Tootfinder

Efficient computation of average subsystem Bures distance in transverse field Ising chain
Zhouhao Guo, M. A. Rajabpour, Jiaju Zhang
https://arxiv.org/abs/2508.09417 https://

Efficient computation of average subsystem Bures distance in transverse field Ising chain
The average subsystem trace distance has been proposed as an indicator of quantum many-body chaos and integrability. In integrable systems, evaluating the trace distance faces two challenges: the computational cost for large systems and ambiguities in defining and ordering eigenstates. In this paper, we calculate the average subsystem Bures distance in the spin-1/2 transverse-field Ising chain. We develop an efficient algorithm to evaluate the Bures distance between two Gaussian states, which a…

Gravitational wave distance estimation using intrinsic signal properties: dark sirens as distance indicators
Trisha V (Christ University, Bangalore), Rakesh V (Christ University, Bangalore), Arun Kenath (Christ University, Bangalore)
https://arxiv.org/abs/2508.09493

Gravitational wave distance estimation using intrinsic signal properties: dark sirens as distance indicators
Gravitational Waves (GWs) provide a powerful means for cosmological distance estimation, circumventing the systematic uncertainties associated with traditional electromagnetic (EM) indicators. This work presents a model for estimating distances to binary black hole (BBH) mergers using only GW data, independent of EM counterparts or galaxy catalogs. By utilizing the intrinsic properties of the GW signal, specifically the strain amplitude and merger frequency, our model offers a computationally e…

Dialing a phone number in the same area code as your own yet still getting charged long distance fees because the number was an exception & outside of your local zone.
Heck, long distance charges for domestic calling in it of itself is probably a foreign concept to Millennials & GenZ.

A Novel Branch-and-Prune Algorithmic Framework for the 3D Interval Discretizable Distance Geometry Problem: An Approach Based on Torsion Angles of Molecular Structures
Wagner A. A. da Rocha, Carlile Lavor, Leo Liberti, Leticia de Melo Costa, Leonardo D. Secchin, Therese E. Malliavin
https://arxiv.org/abs/2508.09143

A Novel Branch-and-Prune Algorithmic Framework for the 3D Interval Discretizable Distance Geometry Problem: An Approach Based on Torsion Angles of Molecular Structures
Distance Geometry plays a central role in determining protein structures from Nuclear Magnetic Resonance (NMR) data, a task known as the Molecular Distance Geometry Problem (MDGP). A subclass of this problem, the Discretizable Distance Geometry Problem (DDGP), allows a recursive solution via the combinatorial Branch-and-Prune (BP) algorithm by exploiting specific vertex orderings in protein backbones. To accommodate the inherent uncertainty in NMR data, the interval Branch-and-Prune (\textit{i}…

Computing the Fr\'echet Distance When Just One Curve is $c$-Packed: A Simple Almost-Tight Algorithm
Jacobus Conradi, Ivor van der Hoog, Thijs van der Horst, Tim Ophelders
https://arxiv.org/abs/2508.10537

Computing the Fréchet Distance When Just One Curve is $c$-Packed: A Simple Almost-Tight Algorithm
We study approximating the continuous Fréchet distance of two curves with complexity $n$ and $m$, under the assumption that only one of the two curves is $c$-packed. Driemel, Har{-}Peled and Wenk DCG'12 studied Fréchet distance approximations under the assumption that both curves are $c$-packed. In $\mathbb{R}^d$, they prove a $(1+\varepsilon)$-approximation in $\tilde{O}(d \, c\,\frac{n+m}{\varepsilon})$ time. Bringmann and Künnemann IJCGA'17 improved this to $\tilde{O}(c\,\frac{n + m }{\sq…

Mallows Model with Learned Distance Metrics: Sampling and Maximum Likelihood Estimation
Yeganeh Alimohammadi, Kiana Asgari
https://arxiv.org/abs/2507.08108

Mallows Model with Learned Distance Metrics: Sampling and Maximum Likelihood Estimation
\textit{Mallows model} is a widely-used probabilistic framework for learning from ranking data, with applications ranging from recommendation systems and voting to aligning language models with human preferences~\cite{chen2024mallows, kleinberg2021algorithmic, rafailov2024direct}. Under this model, observed rankings are noisy perturbations of a central ranking $σ$, with likelihood decaying exponentially in distance from $σ$, i.e, $P (π) \propto \exp\big(-β\cdot d(π, σ)\big),$ where $β> 0…

from my link log —
Distance-based ISA for efficient register renaming.
https://www.sigarch.org/distance-based-isa-for-efficient-register-management/
saved 2025-06-04

Distance-Based ISA for Efficient Register Management
CPU cores have become significantly wider over the past decade. Ten years ago, the highest-performance CPUs could decode only up to four instructions simultaneously and execute up to eight instruct…

The optimal Pad\'{e} polynomial for reconstruction of luminosity distance based on 10-fold cross-validation
Bo Yu, Wenhu Liu, XiaoFeng Yang, Tong-Jie zhang, Yanke Tang
https://arxiv.org/abs/2507.08695

The optimal Padé polynomial for reconstruction of luminosity distance based on 10-fold cross-validation
The cosmography known as the Padé polynomials has been widely used in the reconstruction of luminosity distance, and the orders of Padé polynomials influence the reconstructed result derived from Padé approximation. In this paper, we present a more general scheme of selecting optimal Padé polynomial for reconstruction of luminosity distance based on 10-fold cross-validation. Then the proposed scheme is applied to Pantheon+ dataset. The numerical results clearly indicate that the proposed pr…

I took this photo pretty close after the last that I posted. I just turned around to see what's behind me. I assumed just the bushes and the trail.
But obviously I was high enough that I already got some nice view into the distance.
If you're wondering why it's so flat in the distance: I am directly at the northern end of the #alps. To the south, there are

The distance spectrum of the line graph of the crown graph
S. Morteza Mirafzal
https://arxiv.org/abs/2508.07202 https://arxiv.org/pdf/2508.07202

The distance spectrum of the line graph of the crown graph
The distance eigenvalues of a connected graph $G$ are the eigenvalues of its distance matrix $D(G)$. A graph is called distance integral if all of its distance eigenvalues are integers. Let $n \geq 3$ be an integer. The crown graph $Cr(n)$ is a graph obtained from the complete bipartite graph $K_{n,n}$ by removing a perfect matching. Let $L(Cr(n))$ denote the line graph of the crown graph $Cr(n)$. Using the equitable partition method, the set of distinct distance eigenvalues of the graph $L(Cr(…

Carath\'eodory distance-preserving maps between bounded symmetric domains
Bas Lemmens, Cormac Walsh
https://arxiv.org/abs/2507.08639 https://

Carathéodory distance-preserving maps between bounded symmetric domains
We study the rigidity of maps between bounded symmetric domains that preserve the Carathéodory/Kobayashi distance. We show that such maps are only possible when the rank of the co-domain is at least as great as that of the domain. When the ranks are equal, and the domain is irreducible, we prove that the map is either holomorphic or antiholomorphic. In the holomorphic case, we show that the map is in fact a triple homomorphism, under the additional assumption that the origin is mapped to the o…

Generalized Bicycle Codes with Low Connectivity: Minimum Distance Bounds and Hook Errors
Reza Dastbasteh, Olatz Sanz Larrarte, Arun John Moncy, Pedro M. Crespo, Josu Etxezarreta Martinez, Ruben M. Otxoa
https://arxiv.org/abs/2508.09082

Generalized Bicycle Codes with Low Connectivity: Minimum Distance Bounds and Hook Errors
We present new upper and lower bounds on the minimum distance of certain generalized bicycle (GB) codes beyond the reach of techniques for classical codes capable of even capturing the true minimum distance for some cases. These bounds are then applied to illustrate the existence and analyze two highly degenerate GB code families with parameters $[[d^2+1,2,d]]$ for odd $d \geq 3$ and $[[d^2,2,d]]$ for even $d \geq 4$, both having the property that each check qubit is connected to exactly four d…

