ABSTRACTRationaleLyon and coworkers demonstrated that multiple random fragmentation events can bias intensity distributions toward smaller terminal fragment ions. With any high‐yield method of dissociation, such as high‐energy collisional activation, this phenomenon can greatly influence the intensity distribution of product ions in MS/MS spectra. Previously, multiple fragmentation events were simulated with computationally intensive stochastic studies. The goal of this work is to provide a mathematical model that explains the results obtained from computational stochastic studies.MethodsWe present a probabilistic model that predicts terminal and internal product ion intensities based on polypeptide size and the number of fragmentation events. This model is validated by demonstrating convergence with the previous stochastic model and described that the intensity trend from smaller fragments to larger fragments follows the probability of multiple fragmentation events on peptide backbone.ResultsUnder the stated assumptions, the analytical expressions formally demonstrate that the “missing middle” is a necessary mathematical consequence of multiple fragmentation events, and they reproduce the stochastic simulation results with exact agreement while reducing computation time from hours to less than 1 s. Our method consistently offers greater accuracy and mathematically proves the mechanistic necessity of “missing middle” phenomenon in top‐down MS. The abundances of fragments from stochastic simulation distribute around the average value calculated by the probability formula within twofold coefficient variance (%CV).ConclusionThe closed‐form probability expressions accurately describe the combinatorial consequences of multiple fragmentation events under the stated assumptions. Because they are computationally inexpensive and differentiable, these expressions could be integrated with sequence‐dependent fragmentation propensities in future machine learning models for MS/MS spectral prediction.

Structural semiotics, as developed by A. J. Greimas and the Paris School, provides a powerful framework for analyzing narrative meaning through actantial roles, modalities, and hierarchical narrative structures. Despite its longstanding engagement with formal reasoning and diagrammatic tools, it has seen relatively few explicit mathematical formalizations. This article proposes a diagrammatic reconstruction of key Greimassian concepts using the language of symmetric monoidal and hypergraph categories. We treat the actantial model as a typing schema and introduce wiring diagrams as a formal semantics for representing narrative configurations, modal transformations, and actantial redistribution. Modal operations such as knowing-how-to-do, wanting-to-do, and causing-to-do are modeled as typed morphisms, while Frobenius structures account for duplication, erasure, and persistence of actants across narrative time. We show how operadic nesting captures hypotaxis, and how diagrammatic factorization yields higher-level abstractions corresponding to the hypotactical clusters of the canonical narrative schema. The approach is illustrated through a detailed analysis of Aesop’s The Fox & the Crow, culminating in a formal account of discoursivization via actorialization, spatialization, and temporalization. Rather than replacing structural semiotics, this work provides it with a compositional and mathematically explicit toolkit that clarifies existing concepts and opens new possibilities for comparative, computational, and interdisciplinary analysis.

Abstract We give a new definition of a Frobenius structure on an algebra object in a monoidal category, generalising Frobenius algebras in the category of vector spaces. Our definition allows Frobenius forms valued in objects other than the unit object and can be seen as a categorical version of Frobenius extensions of the second kind. When the monoidal category is pivotal, we define a Nakayama morphism for the Frobenius structure and explain what it means for this morphism to have finite order. Our main example is a well-studied algebra object in the (additive and idempotent completion of the) Temperley–Lieb category at a root of unity. We show that this algebra has a Frobenius structure and that its Nakayama morphism has order 2. As a consequence, we obtain information about Nakayama morphisms of preprojective algebras of Dynkin type, considered as algebras over the semisimple algebras on their vertices.

We define a (3+1)-TQFT associated with possibly non-semisimple finite unimodular ribbon tensor categories using skein theory. This gives an explicit realization of a TQFT predicted by the cobordism hypothesis, based on recent results on dualizability. State spaces are given by admissible skein modules, and we prescribe the TQFT on handle attachments. We give some explicit algebraic conditions on the input category to define this TQFT, namely to be ''chromatic non-degenerate''. As a by-product, we obtain an invariant of 4-manifolds equipped with a ribbon graph in their boundary, and in the ''twist non-degenerate'' case, an invariant of 3-manifolds. Our construction generalizes the Crane-Yetter-Kauffman TQFTs in the semi-simple case, and the Lyubashenko (hence also Hennings and WRT) invariants of 3-manifolds. The whole construction is very elementary, and we can easily characterize the invertibility of the TQFTs, study their behavior under connected sums and provide some examples.

