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The growing number of gravitational-wave (GW) observations allows for constraints to be placed on the underlying population of black holes; current estimates show that black hole spins are small, with binaries more likely to have comparable component masses. Since general relativistic effects, such as spin-induced orbital precession and higher order multipole moments, are more likely to be observed for asymmetric binary systems, a direct measurement remains unlikely. Nevertheless, we continue to consistently probe these effects by performing Bayesian inference with our most accurate and computationally expensive models. As the number of GW detections increases, it may soon become infeasible to consistently use these models for analyses. In this paper, we provide a selection criterion that determines when less accurate and computationally cheaper models can be used without giving biased estimates for the population properties of black holes in the Universe. We show that when using our selection criterion, comparable estimates can be obtained for the underlying mass and spin distribution of black holes for a simulated "worst-case" scenario population, while reducing the overall cost

We demonstrate the renormalisability of quantum field theories in four dimensions with elementary self-interacting Dirac fermions and to leading order in the limit of many fermion flavours $N_{\rm f}$. Starting from the underlying divergence structure and using Gross-Neveu-type interactions as a template, we explain why extended four-fermion theories including higher-derivative interactions are well-defined, renormalisable, and predictive with only a few free parameters. We also provide the exact large-$N_{\rm f}$ leading beta functions of couplings and discuss quantum scaling dimensions, universality, $1/N_{\rm f}$ corrections, and extensions to other types of four fermion interactions. Implications for effective theory and model building are indicated.

As of 2025, Generative Artificial Intelligence (GenAI) has become a central tool for productivity across industries. Beyond text generation, GenAI now plays a critical role in coding, data analysis, and research workflows. As large language models (LLMs) continue to evolve, it is essential to assess the reliability and accuracy of their outputs, especially in specialized, high-stakes domains like finance. Most modern LLMs transform text into numerical vectors, which are used in operations such as cosine similarity searches to generate responses. However, this abstraction process can lead to misinterpretation of emotional tone, particularly in nuanced financial contexts. While LLMs generally excel at identifying sentiment in everyday language, these models often struggle with the nuanced, strategically ambiguous language found in earnings call transcripts. Financial disclosures frequently embed sentiment in hedged statements, forward-looking language, and industry-specific jargon, making it difficult even for human analysts to interpret consistently, let alone AI models. This paper presents findings from the Santa Clara Microsoft Practicum Project, led by Professor Charlie Goldenber

Early results by Borel and Cantelli and Chung (Rendiconti del Circolo Matematico di Palermo, 1909) and Erdős (Transactions of the AMS, 1952) have provided bounds for the measure of a limsup set in terms of measures of its constituent sets and their intersections. Recent work by Beresnevich and Velani (Journal of Mathematical Analysis and its Applications, 2023) states that for sequences of balls the measure of the corresponding limsup set being positive is equivalent to a condition on the relationship between the measures of these balls and their pairwise intersections. In this paper, we show that the condition that the sets are balls is strictly necessary in the result of Beresnevich and Velani. Moreover, let $d \in \mathbb{N}$ and let $[0,1]^d$ be equipped with Lebesgue measure $μ$. Fix $m \in \mathbb{N}$. When we drop the condition that the sets are balls, we can find two sequences of sets $(A_i)_{i \in \mathbb{N}}$ and $(B_i)_{i \in \mathbb{N}}$ in $[0,1]^d$ such that $μ(A_i)=μ(B_i)$ for all $i \in \mathbb{N}$ and for any sequence $(i_1,i_2,...,i_l)$ where for all $l \leq m$ we have $μ(A_{i_1}\cap A_{i_2} \cap... \cap A_{i_l})=μ(B_{i_1}\cap B_{i_2} \cap... \cap B_{i_l})$ but $μ

Let $Σ_{g,d}$ an orientable topological surface of genus $g$ with $d$ punctures. When $g = 0$, Deroin and Tholozan studied the class of supra-maximal representations $π_1(Σ_{0,d})\to \mathrm{PSL}_2(\mathbb{R})$, and they showed that the supra-maximal representations form a compact component of a real relative character variety. We study a collection of rank $n$ local systems on $Σ_{g,d}$ which we call of minimal energy. These are generalizations of supra-maximal representations, and underlie polarizable complex variations of Hodge structure for any choice of complex structure on $Σ_{g,d}$. Like the supra-maximal representations, the minimal energy local systems form a compact connected component of a real relative character variety. We show that when the local monodromy data around the punctures is chosen to be unitary and generic, and the relative character variety is nonempty, these minimal energy local systems always exist. When $g > 0$ we show that the minimal energy local systems come from unitary representations of $π_1(Σ_{g,d})$. If $g = 0$ we show that they do not always come from unitary representations, and we study their structure in general.

Beukers and Heckman gave necessary and sufficient conditions for a hypergeometric function $_n F_{n-1}$ to be algebraic. We give a new proof of this theorem by passing through the Mehta-Seshadri correspondence. In particular, we explicitly write down the parabolic bundle corresponding to a unitary hypergeometric local system.

We study the patterns of multipartite entanglement in Chern-Simons theory with compact simple gauge group $G$ and level $k$ for states defined by the path integral on ``link complements'', i.e., compact manifolds whose boundaries consist of $n$ topologically linked tori. We focus on link complements which can be described topologically as fibrations over a Seifert surface. We show that the entanglement structure of such fibered link complement states is controlled by a topological invariant, the monodromy of the fibration. Thus, the entanglement structure of a Chern-Simons link state is not simply a function of the link, but also of the background manifold in which the link is embedded. In particular, we show that any link possesses an embedding into some background that leads to Greenberger--Horne--Zeilinger state (GHZ)-like entanglement. Furthermore, we demonstrate that all fibered links with periodic monodromy have GHZ-like entanglement, i.e., a partial trace on any link component produces a separable state. These results generalize to any three dimensional topological field theory with a dual chiral rational conformal field theory.

