An approach to non simply laced cluster algebras

Let $\Delta$ be an oriented valued graph equipped with a group of admissible automorphisms satisfying a certain stability condition. We prove that the (coefficient-free) cluster algebra $\mathcal A(\Delta/G)$ associated to the valued quotient graph $\Delta/G$ is a subalgebra of the quotient $\pi(\mathcal A(\Delta))$ of the cluster algebra associated to $\Delta$ by the action of $G$. When $\Delta$ is a Dynkin diagram, we prove that $\mathcal A(\Delta/G)$ and $\pi(\mathcal A(\Delta))$ coincide. As an example of application, we prove that affine valued graphs are mutation-finite, giving an alternative proof to a result of Seven.Comment: 36 pages. Minor correction

Autonomous Acquisition of Natural Situated Communication

An important part of human intelligence, both historically and operationally, is our ability to communicate. We learn how to communicate, and maintain our communicative skills, in a society of communicators – a highly effective way to reach and maintain proficiency in this complex skill. Principles that might allow artificial agents to learn language this way are in completely known at present – the multi-dimensional nature of socio-communicative skills are beyond every machine learning framework so far proposed. Our work begins to address the challenge of proposing a way for observation-based machine learning of natural language and communication. Our framework can learn complex communicative skills with minimal up-front knowledge. The system learns by incrementally producing predictive models of causal relationships in observed data, guided by goal-inference and reasoning using forward-inverse models. We present results from two experiments where our S1 agent learns human communication by observing two humans interacting in a realtime TV-style interview, using multimodal communicative gesture and situated language to talk about recycling of various materials and objects. S1 can learn multimodal complex language and multimodal communicative acts, a vocabulary of 100 words forming natural sentences with relatively complex sentence structure, including manual deictic reference and anaphora. S1 is seeded only with high-level information about goals of the interviewer and interviewee, and a small ontology; no grammar or other information is provided to S1 a priori. The agent learns the pragmatics, semantics, and syntax of complex utterances spoken and gestures from scratch, by observing the humans compare and contrast the cost and pollution related to recycling aluminum cans, glass bottles, newspaper, plastic, and wood. After 20 hours of observation S1 can perform an unscripted TV interview with a human, in the same style, without making mistakes

A new family of standardized and symmetric indices for measuring the intensity and importance of plant neighbour effects

1. Measurements of competition and facilitation between plants often rely upon intensity and importance indices that quantify the net effect of neighbours on the performance of a target plant. A systematic analysis of the mathematical behaviour of the indices is lacking and leads to structural pitfalls, e.g. statistical problems detected in importance indices. 2. We summarize and analyse themathematical properties that the indices should display. We reviewthe properties of the commonly used indices focusing on standardization and symmetry, which are necessary to avoid compromising data interpretation.We introduce a new family of indices ‘Neighbour-effect Indices’ that meet all the proposed properties. 3. Considering the commonly used indices, none of the importance indices are standardized, and onlyRII (Relative Interaction Index) displays all the required mathematical properties. The existing indices show two types of symmetries, namely, additive or commutative, which are currently confounded, potentially resulting in misleading interpretations. Our Neighbour-effect Indices encompass two intensity and two importance indices that are standardized and have different and defined symmetries. 4. Our new additive intensity index, NIntA, is the first of its kind, and it is generally more suitable for assessing competition and facilitation intensity than the widely used RII, which may underestimate facilitation. Our new standardized importance indices solve the main statistical problems that are known to affectCimp and Iimp. Intensity and importance with the same symmetry should be used within the same study. The Neighbour-effect Indices, sharing the same formulation, will allow for unbiased comparisons between intensity and importance, and between types of symmetry.The research of R.D.S. was supported by funding from Ministry of Economy and Competitivity (AGL2015-69151-R). V.R.D. was supported by a Ram on y Cajal fellowship (RYC-2012-10970, MINECO, Spain). The research of M.B. and M.R. was supported by funding from the European Union’s Seventh Framework Programme (FP7/2007–2013), grant agreement 283068 (CASCADE). M.V. was supported by an NWO–ALW ‘open competition’ grant. (Netherlands Science Foundation – Earth and Life Sciences, project number 820.01.020.)