Cancer arises from the accumulation of genetic alterations, including chromosomal translocations and deletions. Faulty repair of DNA double-strand breaks can give rise to such chromosomal rearrangements. In this study, we focus on diverse translocations that share a common partner, BCL6 on chromosome 3, which are implicated in diffuse large B-cell lymphoma (DLBCL). Analysis of patient breakpoints identified several breakpoint clusters within BCL6, of which Cluster III is the focus of this work. Here, we investigate the role of non-B DNA structures in imparting chromosomal fragility. In silico analyses, gel shift assays, and circular dichroism confirmed G-quadruplex (G4) formation at BCL6 Cluster III. Mutation studies revealed multiple G4 conformations utilizing distinct G-stretches, including GNG motifs. Disrupting G4-forming sequences in this region enhanced plasmid propagation in E. coli, indicating structure-dependent replication stalling. Sodium bisulfite modification assays detected single-stranded character here, both in plasmids and chromosomal DNA, suggesting additional fragility hotspots within Cluster III. Ex vivo assays showed that the G4 structure blocks transcription as a roadblock. Together, these data demonstrate that G4 folding in BCL6 Cluster III generates partially single-stranded regions, rendering the locus prone to breakage and translocation.

In this paper, we study the asymptotic behavior of continuous- and discrete-time gradient flows of a “lower-unbounded” convex function f on a Hadamard manifold M, particularly their convergence properties to the boundary [Formula: see text] at infinity of M. We establish a duality theorem that the infimum of the gradient-norm [Formula: see text] of f over M is equal to the supremum of the negative of the recession function [Formula: see text] of f over the boundary [Formula: see text], provided the infimum is positive. Further, the infimum and the supremum are obtained by the limit of the gradient flow of f. Our results feature convex optimization ingredients of the moment-weight inequality for reductive group actions, and are applied to noncommutative optimization. We show that gradient descent of the Kempf-Ness function for an unstable orbit converges to a destabilizing 1-parameter subgroup in the Hilbert-Mumford criterion, and the associated moment-map sequence converges to the minimum-norm point of the moment polytope. We show further refinements for operator scaling—the left-right action on a matrix tuple [Formula: see text]. We characterize the gradient-flow limit of operator scaling by a vector-space generalization of the classical Dulmage-Mendelsohn decomposition of a bipartite graph. For a special case of [Formula: see text], we reveal that the limit determines the Kronecker canonical form of a matrix pencil [Formula: see text]. Funding: H. Hirai was supported by the Japan Society for the Promotion of Science (KAKENHI [Grants JP21K19759 and JP24K21315]). K. Sakabe was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation [Grant 556164098]) and the European Research Council (ERC Starting Grant SYMOPTIC [Grant 101040907]).

Output-feedback stochastic nonlinear adaptive control against Markovian jump actuator failures.

Protein O-fucosyltransferase 1 (POFUT1) catalyzes the transfer of fucose to threonine or serine residues within epidermal growth factor-like domains (EGF-LDs) and is a therapeutic target for Notch-associated O-glycosylation disorders. Unlike classical inverting glycosyltransferases, POFUT1 employs a catalytic asparagine that tautomerizes to its imidic acid form during the reaction. How the enzyme subsequently restores the canonical amidic form of Asn51 has remained unclear. Here, quantum mechanics/molecular mechanics simulations reveal that active-site water molecules mediate Asn51 retautomerization through a Grotthuss-type proton relay involving a low free energy barrier (<6 kcal·mol-1). This process can occur regardless of the presence of product molecules in the active site, although it is most favorable after product release. These findings elucidate how POFUT1 resets its catalytic machinery after turnover, underscore the essential role of water molecules in enzyme catalysis, and suggest that similar water-mediated strategies may operate in other enzymes in which catalytic residues undergo protonation changes during turnover.

