Poisson distribution
View article: The Convergent Indian Buffet Process
The Convergent Indian Buffet Process Open
We propose a new Bayesian nonparametric prior for latent feature models, called the Convergent Indian Buffet Process (CIBP). We show that under the CIBP, the number of latent features is distributed as a Poisson distribution, with the mean…
View article: Geometry of Arithmetic Chaos - Unifying the distribution of prime numbers and zeros of the Riemann zeta function and the Hilbert–Pólya program in a modular multitorus model
Geometry of Arithmetic Chaos - Unifying the distribution of prime numbers and zeros of the Riemann zeta function and the Hilbert–Pólya program in a modular multitorus model Open
This work introduces a geometric method for analysing arithmetic sequences based on a modular multitorus decomposition. Applying it to prime numbers and zeros of the Riemann zeta function reveals that both systems share the same global mod…
View article: bluegreen-labs/skytrackr: skytrackr v2.0
bluegreen-labs/skytrackr: skytrackr v2.0 Open
This is an update to the {skytrackr} package (given the changes, see below, I will increase the major version number to 2.0). The packages estimates the position of animals using geolocation by light through inverse model optimization and …
View article: Geometry of Arithmetic Chaos - Unifying the distribution of prime numbers and zeros of the Riemann zeta function and the Hilbert–Pólya program in a modular multitorus model
Geometry of Arithmetic Chaos - Unifying the distribution of prime numbers and zeros of the Riemann zeta function and the Hilbert–Pólya program in a modular multitorus model Open
This work introduces a geometric method for analysing arithmetic sequences based on a modular multitorus decomposition. Applying it to prime numbers and zeros of the Riemann zeta function reveals that both systems share the same global mod…
View article: The Dual Nature of Prime Gaps
The Dual Nature of Prime Gaps Open
1️⃣ Description – PDF File: The Dual Nature of Prime Gaps.pdf This preprint investigates the statistical structure of prime gaps through a dual lens: Random Matrix Theory on the one hand, and the Hardy–Littlewood singular series (Prime Cos…
View article: The Dual Nature of Prime Gaps
The Dual Nature of Prime Gaps Open
1️⃣ Description – PDF File: The Dual Nature of Prime Gaps.pdf This preprint investigates the statistical structure of prime gaps through a dual lens: Random Matrix Theory on the one hand, and the Hardy–Littlewood singular series (Prime Cos…
View article: Hypocoercive Renormalisation
Hypocoercive Renormalisation Open
Our previous work has shown that a single Fisher information metric on densities and a single operator decomposition suffice to unify reversible quantum dynamics, irreversible Markov and Fokker-Planck flows, and weak field Fisher gravity. …
View article: Spacing Statistics of Centres with High Nesting Depth in Symmetric Prime Pairs
Spacing Statistics of Centres with High Nesting Depth in Symmetric Prime Pairs Open
We examine the distribution of gaps between consecutive integers m such that the nesting depth N(m;R) (the count of symmetric prime pairs exceeds a fixed threshold k. Computations with M=10^8 and R ranging from 1000 to 3000 show that as k …
View article: Seeing Space and the Emergence of Things: An Operational N–Q–S Theory with Inversive Duality and an AdS/CFT/dS–Style Dictionary
Seeing Space and the Emergence of Things: An Operational N–Q–S Theory with Inversive Duality and an AdS/CFT/dS–Style Dictionary Open
We take the operational stance that the world is fundamentally quantum (noncommutative probability), and that what humans call the "classical world" is the stable record layer induced by observation. We formalize the "seeing space" N as a …
View article: Getting it right: Methods for risk ratios and risk differences cluster randomized trials with a small number of clusters
Getting it right: Methods for risk ratios and risk differences cluster randomized trials with a small number of clusters Open
Most cluster randomized trials (CRTs) randomize fewer than 30-40 clusters in total. When performing inference for such ``small'' CRTs, it is important to use methods that appropriately account for the small sample size. When the generalize…
