Tootfinder

Optimal regularity results in Sobolev-Lorentz spaces for lilnear elliptic equations with $L^1$- or measure data
Hyunseok Kim, Young-Ran Lee, Jihoon Ok
https://arxiv.org/abs/2506.15005

Optimal regularity results in Sobolev-Lorentz spaces for lilnear elliptic equations with $L^1$- or measure data
It has been well known that if $Ω$ is a bounded $C^1$-domain in $\R^n,\ n \ge 2$, then for every Radon measure $f$ on $Ω$ with finite total variation, there exists a unique weak solution $u\in W_0^{1,1}(Ω)$ of the Poisson equation $-Δu=f$ in $Ω$ satisfying $\nabla u \in L^{n/(n-1),\infty}(Ω;\R^n )$. In this paper, optimal regularity properties of the solution $u$ are established in Sobolev-Lorentz spaces $L_α^{p,q}(Ω)$ of order $ α$ less than but arbitrarily close to $2$. More precisel…

Ravens HC John Harbaugh on QB Lamar Jackson's OTAs absences: I measure 'how they play,' not 'the attendance' https://www.nfl.com/news/ravens-hc-john-harbaugh-on-qb-lamar-jackson-s-otas-abs…

A General Theory of Risk Sharing
Vasily Melnikov
https://arxiv.org/abs/2505.19276 https://arxiv.org/pdf/2505.19276

A General Theory of Risk Sharing
We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have potentially heterogeneous risk preferences modeled by risk measures. The existence of risk minimizing allocations is proved when constrained to satisfy economically convincing conditions. In the unconstrained case, we derive the dual representation of the value f…

Multi-mode feedback cooling of the collective modes of a Bose-Einstein condensate
Ryan J. Thomas, Jordan A. McMahon, Zain Mehdi, Stuart S. Szigeti, Simon A. Haine, Samuel Legge, John D. Close, Joseph J. Hope
https://arxiv.org/abs/2506.19739

Multi-mode feedback cooling of the collective modes of a Bose-Einstein condensate
We experimentally demonstrate cavity-free feedback cooling of the three lowest-lying collective modes of a Bose-Einstein condensate in a prolate harmonic trap. Using shadowgraph imaging as an \textit{in situ} probe of the atomic density, we measure the time-dependent centers-of-mass and widths of the condensate in two dimensions and use these measurements to damp oscillations in the two visible dipole modes and the low-frequency quadrupole mode. By inducing oscillations in the condensate, we sh…

Low Overhead Allocation Sampling in a Garbage Collected Virtual Machine
Christoph Jung, C. F. Bolz-Tereick
https://arxiv.org/abs/2506.16883 https://…

Low Overhead Allocation Sampling in a Garbage Collected Virtual Machine
Compared to the more commonly used time-based profiling, allocation profiling provides an alternate view of the execution of allocation heavy dynamically typed languages. However, profiling every single allocation in a program is very inefficient. We present a sampling allocation profiler that is deeply integrated into the garbage collector of PyPy, a Python virtual machine. This integration ensures tunable low overhead for the allocation profiler, which we measure and quantify. Enabling alloca…

Networked pointing system: Bearing-only target localization and pointing control
Shiyao Li, Bo Zhu, Yining Zhou, Jie Ma, Baoqing Yang, Fenghua He
https://arxiv.org/abs/2506.18460 …

Networked pointing system: Bearing-only target localization and pointing control
In the paper, we formulate the target-pointing consensus problem where the headings of agents are required to point at a common target. Only a few agents in the network can measure the bearing information of the target. A two-step solution consisting of a bearing-only estimator for target localization and a control law for target pointing is constructed to address this problem. Compared to the strong assumptions of existing works, we only require two agents not collinear with the target to ensu…

Replaced article(s) found for math.CA. https://arxiv.org/list/math.CA/new
[1/1]:
- On the Packing Functions of some Linear Sets of Lebesgue Measure Zero
Austin Anderson, Steven Damelin

DRIVE Through the Unpredictability:From a Protocol Investigating Slip to a Metric Estimating Command Uncertainty
Nicolas Samson, William Larriv\'ee-Hardy, William Dubois, \'Elie Roy-Brouard, Edith Brotherton, Dominic Baril, Julien L\'epine, Fran\c{c}ois Pomerleau
https://arxiv.org/abs/2506.16593

DRIVE Through the Unpredictability:From a Protocol Investigating Slip to a Metric Estimating Command Uncertainty
Off-road autonomous navigation is a challenging task as it is mainly dependent on the accuracy of the motion model. Motion model performances are limited by their ability to predict the interaction between the terrain and the UGV, which an onboard sensor can not directly measure. In this work, we propose using the DRIVE protocol to standardize the collection of data for system identification and characterization of the slip state space. We validated this protocol by acquiring a dataset with two…

On the day after Assemblyman Zohran Mamdani emerged as the likely Democratic nominee for mayor of New York City, Representative Jerrold Nadler endorsed him in November’s general election, giving Mr. Mamdani a key measure of support from one of the city’s most prominent Jewish leaders.
Mr. Nadler, a Democrat, said Wednesday that Mr. Mamdani’s apparent victory was a “seismic election for the Democratic Party that I can only compare to Barack Obama’s in 2008.”
https://www.nytimes.com/live/2025/06/25/nyregion/zohran-mamdani-nyc-mayor-election

The CPJ has directed a law firm to set up a legal entity in the UK, in part as a precautionary measure against potential Trump EOs targeting American nonprofits (Prashant Rao/Semafor)
https://www.semafor.com/article/06/11/2025

Fearing Trump action, US nonprofits seek shelter in the UK
Several American nonprofits are exploring setting up legal entities in Britain, in part as a precautionary measure against feared executive orders.

