Yi i.i.d. ∼ pθ∗ , i = {1, . . . , n} where θ∗ ∈ Θ. We can view pθ∗ as a member of a parametric class of distributions, P = {pθ}θ∈Θ. Our goal is to use the observations {Yi} to select an appropriate distribution (e.g., model) from P. We would like the selected distribution to be close to pθ in some sense. We use the negative log-likelihood loss function, defined as l(θ, Yi) = − log pθ(Yi). The e...

One of the main problems in interval computations is solving systems of equations under interval uncertainty. Usually, interval computation packages consider united, tolerance, and control solutions. In this paper, we explain the practical need for algebraic (equality-type) solutions, when we look for solutions for which both sides are equal. In situations when such a solution is not possible, ...

Yi i.i.d. ∼ pθ∗ , i = {1, . . . , n} where θ∗ ∈ Θ. We can view pθ∗ as a member of a parametric class of distributions, P = {pθ}θ∈Θ. Our goal is to use the observations {Yi} to select an appropriate distribution (e.g., model) from P. We would like the selected distribution to be close to pθ in some sense. We use the negative log-likelihood loss function, defined as l(θ, Yi) = − log pθ(Yi). The e...

We prove, that for each r∈N, n∈N and s∈N there are a collection {yi}i=12s of points y2s0 is constant, depending only on r. Moreover, we ...

On 7 February 2022, Professor Yi Lijun passed away in Beijing. She was the most outstanding Chinese Polish scholar, and known as ambassador of literature China. closely linked with University Gdańsk. In 2007, she received an honorary doctorate from University, a member Academic Council Centre for East Asian Studies at Gdańskand scholarly bi-annual journal Gdańsk Studies. born on 4 December 1934...

Let X be a metric space, {xi}i∈N a sequence of points in X (thought of as a sequence of centers), and {di}i∈N a sequence of scaling factors such that di → ∞, and an ultrafilter ω. I’m not going to get into the details of ultrafilters here, but the main property of an ultrafilter is that it lets you define the ultralimit limω ai of any bounded sequence ai. Ultralimits use the axiom of choice to ...

Acute Respiratory Infections (ARIs) are responsible for considerable morbidity and mortality worldwide. Documentation of respiratory specimens can help for an appropriate clinical management with a significant effect on the disease progress in patient, the antimicrobial therapy used and the risk of secondary spread of infection. Here, we compared the performances of four commercial multiplex ki...