Solution of a problem in monoidal categorification by additive categorification

Four experiments tested the generality of Hummel's (2001) dual-route model of human object recognition with regard to object-selective attention. According to the model, objects are represented and processed in two different formats-analytic and holistic-that differ in their attentional demands and their invariance properties. A sequential-matching paradigm was used that employed compound stimuli consisting of a picture of an everyday object and a superimposed horizontal or oblique line. On each trial, a reference stimulus was followed by two lateral stimuli, a target and a distractor. Observers either attended (matched) the line (thus ignoring the object) or attended/matched the object (thus ignoring the line) within the compound stimulus. For the picture stimulus, visual similarity between target and reference was manipulated by using either an identical object image, its mirror-reflection, a split image, or an inverted version in the reference. The task was always to semantically match the reference to the target. The results showed distinct facilitation effects, in terms of a reduced response latency relative to a same-category-different-exemplar baseline, which were significantly larger for attended than ignored objects. Furthermore, the facilitation was reduced in the mirror and split relative to the identical condition, and for the inverted relative to the mirror condition. The effects of attention and manipulation were strictly additive-in line with the predictions of the dual-route model. Implications for theories of object recognition are discussed. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

NMDA-receptor blockade changed microRNAs expression and apoptotic gene levels in dorsolateral striatal glioblastoma to reduce tumor growth and reverse behavioral impairments in rats.

INTRODUCTION . As part of the “Belt and Road” Initiative, which promotes cultural and industrial exchange between China, Russia and the CIS countries, automobile brands from Guangxi use regional cultural characteristics to enter the Russian-speaking market. The aim is to examine linguistic and cultural differences that have become the main obstacle to the accurate and clear translation of car brand names (autonyms) into Russian as an object of brand identity, culture and image of the region in the context of global competition and cultural distance. MATERIALS AND METHODS . The research material includes the names of well-known brands of Chinese cars (autonyms), removed from scientific, popular science and advertising Chinese and Russian publications. In the course of the research, methods of continuous sampling, classification and interpretation were used, the main method is descriptive, aimed at synchronous description of automobile nominations. RESULTS AND DISCUSSION . Three main linguistic and cultural problems that nominees face when creating brand identity are identified: “Russian semantic deviations in Guangxi automotive cultural terminology”, “intercultural barriers to regional automotive symbols”, and “misuse of local automotive concepts in the Russian context”. CONCLUSION . The conclusions obtained in the course of this study can be used to further study the identity of an automobile brand correlated with unique regional autonyms.

We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational probabilistic theories. We do so by providing a simple definition of locally-applicable transformation on a monoidal category. The definition can be rephrased in the language of category theory using the principle of naturality, and can be given an intuitive diagrammatic representation in terms of which all proofs are presented. In our main technical contribution, we use this diagrammatic representation to show that locally-applicable transformations on quantum channels are in one-to-one correspondence with deterministic quantum supermaps. This alternative characterization of quantum supermaps is proven to work for more general multiple-input supermaps such as the quantum switch and on arbitrary normal convex spaces of quantum channels such as those defined by satisfaction of signaling constraints.

Abstract We present a proof of the fact that in a symmetric monoidal category over a field of characteristic zero, objects with an invertible exterior power are rigid. As an application we prove two recent conjectures on dimensions in symmetric monoidal categories by Baez, Moeller and Trimble and further conjectures by Baez and Trimble.

In recent work with Harman, we introduced a new notion of measure for oligomorphic groups, and showed how they can be used to produce interesting tensor categories. Determining the measures for an oligomorphic group is an important and difficult combinatorial problem, which has only been solved in a handful of cases. The purpose of this paper is to solve this problem for a certain infinite family of oligomorphic groups, namely, the automorphism group of the n -colored circle (for each n \ge 1 ).

Abstract In our article [ arxiv:1511.05226 ], we studied the commutant $$\mathcal {C}'\subset \operatorname {Bim}(R)$$ C ′ ⊂ Bim ( R ) of a unitary fusion category $$\mathcal {C}$$ C , where R is a hyperfinite factor of type $$\mathrm II_1$$ I I 1 , $$\mathrm II_\infty $$ I I ∞ , or $$\mathrm III_1$$ I I I 1 , and showed that it is a bicommutant category. In other recent work [ arxiv:1607.06041 , arxiv:2301.11114 ] we introduced the notion of a (unitary) anchored planar algebra in a (unitary) braided pivotal category $$\mathcal {D}$$ D , and showed that they classify (unitary) module tensor categories for $$\mathcal {D}$$ D equipped with a distinguished object. Here, we connect these two notions and show that finite depth objects of $$\mathcal {C}'$$ C ′ are classified by connected finite depth unitary anchored planar algebras in $$\mathcal {Z}(\mathcal {C})$$ Z ( C ) . This extends the classification of finite depth objects of $$\operatorname {Bim}(R)$$ Bim ( R ) by connected finite depth unitary planar algebras.