Systematic Biases from ARM-Based Sensitivity and Imaging in Compton Cameras
Tomonori Ikeda, Tatsuya Sawano, Naomi Tsuji, Yoshitaka Mizumura
https://arxiv.org/abs/2506.18659

Systematic Biases from ARM-Based Sensitivity and Imaging in Compton Cameras
The angular resolution measure (ARM) is widely used in Compton camera analyses to characterize angular uncertainty and to define event selection criteria. However, the ARM distribution is fundamentally different from the point spread function (PSF), which represents the true spatial imaging response of the system on the celestial sphere. In this study, motivated by applications in gamma-ray astrophysics, we investigated the consequences of using ARM-based definitions in sensitivity estimation a…

FARFETCH'D: A Side-Channel Analysis Framework for Privacy Applications on Confidential Virtual Machines
Ruiyi Zhang, Albert Cheu, Adria Gascon, Daniel Moghimi, Phillipp Schoppmann, Michael Schwarz, Octavian Suciu
https://arxiv.org/abs/2506.15924

FARFETCH'D: A Side-Channel Analysis Framework for Privacy Applications on Confidential Virtual Machines
Confidential virtual machines (CVMs) based on trusted execution environments (TEEs) enable new privacy-preserving solutions. Yet, they leave side-channel leakage outside their threat model, shifting the responsibility of mitigating such attacks to developers. However, mitigations are either not generic or too slow for practical use, and developers currently lack a systematic, efficient way to measure and compare leakage across real-world deployments. In this paper, we present FARFETCH'D, an ope…

A residual a posteriori error estimate for the Stabilization-free Virtual Element Method
Stefano Berrone, Andrea Borio, Davide Fassino, Francesca Marcon
https://arxiv.org/abs/2506.17947

A residual a posteriori error estimate for the Stabilization-free Virtual Element Method
In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The abscence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably defined error measure and standard residual error estimators, which is not obtained in general for stabilized virtual elements. Several numerical experiments are carried out, confirming the expected behaviour of the estimator in the presence of different mes…

On the Invariance of Expansive Measures for Flows
Eduardo Pedrosa, Elias Rego, Alexandre Trilles
https://arxiv.org/abs/2506.21533 https://

On the Invariance of Expansive Measures for Flows
We study expansive measures for continuous flows without fixed points on compact metric spaces, as introduced in [6]. We provide a new characterization of expansive measures through dynamical balls that, in contrast to the dynamical balls considered in [6], are actually Borel sets. This makes the theory more amenable to measure-theoretic analysis. We then establish a version of the Brin-Katok local entropy formula for flows using these generalized dynamical balls. As an application, we prove th…

Asymptotic Schur orthogonality relations for Heisenberg groups over local fields
Malay Mandal, Arghya Mondal
https://arxiv.org/abs/2506.18300 https://

Asymptotic Schur orthogonality relations for Heisenberg groups over local fields
Asymptotic Schur orthogonality relations are for irreducible unitary representations of locally compact groups that need not be discrete series, where $L^2$ pairing of matrix coefficients with respect to Haar measure is replaced by a limit of that with respect to a sequence of bounded measures. We show that such relations hold for Heisenberg groups over local fields. This is achieved in the framework of c-temperedness introduced by Kazhdan and Yom Din. The related condition of convergence to br…

Class of extensions of real field and their topological properties
E. V. Alexandrov
https://arxiv.org/abs/2506.14838 https://arxiv.or…

Class of extensions of real field and their topological properties
Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and multiplication), and not connected, in this case this extension is linearly ordered field. In the future these constructions can be applied to building measure that "feels" set of zero Lebesgue measure.

Topological Correlation
Isabella Mastroianni, Ulderico Fugacci
https://arxiv.org/abs/2506.16985 https://arxiv.org/pdf/2506.16985

Topological Correlation
We introduce two novel concepts, topological difference and topological correlation, that offer a new perspective on the discriminative power of multiparameter persistence. The former quantifies the discrepancy between multiparameter and monoparameter persistence, while the other leverages this gap to measure the interdependence of filtering functions. Our framework sheds light on the expressive advantage of multiparameter over monoparameter persistence and suggests potential applications.

Maximal inequalities for square functions associated to group metric measure spaces
Panchugopal Bikram, Diptesh Saha
https://arxiv.org/abs/2506.18589 https…

Maximal inequalities for square functions associated to group metric measure spaces
In this article, we establish weighted strong and weak type inequalities for non-commutative square functions associated with the differences of ball averages and martingales over group metric measure spaces. These results generalise the main outcome of \cite{saha-rayweighted}.

