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heise | Neue Funktionen für die Vision Pro: Was noch vor visionOS 26 kam
Mit visionOS 2.4 und 2.5 bringt Apple sein KI-System auf die Vision Pro und verbessert den eingeschränkten Gastmodus. Das ist aber nicht alles.

Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models
Hedayat Fathi, Marzia A. Cremona, Federico Severino
https://arxiv.org/abs/2506.17773

Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models
In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or, more generally, regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of this Hilbert space. …

ChromeOS: Google kündigt neue KI-Funktionen und Chromebook mit Mediatek-Chip an
Google hat gemeinsam mit Lenovo ein neues Chromebook-Plus-Modell mit Mediatek-ARM-Chip angekündigt, das mehr KI-Aufgaben direkt auf dem Gerät ausführen kann. 

Balanced Boolean functions with few-valued Walsh spectra parameterized by $P(x^2 x)$
Qiancheng Zhang, Kangquan Li, Longjiang Qu
https://arxiv.org/abs/2506.19521

Balanced Boolean functions with few-valued Walsh spectra parameterized by $P(x^2+x)$
Boolean functions with few-valued spectra have wide applications in cryptography, coding theory, sequence designs, etc. In this paper, we further study the parametric construction approach to obtain balanced Boolean functions using $2$-to-$1$ mappings of the form $P(x^2+x)$, where $P$ denotes carefully selected permutation polynomials. The key contributions of this work are twofold: (1) We establish a new family of four-valued spectrum Boolean functions. This family includes Boolean functions w…

Liouville function, von Mangoldt function and norm forms at random binary forms
Yijie Diao
https://arxiv.org/abs/2506.18065 https://a…

Liouville function, von Mangoldt function and norm forms at random binary forms
We analyze the average behavior of various arithmetic functions at the values of degree $d$ binary forms ordered by height, with probability $1$. This approach yields averaged versions of the Chowla conjecture and the Bateman-Horn conjecture for random binary forms. Furthermore, we show that the rational Hasse principle holds for almost all Châtelet varieties defined by a fixed norm form of degree $e$ and by varying binary forms of fixed degree $d$, provided $e$ divides $d$. This proves an ave…

Moment-like maps and real algebraic functions with prescribed preimages
Naoki Kitazawa
https://arxiv.org/abs/2506.17791 https://arxiv…

Moment-like maps and real algebraic functions with prescribed preimages
We discuss a problem on singularity theory of differentiable (smooth) or real algebraic maps which is different from knowing existence and has been difficult: constructing explcit real algebraic functions. We discuss construction of real algebraic functions with exactly one singular value, the singular points being of definite type, and prescribed preimages of single points. We discuss generalizations of the canonical projection of the unit sphere around the pole and the Morse-Bott functions …

Functional programming isn't just for Haskell developers. It's for #PHP developers, too. "Thinking Functionally in PHP" is available from LeanPub.
https://leanpub.com/thinking-functiona

The noncommutative residue, divergence theorems and the spectral geometry functional
Jian Wang, Yong Wang
https://arxiv.org/abs/2506.18038 https://

The noncommutative residue, divergence theorems and the spectral geometry functional
In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the B-algebra. Furthermore, we present some spectral geometric functionals which we call spectral divergence functionals, and we calculate the spectral divergence functionals of manifolds with (or without) boundary.

FuncVul: An Effective Function Level Vulnerability Detection Model using LLM and Code Chunk
Sajal Halder, Muhammad Ejaz Ahmed, Seyit Camtepe
https://arxiv.org/abs/2506.19453

FuncVul: An Effective Function Level Vulnerability Detection Model using LLM and Code Chunk
Software supply chain vulnerabilities arise when attackers exploit weaknesses by injecting vulnerable code into widely used packages or libraries within software repositories. While most existing approaches focus on identifying vulnerable packages or libraries, they often overlook the specific functions responsible for these vulnerabilities. Pinpointing vulnerable functions within packages or libraries is critical, as it can significantly reduce the risks associated with using open-source softw…

Paracetamol aus Plastik: Wissenschaftler stellen Schmerzmittel aus Müll her
Wissenschaftler haben einen Weg gefunden, Schmerzmittel aus Plastikflaschen zu produzieren. Wie das funktioniert und wo es noch Optimierungsbedarf gibt.