Inevitability of Phase-locking in a Charge Pump Phase Lock Loop using Deductive Verification

Phase-locking in a charge pump (CP) phase lock loop (PLL) is said to be inevitable if all possible states of the CP PLL eventually converge to the equilibrium, where the input and output phases are in lock and the node voltages vanish. We verify this property for a CP PLL using deductive verification. We split this complex property into two sub-properties defined in two disjoint subsets of the state space. We deductively verify the first property using multiple Lyapunov certificates for hybrid systems, and use the Escape certificate for the verification of the second property. Construction of deductive certificates involves positivity check of polynomial inequalities (which is an NP-Hard problem), so we use the sound but incomplete Sum of Squares (SOS) relaxation algorithm to provide a numerical solution

Structural Mechanism of Smad4 Recognition by the Nuclear Oncoprotein Ski Insights on Ski-Mediated Repression of TGF-β Signaling

AbstractThe Ski family of nuclear oncoproteins represses TGF-β signaling through interactions with the Smad proteins. The crystal structure of the Smad4 binding domain of human c-Ski in complex with the MH2 domain of Smad4 reveals specific recognition of the Smad4 L3 loop region by a highly conserved interaction loop (I loop) from Ski. The Ski binding surface on Smad4 significantly overlaps with that required for binding of the R-Smads. Indeed, Ski disrupts the formation of a functional complex between the Co- and R-Smads, explaining how it could lead to repression of TGF-β, activin, and BMP responses. Intriguingly, the structure of the Ski fragment, stabilized by a bound zinc atom, resembles the SAND domain, in which the corresponding I loop is responsible for DNA binding

Formal verification of a digital PLL

Common AMS circuit are composed from blocks that can be modeled accurately using linear differential inclusions to enable verification of important properties using reachability analysis. This dissertation presents a formal verification of Digital Phase Locked Loop (PLL) using reachability techniques. PLLs are ubiquitous in analog mixed signal (AMS) designs and are widely used in modern communication equipment, clock generation for CPUs in computers, clock-acquisition in high-speed links etc. The most important property of a PLL is convergence, which means starting from any possible initial conditions, the PLL will eventually lock to the desired equilibrium. We model the digital PLL as a set of Ordinary Differential equation (ODEs), and discretize the weakly non-linear ODEs to linear differential inclusions. The transformation not only provides us an over approximation of the verification problem but also provides the basis for a sound proof. We present the verification of a digital PLL using real tools, SpaceEx and Coho. In particular, we show how each component of the digital PLL can be modelled as a hybrid automaton. Due to the large number of transitions caused by the model, the whole proof is established by several lemmas. Interesting problems such as a timing glitch in the Phase Frequency Detector (PFD) are discussed and triggering conditions are formally proved in the dissertation. Global convergence is demonstrated by both tools. Based on the digital PLL circuit and the challenges that arose during our verification, the error bounds, limitations, implementation differences and usability of the two leading tools are carefully evaluated. SpaceEx provides a graphical user interface that makes it easy to get started with simple examples but requires extensive user interaction for larger problems. The interface to Coho is a MATLAB API. While this lacks the packaged-tool feel of SpaceEx, it provides a flexible way to break a large verification problem into smaller lemmas and allows the proof to be ''re-executed'' simply by re-executing the MATLAB script.Science, Faculty ofComputer Science, Department ofGraduat

Exchange Bias Effect in LaFeO3: La0.7Ca0.3MnO3 Composite Thin Films

Composite thin films arouse great interests owing to the multifunctionalities and heterointerface induced physical property tailoring. The exchange bias effect aroused from the ferromagnetic (FM)–antiferromagnetic (AFM) heterointerface is applicable in various applications such as magnetic storage. In this work, (LaFeO3)x:(La0.7Ca0.3MnO3)1−x composite thin films have been deposited via pulsed laser deposition (PLD) and the exchange bias effect was investigated. In such system, LaFeO3 (LFO) is an antiferromagnet while La0.7Ca0.3MnO3 (LCMO) is a ferromagnet, which results in the exchange bias interfacial coupling at the FM/AFM interface. The composition variation of the two phases could lead to the exchange bias field (HEB) tuning in the composite system. This work demonstrates a new composite thin film system with FM-AFM interfacial exchange coupling, which could be applied in various spintronic applications