Local classical correlations between physical electrons in the Hubbard model
Gabriele Bellomia, Adriano Amaricci, Massimo Capone
https://arxiv.org/abs/2506.18709

Local classical correlations between physical electrons in the Hubbard model
We demonstrate that the local nonfreeness, an unbiased measure of correlation between electrons at a single lattice site, can be computed as the mutual information between local natural spin orbitals. Using this concept, we prove that local electron correlations in the Hubbard model are fully classical: in the natural basis the local reduced density matrix is separable and no quantum correlations beyond entanglement are present. Finally, we compare different theoretical descriptions of magnetic…

Quantifying Gibbs measures of disordered crystals up to the solid-liquid phase transition
Vladislav Efremkin, Julian Heske, Thomas D. K\"uhne, Emil Prodan
https://arxiv.org/abs/2506.18190

Quantifying Gibbs measures of disordered crystals up to the solid-liquid phase transition
Quantifying the configuration space and the Gibbs measure of thermally disordered condensed matter systems has been a long standing problem. The challenge is to avoid the Gibbs paradox, which forbids any ordering or labeling of the atoms. Our key observation is that the lattice of a thermally disordered condensed matter system, in either solid, liquid or gas phase, can be fully reconstructed from the Voronoi cells of the atoms alone, even if these Voronoi cells are disassembled and randomly scr…

Join Nikolay Sivko at this year's Berlin Buzzwords for his talk, in which he will delve into delay accounting — a frequently overlooked feature that provides valuable insights into CPU time shortages and application latency. Discover how to use these kernel metrics to improve performance analysis and system optimisation.
Learn more:

Tensor network calculation of boundary and corner magnetization
Roman Krcmar, Jozef Genzor, Andrej Gendiar, Tomotoshi Nishino
https://arxiv.org/abs/2506.17194

Tensor network calculation of boundary and corner magnetization
The Corner Transfer Matrix Renormalization Group (CTMRG) algorithm is modified to measure the magnetization at the boundary of the system, including the corners of the square-shaped lattice. Using automatic differentiation, we calculate the magnetization's first derivative, allowing us to determine the boundary critical exponent $β$ accurately.

Why AI can't possibly make you more productive; long
#AI and "productivity", some thoughts:
Productivity is a concept that isn't entirely meaningless outside the context of capitalism, but it's a concept that is heavily inflected in a capitalist context. In many uses today it effectively means "how much you can satisfy and/or exceed your boss' expectations." This is not really what it should mean: even in an anarchist utopia, people would care about things like how many shirts they can produce in a week, although in an "I'd like to voluntarily help more people" way rather than an "I need to meet this quota to earn my survival" way. But let's roll with this definition for a second, because it's almost certainly what your boss means when they say "productivity", and understanding that word in a different (even if truer) sense is therefore inherently dangerous.
Accepting "productivity" to mean "satisfying your boss' expectations," I will now claim: the use of generative AI cannot increase your productivity.
Before I dive in, it's imperative to note that the big generative models which most people think of as constituting "AI" today are evil. They are 1: pouring fuel on our burning planet, 2: psychologically strip-mining a class of data laborers who are exploited for their precarity, 3: enclosing, exploiting, and polluting the digital commons, and 4: stealing labor from broad classes of people many of whom are otherwise glad to give that labor away for free provided they get a simple acknowledgement in return. Any of these four "ethical issues" should be enough *alone* to cause everyone to simply not use the technology. These ethical issues are the reason that I do not use generative AI right now, except for in extremely extenuating circumstances. These issues are also convincing for a wide range of people I talk to, from experts to those with no computer science background. So before I launch into a critique of the effectiveness of generative AI, I want to emphasize that such a critique should be entirely unnecessary.
But back to my thesis: generative AI cannot increase your productivity, where "productivity" has been defined as "how much you can satisfy and/or exceed your boss' expectations."
Why? In fact, what the fuck? Every AI booster I've met has claimed the opposite. They've given me personal examples of time saved by using generative AI. Some of them even truly believe this. Sometimes I even believe they saved time without horribly compromising on quality (and often, your boss doesn't care about quality anyways if the lack of quality is hard to measure of doesn't seem likely to impact short-term sales/feedback/revenue). So if generative AI genuinely lets you write more emails in a shorter period of time, or close more tickets, or something else along these lines, how can I say it isn't increasing your ability to meet your boss' expectations?
The problem is simple: your boss' expectations are not a fixed target. Never have been. In virtue of being someone who oversees and pays wages to others under capitalism, your boss' game has always been: pay you less than the worth of your labor, so that they can accumulate profit and this more capital to remain in charge instead of being forced into working for a wage themselves. Sure, there are layers of manservant caught in between who aren't fully in this mode, but they are irrelevant to this analysis. It matters not how much you please your manager if your CEO thinks your work is not worth the wages you are being paid. And using AI actively lowers the value of your work relative to your wages.
Why do I say that? It's actually true in several ways. The most obvious: using generative AI lowers the quality of your work, because the work it produces is shot through with errors, and when your job is reduced to proofreading slop, you are bound to tire a bit, relax your diligence, and let some mistakes through. More than you would have if you are actually doing and taking pride in the work. Examples are innumerable and frequent, from journalists to lawyers to programmers, and we laugh at them "haha how stupid to not check whether the books the AI reviewed for you actually existed!" but on a deeper level if we're honest we know we'd eventually make the same mistake ourselves (bonus game: spot the swipe-typing typos I missed in this post; I'm sure there will be some).
But using generative AI also lowers the value of your work in another much more frightening way: in this era of hype, it demonstrates to your boss that you could be replaced by AI. The more you use it, and no matter how much you can see that your human skills are really necessary to correct its mistakes, the more it appears to your boss that they should hire the AI instead of you. Or perhaps retain 10% of the people in roles like yours to manage the AI doing the other 90% of the work. Paradoxically, the *more* you get done in terms of raw output using generative AI, the more it looks to your boss as if there's an opportunity to get enough work done with even fewer expensive humans. Of course, the decision to fire you and lean more heavily into AI isn't really a good one for long-term profits and success, but the modern boss did not get where they are by considering long-term profits. By using AI, you are merely demonstrating your redundancy, and the more you get done with it, the more redundant you seem.
In fact, there's even a third dimension to this: by using generative AI, you're also providing its purveyors with invaluable training data that allows them to make it better at replacing you. It's generally quite shitty right now, but the more use it gets by competent & clever people, the better it can become at the tasks those specific people use it for. Using the currently-popular algorithm family, there are limits to this; I'm not saying it will eventually transcend the mediocrity it's entwined with. But it can absolutely go from underwhelmingly mediocre to almost-reasonably mediocre with the right training data, and data from prompting sessions is both rarer and more useful than the base datasets it's built on.
For all of these reasons, using generative AI in your job is a mistake that will likely lead to your future unemployment. To reiterate, you should already not be using it because it is evil and causes specific and inexcusable harms, but in case like so many you just don't care about those harms, I've just explained to you why for entirely selfish reasons you should not use it.
If you're in a position where your boss is forcing you to use it, my condolences. I suggest leaning into its failures instead of trying to get the most out of it, and as much as possible, showing your boss very clearly how it wastes your time and makes things slower. Also, point out the dangers of legal liability for its mistakes, and make sure your boss is aware of the degree to which any of your AI-eager coworkers are producing low-quality work that harms organizational goals.
Also, if you've read this far and aren't yet of an anarchist mindset, I encourage you to think about the implications of firing 75% of (at least the white-collar) workforce in order to make more profit while fueling the climate crisis and in most cases also propping up dictatorial figureheads in government. When *either* the AI bubble bursts *or* if the techbros get to live out the beginnings of their worker-replacement fantasies, there are going to be an unimaginable number of economically desperate people living in increasingly expensive times. I'm the kind of optimist who thinks that the resulting social crucible, though perhaps through terrible violence, will lead to deep social changes that effectively unseat from power the ultra-rich that continue to drag us all down this destructive path, and I think its worth some thinking now about what you might want the succeeding stable social configuration to look like so you can advocate towards that during points of malleability.
As others have said more eloquently, generative AI *should* be a technology that makes human lives on average easier, and it would be were it developed & controlled by humanists. The only reason that it's not, is that it's developed and controlled by terrible greedy people who use their unfairly hoarded wealth to immiserate the rest of us in order to maintain their dominance. In the long run, for our very survival, we need to depose them, and I look forward to what the term "generative AI" will mean after that finally happens.

