Physical Sciences Forum, Volume 5, Issue 1

This study considers dualistic structures of the probability simplex from the information geometry perspective. We investigate a foliation by deformed probability simplexes for the transition of $\alpha$-parameters, not for a fixed $\alpha$-parameter....

The forty-first International Conference on Bayesian and Maximum Entropy methods in Science and Engineering (41st MaxEnt’22) was held in Institut Henri Poincaré (IHP), Paris, 18–22 July 2022 (https://maxent22 [...]

The Atacama Large Millimeter/submillimeter Array (ALMA) is currently revolutionizing observational astrophysics. The aperture synthesis technique provides angular resolution otherwise unachievable with the conventional single-aperture telescope. Howe...

We present a method for improving the performance of nested sampling as well as its accuracy. Building on previous work we show that posterior repartitioning may be used to reduce the amount of time nested sampling spends in compressing from prior to...

The Atacama large millimeter/submillimeter array with the planned electronic upgrades will deliver an unprecedented number of deep and high resolution observations. Wider fields of view are possible with the consequential cost of image reconstruction...

Machine improvisation is the ability of musical generative systems to interact with either another music agent or a human improviser. This is a challenging task, as it is not trivial to define a quantitative measure that evaluates the creativity of t...

In many Bayesian computations, we first obtain the expression of the joint distribution of all the unknown variables given the observed data. In general, this expression is not separable in those variables. Thus, obtaining the marginals for each vari...

One of the key issues in machine learning is the characterization of the learnability of a problem. Regret is a way to quantify learnability. Quantum tomography is a special case of machine learning where the training set is a set of quantum measurem...

Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo derivatives ha...

Epilepsy is a multiscale disease in which small alterations at the cellular scale affect the electroencephalogram (EEG). We use a computational model to bridge the cellular scale to EEG by evaluating the ionic conductance of the Hodkin–Huxley (...

We study reciprocity relations between fluctuations of the probability distributions corresponding to position and momentum, and other observables, in quantum theory. These kinds of relations have been previously studied in terms of quantifiers based...

Quivers are oriented graphs that have profound connections to various areas of mathematics, including representation theory and geometry. Quiver representations correspond to a vast generalization of classical linear algebra problems. The geometry of...

Materials in fission reactors or fusion tokamaks are exposed to neutron irradiation, which creates defects in the microstructure. With time, depending on the temperature, defects diffuse and form, among others, nanocavities, altering the material per...

As physicists, we wish to make mental models of the world around us. For this to be useful, we need to be able to classify features of the world into symbols and develop a rational calculus for their manipulation. In seeking maximal generality, we ai...

Social communication is omnipresent and a fundamental basis of our daily lives. Especially due to the increasing popularity of social media, communication flows are becoming more complex, faster and more influential. It is therefore not surprising th...

In 1928, the Henri Poincaré Institute opened in Paris thanks to the efforts of the mathematician Emile Borel and the support of the Rockefeller Foundation. Teaching and research on the mathematics of chance were placed by Borel at the center o...

This paper summarises a new framework of Stochastic Geometric Mechanics that attributes a fundamental role to Hamilton–Jacobi–Bellman (HJB) equations. These are associated with geometric versions of probabilistic Lagrangian and Hamiltonia...

Data for complex plasma–wall interactions require long-running and expensive computer simulations of codes like EIRENE or SOLPS. Furthermore, the number of input parameters is large, which results in a low coverage of the (physical) parameter s...

The entropic dynamics (ED) approach to quantum mechanics is ideally suited to address the problem of measurement because it is based on entropic and Bayesian methods of inference that have been designed to process information and data. The approach s...

We discuss the geometric aspects of a recently described unfolding procedure and show the form of objects relevant in the field of quantum information geometry in the unfolding space. In particular, we show the form of the quantum monotone metric ten...

Science aims at identifying suitable models that best describe a population based on a set of features. Lacking information about the relationships among features there is no justification to a priori fix a certain model. Ideally, we want to incorpor...

We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of a near-ring. This gives a unified understanding tow...

The inverse Ising model is used in computational neuroscience to infer probability distributions of the synchronous activity of large neuronal populations. This method allows for finding the Boltzmann distribution with single neuron biases and pairwi...

Bayesian imaging algorithms are becoming increasingly important in, e.g., astronomy, medicine and biology. Given that many of these algorithms compute iterative solutions to high-dimensional inverse problems, the efficiency and accuracy of the instru...

In many areas of computer science, it is of primary importance to assess the randomness of a certain variable X. Many different criteria can be used to evaluate randomness, possibly after observing some disclosed data. A “sufficiently random&rd...

Accurate determination of skeletal maturation indicators is crucial in the orthodontic process. Chronologic age is not a reliable skeletal maturation indicator, thus physicians use bone age. In orthodontics, the treatment timing depends on Cervical V...