View article: The Geometry of Natural Constants - Die Geometrie der Naturkonstanten
The Geometry of Natural Constants - Die Geometrie der Naturkonstanten Open
Title: The Geometry of Natural Constants: Separating Static Lattice Topology and Helical Dynamics in the QCK Vacuum Description: This paper presents a geometric unification of fundamental physical constants based on the QCK Framework (Quan…
View article: Hypocoercive Renormalisation
Hypocoercive Renormalisation Open
Our previous work has shown that a single Fisher information metric on densities and a single operator decomposition suffice to unify reversible quantum dynamics, irreversible Markov and Fokker-Planck flows, and weak field Fisher gravity. …
View article: A Multi-Phase Dual-PINN Framework: Soft Boundary-Interior Specialization via Distance-Weighted Priors
A Multi-Phase Dual-PINN Framework: Soft Boundary-Interior Specialization via Distance-Weighted Priors Open
Physics-informed neural networks (PINNs) often struggle with multi-scale PDEs featuring sharp gradients and nontrivial boundary conditions, as the physics residual and boundary enforcement compete during optimization. We present a dual-net…
View article: A Multi-Phase Dual-PINN Framework: Soft Boundary-Interior Specialization via Distance-Weighted Priors
A Multi-Phase Dual-PINN Framework: Soft Boundary-Interior Specialization via Distance-Weighted Priors Open
Physics-informed neural networks (PINNs) often struggle with multi-scale PDEs featuring sharp gradients and nontrivial boundary conditions, as the physics residual and boundary enforcement compete during optimization. We present a dual-net…
View article: Seeing Space and the Emergence of Things: An Operational N–Q–S Theory with Inversive Duality and an AdS/CFT/dS–Style Dictionary
Seeing Space and the Emergence of Things: An Operational N–Q–S Theory with Inversive Duality and an AdS/CFT/dS–Style Dictionary Open
We take the operational stance that the world is fundamentally quantum (noncommutative probability), and that what humans call the "classical world" is the stable record layer induced by observation. We formalize the "seeing space" N as a …
View article: Getting it right: Methods for risk ratios and risk differences cluster randomized trials with a small number of clusters
Getting it right: Methods for risk ratios and risk differences cluster randomized trials with a small number of clusters Open
Most cluster randomized trials (CRTs) randomize fewer than 30-40 clusters in total. When performing inference for such ``small'' CRTs, it is important to use methods that appropriately account for the small sample size. When the generalize…
View article: Spacing Statistics of Centres with High Nesting Depth in Symmetric Prime Pairs
Spacing Statistics of Centres with High Nesting Depth in Symmetric Prime Pairs Open
We examine the distribution of gaps between consecutive integers m such that the nesting depth N(m;R) (the count of symmetric prime pairs exceeds a fixed threshold k. Computations with M=10^8 and R ranging from 1000 to 3000 show that as k …
View article: Event-Driven Average Estimation with Dispersion-Tolerant Poisson–Inverse Gaussian Approach
Event-Driven Average Estimation with Dispersion-Tolerant Poisson–Inverse Gaussian Approach Open
Overdispersion is a major problem in the context of count data analysis, and the classical Poisson regression estimators are, in general, unreliable since they imply that the mean equals its variance. In this article, an event-driven class…
View article: The Geometry of Natural Constants - Die Geometrie der Naturkonstanten
The Geometry of Natural Constants - Die Geometrie der Naturkonstanten Open
Title: The Geometry of Natural Constants: Separating Static Lattice Topology and Helical Dynamics in the QCK Vacuum Description: This paper presents a geometric unification of fundamental physical constants based on the QCK Framework (Quan…
View article: On linear-quadratic Poisson pencils on trivial central extensions of semisimple Lie algebras
On linear-quadratic Poisson pencils on trivial central extensions of semisimple Lie algebras Open
View article: Mean First-Passage Time in a Sphere Traversed by a Cylinder
Mean First-Passage Time in a Sphere Traversed by a Cylinder Open