High-speed quantitative nanomechanical mapping by photothermal off-resonance atomic force microscopy
Hans Gunstheimer, Gotthold Fl\"aschner, Jonathan D. Adams, Hendrik H\"olscher, Bart W. Hoogenboom
https://arxiv.org/abs/2506.16226

High-speed quantitative nanomechanical mapping by photothermal off-resonance atomic force microscopy
Atomic force microscopy (AFM) is widely used to measure surface topography of solid, soft, and living matter at the nanoscale. Moreover, by mapping forces as a function of distance to the surface, AFM can provide a wealth of information beyond topography, with nanomechanical properties as a prime example. Here we present a method based on photothermal off-resonance tapping (PORT) to increase the speed of such force spectroscopy measurements by at least an order of magnitude, thereby enabling hi…

STM32-Based IoT Framework for Real-Time Environmental Monitoring and Wireless Node Synchronization
Ahmed Faizul Haque Dhrubo, Sazid Hasan, Mohammad Abdul Qayum
https://arxiv.org/abs/2506.17295

STM32-Based IoT Framework for Real-Time Environmental Monitoring and Wireless Node Synchronization
The fast pace of technological growth has created a heightened need for intelligent, autonomous monitoring systems in a variety of fields, especially in environmental applications. This project shows the design process and implementation of a proper dual node (master-slave) IoT-based monitoring system using STM32F103C8T6 microcontrollers. The structure of the wireless monitoring system studies the environmental conditions in real-time and can measure parameters like temperature, humidity, soil …

Hierarchical constraints on gravitational waves from horizonless compact objects
Rajrupa Mondal, Julian Westerweck, Yotam Sherf, Collin D. Capano
https://arxiv.org/abs/2506.17215 …

Hierarchical constraints on gravitational waves from horizonless compact objects
We use the data of several promising gravitational wave observations to obtain increasingly stringent bounds on near-horizon deviations of their sources from the Kerr geometry. A range of horizonless compact objects proposed as alternatives to black holes of general relativity would possess a modified gravitational wave emission after the merger. Modelling these objects by introducing reflection of gravitational waves near the horizon, we can measure deviations from Kerr in terms of a single ad…

