Ordinary Categories Research Articles

Statistics of unidirectional wave groups with and without freak waves observed in the Norwegian Sea

The statistical properties of observed wave groups are essential for designing marine structures. However, the characteristics of group energy, length, and profiles remain unclear. This paper analyzes more than 1 million measured ocean unidirectional wave groups in deep water of the Norwegian Sea during a decade. By classifying wave groups into ordinary and extreme categories based on the presence of a freak wave, it is found that both the distributions of the non-dimensional group energy and group duration follow the Generalized extreme value functions. Moreover, the statistics of wave groups are significantly influenced by the spectral width, with wave steepness having negligible effects. The ratio of the average group duration between extreme and ordinary categories varies slightly from 1.4 to 1.8, although the energy of extreme wave groups can reach 3.0–4.5 times than that of ordinary wave groups. Furthermore, unlike the typical shape of a freak wave with a high wave crest or deep wave trough significantly larger than the surrounding waves, consecutive large waves resembling the “three sisters” are quite common in this location. However, NewWave theory generally underestimates the wave amplitudes surrounding a freak wave, leading to the predicted energy of the most likely extreme wave groups being only about 50–80% of the measured values. Finally, a new modified model is proposed to predict the average shapes of extreme wave groups. After testing numerous wave cases, the model accurately captures the mean morphology of extreme wave groups in the Norwegian Sea.

Thinking Together: Advising as Collaborative Deliberation

We spend a good deal of time thinking about how and when to advise others, and how to respond to others advising us. But philosophical discussions of the nature and norms of advising have been scattered and somewhat disconnected. The most focused discussion has come from philosophers of language interested in whether advising is an assertive or directive kind of speech act. This paper argues that the ordinary category of advising is much more heterogenous than has been appreciated: it is possible to advise by asserting relevant facts, by issuing directives, by asking questions, and by other kinds of adviceless advising. The heterogeneity of advising makes speech act-theoretic accounts of advising look like accounts of special cases, which motivates us to look elsewhere for an account of what advising is. I suggest that we think about advising as a distinctive species of joint practical thinking, which I shall call collaborative deliberation, and show how our need for a concept to pick out this kind of joint activity emerges from our practical needs as deliberators. This view helps to illuminate a number of puzzling features of advising, and offers some guidance to be better at advising and at being advised.

Analysis Level Physical Condition of Female Volleyball Athletes in Blitar City

This study aimed to analyze the physical condition of female volleyball athletes in Blitar City. A total of 50 athletes from various clubs and teams were assessed using a battery of physical fitness tests, including BMI, Strength, Endurance, Explosive power and Flexibility.The subjects of this research were 12 female athletes and received the same training program. Physical condition test for volleyball athletes based on BMI add up to 271.5 with an normal of 22.6 and ordinary category. Strength gets 551 comes about and an normal of 45.9 with the less category. Endurance is 380.6 with an normal of 31.7 and sufficient category. Explosive power totaled 589 with an normal of 49.1 within the adequate category. Flexibility totaled 493.4 with an normal of 41.1 and the category sufficient. BMI comes about get comes about with a rate of 58.3% within the typical category. Strength percentage is 41.6% within the less category. Continuance rate is 83.3% within the sufficient category. Explosive power comes about with a rate of 75% within the sufficient category. Flexibility with a rate of 66.6% within the sufficient category. Generally, the competitors appeared a moo level of physical wellness, with solid execution within the BMI, strength, flexibility, explosive power and endurance tests. In any case, there were varieties in execution levels among the competitors, demonstrating the require for individualized preparing programs.

