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It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
This paper develops our previous work on properness of a class of maps related to the Jacobian conjecture. The paper has two main parts: - In part 1, we explore properties of the set of non-proper values $S_f$ (as introduced by Z. Jelonek)…
The Long Now Foundation is building a mechanical clock that is designed to keep time for the next 10,000 years. The clock maintains its long-term accuracy by synchronizing to the Sun. The 10,000-Year Clock keeps track of five different…
The Medusa algorithm takes as input two postcritically finite quadratic polynomials and outputs the quadratic rational map which is the mating of the two polynomials (if it exists). Specifically, the output is a sequence of approximations…
The celebrated Skolem-Mahler-Lech Theorem states that the set of zeros of a linear recurrence sequence is the union of a finite set and finitely many arithmetic progressions. The corresponding computational question, the Skolem Problem,…
The Boolean function implicit in the famous Dayenu song, sung at the Passover meal, is expressed in full conjunctive normal form, and it is proved that if there are n miracles the number of truth-vectors satisfying it is $2^n -(n+1)$.
Frequently, a set of objects has to be evaluated by a panel of assessors, but not every object is assessed by every assessor. A problem facing such panels is how to take into account different standards amongst panel members and varying…
Ramanujan made many beautiful and elegant discoveries in his short life of 32 years, and one of them that has attracted the attention of several mathematicians over the years is his intriguing formula for $\zeta(2n+1)$. To be sure,…
Relation Detection is a task to determine whether two entities are related or not. In this paper, we employ neural network to do relation detection between two named entities for Indonesian Language. We used feature such as word embedding,…
We introduce a fully automated static analysis that takes a sequential Java bytecode program P as input and attempts to prove that there exists an infinite execution of P. The technique consists in compiling P into a constraint logic…
Forecasts of various processes have always been a sophisticated problem for statistics and data science. Over the past decades the solution procedures were updated by deep learning and kernel methods. According to many specialists, these…
We use the Maple system to check the investigations of S. S. Gupta regarding the Smarandache consecutive and the reversed Smarandache sequences of triangular numbers [Smarandache Notions Journal, Vol. 14, 2004, pp. 366-368]. Furthermore, we…
Judgmental forecasting employs human opinions to make predictions about future events, rather than exclusively historical data as in quantitative forecasting. When these opinions form an argumentative structure around forecasts, it is…
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Ripser. The cup product operation which is available at…
This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
We present jorbit, a python/JAX library designed to enable modern data-driven numerical studies of the solar system. Written entirely in JAX, an auto-differentiable and optionally GPU accelerated language behind many current large-scale…
The Earth, Mars, Sun, Jupiter system allows for a sensitive test of the strong equivalence principle (SEP) which is qualitatively different from that provided by Lunar Laser Ranging. Using analytic and numerical methods we demonstrate that…