Proteasomes are large multisubunit protease complexes found in all domains of life, where they execute regulatory and quality control degradation critical for organismal health. The canonical form of the proteasome, known as the 26S proteasome, consists of a 28-subunit barrel-shaped proteolytic core particle (CP) that is capped on its barrel ends by the 19-subunit regulatory particle (RP). The RP recognizes and captures substrates destined for degradation, mechanically unfolds them using energy derived from ATP, and translocates them through a gated pore at the surface of the CP into the proteolytic sites housed in its hollow center. Due to their exceptional size and subunit complexity, biogenesis of 26S proteasomes is a highly orchestrated process facilitated by dedicated assembly chaperones and conserved features of its subunits. Since the initial discovery of canonical 26S proteasomes, numerous noncanonical CPs harboring distinct subunit compositions have been detected, as have several alternative non-RP regulators of CP function. Here, we review the structure and assembly of canonical and noncanonical forms of the proteasome and highlight recent structural studies that have greatly clarified our understanding of how these fascinating and complicated molecular machines form rapidly and faithfully in the cellular milieu. In addition, we explore the assembly mechanisms that yield plasticity in the subunit composition of proteasomes, as well as emerging evidence of plasticity in the assembly pathways by which proteasomes are built in cells.

This paper introduces a new conceptual framework of the intersection of graph theory and abstract algebra, creating a new avenue for the applications of Boolean algebra and graph theory in cryptography. The integration of Boolean graphs with cryptographic principles offers a novel approach in the construction of the Camouflaged-Graph Cryptosystem[Formula: see text]CGC[Formula: see text] using symbolic representations of the graphs. We explore the graphs satisfying Boolean identities, and introduce Boolean structures on the set of all simple undirected graphs with a common vertex set. We introduce the concepts of Boolean graphs, atoms, and coatoms of Boolean graphs, and explore properties of the lattices of graphs, presenting the intricate relationships within graph structures. The introduction of auxiliary vertices representing Boolean OR/AND operations and defining the Boolean graph complements is a novel approach in the construction of the CGC, building on the symbolic Boolean to graph representation that may be used during the decryption process to restore the graph’s canonical form after a cryptographic obfuscation or a camouflaged Boolean graph has been created during encryption.

Autophagy represents a conserved lysosome-dependent catabolic mechanism that safeguards cellular energetic homeostasis and supports adaptive metabolic remodelingunder diverse stress conditions. In cancer, autophagy displays a highly context-dependent "double-edged sword" behavior. During the early stages of tumorigenesis, autophagy can suppress malignant transformation by preserving genomic stability, restraining chronic inflammation, and limiting the acquisition of malignant stemness, thereby helping preserve cellular integrity in early tumorigenesis. However, as tumors progress, autophagy can be reprogrammed into an adaptive survival mechanism that supplies tumor growth, metastatic dissemination, and resistance to multiple therapeutic modalitiesin response to hypoxia, nutrient deprivation, and therapeutic stress. Within the framework of tumor evolution, this review systematically integrates the molecular mechanisms and regulatory networks underlying different forms of autophagy, including canonical, non-canonical, and selective forms. We explore how autophagy intersects with metabolic reprogramming, immune signaling, DNA damage responses, and regulated cell death, and discuss its involvement in tumor progression, microenvironment remodeling, metastasis, and therapy resistance,with relevance to interactions between tumor cells and the surrounding microenvironment. We also summarize recent developments in autophagy-targeted approaches, including chloroquine derivatives, emerging small-molecule inhibitors, and natural compounds, and consider the challenges that remain for clinical translation,especially those related to context-dependent effects and therapeutic application. Collectively, this review provides an updated understanding of autophagy in tumor evolution and informs future mechanistic and therapeutic investigations.

