Multiply intersecting families of sets

AbstractLet [n] denote the set {1,2,…,n}, 2[n] the collection of all subsets of [n] and F⊂2[n] be a family. The maximum of |F| is studied if any r subsets have an at least s-element intersection and there are no ℓ subsets containing t+1 common elements. We show that |F|⩽∑i=0t−sn−si+t+ℓ−st+2−sn−st+1−s+ℓ−2 and this bound is asymptotically the best possible as n→∞ and t⩾2s⩾2, r,ℓ⩾2 are fixed

Application of hypergraph Hoffman’s bound to intersecting families

Using the Filmus-Golubev-Lifshitz method to bound the independence number of a hypergraph, we solve some problems concerning multiply intersecting families with biased measure. Among other results we obtain a stability result of a measure version of the Erdos-Ko-Rado theorem for multiply intersecting families

Medical Interpreters\u27 Experience Working with Distressed Families in Pediatric Settings

Effective communication between families and pediatric clinicians is essential for mitigating family stress and improving quality of care. Families who speak a primary language other than English must contend with the added stress of language barriers during stressful encounters, which could impact the quality of patient care and health outcomes. Trained medical interpreters facilitate communication, including distress expressions, during interpreted medical encounters (IME). Little is known about how interpreters identify distress and what factors impact distress identification during IME. This project describes how interpreters identify distress of families during IME, and how they identify cultural nuances in distress expression and communication of families during IME. Special attention is placed on factors that influence why and how interpreters identify distress expression, such as their intersecting social identities and lived personal and professional experiences. Interpreters from the current study collectively reported that families in IME expressed distress in various ways: through visual, auditory, interpersonal, and contextual cues. Interpreters also perceived that distress expression among Spanish-speaking families in IME is diverse and simultaneously culture-specific and universal, influenced by cultural norms specific to the families’ intersecting social identities. Therefore, cultural concepts of distress and more covert culture bound expressions of distress (e.g., withdrawal) should be considered when evaluating family distress. Medical care teams inclusive of health care clinicians and medical interpreters should continue to cultivate their own cultural and emotional intelligence to better understand cultural concepts of distress among families from multiply minoritized backgrounds in the health care system. Clinicians and medical interpreters may benefit from collaboratively working together to better identify and respond when families are distressed

Magnetic Monopoles and Free Fractionally Charged States at Accelerators and in Cosmic Rays

Unified theories of strong, weak and electromagnetic interactions which have electric charge quantization predict the existence of topologically stable magnetic monopoles. Intermediate scale monopoles are comparable with detection energies of cosmic ray monopoles at IceCube and other cosmic ray experiments. Magnetic monopoles in some models can be significantly lighter and carry two, three or possibly even higher quanta of the Dirac magnetic charge. They could be light enough for their effects to be detected at the LHC either directly or indirectly. An example based on a D-brane inspired $SU(3)_C\times SU(3)_L\times SU(3)_R$ (trinification) model with the monopole carrying three quanta of Dirac magnetic charge is presented. These theories also predict the existence of color singlet states with fractional electric charge which may be accessible at the LHC.Comment: 18 pages, 2 figures, minor revisions, references adde