Related papers: Qualitative integrals on Dragonfly algebras
It is well-known that the theories of semi-vector spaces and semi-algebras -- which were not much studied over time -- are utilized/applied in Fuzzy Set Theory in order to obtain extensions of the concept of fuzzy numbers as well as to…
Many state-of-the-art technologies developed in recent years have been influenced by machine learning to some extent. Most popular at the time of this writing are artificial intelligence methodologies that fall under the umbrella of deep…
Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a…
Most theoretically motivated work in the offline reinforcement learning setting requires precise uncertainty estimates. This requirement restricts the algorithms derived in that work to the tabular and linear settings where such estimates…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
The paper starts from the observation on the complexity of the manipulation of fuzzy processes that increases very rapidly with the extents of the processes representation. Therefore, a productive approach is to divide the problem into…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and…
Though deep neural networks have achieved impressive success on various vision tasks, obvious performance degradation still exists when models are tested in out-of-distribution scenarios. In addressing this limitation, we ponder that the…
In the present study, we have introduced Ces\`{a}ro summability of integrals of fuzzy-number-valued functions and given one-sided Tauberian conditions under which convergence of improper fuzzy Riemann integrals follows from Ces\`{a}ro…
The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…
The vast majority of theoretical results in machine learning and statistics assume that the available training data is a reasonably reliable reflection of the phenomena to be learned or estimated. Similarly, the majority of machine learning…
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…
Ensemble learning combines several individual models to obtain better generalization performance. Currently, deep learning architectures are showing better performance compared to the shallow or traditional models. Deep ensemble learning…
In this paper, we show that coherent sets of gambles and coherent lower and upper previsions can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical…
We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of noninteger order on discrete,…
Group representable relation algebras play an important role in the study of representable relation algebras. The class of distributive involutive FL-algebras (DInFL-algebras) generalises relation algebras, as well as Sugihara monoids and…
Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over…