k-Trails: Recognition, Complexity, and Approximations

The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First results highlight several interesting advantages of k-trails compared to previous routing approaches. However, so far, only little is known regarding computational aspects of k-trails. In this work we aim to fill this gap by presenting how k-trails can be analyzed using techniques from algorithmic matroid theory. Exploiting this connection, we resolve several open questions about k-trails. In particular, we show that one can recognize efficiently whether a graph is a k-trail. Furthermore, we show that deciding whether a graph contains a k-trail is NP-complete; however, every graph that contains a k-trail is a (k+1)-trail. Moreover, further leveraging the connection to matroids, we consider the problem of finding a minimum weight k-trail contained in a graph G. We show that one can efficiently find a (2k-1)-trail contained in G whose weight is no more than the cheapest k-trail contained in G, even when allowing negative weights. The above results settle several open questions raised by Molnar, Newman, and Sebo

Fetal-derived trophoblast use the apoptotic cytokine tumor necrosis factor-alpha-related apoptosis-inducing ligand to induce smooth muscle cell death.

Remodeling of the uterine spiral arteries during pregnancy transforms them from high to low resistance vessels that lack vasoconstrictive properties. This process is essential to meet the demand for increased blood flow imposed by the growing fetus. Loss of endothelial and smooth muscle cells (SMC) is evident in remodeled arteries but the mechanisms underlying this transformation remain unknown. This study investigated the hypothesis that fetal trophoblast invading from the placenta instigate remodeling by triggering cell death in vascular SMC. Specifically, a role for trophoblast-derived death inducing cytokine tumor necrosis factor-α–related apoptosis-inducing ligand (TRAIL) was investigated. Expression of the activating TRAIL receptors R1 and R2 was detected by flow cytometry on human aortic SMC and by immunohistochemistry on spiral artery SMC. Recombinant human TRAIL induced human aortic SMC apoptosis, which was inhibited by antibodies against TRAIL-R1 or -R2. Perfusion of denuded spiral artery segments with recombinant human TRAIL also induced SMC apoptosis. Trophoblasts isolated from first trimester placenta expressed membrane-associated TRAIL and induced apoptosis of human aortic SMC; apoptosis was significantly inhibited by a recombinant human TRAIL-R1:Fc construct. Trophoblast within the first trimester placental bed also expressed TRAIL. These data show that: 1) TRAIL causes SMC death; 2) trophoblast produce the apoptotic cytokine TRAIL; and 3) trophoblast induce SMC apoptosis via a TRAIL-dependent mechanism. We conclude that TRAIL produced by trophoblast causes apoptosis of SMC and thus may contribute to SMC loss during spiral artery remodeling in pregnancy

The dynamical Green's function and an exact optical potential for electron-molecule scattering including nuclear dynamics

We derive a rigorous optical potential for electron-molecule scattering including the effects of nuclear dynamics by extending the common many-body Green's function approach to optical potentials beyond the fixed-nuclei limit for molecular targets. Our formalism treats the projectile electron and the nuclear motion of the target molecule on the same footing whereby the dynamical optical potential rigorously accounts for the complex many-body nature of the scattering target. One central result of the present work is that the common fixed-nuclei optical potential is a valid adiabatic approximation to the dynamical optical potential even when projectile and nuclear motion are (nonadiabatically) coupled as long as the scattering energy is well below the electronic excitation thresholds of the target. For extremely low projectile velocities, however, when the cross sections are most sensitive to the scattering potential, we expect the influences of the nuclear dynamics on the optical potential to become relevant. For these cases, a systematic way to improve the adiabatic approximation to the dynamical optical potential is presented that yields non-local operators with respect to the nuclear coordinates.Comment: 22 pages, no figures, accepted for publ., Phys. Rev.

Modified effective-range theory for low energy e-N2 scattering

We analyze the low-energy e-N2 collisions within the framework of the Modified-Effective Range Theory (MERT) for the long-range potentials, developed by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. In comparison to the traditional MERT we do not expand the total cross-section in the series of the incident momentum \hbar k, but instead we apply the exact analytical solutions of the Schroedinger equation for the long-range polarization potential, as proposed in the original formulation of O'Malley et al. This extends the applicability of MERT up to few eV regime, as we confirm using some simplified model potential of the electron-molecule interaction. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross sections in the 0.1 - 1.0 eV energy range by fitting procedure. Surprisingly, our treatment predicts a shape resonance that appears slightly higher than experimentally well known resonance in the total cross section. Agreement with the experimentally observed shape-resonance can be improved by assuming the position of the resonance in a given partial wave. Influence of the quadrupole potential on resonances is also discussed: we show that it can be disregarded for N2. In conclusion, the modified-effective range formalism treating the long-range part of the potential in an exact way, reproduces well both the very low-energy behavior of the integral cross section as well as the presence of resonances in the few eV range.Comment: 9 pages, LaTex, 4 eps figures, EPJ style; extended and upgraded version of arXiv:0708.2991, now considering only e-N2 scatterin

5-ht inhibition of rat insulin 2 promoter cre recombinase transgene and proopiomelanocortin neuron excitability in the mouse arcuate nucleus

A number of anti-obesity agents have been developed that enhance hypothalamic 5-HT transmission. Various studies have demonstrated that arcuate neurons, which express proopiomelanocortin peptides (POMC neurons), and neuropeptide Y with agouti-related protein (NPY/AgRP) neurons, are components of the hypothalamic circuits responsible for energy homeostasis. An additional arcuate neuron population, rat insulin 2 promoter Cre recombinase transgene (RIPCre) neurons, has recently been implicated in hypothalamic melanocortin circuits involved in energy balance. It is currently unclear how 5-HT modifies neuron excitability in these local arcuate neuronal circuits. We show that 5-HT alters the excitability of the majority of mouse arcuate RIPCre neurons, by either hyperpolarization and inhibition or depolarization and excitation. RIPCre neurons sensitive to 5-HT, predominantly exhibit hyperpolarization and pharmacological studies indicate that inhibition of neuronal firing is likely to be through 5-HT1F receptors increasing current through a voltage-dependent potassium conductance. Indeed, 5-HT1F receptor immunoreactivity co-localizes with RIPCre green fluorescent protein expression. A minority population of POMC neurons also respond to 5-HT by hyperpolarization, and this appears to be mediated by the same receptor-channel mechanism. As neither POMC nor RIPCre neuronal populations display a common electrical response to 5-HT, this may indicate that sub-divisions of POMC and RIPCre neurons exist, perhaps serving different outputs

The Cowl - v.10 - n.3 - Oct 22, 1947

The Cowl - student newspaper of Providence College. Volume 10, Number 3 - Oct 22, 1947. 6 pages