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