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Let $π=\{ 2, q \}$ where $q$ is an odd prime. Let $G$ be a finite group of order divisible by a prime $p \in π$. We show that the principal $p$-block of $G$ contains a nontrivial irreducible character of degree not divisible by $2$ nor $q$ and with field of values contained in the $q$th cyclotomic extension. This statement simultaneously provides a principal block version of results of Navarro--Tiep and Giannelli--Hung--Schaeffer Fry--Vallejo.

In these notes, we emphasize Theorems rather than Theories concerning turbulent fluid motion. Such theorems can be viewed as constraints on the theoretical predictions and expectations of some of the greatest scientific minds of the 20th century: Lars Onsager, Andrey Kolmogorov, Lev Landau, Lewis Fry Richardson among others.

Singing style is a crucial aspect of a natural and expressive singing voice. Singers utilize singing styles to convey the feeling or emotion of the songs. Several works have been proposed to control singing style for making the more expressive singing voice. Recently, VibE-SVC successfully controls vibrato by predicting high-frequency F0 contour. In this paper, we introduce a singing voice conversion framework, called VibE-SVC2, to improve singing style conversion performance and controllability. The model offers control over two types of singing styles: a pitch style and a timbre style. For the pitch style, to resolve the pitch-energy entanglement issue that is unresolved in our previous work, we introduce a novel Energy Style Converter to address remaining style information in the energy contour. In addition, we propose a Zero-shot Pitch Style Converter, which mimics the pitch style of reference audio. To expand the controllability of the model, we propose vibrato rate scaling that is an independent control of vibrato extent, which is unavailable in VibE-SVC. For the timbre style, we extend the model to handle a variety of phonation styles. However, addressing specific styles suc

In this paper, we prove one direction of a conjecture of Navarro-Rizo-Schaeffer Fry-Vallejo positing an algorithm to determine from the character table whether a finite group has $2$-generated Sylow $3$-subgroups. This gives further evidence of the blockwise version of the Galois-McKay conjecture (also known as the Alperin-McKay-Navarro conjecture). A key step involves proving the Isaacs-Navarro Galois conjecture for principal blocks for finite groups with a certain structure.

In complex production lines, it is essential to have strict, fast-acting rules to determine whether the system is In Control (InC) or Out of Control (OutC). This study explores a bio-inspired method that digitally mimics ant colony behavior to classify InC/OutC states and forecast imminent transitions requiring maintenance. A case study on industrial potato chip frying provides the application context. During each two-minute frying cycle, sequences of eight temperature readings are collected. Each sequence is treated as a digital ant depositing virtual pheromones, generating a Base Score. New sequences, representing new ants, can either reinforce or weaken this score, leading to a Modified Base Score that reflects the system's evolving condition. Signals such as extreme temperatures, large variations within a sequence, or the detection of change-points contribute to a Threat Score, which is added to the Modified Base Score. Since pheromones naturally decay over time unless reinforced, an Environmental Score is incorporated to reflect recent system dynamics, imitating real ant behavior. This score is calculated from the Modified Base Scores collected over the past hour. The resultin

Let $G$ be a finite group of order divisible by two distinct primes $p$ and $q$. We show that $G$ possesses a non-trivial irreducible character of degree not divisible by $p$ nor $q$ lying in both the principal $p$- and $q$-block whenever $G$ is one of the following: an alternating group $\mathfrak{A}_n$, $n\geq 4$, a symmetric group $\mathfrak{S}_n$, $n\geq 3$, or a finite simple classical group of type A, B, or C, defined in characteristic distinct from $p$ and $q$. This extends earlier results of Navarro-Rizo-Schaeffer Fry for $2\in\{p,q\}$, and in particular completes the proof of an instance of a conjecture of the same authors, e.g., in the case of symmetric and alternating groups.

We describe the methodology used to alias the free-text author/committer identities of the entire World of Code (WoC) collection (version V2604, ~107M distinct author strings over ~6B commits) into canonical persons, extending the fingerprint-based anti-aliasing of ALFAA and the 38M-identity resolution of Fry et al. by an order of magnitude. At this scale the central problem is over-merge, not missed merges: a few bridge identities (bots, role accounts, placeholder emails, multi-author commit fields) transitively weld unrelated clusters through the global union step into million-member "mega-clusters." We report the full experimental record (more than twenty experiments, including unsuccessful ones) behind the deployed design. Node-level gates (information score, project spread, degree) preserve recall but cannot dissolve the mega-cluster; per-value blocklists of high-quality-but-shared attributes are recall-safe but cannot break a redundant mesh; the working composition is a betweenness cut over the exact union graph plus a per-edge classifier trained on 2.6M labels mined from GitHub no-reply identifiers. That classifier, filtering dormant cross-project shingle groups and joined b

Let $G$ be a finite group and let $p$ be a prime. In this paper, we prove a strengthened version of Brauer's height zero conjecture for the principal $p$-block of $G$ that takes the action of a certain group of Galois automorphisms into account. This answers a conjecture recently proposed by Malle, Moretó, Rizo and Schaeffer Fry. We then use this to obtain a structural result which can be seen as a Galois version of the Itô-Michler theorem.

