Time Dependent Saddle Node Bifurcation: Breaking Time and the Point of No Return in a Non-Autonomous Model of Critical Transitions

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered the discourse of the general public in relation to ecology, medicine, and public health. The saddle-node bifurcation and its associated theory of catastrophe as put forth by Thom and Zeeman has seen applications in a wide range of fields including molecular biophysics, mesoscopic physics, and climate science. In this paper, we investigate a simple model of a non-autonomous system with a time-dependent parameter $p(\tau)$ and its corresponding `dynamic' (time-dependent) saddle-node bifurcation by the modern theory of non-autonomous dynamical systems. We show that the actual point of no return for a system undergoing tipping can be significantly delayed in comparison to the {\em breaking time} $\hat{\tau}$ at which the corresponding autonomous system with a time-independent parameter $p_{a}= p(\hat{\tau})$ undergoes a bifurcation. A dimensionless parameter $\alpha=\lambda p_0^3V^{-2}$ is introduced, in which $\lambda$ is the curvature of the autonomous saddle-node bifurcation according to parameter $p(\tau)$, which has an initial value of $p_{0}$ and a constant rate of change $V$. We find that the breaking time $\hat{\tau}$ is always less than the actual point of no return $\tau^*$ after which the critical transition is irreversible; specifically, the relation $\tau^*-\hat{\tau}\simeq 2.338(\lambda V)^{-\frac{1}{3}}$ is analytically obtained. For a system with a small $\lambda V$, there exists a significant window of opportunity $(\hat{\tau},\tau^*)$ during which rapid reversal of the environment can save the system from catastrophe

Boosting the precision of virtual call integrity protection with partial pointer analysis for C++

© 2017 Association for Computing Machinery. We present, Vip, an approach to boosting the precision of Virtual call Integrity Protection for large-scale real-world C++ programs (e.g., Chrome) by using pointer analysis for the first time. Vip introduces two new techniques: (1) a sound and scalable partial pointer analysis for discovering statically the sets of legitimate targets at virtual callsites from separately compiled C++ modules and (2) a lightweight instrumentation technique for performing (virtual call) integrity checks at runtime. Vip raises the bar against vtable hijacking attacks by providing stronger security guarantees than the CHA-based approach with comparable performance overhead. Vip is implemented in LLVM-3.8.0 and evaluated using SPEC programs and Chrome. Statically, Vip protects virtual calls more effectively than CHA by significantly reducing the sets of legitimate targets permitted at 20.3% of the virtual callsites per program, on average. Dynamically, Vip incurs an average (maximum) instrumentation overhead of 0.7% (3.3%), making it practically deployable as part of a compiler tool chain

Controlled surface initiated polymerization of N-isopropylacrylamide from polycaprolactone substrates for regulating cell attachment and detachment

Poly(ε-caprolactone) (PCL) substrates were modified with thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) brushes to direct and control cellular attachment and detachment. Prior to brush growth, the surface of PCL was activated by a diamine to allow for initiator coupling. Infrared spectra taken before and after cell culturing demonstrated the covalently attached nature of the PNIPAM brushes. PCL is a biocompatible polymer and to prove that the modifications described above did not change this characteristic property, a cell attachment/detachment study was carried out. The modified substrates showed a lower cell attachment when compared to PCL alone and to PCL films modified with the initiator. The possibility to detach the cells in the form of a sheet was proved using PNIPAM-modified PCL films by lowering the temperature to 25 °C. No relevant detachment was shown by the unmodified or by the initiator modified surfaces. This confirmed that the detachment was temperature dependent and not connected to other factors such as polymer swelling. These functionalized polymeric films can find applications as smart cell culture systems in regenerative medicine applications

Impacts of Large-Scale Circulation on Convection: A 2-D Cloud Resolving Model Study

Studies of impacts of large-scale circulation on convection, and the roles of convection in heat and water balances over tropical region are fundamentally important for understanding global climate changes. Heat and water budgets over warm pool (SST=29.5 C) and cold pool (SST=26 C) were analyzed based on simulations of the two-dimensional cloud resolving model. Here the sensitivity of heat and water budgets to different sizes of warm and cold pools is examined

Processes on the emergent landscapes of biochemical reaction networks and heterogeneous cell population dynamics: differentiation in living matters.

