Intersection Property Research Articles

On maximum-sum matchings of points

Huemer et al. (Discrete Mathematics, 2019) proved that for any two point sets R and B with |R|=|B|, the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the matched pairs, has the property that all the disks induced by the matching have a common point. Each pair of matched points pin R and qin B induces the disk of smallest diameter that covers p and q. Following this research line, in this paper we consider the perfect matching that maximizes the total Euclidean distance. First, we prove that this new matching for R and B does not always ensure the common intersection property of the disks. Second, we extend the study of this new matching for sets of 2n uncolored points in the plane, where a matching is just a partition of the points into n pairs. As the main result, we prove that in this case all disks of the matching do have a common point.

A Sparse Version of Reznick’s Positivstellensatz

If f is a positive definite form, Reznick’s Positivstellensatz states that there exists [Formula: see text] such that [Formula: see text] is a sum of squares of polynomials. Assuming that f can be written as a sum of forms [Formula: see text], where each fl depends on a subset of the initial variables, and assuming that these subsets satisfy the so-called running intersection property, we provide a sparse version of Reznick’s Positivstellensatz. Namely, there exists [Formula: see text] such that [Formula: see text], where σl is a sum of squares of polynomials, Hl is a uniform polynomial denominator, and both polynomials [Formula: see text] involve the same variables as fl for each [Formula: see text]. In other words, the sparsity pattern of f is also reflected in this sparse version of Reznick’s certificate of positivity. We next use this result to also obtain positivity certificates for (i) polynomials nonnegative on the whole space and (ii) polynomials nonnegative on a (possibly noncompact) basic semialgebraic set, assuming that the input data satisfy the running intersection property. Both are sparse versions of a positivity certificate from Putinar and Vasilescu. Funding: V. Magron was supported by the Fondation Mathématique Jacques Hadamard Programme Gaspard Monge for Optimization (Exact Polynomial Optimization with Innovative Certifed Schemes project). This work has benefited from the Tremplin European Research Council Starting [Grant ANR-18-ERC2-0004-01] (Tremplin-Certified Optimization for Cyber-Physical Systems project), the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Actions [Grant 813211] (Polynomial Optimization, Efficiency through Moments and Algebra) as well as from the Artificial Intelligence Interdisciplinary Institute Artificial and Natural Intelligence Toulouse Institute funding, through the French “Investing for the Future Programme d’Investissements d’Avenir3” program [Grant n°ANR-19-PI3A-0004].

Embodying Difference: Iranian Women’s Working Life Experiences in Norway

ABSTRACT With reference to postcolonial intersectional scholarship, this article examines working life narratives of Iranian immigrant women before and after migration to Norway in relation to questions of equality along gender and racial lines. This interview-based study asks, ‘How do Iranian immigrant women who have resettled in Norway narrate their work experiences in their home and host countries, and how does this inform us about processes of othering and discrimination in both contexts?’ To what extent these othering processes can be understood in terms of the intersectional dimensions of gender and race. The study shows that although the move from a state considered repressive to one considered a model of gender equality entails positive experiences at work along gendered lines, these positive experiences are often encountered by the processes of racial and ethnic sorting, thus leading to distress and alienation. Accordingly, the interviews show a nuanced picture of working life in both countries, with both positive and negative stories of work in each context. Overall, the paper addresses a need to move beyond reductionist interpretations of migration that portrays immigration to the West as an unproblematic journey towards a better life in the accounts of immigrants coming from the East.

#MariellePresente: Black Feminism, Political Power, and Violence in Brazil

This article examines black Brazilian activist and politician Marielle Franco’s importance as a political figure, both during her life and since her assassination in 2018. It explores the intersectional dimensions of Franco’s political life, by locating her within two political genealogies: black women politicians in the city of Rio de Janeiro and black feminist activists in Brazil and the United States. The analysis underscores Franco’s impact on the Brazilian political landscape, and black women politicians in particular, during the 2018 and 2020 elections. It also examines Franco’s positioning within overlapping crises of anti-black genocide, femicide, and anti-LGBT violence in Brazil.