The role of dissipation distance on reconnection-driven multi-messenger signals from blazar jets
Stamatios Ilias Stathopoulos, Maria Petropoulou
https://arxiv.org/abs/2507.08680

The role of dissipation distance on reconnection-driven multi-messenger signals from blazar jets
Blazars are characterized by relativistic jets that are closely aligned with our line of sight. This results in relativistic beaming, making blazars among the most luminous extragalactic sources across the electromagnetic spectrum, from radio waves to gamma-rays and, potentially, in high-energy neutrinos. We present a comprehensive study of multi-messenger emission from blazar jets powered by magnetic reconnection occurring at varying distances from the supermassive black hole (SMBH). By genera…

#silentSunday #RockyMountainNationalPark
View from Many Parks Curve. October 2016

This Thursday the moving truck arrives and the following Tuesday we move into our new home. Therefore, it's time for a new alias, and this poll offers some possible alternatives. Please boost for maximum meaningless results.
Some background:
- we are moving to the Barrie area.
- officially, within the Town of Innisfil
- easy walking distance to Belle Aire Beach
- within Innisfil, we are in the community of Belle Ewart
Disclaimer - I am not legally bound by the results of this survey.
Barrie Beach Bum
Innocuous In Innisfil
Prince of Belle Aire
Ewartian Era

A near-linear time approximation scheme for $(k,\ell)$-median clustering under discrete Fr\'echet distance
Anne Driemel, Jan H\"ockendorff, Ioannis Psarros, Christian Sohler
https://arxiv.org/abs/2508.07008

A near-linear time approximation scheme for $(k,\ell)$-median clustering under discrete Fréchet distance
A time series of complexity $m$ is a sequence of $m$ real valued measurements. The discrete Fréchet distance $d_{dF}(x,y)$ is a distance measure between two time series $x$ and $y$ of possibly different complexity. Given a set of $n$ time series represented as $m$-dimensional vectors over the reals, the $(k,\ell)$-median problem under discrete Fréchet distance aims to find a set $C$ of $k$ time series of complexity $\ell$ such that $$\sum_{x\in P} \min_{c\in C} d_{dF}(x,c)$$ is minimized. In …

Big boomer energy
#lightning #wx

Learning The Minimum Action Distance
Lorenzo Steccanella, Joshua B. Evans, \"Ozg\"ur \c{S}im\c{s}ek, Anders Jonsson
https://arxiv.org/abs/2506.09276

Learning The Minimum Action Distance
This paper presents a state representation framework for Markov decision processes (MDPs) that can be learned solely from state trajectories, requiring neither reward signals nor the actions executed by the agent. We propose learning the minimum action distance (MAD), defined as the minimum number of actions required to transition between states, as a fundamental metric that captures the underlying structure of an environment. MAD naturally enables critical downstream tasks such as goal-conditi…

Weird Greco 🇬🇷
怪异希腊 🇬🇷
📷 Nikon FE
🎞️FOMAPAN Action 400
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

us_air_traffic: U.S. air traffic
Yearly snapshots of flights among all commercial airports in the United States from 1990 to today. Metadata include passengers, distance, carrier, airport located city, state, and month of the flight.
This network has 2278 nodes and 6390340 edges.
Tags: Transportation, Airport, Unweighted, Metadata, Temporal

Truthful Two-Obnoxious-Facility Location Games with Optional Preferences and Minimum Distance Constraint
Xiaojia Han, Wenjing Liu, Qizhi Fang
https://arxiv.org/abs/2508.08036 ht…

Truthful Two-Obnoxious-Facility Location Games with Optional Preferences and Minimum Distance Constraint
In this paper, we study a truthful two-obnoxious-facility location problem, in which each agent has a private location in [0, 1] and a public optional preference over two obnoxious facilities, and there is a minimum distance constraint d between the two facilities. Each agent wants to be as far away as possible from the facilities that affect her, and the utility of each agent is the total distance from her to these facilities. The goal is to decide how to place the facilities in [0, 1] so as t…

Perfect message authentication codes are robust to small deviations from uniform key distributions
Boris Ryabko
https://arxiv.org/abs/2508.09783 https://ar…

Perfect message authentication codes are robust to small deviations from uniform key distributions
We investigate the impact of (possible) deviations of the probability distribution of key values from a uniform distribution for the information-theoretic strong, or perfect, message authentication code. We found a simple expression for the decrease in security as a function of the statistical distance between the real key probability distribution and the uniform one. In a sense, a perfect message authentication code is robust to small deviations from a uniform key distribution.

Meta says Threads has 400M monthly active users, up from 350M MAUs in April; Similarweb says Threads had 15.3M DAUs on mobile in June, below X's 22.9M (Emily Price/Fast Company)
https://www.fastcompany.com/91384230/meta-threads-just-achieved-its-…

Threads just achieved its biggest milestone yet
Meta’s social upstart Threads just hit 400 million users. It's within striking distance of X on mobile engagement.

Null Distance and Temporal Functions
Andrea Nigri
https://arxiv.org/abs/2507.07158 https://arxiv.org/pdf/2507.07158

Null Distance and Temporal Functions
The notion of null distance was introduced by Sormani and Vega as part of a broader program to develop a theory of metric convergence adapted to Lorentzian geometry. Given a time function $τ$ on a spacetime $(M,g)$, the associated null distance $\hat{d}_τ$ is constructed from and closely related to the causal structure of $M$. While generally only a semi-metric, $\hat{d}_τ$ becomes a metric when $τ$ satisfies the local anti-Lipschitz condition. In this work, we focus on temporal functions…

Exploring Efficient Directional and Distance Cues for Regional Speech Separation
Yiheng Jiang, Haoxu Wang, Yafeng Chen, Gang Qiao, Biao Tian
https://arxiv.org/abs/2508.07563 htt…

Exploring Efficient Directional and Distance Cues for Regional Speech Separation
In this paper, we introduce a neural network-based method for regional speech separation using a microphone array. This approach leverages novel spatial cues to extract the sound source not only from specified direction but also within defined distance. Specifically, our method employs an improved delay-and-sum technique to obtain directional cues, substantially enhancing the signal from the target direction. We further enhance separation by incorporating the direct-to-reverberant ratio into th…

Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps
Wentao Zhang, Baoyong Zhang, Deming Yuan, Shengyuan Xu, Vincent K. N. Lau
https://arxiv.org/abs/2508.09411

Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps
This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively minimize the global loss function. To this end, under no-Euclidean distance metrics, we propose a distributed online stochastic mirror descent convex-concave optimization algorithm with time-varying predictive mappings. Taking dynamic saddle point regret as a p…

Office window open at work and I can hear Scotland the Brave in the distance. I do like it when all the pipe bands come to Glasgow and practice across the city ahead of the pipe band championship.

Efficient Uncertainty Propagation with Guarantees in Wasserstein Distance
Eduardo Figueiredo, Steven Adams, Peyman Mohajerin Esfahani, Luca Laurenti
https://arxiv.org/abs/2506.08689

Efficient Uncertainty Propagation with Guarantees in Wasserstein Distance
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input set of distributions close in the Wasserstein distance, we compute a set of distributions centered at a discrete distribution that is guaranteed to contain the pushforward of any distribution in the input set. Our approach is based on approximating a nominal di…

Spectroscopic and femtoscopic insights into vector-baryon interactions in the strangeness $-1$ sector
P. Encarnaci\'on, M. Albaladejo, A. Feijoo, J. Nieves
https://arxiv.org/abs/2507.08466

Spectroscopic and femtoscopic insights into vector-baryon interactions in the strangeness $-1$ sector
We revisit the strangeness $-1$ sector of the interaction between vector mesons of the $ρ-$nonet and $1/2^+$ ground state baryons ($VB$), within the unitary coupled-channel hidden gauge formalism. We adopt a renormalization scheme that induces a reasonable short-distance behavior of the two-hadron wave functions, which is the major limitation of femtoscopy techniques at this time. We perform an exhaustive spectroscopy study, implementing different improvements and considerations, and find comp…

Meta says Threads has 400M monthly active users, up from 350M MAUs in April (Emily Price/Fast Company)
https://www.fastcompany.com/91384230/meta-threads-just-achieved-its-biggest-milestone-yet

Threads just achieved its biggest milestone yet
Meta’s social upstart Threads just hit 400 million users. It's within striking distance of X on mobile engagement.

