Related papers: Constructing Sequences One Step at a Time
The well-quasi-orders (WQO) play an important role in various fields such as Computer Science, Logic or Graph Theory. Since the class of WQOs lacks closure under some important operations, the proof that a certain quasi-order is WQO…
We construct a `weak' version EM^w(K) of Lack & Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between…
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the…
Unlike in TFNP, for which there is an abundance of problems capturing natural existence principles which are incomparable (in the black-box setting), Kleinberg et al. [KKMP21] observed that many of the natural problems considered so far in…
Machine learning algorithms in socially sensitive domains (e.g., credit decisions) often focus on equalizing predictive outcomes. However, satisfying these metrics does not guarantee that models use the same reasoning for different groups.…
As machine learning models are increasingly deployed in high-stakes domains such as legal and financial decision-making, there has been growing interest in post-hoc methods for generating counterfactual explanations. Such explanations…
Well-structured systems, aka WSTSs, are computational models where the set of possible configurations is equipped with a well-quasi-ordering which is compatible with the transition relation between configurations. This structure supports…
In this paper, authors shall introduce a finite element method by using a weakly defined gradient operator over discontinuous functions with heterogeneous properties. The use of weak gradients and their approximations results in a new…
We propose a couple of oracle construction methods for quantum pattern matching. We in turn show that one of the construct can be used with the Grover's search algorithm for exact and partial pattern matching, deterministically. The other…
In the environment of fair lending laws and the General Data Protection Regulation (GDPR), the ability to explain a model's prediction is of paramount importance. High quality explanations are the first step in assessing fairness.…
We provide a method of constructing better-quasi-orders by generalising a technique for constructing operator algebras that was developed by Pouzet. We then generalise the notion of $\sigma$-scattered to partial orders, and use our method…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
The weakly compact reflection principle $\text{Refl}_{\text{wc}}(\kappa)$ states that $\kappa$ is a weakly compact cardinal and every weakly compact subset of $\kappa$ has a weakly compact proper initial segment. The weakly compact…
Adaptive quasicontinuum (QC) methods are important methodologies in molecular mechanics for the simulations of materials with defects, intending to achieve the optimal balance of accuracy and efficiency on the fly. In this study, we propose…
We present the first steps of a predicative reconstruction of the constructive Bishop-Cheng measure theory. Working in a semi-formal elaboration of Bishop's set theory and invoking the notion of a set-indexed family of subsets (of a given…
Current and imminent quantum hardware lacks reliability and applicability due to noise and limited qubit counts. Quantum circuit cutting -- a technique dividing large quantum circuits into smaller subcircuits with sizes appropriate for the…
In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterparts - to prove this statement, a nonstandard…
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…
We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalised convergence proofs along with explicit rates of convergence. More…
In this paper, we propose a weak approximation of the reflection coupling (RC) for stochastic differential equations (SDEs), and prove it converges weakly to the desired coupling. In contrast to the RC, the proposed approximate reflection…