Music-driven generative dance movement teaching game based on a multi-feature fusion strategy

The study aims to develop a music-driven dance teaching game that enhances players' dance learning. By utilizing a multi-feature fusion strategy, the game creates dance movements inspired by music. The model effectively combines music and dance features to generate various dance sequences. In performance tests, the research model successfully matches the tempo and intensity of the music with the generated dance. Overall, this approach improves players' dance movement learning ability. The teaching effectiveness of the research method is significantly superior, with an average value of 95.23 points in the teaching evaluation. In terms of running time, for simple dances, the average generation time is 10 s; for ordinary categories of dances, the average generation time is 15 s; for complex dances, the average generation time is 17 s. The fluency of the generated dances is 97.21 %. The study's findings confirm the effectiveness of the research method. The game's use of multi-feature fusion algorithms allows for adaptive adjustments in difficulty and complexity based on the player's learning situation and ability level. This provides a more diverse and immersive gaming experience, while also presenting innovative ideas for future game development and teaching design.

ASSESSMENT OF THE FIRE RESISTANCE OF BUILDINGS FROM FIREPROOF REINFORCED CONCRETE BUILDING STRUCTURES

The authors conducted an analysis of the current state of evacuation of low-mobility population groups from high-rise residential buildings in the event of a fire. The analysis of the literature made it possible to formulate a number of obstacles to the effective evacuation of people from high-rise residential buildings. Norms in the field of fire safety are not perfect and, as a rule, are aimed at ordinary categories of citizens. The goal of approaches to evacuation calculations is to reduce the time it takes to evacuate residents of a high-rise building in the event of a fire. The authors substantiated the possibility of safe self-evacuation in the event of a fire of the less mobile population groups using fire elevators. Mathematical and graphical calculations of people's evacuation time were carried out using the Pathfinder software complex with the use (without use) of fire elevators. The authors performed a mathematical calculation of the time of evacuation of people and the time of blocking by dangerous factors of fire evacuation routes during a fire in accordance with the methodology of DSTU 8828:2019 Fire safety. Terms. Kyiv: Technical Committee "Fire Safety and Fire Fighting Equipment". To confirm the effectiveness of using fire elevators for the evacuation of people belonging to the M4 population groups with limited mobility (disabled people who move around in wheelchairs), the calculation part was performed. The object of the calculations is a high-rise apartment building on the street. Baidy Vyshnevetskoho, 68 in Cherkasy. The authors determined the dependence of the evacuation time on the movement parameters of people of different mobility groups. The authors compared calculations of evacuation time by stairwell and using fire elevators. Fire elevators are effective when evacuating people from floors for the category of mobility group M4. The researchers proposed management solutions to increase the level of fire safety, ensure the constant readiness and operability of fire elevators for evacuating people with reduced mobility from high-rise residential buildings. Keywords: evacuation routes, evacuation exits, high-rise residential buildings, fire elevators, evacuation time.

A method for automatic identification and separation of wildlife images using ensemble learning

Camera traps have revolutionized wildlife resource surveys by enabling the acquisition of comprehensive ecosystem information. Camera traps usually produce massive images. Snapshot datasets captured in nature reserves proximate to human habitation often comprise a significant volume of human activity images containing humans or livestock. Manually identifying and labeling wildlife images from large-scale datasets is a labor-intensive task that necessitates a substantial number of professionals and incurs expensive personnel costs. By harnessing the capabilities of deep learning technology to automatically differentiate between wildlife and human activity images, ecologists can solely focus on manually labeling wildlife images that account for a minor fraction of the dataset. This strategic shift can significantly reduce personnel expenses and enhance work efficiency. Existing research usually treats human activity images as ordinary categories and utilizes species recognition methods to automatically identify and filter them. However, when human activity images overwhelmingly predominate the dataset, established species recognition methods are susceptible to misclassifying a substantial proportion of wildlife images as human activity images. This misclassification can potentially result in ecologists missing opportunities to discover or observe wildlife. To tackle this challenge, we proposed an ensemble learning method based on a conservative strategy and current mainstream deep learning frameworks to automatically identify wildlife and human activity images. We validated our method on a camera trap dataset from Lasha Mountain (LSM) in Yunnan, China. The experimental results demonstrated that our method automatically identified wildlife images from the dataset with accuracy, recall, and precision of 95.75%, 94.07%, and 83.89%, respectively. This led to an approximately 80% reduction in personnel costs.