Saturday evening picnic at the Telluride Neuromorphic Engineering Workshop. (The local airport is below us, off in the distance, at 9,000 ft / 2.7 km above sea level. ) #telluride #neuromorph #NeuromorphicEngineering

A Structural Analysis of Population Graphs
Kimberly Ayers, Maxwell Kooiker
https://arxiv.org/abs/2508.10058 https://arxiv.org/pdf/2508.10058

A Structural Analysis of Population Graphs
The format of graphing algorithms for genomic data has been a debate in recent biotechnology. In this paper, we discuss the construction of population graphs using said genomic data. We first examine the GENPOFAD distance measurement, developed by Joly et. al., and prove that this constitutes a metric function. We develop an algorithm to construct graphs to visualize the relationships between individuals in a population. We then provide a statistical analysis of these simulated population graph…

Intermediate Interaction Strategies for Collective Behavior
Y. Kikuchi, M. Iwamoto
https://arxiv.org/abs/2507.09457 https://arxiv.org…

Intermediate Interaction Strategies for Collective Behavior
From bird flocks and fish schools to migrating cell sheets, collective motion is a ubiquitous biological phenomenon that inspires quantitative modeling through self-propelled particle (SPP) frameworks. Conventional SPP models prescribe either distance-based (metric) or rank-based (topological) interactions; however, empirical studies indicate that real groups may blend both types of interaction. Motivated by this graded perception, we introduce a new three-dimensional SPP model in which metric …

#TodayILearned there are only 3½ fingers in a hand
(1 finger = ⅞ inch, 1 hand = 4 inches)
https://en.wikipedia.org/wiki/English_units#Length

Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
J. Haydel Collins, Kangan Li, Alexei Lozinski, Guglielmo Scovazzi
https://arxiv.org/abs/2508.09613

Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
We propose and mathematically analyze a new Shifted Boundary Method for the treatment of Dirichlet and Neumann boundary conditions, with provable optimal accuracy in the $L^2$- and $H^1$-norms of the error. The proposed method is built on three stages. First, the distance map between the SBM surrogate boundary and the true boundary is used to construct an approximation to the geometry of the gap between the two. Then, the representations of the numerical solution and test functions are extended…

The Perturbation Theory Approach to Stability in the Scattered Disk
Matthew Belyakov, Konstantin Batygin
https://arxiv.org/abs/2508.10119 https://arxiv.org…

The Perturbation Theory Approach to Stability in the Scattered Disk
Scattered disk objects (SDOs) are distant minor bodies that orbit the sun on highly eccentric orbits, frequently with perhelia near Neptune's orbit. Gravitational perturbations due to Neptune frequently lead to chaotic dynamics, with the degree of chaotic diffusion set by an object's perihelion distance. Batygin et al. (2021) developed a perturbative approach for scattered disk dynamics, finding that, to leading order in semi-major axis ratio, an infinite series of $2:j$ resonances drives the d…

Long post, game design
Crungle is a game designed to be a simple test of general reasoning skills that's difficult to play by rote memory, since there are many possible rule sets, but it should be easy to play if one can understand and extrapolate from rules. The game is not necessarily fair, with the first player often having an advantage or a forced win. The game is entirely deterministic, although a variant determines the rule set randomly.
This is version 0.1, and has not yet been tested at all.
Crungle is a competitive game for two players, each of whom controls a single piece on a 3x3 grid. The cells of the grid are numbered from 1 to 9, starting at the top left and proceeding across each row and then down to the next row, so the top three cells are 1, 2, and 3 from left to right, then the next three are 4, 5, and 6 and the final row is cells 7, 8, and 9.
The two players decide who shall play as purple and who shall play as orange. Purple goes first, starting the rules phase by picking one goal rule from the table of goal rules. Next, orange picks a goal rule. These two goal rules determine the two winning conditions. Then each player, starting with orange, alternate picking a movement rule until four movement rules have been selected. During this process, at most one indirect movement rule may be selected. Finally, purple picks a starting location for orange (1-9), with 5 (the center) not allowed. Then orange picks the starting location for purple, which may not be adjacent to orange's starting position.
Alternatively, the goal rules, movement rules, and starting positions may be determined randomly, or a pre-determined ruleset may be selected.
If the ruleset makes it impossible to win, the players should agree to a draw. Either player could instead "bet" their opponent. If the opponent agrees to the bet, the opponent must demonstrate a series of moves by both players that would result in a win for either player. If they can do this, they win, but if they submit an invalid demonstration or cannot submit a demonstration, the player who "bet" wins.
Now that starting positions, movement rules, and goals have been decided, the play phase proceeds with each player taking a turn, starting with purple, until one player wins by satisfying one of the two goals, or until the players agree to a draw. Note that it's possible for both players to occupy the same space.
During each player's turn, that player identifies one of the four movement rules to use and names the square they move to using that rule, then they move their piece into that square and their turn ends. Neither player may use the same movement rule twice in a row (but it's okay to use the same rule your opponent just did unless another rule disallows that). If the movement rule a player picks moves their opponent's piece, they need to state where their opponent's piece ends up. Pieces that would move off the board instead stay in place; it's okay to select a rule that causes your piece to stay in place because of this rule. However, if a rule says "pick a square" or "move to a square" with some additional criteria, but there are no squares that meet those criteria, then that rule may not be used, and a player who picks that rule must pick a different one instead.
Any player who incorrectly states a destination for either their piece or their opponent's piece, picks an invalid square, or chooses an invalid rule has made a violation, as long as their opponent objects before selecting their next move. A player who makes at least three violations immediately forfeits and their opponent wins by default. However, if a player violates a rule but their opponent does not object before picking their next move, the stated destination(s) of the invalid move still stand, and the violation does not count. If a player objects to a valid move, their objection is ignored, and if they do this at least three times, they forfeit and their opponent wins by default.
Goal rules (each player picks one; either player can win using either chosen rule):
End your turn in the same space as your opponent three turns in a row.
End at least one turn in each of the 9 cells.
End five consecutive turns in the three cells in any single row, ending at least one turn on each of the three.
End five consecutive turns in the three cells in any single column, ending at least one turn on each of the three.
Within the span of 8 consecutive turns, end at least one turn in each of cells 1, 3, 7, and 9 (the four corners of the grid).
Within the span of 8 consecutive turns at least one turn in each of cells 2, 4, 6, and 8 (the central cells on each side).
Within the span of 8 consecutive turns, end at least one turn in the cell directly above your opponent, and end at least one turn in the cell directly below your opponent (in either order).
Within the span of 8 consecutive turns at least one turn in the cell directly to the left of your opponent, and end at least one turn in the cell directly to the right of your opponent (in either order).
End 12 turns in a row without ending any of them in cell 5.
End 8 turns in a row in 8 different cells.
Movement rules (each player picks two; either player may move using any of the four):
Move to any cell on the board that's diagonally adjacent to your current position.
Move to any cell on the board that's orthogonally adjacent to your current position.
Move up one cell. Also move your opponent up one cell.
Move down one cell. Also move your opponent down one cell.
Move left one cell. Also move your opponent left one cell.
Move right one cell. Also move your opponent right one cell.
Move up one cell. Move your opponent down one cell.
Move down one cell. Move your opponent up one cell.
Move left one cell. Move your opponent right one cell.
Move right one cell. Move your opponent left one cell.
Move any pieces that aren't in square 5 clockwise around the edge of the board 1 step (for example, from 1 to 2 or 3 to 6 or 9 to 8).
Move any pieces that aren't in square 5 counter-clockwise around the edge of the board 1 step (for example, from 1 to 4 or 6 to 3 or 7 to 8).
Move to any square reachable from your current position by a knight's move in chess (in other words, a square that's in an adjacent column and two rows up or down, or that's in an adjacent row and two columns left or right).
Stay in the same place.
Swap places with your opponent's piece.
Move back to the position that you started at on your previous turn.
If you are on an odd-numbered square, move to any other odd-numbered square. Otherwise, move to any even-numbered square.
Move to any square in the same column as your current position.
Move to any square in the same row as your current position.
Move to any square in the same column as your opponent's position.
Move to any square in the same row as your opponent's position.
Pick a square that's neither in the same row as your piece nor in the same row as your opponent's piece. Move to that square.
Pick a square that's neither in the same column as your piece nor in the same column as your opponent's piece. Move to that square.
Move to one of the squares orthogonally adjacent to your opponent's piece.
Move to one of the squares diagonally adjacent to your opponent's piece.
Move to the square opposite your current position across the middle square, or stay in place if you're in the middle square.
Pick any square that's closer to your opponent's piece than the square you're in now, measured using straight-line distance between square centers (this includes the square your opponent is in). Move to that square.
Pick any square that's further from your opponent's piece than the square you're in now, measured using straight-line distance between square centers. Move to that square.
If you are on a corner square (1, 3, 7, or 9) move to any other corner square. Otherwise, move to square 5.
If you are on an edge square (2, 4, 6, or 8) move to any other edge square. Otherwise, move to square 5.
Indirect movement rules (may be chosen instead of a direct movement rule; at most one per game):
Move using one of the other three movement rules selected in your game, and in addition, your opponent may not use that rule on their next turn (nor may they select it via an indirect rule like this one).
Select two of the other three movement rules, declare them, and then move as if you had used one and then the other, applying any additional effects of both rules in order.
Move using one of the other three movement rules selected in your game, but if the move would cause your piece to move off the board, instead of staying in place move to square 5 (in the middle).
Pick one of the other three movement rules selected in your game and apply it, but move your opponent's piece instead of your own piece. If that movement rule says to move "your opponent's piece," instead apply that movement to your own piece. References to "your position" and "your opponent's position" are swapped when applying the chosen rule, as are references to "your turn" and "your opponent's turn" and do on.
#Game #GameDesign

