Blackstone agrees to invest an undisclosed sum in South Korea-based Futronic, which makes actuators used in industrial robots, sources say at a ~$675M valuation (Manuel Baigorri/Bloomberg)
https://www.bloomberg.com/news/articles/20
A Hadamard Formula for Equilibrium Envelopes under Parallel Deformation
Ziyu Li
https://arxiv.org/abs/2607.17187 https://arxiv.org/pdf/2607.17187 https://arxiv.org/html/2607.17187
arXiv:2607.17187v1 Announce Type: new
Abstract: Let $(X,\omega_0)$ be a compact K\"ahler manifold, and let $U\Subset X$ have $C^{3,1}$ uniformly strongly pseudoconvex boundary. For the equilibrium envelope $u_0$ associated with $X\setminus U$, the normalized Monge--Amp\`ere measure vanishes on $U$ and equals the background measure $V^{-1}\omega_0^n$ on $X\setminus\overline U$; its remaining component is a singular measure supported on $\partial U$, where $V=\int_X\omega_0^n$. We identify this boundary component as the negative outward Anzellotti trace of a divergence-measure flux current. We then prove a one-sided Hadamard formula for the normalized Monge--Amp\`ere energy along the outward parallel family $U_\varepsilon=\{\rho<\varepsilon\}$. The nonlinear telescoping identity gives the mixed Bedford--Taylor boundary traces that sum up to the trace of the current
\[
\mathcal J_{\mathrm{tot}}
=\frac1V\mathrm{d}^c u_0\wedge\sum_{p=0}^{n-1}(p 1)\omega_{u_0}^p\wedge\omega_0^{n-1-p},
\qquad \omega_{u_0}=\omega_0 \mathrm{d}\mathrm{d}^c u_0.
\]
These results provide a local weak formulation of boundary flux and normal variation for regular interface problems related to Darcy/Hele--Shaw type problems and Monge--Amp\`ere growth.
toXiv_bot_toot
If I had to sum up #Glasgow in one picture ...
He lived his life as if it were a zero-sum game, and at his funeral, everybody agreed his life's contribution was zero-sum.
#humor #gametheory #winwin
Farage's UK far-right party receives record €42 million donation from crypto billionaire. The role of crypto in the tech billionaire push to topple democracy is described in Gil Duran's recent book The Nerd Reich.
https://www.bbc.com/news/articles/c3v4zvyde15o
🔧 The implementation in laravel/horizon#1818 is tiny: sum log1p(size) across all queues, then divide each queue's log1p by that total instead of using the raw job count. No strategy interface, no custom allocator, no new service
🧮 Why log1p? It computes log(1 x), so an empty queue gets weight 0 instead of an undefined log(0). Natural log vs log10 does not matter — the base cancels out during normalization
Bob Iger, Joshua Kushner to buy Lakers from Mark Walter’s ownership group for $12 billion
Less than a year after Dodgers owner Mark Walter bought the Lakers for a record-breaking sum,
L.A.’s iconic NBA franchise is now being sold to Joshua Kushner and Bob Iger for at least $12 billion,
-- $2 billion more than the reported number when Walter bought the team in October from the Buss family.
Joshua Kushner is the founder of venture capital firm Thrive Capital and younge…
It's called Newspeak: war is peace, hate is love.
'Reform UK has received a £36m donation from a British cryptocurrency billionaire - a record for a UK political party.
Ben Delo wrote in the Daily Telegraph, external that he was making the move because he wanted a "fair fight and a level playing field".'
Ben Delo: Reform receives record £36m donation from cryptocurrency billionaire - BBC News
A system is never the sum of its parts its the product of their interaction.
#management #systems_thinking
Citrini Research founder James van Geelen has sold the firm to SemiAnalysis for an undisclosed sum; sources: van Geelen plans to launch a new fund (Bloomberg)
https://www.bloomberg.com/news/articles/2026-09-11/citrini-founder-who…
@… Then you can use the name as a check sum for the “valid from” date of any ID to ensure they really did generate it on the claimed date.
