Related papers: Frobenius Pseudoprimes
This paper, a continuation of [3], involves a closer study of polynomials of supertropical semirings and their version of tropical geometry in which we introduce the concept of relatively prime polynomials and resultants, with the aid of…
Triggered by a recent interesting New Scientist article on the too frequent incorrect use of probabilistic evidence in courts, I introduce the basic concepts of probabilistic inference with a toy model, and discuss several important issues…
The cones of divisors and curves defined by various positivity conditions on a smooth projective variety have been the subject of a great deal of work in algebraic geometry, and by now they are quite well understood. However the analogous…
We develop the Perron-Frobenius theory using a variational approach and extend it to a set of arbitrary matrices, including those that are neither irreducible nor essentially positive, and non-preserved cones. We introduce a new concept…
We study the concept of financial bubble in a market model endowed with a set of probability measures, typically mutually singular to each other. In this setting we introduce the notions of robust bubble and robust fundamental value in a…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
We propose a pseudo-primality test using cyclic extensions of $\mathbb Z/n \mathbb Z$. For every positive integer $k \leq \log n$, this test achieves the security of $k$ Miller-Rabin tests at the cost of $k^{1/2+o(1)}$ Miller-Rabin tests.
In hypothesis testing problems the property of strict unbiasedness describes whether a test is able to discriminate, in the sense of a difference in power, between any distribution in the null hypothesis space and any distribution in the…
We show that in an ultraproduct of finite fields, the mod-$n$ nonstandard size of definable sets varies definably in families. Moreover, if $K$ is any pseudofinite field, then one can assign "nonstandard sizes mod $n$" to definable sets in…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for…
The Sorites paradox is the name of a class of paradoxes that arise when vague predicates are considered. Vague predicates lack sharp boundaries in extension and is therefore not clear exactly when such predicates apply. Several approaches…
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…
This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
Experimental limits on supersymmetry and similar theories are difficult to set because of the enormous available parameter space and difficult to generalize because of the complexity of single points. Therefore, more phenomenological,…
Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g.,…
The aim of this paper is to represent any polynomial in terms of the degenerate Frobenius-Euler polynomials and more generally of the higher-order degenerate Frobenius-Euler polynomials. We derive explicit formulas with the help of umbral…
Recently, Sturma, Drton, and Leung proposed a general-purpose stochastic method for hypothesis testing in models defined by polynomial equality and inequality constraints. Notably, the method remains theoretically valid even near irregular…
By Solovay's celebrated completeness result on formal provability we know that the provability logic $\mathrm GL$ describes exactly all provable structural properties for any sound and strong enough arithmetical theory with a decidable…