The Recoverable Robust Tail Assignment Problem

This is the author accepted manuscript. The final version is available from Institute for Operations Research and the Management Sciences (INFORMS) via the DOI in this record Schedule disruptions are commonplace in the airline industry with many flight-delaying events occurring each day. Recently there has been a focus on introducing robustness into airline planning stages to reduce the effect of these disruptions. We propose a recoverable robustness technique as an alternative to robust optimisation to reduce the effect of disruptions and the cost of recovery. We formulate the recoverable robust tail assignment problem (RRTAP) as a stochastic program, solved using column generation in the master and subproblems of the Benders decomposition. We implement a two-phase algorithm for the Benders decomposition incorporating the Magnanti-Wong [21] enhancement techniques. The RRTAP includes costs due to flight delays, cancellation, and passenger rerouting, and the recovery stage includes cancellation, delay, and swapping options. To highlight the benefits of simultaneously solving planning and recovery problems in the RRTAP we compare our tail assignment solution with the tail assignment generated using a connection cost function presented in Gr¨onkvist [15]. Using airline data we demonstrate that by developing a better tail assignment plan via the RRTAP framework, one can reduce recovery costs in the event of a disruption.Australian Research Council Centre of Excellence for MathematicsMASCOS

Ulam method for the Chirikov standard map

We introduce a generalized Ulam method and apply it to symplectic dynamical maps with a divided phase space. Our extensive numerical studies based on the Arnoldi method show that the Ulam approximant of the Perron-Frobenius operator on a chaotic component converges to a continuous limit. Typically, in this regime the spectrum of relaxation modes is characterized by a power law decay for small relaxation rates. Our numerical data show that the exponent of this decay is approximately equal to the exponent of Poincar\'e recurrences in such systems. The eigenmodes show links with trajectories sticking around stability islands.Comment: 13 pages, 13 figures, high resolution figures available at: http://www.quantware.ups-tlse.fr/QWLIB/ulammethod/ minor corrections in text and fig. 12 and revised discussio

Deceleration of one-dimensional mixing by discontinuous mappings

We present a computational study of a simple one-dimensional map with dynamics composed of stretching, permutations of equal sized cells, and diffusion. We observe that the combination of the aforementioned dynamics results in eigenmodes with long-time exponential decay rates. The decay rate of the eigenmodes is shown to be dependent on the choice of permutation and changes non-monotonically with the diffusion coefficient for many of the permutations. The global mixing rate of the map M in the limit of vanishing diffusivity approximates well the decay rates of the eigenmodes for small diffusivity, however this global mixing rate does not bound the rates for all values of the diffusion coefficient. This counter-intuitively predicts a deceleration in the asymptotic mixing rate with increasing diffusivity rate. The implication of the results on finite time mixing are discussed

A weak characterization of slow variables in stochastic dynamical systems

We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a key role in system analysis and coarse graining. The defining characteristics of these slow variables is that they parametrize a so-called transition manifold, a low-dimensional manifold in a certain density function space that emerges with progressive equilibration of the system's fast variables. The existence of said manifold was previously predicted for certain classes of metastable and slow-fast systems. However, in the original work, the existence of the manifold hinges on the pointwise convergence of the system's transition density functions towards it. We show in this work that a convergence in average with respect to the system's stationary measure is sufficient to yield reaction coordinates with the same key qualities. This allows one to accurately predict the timescale preservation in systems where the old theory is not applicable or would give overly pessimistic results. Moreover, the new characterization is still constructive, in that it allows for the algorithmic identification of a good slow variable. The improved characterization, the error prediction and the variable construction are demonstrated by a small metastable system

Exact Conformal Scalar Field Cosmologies

New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a Friedmann-Robertson-Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour $S(t)\sim t^p$ with $p>1$, while another class exhibits a late time approach to the $S(t)\sim t$ behaviour of the coasting models. Bouncing models which avoid an initial singularity are also obtained. A general discussion of the asymptotic behaviour and of the possibility of occurrence of inflation is provided.Comment: Latex, 27 pages plus 16 figures (not included, available from the authors upon request) DFFCUL-94-01-0

Ruelle-Perron-Frobenius spectrum for Anosov maps

We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (Information on the existence of an SRB measure, its smoothness properties and statistical properties readily follow from such a result.) In dimension $d=2$ we show that the transfer operator associated to smooth random perturbations of the map is close, in a proper sense, to the unperturbed transfer operator. This allows to obtain easily very strong spectral stability results, which in turn imply spectral stability results for smooth deterministic perturbations as well. Finally, we are able to implement an Ulam type finite rank approximation scheme thus reducing the study of the spectral properties of the transfer operator to a finite dimensional problem.Comment: 58 pages, LaTe

