Competitive Allocation of a Mixed Manna

We study the fair division problem of allocating a mixed manna under additively separable piecewise linear concave (SPLC) utilities. A mixed manna contains goods that everyone likes and bads that everyone dislikes, as well as items that some like and others dislike. The seminal work of Bogomolnaia et al. [Econometrica'17] argue why allocating a mixed manna is genuinely more complicated than a good or a bad manna, and why competitive equilibrium is the best mechanism. They also provide the existence of equilibrium and establish its peculiar properties (e.g., non-convex and disconnected set of equilibria even under linear utilities), but leave the problem of computing an equilibrium open. This problem remained unresolved even for only bad manna under linear utilities. Our main result is a simplex-like algorithm based on Lemke's scheme for computing a competitive allocation of a mixed manna under SPLC utilities, a strict generalization of linear. Experimental results on randomly generated instances suggest that our algorithm will be fast in practice. The problem is known to be PPAD-hard for the case of good manna, and we also show a similar result for the case of bad manna. Given these PPAD-hardness results, designing such an algorithm is the only non-brute-force (non-enumerative) option known, e.g., the classic Lemke-Howson algorithm (1964) for computing a Nash equilibrium in a 2-player game is still one of the most widely used algorithms in practice. Our algorithm also yields several new structural properties as simple corollaries. We obtain a (constructive) proof of existence for a far more general setting, membership of the problem in PPAD, rational-valued solution, and odd number of solutions property. The last property also settles the conjecture of Bogomolnaia et al. in the affirmative

Sterile Neutrinos in E_6 and a Natural Understanding of Vacuum Oscillation Solution to the Solar Neutrino Puzzle

If Nature has chosen the vacuum oscillation solution to the Solar neutrino puzzle, a key theoretical challenge is to understand the extreme smallness of the $\Delta m^2_{\nu_e-\nu_X}$ ($\sim 10^{-10} eV^2$) required for the purpose. We find that in a class of models such as [SU(3)]^3 or its parent group E_6, which contain one sterile neutrino, $\nu_{is}$ for each family, the $\Delta m^2_{\nu_i-\nu_{is}}$ is proportional to the cube of the lepton Yukawa coupling. Therefore fitting the atmospheric neutrino data then predicts the $\nu_e-\nu_{es}$ mass difference square to be $\sim (\frac{m_e}{m_{\mu}})^3 \Delta m^2_{atmos}$, where the atmospheric neutrino data is assumed to be solved via the $\nu_{\mu}-\nu_{\mu s}$ oscillation. This provides a natural explanation of the vacuum oscillation solution to the solar neutrino problem.Comment: 7 pages, UMD-PP-99-109; new references added; no other chang

Connecting bimaximal neutrino mixing to a light sterile neutrino

It is shown that if small neutrino masses owe their origin to the conventional seesaw mechanism and the MNS mixing matrix is in the exact bimaximal form, then there exist symmetries in the theory that allow one of the righthanded neutrinos to become naturally massless, making it a candidate for the sterile neutrino discussed in the literature. Departures from the exact bimaximal limit leads to tiny mass for the sterile neutrino as well as its mixing to the active neutrinos. This provides a minimal theoretical framework where a simultaneous explanation of the solar, atmospheric and LSND observations within the so-called 3+1 scenario may be possible.Comment: new references added; paper accepted for publication in Phys. Rev. D.(rapid communications); note adde

Asymmetrical Gene Flow in a Hybrid Zone of Hawaiian Schiedea (Caryophyllaceae) Species with Contrasting Mating Systems

Asymmetrical gene flow, which has frequently been documented in naturally occurring hybrid zones, can result from various genetic and demographic factors. Understanding these factors is important for determining the ecological conditions that permitted hybridization and the evolutionary potential inherent in hybrids. Here, we characterized morphological, nuclear, and chloroplast variation in a putative hybrid zone between Schiedea menziesii and S. salicaria, endemic Hawaiian species with contrasting breeding systems. Schiedea menziesii is hermaphroditic with moderate selfing; S. salicaria is gynodioecious and wind-pollinated, with partially selfing hermaphrodites and largely outcrossed females. We tested three hypotheses: 1) putative hybrids were derived from natural crosses between S. menziesii and S. salicaria, 2) gene flow via pollen is unidirectional from S. salicaria to S. menziesii and 3) in the hybrid zone, traits associated with wind pollination would be favored as a result of pollen-swamping by S. salicaria. Schiedea menziesii and S. salicaria have distinct morphologies and chloroplast genomes but are less differentiated at the nuclear loci. Hybrids are most similar to S. menziesii at chloroplast loci, exhibit nuclear allele frequencies in common with both parental species, and resemble S. salicaria in pollen production and pollen size, traits important to wind pollination. Additionally, unlike S. menziesii, the hybrid zone contains many females, suggesting that the nuclear gene responsible for male sterility in S. salicaria has been transferred to hybrid plants. Continued selection of nuclear genes in the hybrid zone may result in a population that resembles S. salicaria, but retains chloroplast lineage(s) of S. menziesii

Differential clinical features and stool findings in shigellosis and amoebic dysentery

To obtain information that could assist the clinician to differentiate between shigellosis and amoebic dysentery, we compared clinical features and stool findings in 58 adult male patients in Bangladesh. Mean values indicated that patients with invasive amoebiasis were older and had a longer prehospital illness, a lower body weight, less frequent fever, a lower haematocrit and a higher white blood cell count than patients with shigellosis. The mean number of faecal leucocytes per mm3 was significantly higher in shigellosis than in amoebiasis (28,700 vs 10,300) and correlated with the estimated number of faecal leucocytes per microscopic high power field in a wet mount preparation. Patients with shigellosis more often had over 50 white blood cells per high power field. Although the mean stool pH in amoebiasis was lower than in shigellosis (6.26 vs 6.60), the difference was not statistically significant. Concentrations of stool electrolytes did not differ between the two diseases. These findings indicate that age, duration of illness, the presence of fever and the number of faecal leucocytes may help to differentiate between shigellosis and amoebic dysenter

