Related papers: The uniqueness of the core model
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
We study core-periphery structure in networks using inference methods based on a flexible network model that allows for traditional onion-like cores within cores, but also for hierarchical tree-like structures and more general non-nested…
By a classical theorem of Harvey Friedman (1973), every countable nonstandard model $\mathcal{M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding $j$, i.e., $j$ is a self-embedding of $\mathcal{M}$ such that…
Systems design processes are increasingly reliant on simulation models to inform design decisions. A pervasive issue within the systems engineering community is trusting in the models used to make decisions about complex systems. This work…
Using the notions of Topological dynamics, H. Furstenberg defined central sets and proved the Central Sets Theorem. Later V. Bergelson and N. Hindman characterized central sets in terms of algebra of the Stone-\v{C}ech Compactification of…
Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or…
The study of inner models was initiated by G\"odel's analysis of the constructible universe. Later, the study of canonical inner models with large cardinals, e.g., measurable cardinals, strong cardinals or Woodin cardinals, was pioneered by…
The Leinster matrix corresponding to a finite category has entries counting the number of morphisms between objects. A first question is to know which positive integer matrices come from at least one finite category. Here, that question…
In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…
The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in Rm. When we choose the Riesz kernel or the Poisson kernel as the…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
In the 1990s, Steel and Woodin showed that under large cardinal hypotheses, the HOD of $L(\mathbb R)$ admits a fine-structural analysis. Although this theorem sheds light on various problems in descriptive set theory, the fine-structural…
We introduce several novel and computationally efficient methods for detecting "core--periphery structure" in networks. Core--periphery structure is a type of mesoscale structure that includes densely-connected core vertices and…
Embedders play a central role in machine learning, projecting any object into numerical representations that can, in turn, be leveraged to perform various downstream tasks. The evaluation of embedding models typically depends on…
Here, we show that the first isomorphism theorem, the orbit-stabilizer theorem, and the non-uniqueness of solutions of underdetermined linear systems are all manifestations of the same underlying algebraic property. We will call this…
Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise…
We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…
Identity theorem for analytic complex functions says that a function is uniquely defined by its values on a set that contains a density point. The paper presents sufficient conditions for classes of real analytic functions that ensures…
In this paper, we study the singularities of locally flat systems, motivated by the solution, if it exists, of the global motion planning problem for such systems, in the spirit of \cite{CE_14}. More precisely, flat outputs may be only…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…