Ricci flow and black holes

Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the canonical ensemble for gravity in a box. At high temperature the action has three saddle points: hot flat space and a large and small black hole. Adding a time direction, these also give static 5-dimensional Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action. The small black hole has a Gross-Perry-Yaffe-type negative mode, and is therefore unstable under Ricci flow. We numerically simulate the two flows seeded by this mode, finding that they lead to the large black hole and to hot flat space respectively, in the latter case via a topology-changing singularity. In the context of string theory these flows are world-sheet renormalization group trajectories. We also use them to construct a novel free energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space of metrics corrected and expanded, references adde

A simple proof of Perelman's collapsing theorem for 3-manifolds

We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theorem is almost self-contained, accessible to non-experts and advanced graduate students. Perelman's collapsing theorem for 3-manifolds can be viewed as an extension of implicit function theoremComment: v1: 9 Figures. In this version, we improve the exposition of our arguments in the earlier arXiv version. v2: added one more grap

Investigating Off-shell Stability of Anti-de Sitter Space in String Theory

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow, and then show this implies its geometric stability with respect to Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.Comment: 29 pages, references added in this version to appear in Classical and Quantum Gravit

A Collaborative Approach to Human Rights Impact Assessments

This discussion paper, co-authored with the Danish Institute for Human Rights and the Sciences Po Law School Clinic, proposes a new approach to conducting human rights impact assessments (HRIAs) of business operations or projects, which brings together project-affected people, the company, and other stakeholders to jointly design and implement an assessment. The aim of this new approach is to address one of the key challenges of current HRIA practices: the limited engagement and participation of relevant stakeholders, which can undermine effectiveness and trust. The paper outlines factors that will affect the effectiveness of such an approach and describes a number of steps that will be required for a successful process, from ensuring meaningful participation and capacity building of all stakeholders involved in the assessment to carefully governing and funding the process. This collaborative approach is designed to improve communication between relevant stakeholders, increase access to relevant information for rights holders, encourage greater engagement with the findings and recommendations of the assessment, and, most importantly, ensure increased prevention or mitigation of negative human rights impacts. The paper is the result of a two-year long research project, supported by The Tiffany & Co. Foundation, and is based on extensive desktop research; interviews with 49 people with relevant experience, including representatives of companies, civil society organizations, communities, and academia; as well as a roundtable that brought together over a dozen stakeholders and HRIA experts to provide feedback on the research findings and recommendations

A Collaborative Approach to Human Rights Impact Assessments

This discussion paper proposes a new approach to conducting human rights impact assessments (HRIAs) of business operations or projects, which brings together project-affected people, the company, and other stakeholders to jointly design and implement an assessment. The aim of this new approach is to address one of the key challenges of current HRIA practices: the limited engagement and participation of relevant stakeholders, which can undermine effectiveness and trust. The paper outlines factors that will affect the effectiveness of such an approach and describes a number of steps that will be required for a successful process, from ensuring meaningful participation and capacity building of all stakeholders involved in the assessment to carefully governing and funding the process. This collaborative approach is designed to improve communication between relevant stakeholders, increase access to relevant information for rights holders, encourage greater engagement with the findings and recommendations of the assessment, and, most importantly, ensure increased prevention or mitigation of negative human rights impacts. The paper is the result of a two-year long research project, supported by The Tiffany & Co. Foundation, and is based on extensive desktop research; interviews with 49 people with relevant experience, including representatives of companies, civil society organizations, communities, and academia; as well as a round table that brought together over a dozen stakeholders and HRIA experts to provide feedback on the research findings and recommendations

Beyond the KdV: post-explosion development

Several threads of the last 25 years’ developments in nonlinear wave theory that stem from the classical Korteweg–de Vries (KdV) equation are surveyed. The focus is on various generalizations of the KdV equation which include higher-order nonlinearity, large-scale dispersion, and a nonlocal integral dispersion. We also discuss how relatively simple models can capture strongly nonlinear dynamics and how various modifications of the KdV equation lead to qualitatively new, non-trivial solutions and regimes of evolution observable in the laboratory and in nature. As the main physical example, we choose internal gravity waves in the ocean for which all these models are applicable and have genuine importance. We also briefly outline the authors’ view of the future development of the chosen lines of nonlinear wave theory

