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In this work, we propose FastDPM, a unified framework for fast sampling in diffusion probabilistic models. FastDPM generalizes previous methods and gives rise to new algorithms with improved sample quality. We systematically investigate the…
We demonstrate how a prior assumption of smoothness can be used to enhance the reconstruction of free energy profiles from multiple umbrella sampling simulations using the Bayesian Gaussian process regression approach. The method we derive…
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
We study the bispectrum in the Effective Field Theory of Large Scale Structure, consistently accounting for the effects of short-scale dynamics. We begin by proving that, as long as the theory is perturbative, it can be formulated to…
This paper introduces one new multivariate volatility model that can accommodate an appropriately defined network structure based on low-frequency and high-frequency data. The model reduces the number of unknown parameters and the…
We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our…
In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum…
This work presents a formalism for deriving likelihoods of the cosmological density field directly from first principles within Perturbation Theory (PT). By assuming a perturbative expansion around the Gaussian initial density field and…
The subject of study is a neural network with binary neurons, randomly diluted synapses and variable pattern activity. We look at the system with parallel updating using a probabilistic approach to solve the one step dynamics with one…
In principle, sparse neural networks should be significantly more efficient than traditional dense networks. Neurons in the brain exhibit two types of sparsity; they are sparsely interconnected and sparsely active. These two types of…
In rotationally constrained percolation models, a site of a percolation cluster could be occupied more than once from different directions due to the nature of the rotational constraint. A state variable $s_i$ is assigned to each lattice…
Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some…
In the last fifteen the subset sampling method has often been used in reliability problems as a tool for calculating small probabilities. This method is extrapolating from an initial Monte Carlo estimate for the probability content of a…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents $\Delta_q$. In the context of Anderson transitions, the multifractality of critical wave…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…