Smooth invariant foliations without a bunching condition and Belitskii's C1C^{1} linearization for random dynamical systems

Smooth linearization is one of the central themes in the study of dynamical systems. The classical Belitskii's $C^1$ linearization theorem has been widely used in the investigation of dynamical behaviors such as bifurcations, mixing, and chaotic behaviors due to its minimal requirement of partial second order non-resonances and low regularity of systems. In this article, we revisit Belitskii's $C^1$ linearization theorem by taking an approach based on smooth invariant foliations and study this problem for a larger class of dynamical systems ({\it random dynamical systems}). We assumed that the linearized system satisfies the condition of Multiplicative Ergodic Theorem and the associated Lyapunov exponents satisfy Belitskii's partial second order non-resonant conditions. We first establish the existence of $C^{1,\beta}$ stable and unstable foliations without assuming the bunching condition for Lyapunov exponents, then prove a $C^{1,\beta}$ linearization theorem of Belitskii type for random dynamical systems. As a result, we show that the classical Belitskii's $C^1$ linearization theorem for a $C^{2}$ diffeomorphism $F$ indeed holds without assuming all eigenspaces of the linear system $DF(0)$ are invariant under the nonlinear system $F$, a requirement previously imposed by Belitskii in his proof

Secured green communication scheme for interference alignment based networks

In this paper, a new security and green communication scheme is proposed to the Interference-Alignment (IA) based networks. To achieve a secured communication, full-duplex receivers are utilized to transmit artificial noise (AN). Both the signals and the ANs are used to harvest energy to realize green communication. For these reasons, the feasible conditions of this scheme are analyzed first. Secondly, the average transmission rate, the secrecy performance and the harvested energy are investigated. Thirdly, an optimization scheme of simultaneous wireless information and power transfer (SWIPT) is given to optimize the information transmission and the energy harvesting efficiency. Meanwhile, an improved IA iteration algorithm is designed to eliminate both the AN and the interference. Furthermore, relay cooperation is considered and its system performance is analyzed. The simulations show that the target average transmission rate is not affected by AN, while the secrecy performance can be greatly improved. The energy harvesting efficiency is also better than the traditional schemes. As expected, the average transmission rate further is improved with the relay cooperation

Natural Coevolution of Tumor and Immunoenvironment in Glioblastoma.

Isocitrate dehydrogenase (IDH) wild-type glioblastoma (GBM) has a dismal prognosis. A better understanding of tumor evolution holds the key to developing more effective treatment. Here we study GBM\u27s natural evolutionary trajectory by using rare multifocal samples. We sequenced 61,062 single cells from eight multifocal IDH wild-type primary GBMs and defined a natural evolution signature (NES) of the tumor. We show that the NES significantly associates with the activation of transcription factors that regulate brain development, including MYBL2 and FOSL2. Hypoxia is involved in inducing NES transition potentially via activation of the HIF1A-FOSL2 axis. High-NES tumor cells could recruit and polarize bone marrow-derived macrophages through activation of the FOSL2-ANXA1-FPR1/3 axis. These polarized macrophages can efficiently suppress T-cell activity and accelerate NES transition in tumor cells. Moreover, the polarized macrophages could upregulate CCL2 to induce tumor cell migration. SIGNIFICANCE: GBM progression could be induced by hypoxia via the HIF1A-FOSL2 axis. Tumor-derived ANXA1 is associated with recruitment and polarization of bone marrow-derived macrophages to suppress the immunoenvironment. The polarized macrophages promote tumor cell NES transition and migration. This article is highlighted in the In This Issue feature, p. 2711

A Competitive Reconfiguration Approach To Autonomous Fault Handling Using Genetic Algorithms

In this dissertation, a novel self-repair approach based on Consensus Based Evaluation (CBE) for autonomous repair of SRAM-based Field Programmable Gate Arrays (FPGAs) is developed, evaluated, and refined. An initial population of functionally identical (same input-output behavior), yet physically distinct (alternative design or place-and-route realization) FPGA configurations is produced at design time. During run-time, the CBE approach ranks these alternative configurations after evaluating their discrepancy relative to the consensus formed by the population. Through runtime competition, faults in the logical resources become occluded from the visibility of subsequent FPGA operations. Meanwhile, offspring formed through crossover and mutation of faulty and viable configurations are selected at a controlled re-introduction rate for evaluation and refurbishment. Refurbishments are evolved in-situ, with online real-time input-based performance evaluation, enhancing system availability and sustainability, creating an Organic Embedded System (OES). A fault tolerance model called N Modular Redundancy with Standby (NMRSB) is developed which combines the two popular fault tolerance techniques of NMR and Standby fault tolerance in order to facilitate the CBE approach. This dissertation develops two of instances of the NMRSB system - Triple Modular Redundancy with Standby (TMRSB) and Duplex with Standby (DSB). A hypothetical Xilinx Virtex-II Pro FPGA model demonstrates their viability for various applications including a 3-bit x 3-bit multiplier, and the MCNC91 benchmark circuits. Experiments conducted on the model iii evaluate the performance of three new genetic operators and demonstrate progress towards a completely self-contained single-chip implementation so that the FPGA can refurbish itself without requiring a PC host to execute the Genetic Algorithm. This dissertation presents results from the simulations of multiple applications with a CBE model implemented in the C++ programming language. Starting with an initial population of 20 and 30 viable configurations for TMRSB and DSB respectively, a single stuck-at fault is introduced in the logic resources. Fault refurbishment experiments are conducted under supervision of CBE using a fitness state evaluation function based on competing outputs, fitness adjustment, and different level threshold. The device remains online throughout the process by which a complete repair is realized with Hamming Distance and Bitweight voting schemes. The results indicate a Hamming Distance TMRSB approach can prevent the most pervasive fault impacts and realize complete refurbishment. Experimental results also show that the Autonomic Layer demonstrates 100% faulty component isolation for both Functional Elements (FEs) and Autonomous Elements (AEs) with randomly injected single and multiple faults. Using logic circuits from the MCNC-91 benchmark set, availability during repair phases averaged 75.05%, 82.21%, and 65.21% for the z4ml, cm85a, and cm138a circuits respectively under stated conditions. In addition to simulation, the proposed OES architecture synthesized from HDL was prototyped on a Xilinx Virtex II Pro FPGA device supporting partial reconfiguration to demonstrate the feasibility for intrinsic regeneration of the selected circuit

Autonomous Fpga Fault Handling Through Competitive Runtime Reconfiguration

An autonomous self-repair approach for SRAM-based FPGAs is developed based on Competitive Runtime Reconfiguration (CRR). Under the CRR technique, an initial population of functionally identical (same input-output behavior), yet physically distinct (alternative design or place-and-route realization) FPGA configurations is produced at design time. At run-time, these individuals compete for selection based on a fitness function favoring fault-free behavior. Hence, any physical resource exhibiting an operationally-significant fault decreases the fitness of those configurations which use it. Through runtime competition, the presence of the fault becomes occluded from the visibility of subsequent FPGA operations. Meanwhile, the offspring formed through crossover and mutation of faulty and viable configurations are reintroduced into the population. This enables evolution of a customized fault-specific repair, realized directly as new configurations using the FPGA \u27s normal throughput processing operations. Multiple phases of the fault handling process including Detection, Isolation, Diagnosis, and Recovery are integrated into a single cohesive approach. FPGA-based multipliers are examined as a case study demonstrating evolution of a complete repair for a 3-bit × 3-bit multiplier from several stuck-at-faults within a few thousand iterations. Repairs are evolved in-situ, in real-time, without test vectors, while allowing the FPGA to remain partially online