7,116 research outputs found
TACC3-ch-TOG track the growing tips of microtubules independently of clathrin and Aurora-A phosphorylation
No full textThe interaction between TACC3 (transforming acidic coiled coil protein 3) and the microtubule polymerase ch-TOG (colonic, hepatic tumor overexpressed gene) is evolutionarily conserved. Loading of TACC3–ch-TOG onto spindle microtubules requires the phosphorylation of TACC3 by Aurora-A kinase and the subsequent interaction of TACC3 with clathrin to form a microtubule binding surface. Whether there is a pool of TACC3–ch-TOG that is independent of clathrin in human cells, and what is the function of this pool, are open questions. Here, we report that TACC3 is recruited to the plus-ends of microtubules by its association with ch-TOG and that this pool is independent of phosphorylation and binding to clathrin. The plus-end binding of TACC3–ch-TOG persists in interphase and we propose that one cellular function of TACC3–ch-TOG is to modulate cell migration. We also describe the distinct subcellular pools of TACC3, ch-TOG and clathrin. TACC3 is often described as a centrosomal protein, but we show that there is no significant population of TACC3 at centrosomes. The delineation of distinct protein pools reveals a simplified view of how these proteins are organized and controlled by post-translational modification
Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital
No full textThe paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author et al. [26, 27, 28, 29, 30]. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown to coincide with the spatial gradient of the value function evaluated along the trajectory of the system, creating a parallel between Maximum Principle and Dynamic Programming. The abstract model applies, as recalled in one of the first sections, to optimal investment with vintage capital.Linear convex control, Boundary control, Hamilton–Jacobi–Bellman equations, Optimal investment problems, Vintage capital
Construction of Recurrence Relations for the Jacobi Coefficients, Using Maple
No full textIntroduction In the field of numerical analysis, one frequently needs to determine the coefficients a (ff;fi) k [f ] in the expansion of a given function f into a uniformly convergent series of Jacobi polynomials, f(x) = 1 X k=0 a (ff;fi) k [f ] P (ff;fi) k (x) (\Gamma1 x 1); (1) where P (ff;fi) k (x) (ff; fi ? \Gamma1) is the usual notation for the kth Jacobi polynomial (cf. [2], Vol. II, x10.8, or [5], Vol. I, Ch. 8). The particular case of ff = fi = \Gamma 1 2 is c
EFFICIENT MODIFIED JACOBI RELAXATION FOR MINIMIZING THE ENERGY FUNCTIONAL
No full textWe present an efficient scheme of diagonalizing large Hamiltonian matrices in a self-consistent manner. In the framework of the preconditioned conjugate gradient minimization of the energy functional, we replace the modified Jacobi relaxation for preconditioning and use for band-by-band minimization the restricted-block Davidson algorithm, in which only the previous wave functions and the relaxation vectors are included additionally for subspace diagonalization. Our scheme is found to be comparable with the preconditioned conjugate gradient method for both large ordered and disordered Si systems, while it is more rapidly converged for systems with transition-metal elements
Optimal investment models with vintage capital: Dynamic Programming approach
No full textThe Dynamic Programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers (see e.g. [11, 12], [30, 32]) either in cases when explicit solutions can be found or using Maximum Principle techniques. The problem is rephrased into an infinite dimensional setting, it is proven that the value function is the unique regular solution of the associated stationary Hamilton-Jacobi-Bellman equation, and existence and uniqueness of optimal feedback controls is derived. It is then shown that the optimal path is the solution to the closed loop equation. Similar results were proven in the case of finite horizon in [26][27]. The case of infinite horizon is more challenging as a mathematical problem, and indeed more interesting from the point of view of optimal investment models with vintage capital, where what mainly matters is the behavior of optimal trajectories and controls in the long run. The study of infinite horizon is performed through a nontrivial limiting procedure from the corresponding finite horizon problemsOptimal investment, vintage capital, age-structured systems, optimal control, dynamic programming, Hamilton-Jacobi-Bellman equations, linear convex control, boundary control
The Jacobi-Maupertuis Principle in Variational Integrators
