All Stories

  1. Geometry and Dress Groups with Non-symmetric Cost Functions
  2. Node persistence from topological data analysis reveals changes in brain functional connectivity
  3. Impact of symmetry in local learning rules on predictive neural representations and generalization in spatial navigation
  4. Bernhard Riemann — On the Hypotheses Which Lie at the Bases of Geometry
  5. Historical Introduction
  6. Introduction
  7. Modern Research
  8. Presentation of the Text
  9. Reception and Influence of Riemann’s Text
  10. Riemann’s Text
  11. Selected Bibliography with Commentaries
  12. Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation
  13. The Past as a Stochastic Process
  14. How Rough Path Lifts Affect Expected Return and Volatility: A Rough Model under Transaction Cost
  15. The six stages of the convergence of the periodic system to its final structure
  16. Quick Estimate of Information Decomposition for Text Style Transfer
  17. Learning Successor Representations in the Hippocampus: Exploring the Role of Temporally Asymmetric and Symmetric Plasticity
  18. Discrete Ricci curvatures capture age-related changes in human brain functional connectivity networks
  19. Harmonic maps from surfaces of arbitrary genus into spheres
  20. Geometric algebra for sets with betweenness relations
  21. Information Theory and Consciousness
  22. An exploratory study of heuristics for anticipating prices
  23. Biology, geometry and information
  24. Cheeger‐like inequalities for the largest eigenvalue of the graph Laplace operator
  25. Network geometry and market instability
  26. Normalized Laplace operators for hypergraphs with real coefficients
  27. Short-time existence of the α-Dirac-harmonic map flow and applications
  28. Degree difference: a simple measure to characterize structural heterogeneity in complex networks
  29. Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C∗-Algebras
  30. Edge-based analysis of networks: curvatures of graphs and hypergraphs
  31. Biological information
  32. Ricci curvature of random and empirical directed hypernetworks
  33. Ollivier Ricci curvature of directed hypergraphs
  34. From the Jordan Product to Riemannian Geometries on Classical and Quantum States
  35. Deriving pairwise transfer entropy from network structure and motifs
  36. On VT-harmonic maps
  37. The geometry of recombination
  38. Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary
  39. The super-Toda system and bubbling of spinors
  40. Begriffe, Modelle und Strukturen
  41. Biologie
  42. Biologie und Mathematik
  43. Das Kontinuum
  44. Einführung: Die algebraische Struktur der natürlichen Zahlen
  45. Einleitung
  46. Entwicklungsbiologie und Musterbildung
  47. Ethologie (Verhaltensforschung)
  48. Evolutionsbiologie
  49. Geschichte und Struktur der Biologie
  50. Grundprinzipien und Definitionen
  51. Hirnforschung und Kognitionstheorie
  52. Kausalität
  53. Physiologie
  54. Spektren von Ringen und Schemata
  55. Ökologie
  56. The qualitative behavior at the free boundary for approximate harmonic maps from surfaces
  57. Partial regularity for a nonlinear sigma model with gravitino in higher dimensions
  58. Information Decomposition of Target Effects from Multi-Source Interactions: Perspectives on Previous, Current and Future Work
  59. A global weak solution of the Dirac-harmonic map flow
  60. Regularity of Solutions of the Nonlinear Sigma Model with Gravitino
  61. On Extractable Shared Information
  62. Relations and dependencies between morphological characters
  63. Universal moduli spaces of Riemann surfaces
  64. Knowledge
  65. A Short Survey on Curvature and Topology
  66. Chapter 1 Riemannian Manifolds
  67. Chapter 10 Harmonic Maps from Riemann Surfaces
  68. Chapter 11 Variational Problems from Quantum Field Theory
  69. Chapter 2 Lie Groups and Vector Bundles
  70. Chapter 3 The Laplace Operator and Harmonic Differential Forms
  71. Chapter 4 Connections and Curvature
  72. Chapter 5 Geometry of Submanifolds
  73. Chapter 6 Geodesics and Jacobi Fields
  74. Chapter 7 Symmetric Spaces and Kähler Manifolds
  75. Chapter 9 Harmonic Maps Between Riemannian Manifolds
  76. Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets
  77. Self-organization in Balanced State Networks by STDP and Homeostatic Plasticity
  78. Graphs with nonnegative curvature
  79. A Review of Examples
  80. Categories
  81. Foundations
  82. Mathematical Concepts
  83. Overview and Perspective
  84. Relations
  85. Structures
  86. Topoi
  87. Adaptive Information-Theoretical Feature Selection for Pattern Classification
  88. Statistics of Natural Binaural Sounds
  89. Quantifying Unique Information
  90. Introduction
  91. A Formal Framework for Strategic Representations and Conceptual Reorganization
  92. Differentialgeometrie und Minimalflächen
  93. Das Plateau-Problem
  94. Minimalflächen
  95. Minimalflächen und Maximumprinzip
  96. Krümmung und Gestalt
  97. Kurven
  98. Die erste Fundamentalform
  99. Geodäten und Kürzeste
  100. Die tangentiale Ableitung
  101. Innere und äußere Geometrie
  102. Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplace operator
  103. Partial Differential Equations