Crosslisted article(s) found for math.ST. https://arxiv.org/list/math.ST/new
[1/1]:
- Stable convergence of partial sum processes towards discontinuous limits
Johannes Brutsche
https://arxiv.org/abs/2608.12740 https://mastoxiv.page/@arXiv_mathPR_bot/117092840163122403
- Bayesian Inference Procedures for A/B Testing: An Overview
M{\aa}rten Schultzberg, Mattias Fr{\aa}nberg
https://arxiv.org/abs/2608.12949 https://mastoxiv.page/@arXiv_statME_bot/117092799825341949
- Estimation of distribution functions, their jumps and interval probabilities under measurement error
Kairat Mynbaev, Carlos Martins-Filho, Chad Brown
https://arxiv.org/abs/2608.13152 https://mastoxiv.page/@arXiv_econEM_bot/117092724945077876
- Extreme principal minors of Wishart and deformed GOE matrices
Zhanrui Dong, Tiefeng Jiang, Tuan Pham, Jianfeng Yao
https://arxiv.org/abs/2608.13154 https://mastoxiv.page/@arXiv_mathPR_bot/117092881421641444
- Sinkhorn Linearization and the Spectral Proxy: Unifying the Statistical and Algorithmic Theory of...
Han Dong, Jiaming Li, Yongqiang Gong, Ruixi Li, Yin Liu
https://arxiv.org/abs/2608.13201 https://mastoxiv.page/@arXiv_statML_bot/117092803789923153
- Weighted cumulative past inaccuracy and Kullback-Leibler divergence based on extropy: properties,...
Bighneswar Sahoo, Suchandan Kayal
https://arxiv.org/abs/2608.13363 https://mastoxiv.page/@arXiv_statME_bot/117092858417590746
- Nearly sharp comparison results for sliced and max-sliced Wasserstein distances
Jonathan Niles-Weed, Jacob Shkrob
https://arxiv.org/abs/2608.13374 https://mastoxiv.page/@arXiv_mathPR_bot/117092901477246948
- Theoretical Properties of Covariate-Adaptive Randomization with a Diverging Number of Covariates
Yuhang Tao, Li-Xin Zhang
https://arxiv.org/abs/2608.13442 https://mastoxiv.page/@arXiv_statME_bot/117092865494823071
- The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity
Martin J. Wainwright
https://arxiv.org/abs/2608.13520 https://mastoxiv.page/@arXiv_csLG_bot/117092942960850473
toXiv_bot_toot
I agree. Good read.
"I unapologetically think a bias in favor of boring #technology is a good thing, but it’s not the only factor that needs to be considered. Technology choices don’t happen in isolation. They have a scope that touches your entire team, organization, and the system that emerges from the sum total of your choices.
Adding technology to your company comes with a…
Achievement unlocked: Objected to tax assessment, and won the objection. And not for an insignificant sum, either.
I guess that counts as successfully adulting?
A Tale of Two Compact Bosons
Christian Ferko, Vishnu Jejjala, Brandon Robinson
https://arxiv.org/abs/2608.06376 https://arxiv.org/pdf/2608.06376 https://arxiv.org/html/2608.06376
arXiv:2608.06376v1 Announce Type: new
Abstract: Neural network field theory (NN-FT) defines a field theory by a network architecture together with a probability density on its latent variables. For compact theories the local Gaussian sector is only part of the story: one must also sum over discrete topological sectors. We review a mixed continuous/discrete latent-variable construction and apply it to two compact bosons. For the Berezinskii--Kosterlitz--Thouless transition, a random Fourier feature spin-wave sampler supplemented by an explicit Coulomb gas vortex sector reproduces the Gaussian critical line below $T_c$, vortex proliferation above $T_c$, the essential singularity of the correlation length, and the Nelson--Kosterlitz jump. For the bosonic string, oscillator modes augmented by momentum--winding labels reproduce circle T-duality, Buscher transformations on constant toroidal backgrounds, self-dual current algebra enhancement, and a toy T-fold. The common lesson is that the same local neural sampler, paired with different discrete topological data, yields physically distinct compact theories. These proceedings are based on arXiv:2604.02313.
toXiv_bot_toot
All across America, the midterm elections are drowning in dark money.
A New York Times review of advertising data, campaign-finance filings and tax records
revealed that about $1 billion in anonymous money is sloshing through the political landscape in 2026,
a staggering sum and yet almost certainly a low-end estimate,
given how difficult this money is to trace.
