Tootfinder

The circle packing problem: a theoretical comparison of various convexification techniques
Aida Khajavirad
https://arxiv.org/abs/2404.03091 https://…

The circle packing problem: a theoretical comparison of various convexification techniques
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex quadratically constrained optimization problem, which possesses many local optima. We consider several popular convexification techniques, giving rise to linear programming relaxations and semidefinite programming relaxations for the circle packing problem. We co…

This https://arxiv.org/abs/2308.02136 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

World-Model-Based Control for Industrial box-packing of Multiple Objects using NewtonianVAE
The process of industrial box-packing, which involves the accurate placement of multiple objects, requires high-accuracy positioning and sequential actions. When a robot is tasked with placing an object at a specific location with high accuracy, it is important not only to have information about the location of the object to be placed, but also the posture of the object grasped by the robotic hand. Often, industrial box-packing requires the sequential placement of identically shaped objects int…

Okay, friends, any recommendations for audiobooks, podcasts, or other materials to listen to while packing? I'm looking for something that won't require my full attention but will help pass the time. Thanks in advance for any recs!

This https://arxiv.org/abs/2308.08064 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Freedman's link packings
Recently, Freedman [arXiv:2301.00295] introduced the idea of packing a maximal number of links into a bounded region subject to geometric constraints, and produced upper bounds on the packing number in some cases, while commenting that these bounds seemed far too large. We show that the smallest of these "extravagantly large" bounds is in fact sharp by constructing, for any link, a packing of exponentially many copies as a function of the available volume. We also produce improved and generaliz…

Edge open packing: complexity, algorithmic aspects, and bounds
Bo\v{s}tjan Bre\v{s}ar, Babak Samadi
https://arxiv.org/abs/2403.00750 https://

Edge open packing: complexity, algorithmic aspects, and bounds
Given a graph $G$, two edges $e_{1},e_{2}\in E(G)$ are said to have a common edge $e$ if $e$ joins an endvertex of $e_{1}$ to an endvertex of $e_{2}$. A subset $B\subseteq E(G)$ is an edge open packing set in $G$ if no two edges of $B$ have a common edge in $G$, and the maximum cardinality of such a set in $G$ is called the edge open packing number, $ρ_{e}^{o}(G)$, of $G$. In this paper, we prove that the decision version of the edge open packing number is NP-complete even when restricted to g…

This https://arxiv.org/abs/2308.02136 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

World-Model-Based Control for Industrial box-packing of Multiple Objects using NewtonianVAE
The process of industrial box-packing, which involves the accurate placement of multiple objects, requires high-accuracy positioning and sequential actions. When a robot is tasked with placing an object at a specific location with high accuracy, it is important not only to have information about the location of the object to be placed, but also the posture of the object grasped by the robotic hand. Often, industrial box-packing requires the sequential placement of identically shaped objects int…

Edge open packing: complexity, algorithmic aspects, and bounds
Bo\v{s}tjan Bre\v{s}ar, Babak Samadi
https://arxiv.org/abs/2403.00750 https://

Edge open packing: complexity, algorithmic aspects, and bounds
Given a graph $G$, two edges $e_{1},e_{2}\in E(G)$ are said to have a common edge $e$ if $e$ joins an endvertex of $e_{1}$ to an endvertex of $e_{2}$. A subset $B\subseteq E(G)$ is an edge open packing set in $G$ if no two edges of $B$ have a common edge in $G$, and the maximum cardinality of such a set in $G$ is called the edge open packing number, $ρ_{e}^{o}(G)$, of $G$. In this paper, we prove that the decision version of the edge open packing number is NP-complete even when restricted to g…

A Framework for Approximation Schemes on Knapsack and Packing Problems of Hyperspheres and Fat Objects
V\'itor Gomes Chagas, Elisa Dell'Arriva, Fl\'avio Keidi Miyazawa
https://arxiv.org/abs/2405.00246

A Framework for Approximation Schemes on Knapsack and Packing Problems of Hyperspheres and Fat Objects
Geometric packing problems have been investigated for centuries in mathematics. In contrast, works on sphere packing in the field of approximation algorithms are scarce. Most results are for squares and rectangles, and their d-dimensional counterparts. To help fill this gap, we present a framework that yields approximation schemes for the geometric knapsack problem as well as other packing problems and some generalizations, and that supports not only hyperspheres but also a wide range of shapes…

Sometimes I'm like, "he's 12, he should really be packing his own school lunch now." And then he does shit like this.
#parenting

...“hard work” is really packing together numerous ideas in one phrase.
- long hours
- difficult tasks (physically, emotionally or intellectually)
- unrewarding work
- unpleasant tasks
- inflexible #work (It is a “hard job” if it prevents you from, for example, seeing your child’s basketball game. If you were able to see the game and finish up 2 hours of work…

PackVFL: Efficient HE Packing for Vertical Federated Learning
Liu Yang, Shuowei Cai, Di Chai, Junxue Zhang, Han Tian, Yilun Jin, Kun Guo, Kai Chen, Qiang Yang
https://arxiv.org/abs/2405.00482

PackVFL: Efficient HE Packing for Vertical Federated Learning
As an essential tool of secure distributed machine learning, vertical federated learning (VFL) based on homomorphic encryption (HE) suffers from severe efficiency problems due to data inflation and time-consuming operations. To this core, we propose PackVFL, an efficient VFL framework based on packed HE (PackedHE), to accelerate the existing HE-based VFL algorithms. PackVFL packs multiple cleartexts into one ciphertext and supports single-instruction-multiple-data (SIMD)-style parallelism. We f…

Circle radius distributions determine random close packing density
David J. Meer, Isabela Galoustian, Julio Gabriel de Falco Manuel, Eric R. Weeks
https://arxiv.org/abs/2404.02316

Circle radius distributions determine random close packing density
Circles of a single size can pack together densely in a hexagonal lattice, but adding in size variety disrupts the order of those packings. We conduct simulations which generate dense random packings of circles with specified size distributions, and measure the area fraction in each case. While the size distributions can be arbitrary, we find that for a wide range of size distributions the random close packing area fraction $ϕ_{rcp}$ is determined to high accuracy by the polydispersity and ske…

Intel-Pläne eines Packaging-Werks in Italien für Chips aus Magdeburg auf Eis
Intel wollte die in Magdeburg produzierten Chips in Norditalien weiterverarbeiten. Doch der Bau dieses Packaging-Werks in der Veneto-Region ist jetzt ungewiss.