Boundary maps and covariant representations

We extend applications of Furstenberg boundary theory to the study of C ∗ $C^*$ -algebras associated to minimal actions Γ ↷ X $\Gamma \!\curvearrowright \!X$ of discrete groups Γ $\Gamma$ on locally compact spaces X $X$ . We introduce boundary maps on ( Γ , X ) $(\Gamma ,X)$ - C ∗ $C^*$ -algebras and investigate their applications in this context. Among other results, we completely determine when C ∗ $C^*$ -algebras generated by covariant representations arising from stabilizer subgroups are simple. We also characterize the intersection property of locally compact Γ $\Gamma$ -spaces and simplicity of their associated crossed products.

Ways Forward in Preventing Severe Maternal Morbidity and Maternal Health Inequities: Conceptual Frameworks, Definitions, and Data, from a Population Health Perspective.

Ways Forward in Preventing Severe Maternal Morbidity and Maternal Health Inequities: Conceptual Frameworks, Definitions, and Data, from a Population Health Perspective.

Failure of the finitely generated intersection property for ascending HNN extensions of free groups

The main result in this paper is the failure of the finitely generated intersection property (FGIP) of ascending HNN extensions of non-cyclic finite rank free groups. This class of groups consists of free-by-cyclic groups and properly ascending HNN extensions of free groups. We also give a sufficient condition for the failure of the FGIP in the context of relative hyperbolicity, we apply this to free-by-cyclic groups of exponential growth.

New bounds on Cantor maximal operators

We prove $L^p$ bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. Łaba and M. Pramanik and in some cases are sharp up to the endpoint. A consequence of our main result is that there exist Ahlfors-regular Salem Cantor sets of any dimension $>1/2$ such that the associated maximal operator is bounded on $L^2(\mathbb{R})$. We follow the overall scheme of Łaba-Pramanik for the analytic part of the argument, while the probabilistic part is instead inspired by our earlier work on intersection properties of random measures.