Knowledge Q&amp;A, a key application of LLMs, draws much attention. However, LLMs struggle with Chinese abbreviated technical terms due to insufficient domain knowledge, and existing power Q&amp;A methods often neglect text semantic context, limiting performance. This paper proposes an LLM-adaptive RAG method with domain knowledge enhancement for Chinese power Q&amp;A. It first presents an info extraction framework with domain term recognition enhancement, using dual-pointer and generative extraction. Second, a two-way recall RAG method is proposed, predicting entity/relationship links via vectors and keywords, generating canonical forms, and using LLMs to select answers. Experiments show it outperforms mainstream methods in power field and works well generally.

We provide an explicit formula for the dimension of the $*$-congruence orbits and bundles of Hermitian matrix pencils over the field of complex numbers. The formula is given in terms of the sizes of the canonical blocks in the Hermitian Kronecker canonical form of the pencils. This extends the formulas provided only for the generic orbits and bundles in a previous work.

ConspectusSmart materials capable of in situ self-responding to external stimuli are proliferating due to their promising properties for advanced applications, including liquid crystal displays, information encryption, visual sensing, and substance detections. Significant progress has been made in designing and developing novel smart materials ranging from memory polymers to phase-change materials, color-change materials, etc. Inspired by these advances, the integration of intelligent functional groups into organic semiconductors offers a promising path to endow optoelectronic materials with selectively adaptive and dynamic features. This integration enables real-time, controllable, and repeatable responses to environmental changes, which allows optoelectronic materials to dynamically adjust their properties during processes such as carrier transport, energy transfer, and radiative/nonradiative exciton decay in device operation for achieving enhanced device performance. However, the development of intelligent structures remains challenging, and the lack of rational strategies for effectively integrating these structures with functional building blocks continues to impede the progress of smart optoelectronic materials.In this Account, a concise, universal, and effective tactic, called resonance variation-based dynamic adaptation (RVDA), to design and construct smart organic optoelectronic materials by incorporating resonance structures into organic building blocks has been proposed. RVDA materials through facile interconversion between canonical forms enable significant enhancement of optoelectronic properties through dynamic modulation of electronic characteristics including charge distribution, energy levels, spin-orbit coupling (SOC), and charge transport properties. Nevertheless, in-depth and comprehensive reviews on the progress of RVDA are still lacking. Therefore, this Account aims to summarize our research on the molecular design and properties of RVDA materials, along with recent advances across diverse application fields. It begins by introducing the fundamental principles of RVDA in dynamically modulating optoelectronic properties, following by the four systems based on their molecular structure design considerations. We highlight the diverse types of RVDA materials while discussing recent developments, including the latest research on host materials for organic light-emitting diodes (OLEDs), organic ultralong room-temperature phosphorescence (OURTP) materials for data encryption, fluorescence emitters for sensors, and hole transport materials (HTMs) for perovskite solar cells (PSCs). A key objective of this Account is to extract the fundamental design principles of RVDA materials and to uncover the common relationships between molecular structures and their optoelectronic properties across different research areas, systematizing our understanding of this field. Finally, current challenges are analyzed to outline future research directions, aiming to provide insights and guidance for developing next-generation smart materials and thereby expanding their transformative applications in organoelectronics, flexible electronics, bioelectronics, and related fields.

This study presents a novel rotationally invariant data-driven subgrid-scale (SGS) models for large-eddy simulation (LES) of wall-bounded turbulent flows. Previous studies have typically imposed invariance via scalar invariants or the canonical form (e.g. based on its eigenframe of rate-of-strain tensor), whereas this study introduces a modified deep neural network (DNN) architecture that inherently respects rotational invariance. Building upon the multiscale convolutional neural network SGS model (MSC model) developed by the authors, which outputs SGS stress tensors ( τ ij ), the DNN architecture is modified to satisfy the principle of material objectivity by removing bias terms and batch normalisation layers while incorporating a spatial transformer network algorithm. The proposed data-driven SGS models were trained on a turbulent channel flow at Re τ = 180 and evaluated under both non-rotated and rotated input conditions. The models accurately predicted τ ij and key turbulence statistics, including SGS dissipation, backscatter, and SGS transport, for non-rotated inputs. In addition, in the case of rotated inputs, they significantly outperformed the baseline MSC model, reducing the mean absolute error (MAE) of the τ 12 predictions from 0.402 to below 0.047 and achieving up to two orders of magnitude lower MAE in the turbulence statistics. Moreover, the models effectively generalise to unseen rotated inputs, accurately predicting τ ij despite the input configurations not being encountered during the training, indicating the general applicability of the proposed model. These findings highlight that the proposed data-driven SGS models address the key limitations of common data-driven SGS approaches, particularly their sensitivity to rotated input conditions. It also marks an important advancement in data-driven SGS modelling for LES, particularly in flow configurations where rotational effects are non-negligible.