Hitting Meets Packing: How Hard Can it Be?
Jacob Focke, Fabian Frei, Shaohua Li, D\'aniel Marx, Philipp Schepper, Roohani Sharma, Karol W\k{e}grzycki
https://arxiv.org/abs/2402.14927

Hitting Meets Packing: How Hard Can it Be?
We study a general family of problems that form a common generalization of classic hitting (also referred to as covering or transversal) and packing problems. An instance of X-HitPack asks: Can removing k (deletable) vertices of a graph G prevent us from packing $\ell$ vertex-disjoint objects of type X? This problem captures a spectrum of problems with standard hitting and packing on opposite ends. Our main motivating question is whether the combination X-HitPack can be significantly harder tha…

This https://arxiv.org/abs/2312.17296 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Structured Packing in LLM Training Improves Long Context Utilization
Recent developments in long-context large language models have attracted considerable attention. Yet, their real-world applications are often hindered by ineffective context information use. This work shows that structuring training data to increase semantic interdependence is an effective strategy for optimizing context utilization. To this end, we introduce Structured Packing for Long Context (SPLiCe), a method for creating training examples by using information retrieval methods to collate m…

On Greg Olear's Prevail podcast, Dahlia Lithwick talks about #SCOTUS - court packing, judicial mindsets, the Federalist Society, term limits, issues before the court, and more.
"No other constitutional democracy is in thrall to a court the way the United States is."

‎Prevail with Greg Olear: Feelingsball: The Leonard Leo Industrial Complex, SCOTUS Nihilism, and the Doctrine of Sad (with Dahlia Lithwick) on Apple Podcasts
‎Show Prevail with Greg Olear, Ep Feelingsball: The Leonard Leo Industrial Complex, SCOTUS Nihilism, and the Doctrine of Sad (with Dahlia Lithwick) - Mar 1, 2024

Finished packing about 90 @… Merch Bundle bags 🥵🥵🥵

#Project2025 focuses on packing the next GOP administration with extreme loyalists to former President Donald Trump. 
The plan aims to reinstate #ScheduleF, a Trump-era executive order that makes federal employees fireable at-will, stripping tens of thousands of employees of civil service protections.
…

A guide to Project 2025, the extreme right-wing agenda for the next Republican administration
Project 2025, a comprehensive transition plan organized by right-wing think tank The Heritage Foundation to guide the next GOP presidential administration, is the conservative movement’s most robust policy and staffing proposal for a potential second Trump White House — and its extreme agenda represents a threat to democracy, civil rights, the climate, and more.  Project 2025 focuses on packing the next GOP administration with extreme loyalists to former President Donald Trump.  The plan …

This https://arxiv.org/abs/2310.04574 has been replaced.
link: https://scholar.google.com/scholar?q=a

Remarks on soft ball packings in dimensions 2 and 3
We study translative arrangements of centrally symmetric convex domains in the plane (resp., of congruent balls in the Euclidean $3$-space) that neither pack nor cover. We define their soft density depending on a soft parameter and prove that the largest soft density for soft translative packings of a centrally symmetric convex domain with $3$-fold rotational symmetry and given soft parameter is obtained for a proper soft lattice packing. Furthermore, we show that among the soft lattice packing…

Constraint Propagation on GPU: A Case Study for the Bin Packing Constraint
Fabio Tardivo, Laurent Michel, Enrico Pontelli
https://arxiv.org/abs/2402.14821 …

Constraint Propagation on GPU: A Case Study for the Bin Packing Constraint
The Bin Packing Problem is one of the most important problems in discrete optimization, as it captures the requirements of many real-world problems. Because of its importance, it has been approached with the main theoretical and practical tools. Resolution approaches based on Linear Programming are the most effective, while Constraint Programming proves valuable when the Bin Packing Problem is a component of a larger problem. This work focuses on the Bin Packing constraint and explores how GPUs…

Thought I’d listen to some music while packing/throwing stuff away. I figured I’d make a high energy “Moving” playlist to listen to…
OMG I forgot what a *collosal* POS the Apple Music app is! HTF can Apple still ship this crap after all these years!?

"embryos are legally children? In what state?" Shouted Matt Gaetz while packing up some moving boxes.
#uspol

“Too much eye rolling and not enough applause.” -me, after packing a hotel luggage cart Beverly Hillbillies style to make it in one trip. True, it lacked any central ballast, but we made it in one trip!

On the $(1^2,2^4)$-packing edge-coloring of subcubic graphs
Xujun Liu, Gexin Yu
https://arxiv.org/abs/2402.18353 https://arxiv.org/pd…

On the $(1^2,2^4)$-packing edge-coloring of subcubic graphs
An induced matching in a graph $G$ is a matching such that its end vertices also induce a matching. A $(1^{\ell}, 2^k)$-packing edge-coloring of a graph $G$ is a partition of its edge set into disjoint unions of $\ell$ matchings and $k$ induced matchings. Gastineau and Togni (2019), as well as Hocquard, Lajou, and Lužar (2022), have conjectured that every subcubic graph is $(1^2,2^4)$-packing edge-colorable. In this paper, we confirm that their conjecture is true (for connected subcubic graphs…

Hitting Meets Packing: How Hard Can it Be?
Jacob Focke, Fabian Frei, Shaohua Li, D\'aniel Marx, Philipp Schepper, Roohani Sharma, Karol W\k{e}grzycki
https://arxiv.org/abs/2402.14927

Hitting Meets Packing: How Hard Can it Be?
We study a general family of problems that form a common generalization of classic hitting (also referred to as covering or transversal) and packing problems. An instance of X-HitPack asks: Can removing k (deletable) vertices of a graph G prevent us from packing $\ell$ vertex-disjoint objects of type X? This problem captures a spectrum of problems with standard hitting and packing on opposite ends. Our main motivating question is whether the combination X-HitPack can be significantly harder tha…

Finished packing about 90 @… Merch Bundle bags 🥵🥵🥵

The Mathematical Foundation of Post-Quantum Cryptography
Chuanming Zong
https://arxiv.org/abs/2404.19186 https://arxiv.org/pdf/2404.1…

The Mathematical Foundation of Post-Quantum Cryptography
On July 5, 2022, the National Institute of Standards and Technology announced four possible post-quantum cryptography standards, three of them are based on lattice theory and the other one is based on Hash function. It is well-known that the security of the lattice cryptography relies on the hardness of the shortest vector problem (SVP) and the closest vector problem (CVP). In fact, the SVP is a sphere packing problem and the CVP is a sphere covering problem. Furthermore, both SVP and CVP are e…

