Embeddings of 3-manifolds in S^4 from the point of view of the 11-tetrahedron census

This is a collection of notes on embedding problems for 3-manifolds. The main question explored is `which 3-manifolds embed smoothly in the 4-sphere?' The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed 3-manifolds built from 11 or less tetrahedra. There are 13766 manifolds in the census, of which 13400 are orientable. Of the 13400 orientable manifolds, only 149 of them have hyperbolic torsion linking forms and are thus candidates for embedability in the 4-sphere. The majority of this paper is devoted to the embedding problem for these 149 manifolds. At present 41 are known to embed. Among the remaining manifolds, embeddings into homotopy 4-spheres are constructed for 4. 67 manifolds are known to not embed in the 4-sphere. This leaves 37 unresolved cases, of which only 3 are geometric manifolds i.e. having a trivial JSJ-decomposition.Comment: 58 pages, 80+ figures. V6: Included references to libraries valid in Regina 5.0+. Incorporated changes suggested by Ahmed Issa, following from his techniques developed with McCoy. Included a few recent references. To appear in Experimental Mathematic

Triangulating a Cappell-Shaneson knot complement

We show that one of the Cappell-Shaneson knot complements admits an extraordinarily small triangulation, containing only two 4-dimensional simplices.Comment: 9 pages, 5 figures. V2->V3: Primary figures now display a symmetry of order two. Attaching maps made "order-preserving". A new figure describing the dual 2-cells is included. Previous arguments simplified a little, due to the symmetr

BV-structures on the homology of the framed long knot space

We introduce BV-algebra structures on the homology of the space of framed long knots in $\mathbb{R}^n$ in two ways. The first one is given in a similar fashion to Chas-Sullivan's string topology. The second one is defined on the Hochschild homology associated with a cyclic, multiplicative operad of graded modules. The latter can be applied to Bousfield-Salvatore spectral sequence converging to the homology of the space of framed long knots. Conjecturally these two structures coincide with each other.Comment: 13 pages, 3 figures, to appear in Journal of Homotopy and Related Structure

Palaeomagnetism of the Bayan Gol formation, western Mongolia

Oriented samples of the Lower Cambrian Bayan Gol Formation from Salaany Gol, Mongolia, were collected at roughly 5 m stratigraphic intervals for palaeomagnetic analysis. Progressive alternating-field and thermal demagnetization isolated two magnetic components: a present-field overprint, typically removed by 10 mT fields and ~200°C heating; and a high-coercivity, high-unblocking-temperature (550–600 °C), predominantly single-polarity component that was imparted to the rocks prior to early or middle Palaeozoic deformation. Single-polarity magnetization at Salaany Gol contrasts with results from Lower Cambrian rocks on the Siberian platform, previously considered correlative with the Bayan Gol Formation, which show a prominent change in polarity bias near the top of the Tommotian Stage. Two hypotheses can explain this discrepancy. First, the entire Bayan Gol Formation may correlate with the predominantly reversely polarized, lower half of the Tommotian Stage in Siberia. This model is consistent with plausible interpretations of δ^(13)C profiles for the Zavkhan basin and the Siberian platform. Alternatively, the characteristic magnetic direction from our samples may be a pre-fold overprint. If post-accretionary, then comparison with Siberian palaeomagnetic results suggest a Silurian–Devonian remagnetization age, and existing bioand chemostratigraphic correlations provide the most reliable spatial and temporal links between the Zavkhan basin and the Siberian platform. If the observed magnetic directions are primary or an immediate overprint then they may be used to constrain the early Cambrian palaeogeography of the Zavkhan basin and the Palaeo-Pacific Ocean. Mean inclination of 62 ± 4° corresponds to a palaeolatitude of 44 ± 5°, several thousand kilometres from the equatorial Siberian craton

It\u27s way more than just writing a prescription : A qualitative study of preferences for integrated versus non-integrated treatment models among individuals with opioid use disorder

