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arXiv Preprints
Finite-size catalysis in quantum resource theories
Quantum catalysis, the ability to enable previously impossible transformations by using auxiliary systems without degrading them, has emerged as a powerful tool in various resource theories. Although catalytically enabled state transformations have b...
physics:quant-phphysics:physics:atom-ph
arXiv Preprints
Cables of the figure-eight knot via real Frøyshov invariants
We prove that the $(2n,1)$-cable of the figure-eight knot is not smoothly slice when $n$ is odd, by using the real Seiberg-Witten Frøyshov invariant of Konno-Miyazawa-Taniguchi. For the computation, we develop an $O(2)$-equivariant version of the la...
math:math:GT
arXiv Preprints
A consolidated and accessible security proof for finite-size decoy-state quantum key distribution
In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a full under...
physics:quant-ph
arXiv Preprints
Reliable OOD Virtual Screening with Extrapolatory Pseudo-Label Matching
Machine learning (ML) models are increasingly deployed for virtual screening in drug discovery, where the goal is to identify novel, chemically diverse scaffolds while minimizing experimental costs. This creates a fundamental challenge: the most valu...
cs:cs:LGcs:cs:AI
arXiv Preprints
Spectral sequences via linear presheaves
We study homotopy theory of the category of spectral sequences with respect to the class of weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We introduce the category of extended spectral sequences and show that this is b...
math:math:ATmath:math:CT
arXiv Preprints
Galois groups of reciprocal polynomials and the van der Waerden-Bhargava theorem
We study the Galois groups $G_f$ of degree $2n$ reciprocal (a.k.a. palindromic) polynomials $f$ of height at most $H$, finding that $G_f$ falls short of the maximal possible group $S_2 \wr S_n$ for a proportion of all $f$ bounded above and below by c...
math:math:NT
arXiv Preprints
Unconditional Stability Analysis of N-Port Networks Based on Structured Singular Value Computation
In this paper, a novel approach based on robust stability concepts and tools is introduced to evaluate the unconditional stability of microwave active $\textit{n}$-port devices. An efficient calculation of the Structured Singular Value of the $\texti...
eess:eess:SYcs:cs:SY
arXiv Preprints
Nonequilibrium dynamics and thermodynamics provide the underlying physical mechanism of the perceptual rivalry
Perceptual rivalry, where conflicting sensory information leads to alternating perceptions crucial for associated cognitive function, has attracted researcher's attention for long. Despite progresses being made, recent studies have revealed limi...
q-bio:q-bio:NCphysics:physics:bio-ph
arXiv Preprints
The $S_3$-symmetric tridiagonal algebra
The tridiagonal algebra is defined by two generators and two relations, called the tridiagonal relations. Special cases of the tridiagonal algebra include the $q$-Onsager algebra, the positive part of the $q$-deformed enveloping algebra $U_q({\wideha...
math:math:COmath:math:QA
arXiv Preprints
Clusterpath Gaussian Graphical Modeling
Graphical models serve as effective tools for visualizing conditional dependencies between variables. However, as the number of variables grows, interpretation becomes increasingly difficult, and estimation uncertainty increases due to the large numb...
stat:stat:MLcs:cs:LG
arXiv Preprints
Abstract Markov Random Fields
Markov random fields are known to be fully characterized by properties of their information diagrams, or I-diagrams. In particular, for Markov random fields, regions in the I-diagram corresponding to disconnected vertex sets in the graph vanish. Rece...
cs:cs:ITmath:math:IT
arXiv Preprints
Insect-Scale Tailless Robot with Flapping Wings: A Simple Structure and Drive for Yaw Control
Insect-scale micro-aerial vehicles, especially lightweight, flapping-wing robots, are becoming increasingly important for safe motion sensing in spatially constrained environments such as living spaces. However, yaw control using flapping wings is fu...
cs:cs:RO
arXiv Preprints
Mating parabolic rational maps with Hecke groups
We prove that any degree $d$ rational map having a parabolic fixed point of multiplier $1$ with a fully invariant and simply connected immediate basin of attraction is mateable with the Hecke group $H_{d+1}$, with the mating realized by an algebraic ...
math:math:DSmath:math:CVmath:math:GR
arXiv Preprints
SOAP: Enhancing Spatio-Temporal Relation and Motion Information Capturing for Few-Shot Action Recognition
High frame-rate (HFR) videos of action recognition improve fine-grained expression while reducing the spatio-temporal relation and motion information density. Thus, large amounts of video samples are continuously required for traditional data-driven ...
cs:cs:CVcs:cs:AI
arXiv Preprints
Numerical modeling of SNSPD absorption utilizing optical conductivity with quantum corrections
Superconducting nanowire single-photon detectors are widely used in various fields of physics and technology, due to their high efficiency and timing precision. Although, in principle, their detection mechanism offers broadband operation, their wavel...
physics:cond-mat:supr-conphysics:physics:ins-det
arXiv Preprints
The nucleus of a $Q$-polynomial distance-regular graph
Let $Γ$ denote a $Q$-polynomial distance-regular graph with diameter $D\geq 1$. For a vertex $x$ of $Γ$ the corresponding subconstituent algebra $T=T(x)$ is generated by the adjacency matrix $A$ of $Γ$ and the dual adjacency matrix $A^*=A^*(x)$ of...
math:math:COmath:math:QA
arXiv Preprints
Deletion-addition of a smooth conic for free curves
We describe the behaviour of a free reduced plane projective curve with respect to the deletion, respectively addition, of a smooth conic. These results apply in particular to conic-line arrangements. We present some obstructions to the geometry and ...
math:math:AGmath:math:AC
arXiv Preprints
Multi-variable Quantification of BDDs in External Memory using Nested Sweeping (Extended Paper)
Previous research on the Adiar BDD package has been successful at designing algorithms capable of handling large Binary Decision Diagrams (BDDs) stored in external memory. To do so, it uses consecutive sweeps through the BDDs to resolve computations....
cs:cs:DScs:cs:DB
arXiv Preprints
The Benard-Conway invariant of two-component links
The Benard-Conway invariant of links in the 3-sphere is a Casson-Lin type invariant defined by counting irreducible SU(2) representations of the link group with fixed meridional traces. For two-component links with linking number one, the invariant h...
math:math:GT
arXiv Preprints
Near coincidences and nilpotent division fields
Let $E/\mathbb{Q}$ be an elliptic curve. We say that $E$ has a near coincidence of level $(n,m)$ if $m \mid n$ and $\mathbb{Q}(E[n]) = \mathbb{Q}(E[m],ζ_{n})$. We classify near coincidences of prime power level and use this result to give a classifi...
math:math:NT