Tootfinder

Toll, wie sich #Google um die #Sicherheit der Kinder kümmert, nicht? 🥹
Einfach ein Google-Konto eröffnen und dann das Surf-Verhalten damit überwachen. Natürlich mit Chrome. 🤦‍♂️
Vermutlich ist es sogar wirklich «gut gemeint». 🤪

This https://arxiv.org/abs/2004.13938 has been replaced.
link: https://scholar.google.com/scholar?q=a

Families of sequences with good family complexity and cross-correlation measure
In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity ($f$-complexity) and the cross-correlation measure of order $\ell$. We consider sequences not only on binary alphabet but also on $k$-symbols ($k$-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the $f$-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible p…

My niece is adorable and just turned 15; she got a new phone but she needs to set up [[family link]] in it. Is this normal nowadays or over-protective you would think (if you want to share)?
I ask because at late 15-16 I was using icq98 and full internet access (after a period having access only to local IRC) and loving it

This https://arxiv.org/abs/2212.12919 has been replaced.
link: https://scholar.google.com/scholar?q=a

Scalar Curvature of the Quantum Exponential Family for the Transverse-Field Ising Model and the Quantum Phase Transition
Unlike for classical many-body systems, the scalar curvature of the exponential family for quantum many-body systems has been not so investigated, and its physical meaning remains unclear. In this paper, we analytically study the scalar curvature of the space of Gibbs thermal states, belonging to the quantum exponential family, equipped with the Bogoliubov-Kubo-Mori metric for the zero- and one-dimensional transverse-field Ising model at low and high temperatures. We find that these scalar curv…

This https://arxiv.org/abs/1810.07308 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bethe subalgebras in Yangians and the wonderful compactification
We study the family of Bethe subalgebras in the Yangian $Y(\mathfrak{g})$ parameterized by the corresponding adjoint Lie group $G$. We describe their classical limits as subalgebras in the algebra of polynomial functions on the formal Lie group $G_1[[t^{-1}]]$. In particular we show that, for regular values of the parameter, these subalgebras are free polynomial algebras with the same Poincare series as the Cartan subalgebra of the Yangian. Next, we extend the family of Bethe subalgebras to the…

This https://arxiv.org/abs/2210.14781 has been replaced.
link: https://scholar.google.com/scholar?q=a

On K-moduli of quartic threefolds
The family of smooth Fano 3-folds with Picard rank 1 and anticanonical volume 4 consists of quartic 3-folds and of double covers of the 3-dimensional quadric branched along an octic surface. They can all be parametrised as complete intersections of a quadric and a quartic in the weighted projective space $\mathbb{P}(1,1,1,1,1,2)$, denoted by $X_{2,4} \subset \mathbb{P}(1^5,2)$; all such smooth complete intersections are K-stable. With the aim of investigating the compactification of the moduli …

This https://arxiv.org/abs/2211.13913 has been replaced.
link: https://scholar.google.com/scholar?q=a

Constants for Artin like problems in Kummer and division fields
We apply the character sums method of Lenstra, Moree, and Stevenhagen, to explicitly compute the constants in the Titchmarsh divisor problem for Kummer fields and for division fields of Serre curves. We derive our results as special cases of a general result on the product expressions for the sums in the form $$\sum_{n=1}^{\infty}\frac{g(n)}{\#G(n)}$$ in which $g(n)$ is a multiplicative arithmetic function and $\{G(n)\}$ is a certain family of Galois groups. Our results extend the application o…

This https://arxiv.org/abs/2011.00264 has been replaced.
link: https://scholar.google.com/scholar?q=a

Playing With Friends -- The Importance of Social Play During the COVID-19 Pandemic
In early 2020, the virus SARS-CoV-2 evolved into a new pandemic, forcing governments worldwide to establish social distancing measures. Consequently, people had to switch to online media, such as social networks or videotelephony, to keep in touch with friends and family. In this context, online games, combining entertainment with social interactions, also experienced a notable growth. In our work, we focused on the potential of games as a replacement for social contacts in the COVID-19 crisis.…

This https://arxiv.org/abs/2209.06674 has been replaced.
link: https://scholar.google.com/scholar?q=a

Analytic aspects of $q,r$-analogue of poly-Stirling numbers of both kinds
The Stirling numbers of type $B$ of the second kind count signed set partitions. In this paper we provide new combinatorial and analytical identities regarding these numbers as well as Broder's $r$-version of these numbers. Among these identities one can find recursions, explicit formulas based on the inclusion-exclusion principle, and also exponential generating functions. These Stirling numbers can be considered as members of a wider family of triangles of numbers that are characterized usi…

This https://arxiv.org/abs/2212.12919 has been replaced.
link: https://scholar.google.com/scholar?q=a

Scalar Curvature of the Quantum Exponential Family for the Transverse-Field Ising Model and the Quantum Phase Transition
Unlike for classical many-body systems, the scalar curvature of the exponential family for quantum many-body systems has been not so investigated, and its physical meaning remains unclear. In this paper, we analytically study the scalar curvature of the space of Gibbs thermal states, belonging to the quantum exponential family, equipped with the Bogoliubov-Kubo-Mori metric for the zero- and one-dimensional transverse-field Ising model at low and high temperatures. We find that these scalar curv…

This https://arxiv.org/abs/2402.05363 has been replaced.
link: https://scholar.google.com/scholar?q=a

A short proof for Rankin--Cohen brackets and generating operators
Motivated by the concept of "generating operators" for a countable family of operators introduced in the recent paper (arXiv:2306.16800), we find a method to reconstruct the Rankin--Cohen brackets from a very simple multivariable contour integral, and obtain a new proof of their covariance. We also establish a closed formula of the "generating operator" for the Rankin--Cohen brackets in full generality.