BACKGROUND: Increasingly, treatment for opioid use disorder (OUD) is offered in integrated treatment models addressing both substance use and other health conditions within the same system. This often includes offering medications for OUD in general medical settings. It remains uncertain whether integrated OUD treatment models are preferred to non-integrated models, where treatment is provided within a distinct treatment system. This study aimed to explore preferences for integrated versus non-integrated treatment models among people with OUD and examine what factors may influence preferences. METHODS: This qualitative study recruited participants (n = 40) through Craigslist advertisements and flyers posted in treatment programs across the United States. Participants were 18 years of age or older and scored a two or higher on the heroin or opioid pain reliever sections of the Tobacco, Alcohol, Prescription Medications, and Other Substances (TAPS) Tool. Each participant completed a demographic survey and a telephone interview. The interviews were coded and content analyzed. RESULTS: While some participants preferred receiving OUD treatment from an integrated model in a general medical setting, the majority preferred non-integrated models. Some participants preferred integrated models in theory but expressed concerns about stigma and a lack of psychosocial services. Tradeoffs between integrated and non-integrated models were centered around patient values (desire for anonymity and personalization, fear of consequences), the characteristics of the provider and setting (convenience, perceived treatment effectiveness, access to services), and the patient-provider relationship (disclosure, trust, comfort, stigma). CONCLUSIONS: Among this sample of primarily White adults, preferences for non-integrated versus integrated OUD treatment were mixed. Perceived benefits of integrated models included convenience, potential for treatment personalization, and opportunity to extend established relationships with medical providers. Recommendations to make integrated treatment more patient-centered include facilitating access to psychosocial services, educating patients on privacy, individualizing treatment, and prioritizing the patient-provider relationship. This sample included very few minorities and thus findings may not be fully generalizable to the larger population of persons with OUD. Nonetheless, results suggest a need for expansion of both OUD treatment in specialty and general medical settings to ensure access to preferred treatment for all

“It’s way more than just writing a prescription”: A qualitative study of preferences for integrated versus non-integrated treatment models among individuals with opioid use disorder

Background: Increasingly, treatment for opioid use disorder (OUD) is offered in integrated treatment models addressing both substance use and other health conditions within the same system. This often includes offering medications for OUD in general medical settings. It remains uncertain whether integrated OUD treatment models are preferred to non-integrated models, where treatment is provided within a distinct treatment system. This study aimed to explore preferences for integrated versus non-integrated treatment models among people with OUD and examine what factors may influence preferences. Methods: This qualitative study recruited participants (n = 40) through Craigslist advertisements and flyers posted in treatment programs across the United States. Participants were 18 years of age or older and scored a two or higher on the heroin or opioid pain reliever sections of the Tobacco, Alcohol, Prescription Medications, and Other Substances (TAPS) Tool. Each participant completed a demographic survey and a telephone interview. The interviews were coded and content analyzed. Results: While some participants preferred receiving OUD treatment from an integrated model in a general medical setting, the majority preferred non-integrated models. Some participants preferred integrated models in theory but expressed concerns about stigma and a lack of psychosocial services. Tradeoffs between integrated and non-integrated models were centered around patient values (desire for anonymity and personalization, fear of consequences), the characteristics of the provider and setting (convenience, perceived treatment effectiveness, access to services), and the patient-provider relationship (disclosure, trust, comfort, stigma). Conclusions: Among this sample of primarily White adults, preferences for non-integrated versus integrated OUD treatment were mixed. Perceived benefits of integrated models included convenience, potential for treatment personalization, and opportunity to extend established relationships with medical providers. Recommendations to make integrated treatment more patient-centered include facilitating access to psychosocial services, educating patients on privacy, individualizing treatment, and prioritizing the patient-provider relationship. This sample included very few minorities and thus findings may not be fully generalizable to the larger population of persons with OUD. Nonetheless, results suggest a need for expansion of both OUD treatment in specialty and general medical settings to ensure access to preferred treatment for all

Workshop on the Development and Evaluation of Digital Therapeutics for Health Behavior Change: Science, Methods, and Projects

