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...

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...

BACKGROUND Years of Life Lost (YLL) is one of the methods used to estimate the duration of time lost due to premature death. While previous studies of disease burden have been reported using YLL, there have been no studies investigating YLL of Yi people in rural China. Yunnan Province ranks first in terms of Yi people in China. This paper uses YLL to estimate the disease burden of Yi people in ...

and Applied Analysis 3 then HIDS will reduce to the following fixed point problem P3 : P3 Find v v i∈I ∈ Y such that vi ∈ Fi vi and v ∈ Gi v, yi for all yi ∈ Ti v for all i ∈ I. Example 1.4. For each i ∈ I, let Fi : X × Yi Ui and Gi : Y × Yi Zi be multivalued maps with nonempty values. If Hi and Ai are defined as follows: Hi { yi ∈ Yi : θUi / ∈ Fi ( u, yi )} , Ai ( y ) { zi ∈ Yi : θZi / ∈ Gi ( ...