Related papers: Decrement Operators in Belief Change
We study coinductive invertibility of cells in weak $\omega$-categories. We use the inductive presentation of weak $\omega$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all…
In this paper we analyze iterations of the obstacle problem for two different operators. We solve iteratively the obstacle problem from above or below for two different differential operators with obstacles given by the previous functions…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of `doubled kets' (i.e. mixing), and by tracing out part of a `doubled' two-system ket (i.e. dilation). Both…
We analyze two weak random operators, initially motivated from processes in random environment. Intuitively speaking these operators are ill-defined, but using bilinear forms one can deal with them in a rigorous way. This point of view can…
Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be…
This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition. Various viewpoints of this method in the literature are synergized and are compared and contrasted; included in…
State-of-the-art methods for Transformer-based semantic segmentation typically adopt Transformer decoders that are used to extract additional embeddings from image embeddings via cross-attention, refine either or both types of embeddings…
Many Properties of a category X, as for instance the existence of an adjoint or a factorization system, are a consequence of the cowellpoweredness of X. In the absence of cowellpoweredness, for general results, fairly strong assumption on…
We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional…
Ill-posed linear inverse problems appear in many image processing applications, such as deblurring, super-resolution and compressed sensing. Many restoration strategies involve minimizing a cost function, which is composed of fidelity and…
In response to the continuously changing feedstock supply and market demand for products with different specifications, the processes need to be operated at time-varying operating conditions and targets (e.g., setpoints) to improve the…
Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that…
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…
Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…
Natural language processing has greatly benefited from the introduction of the attention mechanism. However, standard attention models are of limited interpretability for tasks that involve a series of inference steps. We describe an…
Recent studies on frequent itemset mining algorithms resulted in significant performance improvements. However, if the minimal support threshold is set too low, or the data is highly correlated, the number of frequent itemsets itself can be…
The AGM theory of belief revision has become an important paradigm for investigating rational belief changes. Unfortunately, researchers working in this paradigm have restricted much of their attention to rather simple representations of…