Tissue sampling methods and standards for vertebrate genomics

The recent rise in speed and efficiency of new sequencing technologies have facilitated high-throughput sequencing, assembly and analyses of genomes, advancing ongoing efforts to analyze genetic sequences across major vertebrate groups. Standardized procedures in acquiring high quality DNA and RNA and establishing cell lines from target species will facilitate these initiatives. We provide a legal and methodological guide according to four standards of acquiring and storing tissue for the Genome 10K Project and similar initiatives as follows: four-star (banked tissue/cell cultures, RNA from multiple types of tissue for transcriptomes, and sufficient flash-frozen tissue for 1 mg of DNA, all from a single individual); three-star (RNA as above and frozen tissue for 1 mg of DNA); two-star (frozen tissue for at least 700 μg of DNA); and one-star (ethanol-preserved tissue for 700 μg of DNA or less of mixed quality). At a minimum, all tissues collected for the Genome 10K and other genomic projects should consider each species’ natural history and follow institutional and legal requirements. Associated documentation should detail as much information as possible about provenance to ensure representative sampling and subsequent sequencing. Hopefully, the procedures outlined here will not only encourage success in the Genome 10K Project but also inspire the adaptation of standards by other genomic projects, including those involving other biota

Tissue Sampling Methods and Standards for Vertebrate Genomics

The recent rise in speed and efficiency of new sequencing technologies have facilitated high-throughput sequencing, assembly and analyses of genomes, advancing ongoing efforts to analyze genetic sequences across major vertebrate groups. Standardized procedures in acquiring high quality DNA and RNA and establishing cell lines from target species will facilitate these initiatives. We provide a legal and methodological guide according to four standards of acquiring and storing tissue for the Genome 10K Project and similar initiatives as follows: four-star (banked tissue/cell cultures, RNA from multiple types of tissue for transcriptomes, and sufficient flash-frozen tissue for 1 mg of DNA, all from a single individual);three-star (RNA as above and frozen tissue for 1 mg of DNA); two-star (frozen tissue for at least 700 μg of DNA); and one-star (ethanol-preserved tissue for 700 μg of DNA or less of mixed quality). At a minimum, all tissues collected for the Genome 10K and other genomic projects should consider each species’ natural history and follow institutional and legal requirements. Associated documentation should detail as much information as possible about provenance to ensure representative sampling and subsequent sequencing. Hopefully, the procedures outlined here will not only encourage success in the Genome 10K Project but also inspire the adaptation of standards by other genomic projects, including those involving other biota

Analysis of the FGF gene family provides insights into aquatic adaptation in cetaceans

Cetacean body structure and physiology exhibit dramatic adaptations to their aquatic environment. Fibroblast growth factors (FGFs) are a family of essential factors that regulate animal development and physiology; however, their role in cetacean evolution is not clearly understood. Here, we sequenced the fin whale genome and analysed FGFs from 8 cetaceans. FGF22, a hair follicle-enriched gene, exhibited pseudogenization, indicating that the function of this gene is no longer necessary in cetaceans that have lost most of their body hair. An evolutionary analysis revealed signatures of positive selection for FGF3 and FGF11, genes related to ear and tooth development and hypoxia, respectively. We found a D203G substitution in cetacean FGF9, which was predicted to affect FGF9 homodimerization, suggesting that this gene plays a role in the acquisition of rigid flippers for efficient manoeuvring. Cetaceans utilize low bone density as a buoyancy control mechanism, but the underlying genes are not known. We found that the expression of FGF23, a gene associated with reduced bone density, is greatly increased in the cetacean liver under hypoxic conditions, thus implicating FGF23 in low bone density in cetaceans. Altogether, our results provide novel insights into the roles of FGFs in cetacean adaptation to the aquatic environment.ope