We experimentally demonstrate that a squeezed probe optical field can improve the sensitivity of the magnetic field measurements based on nonlinear magneto-optical rotation (NMOR) with an amplitude-modulated pump when compared to a coherent probe field under identical conditions. To realize an all-atomic magnetometer prototype, we utilize a nonlinear atomic interaction, known as polarization self-rotation(PSR), to produce a squeezed probe field. An independent pump field, amplitude-modulated at the Larmor frequency of the bias magnetic field, allows us to extend the range of most sensitive NMOR measurements to sub-Gauss magnetic fields. While the overall sensitivity of the magnetometer is rather low ($>250\mathrm{pT}/\sqrt{\mathrm{Hz}}$, we clearly observe a $15\%$ sensitivity improvement when the squeezed probe is used. Our observations confirm the recently reported quantum enhancement in a modulated atomic magnetometer arXiv:2108.01519 [quant-ph].

Conventional noise analysis in atomic-ensemble sensing assumes a continuous-medium approximation, thereby treating the atomic system as a deterministic dielectric. Here, we demonstrate that this assumption breaks down due to the discrete, particulate nature of the ensemble, giving rise to an intrinsic "atomic granularity noise" (AGN) that fundamentally competes with the optical measurement noise (OMN, typically photon shot noise). By introducing a discrete-atom statistical framework, we derive a unified noise-scaling law governed by a single dimensionless resource ratio, $\mathcal{R} = \bar{N}_{\mathrm{ph}}/\bar{N}_{\mathrm{at}}$ at (the photon-to-atom flux ratio). This law predicts a continuous crossover from an OMN-limited regime to an AGN-limited regime. Crucially, our results reveal a counter-intuitive constraint for sensor optimization: increasing optical probe power -- standard practice to mitigate OMN -- can paradoxically degrade sensitivity by driving the system into the AGN-dominated regime. Furthermore, we identify a critical resource threshold, $\mathcal{R}_{\mathrm{crit}}$, beyond which quantum-enhanced metrology using non-classical light fails to improve sensitivity, as it becomes limited by the AGN.

I re-examine a recent work by G. Landi and G. E. Landi. [arXiv:1808.06708 [physics.ins-det]], in which the authors claim that the resolution of a tracker ca vary linearly with the number of detection layers, $N$, that is, faster than the commonly known $\sqrt{N}$ variation, for a tracker of fixed length, in case the precision of the position measurement is allowed to vary from layer to layer, i.e. heteroscedasticity, and an appropriate analysis method, a weighted least squares fit, is used.

General reasoning represents a long-standing and formidable challenge in artificial intelligence (AI). Recent breakthroughs, exemplified by large language models (LLMs)1,2 and chain-of-thought (CoT) prompting3, have achieved considerable success on foundational reasoning tasks. However, this success is heavily contingent on extensive human-annotated demonstrations and the capabilities of models are still insufficient for more complex problems. Here we show that the reasoning abilities of LLMs can be incentivized through pure reinforcement learning (RL), obviating the need for human-labelled reasoning trajectories. The proposed RL framework facilitates the emergent development of advanced reasoning patterns, such as self-reflection, verification and dynamic strategy adaptation. Consequently, the trained model achieves superior performance on verifiable tasks such as mathematics, coding competitions and STEM fields, surpassing its counterparts trained through conventional supervised learning on human demonstrations. Moreover, the emergent reasoning patterns exhibited by these large-scale models can be systematically used to guide and enhance the reasoning capabilities of smaller models. A new artificial intelligence model, DeepSeek-R1, is introduced, demonstrating that the reasoning abilities of large language models can be incentivized through pure reinforcement learning, removing the need for human-annotated demonstrations.

In the quiet backwaters of cs.CV, cs.LG and stat.ML, a cornucopia of new learning systems is emerging from a primordial soup of mathematics-learning systems with no need for external supervision. To date, little thought has been given to how these self-supervised learners have sprung into being or the principles that govern their continuing diversification. After a period of deliberate study and dispassionate judgement during which each author set their Zoom virtual background to a separate Galapagos island, we now entertain no doubt that each of these learning machines are lineal descendants of some older and generally extinct species. We make five contributions: (1) We gather and catalogue row-major arrays of machine learning specimens, each exhibiting heritable discriminative features; (2) We document a mutation mechanism by which almost imperceptible changes are introduced to the genotype of new systems, but their phenotype (birdsong in the form of tweets and vestigial plumage such as press releases) communicates dramatic changes; (3) We propose a unifying theory of self-supervised machine evolution and compare to other unifying theories on standard unifying theory benchmarks, where we establish a new (and unifying) state of the art; (4) We discuss the importance of digital biodiversity, in light of the endearingly optimistic Paris Agreement.

See math-ph/0205036 for an expanded version.

This is a survey of the existing digital collections of French mathematical literature, run by non-profit organizations. This includes research monographs, serials, proceedings, Ph. D. theses, collected works, books and personal websites.

The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this article provides a stepping stone towards a solution to this problem. In particular, we determine new examples of type I and non-type-I groups in this class, and we completely classify the irreducible unitary representations of the torsion-free groups, which are shown to be type I. When these groups are totally disconnected, they admit a faithful action by automorphisms on an infinite locally-finite regular tree; this work thus provides new examples of automorphism groups of regular trees with interesting representation theory, adding to recent work on this topic.

In this paper it is argued that Barad's Agential Realism, an approach to quantum mechanics originating in the philosophy of Niels Bohr, can be the basis of a 'theory of everything' consistent with a proposal of Wheeler that observer-participancy is the foundation of everything. On the one hand, agential realism can be grounded in models of self-organisation such as the hypercycles of Eigen, while on the other agential realism, by virtue of the 'discursive practices' that constitute one aspect of the theory, implies the possibility of the generation of physical phenomena through acts of specification originating at a more fundamental level. Included in phenomena that may be generated by such a mechanism are the origin and evolution of life, and human capacities such as mathematical and musical intuition.

We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any "Theory of Everything" obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation-theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras in the spirit of Dynkin's classic papers and are written for mathematicians.