Solid-state batteries (SSBs) are considered next-generation energy storage technologies due to their intrinsic safety and high energy density. However, their widespread commercial introduction is still hindered by slow ion transport and unstable interfaces. Reticular compounds, including metal-organic frameworks (MOFs) and covalent organic frameworks (COFs), offer a growing toolset to address these limitations through ordered porosity, modular chemical functionality, and structural tunability. Solid electrolytes with directed ion pathways, mechanically flexible cathodes to stabilize high-voltage chemistries, and anode interfaces that regulate ion flow and prevent dendritic growth can all be effectively engineered throughreticular chemistry. This review first outlines the primary challenges of SSBs, subsequently conducting a critical role of reticular compounds within electrolytes, cathodes, and anodes, emphasizing the influence of reticular modulation strategies and the recent plethora in framework-integrated batteries. Operando and multiscale characterizations are essential for elucidating these framework behaviors, and a dedicated section is also included to contextualize these design concepts and demonstrate how such modularity functions in practical SSBs. Finally, future directions are proposed to guide the systematic design of reticular compounds based SSBs, aiming to motivate the wider community in advancing safe, high-performance, and scalable solid-state energy storage systems.

MeTime is an opensource R package for reproducible analysis of longitudinal metabolomics data. It builds upon a central S4 container, metime_analyser, that stores multiple datasets, associated metadata and analysis outputs, enabling unified handling of complex longitudinal studies. Analyses are constructed by piping modular functions, beginning with data transformations (mod_), followed by calculations (calc_), and optional meta-analysis (meta_), so entire workflows remain transparent and easy to modify. MeTime wraps numerous existing methods within a consistent interface, including sample and metabolite distributions, correlation and distance matrices, dimensionality reduction (PCA, UMAP, tSNE), random forest imputation and feature selection via Boruta, eigenmetabolites and WGCNA based clustering, conservation index analysis, regression models (linear, mixed effects, and generalized additive), and partial correlation networks. By retaining all intermediate results and provenance within the container, MeTime facilitates iterative exploration and ensures reproducible reporting via automatically generated HTML and PDF outputs. Comprehensive user guides, case studies and reference documentation accompany the package, making MeTime a versatile platform for longitudinal omics workflows.

Abstract Modular product architecture creation methods often fail to fully account for assembly constraints, limiting their practical applicability. This challenge is spread across industry but has greater consequences for small and medium-sized enterprises (SMEs), where design decisions must align with constrained production capabilities. This study examines how the integration of Design for Assembly (DfA) principles into Modular Function Deployment (MFD) can enhance the development of modular product architectures. Through a retrospective, case-based analysis of the Senseair RDS (refrigerant detection system), the research reconstructs key design and organisational decisions and evaluates how a DfA-expanded MFD method could have influenced them. The analysis combines document review, two participatory workshops, and entry–exit surveys to map decisions, challenges, and barriers. Results show that early modular reasoning was constrained by resource pressure, compliance demands, and departmental separation, leading to duplicated work and late clarification of interfaces. Application of the proposed method highlighted opportunities for earlier identification of assembly trade-offs, clearer justification of architectural choices, and improved cross-functional communication. Participants found the method conceptually useful but effort-intensive, emphasising the need for lightweight training and adaptation to existing SME routines. Mapping of workshop findings to the Technological-Economic-Regulatory-Organisational (TERO) framework revealed that organisational and economic barriers dominate over purely technical ones. The study concludes that structured approaches such as the DfA-MFD method act most effectively as sense-making tools that formalise existing knowledge, promote assembly-oriented design decisions, and support incremental improvement of modular architectures under industrial constraints.

In this paper, we determine mod 2 Galois representations ρ ¯ ψ , 2 : G K : = Gal ( K ¯ / K ) → GSp 4 ( 𝔽 2 ) associated to the mirror motives of rank 4 with pure weight 3 coming from the Dwork quintic family X 0 5 + X 1 5 + X 2 5 + X 3 5 + X 4 5 - 5 ψ X 0 X 1 X 2 X 3 X 4 = 0 , ψ ∈ K defined over a number field K under the irreducibility condition of the quintic trinomial f ψ below. Applying this result, when K = F is a totally real field, for some at most quadratic totally real extension M / F , we prove that ρ ¯ ψ , 2 | G M is associated to a Hilbert–Siegel modular Hecke eigen cusp form for GSp 4 ( 𝔸 M ) of parallel weight three. In the course of the proof, we observe that the image of such a mod 2 representation is governed by reciprocity of the quintic trinomial f ψ ( x ) = 4 x 5 - 5 ψ x 4 + 1 , ψ ∈ K whose decomposition field is generically of type 5-th symmetric group S 5 . This enable us to use results on the modularity of 2-dimensional, totally odd Artin representations of Gal ( F ¯ / F ) due to Shu Sasaki or Pilloni–Shu and several Langlands functorial lifts for Hilbert cusp forms. Then, it guarantees the existence of a desired Hilbert–Siegel modular cusp form of parallel weight three matching with the Hodge type of the compatible system in question. A twisted version is also discussed and it is related to general quintic trinomials.

