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The classical Ham Sandwich theorem states that any |$d$| point sets in |${\mathbb {R}}^{d}$| can be simultaneously bisected by a single affine hyperplane. A generalization of Dolnikov asserts that any |$d$| families of pairwise intersecting compact, convex sets in |${\mathbb {R}}^{d}$| admit a common hyperplane transversal. We extend Dolnikov's theorem by showing that families of compact convex sets satisfying more general non-disjointness conditions admit common transversals by multiple hyperplanes. In particular, these generalize all known optimal results to the long-standing Grünbaum–Hadwiger–Ramos measure equipartition problem in the case of two hyperplanes. Our proof proceeds by establishing topological Radon-type intersection theorems and then applying Gale duality in the linear setting. For a single hyperplane, this gives a new proof of Dolnikov's original result via Sarkaria's non-embedding criterion for simplicial complexes. [ABSTRACT FROM AUTHOR]

This paper is devoted to coregular submanifolds in Poisson geometry. We show that their local Poisson saturation is an embedded Poisson submanifold, and we give a normal form for this Poisson submanifold around the coregular submanifold. This result recovers the normal form around Poisson transversals, and it yields Poisson versions of some normal form/rigidity results around constant rank submanifolds in symplectic geometry. As an application, we prove a uniqueness result concerning coisotropic embeddings of Dirac manifolds in Poisson manifolds. We also show how our results generalize to the setting of coregular submanifolds in Dirac geometry. [ABSTRACT FROM AUTHOR]

Our everyday life is entangled with products and services of so-called Big Tech companies, such as Amazon, Google, and Facebook. International relations (IR) scholars increasingly seek to reflect on the relationships between Big Tech, capitalism, and institutionalized politics, and they engage with the practices of algorithmic governance and platformization that shape and are shaped by Big Tech. This collective discussion advances these emerging debates by approaching Big Tech transversally, meaning that we problematize Big Tech as an object of study and raise a range of fundamental questions about its politics. The contributions demonstrate how a transversal perspective that cuts across sociomaterial, institutional, and disciplinary boundaries and framings opens up the study of the politics of Big Tech. The discussion brings to the fore perspectives on the ontologies of Big Tech, the politics of the aesthetics and credibility of Big Tech and rethinks the concepts of legitimacy and responsibility. The article thereby provides several inroads for how IR and international political sociology can leverage their analytical engagement with Big Tech and nurture imaginaries of alternative and subversive technopolitical futures. [ABSTRACT FROM AUTHOR]

This article is about the role of youth in transitional justice and art as a medium in furthering that role. It examines Srebrenica Is Dutch History , a travelling memorial both by young people and about young people, as a transgenerational means for dealing with the past, and as an illustration of youth in transitional justice from the perspective of memorialization across both time and location. As much as this article is by me, it is also about me. It is a reflective exercise constituting my first act of ownership over my identities as a child of genocide survivors, a former refugee and a 23-year-old Bosnian-Belgian female scholar. [ABSTRACT FROM AUTHOR]

We study the transversal hard Lefschetz theorem on a transversely symplectic foliation. This article extends the results of transversally symplectic flows (H.K. Pak, "Transversal harmonic theory for transversally symplectic flows", J. Aust. Math. Soc. 84 (2008), 233–245) to general transversely symplectic foliations. [ABSTRACT FROM AUTHOR]

This article discusses the role of language in the collaboration between science, policy, and society. Combining computational methods of corpus linguistics (manifold learning) with sociological field theories, we analyze approximately 30,000 articles that were published in the field of transdisciplinary sustainability studies. We show that the field oscillates between deliberative and technocratic vocabularies and can therefore be characterized as a transversal field. We conclude that researchers who collaborate in science–society interstices are thrown into a semantic pluralism that cannot be boiled down to a common language. For transdisciplinary research practice and corresponding science policies, this involves trade-offs between generating a homogenous language and a collaborative appeal; between creating a stable creole and a situated semantic plurality. A corresponding theoretical viewpoint and science policy approach should be based on a pluralist view on the science–society–policy interplay. [ABSTRACT FROM AUTHOR]