Quantification of Information Flow by Dual Reporter System and Its Application to Bacterial Chemotaxis
Kento Nakamura, Hajime Fukuoka, Akihiko Ishijima, Tetsuya J. Kobayashi
https://arxiv.org/abs/2506.15957

Quantification of Information Flow by Dual Reporter System and Its Application to Bacterial Chemotaxis
Mutual information is a theoretically grounded metric for quantifying cellular signaling pathways. However, its measurement demands characterization of both input and output distributions, limiting practical applications. Here, we present alternative method that alleviates this requirement using dual reporter systems. By extending extrinsic-intrinsic noise analysis, we derive a mutual information estimator that eliminates the need to measure input distribution. We demonstrate our method by anal…

Automorphism groups of measures on the Cantor space. Part II: Abstract homogeneous measures
Piotr Niemiec
https://arxiv.org/abs/2506.20797 https://

Automorphism groups of measures on the Cantor space. Part II: Abstract homogeneous measures
The main aim of the paper is to introduce a new class of (semigroup-valued) measures that are ultrahomogeneous on the Boolean algebra of all clopen subsets of the Cantor space and to study their automorphism groups. A characterisation, in terms of the so-called trinary spectrum of a measure, of ultrahomogeneous measures such that the action of their automorphism groups is (topologically) transitive or minimal is given. Also sufficient and necessary conditions for the existence of a dense (or co…

A systematic characterisation of canopy density based on turbulent-structure penetration
Zishen Chen, Ricardo Garc\'ia-Mayoral
https://arxiv.org/abs/2506.19223

A systematic characterisation of canopy density based on turbulent-structure penetration
Turbulent flows over canopies of rigid elements with different geometries and Reynolds numbers (Re) are investigated to identify and characterise different canopy density regimes. In the sparse regime, turbulence penetrates relatively unhindered within the canopy, whereas in the dense regime, the penetration is limited. A common measure of canopy density is the ratio of frontal to bed area, the frontal density $λ_f$. This is effective for canopies with no preferential orientation, but we obser…

Asymptotic expansion for groupoids and Roe type algebras
Xulong Lu, Qin Wang, Jiawen Zhang
https://arxiv.org/abs/2506.16772 https://a…

Asymptotic expansion for groupoids and Roe type algebras
In this paper, we introduce a notion of expansion for groupoids, which recovers the classical notion of expander graphs by a family of pair groupoids and expanding actions in measure by transformation groupoids. We also consider an asymptotic version for expansion and establish structural theorems, showing that asymptotic expansion can be approximated by domains of expansions. On the other hand, we introduce dynamical propagation and quasi-locality for operators on groupoids and the associated …

The Parliament of #Finland approved the withdrawal from the 1997 #OttawaTreaty, which bans #landmines. Only 18 MPs out of 200 opposed.

MPs approve Finland's withdrawal from Ottawa landmine treaty
Parliament approved the measure to withdraw from the agreement by a vote of 157 to 18.

Detailed Chemical Abundance Analysis of Metal-Poor Turn-Off Stars: One with [Fe/H] < -4 and Three with [Fe/H] < -4
Takuma Suda, Patrick Francois, Shinya Wanajo, Elisabetta Caffau, Wako Aoki, Piercarlo Bonifacio
https://arxiv.org/abs/2506.18286

Detailed Chemical Abundance Analysis of Metal-Poor Turn-Off Stars: One with [Fe/H] < -4 and Three with [Fe/H] < -4
We present the analysis of four new extremely metal poor turn-off stars thanks to high-resolution spectra obtained with the Subaru/HDS spectrograph. We determined the abundances and upper limits of Li, C, Mg, Ca, Sr, and Ba. Metallicities range from [Fe/H] = -3.3 to -4.4 dex. For one of the stars, we measure the lithium abundance Log(Li/H) = 2.1 {\pm} 0.2. Two stars of the sample have low [α/Fe] abundances. The most metal-poor star of the sample with [Fe/H] = -4.42 dex has a high [Sr/Fe] abund…

Measure-Theoretic Aspects of Star-Free and Group Languages
Ryoma Sin'ya, Takao Yuyama
https://arxiv.org/abs/2506.14134 https://ar…

Measure-Theoretic Aspects of Star-Free and Group Languages
A language $L$ is said to be ${\cal C}$-measurable, where ${\cal C}$ is a class of languages, if there is an infinite sequence of languages in ${\cal C}$ that ``converges'' to $L$. We investigate the properties of ${\cal C}$-measurability in the cases where ${\cal C}$ is SF, the class of all star-free languages, and G, the class of all group languages. It is shown that a language $L$ is SF-measurable if and only if $L$ is GD-measurable, where GD is the class of all generalised definite language…

A Formalization of the Ionescu-Tulcea Theorem in Mathlib
Etienne Marion (ENS de Lyon)
https://arxiv.org/abs/2506.18616 https://arxiv.…

A Formalization of the Ionescu-Tulcea Theorem in Mathlib
We describe the formalization of the Ionescu-Tulcea theorem, showing the existence of a probability measure on the space of trajectories of a Markov chain, in the proof assistant Lean using the integrated library Mathlib. We first present a mathematical proof before exposing the difficulties which arise when trying to formalize it, and how they were overcome. We then build on this work to formalize the construction of the product of an arbitrary family of probability measures.

