Related papers: Effective descent morphisms of filtered preorders

We define the notion of a specialization morphism from a locally noetherian analytic adic space to a scheme. This captures the (classical) specialization morphism associated to a formal scheme. There is a well behaved theory of…

Starting from pseudometrics and preorders on sets of integers, we extend the focus to sets of finite sequences of integers, in particular sequences of consecutive integers. We outline existing concepts for deriving centred pseudometrics and…

We define a filtration on the variational bicomplex according to jet order. The filtration is preserved by the interior Euler operator, which is not a module homomorphism with respect to the ring of smooth functions on the jet space.…

We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…

Central to the success of Transformers is the attention block, which effectively models global dependencies among input tokens associated to a dataset. However, we theoretically demonstrate that standard attention mechanisms in transformers…

We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy…

This paper presents predicate transfer, a novel method that optimizes join performance by pre-filtering tables to reduce the join input sizes. Predicate transfer generalizes Bloom join, which conducts pre-filtering within a single join…

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…

We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…

A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where…

A filter lattice is a distributive lattice formed by all filters of a poset in the anti-inclusion order. We study the combinatorial properties of the Hasse diagrams of filter lattices of certain posets, so called Fibonacci-like cubes, in…

We consider profunctors $f : P \promap Q$ between posets and introduce their {\em graph} and {\em ascent}. The profunctors $\Pro(P,Q)$ form themselves a poset, and we consider a partition $\cI \sqcup \cF$ of this into a down-set $\cI$ and…

In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular…

Taxonomies have been widely used in various machine learning and text mining systems to organize knowledge and facilitate downstream tasks. One critical challenge is that, as data and business scope grow in real applications, existing…

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

Recent work has suggested enhancing Bloom filters by using a pre-filter, based on applying machine learning to determine a function that models the data set the Bloom filter is meant to represent. Here we model such learned Bloom filters,,…

For an abelian category C and a filtrant preordered set Lambda, we prove that the derived category of the quasi-abelian category of filtered objects in C indexed by Lambda is equivalent to the derived category of the abelian category of…

Let $(M,\scott X) \models \ACA$ be such that $P_\scott X$, the collection of all unbounded sets in $\scott X$, admits a definable complete ultrafilter and let $T$ be a theory extending first order arithmetic coded in $\scott X$ such that…

When Fourier series are employed to solve partial differential equations, low-pass filters can be used to regularize divergent series that may appear. In this paper we show that the linear low-pass filters defined in a previous paper can be…