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An important tool for proving safety of dynamical systems is the notion of a barrier certificate. In this paper we prove that every robustly safe ordinary differential equation has a barrier certificate. Moreover, we show a construction of such a barrier certificate based on a set of states that is reachable in finite …
In the quiet backwaters of cs.CV, cs.LG and stat.ML, a cornucopia of new learning systems is emerging from a primordial soup of mathematics-learning systems with no need for external supervision. To date, little thought has been given to how these self-supervised learners have sprung into being or the principles that g…
Capped-usage SaaS products -- LLM subscriptions such as Claude Code and ChatGPT, cloud platforms such as Vercel and Cloudflare Workers, corporate benefit platforms, identity-verification services with liability transfer -- share a structural signature with insurance products: a fixed premium decoupled from realized con…
Backpropagation with gradient descent is a common optimization strategy employed by most neural network architectures in machine learning. However, finding optimal hyperparameters to guide training has proven challenging. While it is widely acknowledged that selecting appropriate parameters is crucial for avoiding over…
A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for these l…
In an earlier paper~\cite{Luu:2019jmb} we discussed emergence from the context of effective field theories, particularly as related to the fields of particle and nuclear physics. We argued on the side of reductionism and weak emergence. George Ellis has critiqued our exposition in~\cite{Ellis:2020vij}, and here we prov…
Following Max Planck's hypothesis of quanta (quant-ph/0012069) and the matter wave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed, at the beginning of 1926, the concept of wavefunction and wave equation for it. Though endowed with a realistic undular interpretation by its father, the wavefunct…
Many macroscopic physical processes are known to occur in a time-directed way despite the apparent time-symmetry of the known fundamental laws. A popular explanation is to postulate an unimaginably atypical state for the early universe -- a "Past Hypothesis" (PH) -- that seeds the time-asymmetry from which all others f…
We examine a covariant quantization of electromagnetic fields by using an operator derived from a constant scalar that can be called extended Lorentz gauge. The quantization can avoid an inconsistency between Lorentz gauge and a commutation relation, which can eliminate the need for introduction of physical state defin…
Here within the basic design for a ground-based instrument for measuring the magnitude of the Earth's time-retarded transverse gravitational vector potential is described. The formula for the Earth's transverse vector potential is derived from the known formula for the neoclassical time-retarded transverse gravitationa…