The arithmetic of hyperelliptic curves

We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in particular, those for finding the rank of the Jacobian, and the set of rational points on the curve

Rectification of the Water Permeability in COS-7 Cells at 22, 10 and 0°C

The osmotic and permeability parameters of a cell membrane are essential physico-chemical properties of a cell and particularly important with respect to cell volume changes and the regulation thereof. Here, we report the hydraulic conductivity, Lp, the non-osmotic volume, Vb, and the Arrhenius activation energy, Ea, of mammalian COS-7 cells. The ratio of Vb to the isotonic cell volume, Vc iso, was 0.29. Ea, the activation energy required for the permeation of water through the cell membrane, was 10,700, and 12,000 cal/mol under hyper- and hypotonic conditions, respectively. Average values for Lp were calculated from swell/shrink curves by using an integrated equation for Lp. The curves represented the volume changes of 358 individually measured cells, placed into solutions of nonpermeating solutes of 157 or 602 mOsm/kg (at 0, 10 or 22°C) and imaged over time. Lp estimates for all six combinations of osmolality and temperature were calculated, resulting in values of 0.11, 0.21, and 0.10 µm/min/atm for exosmotic flow and 0.79, 1.73 and 1.87 µm/min/atm for endosmotic flow (at 0, 10 and 22°C, respectively). The unexpected finding of several fold higher Lp values for endosmotic flow indicates highly asymmetric membrane permeability for water in COS-7. This phenomenon is known as rectification and has mainly been reported for plant cell, but only rarely for animal cells. Although the mechanism underlying the strong rectification found in COS-7 cells is yet unknown, it is a phenomenon of biological interest and has important practical consequences, for instance, in the development of optimal cryopreservation

Small Horizons

All near horizon geometries of supersymmetric black holes in a N=2, D=5 higher-derivative supergravity theory are classified. Depending on the choice of near-horizon data we find that either there are no regular horizons, or horizons exist and the spatial cross-sections of the event horizons are conformal to a squashed or round S^3, S^1 * S^2, or T^3. If the conformal factor is constant then the solutions are maximally supersymmetric. If the conformal factor is not constant, we find that it satisfies a non-linear vortex equation, and the horizon may admit scalar hair.Comment: 21 pages, latex. Typos corrected and reference adde

Heterotic Black Horizons

We show that the supersymmetric near horizon geometry of heterotic black holes is either an AdS_3 fibration over a 7-dimensional manifold which admits a G_2 structure compatible with a connection with skew-symmetric torsion, or it is a product R^{1,1} * S^8, where S^8 is a holonomy Spin(7) manifold, preserving 2 and 1 supersymmetries respectively. Moreover, we demonstrate that the AdS_3 class of heterotic horizons can preserve 4, 6 and 8 supersymmetries provided that the geometry of the base space is further restricted. Similarly R^{1,1} * S^8 horizons with extended supersymmetry are products of R^{1,1} with special holonomy manifolds. We have also found that the heterotic horizons with 8 supersymmetries are locally isometric to AdS_3 * S^3 * T^4, AdS_3 * S^3 * K_3 or R^{1,1} * T^4 * K_3, where the radii of AdS_3 and S^3 are equal and the dilaton is constant.Comment: 35 pages, latex. Minor alterations to equation (3.11) and section 4.1, the conclusions are not affecte

State-space Manifold and Rotating Black Holes

We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/ $M$-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric $AdS_5$ black holes, $D_1$-$D_5$ configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scaling property suggest that the brane-brane statistical pair correlation functions divulge an asymmetric nature, in comparison with the others. This approach indicates that all above configurations are effectively attractive and stable, on an arbitrary hyper-surface of the state-space manifolds. It is nevertheless noticed that there exists an intriguing relationship between non-ideal inter-brane statistical interactions and phase transitions. The ramifications thus described are consistent with the existing picture of the microscopic CFTs. We conclude with an extended discussion of the implications of this work for the physics of black holes in string theory.Comment: 44 pages, Keywords: Rotating Black Holes; State-space Geometry; Statistical Configurations, String Theory, M-Theory. PACS numbers: 04.70.-s Physics of black holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics; 04.50.Gh Higher-dimensional black holes, black strings, and related objects. Edited the bibliograph

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

Women and postfertilization effects of birth control: consistency of beliefs, intentions and reported use

BACKGROUND: This study assesses the consistency of responses among women regarding their beliefs about the mechanisms of actions of birth control methods, beliefs about when human life begins, the intention to use or not use birth control methods that they believe may act after fertilization or implantation, and their reported use of specific methods. METHODS: A questionnaire was administered in family practice and obstetrics and gynecology clinics in Salt Lake City, Utah, and Tulsa, Oklahoma. Participants included women ages 18–50 presenting for any reason and women under age 18 presenting for family planning or pregnancy care. Analyses were based on key questions addressing beliefs about whether specific birth control methods may act after fertilization, beliefs about when human life begins, intention to use a method that may act after fertilization, and reported use of specific methods. The questionnaire contained no information about the mechanism of action of any method of birth control. Responses were considered inconsistent if actual use contradicted intentions, if one intention contradicted another, or if intentions contradicted beliefs. RESULTS: Of all respondents, 38% gave consistent responses about intention to not use or to stop use of any birth control method that acted after fertilization, while 4% gave inconsistent responses. The corresponding percentages for birth control methods that work after implantation were 64% consistent and 2% inconsistent. Of all respondents, 34% reported they believed that life begins at fertilization and would not use any birth control method that acts after fertilization (a consistent response), while 3% reported they believed that life begins at fertilization but would use a birth control method that acts after fertilization (inconsistent). For specific methods of birth control, less than 1% of women gave inconsistent responses. A majority of women (68% or greater) responded accurately about the mechanism of action of condoms, abstinence, sterilization, and abortion, but a substantial percentage of women (between 19% and 57%) were uncertain about the mechanisms of action of oral contraceptives, intrauterine devices (IUDs), Depo-Provera, or natural family planning. CONCLUSION: Women who believe that life begins at fertilization may not intend to use a birth control method that could have postfertilization effects. More research is needed to understand the relative importance of postfertilization effects for women in other populations, and in relation to other properties of and priorities for birth control methods. However, many women were uncertain about the mechanisms of action of specific methods. To respect the principles of informed consent, some women may need more education about what is known and not known about the mechanisms of action of birth control methods

Stationary Black Holes: Uniqueness and Beyond

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998. Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's authorship. Significantly restructured and updated all sections; changes are too numerous to be usefully described here. The number of references increased from 186 to 32

Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Extreme behavioural shifts by baboons exploiting risky, resource-rich, human-modified environments

Abstract A range of species exploit anthropogenic food resources in behaviour known as ‘raiding’. Such behavioural flexibility is considered a central component of a species’ ability to cope with human-induced environmental changes. Here, we study the behavioural processes by which raiding male chacma baboons (Papio ursinus) exploit the opportunities and mitigate the risks presented by raiding in the suburbs of Cape Town, South Africa. Ecological sampling and interviews conducted with ‘rangers’ (employed to manage the baboons’ space use) revealed that baboons are at risk of being herded out of urban spaces that contain high-energy anthropogenic food sources. Baboon-attached motion/GPS tracking collars showed that raiding male baboons spent almost all of their time at the urban edge, engaging in short, high-activity forays into the urban space. Moreover, activity levels were increased where the likelihood of deterrence by rangers was greater. Overall, these raiding baboons display a time-activity balance that is drastically altered in comparison to individuals living in more remote regions. We suggest our methods can be used to obtain precise estimates of management impact for this and other species in conflict with people