Sources: TikTok settles a lawsuit before a second California trial over social media harm to minors for an undisclosed sum; Meta and Snap remain defendants (Bloomberg)
https://www.bloomberg.com/news/articles/2026-06-30/tikto…
@… I think this is particularly interesting in the context of the previous "What is the Fediverse?" (Paraphrasing, don't recall exact wording) poll.
If we generally agree that the Fediverse is the total sum of all ActivityPub messages, then it should become quite obvious that presuming how others must use the protocol is a fool's errand at best.
…
Spectral phase transitions in Gaussian multi-index models
Florent Krzakala, Pierre Mergny, Vanessa Piccolo
https://arxiv.org/abs/2608.12183 https://arxiv.org/pdf/2608.12183 https://arxiv.org/html/2608.12183
arXiv:2608.12183v1 Announce Type: new
Abstract: Recovering a low-dimensional latent subspace from nonlinear observations of Gaussian covariates in high dimensions is a fundamental problem in feature learning. Here, we consider Gaussian multi-index models in which the covariates $\boldsymbol{x}_i \stackrel{\mathrm{i.i.d.}}{\sim} \mathcal{N}(0,\boldsymbol{I}_d)$ and the responses $\boldsymbol{y}_i$ depend on $\boldsymbol{x}_i$ only through its projection onto an unknown $r$-dimensional subspace. Earlier work based on approximate message passing (AMP) identified a sharp threshold for weak recovery [Troiani et al., 2025], raising the question of whether it can be attained, without side information, by a spectral method. We answer this affirmatively and develop a general random matrix theory for matrix-valued spectral estimators of the form \[\boldsymbol{D}_n=\frac{1}{n}\sum_{i=1}^n\boldsymbol{T}(\boldsymbol{y}_i)\otimes\boldsymbol{x}_i\boldsymbol{x}_i^\top,\] where $\boldsymbol{T}$ is an arbitrary bounded symmetric matrix-valued preprocessing map of fixed dimension. As $n,d \to \infty$ with $n/d\to\alpha$, we prove that the empirical spectral measure of $\boldsymbol{D}_n$ converges almost surely to a deterministic compactly supported distribution characterized by a matrix-valued self-consistent equation. We then establish a spectral phase transition for the largest eigenvalue: below threshold it sticks to the bulk edge, while above threshold an outlier emerges. We characterize the outlier location through a finite-dimensional deterministic equation and show that the associated spectral estimator achieves weak recovery of the latent subspace. Finally, we prove that the AMP-derived preprocessing of [Defilippis et al., 2025] is optimal among all bounded matrix-valued preprocessing maps of any fixed dimension. Its transition coincides with the AMP weak-recovery threshold, proving the general spectral conjecture of [Defilippis et al., 2025].
toXiv_bot_toot
LSR-Net: Long-Short-Range Operator Learning for Pattern Dynamics on Manifolds
Qian Serena Hou, Zecheng Gan
https://arxiv.org/abs/2607.00750 https://arxiv.org/pdf/2607.00750 https://arxiv.org/html/2607.00750
arXiv:2607.00750v1 Announce Type: new
Abstract: We propose the Long-Short-Range Neural Network (LSR-Net), an extensible operator-learning framework for predicting pattern dynamics on planar domains, spherical surfaces, and general manifolds. The method decomposes the forward evolution operator into a long-range component, represented by a compact Fourier multiplier constructed via the Sum-of-Exponentials (SOE) approximation, and a short-range component adapted to the underlying geometry and its intrinsic symmetries. For general manifolds represented by irregularly sampled point clouds, the long-range component is implemented by Gaussian gridding onto an auxiliary regular grid, where the Fourier multiplier is efficiently applied in k-space using FFT and the result is interpolated back to the original sample points. We evaluate LSR-Net on several benchmark systems, including the Allen-Cahn, Cahn-Hilliard, Schnakenberg, and Turing systems, over planar domains, spherical surfaces, and a blob-shaped manifold. Numerical results demonstrate that LSR-Net consistently achieves higher accuracy and improved stability compared with baseline operator-learning models. In particular, for Allen-Cahn dynamics on the sphere, the RMSE is reduced by approximately three orders of magnitude compared with the Spherical Fourier Neural Operator (SFNO). Rotation and reflection equivariance tests further confirm that the learned operator is consistent with these geometric transformations. These results indicate that LSR-Net provides an effective and robust approach for learning pattern dynamics on complex geometries.
