Applications of Equivariant Topology In Cascading Makeev Problems

Many solutions to problems arising in discrete geometry have come from insights in equivariant topology. Configuration-Space/Test Map (CS/TM) type setups, pioneered by Zivaljevic, offer reductions of combinatorial or geometric facts to showing the nonexistence of certain $G$-equivariant maps $f:X \to V\setminus Z$. In particular, partitions of objects by arcs, planes, and convex sets, and Tverberg theorems have been particularly amenable to topological methods , since their solutions affect the global structure of the relevant topological objects. However, there have been limits to the method as demonstrated by a failure to solve of the celeberated and now settled Topological Tverberg conjecture and, more generally, difficulty in finding sharp bounds for various conjectures. Nonetheless, we seek to employ characteristic classes, a cohomological invariant common to Borsuk-Ulam type problems, since these allow us to use explicit polynomial calculations to sharpen results to related problems. While determining sharp topological results for equipartition problems is a hard problem, there has been recent success in finding precise solutions by adding geometric constraints to the problem of plane equipartitions. This suggests that the polynomial method still has its use in related problems, and we employ these methods to``cascading Makeev type problems

Plio-Pleistocene time-averaged field in southern Patagonia recorded in lava flows

Paleomagnetic directions were obtained from stepwise alternating-field or thermal demagnetization of 53 lava flows from southern Patagonia (latitudes 49.5°-52.1 °S) that include the Pali-Aike volcanic field and the Meseta Viscachas plateau lavas. In addition to previous Miocene-late Quaternary ages of these flows, 40Ar/39Ar dates spanning from 0.1 to 15.4 Ma were obtained for 17 of the sites. All except one of the magnetic polarities coincide with the expected polarities of the magnetic polarity timescale [Cande and Kent, 1995] for the obtained 40Ar/39Ar ages. The mean direction from 33 sites (eliminating sites <4 Ma) that pass a selection criteria of α95 ≤5° is Dec = 358.7°,Inc = - 68.2°, α95 = 3.5°, a value that coincides within the statistical uncertainty with the direction of the geocentric axial dipole for that area (Inc = - 68.1°). Likewise, the mean virtual geomagnetic pole (VGP) coincides within the statistical uncertainty with the geographic North Pole. The secular variation described by the VGP angular standard deviation for these sites is 17.1°, a value expected for that latitude according to Model G of paleosecular variation [McFadden et al., 1988]. The characteristics of the data presented are optimum for time-averaged field (TAF) studies because of the good age control and good quality of the paleomagnetic data: (1) primary components of magnetization were obtained using principal component analysis [Kirschvink, 1980] from at least five points and maximum angular deviation ≤5°, (2) site means were calculated with Fisher statistics using at least three samples, and (c) 38 of the 53 flows had α95 ≤ 5°. No results (five sites) or high α95 values (≤5°) were obtained primarily from sites affected by lightning.Fil: Mejia, V.. University of Florida; Estados UnidosFil: Opdyke, N. D.. University of Florida; Estados UnidosFil: Vilas, Juan Francisco A.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Geología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires; ArgentinaFil: Singer, B. S.. University of Wisconsin; Estados UnidosFil: Stoner, J. S.. State University of Colorado at Boulder; Estados Unido

Strain and order-parameter coupling in Ni-Mn-Ga Heusler alloys from resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy and magnetic susceptibility experiments have been used to characterize strain coupling phenomena associated with structural and magnetic properties of the shape-memory Heusler alloy series Ni$_{50+x}$Mn$_{25-x}$Ga$_{25}$ ($x=0$, 2.5, 5.0, and 7.5). All samples exhibit a martensitic transformation at temperature $T_M$ and ferromagnetic ordering at temperature $T_C$, while the pure end member ($x=0$) also has a premartensitic transition at $T_{PM}$, giving four different scenarios: $T_C>T_{PM}>T_M$, $T_C>T_M$ without premartensitic transition, $T_C\approx T_M$, and $T_C<T_M$. Fundamental differences in elastic properties i.e., stiffening versus softening, are explained in terms of coupling of shear strains with three discrete order parameters relating to magnetic ordering, a soft mode and the electronic instability responsible for the large strains typical of martensitic transitions. Linear-quadratic or biquadratic coupling between these order parameters, either directly or indirectly via the common strains, is then used to explain the stabilities of the different structures. Acoustic losses are attributed to critical slowing down at the premartensite transition, to the mobility of interphases between coexisting phases at the martensitic transition and to mobility of some aspect of the twin walls under applied stress down to the lowest temperatures at which measurements were made.Comment: 9 pages, 5 figure

Reconstructing Fourier's law from disorder in quantum wires

The theory of open quantum systems is used to study the local temperature and heat currents in metallic nanowires connected to leads at different temperatures. We show that for ballistic wires the local temperature is almost uniform along the wire and Fourier's law is invalid. By gradually increasing disorder, a uniform temperature gradient ensues inside the wire and the thermal current linearly relates to this local temperature gradient, in agreement with Fourier's law. Finally, we demonstrate that while disorder is responsible for the onset of Fourier's law, the non-equilibrium energy distribution function is determined solely by the heat baths

