Multilingual media components directly embeddable in open educational resources in science and technology

The use and reuse of OER (Open Educational Resources) depends on several conditions. Amongst others, the richness of their metadata, their granularity and the languages ​​in which they are made available. This work aims to facilitate efficient production of graphical and language-neutral components. It is assumed that the STEM areas (Science, Technology, Engeneering and Mathematics) share a common mathematical language and, more intuitively, an iconographic approach linked to the structures that satisfy the formulas used in each case. The work is limited to these areas of knowledge, primarily as presentations and animations of very low granularity, which can be directly integrated into larger resources in any language. The overall research design consists of four stages: 1. Initially, the manual generation of presentations and animations, with no literal in any language, and very concisely focused (mainly, definitions of a single concept for each animation). Determination of common graphics primitives to differentiate the common subtasks: presentation of examples to make the concept emerge inductively, graphical construction of the definition, highlighting the generalization or instantiation steps, homogeneous use of icons for emphasising or posing a question to the observer .. . 2. Evaluation of the expressiveness and effectiveness of these resources. Currently, these resources are being presented to small groups of students. This fall begins a multilingual evaluation process on a larger scale: as part of a regular course at the UNED and as LabSpace course in the Open University. Here we attempt to clarify the appropriate assessment tools (preferably in the same graphics language) with the minimum amount of additional external comments to constitute a course in a particular language. 3. The first two stages must provide an intuitive and graphical interface of the selected formalism (mainly Discrete Mathematics and Logic). The third stage addresses the effect of changing the output device on the selection of the graphics primitives for each generic subtask. Possible variations of the graphical language will be studied in the context of HCI analyses. 4. Finally the approach addresses semi-automatic generation, via script, of these resources: from formal description of the definitions or processes (as described, for example, in OMDoc) to the production of the corresponding animation. Additionally, the injection of semantics should facilitate the link between different animations, the navigation and search of conceptual dependency and the identification of concepts that have supporting collections of resources as described. At this point, the current development of this work provides results for the first two stages described

Partially ordered models

We provide a formal definition and study the basic properties of partially ordered chains (POC). These systems were proposed to model textures in image processing and to represent independence relations between random variables in statistics (in the later case they are known as Bayesian networks). Our chains are a generalization of probabilistic cellular automata (PCA) and their theory has features intermediate between that of discrete-time processes and the theory of statistical mechanical lattice fields. Its proper definition is based on the notion of partially ordered specification (POS), in close analogy to the theory of Gibbs measure. This paper contains two types of results. First, we present the basic elements of the general theory of POCs: basic geometrical issues, definition in terms of conditional probability kernels, extremal decomposition, extremality and triviality, reconstruction starting from single-site kernels, relations between POM and Gibbs fields. Second, we prove three uniqueness criteria that correspond to the criteria known as bounded uniformity, Dobrushin and disagreement percolation in the theory of Gibbs measures.Comment: 54 pages, 11 figures, 6 simulations. Submited to Journal of Stat. Phy

A measure of conductivity for lattice fermions at finite density

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible.Comment: version to be published in Physics Letters

A note on the computation of the Frobenius number of a numerical semigroup

In this note we observe that the Frobenius number and therefore the conductor of a numerical semigroup can be obtained from the maximal socle degree of the quotient of the corresponding semigroup algebra by the ideal generated by the biggest generator of the semigroup.Comment: Some typos in the introduction have been correcte

Trees, homology, and automorphism groups of right-angled Artin groups

We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this subgroup, based on the number and degree of a certain type of vertices, which we call deep. We then use combinatorial methods to analyze the average value of this Betti number, in terms of the size of the defining tree

Live demonstration: Neuro-inspired system for realtime vision tilt correction

Correcting digital images tilt needs huge quantities of memory, high computational resources, and use to take a considerable amount of time. This demonstration shows how a spikes-based silicon retina dynamic vision sensor (DVS) tilt can corrected in real time using a commercial accelerometer. DVS output is a stream of spikes codified using the address-event representation (AER). Event-based processing is focused on change in real time DVS output addresses. Taking into account this DVS feature, we present an AER based layer able to correct in real time the DVS tilt, using a high speed algorithmic mapping layer and introducing a minimum latency in the system. A co-design platform (the AER-Robot platform), based into a Xilinx Spartan 3 FPGA and an 8051 USB microcontroller, has been used to implement the system