Related papers: Teaching Newton with anticipation(...)
This article revisits the historiography of the problem of inertial frames. Specifically, the case of the twins in the clock paradox is considered to see that some resolutions implicitly assume inertiality for the non-accelerating twin. If…
Humans can possess good mechanics intuitions by learning from a few examples, which leads to the question of how to develop artificial mechanics intuitions that can be learned from small data, as we are eagerly entering the era of…
In the present essay we attempt to reconstruct Newtonian mechanics under the guidance of logical principles and of a constructive approach related to the genetic epistemology of J. Piaget and R. Garc\'ia \citep{piag89}. Instead of…
The aim of this paper is twofold: First, we give a formal introduction to the basics of the mathematical framework of classical mechanics. Along the way, we prove a Hamiltonian and a Lagrangian version of Noether's Theorem, an important…
The derivation of the transformations between inertial frames made by Mansouri and Sexl is generalised to three dimensions for an arbitrary direction of the velocity. Assuming lenght contraction and time dilation to have their relativistic…
This paper is a contribution towards interpretability of the deep learning models in different applications of time-series. We propose a temporal attention layer that is capable of selecting the relevant information to perform various…
We present an algorithm for active learning of deterministic timed automata with multiple clocks. The algorithm is within the querying framework of Angluin's $L^*$ algorithm and follows the idea proposed in existing work on the active…
One of the most annoying aspects in the formalization of mathematics is the need of transforming notions to match a given, existing result. This kind of transformations, often based on a conspicuous background knowledge in the given…
Current robot architectures for modeling interaction behavior are not well suited to the dual task of sequencing discrete actions and incorporating information instantly. Additionally, for communication based on body motion, actions also…
Foreseeing the future is one of the key factors of intelligence. It involves understanding of the past and current environment as well as decent experience of its possible dynamics. In this work, we address future prediction at the abstract…
One fundamental goal of learning is preparation for future learning (PFL) and being able to extend acquired skills and problem-solving strategies to different domains and environments. While substantial research has shown that PFL can be…
We draw a picture of physical systems that allows us to recognize what is this thing called "time" by requiring consistency not only with our notion of time but also with the way time enters the fundamental laws of Physics, independently of…
Planck's formula and General Relativity indicate that potential energy influences spacetime. Using Einstein's Equivalence Principle and an extension of his Chock Hypothesis, an explicit description of this influence is derived. We present a…
Reinforcement learning has been applied to many interesting problems such as the famous TD-gammon and the inverted helicopter flight. However, little effort has been put into developing methods to learn policies for complex persistent tasks…
Data-driven modeling of physical systems often relies on learning both positions and momenta to accurately capture Hamiltonian dynamics. However, in many practical scenarios, only position measurements are readily available. In this work,…
Which geometries on a smooth manifold (apart from Lorentzian metrics) can serve as a spacetime structure? This question is comprehensively addressed from first principles in eight lectures, exploring the kinematics and gravitational…
In the history of mechanics, there have been two points of view for studying mechanical systems: Newtonian and Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential…
In this work we show that the null result of the Michelson-Morley experiment in vacuum is deeply connected with the notion of time. It can be deduced without any mathematics only from the assumption that all good clocks can be used to…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
This contribution shows that the main topics of Relativity can be discussed at an elementary level and in a considerable extent - including the formal results of "Time Dilation" and "Lorentz Contraction" - by a minor modification of the…