Related papers: Characterization of generic parameter families of …
Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…
Score-based generative models (SGMs) have emerged as one of the most popular classes of generative models. A substantial body of work now exists on the analysis of SGMs, focusing either on discretization aspects or on their statistical…
This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of…
A subset $S$ of vertices of $G$ is a \textit{dominating set} of $G$ if every vertex in $V(G)-S$ has a neighbor in $S$. The \textit{domination number} \(\gamma(G)\) is the minimum cardinality of a dominating set of $G$. A dominating set $S$…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
Every set of natural numbers determines a generating function convergent for $q \in (-1,1)$ whose behavior as $q \rightarrow 1^-$ determines a germ. These germs admit a natural partial ordering that can be used to compare sets of natural…
We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…
The observed replication of fermions in three families is undoubtedly a reflection of a deeper symmetry underlying the standard model. In this paper we investigate one very elementary possibility, that physics above the grand unification…
Vectorial Genetic Programming (Vec-GP) extends GP by allowing vectors as input features along regular, scalar features, using them by applying arithmetic operations component-wise or aggregating vectors into scalars by some aggregation…
A skip graph is a resilient application-layer routing structure that supports range queries of distributed k-dimensional data. By sorting deterministic keys into groups based on locally computed random membership vectors, nodes in a…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
We study jets of germs of holomorphic maps between two strongly pseudoconvex domains under the condition that the image of one domain is contained into the other and a given boundary point is (non-tangentially) mapped to a given boundary…
An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and…
We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…
In the study of equisingularity of families of mappings Gaffney introduced the crucial notion of excellent unfoldings. This definition essentially says that the family can be stratified so that there are no strata of dimension 1 other than…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections between the global and local structure of such a group.…
Special generic maps are smooth maps at each singular point of which we can represent as $(x_1, \cdots, x_m) \mapsto (x_1,\cdots,x_{n-1},\sum_{k=n}^{m}{x_k}^2)$ for suitable coordinates. Morse functions with exactly two singular points on…
Let $K=\mathbb{F}_q(C)$ be the global function field of rational functions over a smooth and projective curve $C$ defined over a finite field $\mathbb{F}_q$. The ring of regular functions on $C-S$ where $S \neq \emptyset$ is any finite set…
This paper unifies the theory of consistent-set maximization for robust outlier detection in a simultaneous localization and mapping framework. We first describe the notion of pairwise consistency before discussing how a consistency graph…