Perfect Recovery Research Articles

Binary Signal Perfect Recovery From Partial DFT Coefficients

How to perfectly recover a binary signal from its discrete Fourier transform (DFT) coefficients is studied. The theoretic lower bound and a practical recovery strategy are derived and developed. The concept of ambiguity pair is introduced. This pair of signals has almost the same DFT coefficients except for some positions. It can prove that when the signal length is <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula>, then at least <inline-formula><tex-math notation="LaTeX">$\tau (N)$</tex-math></inline-formula> DFT coefficients must be sampled, where <inline-formula><tex-math notation="LaTeX">$\tau (N)$</tex-math></inline-formula> is the number of factors of the signal length <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula>. A recovery algorithm is proposed and implemented. It can achieve the lowed bound for length <inline-formula><tex-math notation="LaTeX">$N=2^{m}, m \leq 6$</tex-math></inline-formula>. To overcome the length limitation problem, a more practical recovery method is also proposed and implemented for <inline-formula><tex-math notation="LaTeX">$N=2^{m}, m&gt;6$</tex-math></inline-formula>. We can sample 11&#x0025; of the total DFT coefficients to perfectly recover the binary signal. We also extend the concept of ambiguity pair to other discrete transforms (DCT and WHT) and two-dimensional DFT cases.

Reversal of pixel rotation: A reversible data hiding system towards cybersecurity in encrypted images

Due to privacy and security concerns, the researches of reversible data hiding in encrypted images (RDHEI) have become increasingly important. Conventional schemes vacate the spare room after image encryption (VRAE) suffer from the low embedding rate, high error rate of data extraction, and imperfect image recovery. To address these issues, we propose a separable reversible data hiding scheme for encrypted images that utilizes a novel pixel rotation technique to embed data into fully encrypted images. The block complexities of four decrypted rotation states are considered when recovering image. To realize perfect image recovery, we further devise a lossless version (LPR-RDHEI). Experimental results demonstrate that the proposed PR-RDHEI scheme achieves an embedding rate of 0.4994 bpp on average and ensures lossless data extraction. Meanwhile, the proposed LPR-RDHEI scheme still has a 0.4494 bpp embedding rate on average. The embedding rates of our two schemes are significantly improved compared with state-of-the-arts.

Investigations of mechanical properties and deformation behaviors of the Cr modified Ti–Au shape memory alloys

In view of the population aging issues, the functional materials, Ti–Au–Cr shape memory alloys (SMAs), have been explored in this study for the crucial biomaterial applications. This ternary system was chosen for solving the hypersensitivity problem in the conventional SMAs containing Ni and also for its high X–ray contrast, which is an essential requirement in medical applications. Physical metallurgy methods were utilized for the specimen preparation and the fundamental properties and functional performances were also evaluated. Cold–workability was greatly improved with the Cr addition. The parent β–phase was stabilized by 4.5 at.% Cr alloying concentration, while the discrimination of the α′–martensite phase and the α′′–martensite phase at low Cr addition concentrations was clarified. Lattice parameters and the deformation strains were further calculated based on the results of the X–ray diffraction analysis. Most of the specimens possessed shape recovery upon heating, while the Ti–4.0Au–5.5Cr alloy showed an almost perfect shape recovery rate of 96.7%. Pseudoelastic behavior was observed in most of the alloys. The austenite transformation temperatures were determined by the step–by–step heating processes.

The planted matching problem: Phase transitions and exact results

We study the problem of recovering a planted matching in randomly weighted complete bipartite graphs Kn,n. For some unknown perfect matching M∗, the weight of an edge is drawn from one distribution P if e∈M∗ and another distribution Q if e∉M∗. Our goal is to infer M∗, exactly or approximately, from the edge weights. In this paper we take P=exp(λ) and Q=exp(1/n), in which case the maximum-likelihood estimator of M∗ is the minimum-weight matching Mmin. We obtain precise results on the overlap between M∗ and Mmin, that is, the fraction of edges they have in common. For λ≥4 we have almost perfect recovery, with overlap 1−o(1) with high probability. For λ<4 the expected overlap is an explicit function α(λ)<1: we compute it by generalizing Aldous’ celebrated proof of the ζ(2) conjecture for the unplanted model, using local weak convergence to relate Kn,n to a type of weighted infinite tree, and then deriving a system of differential equations from a message-passing algorithm on this tree.

