On the representation theory of finite J-trivial monoids

In 1979, Norton showed that the representation theory of the 0-Hecke algebra admits a rich combinatorial description. Her constructions rely heavily on some triangularity property of the product, but do not use explicitly that the 0-Hecke algebra is a monoid algebra. The thesis of this paper is that considering the general setting of monoids admitting such a triangularity, namely J-trivial monoids, sheds further light on the topic. This is a step to use representation theory to automatically extract combinatorial structures from (monoid) algebras, often in the form of posets and lattices, both from a theoretical and computational point of view, and with an implementation in Sage. Motivated by ongoing work on related monoids associated to Coxeter systems, and building on well-known results in the semi-group community (such as the description of the simple modules or the radical), we describe how most of the data associated to the representation theory (Cartan matrix, quiver) of the algebra of any J-trivial monoid M can be expressed combinatorially by counting appropriate elements in M itself. As a consequence, this data does not depend on the ground field and can be calculated in O(n^2), if not O(nm), where n=|M| and m is the number of generators. Along the way, we construct a triangular decomposition of the identity into orthogonal idempotents, using the usual M\"obius inversion formula in the semi-simple quotient (a lattice), followed by an algorithmic lifting step. Applying our results to the 0-Hecke algebra (in all finite types), we recover previously known results and additionally provide an explicit labeling of the edges of the quiver. We further explore special classes of J-trivial monoids, and in particular monoids of order preserving regressive functions on a poset, generalizing known results on the monoids of nondecreasing parking functions.Comment: 41 pages; 4 figures; added Section 3.7.4 in version 2; incorporated comments by referee in version

The biHecke monoid of a finite Coxeter group and its representations

For any finite Coxeter group W, we introduce two new objects: its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W. The construction of the biHecke monoid relies on the usual combinatorial model for the 0-Hecke algebra H_0(W), that is, for the symmetric group, the algebra (or monoid) generated by the elementary bubble sort operators. The authors previously introduced the Hecke group algebra, constructed as the algebra generated simultaneously by the bubble sort and antisort operators, and described its representation theory. In this paper, we consider instead the monoid generated by these operators. We prove that it admits |W| simple and projective modules. In order to construct the simple modules, we introduce for each w in W a combinatorial module T_w whose support is the interval [1,w]_R in right weak order. This module yields an algebra, whose representation theory generalizes that of the Hecke group algebra, with the combinatorics of descents replaced by that of blocks and of the cutting poset.Comment: v2: Added complete description of the rank 2 case (Section 7.3) and improved proof of Proposition 7.5. v3: Final version (typo fixes, picture improvements) 66 pages, 9 figures Algebra and Number Theory, 2013. arXiv admin note: text overlap with arXiv:1108.4379 by other author

Does stress induce salt intake?

Psychological stress is a common feature of modern day societies, and contributes to the global burden of disease. It was proposed by Henry over 20 years ago that the salt intake of a society reflects the level of stress, and that stress, through its effect on increasing salt intake, is an important factor in the development of hypertension. This review evaluates the evidence from animal and human studies to determine if stress does induce a salt appetite and increase salt consumption in human subjects. Findings from animal studies suggest that stress may drive salt intake, with evidence for a potential mechanism via the sympatho-adrenal medullary system and/or the hypothalamo&ndash;pituitary&ndash;adrenal axis. In contrast, in the few laboratory studies conducted in human subjects, none has found that acute stress affects salt intake. However, one study demonstrated that life stress (chronic stress) was associated with increased consumption of snack foods, which included, but not specifically, highly salty snacks. Studies investigating the influence of chronic stress on eating behaviours are required, including consumption of salty foods. From the available evidence, we can conclude that in free-living, Na-replete individuals, consuming Na in excess of physiological requirements, stress is unlikely to be a major contributor to salt intake.<br /

Making sense of the experience of visual hallucinations in psychosis: an interpretative phenomenological analysis

Volume I is comprised of a systematic meta-analysis, an empirical research paper and a press release. The meta-analysis reviews literature that investigated the impact of cognitive behavioural approaches on distress for those with a first or early episode psychosis. No main significant effect was found but, a significant effect was found within non-specialised services. The empirical research paper used interpretative phenomenological analysis to explore how visual hallucinations are experienced and made sense of within a schizophrenia spectrum diagnosis. Five superordinate themes were identified: ‘It’s not only a visual experience’, ‘Agency’, ‘Role of others, ‘Coming to know the experience’ and ‘Creating a narrative’