This article brilliantly makes fun of so many industries we're normally upset about. And in just one go. Heroic!
(And if you plan to buy a printer, despite already having three, do it through their #affiliate link)
#Fun #Publishing #SEO #Marketing #Advertising #AdTech #LockIn #ElectronicWaste #ManyMore
https://www.theverge.com/2024/4/2/24117976/best-printer-2024-home-use-office-use-labels-school-homework

Metallic mean fractal systems and their tilings
Sam Coates
https://arxiv.org/abs/2405.04458 https://arxiv.org/pdf/2405.04458

Metallic mean fractal systems and their tilings
Fractals and quasiperiodic structures share self-similarity as a structural property. Motivated by the link between Fibonacci fractals and quasicrystals which are scaled by the golden mean ratio $\frac{1+\sqrt{5}}{2}$, we introduce and characterize a family of metallic-mean ratio fractals. We calculate the spatial properties of this generalized family, including their boundaries, which are also fractal. We then demonstrate how these fractals can be related to aperiodic tilings, and show how we …

This https://arxiv.org/abs/2210.01988 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bicoptor: Two-round Secure Three-party Non-linear Computation without Preprocessing for Privacy-preserving Machine Learning
The overhead of non-linear functions dominates the performance of the secure multiparty computation (MPC) based privacy-preserving machine learning (PPML). This work introduces a family of novel secure three-party computation (3PC) protocols, Bicoptor, which improve the efficiency of evaluating non-linear functions. The basis of Bicoptor is a new sign determination protocol, which relies on a clever use of the truncation protocol proposed in SecureML (S\&P 2017). Our 3PC sign determination prot…

This https://arxiv.org/abs/2210.11521 has been replaced.
link: https://scholar.google.com/scholar?q=a

Decomposable context-specific models
We introduce a family of discrete context-specific models, which we call decomposable. We construct this family from the subclass of staged tree models known as CStree models. We give an algebraic and combinatorial characterization of all context-specific independence relations that hold in a decomposable context-specific model, which yields a Markov basis. We prove that the moralization operation applied to the graphical representation of a context-specific model does not affect the implied in…

This https://arxiv.org/abs/1405.0993 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

The Vandermonde determinant identity in higher dimension
We generalise the Vandermonde determinant identity to one which tests whether a family of hypersurfaces in $\mathbf{P}^n$ has an unexpected intersection point.

This https://arxiv.org/abs/2110.14046 has been replaced.
link: https://scholar.google.com/scholar?q=a

Open Markets and Hybrid Jacobi Processes
We propose a unified approach to several problems in Stochastic Portfolio Theory (SPT), which is a framework for equity markets with a large number $d$ of stocks. Our approach combines open markets, where trading is confined to the top $N$ capitalized stocks as well as the market portfolio consisting of all $d$ assets, with a parametric family of models which we call hybrid Jacobi processes. We provide a detailed analysis of ergodicity, particle collisions, and boundary attainment, and use thes…

This https://arxiv.org/abs/2103.01215 has been replaced.
link: https://scholar.google.com/scholar?q=a

Isoperiodic families of Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal pencil
Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal family naturally arise in the analysis of the numerical range and Blaschke products. We examine the behaviour of such polygons when the inscribed conic varies through a confocal pencil and discover cases when each conic from the confocal family is inscribed in an $n$-polygon, which is inscribed in the circle, with the same $n$. Complete geometric characterization of such cases for $n\in\{4,6\}$ is given and p…

This https://arxiv.org/abs/2404.00934 has been replaced.
link: https://scholar.google.com/scholar?q=a

ChatGLM-RLHF: Practices of Aligning Large Language Models with Human Feedback
ChatGLM is a free-to-use AI service powered by the ChatGLM family of large language models (LLMs). In this paper, we present the ChatGLM-RLHF pipeline -- a reinforcement learning from human feedback (RLHF) system -- designed to enhance ChatGLM's alignment with human preferences. ChatGLM-RLHF encompasses three major components: the collection of human preference data, the training of the reward model, and the optimization of policies. Throughout the process of integrating ChatGLM-RLHF into produ…

Splitting links by integer homology spheres
Marco Golla, Marco Marengon
https://arxiv.org/abs/2403.00064 https://arxiv.org/pdf/2403.0…

Splitting links by integer homology spheres
For every $n \ge 3$, we construct 2-component links in $S^{n+1}$ that are a split by an integer homology $n$-sphere, but not by $S^n$. In the special case $n=3$, i.e. that of 2-links in $S^4$, we produce an infinite family of links $L_\ell$ and of integer homology spheres $Y_\ell$ such that the link $L_\ell$ is (topologically or smoothly) split by $Y_\ell$ and by no other integer homology sphere in the family.

This https://arxiv.org/abs/2101.10867 has been replaced.
link: https://scholar.google.com/scholar?q=a

On metrics robust to noise and deformations
We study the properties of a family of distances between functions of a single variable. These distances are examples of integral probability metrics, and have been used previously for comparing probability measures on the line; special cases include the Earth Mover's Distance and the Kolmogorov Metric. We examine their properties for general signals, proving that they are robust to a broad class of deformations. We also establish corresponding robustness results for the induced sliced distance…

This https://arxiv.org/abs/2402.04308 has been replaced.
link: https://scholar.google.com/scholar?q=a

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter family of boundary conditions, parameterized by a constant $p$, where a suitably Weyl rescaled boundary metric is fixed, and all give a well-posed elliptic system. Anderson and Dirichlet boundary conditions can be seen as the limits $p \to 0$ and $\infty$ of t…

Apologies for the Instagram link, but here's a video of the people waiting at a bus stop being hit by a reckless driver (everyone survived).
Not to be confused with recent fatalities on Fulton or at bus stops.
This road - a highway, almost - encourages this kind of reckless driving. Until Fulton is completely redesigned, this will keep happening.

Richmond Family SF on Instagram: "⚠️ Content warning ⚠️ We obtained footage of the crash where a driver struck a @sfmta_muni bus shelter on Saturday at Fulton and Funston Streets in the Richmond District of San Francisco. An innocent bystander was sent to the hospital, which is horrific and appalling. It was a miracle no one died. 🔗 in bio to send a pre-written email to City officials. Make Fulton Safe! #MakeFultonSafe #VisionZero #FultonFreeway @kron4tv @ktvu2 @richmondsunsetnews"
15 likes, 3 comments - richmondfamilysf on March 25, 2024: "⚠️ Content warning ⚠️ We obtained footage of the crash where a driver struck a @sfmta_muni bus shelter on Saturday at Fulton and..."

This https://arxiv.org/abs/2204.05062 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Locally Rationalizable Social Choice Functions
We consider a notion of rationalizability, where the rationalizing relation may depend on the set of feasible alternatives. More precisely, we say that a choice function is locally rationalizable if it is rationalized by a family of rationalizing relations such that a strict preference between two alternatives in some feasible set is preserved when removing other alternatives. Tyson (2008) has shown that a choice function is locally rationalizable if and only if it satisfies Sen's $γ$. We expa…

This https://arxiv.org/abs/2204.07007 has been replaced.
link: https://scholar.google.com/scholar?q=a

Symplectic monodromy at radius zero and equimultiplicity of $μ$-constant families
We show that every family of isolated hypersurface singularity with constant Milnor number has constant multiplicity. To achieve this, we endow the A'Campo model of "radius zero" monodromy with a symplectic structure. This new approach allows to generalize a spectral sequence of McLean converging to fixed point Floer homology of iterates of the monodromy to a more general setting which is well suited to study $μ$-constant families.