No full textIn this paper, we develop a hybrid variational integrator based on the Jacobi-Maupertuis Principle of Least Action. The Jacobi-Maupertuis principle states that for a mechanical system with total energy E and potential energy V(q), the curve traced out by the system on a constant energy surface minimizes the action given by ∫√[2(E-V(q))] ds where ds is the line element on the constant energy surface with respect to the kinetic energy of the system. The key feature is that the principle is a parametrization independent geodesic problem. We show that this principle can be combined with traditional variational integrators and can be used to efficiently handle high velocity regions where small time steps would otherwise be required. This is done by switching between the Hamilton principle and the Jacobi-Maupertuis principle depending upon the kinetic energy of the system. We demonstrate our technique for the Kepler problem and discuss some ongoing and future work in studying the energy and momentum behavior of the resulting integrator
Equilibrium Points for Optimal Investment with Vintage Capital
No full textThe paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the general case are given and later applied to the economic problem of optimal investment with vintage capital. Explicit computation of equilibria for the economic problem in some relevant examples is also provided. Indeed the challenging issue here is showing that a theoretical machinery, such as optimal control in infinite dimension, may be effectively used to compute solutions explicitly and easily, and that the same computation may be straightforwardly repeated in examples yielding the same abstract structure. No stability result is instead provided: the work here contained has to be considered as a first step in the direction of studying the behavior of optimal controls and trajectories in the long run.Linear convex control, Boundary control, Hamilton–Jacobi–Bellman equations, Optimal investment problems, Vintage capital
PROBING THE REACTION PATH OF CH + H CH CH + H AND ISOTOPOLOGUES
No full textZ. Jin, B. J. Braams, J. M. Bowman, J. Phys. Chem. A 110, 1569 (2006).A. B. McCoy, B. J. Braams, A. Brown, X. Huang., Z. Jin, J. M. Bowman, J. Phys. Chem. A 108, 4991 (2004).Author Institution: Department of Chemistry, The Ohio State University, Columbus; OH 43210Protonated methane has long been of interest to astrochemists due to its presumed importance as a reaction intermediate in the reaction involving CH + HD within the interstellar medium. Within the interstellar medium there is a nonstatistical H/D isotopic abundance observed for isotopologues of CH. While classical trajectory calculations have been performed dissociating CH and CHD into the fragments, CH + H, CHD + H and CH + HD{}, these calculations do not account for a large portion of the available energy being tied up in the zero point energy of the reactants and products. Earlier work in our group on CHD{} showed the deuterium atoms were localized to the CH group, rather than the H moiety. Classical calculations fail to account for this observed localization, instead showing full delocalization of D between both CH and H. With a quantum mechanical treatment, the energetics and wave functions will depend on which asymptotic channel is chosen, while in the classical treatment, these channels will be energetically equivalent. By performing Diffusion Monte Carlo simulations in Jacobi coordinates, we can constrain the distance between the CH and H subunits. Using this technique we have evaluated a one-dimensional reaction potential that includes the full anharmonic zero point energy in the remaining degrees of freedom and can determine how energetics of this reaction change upon partial deuteration of CH or H. We have also evaluated the probability amplitude associated with the wave functions that are obtained in the DMC simulations at various values of the reaction coordinate
On a periodic Jacobi-Perron type algorithm
No full textIn this paper we introduce a new modification of the Jacobi-Perron algorithm
in three dimensional case and prove its periodicity for the case of
totally-real conjugate cubic vectors. This provides an answer in the
totally-real case to the question son algebraic periodicity for cubic
irrationalities posed in 1849 by Ch.~Hermite
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Solutions of vectorial Hamilton-Jacobi equations are rank-one absolute minimisers in L∞
No full textGiven the supremal functional E∞(u,Ω′)=esssupΩ′H(⋅,Du)E∞(u,Ω′)=esssupΩ′H(⋅,Du) defined on W1,∞loc(Ω,RN)Wloc1,∞(Ω,RN), Ω′⋐Ω⊆RnΩ′⋐Ω⊆Rn, we identify a class of vectorial rank-one Absolute Minimisers by proving a statement slightly stronger than the next claim: vectorial solutions of the Hamilton-Jacobi equation H(⋅,Du)=cH(⋅,Du)=c are rank-one Absolute Minimisers if they are C1C1. Our minimality notion is a generalisation of the classical L∞L∞ variational principle of Aronsson to the vector case and emerged in earlier work of the author. The assumptions are minimal, requiring only continuity and rank-one convexity of the level sets
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