Related papers: Counterexample to a transition probability formula…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to…
Probabilistic computers replace logic gates with networks of interacting random variables, creating bidirectional systems that can back-derive inputs from outputs. Such architectures enable efficient generation of random samples,…
The properties of decays that take place during jet formation cannot be easily deduced from the final distribution of particles in a detector. In this work, we first simulate a system of particles with well defined masses, decay channels,…
The $N$-particle branching random walk is a discrete time branching particle system with selection. We have $N$ particles located on the real line at all times. At every time step each particle is replaced by two offspring, and each…
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…
We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also…
A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated…
Resampling is a standard step in particle filters and more generally sequential Monte Carlo methods. We present an algorithm, called chopthin, for resampling weighted particles. In contrast to standard resampling methods the algorithm does…
Population annealing is a powerful sequential Monte Carlo algorithm designed to study the equilibrium behavior of general systems in statistical physics through massive parallelism. In addition to the remarkable scaling capabilities of the…
In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
We present a new method for simulating Markovian jump processes with time-dependent transitions rates, which avoids the transformation of random numbers by inverting time integrals over the rates. It relies on constructing a sequence of…
While for deterministic systems, a counterexample to a property can simply be an error trace, counterexamples in probabilistic systems are necessarily more complex. For instance, a set of erroneous traces with a sufficient cumulative…
We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…
Take a continuous-time Galton-Watson tree. If the system survives until a large time $T$, then choose $k$ particles uniformly from those alive. What does the ancestral tree drawn out by these $k$ particles look like? Some special cases are…
One approach to estimating a species tree from a collection of gene trees is to first estimate probabilities of clades from the gene trees, and then to construct the species tree from the estimated clade probabilities. While a greedy…
A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods:…
This paper discusses variance estimation in sequential Monte Carlo methods, alternatively termed particle filters. The variance estimator that we propose is a natural modification of that suggested by H. P. Chan and T. L. Lai [A general…