We compute various averages over bulk geometries of quantum states prepared by the Chern-Simons path integral, for any level $k$ and compact simple gauge group $G$. We do so by carefully summing over all topologically distinct bulk geometries which have $n$ disjoint boundary tori and a decomposition into space$\times$time of fixed spatial topology. We find that to leading order in the complexity of the state, the typical state contains many types of multiparty entanglement, proving a conjecture of Balasubramanian et al. Additionally, we compute an averaged wave function which captures the leading order statistics of boundary observables in the $n$ torus Chern-Simons Hilbert space.

SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno's software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competiti

Internal spacetime geometry was recently introduced to model certain quantum phenomena using spacetime metrics that are degenerate. We use the Ricci tensors of these metrics to derive a ratio of the bare up and down quark masses, obtaining $m_u/m_d = 9604/19683 \approx .4879$. This value is within the lattice QCD value $.473 \pm .023$, obtained at $2 \operatorname{GeV}$ in the minimal subtraction scheme using supercomputers. Moreover, using the Levi-Cevita Poisson equation, we derive ratios of the dressed electron mass and bare quark masses. For a dressed electron mass of $.511 \operatorname{MeV}$, these ratios yield the bare quark masses $m_u \approx 2.2440 \operatorname{MeV}$ and $m_d \approx 4.599 \operatorname{MeV}$, which are within/near the lattice QCD values $m^{\overline{\operatorname{MS}}}_u = (2.20\pm .10) \operatorname{MeV}$ and $m^{\overline{\operatorname{MS}}}_d = (4.69 \pm .07) \operatorname{MeV}$. Finally, using $4$-accelerations, we derive the ratio $\tilde{m}_u/\tilde{m}_d = 48/49 \approx .98$ of the constituent up and down quark masses. This value is within the $.97 \sim 1$ range of constituent quark models. All of the ratios we obtain are from first principles al

Does talking to others make people more accurate or less accurate on numeric estimates such as quantitative evaluations or probabilistic forecasts? Research on peer-to-peer communication suggests that discussion between people will usually improve belief accuracy, while research on social networks suggests that error can percolate through groups and reduce accuracy. One challenge to interpreting empirical literature is that some studies measure accuracy at the group level, while others measure individual accuracy. We explain how social influence impacts belief accuracy by analyzing a formal model of opinion formation to identify the relationship between individual accuracy, group accuracy, and the network dynamics of belief formation. When opinions become more similar over time, change in individual error is always strictly better than change in group error, by a value equal to the change in variance. We show that change in group error can be decomposed into the influence network centralization, the accuracy/influence correlation ("calibration"), and the averageness/influence correlation ("herding"). Because group dynamics both theoretically and empirically lead people to become mo

The ATLAS collaboration at the LHC has published inclusive cross-section measurements for the single-top and $t\overline{t}$ production modes at center-of-mass energies of $\sqrt{s} = 5.02, 8.16$, $13$, and $13.6$ TeV. Single-top measurements are conducted in the $t$-channel and $tW$ channel. In addition to the nominal cross-section measurements, various measurements of other interesting observables such as the $V_{tb}$ element of the Cabibbo Kobayashi Maskawa (CKM) quark-mixing matrix, the ratio of the inclusive cross-sections between $tq$ and $t\overline{q}$, the ratio of inclusive cross-sections between $t\overline{t}$ and $Z\rightarrow \ell\ell$, and the nuclear modification factor (defined as the ratio of the inclusive $t\overline{t}$ cross section in heavy-ion collisions to the inclusive $t\overline{t}$ cross-section in $pp$ collisions) are also reported. These results are compared to their corresponding SM predictions, calculated at (N)NLO in QCD. All results are in good agreement with SM predictions.

We present unit scaling, a paradigm for designing deep learning models that simplifies the use of low-precision number formats. Training in FP16 or the recently proposed FP8 formats offers substantial efficiency gains, but can lack sufficient range for out-of-the-box training. Unit scaling addresses this by introducing a principled approach to model numerics: seeking unit variance of all weights, activations and gradients at initialisation. Unlike alternative methods, this approach neither requires multiple training runs to find a suitable scale nor has significant computational overhead. We demonstrate the efficacy of unit scaling across a range of models and optimisers. We further show that existing models can be adapted to be unit-scaled, training BERT-Large in FP16 and then FP8 with no degradation in accuracy.

We develop a formalism for calculating the entanglement entropy of an arbitrary spatial region of a gravitating spacetime at a moment of time symmetry. The crucial ingredient is a path integral over embeddings of the region into the overall spacetime, interpretable as a sum over the edge modes associated with the region. We find that the entanglement entropy of a gravitating region equals the minimal surface area among all regions that enclose it. This suggests a notion of "terrestrial holography" where regions of space can encode larger ones, in contrast to the standard form of holography, in which degrees of freedom on the celestial sphere at the boundary of the universe encode the interior.

Approximating Martingale Process (AMP) is proven to be effective for variance reduction in reinforcement learning (RL) in specific cases such as Multiclass Queueing Networks. However, in the already proven cases, the state space is relatively small and all possible state transitions can be iterated through. In this paper, we consider systems in which state space is large and have uncertainties when considering state transitions, thus making AMP a generalized variance-reduction method in RL. Specifically, we will investigate the application of AMP in ride-hailing systems like Uber, where Proximal Policy Optimization (PPO) is incorporated to optimize the policy of matching drivers and customers.