Accounting Problems Under the Excess Profits Tax

DNA vaccines based on subunits from pathogens have several advantages over other vaccine strategies. DNA vaccines can easily be modified, they show good safety profiles, are stable and inexpensive to produce, and the immune response can be focused to the antigen of interest. However, the immunogenicity of DNA vaccines which is generally quite low needs to be improved. Electroporation and co-delivery of genetically encoded immune adjuvants are two strategies aiming at increasing the efficacy of DNA vaccines. Here, we have examined whether targeting to antigen-presenting cells (APC) could increase the immune response to surface envelope glycoprotein (Env) gp120 from Human Immunodeficiency Virus type 1 (HIV- 1). To target APC, we utilized a homodimeric vaccine format denoted vaccibody, which enables covalent fusion of gp120 to molecules that can target APC. Two molecules were tested for their efficiency as targeting units: the antibody-derived single chain Fragment variable (scFv) specific for the major histocompatilibility complex (MHC) class II I-E molecules, and the CC chemokine ligand 3 (CCL3). The vaccines were delivered as DNA into muscle of mice with or without electroporation. Targeting of gp120 to MHC class II molecules induced antibodies that neutralized HIV-1 and that persisted for more than a year after one single immunization with electroporation. Targeting by CCL3 significantly increased the number of HIV-1 gp120-reactive CD8(+) T cells compared to non-targeted vaccines and gp120 delivered alone in the absence of electroporation. The data suggest that chemokines are promising molecular adjuvants because small amounts can attract immune cells and promote immune responses without advanced equipment such as electroporation.Funding Agencies|Research Council of Norway; Odd Fellow</p

Sucrose Counteracts the Anti-Inflammatory Effect of Fish Oil in Adipose Tissue and Increases Obesity Development in Mice

BACKGROUND: Polyunsaturated n-3 fatty acids (n-3 PUFAs) are reported to protect against high fat diet-induced obesity and inflammation in adipose tissue. Here we aimed to investigate if the amount of sucrose in the background diet influences the ability of n-3 PUFAs to protect against diet-induced obesity, adipose tissue inflammation and glucose intolerance. METHODOLOGY/PRINCIPAL FINDINGS: We fed C57BL/6J mice a protein- (casein) or sucrose-based high fat diet supplemented with fish oil or corn oil for 9 weeks. Irrespective of the fatty acid source, mice fed diets rich in sucrose became obese whereas mice fed high protein diets remained lean. Inclusion of sucrose in the diet also counteracted the well-known anti-inflammatory effect of fish oil in adipose tissue, but did not impair the ability of fish oil to prevent accumulation of fat in the liver. Calculation of HOMA-IR indicated that mice fed high levels of proteins remained insulin sensitive, whereas insulin sensitivity was reduced in the obese mice fed sucrose irrespectively of the fat source. We show that a high fat diet decreased glucose tolerance in the mice independently of both obesity and dietary levels of n-3 PUFAs and sucrose. Of note, increasing the protein∶sucrose ratio in high fat diets decreased energy efficiency irrespective of fat source. This was accompanied by increased expression of Ppargc1a (peroxisome proliferator-activated receptor, gamma, coactivator 1 alpha) and increased gluconeogenesis in the fed state. CONCLUSIONS/SIGNIFICANCE: The background diet influence the ability of n-3 PUFAs to protect against development of obesity, glucose intolerance and adipose tissue inflammation. High levels of dietary sucrose counteract the anti-inflammatory effect of fish oil in adipose tissue and increases obesity development in mice

Tetradecylthioacetic Acid Increases Hepatic Mitochondrial β-Oxidation and Alters Fatty Acid Composition in a Mouse Model of Chronic Inflammation

The administration of tetradecylthioacetic acid (TTA), a hypolipidemic and anti-inflammatory modified bioactive fatty acid, has in several experiments based on high fat diets been shown to improve lipid transport and utilization. It was suggested that increased mitochondrial and peroxisomal fatty acid oxidation in the liver of Wistar rats results in reduced plasma triacylglycerol (TAG) levels. Here we assessed the potential of TTA to prevent tumor necrosis factor (TNF) α-induced lipid modifications in human TNFα (hTNFα) transgenic mice. These mice are characterized by reduced β-oxidation and changed fatty acid composition in the liver. The effect of dietary treatment with TTA on persistent, low-grade hTNFα overexpression in mice showed a beneficial effect through decreasing TAG plasma concentrations and positively affecting saturated and monounsaturated fatty acid proportions in the liver, leading to an increased anti-inflammatory fatty acid index in this group. We also observed an increase of mitochondrial β-oxidation in the livers of TTA treated mice. Concomitantly, there were enhanced plasma levels of carnitine, acetyl carnitine, propionyl carnitine, and octanoyl carnitine, no changed levels in trimethyllysine and palmitoyl carnitine, and a decreased level of the precursor for carnitine, called γ-butyrobetaine. Nevertheless, TTA administration led to increased hepatic TAG levels that warrant further investigations to ascertain that TTA may be a promising candidate for use in the amelioration of inflammatory disorders characterized by changed lipid metabolism due to raised TNFα levels