A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42

Necessity of integral formalism

To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 445], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D. 12 (1975) 3845]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schrodinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schrodinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description.Comment: 13Page; Schrodinger differential equation shall lead to vanishing Berry phas

Strictly Toral Dynamics

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points $ine(f)$ is shown to be a disjoint union of periodic topological disks ("elliptic islands"), while the set of essential points $ess(f)$ is an essential continuum, with typically rich dynamics (the "chaotic region"). This generalizes and improves a similar description by J\"ager. The key result is boundedness of these "elliptic islands", which allows, among other things, to obtain sharp (uniform) bounds of the diffusion rates. We also show that the dynamics in $ess(f)$ is as rich as in $\mathbb{T}^2$ from the rotational viewpoint, and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points.Comment: Incorporates suggestions and corrections by the referees. To appear in Inv. Mat

Aryl hydrocarbon receptor-mediated activity of gas-phase ambient air derived from passive sampling and an \u3cem\u3ein vitro\u3c/em\u3e bioassay

The gaseous fraction of hydrophobic organic contaminants (HOCs) in ambient air appears to be responsible for a significant portion of aryl hydrocarbon receptor (AhR)‐mediated activity, but the majority of compounds contributing to this activity remain unidentified. This study investigated the use of polyethylene passive samplers (PEs) to isolate gaseous HOCs from ambient air for use in in vitro bioassays and to improve our understanding of the toxicological relevance of the gaseous fraction of ambient air in urban and residential environments. Concentrations of polycyclic aromatic hydrocarbons (PAHs) and organic flame retardants (OFRs) were measured in PE extracts. Extracts were also analyzed using an in vitro bioassay to measure AhR‐mediated activity. Bioassay‐derived benzo[a]pyrene (BaP) equivalents (BaP‐Eqbio), a measure of potency of HOC mixtures, were greatest in the downtown Cleveland area and lowest at rural/residential sites further from the city center. BaP‐Eqbio was weakly correlated with concentrations of 2‐ring alkyl/substituted PAHs and one organophosphate flame retardant, ethylhexyl diphenyl phosphate (EHDPP). Potency predicted based on literature‐derived induction equivalency factors (IEFs) explained only 2‐23% of the AhR‐mediated potency observed in bioassay experiments. This study suggests that health risks of gaseous ambient air pollution predicted using data from targeted chemical analysis may underestimate risks of exposure, most likely due to augmentation of potency by unmonitored chemicals in the mixture, and the lack of relevant IEFs for many targeted analytes

Thermodynamic behaviour and structural properties of an aqueous sodium chloride solution upon supercooling

We present the results of a molecular dynamics simulation study of thermodynamic and structural properties upon supercooling of a low concentration sodium chloride solution in TIP4P water and the comparison with the corresponding bulk quantities. We study the isotherms and the isochores for both the aqueous solution and bulk water. The comparison of the phase diagrams shows that thermodynamic properties of the solution are not merely shifted with respect to the bulk. Moreover, from the analysis of the thermodynamic curves, both the spinodal line and the temperatures of maximum density curve can be calculated. The spinodal line appears not to be influenced by the presence of ions at the chosen concentration, while the temperatures of maximum density curve displays both a mild shift in temperature and a shape modification with respect to bulk. Signatures of the presence of a liquid-liquid critical point are found in the aqueous solution. By analysing the water-ion radial distribution functions of the aqueous solution we observe that upon changing density, structural modifications appear close to the spinodal. For low temperatures additional modifications appear also for densities close to that corresponding to a low density configurational energy minimum.Comment: 10 pages, 13 figures, 2 tables. To be published in J. Chem. Phy

Novel functional roles for \u3cem\u3ePERIANTHIA\u3c/em\u3e and \u3cem\u3eSEUSS\u3c/em\u3e during floral organ identity specification, floral meristem termination, and gynoecial development

The gynoecium is the female reproductive structure of angiosperm flowers. In Arabidopsis thaliana the gynoecium is composed of two carpels that are fused into a tube-like structure. As the gynoecial primordium arises from the floral meristem, a specialized meristematic structure, the carpel margin meristem (CMM), develops from portions of the medial gynoecial domain. The CMM is critical for reproductive competence because it gives rise to the ovules, the precursors of the seeds. Here we report a functional role for the transcription factor PERIANTHIA (PAN) in the development of the gynoecial medial domain and the formation of ovule primordia. This function of PAN is revealed in pan aintegumenta (ant) as well as seuss (seu) pan double mutants that form reduced numbers of ovules. Previously, PAN was identified as a regulator of perianth organ number and as a direct activator of AGAMOUS (AG) expression in floral whorl four. However, the seu pan double mutants display enhanced ectopic AG expression in developing sepals and the partial transformation of sepals to petals indicating a novel role for PAN in the repression of AG in floral whorl one. These results indicate that PAN functions as an activator or repressor of AG expression in a whorl-specific fashion. The seu pan double mutants also display enhanced floral indeterminacy, resulting in the formation of fifth whorl structures and disruption of WUSCHEL (WUS) expression patterns revealing a novel role for SEU in floral meristem termination

Novel functional roles for \u3cem\u3ePERIANTHIA\u3c/em\u3e and \u3cem\u3eSEUSS\u3c/em\u3e during floral organ identity specification, floral meristem termination, and gynoecial development