More Than Just Yoga: Physician Burnout, Effects of COVID, and Minoritized Status

Back to table of contents Previous article Next article Annual MeetingFull AccessMore Than Just Yoga: Physician Burnout, Effects of COVID, and Minoritized StatusAdrian Jacques Ambrose, M.D., M.P.H.Adrian Jacques AmbroseSearch for more papers by this author, M.D., M.P.H.Published Online:24 Mar 2022https://doi.org/10.1176/appi.pn.2022.04.4.44AbstractThe stress related to being a physician has been made only worse due to the COVID-19 pandemic. What can psychiatrists do to guard against burnout and protect their mental health and well-being?iStock/SanyaSMAs physicians are facing an inordinate amount of stress inflamed by COVID-19, several APA Annual Meeting sessions will address the alarming prevalence rates of burnout symptoms for both trainees and practicing physicians. Affecting both personal and professional domains, burnout may be associated with a decrease in professionalism, higher medical mistakes, substance use, and mood disorders. For psychiatrists, the APA Board of Trustees Workgroup on Psychiatrist Well-Being and Burnout found that 78% of respondents to an APA survey were at an increased risk of burnout, and 16% reported symptoms consistent with moderate to severe depression.While a significant aspect of psychiatric clinical care was facilitated by telehealth technology, the pandemic nonetheless dramatically shifted the clinical and work culture for many psychiatrists. With the increased burden, psychiatrists reported higher prevalence of burnout symptoms during the pandemic (47% versus 42% in the previous year). In addition, psychiatrist participants in a survey conducted by Medscape earlier this year identified the high volume of bureaucratic/nonclinical tasks, long work hours, and the lack of respect as the top three contributing factors to their burnout symptoms.Consistent throughout many studies, female psychiatrists were significantly more likely to report burnout and depressive symptoms in comparison with their male colleagues. For female psychiatrists, potential factors adding to burnout may be social expectations of child care, higher demands of work-home balance, and gender-related discriminations. Similarly, sexual minority medical students were eight times more likely to report burnout in comparison with their heterosexual counterparts due to perceived hostile environment, mistreatments, and discrimination. However, for ethnic and racial minorities, the varying and sometimes contradictory results highlight the multifactorial complexity of examining burnout—ranging from fewer burnout symptoms and increased rates of burnout to no significant difference in burnout rates compared with White peers. A systematic review of 16 studies similarly found inconclusive differences among ethnic and racial minorities and their nonminority peers, which may be related to variations between the two groups or other covariates (for example, socioeconomic status and specialty).Highlighted by presentations at the APA Annual Meeting, the increased burnout in female and underrepresented trainees and physicians needs individualized examination and solutions. With the recently galvanized national attention toward diversity, equity, and inclusion issues, more in-depth studies on physician burnout are needed on women, sexual minorities, and ethnic and racial minorities. For minority physicians, compounding factors, such as interpersonal microaggressions and individual or structural discriminations, may pose as additional stressors to burnout.The proposed solutions to burnout have ranged from individual-level changes (for example, building resilience, yoga, and meditation) to system-level changes (for example, reducing administrative burden, increasing time available for patient care, and promoting team-based work). It is important to note that while resilience may be inversely correlated with burnout, one study found that physicians with the highest resilient scores still demonstrated substantial burnout symptoms. Furthermore, there is a dearth of research targeting burnout solutions in minority and marginalized physicians, especially in the intersectional dimensions. With COVID-19 fueling the current “Great Resignation,” system leaders and health care organizations tackling burnout must address physicians’ physical and emotional depletion, restore the core connection to the work, and reestablish a sense of trust in the workplace—all of which require more than just yoga. ■The titles and schedule of Annual Meeting sessions on physician wellness and burnout can be accessed at the meeting’s Session Search tool here.Adrian Jacques Ambrose, M.D., M.P.H., is an assistant professor of psychiatry at the Columbia University Irving Medical Center of the Columbia Vagelos College of Physicians and Surgeons. ISSUES NewArchived

Conditions for matchability in groups and field extensions

The origins of the notion of matchings in groups spawn from a linear algebra problem proposed by E. K. Wakeford [On canonical forms. Proc London Math Soc (2). 1920;18:403–410] which was tackled in Fan and Losonczy [Matchings and canonical forms for symmetric tensors. Adv Math. 1996;117(2):228–238]. In this paper, we first discuss unmatchable subsets in abelian groups. Then we formulate and prove linear analogues of results concerning matchings, along with a conjecture that, if true, would extend the primitive subspace theorem. We discuss the dimension m-intersection property for vector spaces and its connection to matching subspaces in a field extension, and we prove the linear version of an intersection property result of certain subsets of a given set.

Bipolar Complex Fuzzy Soft Sets and Their Applications in Decision-Making

This article introduces the notion of bipolar complex fuzzy soft set as a generalization of bipolar complex fuzzy set and soft set. Furthermore, this article contains elementary operations for bipolar complex fuzzy soft sets such as complement, union, intersection, extended intersection, and related properties. The OR and AND operations for bipolar complex fuzzy soft set are also initiated in this study. Moreover, this study contains the decision-making algorithm and real-life examples to display the success and usability of bipolar complex fuzzy soft sets. Finally, the comparative study of initiated notions with some prevailing ideas are also interpreted in this study.

Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model

Topological properties of objects should be maintained and preserved to concisely represent objects. However, the implementation of 2D topological rules requires the decomposition of 3D objects into lower dimensions to determine topological relationships. This results in 2D topological relationships although the connected objects are in 3D. Hence, accurate representation of 3D connectivity in 3D models is limited. 3D topological rules can be implemented to include topological connectivity in 3D space. This paper implemented an extension of the 27-Intersection Model (27-IM) called the 36-Intersection Model (36-IM) to represent 3D topological adjacencies of two objects in 3D space. This resulted in a 12 × 3 intersection matrix or 36-IM that represented the intersections in terms of dimension and number of separations. Six cases were tested, consisting of “meets”, “disjoint” “intersects at a line”, “intersects at a point”, “contains”, and “overlaps”. The resulting 36-IM matrices provided an accurate representation of how the objects in 3D space were related and their dimension of intersections. The formalisms of the 36-IM matrices were also interoperable which allowed the interpretation of 36-IM using the 9IM and DE-9IM to determine general topological relationships. By examining the intersection of interiors, boundaries and exteriors of 3D objects without object decomposition, 3D topological relationships can be determined as well as the dimension and manner of intersection.

Selection of open or closed boundaries in a cellular automata model for heterogeneous non-lane-based traffic

Cellular automata (CA) simulation models developed for traffic are either closed or open boundary type. The selection and difference of boundaries has been studied extensively for ideal and single-lane homogeneous traffic conditions. However, the effect of these on multi-lane-heterogeneous traffic still needs attention because most of the traffic observed in many parts of the world is not single-lane homogeneous traffic. It is evident from multiple studies that open and closed boundaries affect the simulation results. Moreover, these require different inputs for simulation. This study attempts to evaluate the difference in the results of open and closed boundary simulations in heterogeneous non-lane-based traffic. The methodology discussed in this study is relatable to the field conditions. The present study includes some of the common but often ignored features in the model such as seepage of small-sized vehicles. Furthermore, this study also includes some of the previously unnoticed features while modeling the non-lane-based traffic at intersections. The modeling of open boundaries simulation can be better and easy in most of the situations compared to the closed boundaries. Closed boundary simulation results for flow-density curve show a smooth trend, whereas open boundary simulation results are scattered as observed in the field. This study further concludes that the size of the vehicle does not change the fundamental diagrams except when other characteristics such as seepage, lane change, and different maximum speeds for different modes are considered. The study used field observed influence zone of intersections to decide the dimension of intersection in the simulation model.

Afro-Colombian Women’s Organisations in Post- Accord Colombia: Gendering and Racialising Violent Pluralism across the Conflict Continuum in Bogotá, Colombia

This article will examine the mobilisation strategies of two groups of Afro-Colombian women now living in Bogotá – AFROMUPAZ and the Colectiva Matamba – in order to add an intersectional dimension to growing calls for ongoing theories on the gender of violent pluralism. Indeed, by recognising and addressing the specific ways in which Afro-Colombian women experience violence because of their positions in society, we will be able to better understand the strategies they continue to employ in an attempt to obtain guarantees on their rights as citizens, as victims, and as women.

On simultaneous linearization of certain commuting nearly integrable diffeomorphisms of the cylinder

AbstractLet $$\mathcal {F}$$ F and $$\mathcal {K}$$ K be commuting $$C^\infty $$ C ∞ diffeomorphisms of the cylinder $$\mathbb {T}\times \mathbb {R}$$ T × R that are, respectively, close to $$\mathcal {F}_0 (x, y)=(x+\omega (y), y)$$ F 0 ( x , y ) = ( x + ω ( y ) , y ) and $$T_\alpha (x, y)=(x+\alpha , y)$$ T α ( x , y ) = ( x + α , y ) , where $$\omega (y)$$ ω ( y ) is non-degenerate and $$\alpha $$ α is Diophantine. Using the KAM iterative scheme for the group action we show that $$\mathcal {F}$$ F and $$\mathcal {K}$$ K are simultaneously $$C^\infty $$ C ∞ -linearizable if $$\mathcal {F}$$ F has the intersection property (including the exact symplectic maps) and $$\mathcal {K}$$ K satisfies a semi-conjugacy condition. We also provide examples showing necessity of these conditions. As a consequence, we get local rigidity of certain class of $$\mathbb {Z}^2$$ Z 2 -actions on the cylinder, generated by commuting twist maps.