Maximum Polygon Packing: The CG:SHOP Challenge 2024
S\'andor P. Fekete, Phillip Keldenich, Dominik Krupke, Stefan Schirra
https://arxiv.org/abs/2403.16203

Maximum Polygon Packing: The CG:SHOP Challenge 2024
We give an overview of the 2024 Computational Geometry Challenge targeting the problem \textsc{Maximum Polygon Packing}: Given a convex region $P$ in the plane, and a collection of simple polygons $Q_1, \ldots, Q_n$, each $Q_i$ with a respective value $c_i$, find a subset $S \subseteq \{1, \ldots,n\}$ and a feasible packing within $P$ of the polygons $Q_i$ (without rotation) for $i \in S$, maximizing $\sum_{i \in S} c_i$. Geometric packing problems, such as this, present significant computation…

Leveraging Symbolic Regression for Heuristic Design in the Traveling Thief Problem
Andrew Ni, Lee Spector
https://arxiv.org/abs/2404.12750 https://<…

Leveraging Symbolic Regression for Heuristic Design in the Traveling Thief Problem
The Traveling Thief Problem is an NP-hard combination of the well known traveling salesman and knapsack packing problems. In this paper, we use symbolic regression to learn useful features of near-optimal packing plans, which we then use to design efficient metaheuristic genetic algorithms for the traveling thief algorithm. By using symbolic regression again to initialize the metaheuristic GA with near-optimal individuals, we are able to design a fast, interpretable, and effective packing initi…

Critical scaling for dense granular flow between parallel plates near jamming
Michio Otsuki, Kenta Hayashi, Kiwamu Yoshii
https://arxiv.org/abs/2403.00256 …

Critical scaling for dense granular flow between parallel plates near jamming
We numerically study the flow of dense granular materials between parallel plates driven by an external force. The granular materials form a jammed solid-like state when the external force is below a critical force, while they flow like fluids above the critical force. The transition is characterized by the mass flux. The critical force depends on the average packing fraction and the distance between the plates. The scaling laws for the critical force and the mass flux are predicted theoretical…

While dressing and packing you gear in the hotel before checkout: Wondering why you have an odd number of socks, where has one gone? A few minutes later you realise you are wearing a sock on just one foot so far.

Forced labor was the foundation of an economic system that knew no color boundaries; like an open sore the plantations grew upon the Caribbean, and when the Indians died, and the supply of white trash failed to meet demand, the merchants tapped deeper into Africa, drawing away men and women not because they were black, but because they were cheap, limitless in number, and better. European class societies whose elite thought nothing of hanging an English child for petty theft, or packing indentured workers, white or black, like herring into the festering holds of ships, cared less about the origins of their laborers than the production of their labor. Slavery was not born of racism; rather, racism was the consequence of slavery. In the first days of colonialism, when the merchants sailed away from the insular world of Europe, the color of the worker’s skin meant no more to them than it did to the kings of Africa, rulers who lorded over thousands of their own slaves, and who for a suitable profit were more than willing to pass them along. Of course, all of this mattered little to the men and women unloaded into bondage in Saint Domingue. For them the enemy had a face, and there was no doubt as to its color.
Wade Davis -- The Serpent and the Rainbow
#Slavery #Racism #Abolition #Haiti #Capitalism

This https://arxiv.org/abs/2308.03925 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sphere Packings in Euclidean Space with Forbidden Distances
In this paper we study the sphere packing problem in Euclidean space where we impose additional constraints on the separations of the center points. We prove that any sphere packing in dimension $48$, with spheres of radii $r$, such that \emph{no} two centers $x_1$ and $x_2$ satisfy $\sqrt{\tfrac{4}{3}} < \frac{1}{2r}|x_1-x_2| <\sqrt{\tfrac{5}{3}}$, has center density less or equal than $(3/2)^{24}$. Equality occurs for lattice packings if and only if the packing is given by a $48$-di…

A last long day in the field and in discussion with colleagues. Snow, narwhals, local community discussions, a new snow site and perhaps a new proposal. A lot to process and tomorrow will be busy packing and preparing..
Good night all.
#Greenland #Fieldwork2024

Packing measure of the linear Gauss system
Rafa{\l} Tryniecki
https://arxiv.org/abs/2404.12012 https://arxiv.org/pdf/2404.12012

Packing measure of the linear Gauss system
For every $k \in \mathbb{N}$ let $f_k:[\frac{1}{k+1}, \frac{1}{k}] \to [0,1]$ be decreasing, linear functions such that $f_k(\frac{1}{k+1}) = 1$ and $f_k(\frac{1}{k}) = 0$, $k = 1, 2, \dots$. We define iterated function system (IFS) $S_n$ by limiting the collection of functions $f_k$ to first n, meaning $S_n = \{f_k \}_{k=1}^n$. Let $J_n$ denote the limit set of $S_n$. Then $\lim\limits_{n\to \infty} \mathcal{P}_{h_n}(J_n) = 2$, where $h_n$ is the packing dimension of $J_n$ and $\mathcal{P}_{h_…

Calculating the sequences behind a hexagonal lattice based equal circle packing in the Euclidian plane
Jure Voglar, Aljo\v{s}a Peperko
https://arxiv.org/abs/2403.10530

Calculating the sequences behind a hexagonal lattice based equal circle packing in the Euclidian plane
The article presents the mathematical sequences describing circle packing densities in four different geometric configurations involving a hexagonal lattice based equal circle packing in the Euclidian plane. The calculated sequences take form of either polynomials or rational functions. If the circle packing area is limited with a circle, the packing densities tend to decrease with increasing number of the packed circles and converge to values lower than π/(2\sqrt{3}). In cases with packing ar…

This https://arxiv.org/abs/2308.09334 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Packing Integral Tori in Del Pezzo Surfaces
We extend a packing result of R. Hind and E. Kerman for integral Lagrangian tori in $\mathbb{S}^{2} \times \mathbb{S}^{2}$ to the Del Pezzo surfaces $(\mathbb{D}_{n}, ω_{\mathbb{D}_{n}})$ for $n = 1, \dots, 5$. An integral torus is one whose relative area homomorphism is integer-valued, and we seek a maximal integral packing. By definition, this is a disjoint collection $\{L_{i}\}$ of integral Lagrangian tori with the following property: any other integral Lagrangian torus not in this collecti…

