Related papers: The Chain Fountain Again
In this work, we explore whether modeling recurrence into the Transformer architecture can both be beneficial and efficient, by building an extremely simple recurrent module into the Transformer. We compare our model to baselines following…
A new simply constructed, easy-to-make demonstration of Hero's fountain is presented. The apparatus doesn't have a vessel above a fountain nozzle or a pump and can be considered as one of the best demonstration of Pascal and Bernoulli's…
I show the equivalence between a model of financial contagion and the threshold model of global cascades proposed by Watts (2002). The model financial network comprises banks that hold risky external assets as well as interbank assets. It…
We present design and implementation of a chain of particles that can be programmed to fold the chain into a given curve. The particles guide an external force to fold, therefore the particles are simple and amenable for miniaturization. A…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
Cascading failures triggered by trivial initial events are encountered in many complex systems. It is the interaction and coupling between components of the system that causes cascading failures. We propose a simple model to simulate…
We present a simple inductive proof of the Lagrange Inversion Formula.
A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities.
A simple example of especially constructed potential barrier enables to show analytically (not numerically) the existence of tunneling effect for a Sommerfeld particle.
The problem of a conducting checkerboard has recently been solved via an elliptic function whose argument is another elliptic function. The behavior of the fields and currents near a vertex of the checkerboard pattern can be discussed by…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex…
We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.
We give a factorization of the cycle of a bounded complex of vector bundles in terms of certain associated differential forms and residue currents. This is a generalization of previous results in the case when the complex is a locally free…
A Short Course on Frame Theory.
An improved mass-spring model for a dripping faucet is presented. The model is constructed based on the numerical results which we recently obtained from fluid dynamical calculations. Both the fluid dynamical calculations and the present…
Computational materials design often profits from the fact that some complicated contributions are not calculated for the real material, but replaced by results of models. We turn this approximation into a very general and in principle…
Expository observation on the $\mu$-invariant of singularity models for Ricci Flow.
We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact,…
In the context of the stream calculus, we present an Implicit Function Theorem (IFT) for polynomial systems, and discuss its relations with the classical IFT from calculus. In particular, we demonstrate the advantages of the stream IFT from…