An exactly solvable quantum-mechanical model of DNA bases is presented. The proposed model is based on the harmonic approximation of the potential energy of the canonical and tautomeric forms for the bases in question. The transition rate of single-proton transfer in the base pairs adenine-thymine and guanine-cytosine is determined within this model using the Fermi Golden Rule. The transition rates derived from the application of the 'bare' Fermi Golden Rule can be approximated by the Fano line curves. In turn, the application of the thermally averaged Fermi Golden Rule leads to an exponential increase in transition rates across the biologically relevant temperature range for the base pairs under consideration. The kinetic isotope effect for the base pairs at room temperature is also estimated. All calculations are consistently carried out in a phase-space representation using the Wigner distribution function.

This paper proposes a novel control scheme for Fault-Tolerant Control (FTC) and Fault Diagnosis (FD) in nonlinear Fractional-Order (FO) systems. The control scheme is based on an FO dynamic controller, a FO state estimator, and FO estimators for the faults. Considering the FO dynamic controller, a special FO canonical form allows us to design it naturally. Furthermore, using a theory based on condensing operators and the Sadovskii fixed point theorem, we provide the conditions under which the solution of the FO dynamic controller exists and is unique. Meanwhile, the estimators for the states and faults are designed using two different approaches; therefore, the control scheme is a hybrid type. Besides, a separation principle for nonlinear FO systems is proposed via the stability analysis of the scheme. It is important to mention that the faults discussed in this article are incipient, intermittent, or sudden, as well as modelled in an additive and multiplicative manner. Additionally, the scheme accounts for the presence of parametric uncertainty in the system. Finally, three examples are provided. The first example illustrates the special FO canonical form, while the others apply the proposed control scheme to the Van der Pol oscillator and the glucose-insulin interaction FO models.

We present the simlandr package for R, which provides a set of tools for constructing potential landscapes for dynamical systems using Monte Carlo simulation. Potential landscapes can be used to quantify the stability of system states. While the canonical form of a potential function is defined for gradient systems, generalized potential functions can also be defined for non-gradient dynamical systems. Our method is based on the potential landscape definition from the steady-state distribution, and can be used for a large variety of models. To facilitate simulation and computation, we introduce several novel features, including data structures optimized for batch simulations under varying conditions, an out-of-memory computation tool with integrated hash-based file-saving systems, and an algorithm for efficiently searching the minimum energy path. Using a multistable cell differentiation model as an example, we illustrate how simlandr can be used for model simulation, landscape construction, and barrier height calculation. The simlandr package is available at https://CRAN.R-project.org/package=simlandr, under GPL-3 license.

This article investigates how Job 1–3 may be read as a single narrative–dramatic unit shaped by a ritual process of mourning, with particular attention to the transition from the prose tale (Job 1–2) to the poetic imprecation (Job 3). The enquiry proceeds by means of a comparative analysis of the prologues of the Ugaritic epics Keret (KTU 1.14 I:1–II:5) and Aqhat (KTU 1.17 I:1–47), texts frequently invoked for contextualising Job within Ancient West Asia. In a first stage, close reading of these Ugaritic prologues identifies narrative techniques for signalling ritual practices—especially lament and incubatio—while remaining largely allusive rather than descriptive. In a second stage, the study turns to the canonical form of Job 1–3 and re-examines its scene arrangement, pacing, and speech-acts against that epic model, including the function of framing formulae and temporal markers. The analysis is intentionally confined to the present form of the text. The paper thus offers a controlled methodological work in comparative poetics and ritual analysis, asking how far Ugaritic epic conventions can illuminate continuity across genre and register at the opening of Job.

