Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

Gender Comparisons of Mechanomyographic Amplitude and Mean Power Frequency Versus Isometric Torque Relationships

This is the publisher's version, also found at http://ehis.ebscohost.com/ehost/detail?sid=e7a03093-e666-4634-b895-d6b4313857c2%40sessionmgr13&vid=1&hid=17&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=s3h&AN=15943883This study compared the patterns of mechanomyographic (MMG) amplitude and mean power frequency vs. torque relationships in men and women during isometric muscle actions of the biceps brachii. Seven men (mean age 23.9 ± 3.5 yrs) and 8 women (mean 21.0 ± 1.3 yrs) performed submaximal to maximal isometric muscle actions of the dominant forearm flexors. Following determination of the isometric maximum voluntary contraction (MVC), they randomly performed submaximal step muscle actions in 10% increments from 10% to 90% MVC. Polynomial regression analyses indicated that the MMG amplitude vs. isometric torque relationship for the men was best fit with a cubic model (R2 = 0.983), where MMG amplitude increased slightly from 10% to 20% MVC, increased rapidly from 20% to 80% MVC, and plateaued from 80% to 100% MVC. For the women, MMG amplitude increased linearly (r2 = 0.949) from 10% to 100% MVC. Linear models also provided the best fit for the MMG mean power frequency vs. isometric torque relationship in both the men (r2 = 0.813) and women (r2 = 0.578). The results demonstrated gender differences in the MMG amplitude vs. isometric torque relationship, but similar torque-related patterns for MMG mean power frequency. These findings suggested that the plateau in MMG amplitude at high levels of isometric torque production for the biceps brachii in the men, but not the women, may have been due to greater isometric torque, muscle stiffness, and/or intramuscular fluid pressure in the men, rather than to differences in moto

Evolution and comparative analysis of the MHC Class III inflammatory region

BACKGROUND: The Major Histocompatibility Complex (MHC) is essential for immune function. Historically, it has been subdivided into three regions (Class I, II, and III), but a cluster of functionally related genes within the Class III region has also been referred to as the Class IV region or "inflammatory region". This group of genes is involved in the inflammatory response, and includes members of the tumour necrosis family. Here we report the sequencing, annotation and comparative analysis of a tammar wallaby BAC containing the inflammatory region. We also discuss the extent of sequence conservation across the entire region and identify elements conserved in evolution. RESULTS: Fourteen Class III genes from the tammar wallaby inflammatory region were characterised and compared to their orthologues in other vertebrates. The organisation and sequence of genes in the inflammatory region of both the wallaby and South American opossum are highly conserved compared to known genes from eutherian ("placental") mammals. Some minor differences separate the two marsupial species. Eight genes within the inflammatory region have remained tightly clustered for at least 360 million years, predating the divergence of the amphibian lineage. Analysis of sequence conservation identified 354 elements that are conserved. These range in size from 7 to 431 bases and cover 15.6% of the inflammatory region, representing approximately a 4-fold increase compared to the average for vertebrate genomes. About 5.5% of this conserved sequence is marsupial-specific, including three cases of marsupial-specific repeats. Highly Conserved Elements were also characterised. CONCLUSION: Using comparative analysis, we show that a cluster of MHC genes involved in inflammation, including TNF, LTA (or its putative teleost homolog TNF-N), APOM, and BAT3 have remained together for over 450 million years, predating the divergence of mammals from fish. The observed enrichment in conserved sequences within the inflammatory region suggests conservation at the transcriptional regulatory level, in addition to the functional level

Beyond words: Aesthetic knowledge and knowing in design

Aesthetic knowledge comes from practitioners understanding the look, feel, smell, taste and sound of things. It is vital to work in many organizational contexts. In this paper, we explore aesthetic knowledge and knowing in organizations through detailed observation of design work in the architectural practice Edward Cullinan Architects. Through our research, we explore aesthetic knowledge in the context of architectural work, we unpack what it is, how it is generated, and how it is applied in design projects, shared between practitioners and developed at the level of the organization. Our analysis suggests that aesthetic knowledge plays an important part in organizational practice, not only as the symbolic context for work, but as an integral part of the work that people do. It suggests that aesthetic reflexivity, which involves an opening up and questioning of what is known, is experienced as part of practice as well as a `time out' from practice

Research review: young people leaving care

This paper reviews the international research on young people leaving care. Set in the context of a social exclusion framework, it explores young people's accelerated and compressed transitions to adulthood, and discusses the development and classification of leaving care services in responding to their needs. It then considers the evidence from outcome studies and argues that adopting a resilience framework suggests that young people leaving care may fall into three groups: young people 'moving on', 'survivors' and 'victims'. In concluding, it argues that these three pathways are associated with the quality of care young people receive, their transitions from care and the support they receive after care