Related papers: Path of pathology
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
Machine Learning has been applied to pathology images in research and clinical practice with promising outcomes. However, standard ML models often lack the rigorous evaluation required for clinical decisions. Machine learning techniques for…
We call any measure on a path space, a path measure. Some notions about path measures which appear naturally when solving the Schr\"odinger problem are presented and worked out in detail.
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We present several results, including some remarks on the Hopf Lemma.
In this article, we propose a new method to compute the effective properties of non-linear disordered media. We use the fact that the effective constants can be defined through the minimum of an energy functional. We express this minimum in…
In this paper, we prove that the path ideals of both paths and cycles have minimal cellular resolutions. Specifically, these minimal free resolutions coincide with the Barile-Macchia resolutions for paths, and their generalized counterparts…
The purpose of this short expository note is to provide an example exhibiting some of the pathological properties of real-analytic subvarieties, where the pathology can be visualized, and the proofs use only elementary properties of…
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…
In this paper we give a unified approach for several results concerning the fiber cone of ideals
We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.
We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune-free…
The combination of data analysis methods, increasing computing capacity, and improved sensors enable quantitative granular, multi-scale, cell-based analyses. We describe the rich set of application challenges related to tissue…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
We introduce and analyze a new quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of…
It is often desirable to summarise a probability measure on a space $X$ in terms of a mode, or MAP estimator, i.e.\ a point of maximum probability. Such points can be rigorously defined using masses of metric balls in the small-radius…
The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).
We give a survey on b-function, spectrum, and multiplier ideals together with certain interesting relations among them including the case of arbitrary subvarieties.
Estimating causal effects is particularly challenging when outcomes arise in complex, non-Euclidean spaces, where conventional methods often fail to capture meaningful structural variation. We develop a framework for topological causal…