Structural Analysis of a Functional DIAP1 Fragment Bound to Grim and Hid Peptides

The inhibitor of apoptosis protein DIAP1 suppresses apoptosis in Drosophila, with the second BIR domain (BIR2) playing an important role. Three proteins, Hid, Grim, and Reaper, promote apoptosis, in part by binding to DIAP1 through their conserved N-terminal sequences. The crystal structures of DIAP1-BIR2 by itself and in complex with the N-terminal peptides from Hid and Grim reveal that these peptides bind a surface groove on DIAP1, with the first four amino acids mimicking the binding of the Smac tetrapeptide to XIAP. The next 3 residues also contribute to binding through hydrophobic interactions. Interestingly, peptide binding induces the formation of an additional α helix in DIAP1. Our study reveals the structural conservation and diversity necessary for the binding of IAPs by the Drosophila Hid/Grim/Reaper and the mammalian Smac proteins

Development and Optimization of a Two-Degree-of-Freedom Piezoelectric Harvester Based on Parallel Cantilever Structure With Magnetic Coupling

Vibration energy harvesting using the piezoelectric effect has recently attracted significant attention from scholars. The main concern in the research of piezoelectric vibration energy harvesters is to improve the operating bandwidth and output power in low-frequency vibration environments with random and time-varying nature. A novel piezoelectric vibration energy harvester (PVEH) with three parallel cantilevers and repulsive magnet pair structures is proposed in this work to achieve the above goal. The proposed PVEH has the potential to take full advantage of the synergistic effect of the multi-frequency and magnetic nonlinear performance enhancement techniques. The characteristics of the harvester are systematically studied by theoretical modeling, simulation, and experiments. The influence of the critical parameters (i.e. the tip mass of the inner beam, the tip mass of the outer beam, and the magnet spacing) on the output performance of the PVEH is discussed and optimized in detail, and then the internal mechanism of the proposed energy harvesting method based on multi-frequency and magnetic cooperation is revealed. The results show that the improvement rate of the output power of the fabricated prototype under the condition of first-order and second-order operating frequency reaches 23.35% and 38.10%, respectively, compared with the non-magnetic structure. Finally, the optimal configuration of the harvester ( $M_{\mathrm {i}}$ = 6.70 g, $M_{\mathrm {o}}$ = 5.00 g, $s=22$ mm) obtains a maximum half-power bandwidth of 1.052 Hz and a maximum output power of 2.80 mW under 0.2g with 0.155 $\text{M}\Omega$ load resistance. The proposed energy harvesting system is expected to be a promising alternative to efficient vibration energy harvesters

Molecular mechanism of Reaper-Grim-Hid-mediated suppression of DIAP1-dependent Dronc ubiquitination

The inhibitor of apoptosis protein DIAP1 inhibits Dronc-dependent cell death by ubiquitinating Dronc. The pro-death proteins Reaper, Hid and Grim (RHG) promote apoptosis by antagonizing DIAP1 function. Here we report the structural basis of Dronc recognition by DIAP1 as well as a novel mechanism by which the RHG proteins remove DIAP1-mediated downregulation of Dronc. Biochemical and structural analyses revealed that the second BIR (BIR2) domain of DIAP1 recognizes a 12-residue sequence in Dronc. This recognition is essential for DIAP1 binding to Dronc, and for targeting Dronc for ubiquitination. Notably, the Dronc-binding surface on BIR2 coincides with that required for binding to the N termini of the RHG proteins, which competitively eliminate DIAP1-mediated ubiquitination of Dronc. These observations reveal the molecular mechanisms of how DIAP1 recognizes Dronc, and more importantly, how the RHG proteins remove DIAP1-mediated ubiquitination of Dronc