Hyperintensionality and Ontological Categories

In this paper, I discuss how to distinguish between ontological categories and ordinary categories. Using an argument against van Inwagen’s proposed account of what makes a category ontological as a springboard, I argue that if ontological categories are modally robust, then ontological categories need to be understood hyperintensionally. This conclusion opens up a wide range of new ways to define ‘ontological category’, and I close by briefly outlining one such way in order to illustrate the advantages of embracing hyperintensionality in this debate.

2-Limits and 2-Terminal Objects are too Different

In ordinary category theory, limits are known to be equivalent to terminal objects in the slice category of cones. In this paper, we prove that the 2-categorical analogues of this theorem relating 2-limits and 2-terminal objects in the various choices of slice 2-categories of 2-cones are false. Furthermore we show that, even when weakening the 2-cones to pseudo- or lax-natural transformations, or considering bi-type limits and bi-terminal objects, there is still no such correspondence.

Quotients of Span Categories that are Allegories and the Representation of Regular Categories

We consider the ordinary category \(\mathsf {Span}({\mathcal {C}})\) of (isomorphism classes of) spans of morphisms in a category \(\mathcal {C}\) with finite limits as needed, composed horizontally via pullback, and give a general criterion for a quotient of \(\mathsf {Span}({\mathcal {C}})\) to be an allegory. In particular, when \({\mathcal {C}}\) carries a pullback-stable, but not necessarily proper, \(({\mathcal {E}},{\mathcal {M}})\)-factorization system, we establish a quotient category \(\mathsf {Span}_{{\mathcal {E}}}({\mathcal {C}})\) that is isomorphic to the category \(\mathsf {Rel}_{{\mathcal {M}}}({\mathcal {C}})\) of \({\mathcal {M}}\)-relations in \({\mathcal {C}}\), and show that it is a (unitary and tabular) allegory precisely when \({\mathcal {M}}\) is a class of monomorphisms in \({\mathcal {C}}\). Without the restriction to monomorphisms, one can still find a least pullback-stable and composition-closed class \({\mathcal {E}}_{\bullet }\) containing \(\mathcal E\) such that \(\mathsf {Span}_{{\mathcal {E}}_{\bullet }}({\mathcal {C}})\) is a unitary and tabular allegory. In this way one obtains a left adjoint to the 2-functor that assigns to every unitary tabular allegory the regular category of its Lawverian maps. With the Freyd-Scedrov Representation Theorem for regular categories, we conclude that every finitely complete category with a stable factorization system has a reflection into the 2-category of all regular categories.

The exact completion for regular categories enriched in posets

We construct the exact completion for regular categories enriched in the cartesian closed category Pos of partially ordered sets and monotone functions by employing a suitable calculus of relations. We then characterize the embedding of any regular category into its completion and use this to obtain examples of concrete categories which arise as such completions. In particular, we prove that the exact completion in this enriched sense of both the categories of Stone and Priestley spaces is the category of compact ordered spaces of L. Nachbin. Finally, we consider the relationship between the enriched exact completion and categories of internal posets in ordinary categories.

Magnitude cohomology

Magnitude homology was introduced by Hepworth and Willerton in the case of graphs, and was later extended by Leinster and Shulman to metric spaces and enriched categories. Here we introduce the dual theory, magnitude cohomology, which we equip with the structure of an associative unital graded ring. Our first main result is a ‘recovery theorem’ showing that the magnitude cohomology ring of a finite metric space completely determines the space itself. The magnitude cohomology ring is non-commutative in general, for example when applied to finite metric spaces, but in some settings it is commutative, for example when applied to ordinary categories. Our second main result explains this situation by proving that the magnitude cohomology ring of an enriched category is graded-commutative whenever the enriching category is cartesian. We end the paper by giving complete computations of magnitude cohomology rings for several large classes of graphs.