This https://arxiv.org/abs/2402.03008 has been replaced.
link: https://scholar.google.com/scholar?q=a

Diffusive Gibbs Sampling
The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we propose Diffusive Gibbs Sampling (DiGS), an innovative family of sampling methods designed for effective sampling from distributions characterized by distant and disconnected modes. DiGS integrates recent developments in diffusion models, leveraging Gaussian co…

🎉 Reflecting on key milestones today! From 2 years of weekly blogging to my daughter's school graduation—life's full of big moments. Read more here: [Link] 🎓✍️ #Milestones #FamilyLife #BloggingJourney

Life’s Milestones: Embracing Changes and New Opportunities – Bob Mueller
Reflecting on milestones in blogging and family life, from weekly post streaks to celebrating school graduations and new chapters in life

This https://arxiv.org/abs/1904.02310 has been replaced.
link: https://scholar.google.com/scholar?q=a

Steiner systems $S(2,4,2^m)$ supported by a family of extended cyclic codes
In [C. Ding, An infinite family of Steiner systems $S(2,4,2^m)$ from cyclic codes, {\em J. Combin. Des.} 26 (2018), no.3, 126--144], Ding constructed a family of Steiner systems $S(2,4,2^m)$ for all $m \equiv 2 \pmod{4}$ from a family of extended cyclic codes. The objective of this paper is to present a family of Steiner systems $S(2,4,2^m)$ for all $m \equiv 0 \pmod{4}$ supported by a family of extended cyclic codes. The main result of this paper complements the previous work of Ding, and the …

This https://arxiv.org/abs/2103.01194 has been replaced.
link: https://scholar.google.com/scholar?q=a

Structure-preserving numerical schemes for Lindblad equations
We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary high-order accuracy in theory. Moreover, these schemes can also overcome the non-physical issues that arise from many traditional numerical schemes. Due to their preservation of physical nature, these schemes can be straightforwardly used as backbones for further developing randomized and quantum algorithms in simulatin…

This https://arxiv.org/abs/0710.3901 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

A recursive linear time modular decomposition algorithm via LexBFS
A module of a graph G is a set of vertices that have the same set of neighbours outside. Modules of a graphs form a so-called partitive family and thereby can be represented by a unique tree MD(G), called the modular decomposition tree. Motivated by the central role of modules in numerous algorithmic graph theory questions, the problem of efficiently computing MD(G) has been investigated since the early 70's. To date the best algorithms run in linear time but are all rather complicated. By comb…

This https://arxiv.org/abs/2307.00831 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Satisfiability of Local First-Order Logics with Data
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in general, we introduce a family of local fragments. They restrict quantification to the neighbourhood of a given reference point that is bounded by some radius. Our first main result establishes decidability of the satisfiability problem for the local radius-1 fr…

This https://arxiv.org/abs/2402.04308 has been replaced.
link: https://scholar.google.com/scholar?q=a

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter family of boundary conditions, parameterized by a constant $p$, where a suitably Weyl rescaled boundary metric is fixed, and all give a well-posed elliptic system. Anderson and Dirichlet boundary conditions can be seen as the limits $p \to 0$ and $\infty$ of t…

This https://arxiv.org/abs/2402.01214 has been replaced.
link: https://scholar.google.com/scholar?q=a

Notes on zeta ratio stabilization
This semi-expository note clarifies the extent to which recent ideas in homological stability can resolve the Ratios Conjecture over $\mathbb{F}_q(t)$. For large fixed $q$, a uniform power saving at distance $\ge q^{-δ}$ from the critical line is possible. This implies cancellation-beyond-GRH in arbitrarily large ranges of moduli relative to the family of $L$-functions. It has applications to the statistics of low-lying zeros.

This https://arxiv.org/abs/2107.02743 has been replaced.
link: https://scholar.google.com/scholar?q=a

Submodular Order Functions and Assortment Optimization
We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. We give fast algorithms with strong approximation guarantees for maximizing submodular order functions under a variety of constraints and show a nearly tight upper bound on the highe…

This https://arxiv.org/abs/2310.20583 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Conformal welding of quantum disks and multiple SLE: the non-simple case
Two-pointed quantum disks with a weight parameter $W>0$ is a canonical family of finite-volume random surfaces in Liouville quantum gravity. We extend the conformal welding of quantum disks in [AHS23] to the non-simple regime, and give a construction of the multiple SLE associated with any given link pattern for $κ\in(4,8)$. Our proof is based on connections between SLE and Liouville conformal field theory (LCFT), where we show that in the conformal welding of multiple forested quantum disks, …

This https://arxiv.org/abs/2211.09284 has been replaced.
link: https://scholar.google.com/scholar?q=a

Iterative execution of discrete and inverse discrete Fourier transforms with applications for signal denoising via sparsification
We describe a family of iterative algorithms that involve the repeated execution of discrete and inverse discrete Fourier transforms. One interesting member of this family is motivated by the discrete Fourier transform uncertainty principle and involves the application of a sparsification operation to both the real domain and frequency domain data with convergence obtained when real domain sparsity hits a stable pattern. This sparsification variant has practical utility for signal denoising, in…

🎉 Reflecting on key milestones today! From 2 years of weekly blogging to my daughter's school graduation—life's full of big moments. Read more here: [Link] 🎓✍️ #Milestones #FamilyLife #BloggingJourney

Life’s Milestones: Embracing Changes and New Opportunities – Bob Mueller
Reflecting on milestones in blogging and family life, from weekly post streaks to celebrating school graduations and new chapters in life

This https://arxiv.org/abs/2206.12631 has been replaced.
link: https://scholar.google.com/scholar?q=a

Type systems and maximal subgroups of Thompson's group $V$
We introduce the concept of a type system~$\Part$, that is, a partition on the set of finite words over the alphabet~$\{0,1\}$ compatible with the partial action of Thompson's group~$V$, and associate a subgroup~$\Stab{V}{\Part}$ of~$V$. We classify the finite simple type systems and show that the stabilizers of various simple type systems, including all finite simple type systems, are maximal subgroups of~$V$. We also find an uncountable family of pairwise non-isomorphic maximal subgroups of~$…

This https://arxiv.org/abs/2101.07079 has been replaced.
link: https://scholar.google.com/scholar?q=a

Some Examples of Family Floer Mirrors
In this article, we give explicit calculations for the family Floer mirrors of some non-compact Calabi-Yau surfaces. We compare it with the mirror construction of Gross-Hacking-Keel for suitably chosen log Calabi-Yau pairs and the rank two cluster varieties of finite type. In particular, the analytifications of the later two give partial compactifications of the family Floer mirrors that we computed.