We explore the application of machine learning algorithms specifically to enhance the selection process of Russet potato clones in breeding trials by predicting their suitability for advancement. This study addresses the challenge of efficiently identifying high-yield, disease-resistant, and climate-resilient potato varieties that meet processing industry standards. Leveraging manually collected data from trials in the state of Oregon, we investigate the potential of a wide variety of state-of-the-art binary classification models. The dataset includes 1086 clones, with data on 38 attributes recorded for each clone, focusing on yield, size, appearance, and frying characteristics, with several control varieties planted consistently across four Oregon regions from 2013-2021. We conduct a comprehensive analysis of the dataset that includes preprocessing, feature engineering, and imputation to address missing values. We focus on several key metrics such as accuracy, F1-score, and Matthews correlation coefficient (MCC) for model evaluation. The top-performing models, namely a neural network classifier (Neural Net), histogram-based gradient boosting classifier (HGBC), and a support vector

The state recognition of the environment and objects by robots is generally based on the judgement of the current state as a classification problem. On the other hand, state changes of food in cooking happen continuously and need to be captured not only at a certain time point but also continuously over time. In addition, the state changes of food are complex and cannot be easily described by manual programming. Therefore, we propose a method to recognize the continuous state changes of food for cooking robots through the spoken language using pre-trained large-scale vision-language models. By using models that can compute the similarity between images and texts continuously over time, we can capture the state changes of food while cooking. We also show that by adjusting the weighting of each text prompt based on fitting the similarity changes to a sigmoid function and then performing black-box optimization, more accurate and robust continuous state recognition can be achieved. We demonstrate the effectiveness and limitations of this method by performing the recognition of water boiling, butter melting, egg cooking, and onion stir-frying.

Cooking is a sequential and visually grounded activity, where each step such as chopping, mixing, or frying carries both procedural logic and visual semantics. While recent diffusion models have shown strong capabilities in text-to-image generation, they struggle to handle structured multi-step scenarios like recipe illustration. Additionally, current recipe illustration methods are unable to adjust to the natural variability in recipe length, generating a fixed number of images regardless of the actual instructions structure. To address these limitations, we present CookAnything, a flexible and consistent diffusion-based framework that generates coherent, semantically distinct image sequences from textual cooking instructions of arbitrary length. The framework introduces three key components: (1) Step-wise Regional Control (SRC), which aligns textual steps with corresponding image regions within a single denoising process; (2) Flexible RoPE, a step-aware positional encoding mechanism that enhances both temporal coherence and spatial diversity; and (3) Cross-Step Consistency Control (CSCC), which maintains fine-grained ingredient consistency across steps. Experimental results on re

Humans observe various actions being performed by other humans (physically or in videos/images) and can draw a wide range of inferences about it beyond what they can visually perceive. Such inferences include determining the aspects of the world that make action execution possible (e.g. liquid objects can undergo pouring), predicting how the world will change as a result of the action (e.g. potatoes being golden and crispy after frying), high-level goals associated with the action (e.g. beat the eggs to make an omelet) and reasoning about actions that possibly precede or follow the current action (e.g. crack eggs before whisking or draining pasta after boiling). Similar reasoning ability is highly desirable in autonomous systems that would assist us in performing everyday tasks. To that end, we propose a multi-modal task to learn aforementioned concepts about actions being performed in images. We develop a dataset consisting of 8.5k images and 59.3k inferences about actions grounded in those images, collected from an annotated cooking-video dataset. We propose ActionCOMET, a zero-shot framework to discern knowledge present in language models specific to the provided visual input. W

Starting with the density field equation of a self-gravity fluid in a static Universe, using the Schwinger functional differentiation technique, we derive the field equation of the 4-point correlation function (4PCF) of galaxies in the Gaussian approximation, which contains hierarchically 2PCF and 3PCF. By use of the known solutions of 2PCF and 3PCF, the equation of 4PCF becomes an inhomogeneous, Helmholtz equation, and contains only two physical parameters: the mass $m$ of galaxy and the Jeans wavenumber $k_J$, like the equations of the 2PCF and 3PCF. We obtain the analytical solution of 4PCF that consists of four portions, $η= η^0_{odd} + η^0_{even} +η^{FP} +η^I$, and has a very rich structure. $η^0_{odd}$ and $η^0_{even}$ form the homogeneous solution and depend on boundary conditions. The parity-odd $η^0_{odd}$ is more interesting and qualitatively explains the observed parity-odd data of BOSS CMASS, the parity-even $η^0_{even}$ contains the disconnected 4PCF $η^{disc}$ (arising from a Gaussian random process), and both $η^0_{odd}$ and $η^0_{even}$ are prominent at large scales $r\gtrsim 10$Mpc, and exhibit radial oscillations determined by the Jeans wavenumber. $η^{FP}$ and $

In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on asymptotics or on Monte Carlo simulation of a parametric null model. Here, we present a nonparametric test based on resampling the Fry points of the observed point pattern. Empirical levels and powers of the test are investigated in a simulation study for four point process models with anisotropy induced by different mechanisms. Finally, a real data set is tested for isotropy.