All Stories

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