Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in \Er^2

In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed

On the structure of phase transition maps for three or more coexisting phases

This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.Comment: 23 pages, 6 figure

Ground state at high density

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and Likos et al. (2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superposed on the sites of a close-packed lattice.Comment: Note adde

Cloud resource orchestration in the multi-cloud landscape: a systematic review of existing frameworks

The number of both service providers operating in the cloud market and customers consuming cloud-based services is constantly increasing, proving that the cloud computing paradigm has successfully delivered its potential. Nevertheless, the unceasing growth of the cloud market is posing hard challenges on its participants. On the provider side, the capability of orchestrating resources in order to maximise profits without failing customers’ expectations is a matter of concern. On the customer side, the efficient resource selection from a plethora of similar services advertised by a multitude of providers is an open question. In such a multi-cloud landscape, several research initiatives advocate the employment of software frameworks (namely, cloud resource orchestration frameworks - CROFs) capable of orchestrating the heterogeneous resources offered by a multitude of cloud providers in a way that best suits the customer’s need. The objective of this paper is to provide the reader with a systematic review and comparison of the most relevant CROFs found in the literature, as well as to highlight the multi-cloud computing open issues that need to be addressed by the research community in the near future

Off-nuclear star formation and obscured activity in the luminous infrared galaxy NGC 2623

New optical Hubble Space Telescope (HST), Spitzer Space Telescope, and XMM observations of the luminous infrared galaxy (LIRG) NGC 2623 are presented. This galaxy was observed as part of the Great Observatories All-sky LIRG Survey (GOALS). The prominent 3.2 kpc southern extension to the nucleus has been resolved by HST observations into ~100 star clusters, making it one of the richest off-nuclear concentrations of bright clusters observed in GOALS. The clusters have M_(F555W) ~-6.6 to -12.6 mag, which is within the magnitude range of Antennae galaxy clusters and in excess of 30 Doradus clusters at the high end. Their optical colors are primarily consistent with ages of ~1–100 Myr. Archival GALEX data show the off-nuclear region to be extremely bright in the far-ultraviolet, being equivalent in luminosity to the resolved nuclear region at 0.15 µm, but becoming less energetically significant at increasing wavelengths. In addition, [Ne v] 14.3 µm emission is detected with Spitzer IRS, confirming the inference from the X-ray and radio data that an active galactic nucleus (AGN) is present. Thus, the off-nuclear optical clusters are associated with a secondary burst of activity corresponding to a star formation rate ~0.1–0.2 M⊙ yr^(-1); the bulk of infrared (and thus bolometric) luminosity is generated via star formation and an AGN embedded behind dust within the inner kiloparsec of the system. If the infrared luminosity is primarily reprocessed starlight, the off-nuclear starburst accounts for <1% of the present star formation in NGC 2623

Cellular Model of Warburg Effect Identifies Tumor Promoting Function of UCP2 in Breast Cancer and Its Suppression by Genipin

The Warburg Effect is characterized by an irreversible injury to mitochondrial oxidative phosphorylation (OXPHOS) and an increased rate of aerobic glycolysis. In this study, we utilized a breast epithelial cell line lacking mitochondrial DNA (rho0) that exhibits the Warburg Effect associated with breast cancer. We developed a MitoExpress array for rapid analysis of all known nuclear genes encoding the mitochondrial proteome. The gene-expression pattern was compared among a normal breast epithelial cell line, its rho0 derivative, breast cancer cell lines and primary breast tumors. Among several genes, our study revealed that over-expression of mitochondrial uncoupling protein UCP2 in rho0 breast epithelial cells reflects gene expression changes in breast cancer cell lines and in primary breast tumors. Furthermore, over-expression of UCP2 was also found in leukemia, ovarian, bladder, esophagus, testicular, colorectal, kidney, pancreatic, lung and prostate tumors. Ectopic expression of UCP2 in MCF7 breast cancer cells led to a decreased mitochondrial membrane potential and increased tumorigenic properties as measured by cell migration, in vitro invasion and anchorage independent growth. Consistent with in vitro studies, we demonstrate that UCP2 over-expression leads to development of tumors in vivo in an orthotopic model of breast cancer. Genipin, a plant derived small molecule, suppressed the UCP2 led tumorigenic properties, which were mediated by decreased reactive oxygen species and down-regulation of UCP2. However, UCP1, 3, 4 and 5 gene expression was unaffected. UCP2 transcription was controlled by SMAD4. Together, these studies suggest a tumor-promoting function of UCP2 in breast cancer. In summary, our studies demonstrate that i) the Warburg Effect is mediated by UCP2; ii) UCP2 is over-expressed in breast and many other cancers; iii) UCP2 promotes tumorigenic properties in vitro and in vivo and iv) genipin suppresses the tumor promoting function of UCP2

Two models of unawareness: comparing the object-based and the subjective-state-space approaches

In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (2007) and the subjective-state-space approach of Heifetz, Meier and Schipper (2006)

Population based models of cortical drug response: insights from anaesthesia

A great explanatory gap lies between the molecular pharmacology of psychoactive agents and the neurophysiological changes they induce, as recorded by neuroimaging modalities. Causally relating the cellular actions of psychoactive compounds to their influence on population activity is experimentally challenging. Recent developments in the dynamical modelling of neural tissue have attempted to span this explanatory gap between microscopic targets and their macroscopic neurophysiological effects via a range of biologically plausible dynamical models of cortical tissue. Such theoretical models allow exploration of neural dynamics, in particular their modification by drug action. The ability to theoretically bridge scales is due to a biologically plausible averaging of cortical tissue properties. In the resulting macroscopic neural field, individual neurons need not be explicitly represented (as in neural networks). The following paper aims to provide a non-technical introduction to the mean field population modelling of drug action and its recent successes in modelling anaesthesia