This https://arxiv.org/abs/2104.03915 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rotational hypersurfaces family satisfying $\mathbb{L}_{n-3}\mathcal{G}=\mathcal{A}\mathcal{G}$ in ${\mathbb{E}}^{n}$
In this paper, we investigate rotational hypersurfaces family in $n$ -dimensional Euclidean space ${\mathbb{E}}^{n}$. Our focus is on studying the Gauss map $\mathcal{G}$ of this family with respect to the operator $\mathbb{L}_{k}$, which acts on functions defined on the hypersurfaces. The operator $\mathbb{L}_{k}$ can be viewed as a modified Laplacian and is known by various names, including the Cheng--Yau operator in certain cases. Specifically, we focus on the scenario where $k=n-3$ and $n\g…

This https://arxiv.org/abs/2008.10771 has been replaced.
link: https://scholar.google.com/scholar?q=a

MuCo: Publishing Microdata with Privacy Preservation through Mutual Cover
We study the anonymization technique of k-anonymity family for preserving privacy in the publication of microdata. Although existing approaches based on generalization can provide good enough protections, the generalized table always suffers from considerable information loss, mainly because the distributions of QI (Quasi-Identifier) values are barely preserved and the results of query statements are groups rather than specific tuples. To this end, we propose a novel technique, called the Mutua…

This https://arxiv.org/abs/2105.01104 has been replaced.
link: https://scholar.google.com/scholar?q=a

On 13-Crossing-Critical Graphs with Arbitrarily Large Degrees
A recent result of Bokal et al. [Combinatorica, 2022] proved that the exact minimum value of c such that c-crossing-critical graphs do not have bounded maximum degree is c=13. The key to that result is an inductive construction of a family of 13-crossing-critical graphs with many vertices of arbitrarily high degrees. While the inductive part of the construction is rather easy, it all relies on the fact that a certain 17-vertex base graph has the crossing number 13, which was originally verified…

This https://arxiv.org/abs/2201.10367 has been replaced.
link: https://scholar.google.com/scholar?q=a

Characterisation for Exponential Stability of port-Hamiltonian Systems
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for sufficient criteria in the literature by making regularity requirements for the Hamiltonian density largely obsolete. The key assumption for the characterisation (and thus the sufficient critera) to work is a uniform bound for a family of fundamental solutions f…

This https://arxiv.org/abs/2212.09644 has been replaced.
link: https://scholar.google.com/scholar?q=a

Three-family supersymmetric Pati-Salam models with symplectic groups from intersecting D6-branes
We construct new three-family ${\cal N}=1$ supersymmetric Pati-Salam models from intersecting D6-branes with original gauge group ${\rm U}(4)_C \times {\rm USp}(2)_L \times {\rm U}(2)_R$ on a Type IIA $\mathbb{T}^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ orientifold. We find that replacing a ${\rm U}(2)$ with a ${\rm USp}(2)$ group severely restricts the number of three-generation supersymmetric models such that there are only five inequivalent models. Exchanging the left and right sectors, we obtai…

This https://arxiv.org/abs/1707.03020 has been replaced.
link: https://scholar.google.com/scholar?q=a

A family of graphs that cannot occur as character degree graphs of solvable groups
We investigate character degree graphs of solvable groups. In particular, we provide general results that can be used to eliminate which degree graphs can occur as solvable groups. Finally, we show a specific family of graphs cannot occur as a character degree for any solvable group.

I posted this link on #Facebook and it removed the link preview! I'm guessing it will also derank it for my friends and family. https://www.forbes.com/…

How Meta Nuked A Climate Story, And What It Means For Democracy
Mark Zuckerberg's firm is under scrutiny again for allegedly suppressing content it doesn't like. Whatever the explanation, the action has far-reaching implications.

This https://arxiv.org/abs/2010.02848 has been replaced.
link: https://scholar.google.com/scholar?q=a

Unified Robust Estimation
Robust estimation is primarily concerned with providing reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms. In modern penalised generalised linear models (GLM), however, there is limited research on robust estimation that can provide weights to determine the outlier status of the observations. This article proposes a unified framework based on a large family of loss…

This https://arxiv.org/abs/1710.01837 has been replaced.
link: https://scholar.google.com/scholar?q=a

Postquantum Brègman relative entropies
We develop a new approach to construction of Brègman relative entropies over nonreflexive Banach spaces, based on nonlinear mappings into reflexive Banach spaces. We apply it to derive few families of Brègman relative entropies over several radially compact base normed spaces in spectral duality. In particular, we prove generalised pythagorean theorem and norm-to-norm continuity of the corresponding entropic projections for a family induced on preduals of any W$^*$-algebras and of semifinite …

This https://arxiv.org/abs/2209.05923 has been replaced.
link: https://scholar.google.com/scholar?q=a

Koszul complexes and relative homological algebra of functors over posets
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of global minimal relative resolutions. In relative homological algebra of such functors, free functors are replaced by an arbitrary family of functors. Relative Betti diagrams encode the multiplicities of these functors in minimal relative resolutions. In this article we provide conditions under which grading the chosen…

This https://arxiv.org/abs/1804.11171 has been replaced.
link: https://scholar.google.com/scholar?q=a

Meixner $d$-Orthogonal Polynomials Arising from $\mathfrak{su}(1,1)$
In this study, we present a novel family of Meixner-type $d$-orthogonal polynomials, which are distinguished as a particular subset of multiple orthogonal polynomials. We demonstrate their connection to the Lie algebra $\mathfrak{su}(1,1)$ by identifying them as matrix elements of an appropriately defined nonlinear operator. Utilizing Barut-Girardello coherent states, we explicitly outline their key features, including recurrence relations, generating functions, and $d$-orthogonality relations,…

This https://arxiv.org/abs/2011.00059 has been replaced.
link: https://scholar.google.com/scholar?q=a

Coarse Alexander duality for pairs and applications
For a group $G$ (of type $F$) acting properly on a coarse Poincaré duality space $X$, Kapovich-Kleiner introduced a coarse version of Alexander duality between $G$ and its complement in $X$. More precisely, the cohomology of $G$ with group ring coefficients is dual to a certain Čech homology group of the family of increasing neighborhoods of a $G$-orbit in $X$. This duality applies more generally to coarse embeddings of certain contractible simplicial complexes into coarse $PD(n)$ spaces. In …

This https://arxiv.org/abs/2402.03256 has been replaced.
link: https://scholar.google.com/scholar?q=a