Multichannel Hybrid Quantum Cryptography for Submarine Optical Communications
Jes\'us Li\~nares, Xes\'us Prieto-Blanco, Alexandre V\'azquez-Mart\'inez, Eduardo F. Mateo
https://arxiv.org/abs/2508.10521

Multichannel Hybrid Quantum Cryptography for Submarine Optical Communications
We present a multichannel hybrid quantum cryptography approach intended for submarine quantum optical communications between Alice and Bob separated a distance beyond the current QKD possibilities, each located on a coastline. It is based on the difficult of a simultaneous access to $M$ optical submarine channels. The optical lines from the coastline and ideally to the end of the continental platform are governed by the quantum properties of the light under an autocompensating high-dimensional …

Canadians, please confirm this is valid
EDIT: Added in better alt text

A Galactic Interloper: A Study of the Cam OB1 Association's Clusters and its Visitor from the Perseus Arm
Joseph Mullen, Amanda Mast, Marina Kounkel, Keivan Stassun, Alexandre Roman-Lopes, Jonathan Tan
https://arxiv.org/abs/2508.09393

A Galactic Interloper: A Study of the Cam OB1 Association's Clusters and its Visitor from the Perseus Arm
Within the molecular clouds of the Camelopardis OB1 association exists a region previously noted as one subgroup. However, bulk clustering from Gaia astrometry has recently shown three distinctive kinematically coherent groups, all found in a similar location in the sky ($137 \lessapprox l\lessapprox145$ and $-2\lessapprox b \lessapprox5$) and at a similar distance ($\sim$1kpc). In this work, we derive from first principles the three proposed clusters in this region, refine the membership list …

Jitter Sensing and Control for Multi-Plane Phase Retrieval
Caleb G. Abbott, Justin R. Crepp, Brian Sands
https://arxiv.org/abs/2508.09256 https://arxiv.org…

Jitter Sensing and Control for Multi-Plane Phase Retrieval
The family of multi-plane phase retrieval sensors, such as the curvature and nonlinear curvature wavefront sensors (WFS), contain tip/tilt information embedded in their signals. We have built a nonlinear curvature WFS to study different wavefront reconstruction methods and test the ability to extract tip/tilt information. Using reliable and fast centroiding algorithms, combined with knowledge of the measured z-distance to each measurement plane, we demonstrate that image jitter may be sensed an…

Optimal transport, determinantal point processes and the Bergman kernel
William Driot, Laurent Decreusefond
https://arxiv.org/abs/2507.08204 https://

Optimal transport, determinantal point processes and the Bergman kernel
We study the Bergman determinantal point process from a theoretical point of view motivated by its simulation. We construct restricted and restricted-truncated variants of the Bergman kernel and show optimal transport inequalities involving the Kantorovitch-Rubinstein Wasserstein distance to show to what extent it is fair to truncate the restriction of this point process to a compact ball of radius $1 - \varepsilon $. We also investigate the deviation of the number of points of the restricted B…

Characterizing Topological Phase Transition in Non-Hermitian Systems
ZhaoXiang Fang, Yongxu Fu, Guang-Can Guo, Long Xiong
https://arxiv.org/abs/2508.08316 https://

Characterizing Topological Phase Transition in Non-Hermitian Systems
We propose and present a concept of Topological Distance (TD), obtained from the integration of trace distance over the generalized Brillouin zone, in order to characterize the topological transitions of non-Hermitian systems. Specifically, such a quantity is used to measure the overall dissimilarity between eigen wavefunctions upon traversing all possible matter states, and confirms the phase boundaries through observing the divergences of both TD and its partial derivatives; we clarify its or…

Too little sleep, too hot, stagnant air with no breeze, and definitely rudely humid. When it became clear what a struggle this would be, I opted to run for HR zones instead. This included several walking breaks to bring my HR back down. My fitness needs the work.
#Running

Speciation by local adaptation and isolation by distance in extended environments
Lara D. Hissa, Flavia M. D. Marquitti, Marcus A. M. de Aguiar
https://arxiv.org/abs/2508.06719 …

Speciation by local adaptation and isolation by distance in extended environments
Speciation is often associated with geographical barriers that limit gene flow. However, species can also emerge in continuous homogeneous environments through isolation by distance. When the environment is not homogeneous, natural selection contributes to differentiation by local adaptation and tends to facilitate speciation. To explore how isolation by distance and adaptation combine to determine species diversity, we implemented a model regulated by these two components. The first is impleme…

Effects of multiple cycles on the resistance distance of a strand in a homogeneous polymer network
Erica Uehara, Tetsuo Deguchi
https://arxiv.org/abs/2507.06476

Effects of multiple cycles on the resistance distance of a strand in a homogeneous polymer network
We show that the resistance distance between a pair of adjacent vertices in a phantom network generated randomly by a Monte-Carlo method depends on the existence of short cycles around it. Here we assume that phantom networks have no fixed points but their centers of mass are located at a point. The resistance distance corresponds to the mean-square deviation of the end-to-end vector along the strand connecting the adjacent vertices. We generate random networks with fixed valency $f$ but differ…

