Distortion Function Research Articles

Measuring Distortion-Product Otoacoustic Emission With a Single Loudspeaker in the Ear: Stimulus Design and Signal Processing Techniques.

The distortion-product otoacoustic emission (DPOAE) is a backward propagating wave generated inside the cochlea during the wave amplification process. The DPOAE signal can be detected rapidly under relatively noisy conditions. In recent years, the earphone industry demonstrated interest in adopting DPOAE as an add-on feature to make their product “intelligent” of inner-ear status. However, a technical challenge remains to be tackled—the loudspeaker in an earphone generates its own cubic distortion at the same frequency as DPOAE. Unfortunately, the intensity of loudspeaker distortion is typically comparable to that of the DPOAE, if not higher. In this research, we propose two strategies, namely compensation and cancellation, to enable DPOAE measurement with a single loudspeaker. The compensation strategy exploits the part of the growth function of the loudspeaker distortion which is almost linear, and thus suppresses the distortion it generates while retaining a larger portion of DPOAE in the residual signal. The cancellation strategy utilizes a one-dimensional Volterra filter to remove the cubic distortion from the loudspeaker. Testing on normal-hearing ears shows that the compensation strategy improved the DPOAE-to-interference ratio by approximately 7 dB, resulting in a cross-correlation of 0.62 between the residual DPOAE level and the true DPOAE level. Meanwhile, the cancellation strategy directly recovered both the magnitude and the phase of DPOAE, reducing the magnitude estimation error from 15.5 dB to 3.9 dB in the mean-square sense. These pilot results suggest that the cancellation strategy may be suitable for further testing with more subjects.

Structural Relationships Model of Type D Personality and Depression With the Mediation of Cognitive Distortions and Family Functioning in the Citizens of Bandar Abbas

Background and Objectives: Depression is a disorder in which personality factors are one of the presumed causes. The purpose of this study was to test the fit of structural model of personality type D and depression mediated by cognitive distortions and family functioning in the citizens of Bandar Abbas. Methods: This study was a correlation of structural equation modeling. Its population consisted of citizens of Bandar Abbas, from which 239 people were selected by stratified sampling. Measurement tools were Beck Depression Inventory (BDI), Type D Personality Scale (TDPS), Interpersonal Cognitive Distortion Scale (ICDS) and Family Performance Scale (FPS). Data were analyzed using structural equation modeling. Results: The model of this study has an acceptable fit with the data and family functioning has a mediating role between type D and depression, but the two variables of cognitive distortion and family function were not associated with depression. The results also showed that type D has a direct and significant effect on depression, cognitive distortions and family functioning Conclusion: Personality factors, especially type D, play a role in depression. Personality type D can affect family performance and cognition.

A Novel Steganography Scheme for Color Image Based on HLS Translation

In recent years, steganography has attracted extensive attention, but most of steganography schemes are aimed at grayscale images. Therefore, a novel steganography scheme for color image based on HLS translation is proposed in this paper. Firstly, the color cover image is decomposed from RGB three channels to HLS three channels. Then the image of H channel is selected as the cover image for embedding secret information due to its texture feature of original image. The universal distortion function UNIWARD is utilized to embed the secret information into the image of H channel. Finally, the steg image transmitted in common channel is obtained by inverse HLS transform using the single channel image embedding the secret information. The extensive experimental results indicate that our scheme has high security and can also resist the detection of steganalysis schemes based on CNN.

Using the Semantic Information G Measure to Explain and Extend Rate-Distortion Functions and Maximum Entropy Distributions.

In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual Information (MMI) distributions and ME distributions are expressed by Bayes-like formulas, including Negative Exponential Functions (NEFs) and partition functions. Why do these non-probability functions exist in Bayes-like formulas? On the other hand, the rate-distortion function has three disadvantages: (1) the distortion function is subjectively defined; (2) the definition of the distortion function between instances and labels is often difficult; (3) it cannot be used for data compression according to the labels’ semantic meanings. The author has proposed using the semantic information G measure with both statistical probability and logical probability before. We can now explain NEFs as truth functions, partition functions as logical probabilities, Bayes-like formulas as semantic Bayes’ formulas, MMI as Semantic Mutual Information (SMI), and ME as extreme ME minus SMI. In overcoming the above disadvantages, this paper sets up the relationship between truth functions and distortion functions, obtains truth functions from samples by machine learning, and constructs constraint conditions with truth functions to extend rate-distortion functions. Two examples are used to help readers understand the MMI iteration and to support the theoretical results. Using truth functions and the semantic information G measure, we can combine machine learning and data compression, including semantic compression. We need further studies to explore general data compression and recovery, according to the semantic meaning.