toXiv_bot_toot
Axioms of Continuous Separation
Zhongqiang Yang, Nada Wu
https://arxiv.org/abs/2608.13086 https://arxiv.org/pdf/2608.13086 https://arxiv.org/html/2608.13086
arXiv:2608.13086v1 Announce Type: new
Abstract: For a $T_1$-space $X$, let $Cld(X)$ denote all its nonempty closed subsets and $T_4(X)=\{(F_1,F_2)\in Cld(X)^2:F_1\cap F_2=\emptyset\}$. In terms of closed sets, $X$ is $T_4$ iff for each $(F_1,F_2)\in T_4(X)$, there is a pair of closed sets $\phi_1(F_1,F_2)$ and $\phi_2(F_1,F_2)$ such that their union is $X$ and $F_j\cap \phi_j(F_1,F_2)=\emptyset$ for $j=1,2$. Thus, in this paper, for a topology $\tau$ on $Cld(X)$, we introduce the definition: A $T_1$-space $X$ is called $CT_4$ for the topology $\tau$ if the above maps $\phi_j:T_4(X)\to Cld(X)$ are continuous on $\tau$. Similarly, for $i=1,2,3$, we can define a $T_1$-space to be $CT_i$ for $\tau$. We only consider the Vietoris topology on $Cld(X)$ and show that every $CT_4$-space is countably compact, and every $CT_3$-space is a Fr\'{e}chet-Urysohn space, every separable subspace of a $CT_3$-space is metrizable. We give relevant examples. Any finite-dimensional cubes, the infinite-dimensional cube, any finite-dimensional spheres, and all 0-dimensional compact metrizable spaces are $CT_4$. All infinite discrete spaces, all finite-dimensional Euclidean spaces and all countable limit ordinal spaces are $CT_3$ but not $CT_4$. Also, each metrizable space with a unique non-isolated point is $CT_3$, and is $CT_4$ if it is compact. Moreover, the infinite sum of $CT_3$ spaces is $CT_3$ but not $CT_4$. Every countable space with a unique non-isolated point is $CT_2$, and it is $CT_3$ if and only if it is metrizable. All subfields of real numbers and their complement spaces are $CT_2$ but not $CT_4$; and their $CT_3$ status remains unclear. All uncountable ordinal spaces are not $CT_2$. The one-point compactification of any uncountable discrete space is not $CT_2$. $CT_1$ and $T_1$ are equivalent, hence all spaces above are $CT_1$. Open Problems: is there a non-metrizable $CT_3$ or $CT_4$ space? Is any compact $CT_2$ space $CT_3$ or $CT_4$?