BISON: bio-interface for the semi-global analysis of network patterns

BACKGROUND: The large amount of genomics data that have accumulated over the past decade require extensive data mining. However, the global nature of data mining, which includes pattern mining, poses difficulties for users who want to study specific questions in a more local environment. This creates a need for techniques that allow a localized analysis of globally determined patterns. RESULTS: We developed a tool that determines and evaluates global patterns based on protein property and network information, while providing all the benefits of a perspective that is targeted at biologist users with specific goals and interests. Our tool uses our own data mining techniques, integrated into current visualization and navigation techniques. The functionality of the tool is discussed in the context of the transcriptional network of regulation in the enteric bacterium Escherichia coli. Two biological questions were asked: (i) Which functional categories of proteins (identified by hidden Markov models) are regulated by a regulator with a specific domain? (ii) Which regulators are involved in the regulation of proteins that contain a common hidden Markov model? Using these examples, we explain the gene-centered and pattern-centered analysis that the tool permits. CONCLUSION: In summary, we have a tool that can be used for a wide variety of applications in biology, medicine, or agriculture. The pattern mining engine is global in the way that patterns are determined across the entire network. The tool still permits a localized analysis for users who want to analyze a subportion of the total network. We have named the tool BISON (Bio-Interface for the Semi-global analysis Of Network patterns)

The Development of Techie Times

Summer 2020 provided the motivation and opportunity to move summer outreach programs into the virtual world. Faculty and students in the Purdue University School of Engineering Technology moved face-to-face programs into a middle school program called Techie Times. This program was designed to provide students with an organized platform occurring just before the school year started, allowing them to learn at home, working with family, or independently. The program was designed to take place nonconsecutively over eight days, covering five various STEM topics. Some of these activities were already a part of the middle school curriculum; others were not. That provided an opportunity to engage students and teach them principles that support various engineering technology curricula. Students were recruited from across the country. Students were placed into three cohorts sorted by biological age and then into smaller groups to enhance interactions. Volunteers moderated the smaller groups representing corporate engineering retirees, university professors, and others interested in helping. The volunteers were provided with information to support the principles being learned in the activity of the day. They asked the students to demonstrate what they did at home and then asked them questions about what they learned from the activity. In the older age groups, volunteers generated hypotheses and tested them to see if they worked, thus providing a challenge for the older and more experienced students. This camp proved to be well-timed on the summer calendar. Parents expressed their pleasure in their students becoming a bit more disciplined as they transitioned from their summer activities to the upcoming school year. This paper will review the program’s curriculum, observations by the parents/guardians, and feedback from the students. The program is an example of a well-transformed outreach program that engaged and enlightened students

Modest de novo Reactivation of Single HIV-1 Proviruses in Peripheral CD4+ T Cells by Romidepsin

A cure for human immunodeficiency virus (HIV-1) is restricted by the continued presence of a latent reservoir of memory CD4+ T cells with proviruses integrated into their DNA despite suppressive antiretroviral therapy (ART). A predominant strategy currently pursued in HIV-1 cure-related research is the “kick and kill” approach, where latency reversal agents (LRAs) are used to reactivate transcription from integrated proviruses. The premise of this approach is that “kicking” latent virus out of hiding allows the host immune system to recognize and kill infected cells. Clinical trials investigating the efficacy of LRAs, such as romidepsin, have shown that these interventions do induce transient spikes in viral RNA in HIV-1-infected individuals. However, since these trials failed to significantly reduce viral reservoir size or significantly delay time to viral rebound during analytical treatment interruptions, it is questioned how much each individual latent provirus is actually “kicked” to produce viral transcripts and/or proteins by the LRA. Here, we developed sensitive and specific digital droplet PCR-based assays with single-provirus level resolution. Combining these assays allowed us to interrogate the level of viral RNA transcripts from single proviruses in individuals on suppressive ART with or without concomitant romidepsin treatment. Small numbers of proviruses in peripheral blood memory CD4+ T cells were triggered to become marginally transcriptionally active upon romidepsin treatment. These novel assays can be applied retrospectively and prospectively in HIV-1 cure-related clinical trials to gain crucial insights into LRA efficacy at the single provirus level

Polydispersity and ordered phases in solutions of rodlike macromolecules

We apply density functional theory to study the influence of polydispersity on the stability of columnar, smectic and solid ordering in the solutions of rodlike macromolecules. For sufficiently large length polydispersity (standard deviation $\sigma>0.25$) a direct first-order nematic-columnar transition is found, while for smaller $\sigma$ there is a continuous nematic-smectic and first-order smectic-columnar transition. For increasing polydispersity the columnar structure is stabilized with respect to solid perturbations. The length distribution of macromolecules changes neither at the nematic-smectic nor at the nematic-columnar transition, but it does change at the smectic-columnar phase transition. We also study the phase behaviour of binary mixtures, in which the nematic-smectic transition is again found to be continuous. Demixing according to rod length in the smectic phase is always preempted by transitions to solid or columnar ordering.Comment: 13 pages (TeX), 2 Postscript figures uuencode

Vitamin and mineral supplementation for maintaining cognitive function in cognitively healthy people in mid and late life

Vitamins and minerals play multiple functions within the central nervous system which may help to maintain brain health and optimal cognitive functioning. Supplementation of the diet with various vitamins and minerals has been suggested as a means of maintaining cognitive function, or even of preventing dementia, in later life