If C is a category of algebras closed under finite direct products, and M C the commutative monoid of isomorphism classes of members of C , with operation induced by direct product, A. Tarski defined a nonidentity element p of M C to be prime if, whenever it divides a product of two elements, it divides one of them, and defined an object of C to be prime if its isomorphism class has this property. McKenzie, McNulty and Taylor [9, p. 263] ask whether the category of nonempty semigroups has any objects that are prime in this sense. We show in Section 2 that it does not. However, for the category of monoids, and some other subcategories of semigroups, we obtain examples of prime objects in Sections 3–4. In Section 5 two related questions from [9], open so far as I know, are recalled. In Section 6, which can be read independently of the rest of this note, we recall two conditions called primeness by semigroup theorists, and obtain results and examples on the relationships among those conditions and Tarski’s in categories of groups. Section 7 notes a characterization of one of those conditions on finite algebras in an arbitrary variety. Several questions are raised.

(2+1)D topological orders possess emergent symmetries given by a group $\text{Aut}(\mathcal{C})$, which consists of the braided tensor autoequivalences of the modular tensor category $\mathcal{C}$ that describes the anyons. In this paper we discuss cases where $\text{Aut}(\mathcal{C})$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial, which we refer to as soft symmetries. We point out that one can construct topological defects corresponding to such exotic symmetry actions by decorating with a certain class of gauged SPT states that cannot be distinguished by their torus partition function. This gives a physical interpretation to work by Davydov on soft braided tensor autoequivalences. This has a number of important implications for the classification of gapped boundaries, non-invertible spontaneous symmetry breaking, and the general classification of symmetry-enriched topological phases of matter. We also demonstrate analogous phenomena in higher dimensions, such as (3+1)D gauge theory with gauge group given by the quaternion group $Q_8$.

This paper extends the theory of universal measuring comonoids to modules and comodules in braided monoidal categories. We generalise the universal measuring comodule Q(M,N), originally introduced for modules over k-algebras when k is a field, to arbitrary braided monoidal categories. In order to establish its existence, we prove a representability theorem for presheaves on opfibred categories and an adjoint functor theorem for opfibred functors. The global categories of modules and comodules, fibred and opfibred over monoids and comonoids respectively, are shown to exhibit an enrichment of modules in comodules. Additionally, we use our framework to study higher derivations of algebras and modules, defining along the way the non-commutative Hasse-Schmidt algebra.

In this study, the soft usual topology compatible with the usual topology of R is defined, and using its subspace topology on the interval [0,1], the concept of a soft path is introduced. Within this context, the notions of soft-connectedness and soft-path-connectedness are developed, their relationship is analyzed, and it is shown that these properties are preserved under soft-continuous mappings. Moreover, the behavior of these concepts within soft-topological groups is investigated in detail. Finally, the category of soft-topological groups is constructed, its morphisms are identified, and it is shown that this category forms a symmetric monoidal category.

Abstract We consider quantum group representations Rep ⁡ ( G q ) \operatorname{Rep}(G_{q}) for a semisimple algebraic group 𝐺 at a complex root of unity 𝑞. Here we allow 𝑞 to be of any order. We first show that the Tannakian center in Rep ⁡ ( G q ) \operatorname{Rep}(G_{q}) is calculated via a twisting of Lusztig’s quantum Frobenius functor Rep ⁡ ( G ̌ ) → Rep ⁡ ( G q ) \operatorname{Rep}(\check{G})\to\operatorname{Rep}(G_{q}) , where G ̌ \check{G} is a dual group to 𝐺. We then consider the associated fiber category Vect ⊗ Rep ⁡ ( G ̌ ) Rep ⁡ ( G q ) \mathrm{Vect}\otimes_{\operatorname{Rep}{(\check{G})}}\operatorname{Rep}(G_{q}) over B ⁢ G ̌ B\check{G} , and show that this fiber is a finite, integral braided tensor category. Furthermore, when 𝐺 is simply connected and 𝑞 is of even order, the fiber in question is shown to be a modular tensor category. Finally, we exhibit a finite-dimensional quasitriangular quasi-Hopf algebra (also known as small quantum group) whose representations recover the tensor category Vect ⊗ Rep ⁡ ( G ̌ ) Rep ⁡ ( G q ) \mathrm{Vect}\otimes_{\operatorname{Rep}{(\check{G})}}\operatorname{Rep}(G_{q}) , and we describe the representation theory of this algebra in detail. At particular pairings of 𝐺 and 𝑞, our quasi-Hopf algebra is identified with Lusztig’s original finite-dimensional Hopf algebra from the ’90s. This work completes the author’s project from [C. Negron, Log-modular quantum groups at even roots of unity and the quantum Frobenius I, Comm. Math. Phys. 382 (2021), 2, 773–814].