Learning Best-in-Class Policies for the Predict-then-Optimize Framework
We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. These losses directly approximate the downstream decision loss and can be optimized using off-the-shelf gradient-based methods. Importantly, unlike existing surrogate losses, the approximation error of our PG losses vanishes as the number of samples grows. This implies that optimizing our surrogate loss yields a best-in-class policy asymptotically, eve…

This https://arxiv.org/abs/2402.00060 has been replaced.
link: https://scholar.google.com/scholar?q=a

Treatment of Epistemic Uncertainty in Conjunction Analysis with Dempster-Shafer Theory
The paper presents an approach to the modelling of epistemic uncertainty in Conjunction Data Messages (CDM) and the classification of conjunction events according to the confidence in the probability of collision. The approach proposed in this paper is based on the Dempster-Shafer Theory (DSt) of evidence and starts from the assumption that the observed CDMs are drawn from a family of unknown distributions. The Dvoretzky-Kiefer-Wolfowitz (DKW) inequality is used to construct robust bounds on su…

This https://arxiv.org/abs/2105.07947 has been replaced.
link: https://scholar.google.com/scholar?q=a

Abelian covers and second fundamental form
We give some conditions on a family of abelian covers of ${\mathbb P}^1$ of genus $g$ curves, that ensure that the family yields a subvariety of ${\mathsf A}_g$ which is not totally geodesic, hence it is not Shimura. As a consequence, we show that for any abelian group $G$, there exists an integer $M$ which only depends on $G$ such that if $g >M$, then the family yields a subvariety of ${\mathsf A}_g$ which is not totally geodesic. We prove then analogous results for families of abelian covers …

This https://arxiv.org/abs/2402.05730 has been replaced.
link: https://scholar.google.com/scholar?q=a

Deriving two dualities simultaneously from a family of identities for multiple harmonic sums
We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two kinds of limit operations, we obtain new proofs of both the duality for multiple zeta values and the duality for finite multiple zeta values.

This https://arxiv.org/abs/2105.11810 has been replaced.
link: https://scholar.google.com/scholar?q=a

Algebraic structures in the family of non-Lebesgue measurable sets
In the additive topological group $(\mathbb{R},+)$ of real numbers, we construct families of sets for which elements are not measurable in the Lebesgue sense. The constructed families have algebraic structures of being semigroups (i.e., closed under finite unions of sets), and invariant under the action of the group $Φ(\mathbb{R})$ of all translations of $\mathbb{R}$ onto itself. Those semigroups are constructed by using Vitali selectors and Bernstein subsets on $\mathbb{R}$. In particular, we…

This https://arxiv.org/abs/2105.01104 has been replaced.
link: https://scholar.google.com/scholar?q=a

On 13-Crossing-Critical Graphs with Arbitrarily Large Degrees
A recent result of Bokal et al. [Combinatorica, 2022] proved that the exact minimum value of c such that c-crossing-critical graphs do not have bounded maximum degree is c=13. The key to that result is an inductive construction of a family of 13-crossing-critical graphs with many vertices of arbitrarily high degrees. While the inductive part of the construction is rather easy, it all relies on the fact that a certain 17-vertex base graph has the crossing number 13, which was originally verified…

This https://arxiv.org/abs/2205.09847 has been replaced.
link: https://scholar.google.com/scholar?q=a

Strict irreducibility of Markov chains and ergodicity of skew products
We consider a family of measure preserving transformations, which act on a common probability space and are chosen at random by a stationary ergodic Markov chain. This setting defines an instance of a random dynamical system (RDS), which may be described in terms of a step skew product. In many contexts it is desirable to know whether ergodicity of the family implies ergodicity of the skew product. Introducing the notion of strict irreducibility for Markov kernels we shall characterize the clas…

This https://arxiv.org/abs/2109.12503 has been replaced.
link: https://scholar.google.com/scholar?q=a

Maximal subgroups of a family of iterated monodromy groups
The Basilica group is a well-known 2-generated weakly branch, but not branch, group acting on the binary rooted tree. Recently a more general form of the Basilica group has been investigated by Petschick and Rajeev, which is an $s$-generated weakly branch, but not branch, group that acts on the $m$-adic tree, for $s,m > 1$. A larger family of groups, which contains these generalised Basilica groups, is the family of iterated monodromy groups. With the new developments by Francoeur, the study of…

This https://arxiv.org/abs/2007.02553 has been replaced.
link: https://scholar.google.com/scholar?q=a

On robust fundamental theorems of asset pricing in discrete time
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our technical assumption is the continuity of the price processes with respect to uncertain parameters. In this setting, we introduce a new topological framework which allows us to use the classical arguments in arbitrage pricing theory involving $L^p$ spaces, th…

This https://arxiv.org/abs/2401.07914 has been replaced.
link: https://scholar.google.com/scholar?q=a

Graphical Symplectic Algebra
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical systems, as well as odd-prime-dimensional stabiliser quantum circuits. To this end, we present affine Lagrangian relations by a particular class of undirected coloured graphs. In order to reason about composite systems, we introduce a powerful scalable notation …

This https://arxiv.org/abs/2211.01987 has been replaced.
link: https://scholar.google.com/scholar?q=a

Exact calculation of quantizer constants for arbitrary lattices
We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond 12, which previous methods could not achieve. The new algorithm is applied to the Coxeter-Todd lattice $K_{12}$ as well as to a family of lattices obtained from laminating $K_{12}$. By optimizing this family, we obtain a new best 13-dimensional lattice quantize…

This https://arxiv.org/abs/2111.00652 has been replaced.
link: https://scholar.google.com/scholar?q=a

Eguchi--Hanson metrics arising from Kahler--Einstein edge metrics
Calabi--Hirzebruch manifolds are higher-dimensional generalizations of both the football and Hirzebruch surfaces. We construct a family of Kahler--Einstein edge metrics singular along two disjoint divisors on the Calabi--Hirzebruch manifolds and study their Gromov--Hausdorff limits when either cone angle tends to its extreme value. As a very special case, we show that the celebrated Eguchi--Hanson metric arises in this way naturally as a Gromov--Hausdorff limit. We also completely describe all …

This https://arxiv.org/abs/2011.00059 has been replaced.
link: https://scholar.google.com/scholar?q=a

Coarse Alexander duality for pairs and applications
For a group $G$ (of type $F$) acting properly on a coarse Poincaré duality space $X$, Kapovich-Kleiner introduced a coarse version of Alexander duality between $G$ and its complement in $X$. More precisely, the cohomology of $G$ with group ring coefficients is dual to a certain Čech homology group of the family of increasing neighborhoods of a $G$-orbit in $X$. This duality applies more generally to coarse embeddings of certain contractible simplicial complexes into coarse $PD(n)$ spaces. In …

This https://arxiv.org/abs/2112.01352 has been replaced.
link: https://scholar.google.com/scholar?q=a

Boundedness of elliptic Calabi-Yau threefolds
We show that elliptic Calabi--Yau threefolds form a bounded family. We also show that the same result holds for minimal terminal threefolds of Kodaira dimension 2, upon fixing the rate of growth of pluricanonical forms and the degree of a multisection of the Iitaka fibration. Both of these hypotheses are necessary to prove the boundedness of such a family.

