arXiv subjects

Krzysztof Nowak

Publications and source records attributed to Krzysztof Nowak.

5 recordsLinked to original sources

arXiv2025

A Lorentzian FRG Investigation of the Quasi-Static Weak-Field Infrared Limit of Gravity

A common assumption in the Effective Field Theories of gravity is that their quasi-static weak-field infrared limit yields the well-known second-order Poisson operator. We examine this limit for the universality class of parity-even, symmetric, analytic gravitational theories admitting a local derivative expansion using Lorentzian FRG methods. We find that, in the curvature-squared truncation, the scalar-trace sector self-closes at $\mathcal{O}(q^4),$ allowing the projected flow to be obtained by analytic continuation of the corresponding Euclidean result. This yields a screened d'Alambertian $D_\ell \equiv (1+\ell^2 \Box)\Box$ characterised by an emergent correlation length $\ell$. We show the operator is consistent with the ADM constraint structure and thus it does not introduce propagating scalar ghosts in the scalar-trace sector. We further derive its retarded response kernel and show its static-limit Green's function in response to a point source, which reduces to Newtonian gravity for $\ell \rightarrow 0$.

gr-qc↗

arXiv2024

eFontes. Part of Speech Tagging and Lemmatization of Medieval Latin Texts.A Cross-Genre Survey

This study introduces the eFontes models for automatic linguistic annotation of Medieval Latin texts, focusing on lemmatization, part-of-speech tagging, and morphological feature determination. Using the Transformers library, these models were trained on Universal Dependencies (UD) corpora and the newly developed eFontes corpus of Polish Medieval Latin. The research evaluates the models' performance, addressing challenges such as orthographic variations and the integration of Latinized vernacular terms. The models achieved high accuracy rates: lemmatization at 92.60%, part-of-speech tagging at 83.29%, and morphological feature determination at 88.57%. The findings underscore the importance of high-quality annotated corpora and propose future enhancements, including extending the models to Named Entity Recognition.

cs.CL↗

arXiv2016

Two-dimensional Shannon type expansions via one-dimensional affine and wavelet lattice actions

It is rather unexpected, but true, that it is possible to construct reproducing formulae and orthonormal bases of $L^2 (\mathbb{R}^2)$ just by applying the standard one dimensional wavelet action of translations and dilations to the first variable $x_1$ of the generating function $ψ(x_1,x_2)$, $ψ\in L^2 (\mathbb{R}^2)$, i.e., by making use of building blocks $$ψ_{u,s}(x_1,x_2)=s^{-1/2}ψ\left(\frac{x_1-u}{s},x_2\right), \text{where } u\in \mathbb{R}, s>0,$$ in the case of reproducing formulae, and $$ψ_{k,m}(x_1,x_2)=2^{-k/2} ψ\left(\frac{x_1-2^k m}{2^k},x_2 \right), \text{where } k,m\in \mathbb{Z},$$ in the case of orthonormal bases. It is possible to compensate the fact, that the second variable $x_2$ is not acted upon, by a careful selection of the generating function $ψ$. Shannon wavelet tiling of the time-frequency plane $\mathbb{R}^2$, a standard illustration of orthogonality and completeness phenomena corresponding to the Shannon wavelet, $$ χ_{(2^km,2^k(m+1)]}(x) χ_{2^{-k}I}(ξ),\, k,m\in \mathbb{Z}, \,I=- (1/2,1]\cup (1/2,1], $$ with $x$ representing time and $ξ$ frequency, is substituted by a phase space tiling of $\mathbb{R}^4$ with unbounded, hyperboloid type blocks of the form $$ χ_{(2^km,2^k(m+1)]}(x_1)\sum_{n,l}χ_{2^{-k}I_{D(n,l)}}(ξ_1) χ_{(n,n+1]}(x_2)χ_{(l,l+1]}(ξ_2),\, k,m\in \mathbb{Z} $$ where $I_r=2^{-r}I$, $ r\ge 1$, and $D:\mathbb{Z} \times \mathbb{Z} \rightarrow \mathbb{N}$ is a bijection, an additional parameter of the generating function, needed for the lift from $L^2(\mathbb{R})$ to $L^2(\mathbb{R}^2)$. Variables $x_1,x_2$ are coordinates of position and variables $ξ_1,ξ_2$ of momentum.

math.CA↗

arXiv2016

GTOC8: Results and Methods of ESA Advanced Concepts Team and JAXA-ISAS

We consider the interplanetary trajectory design problem posed by the 8th edition of the Global Trajectory Optimization Competition and present the end-to-end strategy developed by the team ACT-ISAS (a collaboration between the European Space Agency's Advanced Concepts Team and JAXA's Institute of Space and Astronautical Science). The resulting interplanetary trajectory won 1st place in the competition, achieving a final mission value of $J=146.33$ [Mkm]. Several new algorithms were developed in this context but have an interest that go beyond the particular problem considered, thus, they are discussed in some detail. These include the Moon-targeting technique, allowing one to target a Moon encounter from a low Earth orbit; the 1-$k$ and 2-$k$ fly-by targeting techniques, enabling one to design resonant fly-bys while ensuring a targeted future formation plane% is acquired at some point after the manoeuvre ; the distributed low-thrust targeting technique, admitting one to control the spacecraft formation plane at 1,000,000 [km]; and the low-thrust optimization technique, permitting one to enforce the formation plane's orientations as path constraints.

physics.space-ph↗

arXiv2013

Continuous rational functions on real and $p$-adic varieties II

This note replaces two earlier preprints (1101.3737 by Kollár) and (1211.6681 by Nowak). It studies, and partially solves, 3 elementary questions about continuous rational functions on real (and p-adic) algebraic varieties: Can one restrict such a function to a subvariety? Can one extend such a function from a subvariety? Which linear equations can be solved using such functions? v.2: Section 3 simplified and typos corrected.

math.AG↗