In practice: bovine nematode control in the face of resistance: fourteen years of adaptive strategies

Integrated Nematode control of bovines in Argentina has been considered "state of the art" for many years because it comprises diagnosis, reasonable use of drugs and epidemiology, and it involves a veterinarian with a holistic vision of the farm’s health and production objectives. In the year 2000 resistance to macrocyclic lactones was discovered and three years later, we found resistance to benzimidazol drugs.Fil: Mejia, M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Licoff, N.. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Lacau, Isabel María. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaXXVIII World Buiatrics CongressCairnsAustraliaWorld association for Buiatric

Quadrupolar interactions between acceptor pairs in p-doped semiconductors

We consider the interaction between acceptor pairs in doped semiconductors in the limit of large inter-acceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-j symbol. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating p-type semiconductors.Comment: 12 pages, 6 figures, as published in PR

Heat flux operator, current conservation and the formal Fourier's law

By revisiting previous definitions of the heat current operator, we show that one can define a heat current operator that satisfies the continuity equation for a general Hamiltonian in one dimension. This expression is useful for studying electronic, phononic and photonic energy flow in linear systems and in hybrid structures. The definition allows us to deduce the necessary conditions that result in current conservation for general-statistics systems. The discrete form of the Fourier's Law of heat conduction naturally emerges in the present definition

Volumetric and anatomical MRI for hypoxic-ischemic encephalopathy: relationship to hypothermia therapy and neurosensory impairments.

OBJECTIVE: To relate volumetric magnetic resonance imaging (MRI) findings to hypothermia therapy and neurosensory impairments. STUDY DESIGN: Newborns \u3e or =36 weeks\u27 gestation with hypoxic-ischemic encephalopathy who participated in the National Institute of Child Health and Human Development hypothermia randomized trial at our center were eligible. We determined the relationship between hypothermia treatment and usual care (control) to absolute and relative cerebral tissue volumes. Furthermore, we correlated brain volumes with death or neurosensory impairments at 18 to 22 months. RESULT: Both treatment groups were comparable before randomization. Total brain tissue volumes did not differ in relation to treatment assignment. However, relative volumes of subcortical white matter were significantly larger in hypothermia-treated than control infants. Furthermore, relative total brain volumes correlated significantly with death or neurosensory impairments. Relative volumes of the cortical gray and subcortical white matter also correlated significantly with Bayley Scales psychomotor development index. CONCLUSION: Selected volumetric MRI findings correlated with hypothermia therapy and neurosensory impairments. Larger studies using MRI brain volumes as a secondary outcome measure are needed

Elevational richness patterns of sphingid moths support area effects over climatic drivers in a near‐global analysis

Not sure if this is the pre-refereed or final submitted version.Aim We test hypotheses on the environmental control of elevational richness patterns of sphingid moths for their global applicability and generality. Specifically, we compare effects of area with climate‐related drivers, such as primary productivity and temperature, while also considering direct effects of precipitation. Major taxa Sphingid moths (Lepidoptera). Location Eighty‐six mountain ranges of the Old World and the Australia/Pacific region, from Scandinavia and Siberia through the African and Australasian tropics to South Africa and Southern Australia. Methods We used a large compilation of point locality records for 744 species, in addition to fine‐grained range maps derived from species distribution modelling of these records, to characterize the elevational pattern of species richness in 86 custom‐delineated mountain regions. For both types of data, we compared the effects of environmental drivers on richness by comparing standardized coefficients of multivariate models for pooled data after accounting for between‐region variation in richness. Results We observed varying patterns of elevational richness across the research region, with a higher prevalence of midpeaks in arid regions. We found overwhelming support for area as a main determinant of richness, modulated by temperature and productivity, whereas we detected no effect of precipitation. Main conclusions Area, productivity and temperature are the main environmental predictors explaining a large proportion of variability in sphingid richness. This is consistent not only with other elevational studies, but also with empirical and theoretical biodiversity research in a non‐elevational context (with the caveat of some unresolved issues in elevational area effects). However, distinct differences in elevational patterns remain even within the same mountain ranges when comparing with other Lepidoptera, that is, geometrid moths, which highlights the importance of understanding higher clade differentiation in ecological responses, within insects and in other groups.© 2019 John Wiley & Sons Ltd. This is the pre-peer reviewed version of the following article: Bärtschi, F, McCain, CM, Ballesteros‐Mejia, L, Kitching, IJ, Beerli, N, Beck, J. Elevational richness patterns of sphingid moths support area effects over climatic drivers in a near‐global analysis. Global Ecol Biogeogr. 2019; 28: 917– 927. https://doi.org/10.1111/geb.12903, which has been published in final form at doi:10.1111/geb.12903. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.