This https://arxiv.org/abs/2212.11379 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Inverse of Exact Renormalization Group Flows as Statistical Inference
We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one parameter family of probability distributions solving an integro-differen…

This https://arxiv.org/abs/2201.10367 has been replaced.
link: https://scholar.google.com/scholar?q=a

Characterisation for Exponential Stability of port-Hamiltonian Systems
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for sufficient criteria in the literature by making regularity requirements for the Hamiltonian density largely obsolete. The key assumption for the characterisation (and thus the sufficient critera) to work is a uniform bound for a family of fundamental solutions f…

This https://arxiv.org/abs/2206.13254 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sample compression schemes for balls in graphs
One of the open problems in machine learning is whether any set-family of VC-dimension $d$ admits a sample compression scheme of size $O(d)$. In this paper, we study this problem for balls in graphs. For a ball $B=B_r(x)$ of a graph $G=(V,E)$, a realizable sample for $B$ is a signed subset $X=(X^+,X^-)$ of $V$ such that $B$ contains $X^+$ and is disjoint from $X^-$. A proper sample compression scheme of size $k$ consists of a compressor and a reconstructor. The compressor maps any realizable sa…

This https://arxiv.org/abs/2112.04160 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Finitely Convergent Cutting Plane, and a Bender's Decomposition Algorithm for Mixed-Integer Convex and Two-Stage Convex Programs using Cutting Planes
We present a finitely convergent cutting-plane algorithm for solving a general mixed-integer convex programs given an oracle for solving general convex programs. This method is extended to solve a family of two-stage mixed-integer convex programs using cutting planes, with applications to solving distributionally-robust two-stage stochastic mixed-integer convex programs. Since algorithms purely using cutting planes are not very practical for implementation, we combined the cut generation with a…

This https://arxiv.org/abs/2205.14223 has been replaced.
link: https://scholar.google.com/scholar?q=a

A short note on inf-sup conditions for the Taylor-Hood family $Q_k$-$Q_{k-1}$
We discuss two types of discrete inf-sup conditions for the Taylor-Hood family $Q_k$-$Q_{k-1}$ for all $k\in \mathbb{N}$ with $k\ge 2$ in 2D and 3D. While in 2D all results hold for a general class of hexahedral meshes, the results in 3D are restricted to meshes of parallelepipeds. The analysis is based on an element-wise technique as opposed to the widely used macroelement technique. This leads to inf-sup conditions on each element of the subdivision as well as to inf-sup conditions on the who…

This https://arxiv.org/abs/2008.10988 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory
We describe the family of supersymmetric twists of $\mathcal N = 4$ super Yang--Mills theory using derived algebraic geometry, starting from holomorphic Chern--Simons theory on $ \mathcal N = 4$ super twistor space. By considering an ansatz for categorical geometric quantization of the family of further twists of a fixed holomorphic twist, we give a quantum field-theoretic synthesis of the categories of twisted D-modules occuring in the quantum geometric Langlands correspondence.

A prop structure on partitions
Coline EmprinENS Paris Saclay, Dana HunterIMJ-PRG, Muriel LivernetIMJ-PRG, Christine VespaI2M, Inna Zakharevich
https://arxiv.org/abs/2402.12895

A prop structure on partitions
Motivated by its link with functor homology, we study the prop freely generated by the operadic suspension of the operad Com. We exhibit a particular family of generators, for which the composition and the symmetric group actions admit simple descriptions. We highlight associated subcategories of its Karoubi envelope which allows us to compute extensions groups between simple functors from free groups. We construct a particular prop structure on partitions whose composition corresponds to the Y…

This https://arxiv.org/abs/2403.08295 has been replaced.
link: https://scholar.google.com/scholar?q=a

Gemma: Open Models Based on Gemini Research and Technology
This work introduces Gemma, a family of lightweight, state-of-the art open models built from the research and technology used to create Gemini models. Gemma models demonstrate strong performance across academic benchmarks for language understanding, reasoning, and safety. We release two sizes of models (2 billion and 7 billion parameters), and provide both pretrained and fine-tuned checkpoints. Gemma outperforms similarly sized open models on 11 out of 18 text-based tasks, and we present compre…

This https://arxiv.org/abs/1811.09315 has been replaced.
link: https://scholar.google.com/scholar?q=a

How to find MH370?
The disappearance of flight MH370 is possibly the greatest mystery in aviation history. A large zone in the Southern Indian Ocean was searched unsuccessfully leaving an open case and an unacceptable situation for the family members. We discuss the scientific difficulties with locating the plane through satellite data and develop an improved analysis using least square curve fitting of analytical non-Euclidean route equations providing robust topology-optimization with perturbation theory handli…

This https://arxiv.org/abs/2403.01213 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the family of elliptic curves $y^2=x^3-m^2x + (pqr)^2$
In this article, we consider a family of elliptic curves defined by $E_{m}: y^2= x^3 -m^2 x + (pqr)^2 $ where $m $ is a positive integer and $p, q, ~\text{and}~ r$ are distinct odd primes and study the torsion as well the rank of $E_{m}(\mathbb{Q})$. More specifically, we proved that if $m \not \equiv 0 \pmod{3}, m \not \equiv 0 \pmod{4} ~\text{and}~ m \equiv 2 \pmod {2^{k}}$ where $k \geq 5$, then the torsion subgroup of $E_{m}(\mathbb{Q})$ is trivial and lower bound of the $\mathbb{Q}$ rank o…

This https://arxiv.org/abs/2007.07879 has been replaced.
link: https://scholar.google.com/scholar?q=a

Preservation Theorems Through the Lens of Topology
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of surjective morphisms, subclasses, sums, products, topological closures, and projective limits. Throughout the paper, we also integrate already known results into this new framework and show how it captures th essence of their proofs.

