Related papers: Automated Generation of Anomalous Cancellations

Anomalous cancellation of fractions is a mathematically inaccurate method where cancelling the common digits of the numerator and denominator correctly reduces it. While it appears to be accidentally successful, the property of anomalous…

Using $E_8$ bundles, we construct some modular forms over $SL(2,{\bf Z})$, $\Gamma^0(2)$ and $\Gamma_0(2)$. By these modular forms, we get some new anomaly cancellation formulas of characteristic forms.

We discuss the generalization to global gauge anomalies of the familiar procedure for the cancellation of local gauge anomalies in effective theories of spontaneously broken symmetries. We illustrate this mechanism in a recently proposed…

The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…

We propose a new approach to nondeterministic random number generation. In theory, the randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon number distribution and that of the consecutive…

These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory. We begin with several derivations of the abelian anomaly: anomalous transformation of the…

Using $E_8$ bundles, we construct some new modular forms over $SL(2,{\bf Z})$, $\Gamma^0(2)$ and $\Gamma_0(2)$ and get some new anomaly cancellation formulas of characteristic forms which generalize some anomaly cancellation formulas in…

We show how methods of number theory can be used to study anomalies in gauge quantum field theories in spacetime dimension two. To wit, the anomaly cancellation conditions for the abelian part of the local anomaly admit solutions if and…

In [5] and [19], the authors gave anomaly cancellation formulas for the gauge groups E8,E8*E8. In this paper, we mainly deal with the case of gauge group E8*E8*E8. Using the E8*E8*E8 bundle, we construct some modular forms over SL2(Z). By…

In 1952, von Neumann introduced the rejection method for random variate generation. We revisit this algorithm when we have a source of perfect bits at our disposal. In this random bit model, there are universal lower bounds for generating a…

In this work, we provide a combinatorial formalism for dealing with the cancellations that have appeared recently in the context of dispersive PDEs with random initial data. The main idea is to transform iterated integrals encoded by…

Smooth manifolds of G_2 holonomy, used to compactify M-theory to four dimensions, give only abelian gauge groups without charged matter multiplets. But singular G_2-manifolds can give abelian or nonabelian gauge groups with chiral fermions.…

Systematic errors in quantum operations can be the dominating source of imperfection in achieving control over quantum systems. This problem, which has been well studied in nuclear magnetic resonance, can be addressed by replacing single…

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well…

We describe a high-speed physical random number generator based on a hybrid Boolean network with autonomous and clocked logic gates, realized on a reconfigurable chip. The autonomous logic gates are arranged in a bidirectional ring topology…

How can we extract theoretical insights from machine learning algorithms? We take a familiar lesson: researchers often turn their intuitions into theoretical insights by constructing "anomalies" -- specific examples highlighting…

Chaos and its applications in the field of secure communications have attracted a lot of attention. Chaos-based pseudo-random number generators are critical to guarantee security over open networks as the Internet. We have previously…

Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…

Despite the fact that almost all real numbers are absolutely normal---that is, the digits in their expansions to any base occur in all possible configurations with the expected frequency---not one specific example of an absolutely normal…

In this work we present a model for computation of random processes in digital computers which solves the problem of periodic sequences and hidden errors produced by correlations. We show that systems with non-invertible non-linearities can…