In this work, a continuous-energy residual Monte Carlo (RMC) algorithm is extended to systems with spatial dependence and inelastic scattering reactions. The method incorporates real continuous-energy data and includes all relevant scattering and fission processes. A piecewise constant finite element trial space is used to approximate the transport solution and construct the residual representation, while importance sampling and weight cancellation techniques are employed to control particle weights and ensure stable convergence. The algorithm is demonstrated in one-dimensional and zero-dimensional continuous-energy problems, including a simple one-dimensional fuel rod. Comparisons with standard Monte Carlo simulations illustrated that, although RMC requires additional precomputation of quadrature terms, the iterative RMC process is more efficient.

Abstract In this paper, we study the variation of Selmer groups in families of modular Galois representations that are congruent modulo a fixed prime $p \geq 5$ . Motivated by analogies with Goldfeld’s conjecture on ranks in quadratic twist families of elliptic curves, we investigate the stability of Selmer groups defined over $\mathbb{Q}$ via Greenberg’s local conditions under congruences of residual Galois representations. Let X be a positive real number. Fix a residual representation $\bar{\rho}$ and a corresponding modular form f of weight 2 and optimal level. We count the number of level-raising modular forms g of weight 2 that are congruent to f modulo p , with level $N_g\leq X$ , such that the p -rank of the Selmer groups of g equals that of f . Under some mild assumptions on $\bar{\rho}$ , we prove that this count grows at least as fast as $X (\log X)^{\alpha - 1}$ as $X \to \infty$ , for an explicit constant $\alpha \gt 0$ . The main result is a partial generalisation of theorems of Ono and Skinner on rank-zero quadratic twists to the setting of modular forms and Selmer groups.

Sentiment analysis for live video comments with variational residual representations

Residual Monte Carlo (RMC) methods have been previously used in neutron transport for monoenergetic and multigroup problems. In this paper, we implement an RMC algorithm for solving continuous energy problems with elastic scattering functions. We use a piecewise constant finite-element trial space to approximate the transport solution and build the residual representation. Because of the complexity of the scattering term, an analytic distribution cannot be computed for the residual; instead, we sample source particles directly from the scattering integrand using unnormalized importance sampling. We achieve exponentially convergent Monte Carlo (MC) with the use of an additional weight cancellation technique to reduce the magnitude of particle weights. We then demonstrate the algorithm on continuous energy problems and compare the results with standard MC simulations to demonstrate the increased efficiency of the RMC method.

Let T E =W 2 be a rank 2 crystalline G ℚ p -representation of weights [0,1] with non-ordinary reduction where W is the ring of integers of some extension of ℚ p , and let T ¯ E be its residual representation. Suppose l≥2 and fix some big enough N which only depends on T E . We show that the group Ext cr,[0,l-1] 1 (T ¯ E ,T ¯ E ) (Definition 2.30) of extensions with crystalline liftings of weights [0,l-1], which are themselves extensions of G ℚ p -representations which are congruent to T E (modp N ), is isomorphic to the group of finite flat extensions Ext fl 1 (T ¯ E ,T ¯ E ) ([18, Chapter 1.1]). In addition, we construct a certain functor 𝒟 of deformations of T ¯ E with liftings of certain type and weights [0,l-1], satisfying certain congruences with T E , show 𝒟 has a representable hull, and demonstrate some evidence that t 𝒟 ⊂Ext cr,[0,l-1] 1 (T ¯ E ,T ¯ E ) and V T 𝔪 ⊗W/𝔪 W ∈𝒟(T 𝔪 ⊗W/𝔪 W ) where T is the Hecke algebra T l (Γ 1 (M)), m is its maximal ideal given by a weight l eigenform of level Γ 1 (M) whose Galois representation is congruent modulo p N to T E , and V T 𝔪 is its associated Galois representation.

Neural Radiance Field (NeRF)-based volumetric video has revolutionized visual media by delivering photorealistic Free-Viewpoint Video (FVV) experiences that provide audiences with unprecedented immersion and interactivity. However, the substantial data volumes pose significant challenges for storage and transmission. Existing solutions typically optimize NeRF representation and compression independently or focus on a single fixed rate-distortion (RD) tradeoff. In this paper, we propose VRVVC, a novel end-to-end joint optimization variable-rate framework for volumetric video compression that achieves variable bitrates using a single model while maintaining superior RD performance. Specifically, VRVVC introduces a compact tri-plane implicit residual representation for inter-frame modeling of long-duration dynamic scenes, effectively reducing temporal redundancy. We further propose a variable-rate residual representation compression scheme that leverages a learnable quantization and a tiny MLP-based entropy model. This approach enables variable bitrates through the utilization of predefined Lagrange multipliers to manage the quantization error of all latent representations. Finally, we present an end-to-end progressive training strategy combined with a multi-rate-distortion loss function to optimize the entire framework. Extensive experiments demonstrate that VRVVC achieves a wide range of variable bitrates within a single model and surpasses the RD performance of existing methods across various datasets.