toXiv_bot_toot
Quantifind, whose AI products help banks combat financial crimes such as money laundering, raised $200M led by Summit Partners (Laura Kreutzer/Wall Street Journal)
https://www.wsj.com/pro/private-equity/summit-partners-leads-a-20…
Crosslisted article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/2]:
- Living on the Edge of Effective Field Theory: Near-Extremal Black Holes in Quadratic Gravity
Kelvin Ka-Ho Lam, Gary T. Horowitz, Nicol\'as Yunes
https://arxiv.org/abs/2608.05268 https://mastoxiv.page/@arXiv_grqc_bot/117053119278147418
- Relative entropy of entanglement of Haar random states
Takato Mori, Beni Yoshida
https://arxiv.org/abs/2608.05274 https://mastoxiv.page/@arXiv_quantph_bot/117053252355717367
- Theory of Measurement-Altered Criticality
Kabir Khanna, Sara Murciano, Romain Vasseur
https://arxiv.org/abs/2608.05289 https://mastoxiv.page/@arXiv_condmatstatmech_bot/117053093687616139
- Self-dual $S_3$ gauge theory in 2 1d: lattice model and topological phase transitions
Da-Chuan Lu, Chong Wang, Ashvin Vishwanath
https://arxiv.org/abs/2608.05294 https://mastoxiv.page/@arXiv_condmatstrel_bot/117053135203168433
- 3-form dark energy and cosmic birefringence
Kohei Kamada, Tucker Manton
https://arxiv.org/abs/2608.05296 https://mastoxiv.page/@arXiv_astrophCO_bot/117053109615577309
- GOOFy-compatible 3HDMs and beyond
I. de Medeiros Varzielas, A. Kun\v{c}inas
https://arxiv.org/abs/2608.05304 https://mastoxiv.page/@arXiv_hepph_bot/117053194550154760
- Beyond Borel Windows: A Systematic Optimization Framework for QCD Sum Rules
Raphael M. Albuquerque
https://arxiv.org/abs/2608.05322 https://mastoxiv.page/@arXiv_hepph_bot/117053194943710217
- Quantum information loss
James Fullwood, Wu-zhong Guo, Boyu Yang
https://arxiv.org/abs/2608.05535 https://mastoxiv.page/@arXiv_quantph_bot/117053277916138502
- Coherent and Stochastic Axion Dark Matter from Thermal Relaxation
Gurmani, Cilli, Channuie, Abdujabbarov, Atamurotov, G\"udekli
https://arxiv.org/abs/2608.05538 https://mastoxiv.page/@arXiv_hepph_bot/117053223846614186
- Asymmetric Quantum Oppenheimer-Snyder Collapse
Micha{\l} Bobula, Tomasz Paw{\l}owski
https://arxiv.org/abs/2608.05818 https://mastoxiv.page/@arXiv_grqc_bot/117053193567517392
- Triviality in a Non-Perturbative Second-Order Mean-Field Theory for $\phi^4_4$
Majdouline Borji
https://arxiv.org/abs/2608.05998 https://mastoxiv.page/@arXiv_mathph_bot/117053148149785707
- Measurement-induced entanglement Hamiltonian
Viktor Eisler, Erik Tonni
https://arxiv.org/abs/2608.06006 https://mastoxiv.page/@arXiv_condmatstatmech_bot/117053217162278663
- An Effective String Theory Toolbox for Quantum Hall Interfaces I: Worldsheet Kinematics and Const...
Ken K. W. Ma
https://arxiv.org/abs/2608.06097 https://mastoxiv.page/@arXiv_condmatmeshall_bot/117053183146860935
toXiv_bot_toot
🇺🇦 #NowPlaying on BBCRadio3's #EssentialClassics
Chiara Margarita Cozzolani, I Gemelli & Emiliano Gonzalez‐Toro:
🎵 Laetatus Sum (Vespers)
#ChiaraMargaritaCozzolani #IGemelli #EmilianoGonzalezToro
Polynomially Deformed Normalized Pochhammer Sequences Having Generating Functions With Only Real Non-positive Zeros
Anna Vishnyakova
https://arxiv.org/abs/2608.03723 https://arxiv.org/pdf/2608.03723 https://arxiv.org/html/2608.03723
arXiv:2608.03723v1 Announce Type: new
Abstract: For a given real number $a>0$ and a given real polynomial $P_n\in \mathbb{R}[x]$ of degree $n=0, 1, 2, \ldots$ it is easy to see that $ \sum_{k=0}^\infty \frac{(a)_k}{k!} P_n(k) z^k =\frac{S_{n, a}(z)}{(1-z)^{a n}}, \ |z|<1, $ where $S_{n, a}$ is a real polynomial of degree not greater than $n.$ Here $(a)_k =a(a 1)\cdot \ldots \cdot (a k-1),\ (a)_0 = 1,$ is the rising factorial, or the Pochhammer symbol. We consider the following open problem: to describe the set of real polynomials $P_n\in \mathbb{R}[x]$ of degree $n=0, 1, 2, \ldots,$ such that the corresponding polynomial $S_{n, a}$ has all real non-positive zeros. In the case $a=1$ this problem has been studied in \cite{vish}. We establish several new necessary conditions and several sufficient conditions, present a number of important examples, and formulate several open problems.
