Related papers: Incremental Selection of Most-Filtering Conjecture…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.
We present a convolutional neural network for the classification of correlation responses obtained by correlation filters. The proposed approach can improve the accuracy of classification, as well as achieve invariance to the image classes…
Combinatorial auctions where agents can bid on bundles of items are desirable because they allow the agents to express complementarity and substitutability between the items. However, expressing one's preferences can require bidding on all…
In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
Certain classes of problems, including perceptual data understanding, robotics, discovery, and learning, can be represented as incremental, dynamically constructed belief networks. These automatically constructed networks can be dynamically…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
New cases of the multiplicity conjecture are considered.
This note proposes a procedure for enhancing the quality of probabilistic prediction algorithms via betting against their predictions. It is inspired by the success of the conformal test martingales that have been developed recently.
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
Using feature attributions for post-hoc explanations is a common practice to understand and verify the predictions of opaque machine learning models. Despite the numerous techniques available, individual methods often produce inconsistent…
We prove Union-Closed sets conjecture.
In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.
We present a case study in {\it experimental} yet {\it rigorous} mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that {\it automatically conjectures}, and then {\it automatically proves}, closed-form…
We present the proofs of the conjectures mentioned in the paper published in the proceedings of the 2024 AAAI conference [1], and discovered by the decomposition methods presented in the same paper.