The Reversing Machine: Reconstructing Memory Assumptions
Mohammad Sina Karvandi, Soroush Meghdadizanjani, Sima Arasteh, Saleh Khalaj Monfared, Mohammad K. Fallah, Saeid Gorgin, Jeong-A Lee, Erik van der Kouwe
https://arxiv.org/abs/2405.00298

The Reversing Machine: Reconstructing Memory Assumptions
Existing anti-malware software and reverse engineering toolkits struggle with stealthy sub-OS rootkits due to limitations of run-time kernel-level monitoring. A malicious kernel-level driver can bypass OS-level anti-virus mechanisms easily. Although static analysis of such malware is possible, obfuscation and packing techniques complicate offline analysis. Moreover, current dynamic analyzers suffer from virtualization performance overhead and create detectable traces that allow modern malware t…

🔊 #NowPlaying on BBCRadio2's #MySoundtrackStories
Jon Brion:
🎵 Packing Up
#JonBrion
https://open.spotify.com/track/6SaFyrUUHTkkMkppyzU4IY

Bin Packing Optimization via Deep Reinforcement Learning
Baoying Wang, Huixu Dong
https://arxiv.org/abs/2403.12420 https://arxiv.org/…

Bin Packing Optimization via Deep Reinforcement Learning
The Bin Packing Problem (BPP) has attracted enthusiastic research interest recently, owing to widespread applications in logistics and warehousing environments. It is truly essential to optimize the bin packing to enable more objects to be packed into boxes. Object packing order and placement strategy are the two crucial optimization objectives of the BPP. However, existing optimization methods for BPP, such as the genetic algorithm (GA), emerge as the main issues in highly computational cost a…

Shadoks Approach to Knapsack Polygonal Packing
Guilherme D. da Fonseca, Yan Gerard
https://arxiv.org/abs/2403.20123 https://arxiv.org…

Shadoks Approach to Knapsack Polygonal Packing
We describe the heuristics used by the Shadoks team in the CG:SHOP 2024 Challenge. Each instance consists of a convex polygon called container and a multiset of items, where each item is a simple polygon and has an associated value. The goal is to pack some of the items inside the container using translations, in order to maximize the sum of their values. Our strategy consists of obtaining good initial solutions and improving them with local search. To obtain the initial solutions we used integ…

The Bottom-Left Algorithm for the Strip Packing Problem
Stefan Hougardy, Bart Zondervan
https://arxiv.org/abs/2402.16572 https://arxi…

The Bottom-Left Algorithm for the Strip Packing Problem
The bottom-left algorithm is a simple heuristic for the Strip Packing Problem. It places the rectangles in the given order at the lowest free position in the strip, using the left most position in case of ties. Despite its simplicity, the exact approximation ratio of the bottom-left algorithm remains unknown. We will improve the more-than-40-year-old value for the lower bound from $5/4$ to $4/3 - \varepsilon$. Additionally, we will show that this lower bound holds even in the special case of sq…

Tornados have interrupted @… Merch Bundle packing operations! 🌪️🫣

Robot Positioning Using Torus Packing for Multisets
Chung Shue Chen, Peter Keevash, Sean Kennedy, \'Elie de Panafieu, Adrian Vetta
https://arxiv.org/abs/2404.09981

Robot Positioning Using Torus Packing for Multisets
We consider the design of a positioning system where a robot determines its position from local observations. This is a well-studied problem of considerable practical importance and mathematical interest. The dominant paradigm derives from the classical theory of de Bruijn sequences, where the robot has access to a window within a larger code and can determine its position if these windows are distinct. We propose an alternative model in which the robot has more limited observational powers, wh…

Packing the largest trees in the tree packing conjecture
Barnab\'as Janzer, Richard Montgomery
https://arxiv.org/abs/2403.10515 https://

Packing the largest trees in the tree packing conjecture
The famous tree packing conjecture of Gyárfás from 1976 says that any sequence of trees $T_1,\ldots,T_n$ such that $|T_i|=i$ for each $i\in [n]$ packs into the complete $n$-vertex graph $K_n$. Packing even just the largest trees in such a sequence has proven difficult, with Bollobás drawing attention to this in 1995 by conjecturing that, for each $k$, if $n$ is sufficiently large then the largest $k$ trees in any such sequence can be packed into $K_n$. This has only been shown for …

Calculating the sequences behind a hexagonal lattice based equal circle packing in the Euclidian plane
Jure Voglar, Aljo\v{s}a Peperko
https://arxiv.org/abs/2403.10530

Calculating the sequences behind a hexagonal lattice based equal circle packing in the Euclidian plane
The article presents the mathematical sequences describing circle packing densities in four different geometric configurations involving a hexagonal lattice based equal circle packing in the Euclidian plane. The calculated sequences take form of either polynomials or rational functions. If the circle packing area is limited with a circle, the packing densities tend to decrease with increasing number of the packed circles and converge to values lower than π/(2\sqrt{3}). In cases with packing ar…

Bounds on the dimension of lineal extensions
Ryan E. G. Bushling, Jacob B. Fiedler
https://arxiv.org/abs/2404.16315 https://arxiv.org…

Bounds on the dimension of lineal extensions
Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq \mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's \textit{line segment extension conjecture} posits that the Hausdorff dimension of $F$ should equal that of $E$. Working in $\mathbb{R}^2$, we use effective methods to prove a strong packing dimension variant of this conjecture, from which the generalized Kakeya conjecture for packing dimension immediately follows. This…

IMPACT: Dallas’ D-line depth cratered by free agency https://www.dallascowboys.com/news/impact-dallas-d-line-depth-cratered-by-free-agency

IMPACT: Dallas’ D-line depth cratered by free agency
With Neville Gallimore heading to the Dolphins and Johnathan Hankins packing up to move to the Pacific Northwest, the Dallas Cowboys have free agency wounds to heal in 2024

Partially bonded crystals: a pathway to porosity and polymorphism
Carina Karner, Emanuela Bianchi
https://arxiv.org/abs/2405.01300 https://

Partially bonded crystals: a pathway to porosity and polymorphism
In recent years, experimental and theoretical investigations have shown that anisotropic colloids can self-organise into ordered porous monolayers, where the interplay of localised bonding sites, so called patches, with the particle's shape is responsible for driving the systems away from close-packing and towards porosity. Until now it has been assumed that patchy particles have to be fully bonded with their neighbouring particles for crystals to form, and that, if full bonding cannot be achie…

This https://arxiv.org/abs/2312.01253 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Merits of Faster-than-Nyquist Signaling in the Finite Blocklength Regime
We identify potential merits of faster-than-Nyquist (FTN) signaling in the finite blocklength (FBL) regime. A unique aspect of FTN signaling is that it can increase the blocklength by packing more data symbols within the same time and frequency to yield strictly higher number of independent signaling dimensions than that of Nyquist rate signaling. Using the finite-blocklength information theory, we provide tight bounds on the maximum channel coding rate (MCCR) of FTN signaling for any finite ti…

I don't know what it is, but lately I've been receiving a lot of online orders without *any* packing material. Just loose stuff in a box. Coincidentally, I've been receiving a lot of broken things, and having to do refunds.

