Tootfinder

Differential invariants and equivalence of 2-order ODEs
Valeriy A. Yumaguzhin
https://arxiv.org/abs/2508.21439 https://arxiv.org/pdf/2508.21439

Differential invariants and equivalence of 2-order ODEs
This paper is devoted to ordinary differential equations of the form $$\frac{\partial^2y}{(\partial x)^2}=a^3(x, y)(\frac{\partial y}{\partial x})^3+a^2(x, y)(\frac{\partial y}{\partial x})^2+a^1(x,y)\frac{\partial y}{\partial x}+a^0(x, y) $$ The algebra of all differential invariants of point transformations is constructed for these equations in general position and the equivalence problem is solved for them.

A new government procurement platform intended to encourage more small businesses to bid for contracts, driving competition, has seen its costs balloon from an intended £1.5 million to £12 million as multinational consultancies won contracts to build and manage it.
https://www.

Cost of streamlined government procurement portal balloons by eight times
A new government procurement platform intended to encourage more small businesses to bid for contracts, driving competition, has seen its costs balloon from an intended ...

Partial Bloch--Kato Selmer groups of $B$-pairs as delta functors
Rustam Steingart
https://arxiv.org/abs/2510.00775 https://arxiv.org/pdf/2510.00775

Partial Bloch--Kato Selmer groups of $B$-pairs as delta functors
In this article we revisit the partial Selmer groups introduced by Ding in cohomological degree one. On the subcategory of partially de Rham positive $B$-pairs we extend them to higher cohomological degree and show that the resulting groups form a cohomological delta functor satisfying a variant of the Euler--Poincaré characteristic formula and Tate duality.

Two things are worth noticing right now:
1. The military brass *did not* respond well to Trump and Hegseth.
2. The deployment to #Portland keeps getting delayed.
The military will never say "no" to the president (unless he's literally ordering them to open fire on unarmed civilians or something equally obviously illegal). But there are ways to not comply that don't necessarily involve refusal. Brass showing that they aren't aligned with Trump may weaken his billionaire backers, who might be realizing now that weak dictators who can't lead their militaries tend to get toppled... and their oligarch-backers tend to end up against walls.
If folks being ordered to send troops to #PDX don't want to comply, delaying until the there's an initial response from the lawsuit would be basically impossible to detect. The deployment to LA went far too fast, running into logistical challenges like troops sleeping on the floor. The delays we've already seen could indicate either a more careful approach or quiet resistance.
Trump will continue to escalate at every chance he gets. I would be surprised if PDX didn't give him a fight. I doubt the troops will become more interested in serving a guy who's stabbed them in the back and wasted their time at every opportunity.
It is still possible troops just won't deploy. Trump will make something up about how just the threat of an intervention was enough to make things safe or something like that. If we see that, it's 100% the military telling him to kick rocks because he's not competent enough to know when to back down.
Honestly, I think Trump wants revenge for the resistance PDX put up at the end of his last term. Any backing down from that is absolutely a big loss for him.

Digital Twins: McKean-Pontryagin Control for Partially Observed Physical Twins
Manfred Opper, Sebastian Reich
https://arxiv.org/abs/2510.00937 https://arxi…

Digital Twins: McKean-Pontryagin Control for Partially Observed Physical Twins
Optimal control for fully observed diffusion processes is well established and has led to numerous numerical implementations based on, for example, Bellman's principle, model free reinforcement learning, Pontryagin's maximum principle, and model predictive control. On the contrary, much fewer algorithms are available for optimal control of partially observed processes. However, this scenario is central to the digital twin paradigm where a physical twin is partially observed and control laws are…

wtf? https://flipboard.com/@gothamist/gothamist-igeoft02z/-/a-jX9GlHNnTEud--xneaXXZg:a:3807498986-/0

NYCHA building partially collapses in Bronx due to explosion, city officials report no injuries
A public housing tower partially collapsed in the South Bronx on Wednesday morning due to an explosion, forcing residents to evacuate, New York City …

On Friday, federal judges in Massachusetts and Rhode Island issued rulings
that could soon bring relief to millions of Americans whose Supplemental Nutrition Assistance Program (SNAP) benefits are set to expire on Nov. 1,
requiring the Trump administration to fund the program, at least partially while the legal proceedings continue.
The SNAP program, commonly referred to as food stamps, is among many government programs affectedby the ongoing shutdown,
and has been one…

JUST IN: Two Federal Judges Rule Trump Admin Must Fund Food Stamps — At Least Partially
On Friday, federal judges in Massachusetts and Rhode Island issued rulings that could soon bring relief to millions of Americans whose Supplemental Nutrition Assistance Program (SNAP) benefits are set to expire on Nov. 1.

So erfolgreich sind Temu und Shein in Deutschland
Verbraucher bestellen gern im Internet. Portale wie Temu und Shein haben stark an Popularität gewonnen, wie eine Studie zeigt.
https://www.he…

The Effective Reactivity for Capturing Brownian Motion by Partially Reactive Patches on a Spherical Surface
Denis S. Grebenkov, Michael J. Ward
https://arxiv.org/abs/2509.26381 …

The Effective Reactivity for Capturing Brownian Motion by Partially Reactive Patches on a Spherical Surface
We analyze the trapping of diffusing ligands, modeled as Brownian particles, by a sphere that has $N$ partially reactive boundary patches, each of small area, on an otherwise reflecting boundary. For such a structured target, the partial reactivity of each boundary patch is characterized by a Robin boundary condition, with a local boundary reactivity $κ_i$ for $i=1,\ldots,N$. For any spatial arrangement of well-separated patches on the surface of the sphere, the method of matched asymptotic ex…

A Dual Ensemble Kalman Filter Approach to Robust Control of Nonlinear Systems: An Application to Partial Differential Equations
Anant A. Joshi, Saviz Mowlavi, Mouhacine Benosman
https://arxiv.org/abs/2508.21684

A Dual Ensemble Kalman Filter Approach to Robust Control of Nonlinear Systems: An Application to Partial Differential Equations
This paper considers the problem of data-driven robust control design for nonlinear systems, for instance, obtained when discretizing nonlinear partial differential equations (PDEs). A robust learning control approach is developed for nonlinear affine in control systems based on Lyapunov redesign technique. The robust control is developed as a sum of an optimal learning control which stabilizes the system in absence of disturbances, and an additive Lyapunov-based robustification term which hand…