This https://arxiv.org/abs/2210.01988 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bicoptor: Two-round Secure Three-party Non-linear Computation without Preprocessing for Privacy-preserving Machine Learning
The overhead of non-linear functions dominates the performance of the secure multiparty computation (MPC) based privacy-preserving machine learning (PPML). This work introduces a family of novel secure three-party computation (3PC) protocols, Bicoptor, which improve the efficiency of evaluating non-linear functions. The basis of Bicoptor is a new sign determination protocol, which relies on a clever use of the truncation protocol proposed in SecureML (S\&P 2017). Our 3PC sign determination prot…

This https://arxiv.org/abs/2301.06573 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On chain link surgeries bounding rational homology balls and $χ$-slice 3-braid closures
We determine which integral surgeries on a large class of circular chain links bound rational homology balls. Our key tool is the lattice-theoretic cubiquity obstruction recently developed by Greene and Owens. We discuss a practical method of computing it, and, as an application, prove that a generalisation of the slice--ribbon conjecture holds for all but one infinite family of quasi-alternating 3-braid links. This extends previous results of Lisca concerning the conjecture for 3-braid knots.

Link patterns and elliptic Hecke algebra
Andrzej Weber
https://arxiv.org/abs/2404.08911 https://arxiv.org/pdf/2404.08911

Link patterns and elliptic Hecke algebra
We compare the following three families of geometric objects: Schubert varieties in flag manifolds, matrix Schubert varieties, and Borel orbits of 2-nilpotent matrices. The first family is governed by permutations, the second by partial permutations, and the last one by "link patterns". These geometric objects admit characteristic classes in equivariant elliptic cohomology obtained within the framework created by Borisov and Libgober. We construct a Hecke-type algebra for computing elliptic cla…

This https://arxiv.org/abs/2109.09578 has been replaced.
link: https://scholar.google.com/scholar?q=a

Generalized principal eigenvalues of space-time periodic, weakly coupled, cooperative, parabolic systems
This paper is concerned with generalizations of the notion of principal eigenvalue in the context of space-time periodic cooperative systems. When the spatial domain is the whole space, the Krein-Rutman theorem cannot be applied and this leads to more sophisticated constructions and to the notion of generalized principal eigenvalues. These are not unique in general and we focus on a one-parameter family corresponding to principal eigenfunctions that are space-time periodic multiplicative pertur…

This https://arxiv.org/abs/2001.00045 has been replaced.
link: https://scholar.google.com/scholar?q=a

The universal $p$-adic Gross-Zagier formula
Let ${\mathrm G}$ be the group $({\rm GL}_{2}\times {\rm GU}(1))/{\rm GL}_{1}$ over a totally real field $F$, and let $\mathscr{X}$ be a Hida family for ${\rm G}$. Revisiting a construction of Howard and Fouquet, we construct an explicit section $\mathscr{P}$ of a sheaf of Selmer groups over $\mathscr{X}$. We show, answering a question of Howard, that $\mathscr{P}$ is a universal Heegner class, in the sense that it interpolates geometrically defined Heegner classes at all the relevant classical…

This https://arxiv.org/abs/2210.11048 has been replaced.
link: https://scholar.google.com/scholar?q=a

The quadratic linking degree
By using motivic homotopy theory, we introduce a counterpart in algebraic geometry to oriented links and their linking numbers. After constructing the (ambient) quadratic linking degree -- our analogue of the linking number which takes values in the Witt group of the ground field -- and exploring some of its properties, we give a method to explicitly compute it. We illustrate this method on a family of examples which are analogues of torus links, in particular of the Hopf and Solomon links.

This https://arxiv.org/abs/2403.08295 has been replaced.
link: https://scholar.google.com/scholar?q=a

Gemma: Open Models Based on Gemini Research and Technology
This work introduces Gemma, a family of lightweight, state-of-the art open models built from the research and technology used to create Gemini models. Gemma models demonstrate strong performance across academic benchmarks for language understanding, reasoning, and safety. We release two sizes of models (2 billion and 7 billion parameters), and provide both pretrained and fine-tuned checkpoints. Gemma outperforms similarly sized open models on 11 out of 18 text-based tasks, and we present compre…

This https://arxiv.org/abs/2403.01213 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the family of elliptic curves $y^2=x^3-m^2x + (pqr)^2$
In this article, we consider a family of elliptic curves defined by $E_{m}: y^2= x^3 -m^2 x + (pqr)^2 $ where $m $ is a positive integer and $p, q, ~\text{and}~ r$ are distinct odd primes and study the torsion as well the rank of $E_{m}(\mathbb{Q})$. More specifically, we proved that if $m \not \equiv 0 \pmod{3}, m \not \equiv 0 \pmod{4} ~\text{and}~ m \equiv 2 \pmod {2^{k}}$ where $k \geq 5$, then the torsion subgroup of $E_{m}(\mathbb{Q})$ is trivial and lower bound of the $\mathbb{Q}$ rank o…

Character varieties of torus links
\'Angel Gonz\'alez-Prieto, Javier Mart\'inez, Vicente Mu\~noz
https://arxiv.org/abs/2402.12286 https://

Character varieties of torus links
In this paper, we study the geometry of the moduli space of representations of the fundamental group of the complement of a torus link into an algebraic group G, an algebraic variety known as the G-character variety of the torus link. These torus links are a family of links in the 3-dimensional sphere formed by stacking several copies of torus knots. We develop an intrinsic stratification of the variety that allows us to relate its geometry with the one of the underlying torus knot. Using this …

This https://arxiv.org/abs/2206.01721 has been replaced.
link: https://scholar.google.com/scholar?q=a

Orientation of convex sets
We introduce a novel definition of orientation on the triples of a family of pairwise intersecting planar convex sets and study its properties. In particular, we compare it to other systems of orientations on triples that satisfy a so-called interiority condition: $\circlearrowleft(ABD)=~\circlearrowleft(BCD)=~\circlearrowleft(CAD)=1$ imply $\circlearrowleft(ABC)=1$ for any $A,B,C,D$. We call such an orientation a P3O (partial 3-order), a natural generalization of a poset, that has several inte…

This https://arxiv.org/abs/1812.02089 has been replaced.
link: https://scholar.google.com/scholar?q=a

Scalar probes on wormholes in Lovelock theories with unique vacuum
In this paper we present a new family of wormhole geometries in Lovelock theories with a unique vacuum, and study their stability under scalar field perturbations. As the solutions already known in the literature for Chern-Simons gravity on AdS, the new wormholes are characterized by a single integration constant $ρ_{0}$, that parameterizes the contribution to the mass coming from each boundary, which cancel each other, leading to a new example of "mass without mass". The stability of these ne…

This https://arxiv.org/abs/1703.06089 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hasse-Minkowski theorem for quadratic forms on groups
We discuss generalizations of the classic Hasse-Minkowski theorem for integral quadratic forms, to quadratic forms over a family of groups, equipped with systems of reduction maps. This family embraces very interesting classes, like Mordell-Weil groups of abelian varieties over number fields, odd algebraic K-theory groups of number fields, and finitely generated subgroups of the multiplicative groups of number fields.