Unpacking the Fuxnet Malware https://claroty.com/team82/research/unpacking-the-blackjack-groups-fuxnet-malware

🔊 #NowPlaying on BBCRadio2's #MySoundtrackStories
Jon Brion:
🎵 Packing Up
#JonBrion
https://open.spotify.com/track/6SaFyrUUHTkkMkppyzU4IY

This https://arxiv.org/abs/2004.07558 has been replaced.
link: https://scholar.google.com/scholar?q=a

Framework for $\exists \mathbb{R}$-Completeness of Two-Dimensional Packing Problems
The aim in packing problems is to decide if a given set of pieces can be placed inside a given container. A packing problem is defined by the types of pieces and containers to be handled, and the motions that are allowed to move the pieces. The pieces must be placed so that in the resulting placement, they are pairwise interior-disjoint. We establish a framework which enables us to show that for many combinations of allowed pieces, containers and motions, the resulting problem is $\exists \math…

Combinatorial p-th Calabi Flows for Total Geodesic Curvatures in hyperbolic background geometry
Guangming Hu, Ziping Lei, Yi Qi, Puchun Zhou
https://arxiv.org/abs/2403.05777

Combinatorial p-th Calabi Flows for Total Geodesic Curvatures in hyperbolic background geometry
In hyperbolic background geometry, we investigate a generalized circle packing (including circles, horocycles and hypercycles) with conical singularities on a surface with boundary, which has a total geodesic curvature on each generalized circle of this circle packing and a discrete Gaussian curvature on the center of each dual circle. The purpose of this paper is to find this type of circle packings with prescribed total geodesic curvatures on generalized circles and discrete Gaussian curvatur…

This https://arxiv.org/abs/2307.03349 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Point spread function approximation of high rank Hessians with locally supported non-negative integral kernels
We present an efficient matrix-free point spread function (PSF) method for approximating operators that have locally supported non-negative integral kernels. The method computes impulse responses at scattered points, and interpolates these impulse responses to approximate integral kernel entries. Impulse responses are computed by applying the operator to Dirac comb batches of point sources, which are chosen via an ellipsoid packing procedure. Evaluation of kernel entries allows us to construct …

Every subcubic graph is packing $(1,1,2,2,3)$-colorable
Xujun Liu, Xin Zhang, Yanting Zhang
https://arxiv.org/abs/2404.09337 https://…

Every subcubic graph is packing $(1,1,2,2,3)$-colorable
For a sequence $S=(s_1, \ldots, s_k)$ of non-decreasing integers, a packing $S$-coloring of a graph $G$ is a partition of its vertex set $V(G)$ into $V_1, \ldots, V_k$ such that for every pair of distinct vertices $u,v \in V_i$, where $1 \le i \le k$, the distance between $u$ and $v$ is at least $s_i+1$. The packing chromatic number, $χ_p(G)$, of a graph $G$ is the smallest integer $k$ such that $G$ has a packing $(1,2, \ldots, k)$-coloring. Gastineau and Togni asked an open question ``Is it t…

This https://arxiv.org/abs/2308.08064 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Freedman's link packings
Recently, Freedman [arXiv:2301.00295] introduced the idea of packing a maximal number of links into a bounded region subject to geometric constraints, and produced upper bounds on the packing number in some cases, while commenting that these bounds seemed far too large. We show that the smallest of these "extravagantly large" bounds is in fact sharp by constructing, for any link, a packing of exponentially many copies as a function of the available volume. We also produce improved and generaliz…

This https://arxiv.org/abs/2306.01794 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

DiffPack: A Torsional Diffusion Model for Autoregressive Protein Side-Chain Packing
Proteins play a critical role in carrying out biological functions, and their 3D structures are essential in determining their functions. Accurately predicting the conformation of protein side-chains given their backbones is important for applications in protein structure prediction, design and protein-protein interactions. Traditional methods are computationally intensive and have limited accuracy, while existing machine learning methods treat the problem as a regression task and overlook the …

Good Morning #Canada
Canadians are polite, but if we told you to jump off a cliff, then we have the perfect venue. Canada is home to the mountain with the tallest vertical drop, Mt. Thor, located in Auyuittuq National Park, on Baffin Island, Nunavut, Canada. If you fell from the top it would take some 26 seconds before you struck the mountain. Less for me since I'm packing a few extra kilos...
#CanadaIsAwesome #Thor #ParksCanada #Mountains
https://curiocity.com/mount-thor-auyuittuq-national-park/

This https://arxiv.org/abs/2307.16302 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Hadronic structure on the light-front VIII. Light scalar and vector mesons
We use the QCD instanton vacuum model to discuss the emergence of the light scalar and vector mesons on the light front. We take into account both the instanton and anti-instanton single and molecular interactions on the light quarks, in the form of non-local effective interactions. Although the molecular induced interactions are suppressed by a power of the packing fraction, they are still sufficient to bind the vector mesons, while keeping most of the scalar spectrum relatively unchanged. We …

This https://arxiv.org/abs/2304.10889 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On uniquely packable trees
An $i$-packing in a graph $G$ is a set of vertices that are pairwise distance more than $i$ apart. A \emph{packing colouring} of $G$ is a partition $X=\{X_{1},X_{2},\ldots,X_{k}\}$ of $V(G)$ such that each colour class $X_{i}$ is an $i$-packing. The minimum order $k$ of a packing colouring is called the packing chromatic number of $G$, denoted by $χ_ρ(G)$. In this paper we investigate the existence of trees $T$ for which there is only one packing colouring using $χ_ρ(T)$ colours. For the ca…

Asymptotic optimality of dynamic first-fit packing on the half-axis
Philip Ernst, Alexander Stolyar
https://arxiv.org/abs/2404.03797 https://