Approximating High-Dimensional Earth Mover's Distance as Fast as Closest Pair
Lorenzo Beretta, Vincent Cohen-Addad, Rajesh Jayaram, Erik Waingarten
https://arxiv.org/abs/2508.06774

Approximating High-Dimensional Earth Mover's Distance as Fast as Closest Pair
We give a reduction from $(1+\varepsilon)$-approximate Earth Mover's Distance (EMD) to $(1+\varepsilon)$-approximate Closest Pair (CP). As a consequence, we improve the fastest known approximation algorithm for high-dimensional EMD. Here, given $p\in [1, 2]$ and two sets of $n$ points $X,Y \subseteq (\mathbb R^d,\ell_p)$, their EMD is the minimum cost of a perfect matching between $X$ and $Y$, where the cost of matching two vectors is their $\ell_p$ distance. Further, CP is the basic problem of…

Sorry to miss it in person and that I cannot stay for the panels on: teacher, gender, inclusion, decolonisation, and future action. Lovely to see and hear so many wonderful colleagues even from a distance.
My fun memory was the cartoon by the talented (then PhD student) Kalifa Damani during my talk on silent exclusion at the REAL Centre in January 2020 before the world shut, and many fun moments with Pauline Rose over the years.
Congratulations! The achievements are remarkable.

I replaced my ancient phone with a Fairphone 5 and decided to do the ultimate comparison test: how accurate is the GPS when I'm riding my bike? Answer: on a map the tracks are v close but the F5 is consistently better, fewer wobbles. Errors in location mean errors in distance mean errors in speed: this image shows the new speed readings are much more steady. (NB: all speeds above 25 km/h are downhill.)

The M\"obius-Kantor graph is a faithful unit-distance graph
Nino Ba\v{s}i\'c, G\'abor G\'evay, Toma\v{z} Pisanski
https://arxiv.org/abs/2508.06618 https://

The Möbius-Kantor graph is a faithful unit-distance graph
In this paper, it has been shown that the generalized Petersen graph $\mathrm {GP}(8,3)$, also known as the Möbius-Kantor graph, admits a faithful unit-distance representation in the plane.

In the Air - Outside of the Window II ✈️ ☁️
在空中 - 窗外 II ✈️ ☁️
📷 Nikon FE
🎞️FOMAPAN Action 400
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

Yiding Cao Geld mit PayPal.Me senden
Folgen Sie dem Link PayPal.Me/dingsterdingster und geben Sie den Betrag ein. Es ist bequem und sicher. Sie haben noch kein PayPal-Konto? Kein Problem.

Osculating Geometry and Higher-Order Distance Loci
Sandra Di Rocco, Kemal Rose, Luca Sodomaco
https://arxiv.org/abs/2507.02823 https://

Osculating Geometry and Higher-Order Distance Loci
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order tangency. We focus on the data locus of points possessing at least one critical point of the distance function that is normal to a higher-order osculating space. We propose a novel definition of higher-order distance degree as an intersection-theoretic invariant invo…

More reasonable distance today, better weather, meh AQI. Hoping to get in a few more runs in this week. Dropping some medications, so far it has helped a bit in some areas of #longfcovid recovery.
#running

Simulated non-Markovian Noise Resilience of Silicon-Based Spin Qubits with Surface Code Error Correction
Oscar Gravier, Thomas Ayral, Beno\^it Vermersch, Tristan Meunier, Valentin Savin
https://arxiv.org/abs/2507.08713

Simulated non-Markovian Noise Resilience of Silicon-Based Spin Qubits with Surface Code Error Correction
We investigate the resilience of silicon-based spin qubits against non-Markovian noise within the framework of quantum error correction. We consider a realistic non-Markovian noise model that affects both the Larmor frequency and exchange energy of qubits, allowing accurate simulations of noisy quantum circuits. We employ numerical emulation to assess the performance of the distance-3 rotated surface code and its XZZX variant, using a logical qubit coherence time metric based on Ramsey-like exp…

On data-driven robust distortion risk measures for non-negative risks with partial information
Xiangyu Han, Yijun Hu, Ran Wang, Linxiao Wei
https://arxiv.org/abs/2508.10682 http…

On data-driven robust distortion risk measures for non-negative risks with partial information
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is characterized solely by a ball determined by general Wasserstein distance centered at certain empirical distribution function, and then further consider additional constraints of known first moment and any other higher moment of the underlying loss distributio…

Hermitian Self-dual Twisted Generalized Reed-Solomon Codes
Chun'e Zhao, Yuxin Han, Wenping Ma, Tongjiang Yan, Yuhua Sun
https://arxiv.org/abs/2508.09687 https://

Hermitian Self-dual Twisted Generalized Reed-Solomon Codes
Self-dual maximum distance separable (MDS) codes over finite fields are linear codes with significant combinatorial and cryptographic applications. Twisted generalized Reed-Solomon (TGRS) codes can be both MDS and self-dual. In this paper, we study a general class of TGRS codes (A-TGRS), which encompasses all previously known special cases. First, we establish a sufficient and necessary condition for an A-TGRS code to be Hermitian self-dual. Furthermore, we present four constructions of self-du…

Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks
Mary Chriselda Antony Oliver, Emmanuel Hartman, Tom Needham
https://arxiv.org/abs/2508.10888

Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of point clouds or networks. To overcome certain limitations, such as the restriction to comparisons of measures of equal mass and sensitivity to outliers, several unbalanced or partial transport relaxations of the GW distance have been introduced in the recent …

On the signature of squared distance matrices of metric measure spaces
Alexey Kroshnin, Tianyu Ma, Eugene Stepanov
https://arxiv.org/abs/2508.07340 https://

On the signature of squared distance matrices of metric measure spaces
We consider the numbers of positive and negative eigenvalues of matrices of squared distances between randomly sampled i.i.d. points in a given metric measure space. These numbers and their limits, as the number of points grows, in fact contain some important information about the whole space. In particular, by knowing them, we can determine whether this space can be isometrically embedded in the Hilbert space. We show that the limits of these numbers exist almost surely, are nonrandom and the …

Just a quick snap from today's bike and hike.
I'm a bit done now. Photos and video will come later.
#photography #naturephotography #landscapephotography

Cat with giant artichoke plant in the background #Caturday #EveryDayIsCaturday

Interior of distance trees over thin Cantor sets
Yeonwook Jung, Krystal Taylor
https://arxiv.org/abs/2507.07385 https://arxiv.org/pdf…

Interior of distance trees over thin Cantor sets
It is known that if a compact set $E$ in $\mathbb{R}^d$ has Hausdorff dimension greater than $(d+1)/2$, then its $n$-chain distance set $$Δ^n(E) = \left\{\left(\left|x^1-x^2\right|,\cdots, \left|x^{n}- x^{n+1}\right|\right)\in \mathbb{R}^n: x^i \in E, x^i\neq x^j \text{ for } i\neq j \right\}$$ has nonempty interior for any $n\in \mathbb{N}$. In this paper, we prove that for every Cantor set $K\subset \mathbb{R}^d$ and for every $n\in\mathbb{N}$, there exists $\widetilde{K}…

Testing the Cosmic Distance Duality Relation with Neural Kernel Gaussian Process Regression
Xin Luo, Nan Liang
https://arxiv.org/abs/2508.07040 https://arx…

Testing the Cosmic Distance Duality Relation with Neural Kernel Gaussian Process Regression
In this work, we test the cosmic distance duality relation (CDDR) by combining Pantheon+ Type Ia supernova (SNe Ia) data and DESI DR2 baryon acoustic oscillation (BAO) measurements. To resolve the redshift mismatch between the two datasets, we develop a new method called Neural Kernel Gaussian Process Regression (NKGPR), which uses two neural networks to simultaneously learn the mean and kernel functions of a Gaussian process. This approach improves upon traditional Gaussian process regression …