Expansion series of the pairwise velocity generating function and its implications on redshift space distortion modeling

The pairwise velocity generating function G has a deep connection with both the pairwise velocity probability distribution function and modeling of redshift space distortion (RSD). Its implementation into RSD modeling is often faciliated by expansion into a series of pairwise velocity moments . Motivated by the logrithmic transformation of the cosmic density field, we investigate an alternative expansion into series of pairwise velocity cumulants . We numerically evaluate the convergence rate of the two expansions, with three 30723 particle simulations of the CosmicGrowth N-body simulation series. (1) We find that the cumulant expansion performs significantly better, for all the halo samples and redshifts investigated. (2) For modeling RSD at k ∥ < 0.1h Mpc−1, including only the n = 1,2 cumulants is sufficient. (3) But for modeling RSD at k ∥ = 0.2h Mpc−1, we need and only need the n = 1,2,3,4 cumulants. These results provide specific requirements on RSD modeling in terms of m-th order statistics of the large-scale structure.

Concave/convex weighting and utility functions for risk: A new light on classical theorems

This paper analyzes concave and convex utility and probability distortion functions for decision under risk (law-invariant functionals). We characterize concave utility for virtually all existing models, and concave/convex probability distortion functions for rank-dependent utility and prospect theory in complete generality, through an appealing and well-known condition (convexity of preference, i.e., quasiconcavity of the functional). Unlike preceding results, we do not need to presuppose any continuity, let be differentiability.An example of a new light shed on classical results: whereas, in general, convexity/concavity with respect to probability mixing is mathematically distinct from convexity/concavity with respect to outcome mixing, in Yaari's dual theory (i.e., Wang's premium principle) these conditions are not only dual, as was well-known, but also logically equivalent, which had not been known before.

Embedding surfaces inside small domains with minimal distortion

Given two-dimensional Riemannian manifolds $$\mathcal {M},\mathcal {N}$$ , we prove a lower bound on the distortion of embeddings $$\mathcal {M}\rightarrow \mathcal {N}$$ , in terms of the areas’ discrepancy $$V_{\mathcal {N}}/V_{\mathcal {M}}$$ , for a certain class of distortion functionals. For $$V_{\mathcal {N}}/V_{\mathcal {M}} \ge 1/4$$ , homotheties, provided they exist, are the unique energy minimizing maps attaining the bound, while for $$V_{\mathcal {N}}/V_{\mathcal {M}} \le 1/4$$ , there are non-homothetic minimizers. We characterize the maps attaining the bound, and construct explicit non-homothetic minimizers between disks. We then prove stability results for the two regimes. We end by analyzing other families of distortion functionals. In particular we characterize a family of functionals where no phase transition in the minimizers occurs; homotheties are the energy minimizers for all values of $$V_{\mathcal {N}}/V_{\mathcal {M}}$$ , provided they exist.

Secure halftone image steganography based on density preserving and distortion fusion

Most state-of-the-art halftone image steganographic methods measure the flipping distortion according to the statistics of the image database but neglect the characteristic of a single image. In this paper, a halftone image steganography based on density preserving and distortion fusion is proposed for minimizing the flipping distortion. Different from ordinary binary images, halftone images express the texture information by the intensity of local regions that are represented by the pixel density. Based on the density distribution of a halftone image, the embedding costs defined by a single existing distortion function are modified adaptively to maintain the original texture structure as much as possible. Furthermore, to select more appropriate flipped pixels, a distortion fusion strategy is developed from the perspective of anti-steganographic analysis, which can be applied to a batch of distortion functions. Finally, the syndrome-trellis code (STC) is applied to minimize the embedding distortion for playing the advantage of the distortion measurement. Experimental results show that the proposed steganographic scheme achieves great visual quality and strong statistical security without degrading the embedding capacity.