Sparse classification: a scalable discrete optimization perspective

We formulate the sparse classification problem of n samples with p features as a binary convex optimization problem and propose a outer-approximation algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm finds optimal solutions for n and p in the 10,000 s within minutes. On synthetic data our algorithm achieves perfect support recovery in the large sample regime. Namely, there exists an \(n_0\) such that the algorithm takes a long time to find an optimal solution and does not recover the correct support for \(n<n_0\), while for \(n\geqslant n_0\), the algorithm quickly detects all the true features, and does not return any false features. In contrast, while Lasso accurately detects all the true features, it persistently returns incorrect features, even as the number of observations increases. Consequently, on numerous real-world experiments, our outer-approximation algorithms returns sparser classifiers while achieving similar predictive accuracy as Lasso. To support our observations, we analyze conditions on the sample size needed to ensure full support recovery in classification. For k-sparse classification, and under some assumptions on the data generating process, we prove that information-theoretic limitations impose \(n_0 < C \left( 2 + \sigma ^2\right) k \log (p-k)\), for some constant \(C>0\).

A new method to build an associative memory model

An associative memory is an artificial neural network model designed to store and recall input-output patterns pairs by association. A new method for obtaining two associative memories +M and -M is presented in this article, which uses a framework focused on two new binary operations boxplus and boxminus, and a unary operation called projection. The conditions to obtaining perfect recovery and the noise boundaries that the memories can tolerate are studied. Memories +M and -M are robust to additive and subtractive noise, respectively, both types converge in one-step and operate in heteroassociative and autoassociative modes. The performance of the proposed memories is tested against other memory models under identical conditions using the gamma binary distance for measuring similarity between binary patterns. The computer simulation results based on the average of 500 trials with the binary set of 26 lowercase letters of 7x7 pixel size, showed that the proposed memories in autoassociative mode exhibited a gamma binary distance of above .8, .75 and .7 by distorting up to 10 pixels by additive, subtractive, and mixed noise, respectively, which implied that the recovered images had a high similarity. In absence of noise the performance was excellent, i.e., the 100% of the recovered images were identical.

Subsampled Circulant Matrix Based Wideband Spectrum Sensing Using Fusion Based Recovery Algorithm

This paper reflects the problem of wideband spectrum recovery. The demand for spectrum usage is increasing exponentially as the wireless technologies rules the world. To meet these needs, Cognitive Radio is one of the emerging technologies, which intelligently allots the spectrum to the secondary users. Since the spectrum is wideband, the capability of spectrum sensing is improved by introducing sub-nyquist sampling under compressive sensing framework. In this paper, a sub-nyquist sampling technique of Modulated Wideband Converter (MWC) is used as it possesses m-parallel channels providing fast sensing and robust structure. A circulant matrix method is used to improve the hardware complexity of MWC. Also at the reconstruction of MWC, a fusion based recovery algorithm is proposed which became an added benefit for perfect recovery of the support. The results are compared with conventional MWC in terms of support recovery, mean square error and SNR gain. Simulations proved that the proposed algorithm performs superior at low as well as high SNR with increased gain.

Thermodynamic Analysis of a Conceptual Fixed-Bed Solar Thermochemical Cavity Receiver–Reactor Array for Water Splitting Via Ceria Redox Cycling

We propose a novel solar thermochemical receiver–reactor array concept for hydrogen production via ceria redox cycling. The receiver–reactor array can improve the solar-to-fuel efficiency by realizing the heat recuperation, reduction, and oxidation processes synchronously. A linear matrix model and a lumped parameter model are developed to predict thermal performance of the new solar thermochemical system. The system thermal performance is characterized by heat recovery effectiveness of solid-phase and solar-to-fuel efficiency. Investigated parameters include reduction temperature, oxygen partial pressure, number of receiver–reactors, concentration ratio, and gas-phase heat recovery effectiveness. For baseline conditions, the solid-phase heat recovery effectiveness and the solar-to-fuel efficiency are found to be 81% and 27%, respectively. For perfect gas-phase heat recovery and a solar concentration ratio of 5,000, the solar-to-fuel efficiency exceeds 40%.

The perfect recovery? Interactive influence of perfectionism and spillover work tasks on changes in exhaustion and mood around a vacation.

