Approximate optimal guidance for the advanced launch system

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique

Generalised risk-sensitive control with full and partial state observation

This paper generalises the risk-sensitive cost functional by introducing noise dependent penalties on the state and control variables. The optimal control problems for the full and partial state observation are considered. Using a change of probability measure approach, explicit closed-form solutions are found in both cases. This has resulted in a new risk-sensitive regulator and filter, which are generalisations of the well-known classical results

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page

Regulatory role of C5a in LPS-induced IL-6 production by neutrophils during sepsis

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154469/1/fsb2fj030708fje-sup-0001.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154469/2/fsb2fj030708fje.pd

Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon

The raise and peel model of a one-dimensional fluctuating interface (model A) is extended by considering one source (model B) or two sources (model C) at the boundaries. The Hamiltonians describing the three processes have, in the thermodynamic limit, spectra given by conformal field theory. The probability of the different configurations in the stationary states of the three models are not only related but have interesting combinatorial properties. We show that by extending Pascal's triangle (which gives solutions to linear relations in terms of integer numbers), to an hexagon, one obtains integer solutions of bilinear relations. These solutions give not only the weights of the various configurations in the three models but also give an insight to the connections between the probability distributions in the stationary states of the three models. Interestingly enough, Pascal's hexagon also gives solutions to a Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few references are adde

Evidence for a functional role of the second C5a receptor C5L2

During experimental sepsis in rodents after cecal ligation and puncture (CLP), excessive C5a is generated, leading to interactions with C5aR, loss of innate immune functions of neutrophils, and lethality. In the current study, we have analyzed the expression of the second C5a receptor C5L2, the putative â defaultâ or nonsignaling receptor for C5a. Rat C5L2 was cloned, and antibody was developed to C5L2 protein. After CLP, blood neutrophils showed a reduction in C5aR followed by its restoration, while C5L2 levels gradually increased, accompanied by the appearance of mRNA for C5L2. mRNA for C5L2 increased in lung and liver during CLP. Substantially increased C5L2 protein (defined by binding of 125Iâ antiâ C5L2 IgG) occurred in lung, liver, heart, and kidney after CLP. With the use of serum ILâ 6 as a marker for sepsis, infusion of antiâ C5aR dramatically reduced serum ILâ 6 levels, while antiâ C5L2 caused a nearly fourfold increase in ILâ 6 when compared with CLP controls treated with normal IgG. When normal blood neutrophils were stimulated in vitro with LPS and C5a, the antibodies had similar effects on release of ILâ 6. These data provide the first evidence for a role for C5L2 in balancing the biological responses to C5a.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154410/1/fsb2fj043424fje.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154410/2/fsb2fj043424fje-sup-0040.pd

A Grassmann algebra for matroids

We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical Grassmann algebra formalism for linear spaces. The top wedge power of a tropical linear space is its Plucker vector, which we view as a tensor, and a tropical linear space is recovered from its Plucker vector as the kernel of the corresponding wedge multiplication map. We prove that an arbitrary d-tensor satisfies the tropical Plucker relations (valuated exchange axiom) if and only if the d-th wedge power of the kernel of wedge-multiplication is free of rank one. This provides a new cryptomorphism for valuated matroids, including ordinary matroids as a special case