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Record 1 of 4: FN ISI Export Format VR 1.0 PT J AU Chen, ZQ AF Chen, Zhen-Qing TI ON NOTIONS OF HARMONICITY SO PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY LA English DT Article DE Harmonic function; uniformly integrable martingale; symmetric Hunt process; Dirichlet form; Levy system AB In this paper we address the equivalence of the analytic and probabilistic notions of harmonicity in the context of general symmetric Hunt processes on locally compact separable metric spaces. Extensions to general symmetric right processes on Lusin spaces, including infinite dimensional spaces, are mentioned at the end of this paper. C1 Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Chen, ZQ, Univ Washington, Dept Math, Seattle, WA 98195 USA. EM zchen@math.washington.edu FU NSF [DMS-0600206] FX The research of this author is supported in part by NSF Grant DMS-0600206. NR 10 TC 0 PU AMER MATHEMATICAL SOC PI PROVIDENCE PA 201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA SN 0002-9939 J9 PROC AMER MATH SOC JI Proc. Amer. Math. Soc. PD OCT PY 2009 VL 137 IS 10 BP 3497 EP 3510 PG 14 SC Mathematics, Applied; Mathematics GA 500AJ UT ISI:000270269000034 ER EF Record 2 of 4: FN ISI Export Format VR 1.0 PT J AU Ge, H Qian, H AF Ge, Hao Qian, Hong TI Thermodynamic Limit of a Nonequilibrium Steady State: Maxwell-Type Construction for a Bistable Biochemical System SO PHYSICAL REVIEW LETTERS LA English DT Article ID STOCHASTIC DYNAMICS; FLUCTUATIONS; BISTABILITY; MODELS AB We show that the thermodynamic limit of a bistable phosphorylation-dephosphorylation cycle has a selection rule for the "more stable" macroscopic steady state. The analysis is akin to the Maxwell construction. Based on the chemical master equation approach, it is shown that, except at a critical point, bistability disappears in the stochastic model when fluctuation is sufficiently low but unneglectable. Onsager's Gaussian fluctuation theory applies to the unique macroscopic steady state. With an initial state in the basin of attraction of the "less stable" steady state, the deterministic dynamics obtained by the law of mass action is a metastable phenomenon. Stability and robustness in cell biology are emergent stochastic concepts. C1 [Ge, Hao; Qian, Hong] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China. [Ge, Hao; Qian, Hong] Fudan Univ, Ctr Computat Syst Biol, Shanghai 200433, Peoples R China. [Qian, Hong] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. RP Ge, H, Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China. EM gehao@fudan.edu.cn qian@amath.washington.edu NR 39 TC 0 PU AMER PHYSICAL SOC PI COLLEGE PK PA ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA SN 0031-9007 J9 PHYS REV LETT JI Phys. Rev. Lett. PD OCT 2 PY 2009 VL 103 IS 14 AR 148103 DI 10.1103/PhysRevLett.103.148103 PG 4 SC Physics, Multidisciplinary GA 502KR UT ISI:000270458800059 ER EF Record 3 of 4: FN ISI Export Format VR 1.0 PT J AU Williams, MO Kutz, JN AF Williams, Matthew O. Kutz, J. Nathan TI Spatial Mode-Locking of Light Bullets in Planar Waveguide Arrays SO OPTICS EXPRESS LA English DT Article ID MOVING LOCALIZED STRUCTURES; OPTICAL DISCRETE SOLITONS; SATURABLE ABSORBER; QUADRATIC MEDIA; CAVITY SOLITONS; SLOW LIGHT; INCOHERENT; LASERS AB A theoretical proposal is presented for the generation of mode-locked light-bullets in planar waveguide arrays, extending the concept of time-domain mode-locking in waveguide arrays to spatial (transverse) mode-locking in slab waveguides. The model presented yields three-dimensional localized states that act as global attractors to the waveguide array system. Single pulse stationary and time-periodic solutions as well as the transition to multi-pulse solutions as a function of gain are observed to be stabilized in such a system. (C) 2009 Optical Society of America C1 [Williams, Matthew O.; Kutz, J. Nathan] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. RP Williams, MO, Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. EM mowill@amath.washington.edu NR 29 TC 0 PU OPTICAL SOC AMER PI WASHINGTON PA 2010 MASSACHUSETTS AVE NW, WASHINGTON, DC 20036 USA SN 1094-4087 J9 OPT EXPRESS JI Opt. Express PD SEP 28 PY 2009 VL 17 IS 20 BP 18320 EP 18329 PG 10 SC Optics GA 500JP UT ISI:000270295300117 ER EF Record 4 of 4: FN ISI Export Format VR 1.0 PT J AU Huang, QD Qian, H AF Huang, Qingdao Qian, Hong TI Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior SO CHAOS LA English DT Article DE biochemistry; cancer; cellular biophysics; enzymes; perturbation theory; reaction kinetics ID BIOLOGICAL SIGNAL-TRANSDUCTION; MULTISITE PHOSPHORYLATION; SENSITIVITY AMPLIFICATION; CELL-CYCLE; BISTABILITY; SPECIFICITY; SYSTEMS; STATES AB We establish a mathematical model for a cellular biochemical signaling module in terms of a planar differential equation system. The signaling process is carried out by two phosphorylation-dephosphorylation reaction steps that share common kinase and phosphatase with saturated enzyme kinetics. The pair of equations is particularly simple in the present mathematical formulation, but they are singular. A complete mathematical analysis is developed based on an elementary perturbation theory. The dynamics exhibits the canonical competition behavior in addition to bistability. Although widely understood in ecological context, we are not aware of a full range of biochemical competition in a simple signaling network. The competition dynamics has broad implications to cellular processes such as cell differentiation and cancer immunoediting. The concepts of homogeneous and heterogeneous multisite phosphorylation are introduced and their corresponding dynamics are compared: there is no bistability in a heterogeneous dual phosphorylation system. A stochastic interpretation is also provided that further gives intuitive understanding of the bistable behavior inside the cells. C1 [Huang, Qingdao] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. Jilin Univ, Coll Math, Changchun 130012, Peoples R China. RP Huang, QD, Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. FU China Scholarship Council FX We thank Jian-Dong Ding, Jeremy Gunawardena, Boris Kholodenko, Wenjun Qiu, Chao Tang, Liming Wang, Zhi-Xin Wang, and Jianhua Xing for discussions and Melissa Vellela for reading the manuscript. Q. H. is supported by a scholarship from the China Scholarship Council. NR 27 TC 0 PU AMER INST PHYSICS PI MELVILLE PA CIRCULATION & FULFILLMENT DIV, 2 HUNTINGTON QUADRANGLE, STE 1 N O 1, MELVILLE, NY 11747-4501 USA SN 1054-1500 J9 CHAOS JI Chaos PD SEP PY 2009 VL 19 IS 3 AR 033109 DI 10.1063/1.3187790 PG 9 SC Mathematics, Applied; Physics, Mathematical GA 501KV UT ISI:000270381500009 ER EF
