Related papers: An alternative interpretation for the Holm "alpha …
Closure conversion is a program transformation at work in compilers for functional languages to turn inner functions into global ones, by building closures pairing the transformed functions with the environment of their free variables.…
Interpretability methods are developed to understand the working mechanisms of black-box models, which is crucial to their responsible deployment. Fulfilling this goal requires both that the explanations generated by these methods are…
Simulating from a gamma distribution with small shape parameter is a challenging problem. Towards an efficient method, we obtain a limiting distribution for a suitably normalized gamma distribution when the shape parameter tends to zero.…
An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
A structural analysis of construction schemes is developed. That analysis is used to give simple and new constructions of combinatorial objects which have been of interest to set theorists and topologists. We then continue the study of…
We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in…
A recent trend in Non-Rigid Structure-from-Motion (NRSfM) is to express local, differential constraints between pairs of images, from which the surface normal at any point can be obtained by solving a system of polynomial equations. The…
The recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor. The method is hence adapted to treat sequences that are not necessarily towers…
Some work in progress is announced, on the use of algebraic geometry, mostly concerning elliptic curve theory, to model turbulence. Attention is given to flows across the scales, on some convenient model space, and some current trials are…
Turbulent flow remains a challenging subject, despite extensive efforts to find analytical descriptions. Modeling small scales of motion is crucial for saving time and resources in numerical simulations, particularly in industrial…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
The interpretability of ML models is important, but it is not clear what it amounts to. So far, most philosophers have discussed the lack of interpretability of black-box models such as neural networks, and methods such as explainable AI…
This work presents a novel probabilistic interpretation of Slow Feature Analysis (SFA) through the lens of variational inference. Unlike prior formulations that recover linear SFA from Gaussian state-space models with linear emissions, this…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
We propose a new numerical method for $\alpha$-dissipative solutions of the Hunter-Saxton equation, where $\alpha$ belongs to $W^{1, \infty}(\mathbb{R}, [0, 1))$. The method combines a projection operator with a generalized method of…
Simple models are preferred over complex models, but over-simplistic models could lead to erroneous interpretations. The classical approach is to start with a simple model, whose shortcomings are assessed in residual-based model…
The paper proposes an expanded version of the Local Variance Gamma model of Carr and Nadtochiy by adding drift to the governing underlying process. Still in this new model it is possible to derive an ordinary differential equation for the…
Machine learning (ML) has seen significant growth in both popularity and importance. The high prediction accuracy of ML models is often achieved through complex black-box architectures that are difficult to interpret. This interpretability…