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Exact output statistics of Icart's encoding in the exceptional \(j=0\) case
Announce Type: cross Abstract: Icart's encoding is a classical deterministic map from finite fields to elliptic curves and a basic ingredient in early hash-to-curve constructions. We determine the exact one-output distribution of this map in the exceptional \(j=0\) case. More precisely, for \[ E_{0,b}:Y^2=X^3+b,\ q\equiv2\pmod3, \] we compute the complete fibre distribution of \(f_{0,b}:\mathbb F_q\to E_{0,b}(\mathbb F_q)\).
Extreme Points of the $(0,\delta)$-LDP Polytope with Small Input Size and Arbitrary Output Sizes
Announce Type: new Abstract: The structure of locally differentially private (LDP) mechanisms can be understood through the geometry of the corresponding privacy polytope. While the extreme points of the \( (\epsilon,0)\)-LDP polytope are well characterized (Kairouz \emph{et al.}, 2014; Holohan \emph{et al.}, 2017; Pensia \emph{et al.}, 2017), comparatively little is known for the \((\epsilon,\delta)\)-LDP polytope with \(\delta>0\). Recent work (Elangovan and Jog, 2024) has shown that even...
Decentralized Stochastic Nonconvex Optimization under the $(L_0,L_1)$-Smoothness
arXiv:2509.08726v3 Announce Type: replace-cross Abstract: This paper focuses on the decentralized stochastic optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$ over a connected network of $n$ agents, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};{\boldsymbol \xi}_i)\right]$ which satisfies the $(L_0,L_1)$-smooth condition but possibly nonconvex and each random variable ${\boldsymbol \xi}_i$ follows distribution ${\mathcal...
Fast and Robust Convergence Rate for TD(0) with Linear Function Approximation, Universal Learning Steps and I.I.D. Samples
arXiv:2606.05967v1 Announce Type: cross Abstract: In this paper, we study the finite-time behavior of the TD(0) temporal-difference method with linear function approximation (LFA). We consider on-policy independent and identically distributed (i.i.d.) samples, a constant learning step, and the Polyak-Juditsky averaging method.
Fast and Robust Convergence Rate for TD(0) with Linear Function Approximation, Universal Learning Steps and I.I.D. Samples
arXiv:2606.05967v2 Announce Type: replace-cross Abstract: In this paper, we study the finite-time behavior of the TD(0) temporal-difference method with linear function approximation (LFA). We consider on-policy independent and identically distributed (i.i.d.) samples, a constant learning step, and the Polyak-Juditsky averaging method.
Sharp periodic Ge concentration modulations beyond the conduction band valley wavevector $k_0$ in nuclear spin-free Si quantum wells
new Abstract: Periodic Ge modulations within strained Si quantum wells in SiGe heterostructures offer a route to deterministically enhance conduction-band valley splitting in Si, a key requirement for scalable spin-qubit quantum computing. Efficient enhancement requires modulations in the order of the Si valley wavevector $k_0$ (9.7 nm$^{-1}$), corresponding to a period of 0.64 nm and near-monolayer growth control. Using nuclear-spin-free molecular beam epitaxy with $^{28}$Si and $^{72}$Ge,...
Locked in heated rivalry with researcher, Microsoft fixes 0-day they disclosed
Microsoft on Tuesday released fixes for two high-severity zero-days that were disclosed by a researcher who has been locked in a testy beef with the software giant. Nightmare Eclipse, the pseudonym the researcher goes by, released a handful of high-severity vulnerabilities in recent months, making them zero-days that had the potential to be exploited in the wild. The researcher has said the disclosures, which included proof-of-concept code, came after Microsoft reneged on an arrangement the...
Angry bug hunter with Microsoft beef drops new Windows 0-day
They are angry at Redmond and will have their revenge. Nightmare Eclipse, the prolific bug hunter and possibly disgruntled ex-Microsoft employee, disclosed another zero-day vulnerability just hours after Redmond issued a record-breaking number of CVEs and fixes for June Patch Tuesday. The latest zero-day, RoguePlanet, targets Microsoft Defender and works against fully patched Windows 10 and Windows 11 systems, according to the researcher, who also released proof-of-concept exploit code for...
The memory of $\omega$-regular and BC($\Sigma_2^0$) objectives
arXiv:2502.05840v3 Announce Type: replace Abstract: In the context of 2-player zero-sum infinite-duration games played on (potentially infinite) graphs, the memory of an objective is the smallest integer k such that in any game won by Eve, she has a strategy with <= k states of memory. For omega-regular objectives, checking whether the memory equals a given number k was not known to be decidable. In this work, we focus on objectives in BC(Sigma0^2), i.e. recognised by a potentially infinite...