Search for an Anomalous Excess of Single Photons in the MicroBooNE Neutrino Experiment
Lee Hagaman
https://arxiv.org/abs/2506.18956 https://

Search for an Anomalous Excess of Single Photons in the MicroBooNE Neutrino Experiment
Neutrinos are some of the most elusive particles in the standard model, being incredibly common throughout the universe, but interacting with detectors incredibly rarely. Certain properties of neutrinos remain difficult to measure, including their masses, their CP violation properties, and whether or not they are their own antiparticles. Additionally, there have been several anomalous results in neutrino experiments which remain unexplained. MicroBooNE was built in order to study these anomalou…

The AURORA Survey: Tracing Galactic Outflows at $z\gtrsim2.5$ with JWST/NIRSpec NUV Absorption Lines
Emily Kehoe, Alice E. Shapley, Ryan L. Sanders, Naveen A. Reddy, Michael W. Topping, Natalie Lam, Leonardo Clarke, Fergus Cullen, Richard S. Ellis, N. M. Forster Schreiber, Tucker Jones, Ali Ahmad Khostovan, Derek J. McLeod, Ross J. McLure, Desika Narayanan, Pascal Oesch, Anthony J. Pahl

The AURORA Survey: Tracing Galactic Outflows at $z\gtrsim2.5$ with JWST/NIRSpec NUV Absorption Lines
We probe galactic-scale outflows in star-forming galaxies at $z\gtrsim2.5$ drawn from the JWST/NIRSpec AURORA program. For the first time, we directly compare outflow properties from the early universe to the present day using near-UV absorption lines. We measure ISM kinematics from Fe II and Mg II absorption features in 41 and 43 galaxies, respectively, and examine how these kinematics correlate with galaxy properties. We find that galaxies with outflows tend to have higher stellar masses, and…

FINCH EYE: The Optical and Optomechanical Design of a GRISM-based SWIR Hyperspectral Imaging Payload for a 3U CubeSat
Iliya Shofman, Mario Ghio Neto, Theaswanth Ganesh, Kenya He, Aidan Armstrong, Ksenya Narkevich
https://arxiv.org/abs/2506.17480

FINCH EYE: The Optical and Optomechanical Design of a GRISM-based SWIR Hyperspectral Imaging Payload for a 3U CubeSat
Crop residue is an important metric used for agricultural land-use monitoring and climate science research. Estimating crop residue coverage is essential to sustainable agricultural practices. The University of Toronto Aerospace Team is developing FINCH EYE, the optical payload for the upcoming FINCH 3U CubeSat, to measure crop residue cover. We conceived of a novel ultra-compact push-broom architecture with a volume phase-holographic grism dispersive element to keep the design compact and simp…

Operator theoretic measure of causality in linear dynamical systems
Ankit Srivastava, Louis Cattafesta, Scott Dawson
https://arxiv.org/abs/2506.08118 https…

Operator theoretic measure of causality in linear dynamical systems
This paper introduces Linear Operator Causality Analysis (LOCA), a physics-based framework for analyzing causality in linear dynamical systems, with a focus on fluid mechanics. Unlike data-driven statistical methods like Granger causality, LOCA uses the matrix exponential from the system's governing equations to provide a more rigorous and interpretable measure of causal interactions. Our framework reveals that, under certain conditions, common data-driven measures effectively approximate the s…

On Design of Representative Distributionally Robust Formulations for Evaluation of Tail Risk Measures
Anand Deo
https://arxiv.org/abs/2506.16230 https://…

On Design of Representative Distributionally Robust Formulations for Evaluation of Tail Risk Measures
Conditional Value-at-Risk (CVaR) is a risk measure widely used to quantify the impact of extreme losses. Owing to the lack of representative samples CVaR is sensitive to the tails of the underlying distribution. In order to combat this sensitivity, Distributionally Robust Optimization (DRO), which evaluates the worst-case CVaR measure over a set of plausible data distributions is often deployed. Unfortunately, an improper choice of the DRO formulation can lead to a severe underestimation of tai…

Krugman continues:
❝While there is a cadre of Trumpist true believers who will obey the Leader under any circumstances, most of those doing the dirty work of undermining democracy and the rule of law are cowards and opportunists. They’re willing to participate in the destruction of America as we know it because they believe that many others will do the same. As a result, they believe that they are unlikely to face any personal consequences for their actions and may even be rewarded for their lawbreaking.
And what of those who oppose Trumpism? While there are heroes willing to take a stand against tyranny whatever the personal cost, most anti-Trumpists are reluctant to stick their necks out unless they believe that they are part of a widespread resistance that will grant them some measure of safety in numbers.
In other words, the victory or defeat of competitive authoritarianism will depend to a large extent on which side ordinary people believe will win. If Trump looks unstoppable, resistance will wither away and democracy will be lost. On the other hand, if he appears weak and stymied, resistance will grow and — just maybe — American democracy will survive.❞
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Evaluation of machine-learning models to measure individualized treatment effects from randomized clinical trial data with time-to-event outcomes
Elvire Roblin, Paul-Henry Courn\`ede, Stefan Michiels
https://arxiv.org/abs/2506.12277