Enriched category as a model of qualia structure based on similarity judgements

Qualitative relationships between two instances of conscious experiences can be quantified through the perceived similarity. Previously, we proposed that by defining similarity relationships as arrows and conscious experiences as objects, we can define a category of qualia in the context of category theory. However, the example qualia categories we proposed were highly idealized and limited to cases where perceived similarity is binary: either present or absent without any gradation. Here, we introduce enriched category theory to address the graded levels of similarity that arises in many instances of qualia. Enriched categories generalize the concept of a relation between objects as a directed arrow (or morphism) in ordinary category theory to a more flexible notion, such as a measure of distance. As an alternative relation, here we propose a graded measure of perceived dissimilarity between the two objects. We claim that enriched categories accommodate various types of conscious experiences. An important consequence of this claim is the application of the Yoneda lemma in enriched category; we can characterize a quale through a collection of relationships between the quale and the other qualia up to an (enriched) isomorphism.

Weighted limits in an $$(\infty ,1)$$-category

We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits in a quasi-category, and classical weighted limits in an ordinary category. This is accomplished by generalizing Joyal’s approach: we identify a meaningful construction for the quasi-category of weighted cones over a diagram in a quasi-category, whose terminal object is the weighted limit of the considered diagram. We then show that each weighted limit can be expressed as an ordinary limit. When the quasi-category arises as the homotopy coherent nerve of a category enriched over Kan complexes, we generalize an argument by Riehl-Verity to show that the weighted limit agrees with the homotopy weighted limit in the sense of enriched category theory, for which explicit constructions are available. When the quasi-category is complete, tensored and cotensored over the quasi-category of spaces, we discuss a possible comparison of our definition of weighted limit with the approach by Gepner-Haugseng-Nikolaus.

Jacobi geometry and Hamiltonian mechanics: The unit-free approach

We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely identify categories that generalize the ordinary categories of smooth manifolds and vector bundles to account for a lack of choice of a preferred unit, which in standard differential geometry is always given by the global constant function [Formula: see text]. This is what we call the “unit-free” approach. After giving a characterization of local Lie brackets via their symbol maps, we apply our novel categorical language to review Jacobi manifolds and related notions such as Lichnerowicz brackets and Jacobi algebroids. The main advantage of our approach is that Jacobi geometry is recovered as the direct unit-free generalization of Poisson geometry, with all the familiar notions translating in a straightforward manner. We then apply this formalism to the question of whether there is a unit-free generalization of Hamiltonian mechanics. We identify the basic categorical structure of ordinary Hamiltonian mechanics to argue that it is indeed possible to find a unit-free analogue. This paper serves as a prelude to the investigation of dimensioned structures, an attempt at a general mathematical framework for the formal treatment of physical quantities and dimensional analysis.

Per un’educazione alla solidarietà: dalla bioetica globale all’etica della complessità

L’articolo propone un excursus che va dalla critica all’ideologia dell’homo oeconomicus, all’educazione alla bioetica come formazione alla solidarietà, transitando per la bioetica globale di Van Potter ed evidenziandone la curvatura ecologica, per finire con un accostamento tra la bioetica e l’etica della complessità di Edgar Morin. L’insufficienza etica radicale che affligge l’uomo contemporaneo si fonda infatti su una concezione riduzionistica, che risolve l’uomo nella mera istanza economicistica. Si profila pertanto l’urgenza di un rinnovamento delle ordinarie categorie gnoseologiche e morali, che possa riconsegnare l’uomo alla complessità della sua identità, in cui si trovano inscritti i valori dell’altruismo e della solidarietà. In questa missione, la bioetica e il pensiero della complessità si riconoscono nel comune intento della riforma dell’insegnamento.

The enriched Grothendieck construction

We define and study opfibrations of V-enriched categories when V is an extensive monoidal category whose unit is terminal and connected. This includes sets, simplicial sets, categories, or any locally cartesian closed category with disjoint coproducts and connected unit. We show that for an ordinary category B, there is an equivalence of 2-categories between V-enriched opfibrations over the free V-category on B, and pseudofunctors from B to the 2-category of V-categories. This generalizes the classical (Set-enriched) Grothendieck correspondence.