This study examined week-level changes in affective well-being among school teachers as they transitioned into and out of a 1-week vacation. In addition, we investigated the interactive influence of personality characteristics (specifically perfectionism) and spillover work activities during the vacation on changes in teachers' well-being. A sample of 224 teachers completed study measures across 7 consecutive weeks, spanning the period before, during, and after a midterm vacation (providing a total of 1,525 responses across the study period). Results obtained from discontinuous multilevel growth models revealed evidence of a vacation effect, indicated by significant reductions in emotional exhaustion, anxiety, and depressed mood from before to during the vacation. Across 4 working weeks following the vacation, exhaustion and negative mood exhibited a nonlinear pattern of gradual convergence back to prevacation levels. Teachers with a higher level of perfectionistic concerns experienced elevated working week levels of exhaustion, anxious mood, and depressed mood, followed by pronounced reductions in anxious and depressed mood as they transitioned into the vacation. However, a strongly beneficial effect of the vacation was only obtained by perfectionistic teachers who refrained from spillover work tasks during the vacation. This pattern of findings is consistent with a diathesis-stress model, in that the perfectionists' vulnerability was relatively dormant (or deactivated) during a respite from job demands. Our results may provide an explanation for why engaging in work-related activities during vacations has previously exhibited weak relationships with employees' recovery and well-being. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Scalable Incremental Nonconvex Optimization Approach for Phase Retrieval

We aim to find a solution \({\varvec{x}}\in {\mathbb {C}}^n\) to a system of quadratic equations of the form \(b_i=|{\varvec{a}}_i^*{\varvec{x}}|^2\), \(i=1,2,\ldots ,m\), e.g., the well-known NP-hard phase retrieval problem. As opposed to recently proposed state-of-the-art nonconvex methods, we revert to the semidefinite relaxation (SDR) PhaseLift convex formulation and propose a successive and incremental nonconvex optimization algorithm, termed as IncrePR, to indirectly minimize the resulting convex problem on the cone of positive semidefinite matrices. Our proposed method overcomes the excessive computational cost of typical SDP solvers as well as the need of a good initialization for typical nonconvex methods. For Gaussian measurements, which is usually needed for provable convergence of nonconvex methods, restart-IncrePR solving three consecutive PhaseLift problems outperforms state-of-the-art nonconvex gradient flow based solvers with a sharper phase transition of perfect recovery and typical convex solvers in terms of computational cost and storage. For more challenging structured (non-Gaussian) measurements often occurred in real applications, such as transmission matrix and oversampling Fourier transform, IncrePR with several consecutive repeats can be used to find a good initial guess. With further refinement by local nonconvex solvers, one can achieve a better solution than that obtained by applying nonconvex gradient flow based solvers directly when the number of measurements is relatively small. Extensive numerical tests are performed to demonstrate the effectiveness of the proposed method.

Carbonaceous matter degradation by fungal enzyme treatment to improve Ag recovery from an Au-Ag-bearing concentrate

Sequential treatment was applied to carbonaceous Au-Ag-bearing ore concentrate to maximize the Au and Ag recovery. In the preliminary test, the present carbonaceous ore had well liberated and exposed type of gold grains, which are not refractory, but included mainly three types of Ag presented as electrum, hessite (Ag2Te) and Ag-bearing other minerals. Au recovery was ∼100% without any treatment, meanwhile Ag recovery was only 33.3%. The sequential treatment comprises two oxidation steps: (a) mixed culture of iron- and sulfur-oxidizing microorganisms at pH 1.2, followed by (b) cell-free spent medium (CFSM) at pH 4.0 from a white rot-fungus, Phanerochaete chrysosporium, which includes lignin-degrading enzymes. As a result, Ag recovery was 55.5% after the first step and greatly improved to ∼100%, including the dissolved Ag+ concentration in the first step of acid treatment. Although the acidophilic iron-oxidizing microorganisms were inhibited by dissolved Ag+ and Cd2+ ions, the strong acidic conditions dissolved hessite and Ag-bearing oxide minerals. However, the remaining carbonaceous matter acted to sorb Ag(CN)2− in cyanidation, causing the recovery loss. In the next step the lignin-degrading enzymes degraded carbonaceous matter in the ore. This step is necessary to avoid the adsorption of Ag(CN)2− on graphitic carbonaceous matter, leading a mostly perfect recovery of the remaining Ag in the solid residues, without necessity of alkaline washing. The sequential treatment including enzymatic lignin-degrading process was also effective in carbonaceous silver ore avoiding the emission of air pollutants.