toXiv_bot_toot
🇺🇦 #NowPlaying on BBCRadio3's #ThroughTheNight
Henning Voss, Wojciech Parchem, Miroslaw Borzynski, Sine Nomine Chamber Choir, Concerto Polacco Baroque Orchestra, Grzegorz Gerwazy Gorczycki, Olga Pasichnyk & Marek Toporowski:
🎵 Laetatus Sum
#HenningVoss #WojciechParchem
Holographic Renormalization for String-Derived Lovelock--Horndeski Theory
Tianhao Wu
https://arxiv.org/abs/2608.13319 https://arxiv.org/pdf/2608.13319 https://arxiv.org/html/2608.13319
arXiv:2608.13319v1 Announce Type: new
Abstract: String-derived higher-curvature scalar--tensor gravities encode microscopic coupling data in boundary response, raising the question of whether holographic observables can reconstruct the underlying higher-dimensional parameters. We answer this question for the five-dimensional string-derived Lovelock--Horndeski (SDLH) theory on its exact linear-dilaton asymptotically locally AdS branch, constructing the renormalized generating functional for an arbitrary boundary metric and spacetime-dependent scalar source. A boundary-covariant radial hierarchy unifies the variational problem, local backreaction, logarithmic obstruction, finite one-point functions, and Ward identities. Two response determinants organize the recursion, resonant obstructions, and metric--scalar mixing. The Weyl anomaly condenses into an Euler density, a Weyl-squared density, and a single curvature--scalar square whose paired variations generate the metric and scalar obstructions. The resulting renormalized functional carries string-selected coupling data into boundary geometry, operator response, anomaly coefficients, and a calculable interface with gravitational observables. On the regular branch, four scalar-normalization-invariant holographic combinations admit a global rational inverse to the continuous reduced couplings. At fixed compactification dimension the map has maximal rank, while the curvature-anomaly sum reconstructs the higher-dimensional Gauss--Bonnet coefficient without sign ambiguity. Holographic response thus provides an explicit, overdetermined boundary fingerprint of the underlying string reduction.
toXiv_bot_toot
🇺🇦 #NowPlaying on BBCRadio3's #EssentialClassics
Claudio Monteverdi, The Sixteen & Harry Christophers:
🎵 Laetatus sum
#ClaudioMonteverdi #TheSixteen #HarryChristophers
🇺🇦 #NowPlaying on BBCRadio3's #SaturdayMorning
Claudio Monteverdi, Raphaël Pichon & Pygmalion:
🎵 Vespro della Beata Vergine, SV 206: Psalmus "Laetatus sum"
#ClaudioMonteverdi #RaphaëlPichon #Pygmalion
https://open.spotify.com/track/3xvTBGeHBUDIKDeqwWOcbs
🇺🇦 #NowPlaying on KEXP's #PositiveVibrations
Eesah x Echo Slim:
🎵 Sum Ting Nice
#Eesah #EchoSlim
🇺🇦 #NowPlaying on BBCRadio3's #SaturdayMorning
I Fagiolini, The English Cornett and Sackbut Ensemble, Robert Hollingworth & Nicholas Mulroy:
🎵 Vespers of 1610, SV 206: No. 3, Nigra sum
#IFagiolini #TheEnglishCornettandSackbutEnsemble #RobertHollingworth #NicholasMulroy
🇺🇦 #NowPlaying on BBCRadio3's #ThroughTheNight
Claudio Monteverdi, Gabriele Palomba, La Venexiana & Gabriele Palomba:
🎵 Nigra sum, sed formosa
#ClaudioMonteverdi #GabrielePalomba #LaVenexiana
#Spotify
🇺🇦 #NowPlaying on BBCRadio3's #Radio3Breakfast
Grzegorz Gerwazy Gorczycki, Wroclaw Baroque Ensemble, Susan Gilmour Bailey, Matthew Venner, Maciej Gocman, Tomšš Kršl & Andrzej Kosendiak:
🎵 Laetatus sum
#GrzegorzGerwazyGorczycki #WroclawBaroqueEnsemble #SusanGilmourBailey
🇺🇦 #NowPlaying on BBCRadio3's #BBCProms
Claudio Monteverdi, The Sixteen & Harry Christophers:
🎵 Laetatus sum
#ClaudioMonteverdi #TheSixteen #HarryChristophers