We construct a differential operator on sheaves of p-adic modular forms defined over the locus of p-rank ≥ 1 of the Siegel threefold, by applying a revisited version of the approach that S. Howe recently introduced in [7] to construct the theta operator in the elliptic case.

Abstract We study neutrino mass generation within the framework of non-holomorphic modular symmetry proposed by Qu and Ding. In this formalism, neutrino masses are generated via the Type-I seesaw mechanism, where the Yukawa couplings depend on non-holomorphic modular forms. The viability of the model is examined through a $$\chi ^2$$ χ 2 analysis using current neutrino oscillation data. The $$\chi ^2_{min}$$ χ min 2 value is found to be 7.06 for normal hierarchy(NH). All neutrino oscillation parameters are consistent within their $$1\sigma $$ 1 σ allowed ranges, except the atmospheric mixing angle $$\sin ^2\theta _{23},$$ sin 2 θ 23 , which is predicted to lie in the second octant. The Dirac CP-violating phase( $$\delta _{CP}$$ δ CP ) is constrained to the first and fourth quadrants, indicating relatively weak CP violation. These predictions can be tested in future long-baseline neutrino oscillation experiments. The sum of neutrino masses is compatible with the stringent bound proposed by the DESI experiment. However, the inverted hierarchy(IH) is not viable in this model, as the predicted value of $$\chi ^2_{min}$$ χ min 2 exceeds 100, and the mixing angles $$\sin ^2\theta _{12}$$ sin 2 θ 12 and $$\sin ^2\theta _{23}$$ sin 2 θ 23 lie outside the $$3 \sigma $$ 3 σ allowed ranges.

Divisor problems for restricted Fourier coefficients of modular forms

We introduce a method for producing vector-valued automorphic forms on unitary groups from scalar-valued ones. As an application, we construct an explicit example. Our strategy employs certain differential operators. It is inspired by work of Cléry and van der Geer in the setting of Siegel modular forms, but it also requires overcoming challenges that do not arise in the Siegel setting.

Precise and efficient delivery of messenger RNA (mRNA) to extrahepatic tissues remains a major challenge in advancing mRNA-based therapeutics. Although enveloped viruses and virus-like particles (VLPs) serve as natural RNA delivery systems with varied extrahepatic targeting capabilities, their clinical translation is often hampered by bottlenecks in tunability, safety, immunogenicity, and scalability. Here, we developed a bottom-up self-assembling enveloped virus-mimicking particle (EVMP) composed of highly simplified yet high-performance virus-mimicking peptide (VMP) and tissue-targeting envelope phospholipids. By employing virtual screening via molecular dynamics simulation, directed evolution via key assembling domain mutation, strategic N-terminal fatty acylation modifications, and precise adjustments to envelope phospholipid composition, we achieved high-efficiency delivery of mRNA to organs such as the lungs and spleen. Notably, the optimized lung-targeted EVMP achieved transfection in 37% of total lung cells, including 73% of endothelial cells and 28% of immune cells. In a metastatic lung tumor model, the lead EVMP loaded with IL-12 mRNA effectively suppressed tumor progression. Notably, EVMP demonstrated excellent long-term biosafety and the capacity for repeated administration, owing to their minimal immunogenic profile. This biomimetic virus-mimicking nanoplatform represents a transformative advance in mRNA delivery technologies, enabling effective and safe mRNA-based therapy for extrahepatic diseases. Furthermore, it establishes a generalizable strategy for bottom-up engineering of biomimetic materials with programmable tissue tropism and modular functionality.

