The Kinetic Basis of Self-Organized Pattern Formation

In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to produce even the simplest stationary patterns. This paper is aimed to propose a novel model of the analog (continuous state) kinetic automaton and to show that stationary and dynamic patterns can arise in one-component networks of kinetic automata. Possible applicability of kinetic networks to modeling of real-world phenomena is also discussed.Comment: 8 pages, submitted to the 14th International Conference on the Synthesis and Simulation of Living Systems (Alife 14) on 23.03.2014, accepted 09.05.201

A primordial, mathematical, logical and computable, demonstration (proof) of the family of conjectures known as Goldbach´s

licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.In this document, by means of a novel system model and first order topological, algebraic and geometrical free-­‐context formal language (NT-­‐FS&L), first, we describe a new signature for a set of the natural numbers that is rooted in an intensional inductive de-­‐embedding process of both, the tensorial identities of the known as “natural numbers”, and the abstract framework of theirs locus-­‐positional based symbolic representations. Additionally, we describe that NT-­‐FS&L is able to: i.-­‐ Embed the De Morgan´s Laws and the FOL-­‐Peano´s Arithmetic Axiomatic. ii.-­‐ Provide new points of view and perspectives about the succession, precede and addition operations and of their abstract, topological, algebraic, analytic geometrical, computational and cognitive, formal representations. Second, by means of the inductive apparatus of NT-­‐FS&L, we proof that the family of conjectures known as Glodbach’s holds entailment and truth when the reasoning starts from the consistent and finitary axiomatic system herein describedWe wish to thank the Organic Chemistry Institute of the Spanish National Research Council (IQOG/CSIC) for its operative and technical support to the Pedro Noheda Research Group (PNRG). We also thank the Institute for Physical and Information Technologies (ITETI/CSIC) of the Spanish National Research Council for their hospitality. We also thank for their long years of dedicated and kind support Dr. Juan Martínez Armesto (VATC/CSIC), Belén Cabrero Suárez (IQOG/CSIC, Administration), Mar Caso Neira (IQOG/CENQUIOR/CSIC, Library) and David Herrero Ruíz (PNRG/IQOG/CSIC). We wish to thank to Bernabé-­‐Pajares´s brothers (Dr. Manuel Bernabé-­‐Pajares, IQOG/CSIC Structural Chemistry & Biochemistry; Magnetic Nuclear Resonance and Dr. Alberto Bernabé Pajares (Greek Philology and Indo-­‐European Linguistics/UCM), for their kind attention during numerous and kind discussions about space, time, imaging and representation of knowledge, language, transcription mistakes, myths and humans always holding us familiar illusion and passion for knowledge and intellectual progress. We wish to thank Dr. Carlos Cativiela Marín (ISQCH/UNIZAR) for his encouragement and for kind listening and attention. We wish to thank Miguel Lorca Melton for his encouragement and professional point of view as Patent Attorney. Last but not least, our gratitude to Nati, María and Jaime for the time borrowed from a loving husband and father. Finally, we apologize to many who have not been mentioned today, but to whom we are grateful. Finally, let us point out that we specially apologize to many who have been mentioned herein for any possible misunderstanding regarding the sense and intension of their philosophic, scientific and/or technical hard work and milestone ideas; we hope that at least Goldbach, Euler and Feymann do not belong to this last human´s collectivity.Peer reviewe

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

Pix2Map: Cross-modal Retrieval for Inferring Street Maps from Images

Self-driving vehicles rely on urban street maps for autonomous navigation. In this paper, we introduce Pix2Map, a method for inferring urban street map topology directly from ego-view images, as needed to continually update and expand existing maps. This is a challenging task, as we need to infer a complex urban road topology directly from raw image data. The main insight of this paper is that this problem can be posed as cross-modal retrieval by learning a joint, cross-modal embedding space for images and existing maps, represented as discrete graphs that encode the topological layout of the visual surroundings. We conduct our experimental evaluation using the Argoverse dataset and show that it is indeed possible to accurately retrieve street maps corresponding to both seen and unseen roads solely from image data. Moreover, we show that our retrieved maps can be used to update or expand existing maps and even show proof-of-concept results for visual localization and image retrieval from spatial graphs.Comment: 12 pages, 8 figure

Collaborative Dynamic 3D Scene Graphs for Automated Driving

Maps have played an indispensable role in enabling safe and automated driving. Although there have been many advances on different fronts ranging from SLAM to semantics, building an actionable hierarchical semantic representation of urban dynamic scenes from multiple agents is still a challenging problem. In this work, we present Collaborative URBan Scene Graphs (CURB-SG) that enable higher-order reasoning and efficient querying for many functions of automated driving. CURB-SG leverages panoptic LiDAR data from multiple agents to build large-scale maps using an effective graph-based collaborative SLAM approach that detects inter-agent loop closures. To semantically decompose the obtained 3D map, we build a lane graph from the paths of ego agents and their panoptic observations of other vehicles. Based on the connectivity of the lane graph, we segregate the environment into intersecting and non-intersecting road areas. Subsequently, we construct a multi-layered scene graph that includes lane information, the position of static landmarks and their assignment to certain map sections, other vehicles observed by the ego agents, and the pose graph from SLAM including 3D panoptic point clouds. We extensively evaluate CURB-SG in urban scenarios using a photorealistic simulator. We release our code at http://curb.cs.uni-freiburg.de.Comment: Refined manuscript and extended supplementar

Clustering Web Concepts Using Algebraic Topology

In this world of Internet, there is a rapid amount of growth in data both in terms of size and dimension. It consists of web pages that represents human thoughts. These thoughts involves concepts and associations which we can capture. Using mathematics, we can perform meaningful clustering of these pages. This project aims at providing a new problem solving paradigm known as algebraic topology in data science. Professor Vasant Dhar, Editor-In-Chief of Big Data (Professor at NYU) define data science as a generalizable extraction of knowledge from data. The core concept of semantic based search engine project developed by my team is to extract a high frequency finite sequence of keywords by association mining. Each frequent finite keywords sequences represent a human concept in a document set. The collective view of such a collection concepts represent a piece of human knowledge. So this MS project is a data science project. By regarding each keyword as an abstract vertex, a finite sequence of keywords becomes a simplex, and the collection becomes a simplicial complexes. Based on this geometric view, new type of clustering can be performed here. If two concepts are connected by n-simplex, we say that these two simplex are connected. Those connected components will be captured by Homology Theory of Simplicial Complexes. The input data for this project are ten thousand files about data mining which are downloaded from IEEE explore library. The search engine nowadays deals with large amount of high dimensional data. Applying mathematical concepts and measuring the connectivity for ten thousand files will be a real challenge. Since, using algebraic topology is a complete new approach. Therefore, extensive testing has to be performed to verify the results for homology groups obtained