The gynoecium is the female reproductive structure of angiosperm flowers. In Arabidopsis thaliana the gynoecium is composed of two carpels that are fused into a tube-like structure. As the gynoecial primordium arises from the floral meristem, a specialized meristematic structure, the carpel margin meristem (CMM), develops from portions of the medial gynoecial domain. The CMM is critical for reproductive competence because it gives rise to the ovules, the precursors of the seeds. Here we report a functional role for the transcription factor PERIANTHIA (PAN) in the development of the gynoecial medial domain and the formation of ovule primordia. This function of PAN is revealed in pan aintegumenta (ant) as well as seuss (seu) pan double mutants that form reduced numbers of ovules. Previously, PAN was identified as a regulator of perianth organ number and as a direct activator of AGAMOUS (AG) expression in floral whorl four. However, the seu pan double mutants display enhanced ectopic AG expression in developing sepals and the partial transformation of sepals to petals indicating a novel role for PAN in the repression of AG in floral whorl one. These results indicate that PAN functions as an activator or repressor of AG expression in a whorl-specific fashion. The seu pan double mutants also display enhanced floral indeterminacy, resulting in the formation of fifth whorl structures and disruption of WUSCHEL (WUS) expression patterns revealing a novel role for SEU in floral meristem termination

Cooperative Origin of Low-Density Domains in Liquid Water

We study the size of clusters formed by water molecules possessing large enough tetrahedrality with respect to their nearest neighbors. Using Monte Carlo simulation of the SPC/E model of water, together with a geometric analysis based on Voronoi tessellation, we find that regions of lower density than the bulk are formed by accretion of molecules into clusters exceeding a minimum size. Clusters are predominantly linear objects and become less compact as they grow until they reach a size beyond which further accretion is not accompanied by a density decrease. The results suggest that the formation of "ice-like" regions in liquid water is cooperative.Comment: 16 pages, 6 figure

Moderate hypothermia within 6 h of birth plus inhaled xenon versus moderate hypothermia alone after birth asphyxia (TOBY-Xe): a proof-of-concept, open-label, randomised controlled trial

Background Moderate cooling after birth asphyxia is associated with substantial reductions in death and disability, but additional therapies might provide further benefit. We assessed whether the addition of xenon gas, a promising novel therapy, after the initiation of hypothermia for birth asphyxia would result in further improvement. Methods Total Body hypothermia plus Xenon (TOBY-Xe) was a proof-of-concept, randomised, open-label, parallel-group trial done at four intensive-care neonatal units in the UK. Eligible infants were 36–43 weeks of gestational age, had signs of moderate to severe encephalopathy and moderately or severely abnormal background activity for at least 30 min or seizures as shown by amplitude-integrated EEG (aEEG), and had one of the following: Apgar score of 5 or less 10 min after birth, continued need for resuscitation 10 min after birth, or acidosis within 1 h of birth. Participants were allocated in a 1:1 ratio by use of a secure web-based computer-generated randomisation sequence within 12 h of birth to cooling to a rectal temperature of 33·5°C for 72 h (standard treatment) or to cooling in combination with 30% inhaled xenon for 24 h started immediately after randomisation. The primary outcomes were reduction in lactate to N-acetyl aspartate ratio in the thalamus and in preserved fractional anisotropy in the posterior limb of the internal capsule, measured with magnetic resonance spectroscopy and MRI, respectively, within 15 days of birth. The investigator assessing these outcomes was masked to allocation. Analysis was by intention to treat. This trial is registered with ClinicalTrials.gov, number NCT00934700, and with ISRCTN, as ISRCTN08886155. Findings The study was done from Jan 31, 2012, to Sept 30, 2014. We enrolled 92 infants, 46 of whom were randomly assigned to cooling only and 46 to xenon plus cooling. 37 infants in the cooling only group and 41 in the cooling plus xenon group underwent magnetic resonance assessments and were included in the analysis of the primary outcomes. We noted no significant differences in lactate to N-acetyl aspartate ratio in the thalamus (geometric mean ratio 1·09, 95% CI 0·90 to 1·32) or fractional anisotropy (mean difference −0·01, 95% CI −0·03 to 0·02) in the posterior limb of the internal capsule between the two groups. Nine infants died in the cooling group and 11 in the xenon group. Two adverse events were reported in the xenon group: subcutaneous fat necrosis and transient desaturation during the MRI. No serious adverse events were recorded. Interpretation Administration of xenon within the delayed timeframe used in this trial is feasible and apparently safe, but is unlikely to enhance the neuroprotective effect of cooling after birth asphyxia

Molecular modeling of a tandem two pore domain potassium channel reveals a putative binding Site for general anesthetics

[Image: see text] Anesthetics are thought to mediate a portion of their activity via binding to and modulation of potassium channels. In particular, tandem pore potassium channels (K2P) are transmembrane ion channels whose current is modulated by the presence of general anesthetics and whose genetic absence has been shown to confer a level of anesthetic resistance. While the exact molecular structure of all K2P forms remains unknown, significant progress has been made toward understanding their structure and interactions with anesthetics via the methods of molecular modeling, coupled with the recently released higher resolution structures of homologous potassium channels to act as templates. Such models reveal the convergence of amino acid regions that are known to modulate anesthetic activity onto a common three- dimensional cavity that forms a putative anesthetic binding site. The model successfully predicts additional important residues that are also involved in the putative binding site as validated by the results of suggested experimental mutations. Such a model can now be used to further predict other amino acid residues that may be intimately involved in the target-based structure–activity relationships that are necessary for anesthetic binding