This https://arxiv.org/abs/2210.06000 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bounds for DP color function and canonical labelings
The DP-coloring is a generalization of the list coloring, introduced by Dvořák and Postle. Let $\mathcal{H}=(L,H)$ be a cover of a graph $G$ and $P_{DP}(G,\mathcal{H})$ be the number of $\mathcal{H}$-colorings of $G$. The DP color function $P_{DP}(G,m)$ of $G$, introduced by Kaul and Mudrock, is the minimum value of $P_{DP}(G,\mathcal{H})$ where the minimum is taken over all possible $m$-fold covers $\mathcal{H}$ of $G$. For the family of $n$-vertex connected graphs, one can deduce that trees…

This https://arxiv.org/abs/2403.01213 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the family of elliptic curves $y^2=x^3-m^2x + (pqr)^2$
In this article, we consider a family of elliptic curves defined by $E_{m}: y^2= x^3 -m^2 x + (pqr)^2 $ where $m $ is a positive integer and $p, q, ~\text{and}~ r$ are distinct odd primes and study the torsion as well the rank of $E_{m}(\mathbb{Q})$. More specifically, we proved that if $m \not \equiv 0 \pmod{3}, m \not \equiv 0 \pmod{4} ~\text{and}~ m \equiv 2 \pmod {2^{k}}$ where $k \geq 5$, then the torsion subgroup of $E_{m}(\mathbb{Q})$ is trivial and lower bound of the $\mathbb{Q}$ rank o…

This https://arxiv.org/abs/1606.04076 has been replaced.
link: https://scholar.google.com/scholar?q=a

Calabi--Yau complete intersections in exceptional Grassmannians
We classify completely reducible equivariant vector bundles on Grassmannians of exceptional Lie groups which give Calabi--Yau 3-folds as complete intersections. In particular, we find a new family of Calabi--Yau 3-folds in an $E_6$-Grassmannian.

This https://arxiv.org/abs/2107.06974 has been replaced.
link: https://scholar.google.com/scholar?q=a

Multiple twins in permutations
By an $r$-tuplet in a permutation we mean a family of $r$ pairwise disjoint subsequences with the same relative order. The length of an $r$-tuplet is defined as the length of any single subsequence in the family. Let $t^{(r)}(n)$ denote the largest $k$ such that every permutation of length $n$ contains an $r$-tuplet of length $k$. We prove that $t^{(r)}(n)=O\left(n^{\frac r{2r-1}}\right)$ and $t^{(r)}(n)=Ω\left( n^{\frac{R}{2R-1}} \right)$, where $R=\binom{2r-1}r$. We conjecture that the upper…

This https://arxiv.org/abs/2402.03150 has been replaced.
link: https://scholar.google.com/scholar?q=a

Kleitman's conjecture for central families
Chvátal conjectured that a star is amongst the largest intersecting subfamiles of a finite subset-closed family of sets. Kleitman later strengthened Chvátal's conjecture, suggesting that maximal intersecting subfamilies of $2^{[n]}$ when naturally embedded into $\mathbb{R}^{2^{[n]}}$ take on a particular form. We provide a construction which succeeds in expressing certain families as required by Kleitman's conjecture. We then provide a partial characterization of these families, showing centr…

This https://arxiv.org/abs/2208.01531 has been replaced.
link: https://scholar.google.com/scholar?q=a

Picard-Fuchs equations of the generalized Dwork family
We determine the Picard-Fuchs equations of the generalized Dwork families by Katz. As an application, we compute the Frobenius matrix on the rigid cohomology of the family. This was originally done by Kloosterman, while we give an alternative computation with use of the Picard-Fuchs equations.

This https://arxiv.org/abs/2402.05818 has been replaced.
link: https://scholar.google.com/scholar?q=a

$L$-systems and the Lovász number
Given integers $n > k > 0$, and a set of integers $L \subset [0, k-1]$, an \emph{$L$-system} is a family of sets $\mathcal{F} \subset \binom{[n]}{k}$ such that $|F \cap F'| \in L$ for distinct $F, F'\in \mathcal{F}$. $L$-systems correspond to independent sets in a certain generalized Johnson graph $G(n, k, L)$, so that the maximum size of an $L$-system is equivalent to finding the independence number of the graph $G(n, k, L)$. The \emph{Lovász number} $\vartheta(G)$ is a semidefinite…

This https://arxiv.org/abs/2001.10316 has been replaced.
link: https://scholar.google.com/scholar?q=a

Newton non-degenerate $μ$-constant deformations admit simultaneous embedded resolutions
Let $\mathbb{C}^{n+1}_o$ denote the germ of $\mathbb{C}^{n+1}$ at the origin. Let $V$ be a hypersurface germ in $\mathbb{C}^{n+1}_o$ and $W$ a deformation of $V$ over $\mathbb{C}_{o}^{m}$. Under the hypothesis that $W$ is a Newton non-degenerate deformation, in this article we will prove that $W$ is a $μ$-constant deformation if and only if $W$ admits a simultaneous embedded resolution. This result gives a lot of information about $W$, for example, the topological triviality of the family $W$ …

This https://arxiv.org/abs/2210.12888 has been replaced.
link: https://scholar.google.com/scholar?q=a

Turán Problems for Mixed Graphs
We investigate natural Turán problems for mixed graphs, generalizations of graphs where edges can be either directed or undirected. We study a natural \textit{Turán density coefficient} that measures how large a fraction of directed edges an $F$-free mixed graph can have; we establish an analogue of the Erdős-Stone-Simonovits theorem and give a variational characterization of the Turán density coefficient of any mixed graph (along with an associated extremal $F$-free family). This character…

This https://arxiv.org/abs/2206.00594 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sparse graphs with bounded induced cycle packing number have logarithmic treewidth
A graph is $\mathcal{O}_k$-free if it does not contain $k$ pairwise vertex-disjoint and non-adjacent cycles. We prove that "sparse" (here, not containing large complete bipartite graphs as subgraphs) $\mathcal{O}_k$-free graphs have treewidth (even, feedback vertex set number) at most logarithmic in the number of vertices. This is optimal, as there is an infinite family of $\mathcal{O}_2$-free graphs without $K_{2,3}$ as a subgraph and whose treewidth is (at least) logarithmic. Using our resu…