The health care field has integrated advances into digital technology at an accelerating pace to improve health behavior, health care delivery, and cost-effectiveness of care. The realm of behavioral science has embraced this evolution of digital health, allowing for an exciting roadmap for advancing care by addressing the many challenges to the field via technological innovations. Digital therapeutics offer the potential to extend the reach of effective interventions at reduced cost and patient burden and to increase the potency of existing interventions. Intervention models have included the use of digital tools as supplements to standard care models, as tools that can replace a portion of treatment as usual, or as stand-alone tools accessed outside of care settings or direct to the consumer. To advance the potential public health impact of this promising line of research, multiple areas warrant further development and investigation. The Center for Technology and Behavioral Health (CTBH), a P30 Center of Excellence supported by the National Institute on Drug Abuse at the National Institutes of Health, is an interdisciplinary research center at Dartmouth College focused on the goal of harnessing existing and emerging technologies to effectively develop and deliver evidence-based interventions for substance use and co-occurring disorders. The CTBH launched a series of workshops to encourage and expand multidisciplinary collaborations among Dartmouth scientists and international CTBH affiliates engaged in research related to digital technology and behavioral health (eg, addiction science, behavioral health intervention, technology development, computer science and engineering, digital security, health economics, and implementation science). This paper summarizes a workshop conducted on the Development and Evaluation of Digital Therapeutics for Behavior Change, which addressed (1) principles of behavior change, (2) methods of identifying and testing the underlying mechanisms of behavior change, (3) conceptual frameworks for optimizing applications for mental health and addictive behavior, and (4) the diversity of experimental methods and designs that are essential to the successful development and testing of digital therapeutics. Examples were presented of ongoing CTBH projects focused on identifying and improving the measurement of health behavior change mechanisms and the development and evaluation of digital therapeutics. In summary, the workshop showcased the myriad research targets that will be instrumental in promoting and accelerating progress in the field of digital health and health behavior change and illustrated how the CTBH provides a model of multidisciplinary leadership and collaboration that can facilitate innovative, science-based efforts to address the health behavior challenges afflicting our communities

On the geometrization of matter by exotic smoothness

In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein-Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. For sufficient complicated links and knots, there are "connecting tubes" (graph manifolds, torus bundles) which introduce an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components. We also discuss the gauge group of the theory to be U(1)xSU(2)xSU(3).Comment: 30 pages, 3 figures, svjour style, complete reworking now using Fintushel-Stern knot surgery of elliptic surfaces, discussion of Lorentz metric and global hyperbolicity for exotic 4-manifolds added, final version for publication in Gen. Rel. Grav, small typos errors fixe

QUEST: A New Frontiers Uranus Orbiter Mission Concept Study

The ice giant planets, Uranus and Neptune, are fundamentally different from the gas giant and terrestrial planets. Though ice giants represent the most common size of exoplanet and possess characteristics that challenge our understanding of the way our solar system formed and evolved, they remain the only class of planetary object without a dedicated spacecraft mission. The inclusion of a Uranus orbiter as the third highest priority Flagship mission in the NASA Planetary Science Decadal Survey “Vision and Voyages for Planetary Science in the Decade 2013–2022” indicates a high level of support for exploration of the ice giants by the planetary science community. However, given the substantial costs associated with a flagship mission, it is critical to explore lower cost options if we intend to visit Uranus within an ideal launch window of 2029 - 2034 when a Jupiter gravity assist becomes available. In this paper, we describe the Quest to Uranus to Explore Solar System Theories (QUEST), a New Frontiers class Uranus orbiter mission concept study performed at the 30th Annual NASA/JPL Planetary Science Summer Seminar. The proposed QUEST platform is a spin-stabilized spacecraft designed to undergo highly elliptical, polar orbits around Uranus during a notional one-year primary science mission. The proposed major science goals of the mission are (1) to use Uranus as a natural laboratory to better understand the dynamos that drive magnetospheres in the solar system and beyond and (2) to identify the energy transport mechanisms in Uranus' magnetic, atmospheric, and interior environments in contrast with the other giant planets. With substantial mass, power, and cost margins, this mission concept demonstrates a compelling, feasible option for a New Frontiers Uranus orbiter mission