Related papers: Final Topology for Preference Spaces
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…
In this paper, we study some properties of $*-$open and $*-$closed subsets of a space. The collection of all $*-$open subsets of a space $X$ form a topology on $X$ which is denoted by $^{*}O(X)$. We investigate the relations between…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
The random utility model is known to be unidentified, but there are times when the model admits a unique representation. We offer two characterizations for the existence of a unique random utility representation. Our first characterization…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…
We study future-blind preferences, which are preferences that heavily discount the future, within the space of infinite consumption streams. We give two definitions: $N$-blindness, where agents ignore periods beyond a fixed date $N$, and…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
We study the evolution of preferences in multi-population settings that allow matches across distinct populations. Each individual has subjective preferences over potential outcomes, and chooses a best response based on his preferences and…
In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately…
We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial.…
It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result,…
Persistence homology is a tool used to measure topological features that are present in data sets and functions. Persistence pairs births and deaths of these features as we iterate through the sublevel sets of the data or function of…
In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional…
We study here preference revision, considering both the monotonic case where the original preferences are preserved and the nonmonotonic case where the new preferences may override the original ones. We use a relational framework in which…
Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We propose an axiomatic approach which economically underpins the representation of dynamic preferences in terms of a stochastic utility function, sensitive to the information available to the decision maker. Our construction is iterative…