Martensitic Transformation of High-Entropy and Medium-Entropy Shape Memory Alloys

As new generation of high-temperature shape memory alloys, high-entropy alloys (HEAs) have been attracted for strong solid-solution hardened alloys due to their severe lattice distortion and sluggish diffusion. TiPd is the one potential high-temperature shape memory alloys because of its high martensitic transformation temperature above 500 °C. As constituent elements, Zr expected solid-solution hardening, Pt expected increase of transformation temperature, Au expected keeping transformation temperature, and Co expected not to form harmful phase. By changing the alloy composition slightly, two HEAs and two medium entropy alloys (MEAs) were prepared. Only two MEAs, Ti45Zr5Pd25Pt20Au5, and Ti45Zr5Pd25Pt20Co5 had the martensitic transformation. The perfect recovery was obtained in Ti45Zr5Pd25Pt20Co5 during the repeated thermal cyclic test, training, under 200 MPa. On the other hand, the small irrecoverable strain was remained in Ti45Zr5Pd25Pt20Au5 during the training under 150 MPa because of the small solid-solution hardening effect. It indicates that Ti45Zr5Pd25Pt20Co5 is the one possible HT-SMA working between 342 and 450 °C.

Corona Virus (Covid 19) and Pregnancy

Abstract The Corona Virus global has affected many parts of life, through antenatal, intra and postpartum period. Due to immunologically and physically adaptive perinatal variations, this is fully recognized that pregnancy woman usually has an excessed disposition to contamination In spite of this, the majorities of mothers influenced by Corona Virus to time has offered mild symptoms and produce perfect recovery. However, it is no safe evidence for transition of the Corona Virus from pregnant women to neonatal during pregnancy period. The Corona Virus infection didn’t appear to excess probability of requirement for obstetric care during delivery, with well neonatal born through vaginal birth canal to pregnant women with the contamination. Next childbirth, the World Health Organization (WHO) advises mother with Corona Virus start breastfeeding within 1 hour of delivery, and attracts in skin to skin touch and kangaroo woman nursing. In addition to implementation of seek infection control provision, the pregnant women should share in usual preventive actions to avoid infection like washing hands before and after contacting the child and avoiding people who are ill.

Maximum Likelihood Estimation of Time-Varying Sparsity Level for Dynamic Sparse Signals

In the field of Compressed Sensing, estimation of sparsity level is very essential as the sparsity level determines the minimum number of (i) measurements to be obtained of a sparse signal during acquisition and (ii) iterations to be performed for many of the greedy techniques for the perfect recovery of the sparse signal from the obtained measurements. In this paper, we propose a Maximum Likelihood (ML) estimator to estimate the instantaneous sparsity level during acquisition and an ML sequence (MLS) estimator of sparsity levels during recovery. As the sparsity level varies in time due to the continuous birth of newer supporting components and death of existing supporting components, this paper models the sparsity level variation as a stochastic birth-death process. The real-world applications of the proposed estimators are presented on the compression of aircraft vibration signals and the estimation of wireless channels. The simulation results on real-world and model-generated data demonstrate the performance merits of the proposed estimators compared to other existing methods.

Content Based Medical Image Retrieval Using Multilevel Hybrid Clustering Segmentation with Feed Forward Neural Network

Content-Based Image Retrieval (CBIR) is another yet broadly recognized method for distinguishing images from monstrous and unannotated image databases. With the improvement of network and mixed media headways ending up being increasingly famous, customers are not content with the regular information retrieval progresses. So nowadays, Content-Based Image Retrieval (CBIR) is the perfect and fast recovery source. Lately, various strategies have been created to improve CBIR execution. Data clustering is an overlooked method of hiding formatting extraction from large data blocks. With large data sets, there is a possibility of high dimensionality Models are a challenging domain with both massive numerical accuracy and efficiency for multidimensional data sets. The calibration and rich information dataset contain the problem of recovery and handling of medical images. Every day, more medical images were converted to digital format. Therefore, this work has applied these data to manage and file a novel approach, the “Clustering (MHC) Approach Using Content-Based Medical Image Retrieval Hybrid.” This work is implemented as four levels. With each level, the effectiveness of job retention is improved. Compared to some of the existing works that are being done in the analysis of this work’s literature, the results of this work are compared. The classification and learning features are used to retrieve medical images in a database. The proposed recovery system performs better than the traditional approach; with precision, recall, F-measure, and accuracy of proposed method are 97.29%, 95.023%, 4.36%, and 98.55% respectively. The recommended approach is most appropriate for recuperating clinical images for various parts of the body.

