All Stories

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