Related papers: Functions with Diffusive Properties
To guarantee the integrity and security of data transmitted through the Internet, hash functions are fundamental tools. But recent researches have shown that security flaws exist in the most widely used hash functions. So a new way to…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
In surface diffusion, one of the key observables is the so-called intermediate scattering function which is measured directly from the surface technique called Helium spin echo. In this work, we show that this function can be seen as a…
Maximum nonlinear functions on finite fields are widely used in cryptography because the coordinate functions have large distance to linear functions. More precisely, the Hamming distance to the characteristic functions of hyperplanes is…
cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exist many hash functions: MD5, HAVAL, SHA, ... It was reported that these hash…
Security of information transmitted through the Internet is an international concern. This security is guaranteed by tools like hash functions. However, as security flaws have been recently identified in the current standard in this domain,…
Secret sharing schemes create an effective method to safeguard a secret by dividing it among several participants. By using hash functions and the herding hashes technique, we first set up a (t+1, n) threshold scheme which is perfect and…
Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction…
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
A hash function is constructed based on a three-layer neural network. The three neuron-layers are used to realize data confusion, diffusion and compression respectively, and the multi-block hash mode is presented to support the plaintext…
Property-preserving hash functions allow for compressing long inputs $x_0$ and $x_1$ into short hashes $h(x_0)$ and $h(x_1)$ in a manner that allows for computing a predicate $P(x_0, x_1)$ given only the two hash values without having…
We prove that the binary classifiers of bit strings generated by random wide deep neural networks with ReLU activation function are biased towards simple functions. The simplicity is captured by the following two properties. For any given…
In physics, density $\rho(\cdot)$ is a fundamentally important scalar function to model, since it describes a scalar field or a probability density function that governs a physical process. Modeling $\rho(\cdot)$ typically scales poorly…
Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function under aperiodic…
Feature hashing, also known as {\em the hashing trick}, introduced by Weinberger et al. (2009), is one of the key techniques used in scaling-up machine learning algorithms. Loosely speaking, feature hashing uses a random sparse projection…
In this paper, we present a general review of hash functions in a cryptographic sense. We give special emphasis on some particular topics such as cipher block chaining message authentication code (CBC MAC) and its variants. This paper also…
In this note we analyse the harmonic functions in $L^2$-sense for an irreducible diffusion on an interval.
In this article we propose building general-purpose function approximators on top of Haar Scattering Networks. We advocate that this architecture enables a better comprehension of feature extraction, in addition to its implementation…
Functions correspond to one of the key concepts in mathematics and science, allowing the representation and modeling of several types of signals and systems. The present work develops an approach for characterizing the coverage and…
Diffusion models have emerged as powerful generative models, inspiring extensive research into their underlying mechanisms. One of the key questions in this area is the loss functions these models shall train with. Multiple formulations…