Classical Control and Quantum Circuits in Enriched Category Theory

We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language. Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads. We interpret the circuit language not in an ordinary category, but in a category that is enriched in the host category. As an extended example, we recall an earlier result that the category of W*-algebras is dcpo-enriched, and we use this model to extend the circuit language with some recursive types.

Model Topoi and Motivic Homotopy Theory

Given a small simplicial category \mathcal{C} whose underlying ordinary category is equipped with a Grothendieck topology \tau , we construct a model structure on the category of simplicially enriched presheaves on \mathcal{C} where the weak equivalences are the local weak equivalences of the underlying (non-enriched) simplicial presheaves. We show that this model category is a t -complete model topos and describe the Grothendieck topology [\tau] on the homotopy category of \mathcal{C} that corresponds to this model topos. After we first review a proof showing that the motivic homotopy theory is not a model topos, we specialize this construction to the category of smooth schemes of finite type, which is simplicially enriched using the standard algebraic cosimplicial object, and compare the result with the motivic homotopy theory. We also collect some partial positive results on the exactness properties of the motivic localization functor.

Univalent higher categories via complete Semi-Segal types

Category theory in homotopy type theory is intricate as categorical laws can only be stated "up to homotopy", and thus require coherences. The established notion of a univalent category (as introduced by Ahrens et al.) solves this by considering only truncated types, roughly corresponding to an ordinary category. This fails to capture many naturally occurring structures, stemming from the fact that the naturally occurring structures in homotopy type theory are not ordinary, but rather higher categories. Out of the large variety of approaches to higher category theory that mathematicians have proposed, we believe that, for type theory, the simplicial strategy is best suited. Work by Lurie and Harpaz motivates the following definition. Given the first ( n +3) levels of a semisimplicial type S , we can equip S with three properties: first, contractibility of the types of certain horn fillers; second, a completeness property; and third, a truncation condition. We call this a complete semi-Segal n -type . This is very similar to an earlier suggestion by Schreiber. The definition of a univalent (1-) category by Ahrens et al. can easily be extended or restricted to the definition of a univalent n -category (more precisely, ( n ,1)-category) for n ∈ {0,1,2}, and we show that the type of complete semi-Segal n -types is equivalent to the type of univalent n -categories in these cases. Thus, we believe that the notion of a complete semi-Segal n -type can be taken as the definition of a univalent n -category. We provide a formalisation in the proof assistant Agda using a completely explicit representation of semi-simplicial types for levels up to 4.

OnARTMAP: A Fuzzy ARTMAP-based Architecture

Fuzzy ARTMAP (FAM) copes with the stability–plasticity dilemma by the adaptive resonance theory (ART). Despite such an advantage, Fuzzy ARTMAP suffers from a category proliferation problem, which leads to a high number of categories and a decrease in performance for unseen patterns. Such drawbacks are mainly caused by the overlapping region (noise) between classes. To overcome these drawbacks, we propose a Fuzzy ARTMAP-based architecture robust to noise, named OnARTMAP, for both online and batch learning. Our neural networks (OnARTMAP1 and OnARTMAP2) proposed for batch learning have a two-stage learning process, while our neural network (OnARTMAPo) for online and incremental learning has just a single iterative process. Two new modules are proposed, the overlapping region detection module (ORDM) and another one similar to ARTa, called ARTc. The ORDM finds the overlapping region between categories, while the ARTc computes and stores special categories for overlapping areas. In our architecture proposal, the weights for ordinary categories are estimated from data outside the overlapping area. An alternative to the second stage strategy for batch learning is presented and focuses on improving the generalization performance. On the basis of our achievements, one can infer that OnARTMAP can improve the generalization performance and decrease the number of categories. Our proposals were applied to artificial and real datasets, as well as were compared with several counterparts (Fuzzy ARTMAP, ART-EMAP, μARTMAP, and BARTMAP).