This paper is an in-depth examination of split points in Musielak-Orlicz spaces LΦ , giving a full description of their geometry, and answering various outstanding questions about the geometry of these spaces. The discussion is based on the classical duality arguments together with the recent concepts of the theory of non-uniformly convex spaces and variable-exponent analysis. The key achievements of the paper may be concluded as follows. To begin with, we create conditions which are such as to ensure that split points exist. They coincide with the strict convexity of the modular function Φ(x,·), the Δ₂-condition of validity of Φ and the conjugated version, along with some assumptions of spatial symmetry. Second, we obtain a blame-sharing characterization in the form of introducing a correction term D(x,g). This expression is a generalization of the popular system of Giles that includes ideas of the modular fixed-point theory. Third, we examine the computational factors of determining split points. We find that at L(p) > 1 the instability index is computationally difficult. Specifically, we explain the cases where the identification process is unsuccessful in the Lebesgue spaces of variable-exponent Lp(x). Lastly, we demonstrate the applicability of the theory to an application to variable-exponent partial differential equations. Specifically, we consider the use of the property of split points in the norm-attainment of solutions of the equation: -Δ p(x) u = f These results imply a number of possible extensions, such as additional research studies in the context of noncommutative Musielak-Orlicz spaces.

Abstract In this paper, we establish two types of upper bound on the vanishing order of Jacobi forms at infinity. The first type is for classical Jacobi forms, which is optimal in a certain sense. The second type is for Jacobi forms of lattice index. Based on this bound, we obtain a lower bound on the slope of orthogonal modular forms, and we prove that the module of symmetric formal Fourier–Jacobi series on ⁢ O ( m , 2 ) {\mathop{\hbox{}\mathrm{O}}\nolimits(m,2)} has finite rank.

We present MXtalTools, a flexible Python package for the data-driven modeling of molecular crystals, facilitating machine learning studies of the molecular solid state. MXtalTools comprises several classes of utilities: (1) synthesis, collation, and curation of molecule and crystal data sets, (2) integrated workflows for model training and inference, (3) crystal parametrization and representation, (4) crystal structure sampling and optimization, (5) end-to-end differentiable crystal sampling, construction, and analysis. Our modular functions can be integrated into existing workflows or combined and used to build novel modeling pipelines. MXtalTools leverages CUDA acceleration to enable high-throughput crystal modeling. The Python code is available open-source on our GitHub page, with detailed documentation on ReadTheDocs.

Abstract Background Cardiac arrhythmia is one of the major global health burdens being responsible for leading to stroke and heart failure. Managing this high risk disease at an earlier level remained a point of concern for clinicians and researchers [1, 2]. Purpose Our study is focused in identifying such endogenous transcription regulatory microRNAs (miRNAs) that possess the potential to target earlier molecular risks of the arrhythmia including hypertension and renal burden. Methods Hub genes prediction of microRNAs and their potential target genes from the microarray data sets, microRNAs targets prediction on 8mer seed sequences matching bases from miRBAse, and targetscan, Genes functional enrichment analysis, PPI network development, cohort validation of miRNAs and their respective target genes in hub modular form. Results Screening from overlapped expression of arrhythmia causative genes including sinoatrial response regulators, cardiac cells membrane polarity regulators, axis of cardio-nervous regulators and hypertension regulators elucidated the role of set of modulatory endogenous gene silencing microRNAs. Micro RNA 101-3p and microRNA 23-3p with significant risk nexus genes management including ZFH X3, HCN4, KCN3, ADR B1, SOX 6, MED and HSP 9 etc involving management of beta adrenergic receptors activity, sodium importer activity, BMP receptor activity, postsynaptic membrane potential regulators, cation channels and transporters regulation, and dopamine sodium transporter etc. Conclusion These microRNAs with potential of simultaneous regulation of major arrhythmia risks associated genes at the basal molecular level propose their future significance in therapeutic and advanced diagnostic modeling.

A bstract In Type II Calabi-Yau string compactifications, S-duality predicts that suitable generating series of BPS indices counting microstates of D4-D2-D0 black holes are in general mock modular forms of higher depth. The non-holomorphic contributions needed to cancel the anomaly under modular transformations involve certain indefinite theta series with kernels constructed from generalized error functions. Physically, these contributions are expected to arise from a spectral asymmetry in the continuum of scattering states of n BPS dyons with mutually non-local charges. For n = 2, the (standard, depth one) error function completion was derived long ago by explicitly computing the bosonic and fermionic density of states in the two-body supersymmetric quantum mechanics. Here we derive the general non-holomorphic completion for an arbitrary number of centers by evaluating the refined Witten index of the supersymmetric quantum mechanics using localization. In a nutshell, the index reduces to an integral over ℝ 3 n − 3 (the relative location of the centers), and splits into an integral over the 2 n – 2 dimensional phase space of BPS ground states times an integral over n – 1 transverse directions, which ultimately produces the expected generalized error functions.