Power Diagram Enhanced Adaptive Isosurface Extraction from Signed Distance Fields
Pengfei Wang, Ziyang Zhang, Wensong Wang, Shuangmin Chen, Lin Lu, Shiqing Xin, Changhe Tu
https://arxiv.org/abs/2506.09579

Power Diagram Enhanced Adaptive Isosurface Extraction from Signed Distance Fields
Extracting high-fidelity mesh surfaces from Signed Distance Fields has become a fundamental operation in geometry processing. Despite significant progress over the past decades, key challenges remain namely, how to automatically capture the intricate geometric and topological structures encoded in the zero level set of SDFs. In this paper, we present a novel isosurface extraction algorithm that introduces two key innovations: 1. An incrementally constructed power diagram through the addition of…

MicroTrace: A Lightweight R Tool for SNP-Based Pathogen Clustering in Outbreak Detection
Kaitao Lai
https://arxiv.org/abs/2507.08060 https://

MicroTrace: A Lightweight R Tool for SNP-Based Pathogen Clustering in Outbreak Detection
MicroTrace is an open-source R tool that performs SNP-based hierarchical clustering to detect potential transmission clusters from pathogen whole-genome sequencing (WGS) data. Designed for epidemiologists, microbiologists, and genomic surveillance teams, it processes SNP distance matrices and outputs dendrograms and cluster tables with optional metadata integration. MicroTrace enables reproducible outbreak detection workflows with minimal setup.

Neural Parameter-varying Data-enabled Predictive Control of Cold Atmospheric Pressure Plasma Jets
Pegah GhafGhanbari, Mircea Lazar, Javad Mohammadpour Velni
https://arxiv.org/abs/2507.08259

Neural Parameter-varying Data-enabled Predictive Control of Cold Atmospheric Pressure Plasma Jets
Cold Atmospheric Pressure Plasma Jets (APPJs) show significant potential for biomedical applications, but their inherent complexity, characterized by nonlinear dynamics and strong sensitivity to operating conditions like tip-to-surface distance, presents considerable challenges for achieving robust and reliable real-time control. To address these issues, this paper presents the Neural Parameter-Varying Data-enabled Predictive Control (NPV-DeePC) framework. By integrating hyper neural networks (…

us_air_traffic: U.S. air traffic
Yearly snapshots of flights among all commercial airports in the United States from 1990 to today. Metadata include passengers, distance, carrier, airport located city, state, and month of the flight.
This network has 2278 nodes and 6390340 edges.
Tags: Transportation, Airport, Unweighted, Metadata, Temporal

Comparing probability distributions: application to quantum states of light
Soumyabrata Paul, V. Balakrishnan, S. Ramanan, S. Lakshmibala
https://arxiv.org/abs/2506.10760

Comparing probability distributions: application to quantum states of light
Probability distributions play a central role in quantum mechanics, and even more so in quantum optics with its rich diversity of theoretically conceivable and experimentally accessible quantum states of light. Quantifiers that compare two different states or density matrices in terms of `distances' between the respective probability distributions include the Kullback-Leibler divergence $D_{\rm KL}$, the Bhattacharyya distance $D_{\rm B}$, and the $p$-Wasserstein distance $W_{p}$. We present a …

Local Distance Query with Differential Privacy
Weihong Sheng, Jiajun Chen, Bin Cai, Chunqiang Hu, Meng Han, Jiguo Yu
https://arxiv.org/abs/2508.05518 https://

Local Distance Query with Differential Privacy
Differential Privacy (DP) is commonly employed to safeguard graph analysis or publishing. Distance, a critical factor in graph analysis, is typically handled using curator DP, where a trusted curator holds the complete neighbor lists of all vertices and answers queries privately. However, in many real-world scenarios, such a curator may not be present, posing a significant challenge for implementing differentially private distance queries under Local Differential Privacy (LDP). This paper propo…

Some pictures of last night’s sunset: through glass

Equality in the linear algebra bound
G\'abor Heged\"us, Lajos R\'onyai
https://arxiv.org/abs/2508.09698 https://arxiv.org/pdf/2508.09698

Equality in the linear algebra bound
We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information about the extremal configuration. We obtain results on set families satisfying conditions on pairwise intersections, or Hamming distances. Also, we have an application to 2-distance sets in Euclidean spaces.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints
Ashfaq Iftakher, Rahul Golder, M. M. Faruque Hasan
https://arxiv.org/abs/2507.08124 https://arxiv.org/pdf/2507.08124 https://arxiv.org/html/2507.08124
arXiv:2507.08124v1 Announce Type: new
Abstract: Traditional physics-informed neural networks (PINNs) do not guarantee strict constraint satisfaction. This is problematic in engineering systems where minor violations of governing laws can significantly degrade the reliability and consistency of model predictions. In this work, we develop KKT-Hardnet, a PINN architecture that enforces both linear and nonlinear equality and inequality constraints up to machine precision. It leverages a projection onto the feasible region through solving Karush-Kuhn-Tucker (KKT) conditions of a distance minimization problem. Furthermore, we reformulate the nonlinear KKT conditions using log-exponential transformation to construct a general sparse system with only linear and exponential terms, thereby making the projection differentiable. We apply KKT-Hardnet on both test problems and a real-world chemical process simulation. Compared to multilayer perceptrons and PINNs, KKT-Hardnet achieves higher accuracy and strict constraint satisfaction. This approach allows the integration of domain knowledge into machine learning towards reliable hybrid modeling of complex systems.
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Kernel Trace Distance: Quantum Statistical Metric between Measures through RKHS Density Operators
Arturo Castellanos, Anna Korba, Pavlo Mozharovskyi, Hicham Janati
https://arxiv.org/abs/2507.06055

Kernel Trace Distance: Quantum Statistical Metric between Measures through RKHS Density Operators
Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them through a Schatten norm of their kernel covariance operators. We show that this new distance is an integral probability metric that can be framed between a Maximum Mean Discrepancy (MMD) and a Wasserstein distance. In particular, we show that it avoids some pitfa…

This was a very nice loop between #ohlstadt and #garmischpartenkirchen!
Beautiful views to the #mountains, an excellent way, almost no major roads and we also escaped a little rain…

Unified Design of Space-Air-Ground-Sea Integrated Maritime Communications
Zhehan Zhou, Xiaoming Chen, Ming Ying, Zhaohui Yang, Chongwen Huang, Yunlong Cai, Zhaoyang Zhang
https://arxiv.org/abs/2508.09817

Unified Design of Space-Air-Ground-Sea Integrated Maritime Communications
With the explosive growth of maritime activities, it is expected to provide seamless communications with quality of service (QoS) guarantee over broad sea area. In the context, this paper proposes a space-air-ground-sea integrated maritime communication architecture combining satellite, unmanned aerial vehicle (UAV), terrestrial base station (TBS) and unmanned surface vessel (USV). Firstly, according to the distance away from the shore, the whole marine space is divided to coastal area, offshor…

Testing the local supervoid solution to the Hubble tension with direct distance tracers
Richard Stiskalek, Harry Desmond, Sergij Mazurenko, Indranil Banik
https://arxiv.org/abs/2506.10518

Testing the local supervoid solution to the Hubble tension with direct distance tracers
Several observational studies suggest that the local few hundred Mpc around the Local Group are significantly underdense based on source number counts in redshift space across much of the electromagnetic spectrum, particularly in near-infrared galaxy counts. This ``Keenan--Barger--Cowie (KBC) void'', ``Local Hole'', or ``local supervoid'', would have significant ramifications for the Hubble tension by generating outflows that masquerade as an enhanced local expansion rate. We evaluate models fo…

