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Progression through the eukaryotic cell cycle is characterized by specific transitions, where cells move irreversibly from stage i-1 of the cycle into stage i. These irreversible cell cycle transitions are regulated by underlying bistable switches, which share some common features. An inhibitory protein stalls progression, and an activatory protein promotes… (More)

We study a system of three limit cycle oscillators which exhibits two stable steady states. The system is modeled by both phase-only oscillators and by van der Pol oscillators. We obtain and compare the existence, stability and bifurcation of the steady states in these two models. This work is motivated by application to the design of a machine which can… (More)

We analyze a model of gene transcription and protein synthesis which has been previously presented in the biological literature. The model takes the form of an ODE (ordinary differential equation) coupled to a DDE (delay differential equation), the state variables being concentrations of messenger RNA and protein. Linear analysis gives a critical time delay… (More)

This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using LindstedtÕs perturbation method.

- J Bridge, L Mendelowitz, R Rand, S Sah, A Verdugo
- 2008

The dynamics of a ring of three identical relaxation oscillators is shown to exhibit a variety of periodic motions, including clockwise and counterclockwise wave-like modes, and a synchronous mode in which all three oscillators are in phase. The model involves individual oscillators which exhibit sudden jumps, modeling the relaxation oscillations of van der… (More)

We use center manifold theory to analyze a model of gene transcription and protein synthesis which consists of an ordinary differential equation (ODE) coupled to a delay differential equation (DDE). The analysis involves reformulating the problem as an operator differential equation which acts on function space, with the result that an infinite dimensional… (More)

- B Bilki, J Repond, L Xia, G Eigen, M A Thomson, D R Ward +153 others
- 2015

Showers produced by positive hadrons in the highly granular CALICE scintillator-steel analogue hadron calorimeter were studied. The experimental data were collected at CERN and FNAL for single particles with initial momenta from 10 to 80 GeV/c. The calorimeter response and resolution and spatial characteristics of shower development for proton-and… (More)

- G Eigen, T Price, N K Watson, J S Marshall, M A Thomson, D R Ward +146 others
- 2016

The spatial development of hadronic showers in the CALICE scintillator-steel analogue hadron calorimeter is studied using test beam data collected at CERN and FNAL for single positive pions and protons with initial momenta in the range of 10–80 GeV/c. Both longitudinal and radial development of hadron showers are parametrised with two-component functions.… (More)

- M Chefdeville, Y Karyotakis, J Repond, J Schlereth, L Xia, G Eigen +175 others
- 2015

We present a study of showers initiated by electrons, pions, kaons, and protons with momenta from 15 GeV to 150 GeV in the highly granular CALICE scintillator-tungsten analogue hadronic calorimeter. The data were recorded at the CERN Super Proton Synchrotron in 2011. The analysis includes measurements of the calorimeter response to each particle type as… (More)