Asymptotic optimality of dynamic first-fit packing on the half-axis
We revisit a classical problem in dynamic storage allocation. Items arrive in a linear storage medium, modeled as a half-axis, at a Poisson rate $r$ and depart after an independent exponentially distributed unit mean service time. The arriving item sizes are assumed to be independent and identically distributed (i.i.d.) from a common distribution $H$. A widely employed algorithm for allocating the items is the ``first-fit'' discipline, namely, each arriving item is placed in the the left-most v…

Multi-Objective Optimization of Consumer Group Autoscaling in Message Broker Systems
Diogo Landau, Nishant Saurabh, Xavier Andrade, Jorge G Barbosa
https://arxiv.org/abs/2402.06085

Multi-Objective Optimization of Consumer Group Autoscaling in Message Broker Systems
Message brokers often mediate communication between data producers and consumers by adding variable-sized messages to ordered distributed queues. Our goal is to determine the number of consumers and consumer-partition assignments needed to ensure that the rate of data consumption keeps up with the rate of data production. We model the problem as a variable item size bin packing problem. As the rate of production varies, new consumer-partition assignments are computed, which may require rebalanc…

Convolution and Knapsack in Higher Dimensions
Kilian Grage, Klaus Jansen
https://arxiv.org/abs/2403.16117 https://arxiv.org/pdf/2403.…

Convolution and Knapsack in Higher Dimensions
In the Knapsack problem, one is given the task of packing a knapsack of a given size with items in order to gain a packing with a high profit value. In recent years, a connection to the $(\max,+)$-convolution problem has been established, where knapsack solutions can be combined by building the convolution of two sequences. This observation has been used to give conditional lower bounds but also parameterized algorithms. In this paper we want to carry these results into higher dimension. We c…

Generic dimensional and dynamical properties of invariant measures of full-shift systems over countable alphabets
Silas L. Carvalho, Alexander Condori
https://arxiv.org/abs/2403.17398

Generic dimensional and dynamical properties of invariant measures of full-shift systems over countable alphabets
In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a countable set. More specifically, we show that the set of invariant measures with infinite packing dimension equal to infinity is a dense $G_δ$ subset of $\mathcal{M}(T)$, the space of $T$-invariant measures endowed with the weak topology, where the alphabet $M$ is a countable Polish metric space. We …

Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares
Jack Stade, Mikkel Abrahamsen
https://arxiv.org/abs/2404.09835 https://

Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares
We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit squares into a polygon with holes is NP-hard~[Fowler, Paterson, Tanimoto, Inf. Process. Lett., 1981], but the version without holes was conjectured to be polynomial-time solvable more than two decades ago~[Baur and Fekete, Algorithmica, 2001]. Our reduction reli…

This https://arxiv.org/abs/2311.10007 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Dynamic Clustering of Active Rings
A collection of rings made of active Brownian particles (ABPs) for different packing fractions and activities is investigated using computer simulations. We show that active rings display an emergent dynamic clustering instead of the conventional motility-induced phase separation (MIPS) as in the case of collection of ABPs. Surprisingly, increasing packing fraction of rings exhibits a non-monotonicity in the dynamics due to the formation of a large number of small clusters. The conformational f…

An Improved Approximation Algorithm for Metric Triangle Packing
Jingyang Zhao, Mingyu Xiao
https://arxiv.org/abs/2402.08216 https://a…

An Improved Approximation Algorithm for Metric Triangle Packing
Given an edge-weighted metric complete graph with $n$ vertices, the maximum weight metric triangle packing problem is to find a set of $n/3$ vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several simple methods can lead to a 2/3-approximation ratio. However, this barrier is not easy to break. Chen et al. proposed a randomized approximation algorithm with an expected ratio of $(0.66768-\varepsilon)$ for any constant $\varepsilon>0$. In this paper, we i…

PackIt! Gamified Rectangle Packing
Thomas Garrison, Marijn J. H. Heule, Bernardo Subercaseaux
https://arxiv.org/abs/2403.12195 https://

PackIt! Gamified Rectangle Packing
We present and analyze PackIt!, a turn-based game consisting of packing rectangles on an $n \times n$ grid. PackIt! can be easily played on paper, either as a competitive two-player game or in \emph{solitaire} fashion. On the $t$-th turn, a rectangle of area $t$ or $t+1$ must be placed in the grid. In the two-player format of PackIt! whichever player places a rectangle last wins, whereas the goal in the solitaire variant is to perfectly pack the $n \times n$ grid. We analyze conditions for the …

Face embeddings of Archimedean solids
Tommy Murphy, David Weed
https://arxiv.org/abs/2404.15142 https://arxiv.org/pdf/2404.15142

Face embeddings of Archimedean solids
We characterize the Archimedean solids among the convex uniform polyhedra via face embeddings into a regular Tetrahedron. This result has been listed without proof in the literature. As an application, we obtain a lattice packing of $\mathbb{R}^3$ by the truncated Icosahedron whose packing density is notably close to the optimal value obtained in [1].

This https://arxiv.org/abs/2404.09835 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares
We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit squares into a polygon with holes is NP-hard~[Fowler, Paterson, Tanimoto, Inf. Process. Lett., 1981], but the version without holes was conjectured to be polynomial-time solvable more than two decades ago~[Baur and Fekete, Algorithmica, 2001]. Our reduction reli…

ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs
Shinwoo An, Eunjin Oh
https://arxiv.org/abs/2403.11426 https://arxiv.org/pd…

ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs
In this paper, we consider the Cycle Packing problem on unit disk graphs defined as follows. Given a unit disk graph G with n vertices and an integer k, the goal is to find a set of $k$ vertex-disjoint cycles of G if it exists. Our algorithm runs in time $2^{O(\sqrt k)}n^{O(1)}$. This improves the $2^{O(\sqrt k\log k)}n^{O(1)}$-time algorithm by Fomin et al. [SODA 2012, ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis.