Evaluation of machine-learning models to measure individualized treatment effects from randomized clinical trial data with time-to-event outcomes
In randomized clinical trials, regression models can be used to explore the relationships between patients' variables (e.g., clinical, pathological or lifestyle variables, and also biomarker or genomics data) and the magnitude of treatment effect. Our aim is to evaluate the value of flexible machine learning models that can incorporate interactions and nonlinear effects of high-dimensional data to estimate individualized treatment recommendations in the setting of such trials with time-to-event…

Effective Versions of Strong Measure Zero
Matthew Rayman
#toXiv_bot_toot

Macroscopicity of quantum superposition
Xiao-Fu Peng
https://arxiv.org/abs/2506.14458 https://arxiv.org/pdf/2506.14458

Macroscopicity of quantum superposition
In this paper, we define a universal measure of macroscopicity $β$ in the form of, ({\em experimentally observed coherence time})/({\em characteristic time required to repeatably distinguish the components of a quantum superposition state}), to divide the quantum/classical (Q-C) boundary. The analysis shows that, for a matter-wave interferometer, covering systems from electron to macromolecular, the measure of its macroscopicity is expressed by $β=pθd/8\hbar$, and it consistently yields $β<…

The superposition principle for the continuity equation with singular flux
Stefano Almi, Riccarda Rossi, Giuseppe Savar\'e
https://arxiv.org/abs/2506.15333

The superposition principle for the continuity equation with singular flux
Representation results for absolutely continuous curves $μ:[0,T]\to \mathcal{P}_p(\mathbb{R}^d)$, $p>1$, with values in the Wasserstein space $(\mathcal{P}_p(\mathbb{R}^d),W_p)$ of Borel probability measures in $\mathbb{R}^d$ with finite $p$-moment, provide a crucial tool to study evolutionary PDEs in a measure-theoretic setting. They are strictly related to the superposition principle for measure-valued solutions to the continuity equation. This paper addresses the extension of these results …

Sharp $L^p$-estimates for wave equation on $ax b$ groups
Yunxiang Wang, Lixin Yan
https://arxiv.org/abs/2506.17531 https://arxiv.org/…

Sharp $L^p$-estimates for wave equation on $ax+b$ groups
Let $G$ be the group $\mathbb{R}_+\ltimes \mathbb{R}^n$ endowed with Riemannian symmetric space metric $d$ and the right Haar measure $\mathrm{d} ρ$ which is of $ax+b$ type, and $L$ be the positive definite distinguished left invariant Laplacian on $G$. Let $u=u(t,\cdot)$ be the solution of $u_{tt}+Lu=0$ with initial conditions $u|_{t=0}=f$ and $u_t|_{t=0}=g$. In this article we show that for a fixed $t \in{\mathbb R}$ and every $1

Note that nowhere in that definition is there actually any attempt to define or measure “intelligence” — a term which we are scarcely able to define and to measure even for humans!
Note also that the definition is inherently a broad one and a shifting one. It’s relative to humans •and• relative to recent history.
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Distinguishing Ram Pressure from Tidal Interactions: the Size-Shape Difference (SSD) measure
Rory Smith, Stephanie Tonnesen, Katarina Kraljic, Paula Calderon-Castillo, Antonino Marasco, Yara Jaffe, Benedetta Vulcani, Bianca M. Poggianti
https://arxiv.org/abs/2506.13884

Distinguishing Ram Pressure from Tidal Interactions: the Size-Shape Difference (SSD) measure
Context: In dense environments, disk galaxies can be subjected to tidal interactions with other galaxies and/or ram pressure stripping. Some morphological features are clearly associated with one or the other interaction (e.g. tidal bridges vs long one-sided linear gas tails). But, under certain circumstances, both mechanisms can result in morphological features that could be confused, such as lopsided or asymmetric disks and unwinding spiral arms. Aims: Our aim is to develop new measures for…

On measure-valued solutions for a structured population model with transfers
Pierre Magal (IMB), Ga\"el Raoul (CMAP, MERGE)
https://arxiv.org/abs/2506.13225

On measure-valued solutions for a structured population model with transfers
We consider a transfer operator where two interacting cells carrying non-negative traits transfer a random fraction of their trait to each other. These transfers can lead to population having singular distributions in trait. We extend the definition of the transfer operator to non-negative measures with a finite second moment, and we discuss the regularity of the fixed distributions of that transfer operator. Finally, we consider a dynamic transfer model where an initial population distribution…

Measures of Systems of Oscillators and Properties of Trajectories
Vsevolod Sakbaev (Steklov Mathematical Institute of Russian Academy of Sciences), Igor Volovich (Steklov Mathematical Institute of Russian Academy of Sciences)
https://arxiv.org/abs/2506.18093

Measures of Systems of Oscillators and Properties of Trajectories
Properties of trajectories of systems of harmonic oscillators equipped with a point, absolutely continuous or singular measure are considered in this paper. Linear flow of an infinite system of oscillators on an infinite dimensional tori in the phase space are studied. It was shown in [28] that for infinite-dimensional linear flows of a countable system of oscillators there is a new type of trajectories that is not periodic and has no transitive projection on any 4-dimensional symplectic subspa…

This https://arxiv.org/abs/2310.18730 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Beyond $BV$: new pairings and Gauss-Green formulas for measure fields with divergence measure
A new notion of pairing between measure vector fields with divergence measure and scalar functions, which are not required to be weakly differentiable, is introduced. In particular, in the case of essentially bounded divergence-measure fields, the functions may not be of bounded variation. This naturally leads to the definition of $BV$-like function classes on which these pairings are well defined. Despite the lack of fine properties for such functions, our pairings surprisingly preserve many f…