Identification and correction of temporal and spatial distortions in scanning transmission electron microscopy

Scanning transmission electron microscopy (STEM) has become the technique of choice for quantitative characterization of atomic structure of materials, where the minute displacements of atomic columns from high-symmetry positions can be used to map strain, polarization, octahedra tilts, and other physical and chemical order parameter fields. The latter can be used as inputs into mesoscopic and atomistic models, providing insight into the correlative relationships and generative physics of materials on the atomic level. However, these quantitative applications of STEM necessitate understanding the microscope induced image distortions and developing the pathways to compensate them both as part of a rapid calibration procedure for in situ imaging, and the post-experimental data analysis stage. Here, we explore the spatiotemporal structure of the microscopic distortions in STEM using multivariate analysis of the atomic trajectories in the image stacks. Based on the behavior of principal component analysis (PCA), we develop the Gaussian process (GP)-based regression method for quantification of the distortion function. The limitations of such an approach and possible strategies for implementation as a part of in-line data acquisition in STEM are discussed. The analysis workflow is summarized in a Jupyter notebook that can be used to retrace the analysis and analyze the reader's data.

The Optimal Reinsurance Strategy under Conditional Tail Expectation (CTE) and Wang’s Premium Principle

In this study, we take the conditional tail expectation (CTE) as the constraint condition and consider the optimal reinsurance issues under Wang’s premium principle in general insurance contracts. With the confidence level and the distortion function in Wang’s premium principle given by the insurer in advance, a threshold can be obtained. When the insurer’s risk tolerance level is greater than this value, the optimal reinsurance is a proportional reinsurance in which the deductible equals to this value, else the optimal form of reinsurance is a stop-loss reinsurance. Corresponding numerical examples and economic explanations are also given.

Improving the Predictive Value of Phytochrome Photoequilibrium: Consideration of Spectral Distortion Within a Leaf.

The ratio of active phytochrome (Pfr) to total phytochrome (Pr + Pfr), called phytochrome photo-equilibrium (PPE; also called phytochrome photostationary state, PSS) has been used to explain shade avoidance responses in both natural and controlled environments. PPE is commonly estimated using measurements of the spectral photon distribution (SPD) above the canopy and photoconversion coefficients. This approach has effectively predicted morphological responses when only red and far-red (FR) photon fluxes have varied, but controlled environment research often utilizes unique ratios of wavelengths so a more rigorous evaluation of the predictive ability of PPE on morphology is warranted. Estimations of PPE have rarely incorporated the optical effects of spectral distortion within a leaf caused by pigment absorbance and photon scattering. We studied stem elongation rate in the model plant cucumber under diverse spectral backgrounds over a range of one to 45% FR (total photon flux density, 400–750 nm, of 400 μmol m–2 s–1) and found that PPE was not predictive when blue and green varied. Preferential absorption of red and blue photons by chlorophyll results in an SPD that is relatively enriched in green and FR at the phytochrome molecule within a cell. This can be described by spectral distortion functions for specific layers of a leaf. Multiplying the photoconversion coefficients by these distortion functions yields photoconversion weighting factors that predict phytochrome conversion at the site of photon perception within leaf tissue. Incorporating spectral distortion improved the predictive value of PPE when phytochrome was assumed to be homogeneously distributed within the whole leaf. In a supporting study, the herbicide norflurazon was used to remove chlorophyll in seedlings. Using distortion functions unique to either green or white cotyledons, we came to the same conclusions as with whole plants in the longer-term study. Leaves of most species have similar spectral absorbance so this approach for predicting PPE should be broadly applicable. We provide a table of the photoconversion weighting factors. Our analysis indicates that the simple, intuitive ratio of FR (700–750 nm) to total photon flux (far-red fraction) is also a reliable predictor of morphological responses like stem length.

Importance of Distortion Function for the Reconstruction of Original Observations from the Estimates in Wireless Sensor Networks

The volatility of the wireless communication-channel connectivity and multihop data packet transmitting process results in the reception of distorted information by the terminal sensor node in the Wireless Sensor Network. Reconstruction of the source of the event occurrence is of prime importance at the sink. In this paper, we will explore the importance of the distortion function in the reconstruction of the original observations from the estimates. We will also study various distortion functions proposed for different applications like MAC and energy harvesting.

