Related papers: A non-PSLQ route to BBP-type formulas

There is no closed form analytical equation or quick method to calculate probabilities based only on the entropy of a signal or process. Except in the cases where there are constraints on the state probabilities, one must typically derive…

Deep generative models have been shown powerful in generating novel molecules with desired chemical properties via their representations such as strings, trees or graphs. However, these models are limited in recommending synthetic routes…

Attribution methods aim to explain a neural network's prediction by highlighting the most relevant image areas. A popular approach is to backpropagate (BP) a custom relevance score using modified rules, rather than the gradient. We analyze…

We give a necessary and sufficient PBW basis criterion for Hopf algebras generated by skew-primitive elements and abelian group of group-like elements with action given via characters. This class of pointed Hopf algebras has shown great…

A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…

A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.

We provide simple schemes to build Bayesian Neural Networks (BNNs), block by block, inspired by a recent idea of computation skeletons. We show how by adjusting the types of blocks that are used within the computation skeleton, we can…

In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good…

With larger data at their disposal, scientists are emboldened to tackle complex questions that require sophisticated statistical models. It is not unusual for the latter to have likelihood functions that elude analytical formulations. Even…

We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish…

Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a…

The LS-sequences of points recently introduced by the author are a generalization of van der Corput sequences. They were constructed by reordering the points of the corresponding LS-sequences of partitions. Here we present another algorithm…

Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. In several aspects, PLD is close to Decision Tree/Random Forest methods, but it differs significantly in…

Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of…

In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…

Probabilistic programming languages (PPLs) are expressive means for creating and reasoning about probabilistic models. Unfortunately hybrid probabilistic programs, involving both continuous and discrete structures, are not well supported by…

In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…

Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…

The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…

Using the methods developed in [LQW], math.AG/0009132, we obtain a second set of generators for the cohomology ring of the Hilbert scheme of points on an arbitrary smooth projective surface over the field of complex numbers. These…