Innovation and technology acceptance are two fundamental aspects that determine the success of organizations in the digital era. Innovation is not only limited to the creation of new products, but also encompasses how organizations manage business models, build customer experiences, and utilize networks and technology. Keeley (2013) in Ten Types of Innovation emphasizes that innovation can appear in various forms—from internal configurations and product offerings to interactions with customers. However, no matter how good an innovation is, its success is largely determined by the extent to which the technology or system is accepted by users. Davis (1989) with the Technology Acceptance Model (TAM) provides a basic framework for understanding technology acceptance through two main factors: perceived usefulness and perceived ease of use. This model is widely applied in education, healthcare, e-commerce, e-government, and industry. Meanwhile, Venkatesh et al. (2003) expanded this perspective through the Unified Theory of Acceptance and Use of Technology (UTAUT) by adding social factors and supporting conditions, and considering the influence of moderators such as age, gender, experience, and level of voluntary use. This article compares these three frameworks in accessible language, highlighting their relevance in supporting digital transformation across various sectors. By combining the perspectives of innovation and technology acceptance, this paper emphasizes that the success of an innovation depends not only on creativity in creating a new product or service, but also on the ease, benefits, and supportive environment that encourages its adoption. These findings are relevant for researchers, practitioners, and policymakers seeking to design sustainable innovations that are truly accepted and utilized by the wider community.

Most research on flexible job shop scheduling assumes constant processing speeds. However, in real production, machines need to operate at variable speeds to achieve energy-efficient scheduling, which requires balancing multiobjective between production efficiency and green development. Such tradeoffs thus trigger the phenomenon in which massive solutions converge to identical objective values (i.e., the multimodal property), which is often neglected in scheduling problems. To address the above challenges, this work introduces a knowledge-enhanced evolutionary multitasking memetic algorithm (KEMMA) to solve the multimodal multiobjective flexible job shop scheduling problem considering speed (MMFJSP-S). First, self-paced learning motivated us to construct a simple auxiliary task and employ an evolutionary multitasking (EMT) framework to tackle the complex MMFJSP-S. Moreover, a knowledge enhancement and explicit transfer strategy is designed to reduce the effects of negative transfer by reinforcing and sharing beneficial knowledge across tasks. Finally, a mapping transformation mechanism is proposed to handle the multimodal property of the MMFJSP-S in the decision space. By comparing with ten advanced algorithms, the experimental results verify the remarkable superiority ofthe proposed KEMMA in solving MMFJSP-S and reveal the significance of studying the multimodal property.

A bstract The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 4d $$ \mathcal{N}=2 $$ N = 2 superconformal field theories with fractional r-charges, there exists a special notion of high-temperature limit on higher sheets that captures data of three-dimensional topological quantum field theories arising from r-twisted circle reduction. These TQFTs are closely tied with the VOA of the 4d SCFT. We study such high-temperature limits. More specifically, we apply Di Pietro-Komargodski type supersymmetric effective field theory techniques to r-twisted circle reductions of ( A 1 , A 2 n ) Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest $$ \mathcal{N}=1 $$ N = 1 supersymmetry. The result on the second sheet is the Gang-Kim-Stubbs family of 3d $$ \mathcal{N}=2 $$ N = 2 SUSY enhancing rank-0 theories with monopole superpotentials, whose boundary supports the Virasoro minimal model VOAs M (2 , 2 n + 3). Upon topological twist, they give non-unitary TQFTs controlled by the M (2 , 2 n + 3) modular tensor category (MTC). The high-temperature limit on other sheets yields their unitary or non-unitary Galois conjugates. This opens up the prospect of a broader four-supercharge perspective on the celebrated correspondence between 4d $$ \mathcal{N}=2 $$ N = 2 SCFTs and 2d VOAs via interpolating 3d EFTs. Several byproducts follow, including a systematic approach to 3d SUSY enhancement from 4d SUSY enhancement, and a 3d QFT handle on Galois orbits of various MTCs associated with 4d $$ \mathcal{N}=2 $$ N = 2 SCFTs.