Pseudocapacitive charge storage in layered oxides SrLaFe1−xCoxO4−δ (x = 0–1)

Pseudocapacitive energy storage has been demonstrated for three materials belonging to a family of layered oxides. This work is the first report on the observation of charge-storage properties in this family of materials that feature 2-dimensional layers, consisting of MO6 units (M = transition metal). The spaces between layers are occupied by alkaline-earth or rare-earth metals. Systematic trends have been demonstrated, where the charge-storage properties are enhanced as a function of Co-concentration, structural distortion and oxygen-deficiency in SrLaFe1−xCoxO4−δ. Symmetric pseudocapacitor cells based on these materials show substantial specific capacitance, energy density and power density. They are also remarkably stable and retain their charge storage capacity even after 1000 cycles of charge-discharge. The observation of pseudocapacitive charge-storage properties in these materials indicates the potential of this class of layered oxides for utilization in energy storage.

New Formulation and Computation of NRDF for Time-Varying Multivariate Gaussian Processes With Correlated Noise

We derive a new formulation of nonanticipative rate distortion function (NRDF) for time-varying multivariate Gauss-Markov processes driven by correlated noise described by a first order autoregressive moving average (ARMA(1,1)) process with mean-squared error (MSE) distortion constraint. To arrive to this formulation, we first show that the Gauss-Markov process with correlated noise can be compactly written as a linear functional of the lagged by one sample of the sufficient statistic of the correlated noise and its orthogonal innovations process. Then, we use this structural result to a general low delay quantization problem where we choose to design the encoder and the decoder policies of a multi-input multi-output (MIMO) system with given the past sample of the sufficient statistic of the correlated noise process. For jointly Gaussian processes, we find the minimization problem that needs to be solved, obtain its optimal realization and solve it by showing that is semidefinite representable. Interestingly, the optimal realization of this problem reveals that it suffices only the decoder to have access to the given past sufficient statistic of the correlated noise process but not necessarily the encoder. For scalar-valued processes, we also derive a new analytical expression. The generality of our results (both for vector and scalar processes) is shown by recovering various special cases and known results obtained for independent noise processes.

Portfolio optimization under safety first expected utility with nonlinear probability distortion

In this paper, we study a portfolio selection problem under safety first expected utility model with distortion (SFEUD model) where the underlying probability scale is transformed by a nonlinear distortion function. By employing the quantile formulation and the relaxation method, we obtain the general form of optimal solution to the problem, and the necessary and sufficient condition for existing such an optimal solution is also proved. We further demonstrate an analytical solution to the optimal strategies under four different monotonic cases. What’s more, the optimal terminal wealth process is replicated into a portfolio of options and deposits under specific circumstances. In addition, we empirically verify the model implication and figure out that investors’ realization of disaster risk can explain the price change of call options to some degree.

Меры «VaR в степени t» и «ES в степени t» как новые подклассы мер катастрофических финансовых рисков во множестве мер риска искажения (Measures “VaR to the Extent of T” and “ES to the Extent of t” As New Subclasses of Measures of Catastrophic Financial Risks in a Variety of Measures of Risk Distortion)