This https://arxiv.org/abs/2401.04617 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On independent domination and packing numbers of subcubic graphs
In a recent paper, Cho and Kim proved that in subcubic graphs, the independent domination number is at most three times the packing number. They subsequently posed the question of characterizing subcubic graphs that achieve this bound. In this paper, we completely solve the question by proving that exactly four graphs meet this bound. Moreover, we arrive at an interesting result: if $G$ is a connected cubic graph of girth 5 and order $n$, then the packing number of $G$ is at least $\frac{n+1}{8…

This https://arxiv.org/abs/2306.01794 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

DiffPack: A Torsional Diffusion Model for Autoregressive Protein Side-Chain Packing
Proteins play a critical role in carrying out biological functions, and their 3D structures are essential in determining their functions. Accurately predicting the conformation of protein side-chains given their backbones is important for applications in protein structure prediction, design and protein-protein interactions. Traditional methods are computationally intensive and have limited accuracy, while existing machine learning methods treat the problem as a regression task and overlook the …

Fine-tuning the Microstructure and Photophysical Characteristics of Fluorescent Conjugated Copolymers Using Photoalignment and Liquid-crystalline Ordering
Yuping Shi, Katharina Landfester, Stephen M. Morris
https://arxiv.org/abs/2404.19435

Fine-tuning the Microstructure and Photophysical Characteristics of Fluorescent Conjugated Copolymers Using Photoalignment and Liquid-crystalline Ordering
Replicating the microstructure and near-unity excitation energy transfer efficiency in natural light-harvesting complexes (LHCs) remains a major challenge for synthetic energy-harvesting devices. Biological photosynthesis can spontaneously regulate the active ensembles of involved energy absorbing and funnelling chlorophyll-containing proteins in response to fluctuating sunlight. Here we utilize liquid crystalline (LC) ordering to fine-tune the polymer packing and photophysical properties in li…

This https://arxiv.org/abs/2404.09835 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares
We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit squares into a polygon with holes is NP-hard~[Fowler, Paterson, Tanimoto, Inf. Process. Lett., 1981], but the version without holes was conjectured to be polynomial-time solvable more than two decades ago~[Baur and Fekete, Algorithmica, 2001]. Our reduction reli…

This https://arxiv.org/abs/2401.04617 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On independent domination and packing numbers of subcubic graphs
In a recent paper, Cho and Kim proved that in subcubic graphs, the independent domination number is at most three times the packing number. They subsequently posed the question of characterizing subcubic graphs that achieve this bound. In this paper, we completely solve the question by proving that exactly four graphs meet this bound.

This https://arxiv.org/abs/2308.15515 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Scalable Algorithms for 2-Packing Sets on Arbitrary Graphs
A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We develop a new approach to solve this problem on arbitrary graphs using its close relation to the independent set problem. Thereby, our algorithm red2pack uses new data reduction rules specific to the 2-packing set problem as well as a graph transformation. Our e…

This https://arxiv.org/abs/2308.15515 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Scalable Algorithms for 2-Packing Sets on Arbitrary Graphs
A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We develop a new approach to solve this problem on arbitrary graphs using its close relation to the independent set problem. Thereby, our algorithm red2pack uses new data reduction rules specific to the 2-packing set problem as well as a graph transformation. Our e…

This https://arxiv.org/abs/2404.17106 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Edge-connectivity between (edge-)ends of infinite graphs
In infinite graph theory, the notion of ends, first introduced by Freudenthal and Jung for locally finite graphs, plays an important role when generalizing statements from finite graphs to infinite ones. Nash-Willian's Tree-Packing Theorem and MacLane's Planarity Criteria are examples of results that allow a topological approach, in which ends might be considered as endpoints of rays. In fact, there are extensive works in the literature showing that classical theorems of (vertex-)connectivity f…

This https://arxiv.org/abs/2402.08390 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Towards the Densest Polydisperse Disk Packing
Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are known to be protocol dependent. Here, we demonstrate that this variability at transition can be systematically traced to structural measures of packing, as well as to energy measures inside the jamming regime. Unlike …

This https://arxiv.org/abs/2112.03791 has been replaced.
link: https://scholar.google.com/scholar?q=a

Online Sorting and Translational Packing of Convex Polygons
We investigate several online packing problems in which convex polygons arrive one by one and have to be placed irrevocably into a container, while the aim is to minimize the used space. Among other variants, we consider strip packing and bin packing, where the container is the infinite horizontal strip $[0,\infty)\times [0,1]$ or a collection of $1 \times 1$ bins, respectively. We draw interesting connections to the following online sorting problem OnlineSorting$[γ,n]$: We receive a stream …

This https://arxiv.org/abs/2308.15515 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Scalable Algorithms for 2-Packing Sets on Arbitrary Graphs
A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We develop a new approach to solve this problem on arbitrary graphs using its close relation to the independent set problem. Thereby, our algorithm red2pack uses new data reduction rules specific to the 2-packing set problem as well as a graph transformation. Our e…

The Formal Proof of the Kepler Conjecture: a critical retrospective
Thomas Hales
https://arxiv.org/abs/2402.08032 https://arxiv.org/p…

The Formal Proof of the Kepler Conjecture: a critical retrospective
The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. In 1998, Sam Ferguson and I announced a computer-assisted proof of this conjecture. Long delays in the refereeing process sparked a project to give a formal proof of the Kepler conjecture, which was completed in a large collaborative effort in 2014. This article gives a critical reappraisal of that project.

Towards the Densest Polydisperse Disk Packing
Sangwoo Kim, Sascha Hilgenfeldt
https://arxiv.org/abs/2402.08390 https://arxiv.org/pdf/…

Towards the Densest Polydisperse Disk Packing
Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are known to be protocol dependent. Here, we demonstrate that this variability at transition can be systematically traced to structural measures of packing, as well as to energy measures inside the jamming regime. Unlike …

Solution-Hashing Search Based on Layout-Graph Transformation for Unequal Circle Packing
Jianrong Zhou, Jiyao He, Kun He
https://arxiv.org/abs/2403.06211 ht…

Solution-Hashing Search Based on Layout-Graph Transformation for Unequal Circle Packing
The problem of packing unequal circles into a circular container stands as a classic and challenging optimization problem in computational geometry. This study introduces a suite of innovative and efficient methods to tackle this problem. Firstly, we present a novel layout-graph transformation method that represents configurations as graphs, together with an inexact hash method facilitating fast comparison of configurations for isomorphism or similarity. Leveraging these advancements, we propos…

The Traveling Tournament Problem: Improved Algorithms Based on Cycle Packing
Jingyang Zhao, Mingyu Xiao, Chao Xu
https://arxiv.org/abs/2404.10955 https://<…

The Traveling Tournament Problem: Improved Algorithms Based on Cycle Packing
The Traveling Tournament Problem (TTP) is a well-known benchmark problem in the field of tournament timetabling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, minimizing the total distance traveled by all $n$ teams ($n$ is even). TTP-$k$ is the problem with one more constraint that each team can have at most $k$-consecutive home games or away games. In this paper, we investigate schedules for TTP-$k$ and analyze the…