We study Mean First-Passage Times (MFPTs) for diffusive migration in finite three-dimensional domains motivated by organ-vessel architectures and intracellular transport. Focusing on a sphere traversed by a thin cylinder (an idealised orga…
View article: Deck Limit Laws in Axiom Zero
Deck Limit Laws in Axiom Zero Open
This note is part of the Axiom Zero (AZ) programme and assumes familiarity with the core framework developed in Axiom Zero: Structural Irreducibility and the Unpredictability of Primes (DOI: 10.5281/zenodo.16998285). Working in deck and ho…
View article: Giant enhancement of transport driven by active fluctuations: impact of inertia
Giant enhancement of transport driven by active fluctuations: impact of inertia Open
Recently, a paradoxical effect has been demonstrated in which transport of a free Brownian particle driven by active fluctuations in the form of white Poisson shot noise can be significantly enhanced when it is additionally subjected to a …
View article: Generalized Poisson Spatial Autoregressive Modeling of Pneumonia Cases in Children Under Five in Tuban
Generalized Poisson Spatial Autoregressive Modeling of Pneumonia Cases in Children Under Five in Tuban Open
The number of pneumonia cases in children under five in Tuban Regency presents two significant data challenges, namely, overdispersion and spatial dependency. This study aims to develop and apply the Generalized Poisson Spatial Autoregress…
View article: Data from Body Mass Index and Mammographic Density in a Multiracial and Multiethnic Population-Based Study
Data from Body Mass Index and Mammographic Density in a Multiracial and Multiethnic Population-Based Study Open
Background:Mammographic density (MD) is strongly associated with breast cancer risk. We examined whether body mass index (BMI) partially explains racial and ethnic variation in MD.Methods:We used multivariable Poisson regression to estimat…
View article: Deck Limit Laws in Axiom Zero
Deck Limit Laws in Axiom Zero Open
This note is part of the Axiom Zero (AZ) programme and assumes familiarity with the core framework developed in Axiom Zero: Structural Irreducibility and the Unpredictability of Primes (DOI: 10.5281/zenodo.16998285). Working in deck and ho…
View article: Stochastic Pathways to Early Supermassive Black Hole Growth
Stochastic Pathways to Early Supermassive Black Hole Growth Open
The rapid appearance of ∼10 9 M ⊙ black holes by z > 7 remains a major challenge for models of early black hole assembly. Standard Eddington-limited growth produces slow exponential mass increase, requiring either massive initial seeds or …
View article: marco090999/Cubature-scheme-for-likelihood-approximation-guidelines-for-its-setting-parameters: First public release of cubature scheme for likelihood approximation guidelines for its setting parameters
marco090999/Cubature-scheme-for-likelihood-approximation-guidelines-for-its-setting-parameters: First public release of cubature scheme for likelihood approximation guidelines for its setting parameters Open
Public release of the repository related to the work: "Cubature scheme for likelihood approximation: guidelines for its setting parameters in three-dimensional Poisson point processes"
View article: marco090999/Cubature-scheme-for-likelihood-approximation-guidelines-for-its-setting-parameters: First public release of cubature scheme for likelihood approximation guidelines for its setting parameters
marco090999/Cubature-scheme-for-likelihood-approximation-guidelines-for-its-setting-parameters: First public release of cubature scheme for likelihood approximation guidelines for its setting parameters Open
Public release of the repository related to the work: "Cubature scheme for likelihood approximation: guidelines for its setting parameters in three-dimensional Poisson point processes"
View article: An Analytic Expression for a Bayesian D‐Optimality Criterion for the Poisson Model
An Analytic Expression for a Bayesian D‐Optimality Criterion for the Poisson Model Open
We derive the analytic expression for two common Bayesian D‐optimality criteria under the Poisson regression model in the context of optimal design of experiments with a count response. This analytic approach is in contrast with most publi…