Abstract Cryptographic group actions have gained significant attention in recent years for their application on post-quantum Sigma protocols and digital signatures. In NIST’s recent additional call for post-quantum signatures, three relevant proposals are based on group actions: LESS, MEDS, and ALTEQ. This work explores signature optimisations leveraging a group’s factorisation. We show that if the group admits a factorisation as a semidirect product of subgroups, the group action can be restricted on a quotient space under the equivalence relation induced by the factorisation. If the relation is efficiently decidable, we show that it is possible to construct an equivalent Sigma protocol for a relationship that depends only on one of the subgroups. Moreover, if a special class of representative of the quotient space is efficiently computable via a canonical form, the restricted action is effective and does not incur in security loss. Finally, we apply these techniques to the group actions underlying LESS and MEDS, showing how they will affect the length of signatures and public keys.

Wine-red lignin revisited, dirigent proteins, and native lignin macromolecular configuration.

Necroptosis is a form of regulated cell death (RCD) that evolved as a defence against pathogenic infection. Unlike caspase-dependent RCD, necroptosis, in its canonical form, is driven by receptor-interacting protein kinase 1 and 3 (RIPK1 and RIPK3) signalling, culminating in the activation of the pseudokinase mixed lineage kinase domain-like protein (MLKL). Central to this process is the interaction between MLKL and its upstream regulator, RIPK3, forming a functional module called the necrosome that governs the spatiotemporal execution of cell death. Despite progress in our understanding of necroptotic signalling, key open questions remain. The structural organization of MLKL influences its interaction with RIPK3, yet the precise features of their binding surfaces and their regulation are not fully resolved. Additionally, the high-order supramolecular assembly of the necrosome and its transition between different states remain poorly understood, particularly regarding how RIPK3 and MLKL configurations impact necrosome activity and stability. In this review, we summarize current knowledge on the evolution, structure and regulation of the RIPK3-MLKL axis and discuss models of their activation in light of recent discoveries.

What brings Broken April closer to The Time of the Goats is, in my opinion, their universal dimension, their similar construction as a " character novel ", the tragic nature of the character , the polyphonic composition described by the re-appearance in various ethnographic, canonical, mythical and ideological forms. Regarding the work of Ismail Kadare, researcher Ymer Çiraku says: " His pen creates a break with the narrative styles of traditional literature, becoming more powerful, more concentrated and with an existentialist tendency. From work to work, Kadare becomes an explorer of the existential essences of the individual and the nation, on a horizontal and vertical plane, with reflections and stylistic macro and microstructurings, almost dizzying. "

In the era of big data and multimedia communication, securing color images against unauthorized access and attacks is a pressing challenge. While quaternion-based models provide a unified representation for color images, most existing encryption schemes rely on single-image frameworks or lack the mathematical rigor to ensure both security and feasibility. To bridge this gap, this paper introduces a system of generalized Sylvester-type quaternion matrix equations as a novel encryption model. By using the equivalence canonical forms of five matrices arranged in a specific array, we provide necessary and sufficient conditions for the solvability of the generalized Sylvester-type quaternion matrix equation system, depending on the rank of the coefficient matrix. Numerical examples are provided to validate the obtained results. As an example of applications, we develop an encryption scheme for color images based on the proposed quaternion matrix equation system. Experimental results confirm the high feasibility of the proposed scheme. Notably, the proposed model supports dynamic key updates and multi-image secure transmission, making it highly adaptable for real-world applications. By integrating advanced quaternion matrix theory with practical image encryption, this work offers a scalable, secure, and mathematically sound approach to color image protection.