All Stories

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