We summarise recent work on the classical result of Kirillov that any simply connected homogeneous symplectic space of a connected group G is a hamiltonian $\widehat{G}$-space for a one-dimensional central extension $\widehat{G}$ of G, and is thus (by a result of Kostant...

The inference of dynamical fields is of paramount importance in science, technology, and economics. Dynamical field inference can be based on information field theory and used to infer the evolution of fields in dynamical systems from finite data. He...

Quantum process tomography (QPT) methods aim at identifying a given quantum process. QPT is a major quantum information processing tool, since it especially allows one to characterize the actual behavior of quantum gates, which are the building block...

By combining information science and differential geometry, information geometry provides a geometric method to measure the differences in the time evolution of the statistical states in a stochastic process. Specifically, the so-called information l...

By using Brillouin’s perspective on Maxwell’s demon, we determine a new way to describe investor behaviors in financial markets. The efficient market hypothesis (EMH) in its strong form states that all information in the market, public or...

In this tutorial paper the Gull–Skilling kangaroo problem is revisited. The problem is used as an example of solving an under-determined system by variational principles, the maximum entropy principle (MEP), and Information Geometry. The relati...

A statistical transformation model consists of a smooth data manifold, on which a Lie group smoothly acts, together with a family of probability density functions on the data manifold parametrized by elements in the Lie group. For such a statistical...

We consider multivariate-centered Gaussian models for the random vector $(Z^1,\dots ,Z^p)$, whose conditional structure is described by a homogeneous graph and which is invariant under the action of a permutation subgroup. The following paper is concer...

A full-rank lattice in the Euclidean space is a discrete set formed by all integer linear combinations of a basis. Given a probability distribution on ${\mathbb{R}}^n$, two operations can be induced by considering the quotient of the space by such a lattice: wrapp...

This paper introduces an adaptive importance sampling scheme for the computation of group-based convolutions, a key step in the implementation of equivariant neural networks. By leveraging information geometry to define the parameters update rule for...

In this paper, we consider the SEIR (Susceptible-Exposed-Infectious-Removed) model for studying COVID-19. The main contributions of this paper are: (i) a detailed explanation of the SEIR model, with the significance of its parameters. (ii) calibratio...

Credit risk assessments are vital to the operations of financial institutions. These activities depend on the availability of data. In many cases, the records of financial data processed by the credit risk models are frequently incomplete. Several me...

Communication, the exchange of information between intelligent agents, whether human or artificial, is susceptible to deception and misinformation. Reputation systems can help agents decide how much to trust an information source that is not necessar...

The mass density, commonly denoted $\rho (\mathit{x},t)$ as a function of position $\mathit{x}$ and time t, is considered an obvious concept in physics. It is, however, fundamentally dependent on the continuum assumption, the ability of the observer to downscale the mass...

Parametric and non-parametric classifiers often have to deal with real-world data, where corruptions such as noise, occlusions, and blur are unavoidable. We present a probabilistic approach to classify strongly corrupted data and quantify uncertainty...

This paper discusses the use of Equivariant Neural Networks (ENN) for solving Partial Differential Equations by exploiting their underlying symmetry groups. We first show that Group-Convolutionnal Neural Networks can be used to generalize Physics-Inf...

I illustrate an approach that can be exploited for constructing neural networks that a priori obey physical laws. We start with a simple single-layer neural network (NN) but refrain from choosing the activation functions yet. Under certain conditions...

Conditions are highlighted for generalized entropies to allow for non-trivial time-averaged entropy rates for a large class of random sequences, including Markov chains and continued fractions. The axiomatic-free conditions arise from the behavior of...

We present a novel algorithm for learning the parameters of hidden Markov models (HMMs) in a geometric setting where the observations take values in Riemannian manifolds. In particular, we elevate a recent second-order method of moments algorithm tha...

The simplest Bayesian system used to illustrate ideas of probability theory is a coin and a boolean utility function. To illustrate ideas of hypothesis testing, estimation or optimal control, one needs to use at least two coins and a confusion matrix...

The nested sampling (NS) method was originally proposed by John Skilling to calculate the evidence in Bayesian inference. The method has since been utilised in various research fields, and here we focus on how NS has been adapted to sample the Potent...

The fundamental problem with causal inference involves discovering causal relations between variables used to describe observational data. We address this problem within the formalism of information field theory (IFT). Specifically, we focus on the p...

Modern day Bayesian imaging problems in astrophysics as well as other scientific areas often result in non-Gaussian and very high-dimensional posterior probability distributions as their formal solution. Efficiently accessing the information containe...

This paper presents recent methodological advances for performing simulation-based inference (SBI) of a general class of Bayesian hierarchical models (BHMs) while checking for model misspecification. Our approach is based on a two-step framework. Fir...