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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...

arXiv CS 1d ago

Blow-ups of order types of positive density

Announce Type: cross Abstract: Order types are an equivalence relation between point configurations that capture their combinatorial and convexity properties. Let $P$ be a $\kappa$-colored sequence of $n \ge d+1$ points in general position in $\mathbb{R}^d$. Let $\rho$ be a $\kappa$-colored order type on $k \le d+1$ points that has positive density on $P$; that is, for some constant $\delta >0$, there are $\delta \cdot \binom{n}{k}$ $k$-point subsequences of $P$ that have the same order type...

arXiv CS 1d ago

Collisional energy transfer in ethanimine + He system

Announce Type: new Abstract: The ethanimine molecule, CH3CHNH, is one of the prebiotic molecules detected by astronomers in chemically-rich molecular clouds in the Galactic Center. The observations indicate a non-equilibrium distribution of rotational state populations in both the E- and Z-isomers of ethanimine, resulting from the competition between radiative processes and collisions with background gases such as He and H2. Accurate interpretation of these observations requires the use of...

arXiv Physics 1d ago

GenFT: A Generative Parameter-Efficient Fine-Tuning Method for Pretrained Foundation Models

arXiv:2506.11042v2 Announce Type: replace Abstract: Parameter-efficient fine-tuning (PEFT) has emerged as a resource-efficient strategy for adapting Pretrained Foundation Models (PFMs) by learning a small number of task-specific updates $\Delta W$. Existing methods often learn $\Delta W$ largely independently of pretrained weights $W_0$, or exploit $W_0$ mainly through initialization or simple reparameterization. To further leverage the structural information encoded in $W_0$, we propose...

arXiv CS 5d ago

Reversible double cyclic codes over a chain ring

arXiv:2606.06367v1 Announce Type: new Abstract: In this paper, we study the structure of double cyclic codes of length $(\gamma,\delta)$ over $\mathbb F_q+u\mathbb F_q, u^2=0$. We also study the dual of double cyclic code of length $(\gamma,\delta)$ and give a minimal spanning set of double cyclic codes. Moreover, we study the necessary and sufficient conditions for a double cyclic code to be reversible and reversible-complement double cyclic code and with the help of these codes, we...

arXiv CS 5d ago

A Near-Optimal Offline Algorithm for Dynamic All-Pairs Shortest Paths in Planar Digraphs

arXiv:2606.01809v1 Announce Type: new Abstract: In the planar, dynamic All-Pairs Shortest Paths (APSP) problem, a planar, weighted digraph $G$ undergoes a sequence of edge weight updates and the goal is to maintain a data structure on $G$, that can quickly answer distance queries between any two vertices $x,y \in V(G)$. The currently best algorithms for this problem require $\tilde{O}(n^{2/3})$ worst-case update and query time, while conditional lower bounds show that either update or query...

arXiv CS 8d ago

Scaling Self-Evolving Agents via Parametric Memory

arXiv:2606.04536v1 Announce Type: new Abstract: Existing memory-augmented LLM agents store past experience exclusively in prompt space, as textual summaries or retrieved passages, while keeping model parameters frozen throughout a rollout. Such agents can \emph{look up} what they have seen but cannot \emph{learn from} it: their policy is unchanged by experience, and any information dropped from the context is permanently lost. We introduce \texttt{TMEM}, a self-evolving parametric memory...

arXiv CS 6d ago

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...

arXiv CS 7d ago

Chemical tuning of magnetic ordering and cryogenic magnetocaloric response in zircon-type Gd1-xErxVO4

arXiv:2606.08916v1 Announce Type: cross Abstract: Chemical substitution offers an effective route to tune magnetic ordering and magnetocaloric performance in rare-earth oxides for cryogenic refrigeration. Here we investigate the structural evo lution, magnetic properties, and magnetocaloric effect of polycrystalline zircon-type Gd1-xErxVO4 (x=0, 0.1, 0.25, 0.5, and 0.75). Powder X-ray diffraction confirms that all samples crystallize in the tetragonal zircon structure without detectable...

arXiv Physics 1d ago

Pressure-robust and quasioptimal Discontinuous Galerkin discretisations of the $p$-Stokes problem

arXiv:2606.09586v1 Announce Type: new Abstract: In the present paper, we propose Local Discontinuous Galerkin (LDG) approximations for a nonlinear system of $p$-Stokes type, having $(p,\delta)$-structure. On the basis of the primal formulation, we prove well-posedness and stability (a priori estimates) of the methods under truly minimal regularity assumptions. We show that the first method possesses a pressure-robust and quasi-optimal error estimate, and discuss its consequences.

arXiv CS 1d ago