Objectives This prospective cohort study investigated the short term effects of interceptive orthodontic treatment with a removable expansion plate, evaluating the changes in occlusion in all its dimensions: transversal, sagittal and vertical. Subjects and methods A total of 226 patients treated with a removable expansion plate (slow maxillary expansion, SME) by orthodontic residents at the Department of Orthodontics, University Hospitals Leuven, Belgium were included. The patients had a mean age of 8.5 years at the start of the treatment. The mean treatment time was 6.9 months. Transversal measurements (intercanine and intermolar width) and occlusal characteristics (molar occlusion, overjet, overbite and functional shift) were collected before (T0) and after active treatment (T1). Statistical analysis was performed using the Wilcoxon signed rank test, Sign test and McNemar test for assessing changes between T0 and T1. Linear models were used to assess the associations between patient factors and the amount of expansion. Results A significant increase in transversal width at different occlusal landmarks was found. Correction of unilateral, bilateral and frontal crossbites was successful in 99.0%, 95.2% and 93.6% of the cases respectively. Changes in sagittal molar occlusion were significant: 64.9% (right side) and 62.6% (left side) remained stable, 28.4% (right) and 29.3% (left) improved and 6.7% (right) and 8.1% (left) deteriorated. Overbite changes were found to be statistically significant, though clinically irrelevant. Overjet changes were non-significant. Conclusions A removable expansion plate is successful in improving the transversal dental dimensions of the maxilla. Statistically significant sagittal effects on molar occlusion were found. Long-term follow-up is needed to evaluate the long-term stability of this treatment. [ABSTRACT FROM AUTHOR]

This collective discussion proposes a novel understanding of intelligence as a social phenomenon, taking place in a social space that increasingly involves actors and professional fields not immediately seen as part of intelligence. This discussion is a response to the inherent functionalism in Intelligence Studies (IS) that conceives of intelligence as a cycle serving policymakers. Instead, our interventions seek to problematize and break with this notion of the cycle and show what an alternative study of intelligence would look like. In the first part of the discussion, we situate our intervention in the broader fields of IS and International Political Sociology. Espousing a transdisciplinary approach, we build our four interventions as transversal lines cutting through a social space in which agents with differing stakes participate and reframe the meaning and practice of intelligence. Intelligence professionals not only have to reckon with policymakers, but also increasingly with law enforcement agents, representatives from the science and technology sector, judges, lawyers, activists, and Internet users themselves. Each move takes a step further away from the intelligence cycle by introducing new empirical sites, actors, and stakes. [ABSTRACT FROM AUTHOR]

The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra that depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not involutive, one obtains an |$L_\infty $| algebra instead. We develop a simplified method for describing this |$L_\infty $| algebra and use it to prove that the |$L_\infty $| algebras corresponding to different transversals are canonically |$L_\infty $| –isomorphic. In some cases, this isomorphism provides a formality map, as we show in several examples including (quasi)-Poisson geometry, Dirac structures on Lie groups, and Lie bialgebras. Finally, we apply our result to a classical problem in the deformation theory of complex manifolds; we provide explicit formulas for the Kodaira–Spencer deformation complex of a fixed small deformation of a complex manifold, in terms of the deformation complex of the original manifold. [ABSTRACT FROM AUTHOR]

This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poisson structures and Poisson manifolds with closed leaves, we prove that all their compact Poisson transversals represent nontrivial homology classes, generalizing the symplectic case. We discuss several examples in which this property does not hold, as well as a weaker version of this property, which holds for log-symplectic structures. Finally, we extend our results to Dirac geometry. [ABSTRACT FROM AUTHOR]

