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Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to…
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used.…
Learning-based methods have shown promising performance for accelerating motion planning, but mostly in the setting of static environments. For the more challenging problem of planning in dynamic environments, such as multi-arm assembly…
We consider a clock 'paradox' framework where an observer leaves an inertial frame, is accelerated and after an arbitrary trip comes back. We discuss a simple equation that gives, in the 1+1 dimensional case, an explicit relation between…
The ability to predict the future in a given domain can be acquired by discovering empirically from experience certain temporal patterns that tend to repeat unerringly. Previous works in time series analysis allow one to make quantitative…
A case for the teaching of classical thermodynamics with an explicit time variable, with phenomena involving changes in time, is made by presenting and solving a exercise in textbook style, and pointing out that a solution accords with…
Treating time as a local variable permits robust approaches to kinematics that forego questions of extended-simultaneity, which because of their abstract nature might not be addressed explicitly until a first relativity course and even then…
Prediction is arguably one of the most basic functions of an intelligent system. In general, the problem of predicting events in the future or between two waypoints is exceedingly difficult. However, most phenomena naturally pass through…
Generating accurate and efficient predictions for the motion of the humans present in the scene is key to the development of effective motion planning algorithms for robots moving in promiscuous areas, where wrong planning decisions could…
Machine teaching is an algorithmic framework for teaching a target hypothesis via a sequence of examples or demonstrations. We investigate machine teaching for temporal logic formulas -- a novel and expressive hypothesis class amenable to…
This paper re-examines the use of response time to infer problem complexity. It revisits a canonical Wald model of optimal stopping, taking signal-to-noise ratio as a measure of problem complexity. While choice quality is monotone in…
For simple electromagnetic models of a rod and a clock, a change of the shape of the rod and of the rate of the clock when they are set in uniform motion is calculated exactly, employing the correct equation of motion of a charged particle…
It is postulated there is not a precise static instant in time underlying a dynamical physical process at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined.…
A new approach in the Newtonian space and time, based upon the assumption that inertial mass is the quantitative measure of the matter. It has been shown that in case of a special physical system, a supposed matter transfer may reproduce…
We introduce a two-dimensional metric (interval) temporal logic whose internal and external time flows are dense linear orderings. We provide a suitable semantics and a sequent calculus with axioms for equality and extralogical axioms. Then…
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not…
Reinforcement learning and classical planning are typically seen as two distinct problems, with differing formulations necessitating different solutions. Yet, when humans are given a task, regardless of the way it is specified, they can…
We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have…
For many types of learning, spaced training that involves repeated long inter-trial intervals (ITIs) leads to more robust memory formation than does massed training that involves short or no intervals. Several cognitive theories have been…
In a way similar to classical mechanics where we have the concept of inertial time as expressed in the motions of bodies, in the (special) theory of relativity we can regard the inertial time as the only notion of time at play. The inertial…