During high-speed flight, the aircraft causes rapid compression of the surrounding air, creating a complex turbulent flow field. This high-speed flow field interferes with the optical transmission of optical imaging systems, resulting in high-frequency random displacement, blurring, intensity attenuation, or saturation of the target scene. Aero-optical effects severely degrade imaging quality and target recognition capabilities. Based on the spectral characteristics of aero-optical degraded images and the deep learning approach, this paper proposes an adaptive frequency selection network (AFS-NET) for correction. To learn multi-scale and accurate features, we develop cascaded global and local attention mechanism modules to capture long-distance dependency and extensive contextual information. To deeply excavate the frequency component, an adaptive frequency separation and fusion strategy is proposed to guide the image restoration. Integrating both spatial and frequency domain processing and learning the residual representation between the observed data and the underlying ideal data, the proposed method assists in restoring aero-optical degraded images and significantly improves the quality and efficiency of image reconstruction.

Let $G$ be a split semisimple group over a global function field $K$. Given a cuspidal automorphic representation $\Pi$ of $G$ satisfying a technical hypothesis, we prove that for almost all primes $\ell$, there is a cyclic base change lifting of $\Pi$ along any $\mathbb {Z}/\ell \mathbb {Z}$-extension of $K$. Our proof does not rely on any trace formulas; instead it is based on using modularity lifting theorems, together with a Smith theory argument, to obtain base change for residual representations. As an application, we also prove that for any split semisimple group $G$ over a local function field $F$, and almost all primes $\ell$, any irreducible admissible representation of $G(F)$ admits a base change along any $\mathbb {Z}/\ell \mathbb {Z}$-extension of $F$. Finally, we characterize local base change more explicitly for a class of toral representations considered in work of Chan and Oi.

Attributed graph subspace clustering with residual compensation guided by adaptive dual manifold regularization

The gyrus, a pivotal cortical folding pattern, is essential for integrating brain structure-function. This study focuses on 2-Hinge and 3-Hinge folds, characterized by the gyral convergence from various directions. Existing voxel-level studies may not adequately capture the precise spatial relationships within cortical folding patterns, especially when relying solely on local cortical characteristics due to their variable shapes and homogeneous frequency-specific features. To overcome these challenges, we introduced a novel model that combines spatial distribution, morphological structure, and functional magnetic resonance imaging data. We utilized spatio-morphological residual representations to enhance and extract subtle variations in cortical spatial distribution and morphological structure during blood oxygenation, integrating these with functional magnetic resonance imaging embeddings using self-attention for spatio-morphological-temporal representations. Testing these representations for identifying cortical folding patterns, including sulci, gyri, 2-Hinge, and 2-Hinge folds, and evaluating the impact of phenotypic data (e.g. stimulus) on recognition, our experimental results demonstrate the model's superior performance, revealing significant differences in cortical folding patterns under various stimulus. These differences are also evident in the characteristics of sulci and gyri folds between genders, with 3-Hinge showing more variations. Our findings indicate that our representations of cortical folding patterns could serve as biomarkers for understanding brain structure-function correlations.

While visual working memory has a short lifetime, residual representations can persist and disrupt currently maintained information. This phenomenon is known as proactive interference (PI), and the present study investigated whether the representations underpinning item-specific PI lose details over time. This would be expected if the memories underlying PI are susceptible to temporal processes such as decay, which is strongly disputed. In four experiments, a modified version of the recent probes task was used, requiring participants to determine whether a probe matched one of two recently presented targets. The probe sometimes matched an untested target from a previous trial, or varied in its resemblance to it, and the amount of time separating trials varied. Results revealed that PI was specific and highly disruptive at very short intervals, but its effect diminished over time. At longer intervals, a milder form of PI was present and produced by probes that were only similar to a recently encountered target. In summary, residual visual representations may remain accurate for a few seconds after encoding, before losing precise details and continuing to endure in an inexact state. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

For an odd prime p and a supersingular elliptic curve over a number field, this article introduces a multi-signed residual Selmer group, under certain hypotheses on the base field. This group depends purely on the residual representation at p , yet captures information about the Iwasawa theoretic invariants of the signed p^\infty -Selmer group that arise in supersingular Iwasawa theory. Working in this residual setting provides a natural framework for studying congruences modulo p in Iwasawa theory.

