Related papers: The Weak Form Is Stronger Than You Think

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…

In this, partly pedagogical review, I attempt to give a self-contained overview of the basis of (non-relativistic) QM measurement theory expressed in density matrix formalism. The focus is on applications to the theory of weak measurement,…

A theoretical framework for the quantization of gravity has been an elusive Holy Grail since the birth of quantum theory and general relativity. While generations of scientists have attempted solutions to this deep riddle, an alternative…

We present a method for learning generalized Hamiltonian decompositions of ordinary differential equations given a set of noisy time series measurements. Our method simultaneously learns a continuous time model and a scalar energy function…

Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…

One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known…

Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…

Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…

We limit ourselves basically to the SU(2) flavor sector of the CKM matrix, as probed in processes like nuclear $\beta$-decay, normal and radiative muon capture and neutrino reactions. Current interests in this primarily stem from our…

Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant…

The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The…

By revisiting the notion of generalized second fundamental form originally introduced by Hutchinson for a special class of integral varifolds, we define a weak curvature tensor that is particularly well-suited for being extended to general…

A new weak measurement procedure is introduced for finite samples which yields accurate weak values that are outside the range of eigenvalues and which do not require an exponentially rare ensemble. This procedure provides a unique…

One key factor that limits the predictive power of molecular dynamics simulations is the accuracy and transferability of the input force field. Force fields are challenged by heterogeneous environments, where electronic responses give rise…

Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak…

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…

The Weak Gravity Conjecture holds that in a theory of quantum gravity, any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different…

Superoscillations are band-limited functions with the peculiar characteristic that they can oscillate with a frequency arbitrarily faster than their fastest Fourier component. First anticipated in different contexts, such as optics or radar…

The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a…

Physics-informed (PI) methodologies have surged to become a pillar route to solve Differential Equations (DEs), sustained by the growth of machine learning methods in scientific contexts. The main proposition of PI is to minimise…