Sets with large intersection properties in metric spaces

In this work we reproduce the characterization of Gs-sets from the euclidean setting [11] to more general metric spaces. These sets have Hausdorff dimension at least s and are closed by countable intersections, which is particularly useful to estimate the dimension of the so called sets of α-approximable points.

An arbitrary order Mixed Virtual Element formulation for coupled multi-dimensional flow problems

Discrete Fracture and Matrix (DFM) models describe fractured porous media as complex sets of 2D planar polygons embedded in a 3D matrix representing the surrounding porous medium. The numerical simulation of the flow in a DFM requires the discretization of partial differential equations on the three dimensional matrix, the planar fractures and the one dimensional fracture intersections, and suitable coupling conditions between entities of different dimensionality need to be added at the various interfaces to close the problem. The present work proposes an arbitrary order implementation of the Virtual Element method in mixed formulation for such multidimensional problems. Details on effective strategies for mesh generation are discussed and implementation aspects are addressed. Several numerical results in various contexts are provided, which showcase the applicability of the method to flow simulations in complex multidimensional domains.

MODEL COMPLETIONS FOR UNIVERSAL CLASSES OF ALGEBRAS: NECESSARY AND SUFFICIENT CONDITIONS

AbstractNecessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to have a model completion, extending a characterization provided by Wheeler. For varieties of algebras that have equationally definable principal congruences and the compact intersection property, these conditions yield a more elegant characterization obtained (in a slightly more restricted setting) by Ghilardi and Zawadowski. Moreover, it is shown that under certain further assumptions on congruence lattices, the existence of a model completion implies that the variety has equationally definable principal congruences. This result is then used to provide necessary and sufficient conditions for the existence of a model completion for theories of Hamiltonian varieties of pointed residuated lattices, a broad family of varieties that includes lattice-ordered abelian groups and MV-algebras. Notably, if the theory of a Hamiltonian variety of pointed residuated lattices has a model completion, it must have equationally definable principal congruences. In particular, the theories of lattice-ordered abelian groups and MV-algebras do not have a model completion, as first proved by Glass and Pierce, and Lacava, respectively. Finally, it is shown that certain varieties of pointed residuated lattices generated by their linearly ordered members, including lattice-ordered abelian groups and MV-algebras, can be extended with a binary operation to obtain theories that do have a model completion.

A Moser theorem for multiscale mappings

<p style='text-indent:20px;'>In this paper, we study the persistence of invariant tori in nearly integrable multiscale twist mappings with intersection property and high degeneracy in the integrable part. Such results are also presented for the mappings with distinct number of angles and actions, which affirms the existence of lower-dimensional invariant tori in such mappings. Hence we establish a Moser's theorem in multiscales.</p>

The Characterization of Substructures of γ‐Anti Fuzzy Subgroups with Application in Genetics

Fuzzy and anti fuzzy normal subgroups are the current instrument for dealing with ambiguity in various decision‐making challenges. This article discusses γ‐anti fuzzy normal subgroups and γ‐fuzzy normal subgroups. Set‐theoretic properties of union and intersection are examined and it is observed that union and intersection of γ‐anti fuzzy normal subgroups are γ‐anti fuzzy normal subgroups. Employee selection impacts the input quality of employees and hence plays an important part in human resource management. The cost of a group is established in proportion to the fuzzy multisets of a fuzzy multigroup. It was a good idea to introduce anti‐intuitionistic fuzzy sets and anti‐intuitionistic fuzzy subgroups, as well as to demonstrate some of their algebraic features. Product of γ‐anti fuzzy normal subgroups and γ‐fuzzy normal subgroups is defined, the product’s algebraic nature is analyzed, and the findings are supported by presenting γ‐anti typical sections with blurring and γ‐ordinary parts with the weirdness of well‐defined and well‐established groups of genetic codes.