TiPd- and TiPt-Based High-Temperature Shape Memory Alloys: A Review on Recent Advances

In this paper high-temperature shape memory alloys based on TiPd and TiPt are reviewed. The effect of the alloying elements in ternary TiPd and TiPt alloys on phase transformation and strain recovery is also discussed. Generally, the addition of alloying elements decreases the martensitic transformation temperature and improves the strength of the martensite and austenite phases. Additionally, it also decreases irrecoverable strain, but without perfect recovery due to plastic deformation. With the aim to improve the strength of high-temperature shape memory alloys, multi-component alloys, including medium- and high-entropy alloys, have been investigated and proposed as new structural materials. Notably, it was discovered that the martensitic transformation temperature could be controlled through a combination of the constituent elements and alloys with high austenite finish temperatures above 500 °C. The irrecoverable strain decreased in the multi-component alloys compared with the ternary alloys. The repeated thermal cyclic test was effective toward obtaining perfect strain recoveries in multi-component alloys, which could be good candidates for high-temperature shape memory alloys.

Petz map and Python\u2019s lunch

We look at the interior operator reconstruction from the point of view of Petz map and study its complexity. We show that Petz maps can be written as precursors under the condition of perfect recovery. When we have the entire boundary system its complexity is related to the volume/action of the wormhole from the bulk operator to the boundary. When we only have access to part of the system, Python’s lunch appears and its restricted complexity depends exponentially on the size of the subsystem one loses access to.

The Limiting Poisson Law of Massive MIMO Detection With Box Relaxation

Estimating a binary vector from noisy linear measurements is a prototypical problem for MIMO systems. A popular algorithm, called the box-relaxation decoder, estimates the target signal by solving a least squares problem with convex constraints. This article shows that the performance of the algorithm, measured by the number of incorrectly-decoded bits, has a limiting Poisson law. This occurs when the sampling ratio and noise variance, two key parameters of the problem, follow certain scalings as the system dimension grows. Moreover, at a well-defined threshold, the probability of perfect recovery is shown to undergo a phase transition that can be characterized by the Gumbel distribution. Numerical simulations corroborate these theoretical predictions, showing that they match the actual performance of the algorithm even in moderate system dimensions.

Low cost DNA data storage using photolithographic synthesis and advanced information reconstruction and error correction

Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. The current hamstring of DNA data storage systems—both in cost and speed—is synthesis. The key idea for breaking this bottleneck pursued in this work is to move beyond the low-error and expensive synthesis employed almost exclusively in today’s systems, towards cheaper, potentially faster, but high-error synthesis technologies. Here, we demonstrate a DNA storage system that relies on massively parallel light-directed synthesis, which is considerably cheaper than conventional solid-phase synthesis. However, this technology has a high sequence error rate when optimized for speed. We demonstrate that even in this high-error regime, reliable storage of information is possible, by developing a pipeline of algorithms for encoding and reconstruction of the information. In our experiments, we store a file containing sheet music of Mozart, and show perfect data recovery from low synthesis fidelity DNA.

Surface modification of polytetrafluoroethylene thin films by non-coherent UV light and water treatment for electrowetting applications

HypothesisThe electrowetting on dielectric or EWOD phenomenon is used in a wide range of applications, such as Liquid Lenses, Lab-on-Chip devices, or EWOD displays, among others. Its chemical resistance, electrical stability, ease of application, and low cost make polytetrafluoroethylene (PTFE) the preferred hydrophobic dielectric layer for such applications. However, the hydrophobic behaviour represents a challenge for spin coating other layers over its surface. As a consequence, several techniques are implemented to modify the surface of PTFE. These methods are complex, time-consuming, and produce morphology changes over the surface that are difficult and sometimes impossible to recover. In this work, we propose a new surface modification method that is based on a non-coherent UV light exposition method and a specific water treatment, that lead to a change from hydrophobic to hydrophilic, and a perfect recovery from hydrophilic to hydrophobic behaviour. ExperimentsIn this work, the fabrication of the hydrophobic layer treatment starts with the creation of a thin layer of alumina (Al2O3) over a glass substrate using an atomic layer deposition technique (ALD). A mixture of 10:1 FC40 solvent and Teflon Dupont AF1600 was coated over the alumina layer. The Teflon film was exposed to UV light produced by a low-pressure mercury (Hg) lamp for a period that ranges from 3−6 min. The results were analysed by scanning electron microscopy, x-ray spectroscopy, and static deionized water contact angle measurements. FindingsContact angles dependent on UV light exposure time were observed. From the scanning electron microscopy analysis, it was confirmed that the UV treatment does not produce morphology changes over the surface. Nevertheless, the x-ray spectroscopy revealed that the UV exposed samples react when they are brought into contact with deionized water, improving the adhesion of the surface. The original hydrophobic behaviour of the surface is recovered (up to 98 %) after 3 h of thermal treatment. Furthermore, the thermal recovery analysis reveals a correlation between the recovery percentage and the applied temperature.