Matrix methods for perfect signal recovery underlying range space of operators

The purpose of this work is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by a new matrix method. To this end, first we obtain more structures of the canonical $K$-dual. % and survey optimal $K$-dual problem under probabilistic erasures. Then, we survey the problem of recovering and robustness of signals when the erasure set satisfies the minimal redundancy condition or the $K$-frame is maximal robust. Furthermore, we show that the error rate is reduced under erasures if the $K$-frame is of uniform excess. Toward the protection of encoding frame (K-dual) against erasures, we introduce a new concept so called $(r,k)$-matrix to recover lost data and solve the perfect recovery problem via matrix equations. Moreover, we discuss the existence of such matrices by using minimal redundancy condition on decoding frames for operators. We exhibit several examples that illustrate the advantage of using the new matrix method with respect to the previous approaches in existence construction. And finally, we provide the numerical results to confirm the main results in the case noise-free and test sensitivity of the method with respect to noise.

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.

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’s 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.

Severe Median Nerve Injured After Local Corticosteroid Injection in A Carpal Tunnel Syndrome Patient ——A Case Report

Background The corticosteroid injection is known to be an effective and safe treatment for carpal tunnel syndrome, no serious complications was reported in previous literature. We report a severe median nerve injured case after corticosteroid injection. Case presentation: A 55-year-old female patient was admitted to our hospital because of numbness in her right finger for 10 years. Total six corticosteroid injections were performed in the past 2 years, and the symptoms did not relief significantly. She underwent ligament resection and median nerve release. The median nerve epineurium thickened and the scar was obvious during the surgery. The patient made a perfect recovery after surgery. Conclusions: The accurate preoperative assessment and personalized treatment are very important for peripheral nerve entrapment disease.

DANA Universal Dataflow Analysis for Gate-Level Netlist Reverse Engineering

Reverse engineering of integrated circuits, i.e., understanding the internals of Integrated Circuits (ICs), is required for many benign and malicious applications. Examples of the former are detection of patent infringements, hardware Trojans or Intellectual Property (IP)-theft, as well as interface recovery and defect analysis, while malicious applications include IP-theft and finding insertion points for hardware Trojans. However, regardless of the application, the reverse engineer initially starts with a large unstructured netlist, forming an incomprehensible sea of gates.This work presents DANA, a generic, technology-agnostic, and fully automated dataflow analysis methodology for flattened gate-level netlists. By analyzing the flow of data between individual Flip Flops (FFs), DANA recovers high-level registers. The key idea behind DANA is to combine independent metrics based on structural and control information with a powerful automated architecture. Notably, DANA works without any thresholds, scenario-dependent parameters, or other “magic” values that the user must choose. We evaluate DANA on nine modern hardware designs, ranging from cryptographic co-processors, over CPUs, to the OpenTitan, a stateof- the-art System-on-Chip (SoC), which is maintained by the lowRISC initiative with supporting industry partners like Google and Western Digital. Our results demonstrate almost perfect recovery of registers for all case studies, regardless whether they were synthesized as FPGA or ASIC netlists. Furthermore, we explore two applications for dataflow analysis: we show that the raw output of DANA often already allows to identify crucial components and high-level architecture features and also demonstrate its applicability for detecting simple hardware Trojans.Hence, DANA can be applied universally as the first step when investigating unknown netlists and provides major guidance for human analysts by structuring and condensing the otherwise incomprehensible sea of gates. Our implementation of DANA and all synthesized netlists are available as open source on GitHub.

A Systematic Review of various Reversible Data Hiding Techniques in Digital Images

: Nowadays, Internet has become everything, it made things simpler like online transaction, online shopping; sharing images, videos, audios, messages on social media; uploading some important information on Google drives etc. So the very first requirement is to secure and protect digital contents from any unauthorized access. Reversible Data Hiding (RDH) is one of the ways to provide security in digital content, through which useful information can be embedded in the digital content and at the receiver end the perfect recovery of cover media as well as embedded message is possible. In this digital era, digital images are most rapidly used for communication purpose; therefore the security of digital images is in high demand. RDH in digital images has gained a lot of interest during the last few decades. This paper describes and investigates a systematic review on various RDH techniques for digital images, which can be broadly classified into five categories: Lossless Compression Based, Histogram Modification Based, Difference Expansion Based, Interpolation Based and Encrypted image Based techniques.