The notion of an attractor has been widely employed in thinking about the nonlinear dynamics of organisms and biological phenomena as systems and as processes. The notion of a landscape with valleys and mountains encoding multiple attractors, however, has a rigorous foundation only for closed, thermodynamically non-driven, chemical systems, such as a protein. Recent advances in the theory of nonlinear stochastic dynamical systems and its applications to mesoscopic reaction networks, one reaction at a time, have provided a new basis for a landscape of open, driven biochemical reaction systems under sustained chemostat. The theory is equally applicable not only to intracellular dynamics of biochemical regulatory networks within an individual cell but also to tissue dynamics of heterogeneous interacting cell populations. The landscape for an individual cell, applicable to a population of isogenic non-interacting cells under the same environmental conditions, is defined on the counting space of intracellular chemical composition

Failure Assessment for the High-Strength Pipelines with Constant-Depth Circumferential Surface Cracks

In the oil and gas transportation system over long distance, application of high-strength pipeline steels can efficiently reduce construction and operation cost by increasing operational pressure and reducing the pipe wall thickness. Failure assessment is an important issue in the design, construction, and maintenance of the pipelines. The small circumferential surface cracks with constant depth in the welded pipelines are of practical interest. This work provides an engineering estimation procedure based upon the GE/EPRI method to determine the J-integral for the thin-walled pipelines with small constant-depth circumferential surface cracks subject to tension and bending loads. The values of elastic influence functions for stress intensity factor and plastic influence functions for fully plastic J-integral estimation are derived in tabulated forms through a series of three-dimensional finite element calculations for different crack geometries and material properties. To check confidence of the J-estimation solution in practical application, J-integral values obtained from detailed finite element (FE) analyses are compared with those estimated from the new influence functions. Excellent agreement of FE results with the proposed J-estimation solutions for both tension and bending loads indicates that the new solutions can be applied for accurate structural integrity assessment of high-strength pipelines with constant-depth circumferential surface cracks

Hard X-ray and UV Observations of the 2005 January 15 Two-ribbon Flare

In this paper, we present comprehensive analysis of a two-ribbon flare observed in UV 1600{\AA} by Transition Region and Coronal Explorer and in HXRs by Reuven Ramaty High Energy Solar Spectroscopic Imager. HXR (25-100 keV) imaging observations show two kernels of size (FWHM) 15?? moving along the two UV ribbons. We find the following results. (1) UV brightening is substantially enhanced wherever and whenever the compact HXR kernel is passing, and during the HXR transit across a certain region, the UV count light curve in that region is temporally correlated with the HXR total flux light curve. After the passage of the HXR kernel, the UV light curve exhibits smooth monotonical decay. (2)We measure the apparent motion speed of the HXR sources and UV ribbon fronts, and decompose the motion into parallel and perpendicular motions with respect to the magnetic polarity inversion line (PIL). It is found that HXR kernels and UV fronts exhibit similar apparent motion patterns and speeds. The parallel motion dominates during the rise of the HXR emission, and the perpendicular motion starts and dominates at the HXR peak, the apparent motion speed being 10-40 km s-1. (3) We also find that UV emission is characterized by a rapid rise correlated with HXRs, followed by a long decay on timescales of 15-30 minutes. The above analysis provides evidence that UV brightening is primarily caused by beam heating, which also produces thick-target HXR emission. The thermal origin of UV emission cannot be excluded, but would produce weaker heating by one order of magnitude. The extended UV ribbons in this event are most likely a result of sequential reconnection along the PIL, which produces individual flux tubes (post-flare loops), subsequent non-thermal energy release and heating in these flux tubes, and then the very long cooling time of the transition region at the feet of these flux tubes.Comment: 8 figure

An improved calcium chloride method preparation and transformation of competent cells

Transformation is one of the fundamental and essential molecular cloning techniques. In this paper, we have reported a modified method for preparation and transformation of competent cells. This modifiedmethod, improved from a classical protocol, has made some modifications on the concentration of calcium chloride and competent bacteria solution, rotation speed in centrifugation and centrifugationtime. It was found that the optimal transformation efficiency were obtained when the concentration of CaCl2 was 75 mmol/l, OD600 of the culture meets 0.35 to 0.45, the temperature of rotation was 4°C , rotation speed was 1000 g and rotation time was 5 min. Even more, we also found out that the transformation efficiency would increase about 10 to 30 times when adding 15% glycerine into CaCl2 solution. The transformation efficiency, using our new method, reaches 108cf u/μg and higher than ultra-competent Escherichia coli method. This method will improve the efficiency in the molecular cloning and the construction of gene library.Keywords: Competent cells, CaCl2, improved method, transformation, glycerine, transformation efficienc