Joint probability distribution
View article: Entanglement in the S-Field
Entanglement in the S-Field Open
Entanglement in the S-Field 1. Ontic basis of entanglement In the S-framework, each particle is a two-mode S-oscillator: Φ = (Φ_sb , Φ_bs). Entanglement occurs when two or more S-oscillators share a common S-phase structure. This is not in…
View article: Phase Space Regularity of Distributions
Phase Space Regularity of Distributions Open
This paper provides a comprehensive analysis of the concept of phase space regularity of distributions, a fundamental topic with broad implications across diverse fields such as quantum mechanics, signal processing, and the theory of parti…
View article: Entanglement in the S-Field
Entanglement in the S-Field Open
Entanglement in the S-Field 1. Ontic basis of entanglement In the S-framework, each particle is a two-mode S-oscillator: Φ = (Φ_sb , Φ_bs). Entanglement occurs when two or more S-oscillators share a common S-phase structure. This is not in…
View article: Phase Space Regularity of Distributions
Phase Space Regularity of Distributions Open
This paper provides a comprehensive analysis of the concept of phase space regularity of distributions, a fundamental topic with broad implications across diverse fields such as quantum mechanics, signal processing, and the theory of parti…
View article: Statistical learning for multivariate distributional regression with complex dependencies
Statistical learning for multivariate distributional regression with complex dependencies Open
Large, complex datasets are becoming increasingly important in biomedical research. Such datasets typically feature a high number of variables per subject, multiple outcomes and complex dependency structures. While they provide new opportu…
View article: Causal Autoregressive Flows: Bridging Likelihood Maximization and Interventional Robustness
Causal Autoregressive Flows: Bridging Likelihood Maximization and Interventional Robustness Open
Causal inference aims to understand the effect of interventions on a system. However, purely observational data often leads to biased estimates due to confounding. Autoregressive flows, powerful generative models, provide a framework for l…
View article: Bayesian stepwise estimation of qubit rotations
Bayesian stepwise estimation of qubit rotations Open
This work investigates Bayesian stepwise estimation (Se) for measuring the two parameters of a unitary qubit rotation. While asymptotic analysis predicts a precision advantage for SE over joint estimation (JE) in regimes where the quantum …
View article: Deep Distributional Flows: Learning Generative Priors for Calibrated AI
Deep Distributional Flows: Learning Generative Priors for Calibrated AI Open
The pursuit of artificial intelligence systems that are not only performant but also trustworthy and reliable has led to a growing interest in calibrated AI. Calibration ensures that a model's predicted probabilities accurately reflect the…
View article: Regression models for extreme values with random function covariates
Regression models for extreme values with random function covariates Open
A fundamental principle of statistics of extremes is that any realistic quantification of risk requires extrapolating into a distribution’s tail—often beyond the observed extremes in a dataset. Yet, as modern technology advances, an increa…
View article: Nonparametric estimation of the joint and conditional survival functions of the time to an event of interest and associated integrated covariate processes
Nonparametric estimation of the joint and conditional survival functions of the time to an event of interest and associated integrated covariate processes Open
View article: Bayesian stepwise estimation of qubit rotations
Bayesian stepwise estimation of qubit rotations Open
This work investigates Bayesian stepwise estimation (Se) for measuring the two parameters of a unitary qubit rotation. While asymptotic analysis predicts a precision advantage for SE over joint estimation (JE) in regimes where the quantum …
View article: Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets
Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets Open
We derive an expression for the joint distribution function of the first jump times of a continuous state and continuous time branching process with immigration (CBI process) with jump sizes in given Borel sets having finite total Lévy mea…
View article: Causal Autoregressive Flows: Bridging Likelihood Maximization and Interventional Robustness
Causal Autoregressive Flows: Bridging Likelihood Maximization and Interventional Robustness Open
Causal inference aims to understand the effect of interventions on a system. However, purely observational data often leads to biased estimates due to confounding. Autoregressive flows, powerful generative models, provide a framework for l…
View article: Deep Distributional Flows: Learning Generative Priors for Calibrated AI
Deep Distributional Flows: Learning Generative Priors for Calibrated AI Open
The pursuit of artificial intelligence systems that are not only performant but also trustworthy and reliable has led to a growing interest in calibrated AI. Calibration ensures that a model's predicted probabilities accurately reflect the…
View article: Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets
Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets Open
We derive an expression for the joint distribution function of the first jump times of a continuous state and continuous time branching process with immigration (CBI process) with jump sizes in given Borel sets having finite total Lévy mea…
View article: A fresh look at Bivariate Binomial Distributions
A fresh look at Bivariate Binomial Distributions Open
Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-element set {0,1}, where the 1 outcome corresponds to `head'. One…