  104. Sobolev Spaces and L 2 Regularity Theory
  105. Minimum vertex covers and the spectrum of the normalized Laplacian on trees
  106. Testing entropy-based search strategies for a visual classification task
  107. Deficits in Long-Term Recognition Memory Reveal Dissociated Subtypes in Congenital Prosopagnosia
  108. A Short Survey on Curvature and Topology
  109. Chapter 10 Variational Problems from Quantum Field Theory
  110. Chapter 2 Lie Groups and Vector Bundles
  111. Chapter 3 The Laplace Operator and Harmonic Differential Forms
  112. Chapter 4 Connections and Curvature
  113. Chapter 5 Geodesics and Jacobi Fields
  114. Chapter 6 Symmetric Spaces and Kähler Manifolds
  115. Chapter 7 Morse Theory and Floer Homology
  116. Chapter 8 Harmonic Maps between Riemannian Manifolds
  117. Chapter 9 Harmonic Maps from Riemann Surfaces
  118. Riemannian Geometry and Geometric Analysis
  119. Weak Noise in Neurons May Powerfully Inhibit the Generation of Repetitive Spiking but Not Its Propagation
  120. Reliability of Synaptic Transmission at the Synapses of Held In Vivo under Acoustic Stimulation
  121. Response to commentaries on our paper gene and genon concept: coding versus regulation
  122. A nonparametric Bayesian approach to adaptive sampling of psychometric functions
  123. Graph spectra as a systematic tool in computational biology
  124. Geometry
  125. Geometry and Physics
  126. Physics
  127. Mathematics, Biology and Neurobiology
  128. Riemannian Geometry and Geometric Analysis
  129. Luhmanns Gesellschaftstheorie: Anregung und Herausforderung für eine allgemeine Theorie komplexer Systeme
  130. Partial Differential Equations
  131. Compact Riemann Surfaces
  132. Formal Aspects of the Emergence of Institutions
  133. Postmodern Analysis
  134. Dynamical Systems
  135. Noise delays onset of sustained firing in a minimal model of persistent activity
  136. Differentiability
  137. Integrals and Ordinary Differential Equations
  138. Integration by Parts. Weak Derivatives. Sobolev Spaces
  139. Lebesgue Integrable Functions and Sets
  140. Prerequisites
  141. The Convergence Theorems of Lebesgue Integration Theory
  142. The Lebesgue Integral for Semicontinuous Functions. The Volume of Compact Sets
  143. The Maximum Principle
  144. Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli
  145. Compact Riemann Surfaces
  146. Geodesics and Jacobi Fields
  147. Geometric Structures on Riemann Surfaces
  148. Harmonic Maps
  149. Partial Differential Equations
  150. Symmetric Spaces and Kähler Manifolds
  151. Representations of fundamental groups of algebraic manifolds and their restrictions to fibers of a fibration
  152. Green functions and conformal geometry
  153. Characteristic Properties of Differentiable Functions. Differential Equations
  154. Das Dirichletsche Prinzip. Variationsmethoden zur Lösung partieller Differentialgleichungen (Existenzverfahren III)
  155. Das Maximumprinzip
  156. Die Schaudersche Regularitätstheorie unddie Kontinuitätsmethode (ExistenzverfahrenIV)
  157. Die Wärmeleitungsgleichung, Halbgruppen und Brownsche Bewegung
  158. Differentiability
  159. Einleitung: Was sind partielle Differentialgleichungen?
  160. Existenzverfahren II: Parabolische Methoden. Die Wärmeleitungsgleichung
  161. Integration by Parts. Weak Derivatives. Sobolev Spaces
  162. Postmodern Analysis
  163. Preparations. Semicontinuous Functions
  164. Prerequisites
  165. Riemannian Geometry and Geometric Analysis
  166. Sobolevräume und die L2-Regularitätstheorie
  167. The Convergence Theorems of Lebesgue Integration Theory
  168. The Lp-Spaces
  169. The Maximum Principle
  170. The Transformation Formula
  171. Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli
  172. Partielle Differential-gleichungen
  173. Bochner-Matsushima type identities for harmonic maps and rigidity theorems
  174. Compact Riemann Surfaces
  175. Convex functions and centers of mass
  176. Generalized harmonic maps
  177. Harmonic Maps
  178. Introduction
  179. Nonpositive Curvature: Geometric and Analytic Aspects
  180. Topological Foundations
  181. A Short Survey on Curvature and Topology
  182. Foundational Material
  183. Geodesics and Jacobi Fields
  184. Harmonic Maps
  185. The Palais-Smale Condition and Closed Geodesics
  186. Eigenschaften geodätischer Linien. Der Satz von Gauß-Bonnet
  187. Geometric Preliminaries
  188. Geometric applications of harmonic maps
  189. Nonlinear Methods in Riemannian and Kählerian Geometry
  190. Some principles of analysis
  191. The heat flow on manifolds. Existence and uniqueness of harmonic maps into nonpositively curved image manifolds
  192. The parabolic Yang-Mills equation
  193. Geometric Preliminaries
  194. Geometric applications of harmonic maps
  195. Some principles of analysis
  196. A-priori C1,α-estimates
  197. Geometric considerations
  198. Harmonic coordinates. C2, α - a - priori estimates for harmonic maps
  199. Harmonic Maps Between Surfaces (with a Special Chapter on Conformal Mappings)
  200. The existence of harmonic diffeomorphisms which solve a Dirichlet problem
  201. Hysteresis Effects of Changing Parameters of Noncooperative Games