Compiling quantum circuits lends itself to an elegant formulation in the language of rewriting systems on non commutative polynomial algebras $\mathbb Q\langle X\rangle$. The alphabet $X$ is the set of the allowed hardware 2-qubit gates. The set of g...
The aim of this short note is to generalise the result of Rampersad--Shallit saying that an automatic sequence and a Sturmian sequence cannot have arbitrarily long common factors. We show that the same result holds if a Sturmian sequence is replaced...
The file contains PhD Dissertation by Oskar Jakub Szymański. This work ends his study at Doctoral School of Exact and Natural Sciences at Jagiellonian University where the Author has attended in years 2019-2024. The subject of the Thesis is the stab...
In this paper, we review the general features of the out-of-equilibrium dynamics of spin glasses. We use this example as a guideline for a brief description of glassy dynamics in other disordered systems like structural and polymer glasses, colloid...
Our aim is to generalize the result that two generic complex line arrangements are equivalent. In fact for a line arrangement A we associate its defining polynomial, the product of a_ix+b_iy+c_i, so that A = (f=0). We prove that the defining polynomi...
We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar $φ^4$ theory. The results are always multi-linear combinations of ladder integrals, which are in turn built out of classical polylogarit...
DNA and other biopolymers differ from classical polymers due to their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the `torsional directe...
disturbed appetite regulation in women with polycystic ovary syndrome". Gynecological Endocrinology. 19 (2): 79–87. doi:10.1080/09513590400002300. PMID 15624269
Previous research on semiflexible polymers including cytoskeletal networks in cells has suggested the existence of distinct regimes of elastic response, in which the strain field is either uniform (affine) or non-uniform (non-affine) under external...
For a given set $\mathcal{L}$ of species and a set $\mathcal{T}$ of triplets on $\mathcal{L}$, one wants to construct a phylogenetic network which is consistent with $\mathcal{T}$, i.e which represents all triplets of $\mathcal{T}$. The level of a ne...
Recycling has become a predominant subject in industry and science due to a rising concern for the environment driven by high production volume of plastics. Replacement of virgin polymers with their recycled analogs is not always possible because rec...
A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed th...
Pope Francis: Untying the Knots. London: Bloomsbury. p. 22. ISBN 978-1-4729-0370-9. Elliott, Dorinda (14 April 2008). "A Conversation with Madeleine
(Abridged) JWST continues to deliver incredibly detailed infrared (IR) images of star forming regions in the Milky Way and beyond. IR emission from star-forming regions is very spectrally rich due to emission from gas-phase atoms, ions, and polycycli...
Majumder, Reif and Sahu have presented a stochastic model of reversible, error-permitting, two-dimensional tile self-assembly, and showed that restricted classes of tile assembly systems achieved equilibrium in (expected) polynomial time. One open...
The L-loop 4-point ladder diagram of massless phi^3 theory is finite when all 4 legs are off-shell and is given in terms of polylogarithms with orders ranging from L to 2L. We obtain the exact solution of the linear Dyson-Schwinger equation that sums...
Andrea, a 43-year-old software engineer, was once open about being polyamorous. She told family and friends that she maintained multiple romantic relationships simultaneously, with the full knowledge ...
I'm a Korean queer woman who migrated to the US in my mid-20s. As a queer woman who lives in an liberal city who somehow got familiarized with hyper-liberal concepts such as kink and polyamory, in ret...
We introduce a norm on the real 1-cohomology of finite 2-complexes determined by the Euler characteristics of graphs on these complexes. We also introduce twisted Alexander-Fox polynomials of groups and show that they give rise to norms on the real...
In this paper we introduce elementary and completely explicit formulas for the derivative of any order of any function of the type 1/p, where p is a polynomial with known zeros....