Skew-symmetrizable matrices play an essential role in the classification of cluster algebras. We prove that the problem of assigning a positive definite quasi-Cartan companion to a skew-symmetrizable matrix is in polynomial class P. We also present an algorithm to determine the finite type Δ ∈ {𝔸 n ; 𝔻 n ; 𝔹 n ; ℂ n ; 𝔼 6 ; 𝔼 7 ; 𝔼 8 ; 𝔽 4 ; 𝔾 2 } of a cluster algebra associated to the mutation-equivalence class of a connected skew-symmetrizable matrix B, if it has one.

Atrial fibrillation (AF) is the most prevalent type of cardiac arrhythmia. As such, its early detection at a massive population scale is of paramount importance not only to avoid serious risks to people's health but also to ensure the sustainability of health care systems worldwide. Ambulatory monitoring can help mitigate these problems, and wearable devices can play a fundamental role in this regard. These devices can be equipped with sensors to measure cardiac activity, for instance from photoplethysmography (PPG) signals. The use of these sensors in wearable devices for AF screening faces several technological challenges. One of them is their sensitivity to interferences, in particular caused by patient's physical activity, which may be indistinguishable from cardiac activity. This paper presents a method to identify the periods of time during which PPG signals can be used because these effects are not present in them. Experimental results obtained from real patients show that by using the proposed method, a significant amount of valid data can be obtained, improving the usability of wearable devices for affordable AF ambulatory screening.

Inflations algorithm is a procedure that appears implicitly in Ovsienko’s classical proof for the classification of positive definite integral quadratic forms. The best known upper asymptotic bound for its time complexity is an exponential one. In this paper we show that this bound can be tightened to O ( n 6 ) for the naive implementation. Also, we propose a new approach to show how to decide whether an admissible quasi-Cartan matrix is positive definite and compute the Dynkin type in just O ( n 3 ) operations taking an integer matrix as input.

A well known constructive proof for the 𝔸𝔻𝔼-classification of many mathematical objects, such as positive unit forms and their associated quasi-Cartan matrices, has lead to an Inflations Algorithm. However, this algorithm is not known to run in polynomial time. In this paper we use a so called flation transformation and show how its invariants can be used to characterize the Dynkin types 𝔸 and 𝔻 in the language of graph theory. Also, a polynomial-time algorithm for computing the Dynkin type is suggested.

Bicycles today are interfaces between civility and nature, between poetics and technological evolution. Jeffrey Shaw's classical piece The Legible City (1989) involves a stationary bicycle in the context of visual poetry, 3D texts, and geometries of uninhabited cities. The Legible City is an interface to virtual worlds. Text-shaped cities are projected and explored by visitors in a journey of reading. Twenty-two years after Shaw's work, one can use a stationary bicycle to travel through richer worlds, which are narrative applications of geography updated periodically such as Google Earth. In this sense students of Animation and Digital Art program at Tecnológico de Monterrey in Toluca, Mexico, developed four process art applications, using and adapting physical interfaces and videogame motion capture devices as their own take on Shaw's work.

To improve the interaction of people with virtually generated environments we need first to break the barriers that prevent the user from getting an experience as close to reality as possible. The main problem is to give the user the sensation that his/her presence affects the virtual world and then to let the user perceive that the actions he/she takes on the real world can change the virtual one in a smooth natural way in order to achieve virtual biofeedback. Interacting with virtual nature can transport us out from reality. We developed an interactive application with two interfaces on which the user can pretend to be the wind and interact with a virtual pond. Our application makes the user believe and feel that he/she is modifying a 3D virtual pond by the interaction with a small water receptacle in the real world using innovative wave-sensing device. The user, by speaking to a microphone, can also interact with a virtual tree by making it move according to his/her wishes. The physics for the tree are calculated to present the user's action as a wind force making this an entertaining experience.