Note that nowhere in that definition is there actually any attempt to define or measure “intelligence” — a term which we are scarcely able to define and to measure even for humans!
Note also that the definition is inherently a broad one and a shifting one. It’s relative to humans •and• relative to recent history.
4/

On the logarithmic equilibrium measure on curves
Damian D\k{a}browski, Tuomas Orponen
https://arxiv.org/abs/2506.07752 https://arxiv.…

On the logarithmic equilibrium measure on curves
Let $μ$ be the logarithmic equilibrium measure on a compact set $γ\subset \mathbb{R}^{d}$. We prove that $μ$ is absolutely continuous with respect to the length measure on the part of $γ$ which can be locally expressed as the graph of a $C^{1,α}$-function $\mathbb{R} \to \mathbb{R}^{d - 1}$, $α> 0$. For $d = 2$, at least in the case where $γ$ is a compact $C^{1,α}$-graph, our result can also be deduced from the classical fact that $μ$ coincides with the harmonic measure of $Ω=\mathb…

The Hyper-Kamiokande experiment: input to the update of the European Strategy for Particle Physics
Kamiokande Collaboration
https://arxiv.org/abs/2506.16641

The Hyper-Kamiokande experiment: input to the update of the European Strategy for Particle Physics
Hyper-Kamiokande is a large infrastructure for particle and astroparticle physics being built in Japan and aiming to start operations by the end of 2027 whose objective is to address the most important questions in science today, for instance how the universe began and evolved. It aims to measure with the highest precision the leptonic Charge-Parity violation parameter using both a Mega-Watt intense neutrino beam and high-statistics atmospheric neutrino samples. The combination of these sampl…

Expansion Signatures in 35 HII Regions traced by SOFIA [CII] Emission
Timothy Faerber, Loren D. Anderson, Matteo Luisi, Lars Bonne, Nicola Schneider, Volker Ossenkopf-Okada, Alexander Tielens, Robert Simon, Markus R\"ollig
https://arxiv.org/abs/2506.16700

Expansion Signatures in 35 HII Regions traced by SOFIA [CII] Emission
We analyze the expansion signatures of 35 HII regions mapped in [CII] 158 micron emission by the Stratospheric Observatory for Infrared Astronomy (SOFIA). The [CII] emission primarily traces photodissociation regions (PDRs) at the transition between ionized and neutral gas. The brightness and narrow linewidth of [C II] allow us to measure PDR expansion. Bubble-shaped regions often exhibit expansion, while irregular-shaped ones are less likely to. Of the 35 HII regions, 12 (~34%) exhibit clear e…

Generalized $u$-Gibbs measures for $C^\infty$ diffeomorphisms
Snir Ben Ovadia, David Burguet
https://arxiv.org/abs/2506.18238 https://

Generalized $u$-Gibbs measures for $C^\infty$ diffeomorphisms
We show that for every $C^\infty$ diffeomorphism of a closed Riemannian manifold, if there exists a positive volume set of points which admit some expansion with a positive Lyapunov exponent (in a weak sense) then there exists an invariant probability measure with a disintegration by absolutely continuous conditionals on smoothly embedded disks subordinated to unstable leaves. As an application, we prove a strong version of Viana conjecture in any dimension, generalizing a recent result of the …

Dynamical covering sets in self-similar sets
Balazs Barany, Henna Koivusalo, Sascha Troscheit
https://arxiv.org/abs/2506.18447 https://

Dynamical covering sets in self-similar sets
We study the size of \emph{dynamical covering sets} on a self-similar set. Dynamical covering sets are limsup sets generated by placing shrinking target sets around points along an orbit in a dynamical system. In the case when the target sets are balls with sizes depending on the centre, we determine the size of the dynamical covering set as a function of the shrinking rate. In particular, we find sharp conditions guaranteeing when full Dvoretzky-type covering, and full measure occur. We also c…

Adapted Measures for Markov Interval Maps
{\L}ukasz Krzywo\'n
https://arxiv.org/abs/2506.14971 https://arxiv.org/pdf/2506.14971…

Adapted Measures for Markov Interval Maps
Adapted invariant measures, such as the natural area measure (Liouville), have a central place in the development of ergodic theory for billiards. These measures ensure local Pesin charts can be constructed almost everywhere even in the nonuniformly hyperbolic setting. Recently, for Sinai billiards satisfying certain conditions, the unique measure of maximal entropy has been shown to be adapted. However, not all positive entropy measures are. To investigate the connection between entropy and ad…

Attracting measures
Julian Newman, Peter Ashwin
https://arxiv.org/abs/2506.02136 https://arxiv.org/pdf/2506.02136

Attracting measures
Under mild assumptions, the SRB measure $μ$ associated to an Axiom A attractor $A$ has the following properties: (i) the empirical measure starting at a typical point near $A$ converges weakly to $μ$; (ii) the pushforward of any Lebesgue-absolutely continuous probability measure supported near $A$ converges weakly to $μ$. In general, a measure with the first property is called a "physical measure", and physical measures are recognised as generally important in their own right. In this paper,…