Distance to stationarity and open set recurrence for ergodic processes on the unit interval with a Bernstein or a Siegmund dual
Fernando Cordero, Gr\'egoire V\'echambre
https://arxiv.org/abs/2507.07587

Distance to stationarity and open set recurrence for ergodic processes on the unit interval with a Bernstein or a Siegmund dual
We use duality techniques - specifically Siegmund and Bernstein duality - as tools to analyse ergodic and recurrence properties of $[0,1]$-valued Markov processes. These dualities enable the derivation of sharp bounds on the distance to stationarity and allow for a novel approach to establishing topological recurrence, whereby ergodicity implies recurrent visits to neighbourhoods of points in the stationary distribution's support. We first relate Siegmund and Bernstein duality in cases where bo…

A bound for the number of basic feasible solutions generated by the simplex method with the maximum distance rule
Tomonari Kitahara
https://arxiv.org/abs/2507.04672

A bound for the number of basic feasible solutions generated by the simplex method with the maximum distance rule
In this paper, we consider the number of different basic solutions generated by the simplex method with the maximum distance rule. The pivoting rule was recently proposed, and in some cases, it was reported to be more efficient than the renowned steepest edge rule. If the problem is nondegenerate, these results provide bounds on the number of iterations. As far as we know, they are the first theoretical bounds for the maximum distance rule.

A strengthened bound on the number of states required to characterize maximum parsimony distance
Mareike Fischer, Steven Kelk, Sofia Vazquez Alferez
https://arxiv.org/abs/2506.09888

A strengthened bound on the number of states required to characterize maximum parsimony distance
In this article we prove that the distance $d_{\mathrm{MP}}(T_1,T_2) = k$ between two unrooted binary phylogenetic trees $T_1, T_2$ on the same set of taxa can be defined by a character that is convex on one of $T_1, T_2$ and which has at most $2k$ states. This significantly improves upon the previous bound of $7k-5$ states. We also show that for every $k \geq 1$ there exist two trees $T_1, T_2$ with $d_{\mathrm{MP}}(T_1,T_2) = k$ such that at least $k+1$ states are necessary in any character t…

Optimal bounds for the Kobayashi distance near $\mathcal C^2$-smooth boundary points
Nikolai Nikolov, Pascal J. Thomas
https://arxiv.org/abs/2506.06507 htt…

Optimal bounds for the Kobayashi distance near $\mathcal C^2$-smooth boundary points
It is shown that the optimal upper and lower bounds for the Kobayashi distance near $\mathcal C^{2,α}$-smooth strongly pseudoconvex boundary points obtained in L. Kosinski, N. Nikolov, A.Y. Okten: "Precise estimates of invariant distances on strongly pseudoconvex domains", Adv. Math. 478 (2025), 110388, remain true in the general $\mathcal C^2$ strongly pseudoconvex setting. In fact, the upper bound is extended to the general $\mathcal C^{1,1}$-smooth case. We also give upper and lower bounds …

Velocity rotation curves in the gravimagnetic dipole spacetime
Cl\'ementine Dassy, Jan Govaerts
https://arxiv.org/abs/2508.08696 https://arxiv.org/pdf/…

Velocity rotation curves in the gravimagnetic dipole spacetime
The gravimagnetic dipole spacetime consists of two counter-rotating black holes of equal mass connected by a Misner string. For a particular distance in between them, the string is tensionless with the black holes at equilibrium with each other. The geodesics of relativistic massive, or massless particles are considered, leading to the identification of circular rotation trajectories. The velocities of these trajectories are computed.

Fast and efficient long-distance quantum state transfer in long-range spin-$\frac{1}{2}$ models
F. Faria, C. C. Nelmes, T. J. G. Apollaro, T. P. Spiller, I. D'Amico
https://arxiv.org/abs/2508.08182

Fast and efficient long-distance quantum state transfer in long-range spin-$\frac{1}{2}$ models
Quantum state transfer is investigated beyond the nearest-neighbour coupling scheme in long spin-$\frac{1}{2}$ linear chains. Exploiting the properties of the next-nearest neighbour Hamiltonian's dispersion relation, it is shown that with minimal engineering, i.e., an on-site magnetic field on the two end sites and only a few symmetrically-modified end inter-site couplings, an average transfer fidelity above $99\%$ can be achieved. To leading order, the required time scales linearly with the le…

Tree-Structured Parzen Estimator Can Solve Black-Box Combinatorial Optimization More Efficiently
Kenshin Abe, Yunzhuo Wang, Shuhei Watanabe
https://arxiv.org/abs/2507.08053 https://arxiv.org/pdf/2507.08053 https://arxiv.org/html/2507.08053
arXiv:2507.08053v1 Announce Type: new
Abstract: Tree-structured Parzen estimator (TPE) is a versatile hyperparameter optimization (HPO) method supported by popular HPO tools. Since these HPO tools have been developed in line with the trend of deep learning (DL), the problem setups often used in the DL domain have been discussed for TPE such as multi-objective optimization and multi-fidelity optimization. However, the practical applications of HPO are not limited to DL, and black-box combinatorial optimization is actively utilized in some domains, e.g., chemistry and biology. As combinatorial optimization has been an untouched, yet very important, topic in TPE, we propose an efficient combinatorial optimization algorithm for TPE. In this paper, we first generalize the categorical kernel with the numerical kernel in TPE, enabling us to introduce a distance structure to the categorical kernel. Then we discuss modifications for the newly developed kernel to handle a large combinatorial search space. These modifications reduce the time complexity of the kernel calculation with respect to the size of a combinatorial search space. In the experiments using synthetic problems, we verified that our proposed method identifies better solutions with fewer evaluations than the original TPE. Our algorithm is available in Optuna, an open-source framework for HPO.
toXiv_bot_toot

Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
Vahan Arsenyan, Elen Vardanyan, Arnak Dalalyan
https://arxiv.org/abs/2506.09681

Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such examples by mapping a Brownian motion via a diffusion process driven by an estimated score function. In this work, we first provide empirical evidence that DDPMs are robust to constant-variance noise in the score evaluations. We then establish finite-sample guara…

Faster Algorithms for $(2k-1)$-Stretch Distance Oracles
Avi Kadria, Liam Roditty
https://arxiv.org/abs/2507.06721 https://arxiv.org/p…

Faster Algorithms for $(2k-1)$-Stretch Distance Oracles
Let $G=(V, E)$ be an undirected $n$-vertices $m$-edges graph with non-negative edge weights. In this paper, we present three new algorithms for constructing a $(2k-1)$-stretch distance oracle with $O(n^{1+\frac{1}{k}})$ space. The first algorithm runs in $\Ot(\max(n^{1+2/k}, m^{1-\frac{1}{k-1}}n^{\frac{2}{k-1}}))$ time, and improves upon the $\Ot(\min(mn^{\frac{1}{k}},n^2))$ time of Thorup and Zwick [STOC 2001, JACM 2005] and Baswana and Kavitha [FOCS 2006, SICOMP 2010], for every $k > 2$ and $…

Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance
Haruto Nakashima, Siddhartha Ganguly, Kenji Kashima
https://arxiv.org/abs/2508.06052 https://

Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance
We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output data from pre-operational experiments are available. The initial state is modeled as a Gaussian mixture, while the terminal state is required to match a specified Gaussian distribution. We reformulate the resulting optimal control problem as a difference-of-con…

The Erd\H{o}s-Falconer distance problem between arbitrary sets and $k$-coordinatable sets in finite fields
Hunseok Kang, Doowon Koh, Firdavs Rakhmonov
https://arxiv.org/abs/2506.07251