View article: A fresh look at Bivariate Binomial Distributions
A fresh look at Bivariate Binomial Distributions Open
Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-element set {0,1}, where the 1 outcome corresponds to `head'. One…
View article: The Orthogonality Catastrophe in Families of L-functions and the Limiting Distribution of the Error Term in the Prime Number Theorem
The Orthogonality Catastrophe in Families of L-functions and the Limiting Distribution of the Error Term in the Prime Number Theorem Open
The distribution of prime numbers is one of the most profound problems in mathematics, with the error term in the Prime Number Theorem, $E(x) = pi(x) - li(x)$, encoding deep information about the zeros of the Riemann zeta function. Classic…
View article: The Orthogonality Catastrophe in Families of L-functions and the Limiting Distribution of the Error Term in the Prime Number Theorem
The Orthogonality Catastrophe in Families of L-functions and the Limiting Distribution of the Error Term in the Prime Number Theorem Open
The distribution of prime numbers is one of the most profound problems in mathematics, with the error term in the Prime Number Theorem, $E(x) = pi(x) - li(x)$, encoding deep information about the zeros of the Riemann zeta function. Classic…
View article: A modified JPDA algorithm adapted to dense clutter environments
A modified JPDA algorithm adapted to dense clutter environments Open
To address the complexity of the Joint Probabilistic Data Association (JPDA) algorithm, which is unsuitable for real-time multi-target tracking in complex electromagnetic environments, this paper proposes a Modified Joint Probabilistic Dat…
View article: Precursory Cloud Signals Prior to the Onset of Localized Precipitation: Insight gained from the Millimeter-Wave Cloud Radar Network in China
Precursory Cloud Signals Prior to the Onset of Localized Precipitation: Insight gained from the Millimeter-Wave Cloud Radar Network in China Open
1.LP_events.csv is the identification record of localized precipitation events in 2024. 2.CBH_prior_rainfall_120min.nc and TDR_prior_rainfall_120min.nc are the evolution data of cloud base height, reflectivity, and turbulent dissipation ra…
View article: Precursory Cloud Signals Prior to the Onset of Localized Precipitation: Insight gained from the Millimeter-Wave Cloud Radar Network in China
Precursory Cloud Signals Prior to the Onset of Localized Precipitation: Insight gained from the Millimeter-Wave Cloud Radar Network in China Open
1.LP_events.csv is the identification record of localized precipitation events in 2024. 2.CBH_prior_rainfall_120min.nc and TDR_prior_rainfall_120min.nc are the evolution data of cloud base height, reflectivity, and turbulent dissipation ra…
View article: Cognitive Nexus Theory: First Empirical Detection of Forbidden Drift Zones in Multi-Domain Financial–Climate Fields (CNT_FDZ_v1)
Cognitive Nexus Theory: First Empirical Detection of Forbidden Drift Zones in Multi-Domain Financial–Climate Fields (CNT_FDZ_v1) Open
This release presents the first implementation and empirical evidence for Forbidden Drift Zones (FDZs) within the framework of Cognitive Nexus Theory (CNT). FDZs are compact regions of joint drift space that are mathematically accessible a…
View article: Cognitive Nexus Theory: First Empirical Detection of Forbidden Drift Zones in Multi-Domain Financial–Climate Fields (CNT_FDZ_v1)
Cognitive Nexus Theory: First Empirical Detection of Forbidden Drift Zones in Multi-Domain Financial–Climate Fields (CNT_FDZ_v1) Open
This release presents the first implementation and empirical evidence for Forbidden Drift Zones (FDZs) within the framework of Cognitive Nexus Theory (CNT). FDZs are compact regions of joint drift space that are mathematically accessible a…
View article: Phase-Flow Coherence v2
Phase-Flow Coherence v2 Open
Phase-Flow Coherence (PFC) v2 provides a deterministic and geometric reformulation of non-relativistic quantum mechanics. The theory replaces the complex wavefunction with a pair of real fields defined on a compact internal phase fiber S¹ …
View article: Joint Coalescent-Phylogenomic Inference of Divergence Times and Demography
Joint Coalescent-Phylogenomic Inference of Divergence Times and Demography Open
The accurate inference of divergence times and demographic histories is fundamental to understanding evolutionary processes such as speciation, adaptation, and biogeography. Traditional phylogenetic methods often rely on concatenated align…
View article: Diagnostic Checking for Wasserstein Autoregression
Diagnostic Checking for Wasserstein Autoregression Open
Wasserstein autoregression provides a robust framework for modeling serial dependence among probability distributions, with wide-ranging applications in economics, finance, and climate science. In this paper, we develop portmanteau-type di…
View article: Diagnostic Checking for Wasserstein Autoregression
Diagnostic Checking for Wasserstein Autoregression Open
Wasserstein autoregression provides a robust framework for modeling serial dependence among probability distributions, with wide-ranging applications in economics, finance, and climate science. In this paper, we develop portmanteau-type di…
View article: Joint Coalescent-Phylogenomic Inference of Divergence Times and Demography
Joint Coalescent-Phylogenomic Inference of Divergence Times and Demography Open
The accurate inference of divergence times and demographic histories is fundamental to understanding evolutionary processes such as speciation, adaptation, and biogeography. Traditional phylogenetic methods often rely on concatenated align…
View article: Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices
Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices Open
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in com…