Classification of bursting patterns: A tale of two ducks

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple-timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram et al., and then by Golubitsky et al., which together with the Rinzel-Izhikevich proposals provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least two slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the two main families of folded-node bursters, depending upon the phase (active/spiking or silent/non-spiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast-subsystem approach

An Overview of the Kauffman Firm Survey: Results From the 2004-2008 Data

Presents findings from longitudinal data on new businesses founded in 2004, including financing structure; products, services, and innovations; and characteristics of the owners. Examines indicators of growth and survival and effects of the recession

An Overview of the Kauffman Firm Survey: Results From the 2004-2007 Data

Based on surveys conducted over four years, provides an overview of trends among U.S. firms established in 2004 and the business and owner characteristics associated with survival and growth, including level of innovation, structure, and financing

Mixed-mode oscillations in a multiple time scale phantom bursting system

In this work we study mixed mode oscillations in a model of secretion of GnRH (Gonadotropin Releasing Hormone). The model is a phantom burster consisting of two feedforward coupled FitzHugh-Nagumo systems, with three time scales. The forcing system (Regulator) evolves on the slowest scale and acts by moving the slow nullcline of the forced system (Secretor). There are three modes of dynamics: pulsatility (transient relaxation oscillation), surge (quasi steady state) and small oscillations related to the passage of the slow nullcline through a fold point of the fast nullcline. We derive a variety of reductions, taking advantage of the mentioned features of the system. We obtain two results; one on the local dynamics near the fold in the parameter regime corresponding to the presence of small oscillations and the other on the global dynamics, more specifically on the existence of an attracting limit cycle. Our local result is a rigorous characterization of small canards and sectors of rotation in the case of folded node with an additional time scale, a feature allowing for a clear geometric argument. The global result gives the existence of an attracting unique limit cycle, which, in some parameter regimes, remains attracting and unique even during passages through a canard explosion.Comment: 38 pages, 16 figure

Inflection, Canards and Folded Singularities in Excitable Systems: Application to a 3D FitzHugh–Nagumo Model

Specific kinds of physical and biological systems exhibit complex Mixed-Mode Oscillations mediated by folded-singularity canards in the context of slow-fast models. The present manuscript revisits these systems, specifically by analysing the dynamics near a folded singularity from the viewpoint of inflection sets of the flow. Originally, the inflection set method was developed for planar systems [Brøns and Bar-Eli in Proc R Soc A 445(1924):305–322, 1994; Okuda in Prog Theor Phys 68(6):1827–1840, 1982; Peng et al. in Philos Trans R Soc A 337(1646):275–289, 1991] and then extended to N-dimensional systems [Ginoux et al. in Int J Bifurc Chaos 18(11):3409–3430, 2008], although not tailored to specific dynamics (e.g. folded singularities). In our previous study, we identified components of the inflection sets that classify several canard-type behaviours in 2D systems [Desroches et al. in J Math Biol 67(4):989– 1017, 2013]. Herein, we first survey the planar approach and show how to adapt it for 3D systems with an isolated folded singularity by considering a suitable reduction of such 3D systems to planar non-autonomous slow-fast systems. This leads us to the computation of parametrized families of inflection sets of one component of that planar (non-autonomous) system, in the vicinity of a folded node or of a folded saddle. We then show that a novel component of the inflection set emerges, which approximates and follows the axis of rotation of canards associated to folded-node and folded-saddle singularities. Finally, we show that a similar inflection-set component occurs in the vicinity of a delayed Hopf bifurcation, a scenario that can arise at the transition between folded node and folded saddle. These results are obtained in the context of a canonical model for folded-singularity canards and subsequently we show it is also applicable to complex slow-fast models. Specifically, we focus the application towards the self-coupled 3D FitzHugh–Nagumo model, but the method is generically applicable to higher-dimensional models with isolated folded singularities, for instance in conductance-based models and other physical-chemical systems.Ikerbasque (The Basque Foundation for Science

Health Information Technology in the United States: The Information Base for Progress

Health information technology (HIT) has the potential to advance health care quality by helping patients with acute and chronic conditions receive recommended care, diminishing disparities in treatment and reducing medical errors. Nevertheless, HIT dissemination has not occurred rapidly, due in part to the high costs of electronic health record (EHR) systems for providers of care—including the upfront capital investment, ongoing maintenance and short-term productivity loss. Also, many observers are concerned that, if HIT follows patterns observed with other new medical technologies, HIT and EHRs may diffuse in ways that systematically disadvantage vulnerable patient populations, thus increasing or maintaining existing disparities in access to and quality of care. These and other concerns have led to public and private efforts that aim to increase the pace of and reduce disparities in HIT diffusion by formulating national plans for dissemination, catalyzing the development of standards to encourage interoperability and promoting public-private partnerships to develop HIT infrastructures at the local and regional levels

Health Information Technology in the United States: On the Cusp of Change, 2009

In this report we use the data collected for ONCHIT to focus on EHR adoption in the inpatient setting. We report on several important policy issues. These include the rate of adoption of EHRs among U.S. hospitals generally and among safety-net hospitals, changes in both state and federal policy, and the potential of EHRs to change the quality measurement enterprise