To address the unobservability of distribution networks caused by insufficient coverage of measurement terminals as well as communication failures and missing data, and to cope with operating-state fluctuations induced by distributed generation integration and external environmental disturbances, this paper proposes an integrated state-estimation and voltage-regulation strategy that combines distribution-network-partitioning-based optimal PMU placement with pseudo-measurement construction using power transfer distribution factors (PTDFs). First, nodal reactive-power sensitivity information is derived from the power-flow Jacobian matrix, and an improved modularity function is employed to obtain the optimal partitioning of the distribution network, based on which PMUs are deployed at partition boundary buses. Second, PTDF-based power pseudo-measurements are constructed for unobservable buses and incorporated into the measurement model via a measurement transformation; a weighted least-squares method is then adopted to achieve system-wide state estimation. Finally, the estimated voltage states are fed into flexible voltage-regulation devices to enable fast and continuous voltage adjustment across buses. Case studies on the IEEE 33-bus system demonstrate that the proposed method effectively improves voltage quality.

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.

Big-conductance, Ca²+-activated K+ (BK) channels consist of Ca²+- and voltage-sensing, pore-forming α (BKα) subunits and regulatory auxiliary β or γ subunits. Concatenated subunit constructs are powerful tools for elucidating subunit stoichiometry in ion channel gating and regulation, allowing control over subunit arrangement, stoichiometry, and mutation. However, the additional S0 transmembrane segment in BKα places its N- and C-termini on opposite sides of the membrane, preventing tandem BK channel subunit construction by conventional methods. To investigate the atypical 'all-or-none' modulatory function of γ subunits and the subunit stoichiometry of BK channel gating, we developed concatenated constructs containing 2 or 4 BKα subunits by splicing them into modular forms that can be co-expressed to form functional channels. These constructs retained voltage and Ca²+ gating properties similar to intact BK channels. By fusing the LRRC26 (γ1) subunit to the N-terminus of tandem BKα constructs, we found that a single γ1 subunit per α subunit tetramer is sufficient to fully modulate the channel. Furthermore, the L312A mutation in the deep pore region exhibited a stoichiometrically graded effect on voltage-gated BK channel activation. In contrast, a V288A mutation at the selectivity filter induced channel inactivation only when present in all four BKα subunits. Thus, by engineering concatenated BKα constructs, we identified three distinct stoichiometric modes of BK channel gating control by LRRC26, the pore, and the selectivity filter. This study offers new molecular tools and advances our understanding of subunit stoichiometry in BK channel gating and modulation.

The resurgent analysis of asymptotic series has found diverse applications and led to profound insights into our understanding of enumerative geometry, difference equations, and quantum modular forms. Consequently, interactions among these three independent yet intertwined avenues of contemporary research have recently soared. This mini-workshop brought together both senior and junior researchers from each area to clarify the state of the art and establish common ground for collectively addressing the most relevant open questions in the field.

Abstract In specific contract No 12 issued under the framework agreement OC/EFSA/MESE/2023/03, EFSA requested Open Analytics to implement a web application to do a risk assessment for honeybees, solitary bees and bumble bees regarding the use of biocidal products. The software is developed in R and consists of a web‐based tool composed by several modules providing data entry for active substances, uses, metabolites and the modelling of toxicity studies. The application is developed based on the already existing EFSA's web application B‐risk for plant protection products (PPP) in a modular form such that new modules can be added when available, either by the developers of the application or by EFSA.

ABSTRACT Supramolecular cages are powerful tools for molecular recognition and sensing, using well‐defined nanoscale cavities to encapsulate ions, small molecules, and biologically relevant guests with notable selectivity. Over the past three decades, these systems have progressed from simple conceptual assemblies to sophisticated covalent and organometallic architectures that operate in water as chemosensors, delivery vehicles, and separation p. Their analyte detection relies on diverse signal transduction mechanisms, including luminescence, circular dichroism, and Förster resonance energy transfer, enabling the sensing of anions, cations, chiral molecules, drugs, explosives, and environmental pollutants. Relative to classical receptors, cages offer notable advantages such as three‐dimensional preorganization, modular functionalization, and the incorporation of multiple recognition sites within a single discrete framework. However, their broader implementation in real‐world settings is still hampered, primarily by challenges in achieving sufficient stability in water and complex biological fluids. This review outlines design principles for water‐stable cages, discusses analyte‐specific and medium‐related challenges, and surveys recent examples of water‐compatible systems, including their integration into polymeric materials. Finally, we provide a perspective on next‐generation cage‐based chemosensors, emphasizing advanced readout strategies and potential applications in diagnostics, environmental monitoring, and biomedicine.