulent collision magnetized plasma with aligned anisotropic electron density irregularities are investigated using modify smooth perturbation method taking into account diffraction effects. Correlation function and variances of the phase fluctuations are obtained for arbitrary correlation function of the electron density fluctuations. Double-humped Effect is investigated analytically and numerically using the anisotropic Gaussian spectral function of electron density irregularities for the polar ionospheric F-region applying the experimental data. Investigation of the anisotropy of the F layer irregularities is of great interest in ionospheric physics. It is well known that the irregularities are elongated in the direction of the geomagnetic field of lines, but especially at high latitudes they are also found to be anisotropic in the plane perpendicular to the external magnetic field vector. The anisotropy is usually investigated by correlation analysis of radio signals from satellites, observed by space receiver on the ground. The fluctuations in amplitude and phase (scintillations) of radio waves passing through the ionosphere are caused by spatial irregularities in the electron density. The spatial fluctuations in phase cause fluctuations of the angle of arrival at the observation points. Broadening of the spatial power spectrum (SPS) of scattered electromagnetic (EM) waves in the turbulent collision magnetized plasma for both power-law and anisotropic Gaussian correlation functions of electron density fluctuations was analyzed in (1) using the complex ray (-optics) approximation. Double-humped Effect, the features of the SPS, spectral width and shift of its maximum of multiple scattered EM waves in the turbulent collisionless magnetized plasma were considered in (2, 3). The influence of the collision frequency between plasma particles on the statistical characteristics of scattered EM waves in the turbulent magnetized plasma with both electron density and external magnetic field fluctuations was investigated in (4). The present paper reports the results of an analysis of the SPS, which is related to fluctuations of the radio refractive index in the F region. Analytical expressions of the correlation function of phase fluctuations of scattered both ordinary and extraordinary waves are obtained for the arbitrary correlation functions of electron density fluctuation using modify smooth perturbation method taking into account the diffraction effects. The Double-humped Effect in the collision magnetized plasma with elongated electron density irregularities is considered for the first time. Formation of a gap in the SPS of scattered radiation is analyzed numerically for the polar ionospheric F -region using the anisotropic Gaussian spectral function of electron density fluctuations. This spectrum contains angle of aligned plasma irregularities to the direction of an external magnetic field and anisotropy factor. The numerical calculation is computed based on experimental data. Finally, paper concludes the obtained results and their significance.

Extended hierarchy equation of motion for the spin-boson model.

An extended hierarchy equation of motion (HEOM) is proposed and applied to study the dynamics of the spin-boson model. In this approach, a complete set of orthonormal functions are used to expand an arbitrary bath correlation function. As a result, a complete dynamic basis set is constructed by including the system reduced density matrix and auxiliary fields composed of these expansion functions, where the extended HEOM is derived for the time derivative of each element. The reliability of the extended HEOM is demonstrated by comparison with the stochastic Hamiltonian approach under room-temperature classical ohmic and sub-ohmic noises and the multilayer multiconfiguration time-dependent Hartree theory under zero-temperature quantum ohmic noise. Upon increasing the order in the hierarchical expansion, the result obtained from the extended HOEM systematically converges to the numerically exact answer.

ChemInform Abstract: Multidimensional NMR Spectroscopy in a Single Scan

AbstractReview: 59 refs.

Entropy bounds for quantum processes with initial correlations

Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of complete-positive trace preserving maps is no longer valid. The departure from complete positivity means many useful bounds, like entropy production, Holevo, and data processing inequality are no longer applicable to such systems. We address these issues by deriving a generalized bound for entropy valid for quantum dynamics with arbitrary system-environment correlations. We employ superchannels, which map quantum operations performed by the experimenter, represented in terms of completely positive maps, to states. Our bound has information-theoretic applications, as it generalizes the data processing inequality and the Holevo bound. We prove that both data processing inequality and the Holevo are valid even when system is correlated with the environment.

Symmetries of general non-Markovian Gaussian diffusive unravelings

By using a condition of average trace preservation we derive a general class of non-Markovian Gaussian diffusive unravelings [L. Diosi and L. Ferialdi, Phys. Rev. Lett. \textbf{113}, 200403 (2014)], here valid for arbitrary non-Hermitian system operators and noise correlations. The conditions under which the generalized stochastic Schrodinger equation has the same symmetry properties (invariance under unitary changes of operator base) than a microscopic system-bath Hamiltonian dynamics are determined. While the standard quantum diffusion model (standard noise correlations) always share the same invariance symmetry, the generalized stochastic dynamics can be mapped with an arbitrary bosonic environment only if some specific correlation constraints are fulfilled. These features are analyzed for different non-Markovian unravelings equivalent in average. Results based on quantum measurement theory that lead to specific cases of the generalized dynamics [J. Gambetta and H. M. Wiseman, Phys. Rev. A \textbf{66}, 012108 (2002)]\ are studied from the perspective of the present analysis.

Mixing SABR Models for Negative Rates

In the current low-interest-rate environment, extending option models to negative rates has become an important issue. In our previous paper, we introduced the Free SABR model, which is a natural and an attractive extension to the classical SABR model. In spite of its advantages over the Shifted SABR, the Free SABR option pricing formula is based on an approximation. Although this approximation is very good, it cannot guarantee the absence of arbitrage.In this article, we build on an exact option pricing formula for the normal SABR with a free boundary and an arbitrary correlation. First, we derive this formula in terms of a 1D integral, which is suitable for fast calibration. Next, we apply the formula as a control variate to the Free SABR to improve the accuracy of its approximation, especially for high correlations. Finally, we come up with a Mixture SABR model, which is a weighted sum of the normal and free zero-correlation models. This model is guaranteed to be arbitrage free and has a closed-form solution for option prices. Added degrees of freedom also allow the Mixture SABR model to be calibrated to a broader set of trades, in particular, to a joint set of swaptions and CMS payment. We demonstrate this capability with a wide set of numerical examples.