Spectrum of Antley-Bixler Syndrome

Antley-Bixler syndrome (ABS) is an exceptionally rare craniosynostosis syndrome characterized by radiohumeral synostosis present from the perinatal period. There is a wide spectrum of anomalies seen within ABS, and other features include midface hypoplasia; choanal stenosis or atresia; multiple joint contractures; visceral anomalies, particularly of the genitourinary system; and impaired steroidogenesis. The condition of ABS is curious in that mutations of 2 separate genes have been identified and that there seem to be subtle phenotypic differences between the 2 genotypes. Mutations of the P450 oxidoreductase gene have been reported in those patients with genital anomalies and/or impaired steroidogenesis, and the S351C mutation of the fibroblast growth factor receptor 2 gene has been reported predominantly in those patients with normal genitalia and steroidogenesis. We report a series of 4 patients with ABS and review their main findings and management.Karen L. McGlaughlin, Helen Witherow, David J. Dunaway, David J. David and Peter J. Anderso

A qualitative exploration of SMART Recovery meetings in Australia and the role of a digital platform to support routine outcome monitoring

Previous research has reported on the benefits of mutual support groups. However, such groups do not routinely collect data on participant outcomes. Moreover, the effect of collecting outcomes measures on these groups is unknown. The objective of this mixed methods study was to elicit participant views on using a novel, purpose built digital platform for routine outcome monitoring (ROM) as a standard component of a mutual support group. SMART Recovery, or the Self-Management and Recovery Training program, is group-based and uses professional clinicians to facilitate discussion and foster mutual support for a range of addictive behaviours, alongside Cognitive Behavioural Therapy and Motivational Interviewing techniques. This paper reports on the qualitative component of this study and how participants perceive ROMs, and the potential shift to technological resources. Twenty semi-structured telephone interviews were conducted with participants from SMART Recovery groups across New South Wales, Australia. Participants discussed their use of mutual support within group meetings to manage their recovery, including: naming their goals in front of peers; learning from clinicians and group discussion; and developing reciprocal and caring relationships. They also described any previous experience with routine outcomes measures and how digital technologies might enhance or hinder group function. Participants valued mutual support groups and reported that digital technologies could be complementary to physical, weekly group meetings. They were also concerned that the introduction of technological resources might pose a threat to physical meetings, thereby risking their access to mutual support. Findings have implications for the implementation of ROM when delivered via digital mechanisms, and indicate threats and opportunities that warrant consideration for future initiatives

Feasibility of a mobile health app for routine outcome monitoring and feedback in mutual support groups coordinated by SMART recovery Australia: Protocol for a pilot study

Peter J Kelly, Alison K Beck, Amanda L Baker, Frank P Deane, Leanne Hides, Victoria Manning, Anthony Shakeshaft, Briony Larance, Joanne Neale, John Kelly, Christopher Oldmeadow, Andrew Searles, Carla Treloar, Rebecca M Gray, Angela Argent, Ryan McGlaughlin. Originally published in JMIR Research Protocols (http://www.researchprotocols.org), 09.07.2020. This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in JMIR Research Protocols, is properly cited. The complete bibliographic information, a link to the original publication on http://www.researchprotocols.org, as well as this copyright and license information must be included. Background: Despite the importance and popularity of mutual support groups, there have been no systematic attempts to implement and evaluate routine outcome monitoring (ROM) in these settings. Unlike other mutual support groups for addiction, trained facilitators lead all Self-Management and Recovery Training (SMART Recovery) groups, thereby providing an opportunity to implement ROM as a routine component of SMART Recovery groups. Objective: This study protocol aims to describe a stage 1 pilot study designed to explore the feasibility and acceptability of a novel, purpose-built mobile health (mHealth) ROM and feedback app (Smart Track) in SMART Recovery groups coordinated by SMART Recovery Australia (SRAU) The secondary objectives are to describe Smart Track usage patterns, explore psychometric properties of the ROM items (ie, internal reliability and convergent and divergent validity), and provide preliminary evidence for participant reported outcomes (such as alcohol and other drug use, self-reported recovery, and mental health). Methods: Participants (n=100) from the SMART Recovery groups across New South Wales, Australia, will be recruited to a nonrandomized, prospective, single-arm trial of the Smart Track app. There are 4 modes of data collection: (1) ROM data collected from group participants via the Smart Track app, (2) data analytics summarizing user interactions with Smart Track, (3) quantitative interview and survey data of group participants (baseline, 2-week follow-up, and 2-month follow-up), and (4) qualitative interviews with group participants (n=20) and facilitators (n=10). Feasibility and acceptability (primary objectives) will be analyzed using descriptive statistics, a cost analysis, and a qualitative evaluation. Results: At the time of submission, 13 sites (25 groups per week) had agreed to be involved. Funding was awarded on August 14, 2017, and ethics approval was granted on April 26, 2018 (HREC/18/WGONG/34; 2018/099). Enrollment is due to commence in July 2019. Data collection is due to be finalized in October 2019. Conclusions: To the best of our knowledge, this study is the first to use ROM and tailored feedback within a mutual support group setting for addictive behaviors. Our study design will provide an opportunity to identify the acceptability of a novel mHealth ROM and feedback app within this setting and provide detailed information on what factors promote or hinder ROM usage within this context. This project aims to offer a new tool, should Smart Track prove feasible and acceptable, that service providers, policy makers, and researchers could use in the future to understand the impact of SMART Recovery groups