Optimal transportation, topology and uniqueness

The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing the goods to be transported possess (non-trivial) topology. This question turns out to be closely linked to a delicate problem (# 111) of Birkhoff [14]: give a necessary and sufficient condition on the support of a joint probability to guarantee extremality among all measures which share its marginals. Fifty years of progress on Birkhoff's question culminate in Hestir and Williams' necessary condition which is nearly sufficient for extremality; we relax their subtle measurability hypotheses separating necessity from sufficiency slightly, yet demonstrate by example that to be sufficient certainly requires some measurability. Their condition amounts to the vanishing of the measure \gamma outside a countable alternating sequence of graphs and antigraphs in which no two graphs (or two antigraphs) have domains that overlap, and where the domain of each graph / antigraph in the sequence contains the range of the succeeding antigraph (respectively, graph). Such sequences are called numbered limb systems. We then explain how this characterization can be used to resolve the uniqueness of Kantorovich solutions for optimal transportation on a manifold with the topology of the sphere.Comment: 36 pages, 6 figure

Post-radiation increase in VEGF enhances glioma cell motility in vitro

<p>Abstract</p> <p>Background</p> <p>Glioblastoma multiforme (GBM) is among the most lethal of all human tumors, with frequent local recurrences after radiation therapy (RT). The mechanism accounting for such a recurrence pattern is unclear. It has classically been attributed to local recurrence of treatment-resistant cells. However, accumulating evidence suggests that additional mechanisms exist that involve the migration of tumor or tumor stem cells from other brain regions to tumor bed. VEGFs are well-known mitogens and can be up-regulated after RT. Here, we examine the effect of irradiation-induced VEGF on glioma cell motility.</p> <p>Materials and methods</p> <p>U251 and LN18 cell lines were used to generate irradiated-conditioned medium (IR-CM). At 72 h after irradiation, the supernatants were harvested. VEGF level in IR-CM was quantified by ELISA, and expression levels for VEGF mRNA were detected by RT-PCR. <it>In vitro </it>cancer cell motility was measured in chambers coated with/without Matrigel and IR-CM as a cell motility enhancer and a VEGF antibody as a neutralizer of VEGF bioactivity. Immunoblots were performed to evaluate the activity of cell motility-related kinases. Proliferation of GBM cells after treatment was measured by flow cytometry.</p> <p>Results</p> <p>Irradiation increased the level of VEGF mRNA that was mitigated by pre-RT exposure to Actinomycin D. U251 glioma cell motility (migration and invasion) was enhanced by adding IR-CM to un-irradiated cells (174.9 ± 11.4% and 334.2 ± 46% of control, respectively). When we added VEGF antibody to IR-CM, this enhanced cell motility was negated (110.3 ± 12.0% and 105.7 ± 14.0% of control, respectively). Immunoblot analysis revealed that IR-CM increased phosphorylation of VEGF receptor-2 (VEGFR2) secondary to an increase in VEGF, with a concomitant increase of phosphorylation of the downstream targets (Src and FAK). Increased phosphorylation was mitigated by adding VEGF antibody to IR-CM. There was no difference in the mitotic index of GBM cells treated with and without IR-CM and VEGF.</p> <p>Conclusions</p> <p>These results indicate that cell motility can be enhanced by conditioned medium from irradiated cells <it>in vitro </it>through stimulation of VEGFR2 signaling pathways and suggest that this effect involves the secretion of radiation-induced VEGF, leading to an increase in glioma cell motility.</p

Orthogonality of linear combinations of two orthogonal polynomial sequences

14 pages, no figures.-- MSC2000 code: 33C45.MR#: MR1865881 (2002j:33009)Zbl#: Zbl 0990.42007We find necessary and sufficient conditions for some linear combinations of two sequences of orthogonal polynomials to be again orthogonal.The first author (K.H.K.) was partially supported by KOSEF(99-2-101-001-5). The work of the third author (F.M.) was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB96-0120-C03-01.Publicad

Ab initio theoretical investigation of the frequency comb structure and coherence in the vuv-xuv regimes via high-order harmonic generation

This is the published version, also available here: http://dx.doi.org/10.1103/PhysRevA.77.031401.We present a fully ab initio quantum investigation of the frequency comb structure and coherence within each order of the high-order harmonic generation (HHG) spectrum in the high-frequency vuv-xuv regime. The HHG spectrum driven by a train of equal-spacing short laser pulses is calculated by propagating the time-dependent Schrödinger equation accurately and efficiently by means of the time-dependent generalized pseudospectral method. We explore the comb structure and coherence by varying the laser pulse separation τ, the number of pulses N, and the laser intensity. We find that a nested comb structure appears within each of the harmonics, ranging from the first harmonic all the way to the cutoff harmonic, and this global pattern persists regardless of the values of τ and N used. The comb structure of the harmonics originates from quantum interferences among induced dipole pulses. Finally, the frequency comb structure prevails even in the presence of appreciable ionization

A Note on Tachyons in the D3+D3ˉD3+{\bar {D3}} System

The periodic bounce of Born-Infeld theory of $D3$-branes is derived, and the BPS limit of infinite period is discussed as an example of tachyon condensation. The explicit bounce solution to the Born--Infeld action is interpreted as an unstable fundamental string stretched between the brane and its antibrane.Comment: 10 pages, 2 figures. v2: minor changes, acknowledgement added; v3: explanations and references added. Final version to appear in Mod. Phys. Lett.

Prediction of the Feed Values of Maize Silage by Near Infrared Reflectance Spectroscopy

Until recently, feed evaluation of silages in official laboratories and feed factories was based on cutting date, chemical composition and the ammonia fraction. However, in vitro techniques have been developed based on rumen fluid or commercial enzymes to replace laborious, time-consuming and expensive digestibility experiments with animals. In this study the possibility of using near infrared reflectance spectroscopy (NIRS) to predict the chemical composition and digestibility of maize silage was examined

Zeros of Jacobi-Sobolev orthogonal polynomials

10 pages, no figures.-- MSC2000 codes: 33C45.MR#: MR2027148 (2004m:33017)Zbl#: Zbl pre05376428We investigate zeros of Jacobi-Sobolev orthogonal polynomials with respect to \multline \langle f, g\rangle = \int_{-1}^1 f(x)g(x)(1-x)^{ \alpha }(1+x)^{\beta} dx\\ +\gamma \int_{-1}^1 f'(x)g'(x)(1-x)^{ \alpha +1}(1+x)^{ \beta } dx,\endmultline where $\alpha >-1,\ -1 0$.KHK and GJY were partially supported by KOSEF (98-0701-03-01-5) and Hwarangdae Research Institute. FM was partially supported by Dirección General de Investigación (MCYT) of Spain under grant BFM2000-0206-C04-01 and INTAS00-272.Publicad

High throughput evaluation of gamma-H2AX

The DNA double-strand break (DSB) is the primary lethal lesion after therapeutic radiation. Thus, the development of assays to detect and to quantitate these lesions could have broad preclinical and clinical impact. Phosphorylation of histone H2AX to form γ-H2AX is a known marker for irradiation-induced DNA DSBs. However, the first generation assay involves the use of immunofluorescent staining of γ-H2AX foci. This assay is time consuming, operator dependent and is not scalable for high throughput assay development. Thus, we sought to develop a new assay using a high throughput electrochemiluminescent platform from Mesoscale Discovery Systems to quantify γ-H2AX levels. The results show that our assay utilizes significantly less time and labor, has greater intra-assay reproducibility and has a greater dynamic range of γ-H2AX versus irradiation dose