Statistical Analysis of Multiantenna Relay Systems and Power Allocation Algorithms in a Relay With Partial Channel State Information

The performance of a dual-hop MIMO relay network is studied in this paper. The relay is assumed to have access to the statistical channel state information of its preceding and following channels and it is assumed that fading at the antennas of the relay is correlated. The cumulative density function (cdf) of the received SNR at the destination is first studied and closed-form expressions are derived for the asymptotic cases of the fully-correlated and non-correlated scenarios; moreover, the statistical characteristics of the SNR are further studied and an approximate cdf of the SNR is derived for arbitrary correlation. The cdf is a multipartite function which does not easily lend itself to further mathematical calculations, e.g., rate optimization. However, we use it to propose a simple power allocation algorithm which we call "proportional power allocation". The algorithm is explained in detail for the case of two antennas and three antennas at the relay and the extension of the algorithm to a relay with an arbitrary number of the antennas is discussed. Although the proposed method is not claimed to be optimal, the result is indistinguishable from the benchmark obtained using exhaustive search. The simplicity of the algorithm combined with its precision is indeed attractive from the practical point of view.

Hyperdiffusion of quantum waves in random photonic lattices.

A quantum-mechanical analysis of hyperfast (faster than ballistic) diffusion of a quantum wave packet in random optical lattices is presented. The main motivation of the presented analysis is experimental demonstrations of hyperdiffusive spreading of a wave packet in random photonic lattices [L. Levi et al., Nature Phys. 8, 912 (2012)]. A rigorous quantum-mechanical calculation of the mean probability amplitude is suggested, and it is shown that the power-law spreading of the mean-squared displacement (MSD) is 〈x2(t)〉∼tα, where 2<α≤3. The values of the transport exponent α depend on the correlation properties of the random potential V(x,t), which describes random inhomogeneities of the medium. In particular, when the random potential is δ correlated in time, the quantum wave packet spreads according Richardson turbulent diffusion with the MSD ∼t3. Hyperdiffusion with α=12/5 is also obtained for arbitrary correlation properties of the random potential.

Contagious error sources would need time travel to prevent quantum computation

We consider an error model for quantum computing that consists of "contagious quantum germs" that can infect every output qubit when at least one input qubit is infected. Once a germ actively causes error, it continues to cause error indefinitely for every qubit it infects, with arbitrary quantum entanglement and correlation. Although this error model looks much worse than quasi-independent error, we show that it reduces to quasi-independent error with the technique of quantum teleportation. The construction, which was previously described by Knill, is that every quantum circuit can be converted to a mixed circuit with bounded quantum depth. We also consider the restriction of bounded quantum depth from the point of view of quantum complexity classes.

MLHN: A Hypernetwork Model for Multi-Label Classification

Multi-label classification has attracted significant attentions in machine learning. In multi-label classification, exploiting correlations among labels is an essential but nontrivial task. First, labels may be correlated in various degrees. Second, the scalability may suffer from the large number of labels, because the number of combinations among labels grows exponentially as the number of labels increases. In this paper, a multi-label hypernetwork (MLHN) is proposed to deal with these problems. By extending the traditional hypernetwork model, MLHN can represent arbitrary order correlations among labels. The classification model of MLHN is simple and the computational complexity of MLHN is linear with respect to the number of labels, which contribute to the good scalability of MLHN. We perform experiments on a variety of datasets. The results illustrate that the proposed MLHN achieves competitive performances against state-of-the-art multi-label classification algorithms in terms of both effectiveness and scalability with respect to the number of labels.

MultidimensionalNMRspectroscopy in a single scan

Multidimensional NMR has become one of the most widespread spectroscopic tools available to study diverse structural and functional aspects of organic and biomolecules. A main feature of multidimensional NMR is the relatively long acquisition times that these experiments demand. For decades, scientists have been working on a variety of alternatives that would enable NMR to overcome this limitation, and deliver its data in shorter acquisition times. Counting among these methodologies is the so-called ultrafast (UF) NMR approach, which in principle allows one to collect arbitrary multidimensional correlations in a single sub-second transient. By contrast to conventional acquisitions, a main feature of UF NMR is a spatiotemporal manipulation of the spins that imprints the chemical shift and/or J-coupling evolutions being sought, into a spatial pattern. Subsequent gradient-based manipulations enable the reading out of this information and its multidimensional correlation into patterns that are identical to those afforded by conventional techniques. The current review focuses on the fundamental principles of this spatiotemporal UF NMR manipulation, and on a few of the methodological extensions that this form of spectroscopy has undergone during the years.

Country Solidarity in Sovereign Crises

When will solidarity, which emerges spontaneously from the fear of spillovers, be reinforced through contracting? The optimal pact between countries that differ substantially in their probability of distress is a simple debt contract with market financing, a borrowing cap, but no joint liability. While joint liability augments total surplus, the borrowing country cannot compensate the deep-pocket guarantor. By contrast, the optimal pact between two countries symmetrically exposed to shocks with an arbitrary correlation is a simple debt contract with joint liability, provided that shocks are sufficiently independent, spillovers sufficiently large, liquidity needs moderate, and available sanctions sufficiently tough. (JEL D86, F34, H63)