Algorithmic simplification of knot diagrams: new moves and experiments

This note has an experimental nature and contains no new theorems. We introduce certain moves for classical knot diagrams that for all the very many examples we have tested them on give a monotonic complete simplification. A complete simplification of a knot diagram D is a sequence of moves that transform D into a diagram D' with the minimal possible number of crossings for the isotopy class of the knot represented by D. The simplification is monotonic if the number of crossings never increases along the sequence. Our moves are certain Z1, Z2, Z3 generalizing the classical Reidemeister moves R1, R2, R3, and another one C (together with a variant) aimed at detecting whether a knot diagram can be viewed as a connected sum of two easier ones. We present an accurate description of the moves and several results of our implementation of the simplification procedure based on them, publicly available on the web.Comment: 38 pages, 33 figure

vibration fatigue tests by tri axis shaker design of an innovative system for uncoupled bending torsion loading

Abstract An innovative system for bending-torsion fatigue tests by tri-axis shaker is designed and presented. The system mounts a cylindrical specimen with eccentric tip mass, excited by horizontal and vertical base accelerations. A lateral thin plate prevents specimen horizontal displacement and allows torsional and bending deformations to be controlled independently. A lumped-mass model is first used to verify if input accelerations and resultant dynamic forces, required in testing, comply with shaker specifications. A finite element model is then used to perform both modal and harmonic analyses, necessary to determine the system natural frequencies and the dynamic response under horizontal and vertical accelerations. Experimental measures on a prototype are finally used to gather preliminary information for validating the numerical model and to verify that the proposed testing system can control bending and torsion loadings independently

Representation of learning in the post-digital: students’ dropout predictive models with artificial intelligence algorithms

Within the scientific debate on post-digital and education, we present a position paper to describe a research project aimed at the design of a predictive model for students’ low achievements in mathematics in Italy. The model is based on the INVALSI data set, an Italian large-scale assessment test, and we use decision trees as the classification algorithm. In designing this tool, we aim to overcome the use of economic, social, and cultural context indices as the main factors for the prediction of a learning gap occurrence. Indeed, we want to include a suitable representation of students’ learning in the model, by exploiting the data collected through the INVALSI tests. We resort to a knowledge-based approach to address this issue and specifically, we try to understand what knowledge is introduced into the model through the representation of learning. In this sense, our proposal allows a student’s learning encoding, which is transferable to different students’ cohorts. Furthermore, the encoding methods may be applied to other large-scale assessments test. Hence, we aim to contribute to a debate on knowledge representation in AI tools for education

Low-achievement risk assessment with machine learning

In this work, we propose a method for assessing the risk of low-achievement in secondary school with data collected from the Italian ministry of education. Low-achievement is a phenomenon whereby a student, despite completing his or her education, does not reach the level of competence expected by the school system. We train three machine learning models on a large, real dataset through the INVALSI large-scale assessment tests and compare the results in terms of predictive and descriptive performance. We exploit data collected in end-of-primary school mathematics tests to predict the risk of low-achievement at the end of compulsory schooling (5 years later). The promising results of our approach suggest that it is possible to generalise the methodology for other school systems and for different teaching subjects

Student Low Achievement Prediction

In this paper, we propose a method for assessing the risk of low achievement in primary and secondary school. We train three machine learning models with data collected by the Italian Ministry of Education through the INVALSI large-scale assessment tests. We compare the results of the trained models and evaluate the effectiveness of the solutions in terms of performance and interpretability. We test our methods on data collected in end-of-primary school mathematics tests to predict the risk of low achievement at the end of compulsory schooling (5 years later). The promising results of our approach suggest that it is possible to generalise the methodology for other school systems and for different teaching subject

Is right angular gyrus involved in the metric component of the mental body representation in touch and vision? A tdcs study

Several studies have found in the sense of touch a good sensory modality by which to study body representation. Here, we address the “metric component of body representation”, a specific function developed to process the discrimination of tactile distances on the body. The literature suggests the involvement of the right angular gyrus (rAG) in processing the tactile metricity on the body. The question of this study is the following: is the rAG also responsible for the visual metric component of body representation? We used tDCS (anodal and sham) in 20 subjects who were administered an on-body distance discrimination task with both tactile and visual stimuli. They were also asked to perform the same task in a near-body condition. The results allow us to confirm the role of rAG in the estimation of tactile distances. Further, we also showed that rAG might be involved in the discrimination of distances on the body not only in tactile but also in visual modality. Finally, based on the significant effects of anodal stimulation even in a near-body visual discrimination task, we proposed a higher-order function of the AG in terms of a supramodal com-parator of quantities

The “Projection-by-Projection” (PbP) criterion for multiaxial random fatigue loadings: Guidelines to practical implementation

This work is motivated by the increasing interest towards the application of the “Projection-by-Projection” (PbP) spectral method in finite element (FE) analysis of components under multiaxial random loadings. To help users and engineers in developing their software routines, this paper presents a set of numerical case studies to be used as a guideline to implement the PbP method. The sequence of analysis steps in the method are first summarized and explained. A first numerical example is then illustrated, in which various types of biaxial random stress are applied to three materials with different tension/torsion fatigue properties. Results of each analysis step are displayed explicitly to allow a plain understanding of how the PbP method works. The examples are chosen with the purpose to show the capability of the method to take into account the effect of correlation degree among stress components, and the relationship between material and multiaxial stress in relation to the tension/torsion fatigue properties. A case study is finally discussed, in which the method is applied to a FE structural durability analysis of a simple structure subjected to random excitations. The example describes the flowchart and the program by which to implement the method through Ansys APDL software. This final example illustrates how the PbP method is an efficient tool to analyze multiaxial random stresses in complex structures