Towards the Densest Polydisperse Disk Packing
Sangwoo Kim, Sascha Hilgenfeldt
https://arxiv.org/abs/2402.08390 https://arxiv.org/pdf/…

Towards the Densest Polydisperse Disk Packing
Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are known to be protocol dependent. Here, we demonstrate that this variability at transition can be systematically traced to structural measures of packing, as well as to energy measures inside the jamming regime. Unlike …

Controlling polymer translocation with crowded medium and polymer length asymmetry
Vrinda Garg, Rejoy Mathew, Riyan Ibrahim, Kulveer Singh, Surya K. Ghosh
https://arxiv.org/abs/2402.19187

Controlling polymer translocation with crowded medium and polymer length asymmetry
Polymer translocation in crowded environments is a ubiquitous phenomenon in biological systems. We studied polymer translocation through a pore in free, one-sided (asymmetric), and two-sided (symmetric) crowded environments. Extensive Langevin dynamics simulation is employed to model the dynamics of the flexible polymer and crowding particles. We studied how crowding size and packing fraction play a crucial role in the translocation process. After determining the standard scaling properties of …

This https://arxiv.org/abs/2308.15603 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$k$-tuple domination on Kneser graphs
This paper considers multiple domination on Kneser graphs. We focus on $k$-tuple dominating sets, $2$-packings and the associated graph parameters $k$-tuple domination number and $2$-packing number. In particular, we compute the $2$-packing number of Kneser graphs $K(3r-2,r)$ and in odd graphs we obtain minimum $k$-tuple dominating sets of $K(7,3)$ and $K(11,5)$ for every $k$. Besides, we determine the Kneser graphs $K(n,r)$ with $k$-tuple domination number exactly $k+r$ and find all the minimu…

Approximation Schemes for Geometric Knapsack for Packing Spheres and Fat Objects
Pritam Acharya, Sujoy Bhore, Aaryan Gupta, Arindam Khan, Bratin Mondal, Andreas Wiese
https://arxiv.org/abs/2404.03981

Approximation Schemes for Geometric Knapsack for Packing Spheres and Fat Objects
We study the geometric knapsack problem in which we are given a set of $d$-dimensional objects (each with associated profits) and the goal is to find the maximum profit subset that can be packed non-overlappingly into a given $d$-dimensional (unit hypercube) knapsack. Even if $d=2$ and all input objects are disks, this problem is known to be NP-hard [Demaine, Fekete, Lang, 2010]. In this paper, we give polynomial-time $(1+\varepsilon)$-approximation algorithms for the following types of input o…

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…

Combined thermal and particle shape effects on powder spreading in additive manufacturing via discrete element simulations
Sudeshna Roy, Hongyi Xiao, Vasileios Angelidakis, Thorsten P\"oschel
https://arxiv.org/abs/2402.15271

Combined thermal and particle shape effects on powder spreading in additive manufacturing via discrete element simulations
The thermal and mechanical behaviors of powders are important for various additive manufacturing technologies. For powder bed fusion, capturing the temperature profile and the packing structure of the powders prior to melting is challenging due to both the various pathways of heat transfer and the complicated properties of powder system. Furthermore, these two effects can be coupled due to the temperature dependence of particle properties. This study addresses this challenge using a discrete el…

How quickly can you pack short paths? Engineering a search-tree algorithm for disjoint s-t paths of bounded length
Michael Kiran Huber
https://arxiv.org/abs/2404.10469

How quickly can you pack short paths? Engineering a search-tree algorithm for disjoint s-t paths of bounded length
We study the Short Path Packing problem which asks, given a graph $G$, integers $k$ and $\ell$, and vertices $s$ and $t$, whether there exist $k$ pairwise internally vertex-disjoint $s$-$t$ paths of length at most $\ell$. The problem has been proven to be NP-hard and fixed-parameter tractable parameterized by $k$ and $\ell$. Most previous research on this problem has been theoretical with limited practical implemetations. We present an exact FPT-algorithm based on a search-tree approach in comb…

This https://arxiv.org/abs/2403.16961 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Biased ensembles of pulsating active matter
We discover unexpected connections between packing configurations and rare fluctuations in dense systems of active particles subject to pulsation of size. Using large deviation theory, we examine biased ensembles which select atypical realizations of the dynamics exhibiting high synchronization in particle size. We show that the order emerging at high bias can manifest as distinct dynamical states with either a finite or a vanishing size current. Remarkably, transitions between these states ari…

This https://arxiv.org/abs/1905.05655 has been replaced.
link: https://scholar.google.com/scholar?q=a

Online Computation with Untrusted Advice
We study a generalization of the advice complexity model of online computation in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust if the advice is adversarial, and efficient is the advice is foolproof. We focus on four well-studied online problems, namely ski rental, online bidding, bin packing and list update. For ski rental and online bidding, we show how to obtain al…

This https://arxiv.org/abs/2403.03926 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Order in disordered packings with and without permutation symmetry
A disordered solid, such as an athermal jammed packing of soft spheres, exists in a rugged potential-energy landscape in which there are a myriad of stable configurations that defy easy enumeration and characterization. Nevertheless, in three-dimensional monodisperse particle packings, we demonstrate an astonishing regularity in the distribution of basin volumes. The probability of landing randomly in a basin is proportional to its volume. Ordering the basins according to their probability, $P(…

This https://arxiv.org/abs/2209.03684 has been replaced.
link: https://scholar.google.com/scholar?q=a

Packing $K_r$s in bounded degree graphs
We study the problem of finding a maximum-cardinality set of $r$-cliques in an undirected graph of fixed maximum degree $Δ$, subject to the cliques in that set being either vertex-disjoint or edge-disjoint. It is known for $r=3$ that the vertex-disjoint (edge-disjoint) problem is solvable in linear time if $Δ=3$ ($Δ=4$) but APX-hard if $Δ\geq 4$ ($Δ\geq 5$). We generalise these results to an arbitrary but fixed $r \geq 3$, and provide a complete complexity classification for both the ver…

Modulus for bases of matroids
Huy Truong, Pietro Poggi-Corradini
https://arxiv.org/abs/2404.05650 https://arxiv.org/pdf/2404.05650

Modulus for bases of matroids
In this work, we explore the application of modulus in matroid theory, specifically, the modulus of the family of bases of matroids. This study not only recovers various concepts in matroid theory, including the strength, fractional arboricity, and principal partitions, but also offers new insights. In the process, we introduce the concept of a Beurling set. Additionally, our study revisits and provides an alternative approach to two of Edmonds's theorems related to the base packing and base co…