A computably enumerable equivalence relation (ceer) |$X$| is called self-full if whenever |$f$| is a reduction of |$X$| to |$X$|⁠ , then the range of |$f$| intersects all |$X$| -equivalence classes. It is known that the infinite self-full ceers properly contain the dark ceers, i.e. the infinite ceers which do not admit an infinite computably enumerable transversal. Unlike the collection of dark ceers, which are closed under the operation of uniform join, we answer a question from [ 4 ] by showing that there are self-full ceers |$X$| and |$Y$| so that their uniform join |$X\oplus Y$| is non-self-full. We then define and examine the hereditarily self-full ceers, which are the self-full ceers |$X$| so that for any self-full |$Y$|⁠ , |$X\oplus Y$| is also self-full: we show that they are closed under uniform join and that every non-universal degree in |${\operatorname{\textbf{Ceers}}}_{\operatorname{{\mathcal{I}}}}$| have infinitely many incomparable hereditarily self-full strong minimal covers. In particular, every non-universal ceer is bounded by a hereditarily self-full ceer. Thus, the hereditarily self-full ceers form a properly intermediate class in between the dark ceers and the infinite self-full ceers, which is closed under |$\oplus $|⁠. [ABSTRACT FROM AUTHOR]

Objetivos: Adultos con lesión cerebral traumática (LCT) pueden sufrir de una disminución en calidad de vida (CAL) asociada al desarrollo de diagnósticos comórbidos. En Puerto Rico (PR), la información sobre esta población es limitada. Este estudio tuvo como objetivo describir las características sociodemográficas, diagnósticos comórbidos y CAL reportados por un cohorte de pacientes con LCT en PR. Metodología: En este estudio de tipo no experimental transversal, con enfoque cuantitativo y alcance descriptivo, participaron 40 adultos puertorriqueños (23–63 años de edad) con historial de LCT y al menos un año de recuperación. La muestra fue reclutada a través de anuncios virtuales en las redes sociales, anuncios presenciales en reuniones de un grupo de apoyo para personas con LCT, y un Hospital de Trauma. Su participación consistió en completar un cuestionario sociodemográfico y la Escala CAVIDACE-Autoinforme, diseñada para evaluar CAL en adultos con LCT. Resultados: La mayoría de los participantes reportó estar soltero, divorciado o separado (72.5%). Veintisiete participantes (59.5%) reportaron tener bachillerato o grado asociado, y el restante reportó tener un nivel de educación de escuela superior o menor; el 65% reportó estar desempleado. De los participantes, 47.5% reportó LCT severa, 22.5% moderada y 30% leve. Trastornos psiquiátricos comórbidos reportados incluyeron depresión (47.5%), trastornos de ansiedad (40%), trastorno bipolar (10%), trastornos del sueño (32.5%), abuso de alcohol o drogas (10%), psicosis (5%), entre otros. El 70% de los participantes reportó tener CAL a nivel promedio en comparación con la norma (M = 96.58, SD = 13). Conclusiones: Esto datos ayudarán a guiar servicios y futuros estudios con esta población. [ABSTRACT FROM AUTHOR]

Weinvestigate the moduli space of instanton bundles over the quintic del Pezzo threefold for small values of their charge. We prove a new bound for their splitting type on a generic line and an analogue of the Grauert-Mülich theorem for minimal instantons. Moreover, in the first two non-trivial cases, we construct SL2-equivariant embeddings into ℙ5 and into a relative Grassmannian. These results are used to prove the existence of a unique SL2-equivariant instanton of charge 2 and to provide examples of singular theta-characteristics associated with instantons of charge 3. [ABSTRACT FROM AUTHOR]

Extending the work of G. Székelyhidi and T. Br üonnle to Sasakian manifolds, we prove that a small deformation of the complex structure of the cone of a constant scalar curvature Sasakian (cscS) manifold admits a constant scalar curvature structure if it is K-polystable. This also implies that a small deformation of the complex structure of the cone of a constant scalar curvature structure is K-semistable. As applications, we give examples of cscS manifolds which are deformations of toric examples, and we also show that if a 3-Sasakian manifold admits a nontrivial transversal complex deformation, then it admits a nontrivial Sasaki-Einstein deformation. [ABSTRACT FROM AUTHOR]