An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition

In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone op- erator. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. The advantage to an earlier algorithm is demonstrated. Furthermore an example is given which shows how to analyze a given perturbed interconnected system.Comment: 30 pages, 7 figures, 4 table

Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page

Molecular Valves for Controlling Gas Phase Transport Made from Discrete Angstrom-Sized Pores in Graphene

An ability to precisely regulate the quantity and location of molecular flux is of value in applications such as nanoscale 3D printing, catalysis, and sensor design. Barrier materials containing pores with molecular dimensions have previously been used to manipulate molecular compositions in the gas phase, but have so far been unable to offer controlled gas transport through individual pores. Here, we show that gas flux through discrete angstrom-sized pores in monolayer graphene can be detected and then controlled using nanometer-sized gold clusters, which are formed on the surface of the graphene and can migrate and partially block a pore. In samples without gold clusters, we observe stochastic switching of the magnitude of the gas permeance, which we attribute to molecular rearrangements of the pore. Our molecular valves could be used, for example, to develop unique approaches to molecular synthesis that are based on the controllable switching of a molecular gas flux, reminiscent of ion channels in biological cell membranes and solid state nanopores.Comment: to appear in Nature Nanotechnolog

Reduced apoptotic levels in squamous but not basal cell carcinomas correlates with detection of cutaneous human papillomavirus

We have investigated the apoptotic levels and expression of the apoptotic inducer Bak in non-melanoma skin cancers. Squamous cell carcinomas of known human papillomavirus status from immunocompetent patients were analysed for the expression of the Bak protein, and the expression profile was compared both to the presence of apoptotic cells and the proliferation marker Ki-67. We demonstrate an inverse correlation between human papillomavirus positivity and Bak expression in squamous cell carcinomas, with concomitantly fewer apoptoic cells being detected in the human papillomavirus positive tumours. Bak expression was not observed in basal cell carcinomas irrespective of human papillomavirus status, suggesting that Bak only plays a role in signalling apoptosis in squamous, but not basal, cell cancers. No differences were observed in the proliferation rates between papillomavirus positive and negative squamous cell tumours. However, a significant decrease in the number of apoptotic cells was observed in human papillomavirus-positive squamous cell carcinomas which suggests that the virus may have significantly altered the relationship between proliferation and apoptosis in a proportion of these tumours

Rectifying properties and colossal magnetoresistance in La0.9Hf0.1MnO3 /Nb-0.7 wt%-doped SrTiO3 heterojunction

SPIE Proceedings v. 9068 entitled: Technology of Thin Film & Application of Thin FilmA heterojunction with good rectifying properties in a wide temperature range from 20 K to 300 K was fabricated simply by depositing an as-grown La0.9Hf0.1MnO3 (LHMO) film on a commercial 0.7 wt% Nb-doped SrTiO3 single crystal substrate using pulsed laser deposition technique. The current-voltage behavior of the LHMO/STON is measured under applied magnetic fields varying between 0 and 5 T. The heterojunction shows a remarkable magnetoresistance which depends on both the temperature and bias voltages. The sign of the magnetoresistance as function of temperature at either forward or reverse bias voltage is extensively studied by the filling of electrons in the eg and t2g band. The good rectifying behaviors, the magnetic tunable properties and the maximum magnetoresistance obtained at room temperature make this simple heterojunction promising for practical applications. © (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personalLink_to_subscribed_fulltex

Quantitative comparison of myocardial fiber structure between mice, rabbit, and sheep using diffusion tensor cardiovascular magnetic resonance

<p>Abstract</p> <p>Background</p> <p>Accurate interpretations of cardiac functions require precise structural models of the myocardium, but the latter is not available always and for all species. Although scaling or substitution of myocardial fiber information from alternate species has been used in cardiac functional modeling, the validity of such practice has not been tested.</p> <p>Methods</p> <p>Fixed mouse (n = 10), rabbit (n = 6), and sheep (n = 5) hearts underwent diffusion tensor imaging (DTI). The myocardial structures in terms of the left ventricular fiber orientation helix angle index were quantitatively compared between the mouse rabbit and sheep hearts.</p> <p>Results</p> <p>The results show that significant fiber structural differences exist between any two of the three species. Specifically, the subepicardial fiber orientation, and the transmural range and linearity of fiber helix angles are significantly different between the mouse and either rabbit or sheep. Additionally, a significant difference was found between the transmural helix angle range between the rabbit and sheep. Across different circumferential regions of the heart, the fiber orientation was not found to be significantly different.</p> <p>Conclusions</p> <p>The current study indicates that myocardial structural differences exist between different size hearts. An immediate implication of the present findings for myocardial structural or functional modeling studies is that caution must be exercised when extrapolating myocardial structures from one species to another.</p

Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings

Surgical treatment of congenital biliary duct cyst

<p>Abstract</p> <p>Background</p> <p>It is acknowledged that total cyst excision is a safe and ideal surgical treatment for congenital biliary duct cyst, compared to simple internal drainage. The aim of this study was to determine the optimal operation occasion and the effect of laparoscopy on congenital biliary duct cyst based upon total cyst excision.</p> <p>Methods</p> <p>From January 2002 to January 2011, 217 patients were admitted to Southwest Hospital for congenital biliary duct cyst. To determine the optimal surgery occasion, we divided these subjects into three groups, the infant group (age ≤ 3 years), the immaturity group (3 < age ≤ 18 years), and the maturity group (age > 18 years), and then evaluated the feasibility, risk and long-term outcome after surgery in the three groups. To analyze the effect of laparoscopic technique on congenital biliary duct cyst, we divided the patients into the laparoscopy and the open surgery groups.</p> <p>Results</p> <p>Among the three groups, the morbidity from cholangiolithiasis before surgical treatment had obvious discrepancy (p < 0.05) (lowest in the infant group), and intraoperative blood loss also had apparent diversity (p < 0.05). Furthermore, long-term outcomes (secondary cholangiolithiasis, stoma stenosis and cholangiocarcinoma) showed no significant difference between different groups (p > 0.05).</p> <p>Similarly, no significant discrepancy was observed in the morbidity from postoperative complications or long-term postoperative complications (p > 0.05) between the laparoscopic and the open surgery groups.</p> <p>Conclusions</p> <p>We conclude that total cyst excision should be performed as early as possible. The optimal treatment occasion is the infant period, and laparoscopic resection may be a new safe and feasible minimally invasive surgery for this disease.</p