Abstract Let F be a CM number field. We generalise existing automorphy lifting theorems for regular residually irreducible p-adic Galois representations over F by relaxing the big image assumption on the residual representation.

We give a proof of a soft version of the p-converse to a theorem of Gross–Zagier and Kolyvagin for non-CM elliptic curves with good ordinary reduction at \(p >3\) under the irreducibility assumption on the residual representation. In particular, no condition on the conductor is imposed. Combining with the known results, we obtain the equivalence for every elliptic curve E over \(\mathbb {Q}\).

Os agrotóxicos são contaminantes de natureza química que podem ser encontrados nos alimentos. Os de maior representatividade residual incluem os inseticidas, fungicidas e herbicidas. Objetivou-se analisar a presença de resíduos de agrotóxicos em alface (Lactuca sativa L.) comercializada em feiras livres. A pesquisa, com abordagem quantitativa e transversal, foi realizada em feiras livres de Chapecó/SC, com produtores feirantes de vegetais in natura e consumidores. Realizou-se, ainda, análise de resíduos de agrotóxicos em alface de cultivo convencional e orgânico. A coleta de dados constituiu-se na aplicação de um questionário semiestruturado a todos os produtores e a uma amostra de consumidores. As análises de resíduos de agrotóxicos foram realizadas em alface, por ser o alimento mais adquirido pelos consumidores. Os agrotóxicos pesquisados incluíram azoxistrobina, deltametrina, imidacloprido e glifosato, por serem os mais frequentemente utilizados nas propriedades e no cultivo de hortaliças. Dos 67 feirantes em atividade nas sete feiras livres, 30 eram produtores de hortaliças e frutas, e, deles, 17 eram produtores convencionais e 13 de orgânicos. As análises de resíduos de agrotóxicos em alface de produção convencional apresentaram resíduos de azoxistrobina e imidacloprido, porém abaixo dos limites máximos de resíduos permitidos pela Agência Nacional de Vigilância Sanitária (Anvisa). Nas amostras de alface orgânica não foram detectados resíduos dos agrotóxicos pesquisados. Das análises de resíduos em alface, infere-se que o alimento é seguro quanto aos agrotóxicos pesquisados e que políticas públicas municipais devem priorizar o monitoramento sistemático, visando garantir a segurança dos alimentos e estimular a produção de alimentos orgânicos.

Let [Formula: see text] be a prime number and [Formula: see text] a positive even integer less than [Formula: see text]. In this paper, we find the strongly divisible modules corresponding to the Galois stable lattices in each 2-dimensional semi-stable non-crystalline representation of [Formula: see text] with Hodge–Tate weights [Formula: see text] whose mod-[Formula: see text] reductions are corresponding to nontrivial extensions of two distinct characters. We use these results to construct the irreducible components of the semi-stable deformation rings in Hodge–Tate weights [Formula: see text] of the non-split reducible residual representations of [Formula: see text].

The most common disease that is found among people across the world is Diabetes and it is predicted to increase more in the upcoming years by The World Health Organization (WHO). People who are diabetic for a longer period are more likely to have Diabetic Retinopathy (DR), an eye disease which can lead to blindness and this cannot be reversed. One of the severe stage problems of DR is Retinal Neovascularization (RN), i.e., outburst of retinal blood vessels. Residual Network (ResNet) has an effective technique called Skip or Residual Connections which solves the problem of vanishing gradient during backpropagation. ResNet50 has 50 layers which is a deep network that omits signal representations and learns from residual representations leading to predict RN with 88.97% accuracy.

We consider the residues at the poles in the half plane \(Re(s)\ge 0\) of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit, attached to Fourier coefficients admitted by the corresponding residual representation. We find this orbit in each case.

Multimodal medical image fusion using gradient domain guided filter random walk and side window filtering in framelet domain

We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois representations over Q \mathbb {Q} when the residual representation is reducible. Our approach is via a semi-simple local-global compatibility of the completed cohomology and a Taylor-Wiles patching argument for the completed homology in this case. As a key input, we generalize the work of Skinner-Wiles in the ordinary case. In addition, we also treat the residually irreducible case at the end of the paper. Combining with people’s earlier work, we can prove the Fontaine-Mazur conjecture completely in the regular case when p ≥ 5 p\geq 5 .