Related papers: On multidimensional item response theory -- a coor…
Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
Although fundamental to the advancement of Machine Learning, the classic evaluation metrics extracted from the confusion matrix, such as precision and F1, are limited. Such metrics only offer a quantitative view of the models' performance,…
There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely…
Various methods to detect differential item functioning (DIF) in item response models are available. However, most of the methods assume that the responses are binary, for ordered response categories available methods are scarce. In the…
Scene-aware Complementary Item Retrieval (CIR) is a challenging task which requires to generate a set of compatible items across domains. Due to the subjectivity, it is difficult to set up a rigorous standard for both data collection and…
Life continuously changes its own components and states at each moment through interaction with the external world, while maintaining its own individuality in a cyclical manner. Such a property, known as "autonomy," has been formulated…
We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original…
The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
In the study of free arrangements, the most useful result to construct/check free arrangements is the addition-deletion theorem. Recently, the multiple version of the addition theorem is proved, called the multiple addition theorem (MAT) to…
Multiple object tracking (MOT) is a fundamental component of perception systems for autonomous driving, and its robustness to unseen conditions is a requirement to avoid life-critical failures. Despite the urge of safety in driving systems,…
We obtain a series of results in the global theory of free boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteria, such as area, topology and Morse index compare, beyond…
This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's…
The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex…
It is shown that there are seven types of solutions described in the framework of general relativity theory (GRT), the dynamics of empty homogeneous isotropic three-dimensional spaces. Solution of the equations of GRT, which describes the…
We extend the combinatorial Morse complex construction to the arbitrary free chain complexes, and give a short, self-contained, and elementary proof of the quasi-isomorphism between the original chain complex and its Morse complex. Even…
Conformal symmetry is taken as an attribute of theories of massless fields in manifolds with specific dimensionalities. This paper shows that this is not an absolute truth; it is a consequence of the mathematical representation used for the…
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…