Russian Abstract: Меры риска искажения в последние годы широко используются в финансовых и страховых приложениях благодаря своим привлекательным свойствам. Целью работы является исследование вопроса принадлежности мер риска «VaR в степени t», введенных в научный оборот автором к классу мер риска искажения, а также описание соответствующих функций искажения. В данной работе вводится новый класс мер риск «ES в степени t» и также исследуется вопрос о принадлежности этих мер риска, к классу мер риска искажения, а также описания соответствующих функций искажения. В работе описывается композитный метод, как метод построения новых функций искажения и соответствующих мер риска искажения. Этот метод используется для доказательства принадлежности мер риска «VaR в степени t» и «ES в степени t» к классу мер риска искажения. Представлены также различные примеры для иллюстрации соответствующих понятий и результатов, проявляющих важность мер риска «VaR в степени t» и «ES в степени t», как подмножеств мер риска искажения, позволяющих выявлять финансовые риски различной степени катастрофичности. Автор делает вывод, что меры риска «VaR в степени t» и «ES в степени t» может быть полезно в практике риск-менеджмента компаний при оценке маловероятных рисков высокой катастрофичности. English Abstract: Distortion risk measures have been widely used in financial and insurance applications in recent years due to their attractive properties. The aim of the work is to study the issue of belonging to the VaR to degree t risk measures introduced into scientific circulation by the author to the class of distortion risk measures, as well as to describe the corresponding distortion functions. This work introduces a new class of risk measures ES to degree t and also examines the issue of belonging to these risk measures, to the class of distortion risk measures, as well as descriptions of the corresponding distortion functions. The paper describes the composite method as a method for constructing new distortion functions and corresponding distortion risk measures. This method is used to prove that the risk measures VaR to degree t and ES to degree t belong to the class of distortion risk measures. Various examples are also presented to illustrate relevant concepts and outcomes that demonstrate the importance of VaR to degree t and ES to degree t risk measures as subsets of distortion risk measures that identify financial risks of varying degrees of catastrophicity. The author concludes that the risk measures VaR to the extent of t and ES to the extent of t can be useful in the practice of risk management of companies in assessing unlikely risks of high catastrophe.

A generalization of Archimedean and Marshall-Olkin copulas family

In this paper, we consider a new family of multivariate copulas described by a sequence of functions, named as AMO copula. The set of AMO copulas corresponds to a class of multivariate shock models with the Archimedean type of dependence. Sufficient conditions on the involved sequence of functions to obtain a multivariate copula are given and the probabilistic structure of the AMO copula is provided. We show that the family of AMO copulas is a generalization of Archimedean and Marshall-Olkin copulas family, and it includes some well-known copulas as specific cases. An alternative method for generating random vectors from AMO copulas via distortion functions is provided. In addition, a singular component along the main diagonal of the AMO copula is also verified. Finally, the tail behaviors of AMO copulas are discussed and some numerical illustrations are provided.

Non-discrete k-order additivity of a set function and distorted measure

In this study, we generalize the concept of the k-order additivity of a set function. First, we discuss the Möbius transform for a non-discrete set function. Next, we generalize the definition of the k-order additivity of a set function using the Möbius transform and provide the equivalent conditions for the k-order additivity. Furthermore, we consider the k-order additivity of the distorted monotone measure. We prove that under certain conditions, a distorted measure is k-order additive if and only if the distortion function is a polynomial of k-th order.

Range Utility Theory

We introduce range utility theory for decisions under risk. Two functions are implicated in the representation of preferences: a traditional utility function for wealth---or changes in wealth---and a range distortion function. The latter introduces a local deformation of the utility function on the range under consideration, possibly magnifying the sensitivity to intermediate outcomes. In a sense we make precise, range utility theory is an alternative way to extend the binary rank dependent model to more than two outcomes. It can account for the fourfold pattern, as well as for the preference reversal phenomenon. When the range is fixed, range utility is linear in probabilities. We illustrate this advantage in game theory applications.

Monitoring Real-Time Status of Analog Sources: A Cross-Layer Approach

Real-time status updating or monitoring plays a critical role in emerging applications including Industrial Internet of Things (IIoT) and Vehicular-to-Everything (V2X) systems. In these applications, the real-time status is mostly characterized by analog signal samples desiring lossy compression before digital transmissions. However, how to ensure the data freshness while reducing the distortion due to lossy compression still remains open. In this paper, we are interested in a cross-layer framework aiming at achieving low Age-of-Information (AoI) and compression distortion concurrently in real-time monitoring over fading channels. More specifically, a cross-layer optimization is formulated to jointly control the lossy compression in the application layer and data transmission in the physical layer. We present a hierarchical solution method by decomposing the cross-layer optimization into inner and outer problems. The objective of the inner problem, solved by convex optimization, is to minimize an age-weighted distortion function and strike the optimal tradeoff between the instantaneous AoI and compression loss. The objective of the outer problem, solved by dimension-reduced Constrained Markov Decision Process (CMDP), is to acquire the optimal scheduling policy reducing the average AoI and distortion. We demonstrate the structural results of the optimal cross-layer design, which substantially reduces the protocol complexity in practice.