The Erdős-Falconer distance problem between arbitrary sets and $k$-coordinatable sets in finite fields
In this paper, we study the cardinality of the distance set $Δ(A, B)$ determined by two subsets $A$ and $B$ of the $d$-dimensional vector space over a finite field $\mathbb{F}_q$. Assuming that $A$ or $B$ lies in a $k$-coordinate plane up to translations and rotations, we prove that if $|A||B| > 2q^d$, then $|Δ(A, B)| > q/2$, where $|Δ(A, B)|$ denotes the number of distinct distances between elements of $A$ and $B$. In particular, we show that our resu…

Happy weekend, friends

I took this #photo when I thought that I'd be almost there. - Because I had mostly looked about the elevation. But as you might see on the photo, the way flattens a bit towards the summit.
Well, it was a great trail - it just took longer then I assumed.
Some more context and a video are on my blog:

This https://arxiv.org/abs/2505.00968 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Tree-Sliced Wasserstein Distance with Nonlinear Projection
Tree-Sliced methods have recently emerged as an alternative to the traditional Sliced Wasserstein (SW) distance, replacing one-dimensional lines with tree-based metric spaces and incorporating a splitting mechanism for projecting measures. This approach enhances the ability to capture the topological structures of integration domains in Sliced Optimal Transport while maintaining low computational costs. Building on this foundation, we propose a novel nonlinear projectional framework for the Tre…

Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions
Noam Horowicz, Tsvi Kopelowitz
https://arxiv.org/abs/2507.04578 htt…

Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions
In the snippets problem, the goal is to preprocess text $T$ so that given two patterns $P_1$ and $P_2$, one can locate the occurrences of the two patterns in $T$ that are closest to each other, or report their distance. Kopelowitz and Krauthgamer [CPM2016] showed upper bound tradeoffs and conditional lower bounds tradeoffs for the snippets problem, by utilizing connections between the snippets problem and the problem of constructing a color distance oracle (CDO), which is a data structure that …

On two-distance-transitive graphs
Wei Jin, Jack H. Koolen, Chenhui Lv
https://arxiv.org/abs/2508.02010 https://arxiv.org/pdf/2508.02010

On two-distance-transitive graphs
A $2$-distance-transitive graph is a vertex-transitive graph whose vertex stabilizer is transitive on both the first step and the second step neighborhoods. In this paper, we first answer a question of A. Devillers, M. Giudici, C. H. Li and C. E. Praeger in 2012 about vertex-quasiprimitive $2$-distance-transitive graphs for the odd order case. Then we characterize $2$-distance-transitive graphs of valency $p$ or $p+1$ where $p$ is a prime. After that, as an application of the above result, we c…

Fundamental Limits of Learning High-dimensional Simplices in Noisy Regimes
Seyed Amir Hossein Saberi, Amir Najafi, Abolfazl Motahari, Babak H. khalaj
https://arxiv.org/abs/2506.10101

Fundamental Limits of Learning High-dimensional Simplices in Noisy Regimes
In this paper, we establish sample complexity bounds for learning high-dimensional simplices in $\mathbb{R}^K$ from noisy data. Specifically, we consider $n$ i.i.d. samples uniformly drawn from an unknown simplex in $\mathbb{R}^K$, each corrupted by additive Gaussian noise of unknown variance. We prove an algorithm exists that, with high probability, outputs a simplex within $\ell_2$ or total variation (TV) distance at most $\varepsilon$ from the true simplex, provided $n \ge (K^2/\varepsilon^2…

This #photo is pretty soon after the first photo that I posted. I was on the way up and turned around to see the nice little meadow that I just crossed.
The #trail winding through the meadow with the trees around and the

Long-distance device-independent quantum key distribution with standard optics tools
Makoto Ishihara, Anthony Brendan, Wojciech Roga, Masahiro Takeoka
https://arxiv.org/abs/2508.02262

Long-distance device-independent quantum key distribution with standard optics tools
Device-independent quantum key distribution (DI-QKD) enables information-theoretically secure key distribution between remote parties without any assumptions on the internal workings of the devices used for its implementation. However, its communication distance is strictly limited since the loophole-free Bell violation is required to guarantee its security. Therefore, in this paper, we propose two long-distance DI-QKD protocols which use a heralding scheme based on single-photon interference. …

Faster Algorithm for Bounded Tree Edit Distance in the Low-Distance Regime
Tomasz Kociumaka, Ali Shahali
https://arxiv.org/abs/2507.02701 https://

Faster Algorithm for Bounded Tree Edit Distance in the Low-Distance Regime
The tree edit distance is a natural dissimilarity measure between rooted ordered trees whose nodes are labeled over an alphabet $Σ$. It is defined as the minimum number of node edits (insertions, deletions, and relabelings) required to transform one tree into the other. In the weighted variant, the edits have associated costs (depending on the involved node labels) normalized so that each cost is at least one, and the goal is to minimize the total cost of edits. The unweighted tree edit dist…

On packing total coloring
Jasmina Ferme, Da\v{s}a Mesari\v{c} \v{S}tesl
https://arxiv.org/abs/2508.08691 https://arxiv.org/pdf/2508.08691

On packing total coloring
In this paper, we introduce a new concept in graph coloring, namely the \textit{packing total coloring}, which extends the idea of packing coloring to both the vertices and the edges of a given graph. More precisely, for a graph $G$, a packing total coloring is a mapping $c: V(G) \cup E(G) \rightarrow \{1, 2, \ldots\}$ with the property that for any integer $i$, any two distinct elements $A, B \in V(G) \cup E(G)$ with $c(A) = c(B) = i$ must be at distance at least $i+1$ from each other. The sma…

Back from a #cycling loop around the #ammersee !
Unfortunately I forgot to turn on my cycling computer for the first half hour 🥴 Yeah well, the red frame around the statistics page was quite clear but .. well.
Anyways! It was a nice ~50km loop with excellent weather (prepared with a lo…

Perfect state transfer in Grover walks on association schemes and distance-regular graphs
Koushik Bhakta, Bikash Bhattacharjya
https://arxiv.org/abs/2506.07439

Perfect state transfer in Grover walks on association schemes and distance-regular graphs
This paper investigates perfect state transfer in Grover walks, a model of discrete-time quantum walks. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on graphs belonging to an association scheme. Our focus includes specific association schemes, namely the Hamming and Johnson schemes. We characterize all graphs on the classes of Hamming and Johnson schemes that exhibit perfect state transfer. Furthermore, we study perfect state transfer on distanc…

Geodesic transitive graphs of small valency
Jun-Jie Huang
https://arxiv.org/abs/2506.04670 https://arxiv.org/pdf/2506.04670

Geodesic transitive graphs of small valency
For a graph $Γ$, the {\em distance} $d_Γ(u,v)$ between two distinct vertices $u$ and $v$ in $Γ$ is defined as the length of the shortest path from $u$ to $v$, and the {\em diameter} $\mathrm{diam}(Γ)$ of $Γ$ is the maximum distance between $u$ and $v$ for all vertices $u$ and $v$ in the vertex set of $Γ$. For a positive integer $s$, a path $(u_0,u_1,\ldots,u_{s})$ is called an {\em $s$-geodesic} if the distance of $u_0$ and $u_s$ is $s$. The graph $Γ$ is said to be {\em distance transiti…

Distance restricted matching extensions in regular non-bipartite graphs
Jun Fujisawa
https://arxiv.org/abs/2508.04507 https://arxiv.org/pdf/2508.04507

Distance restricted matching extensions in regular non-bipartite graphs
Let $m$ and $r$ be integers with $m \ge r \ge 3$ and let $G$ be an $r$-regular graph of even order. Let $M$ be a matching in $G$ of size $m$ such that each pair of edges in $M$ is at distance at least $3$. In 2023, Aldred et al. proved that if $G$ is cyclically $(mr-r+1)$-edge-connected and $G$ is bipartite, then there exists a perfect matching of $G$ containing $M$. In this paper, we present non-bipartite analogues of Aldred et al.'s theorem. An odd ear of $U \subseteq V(G)$ is a path of odd l…