Strictly Toral Dynamics

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points $ine(f)$ is shown to be a disjoint union of periodic topological disks ("elliptic islands"), while the set of essential points $ess(f)$ is an essential continuum, with typically rich dynamics (the "chaotic region"). This generalizes and improves a similar description by J\"ager. The key result is boundedness of these "elliptic islands", which allows, among other things, to obtain sharp (uniform) bounds of the diffusion rates. We also show that the dynamics in $ess(f)$ is as rich as in $\mathbb{T}^2$ from the rotational viewpoint, and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points.Comment: Incorporates suggestions and corrections by the referees. To appear in Inv. Mat

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Quantum Tomography under Prior Information

We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system to a set of lower dimensionality, then topological obstructions can increase the required number of outcomes by a factor of two over the number of real parameters needed to characterize the system. Conversely, we show that almost every measurement becomes informationally complete with respect to the constrained set if the number of outcomes exceeds twice the Minkowski dimension of the set. We apply the obtained results to determine the minimal number of outcomes of measurements which are informationally complete with respect to states with rank constraints. In particular, we show that 4d-4 measurement outcomes (POVM elements) is enough in order to identify all pure states in a d-dimensional Hilbert space, and that the minimal number is at most 2 log_2(d) smaller than this upper bound.Comment: v3: There was a mistake in the derived finer upper bound in Theorem 3. The corrected upper bound is +1 to the earlier versio

Low-mass pre--main-sequence stars in the Magellanic Clouds

[Abridged] The stellar Initial Mass Function (IMF) suggests that sub-solar stars form in very large numbers. Most attractive places for catching low-mass star formation in the act are young stellar clusters and associations, still (half-)embedded in star-forming regions. The low-mass stars in such regions are still in their pre--main-sequence (PMS) evolutionary phase. The peculiar nature of these objects and the contamination of their samples by the evolved populations of the Galactic disk impose demanding observational techniques for the detection of complete numbers of PMS stars in the Milky Way. The Magellanic Clouds, the companion galaxies to our own, demonstrate an exceptional star formation activity. The low extinction and stellar field contamination in star-forming regions of these galaxies imply a more efficient detection of low-mass PMS stars than in the Milky Way, but their distance from us make the application of special detection techniques unfeasible. Nonetheless, imaging with the Hubble Space Telescope yield the discovery of solar and sub-solar PMS stars in the Magellanic Clouds from photometry alone. Unprecedented numbers of such objects are identified as the low-mass stellar content of their star-forming regions, changing completely our picture of young stellar systems outside the Milky Way, and extending the extragalactic stellar IMF below the persisting threshold of a few solar masses. This review presents the recent developments in the investigation of PMS stars in the Magellanic Clouds, with special focus on the limitations by single-epoch photometry that can only be circumvented by the detailed study of the observable behavior of these stars in the color-magnitude diagram. The achieved characterization of the low-mass PMS stars in the Magellanic Clouds allowed thus a more comprehensive understanding of the star formation process in our neighboring galaxies.Comment: Review paper, 26 pages (in LaTeX style for Springer journals), 4 figures. Accepted for publication in Space Science Review

Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions

We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the special boundary conditions that are obtained from an m x n grid with free boundary conditions by adjoining one new vertex adjacent to all the sites in the leftmost column and a second new vertex adjacent to all the sites in the rightmost column. We provide numerical evidence that the partition-function zeros are becoming dense everywhere in the complex q-plane outside the limiting curve B_\infty(sq) for this model with ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the infinite-volume free energy is perfectly analytic in this region.Comment: 114 pages (LaTeX2e). Includes tex file, three sty files, and 23 Postscript figures. Also included are Mathematica files data_Eq.m, data_Neq.m,and data_Diff.m. Many changes from version 1, including several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

HIV viral suppression trends over time among HIV-infected patients receiving care in the United States, 1997 to 2015 a cohort study

Background: Because HIV viral suppression is essential for optimal outcomes and prevention efforts, understanding trends and predictors is imperative to inform public health policy. Objective: To evaluate viral suppression trends in people living with HIV (PLWH), including the relationship of associated factors, such as demographic characteristics and integrase strand transfer inhibitor (ISTI) use. Design: Longitudinal observational cohort study. Setting: 8 HIV clinics across the United States. Participants: PLWH receiving clinical care. Measurements: To understand trends in viral suppression (≤400 copies/mL), annual viral suppression rates from 1997 to 2015 were determined. Analyses were repeated with tests limited to 1 random test per person per year and using inverse probability of censoring weights to address loss to follow-up. Joint longitudinal and survival models and linear mixed models of PLWH receiving antiretroviral therapy (ART) were used to examine associations between viral suppression or continuous viral load (VL) levels and demographic factors, substance use, adherence, and ISTI use. Results: Viral suppression increased from 32% in 1997 to 86% in 2015 on the basis of all tests among 31 930 PLWH. In adjusted analyses, being older (odds ratio [OR], 0.76 per decade [95% CI, 0.74 to 0.78]) and using an ISTI-based regimen (OR, 0.54 [CI, 0.51 to 0.57]) were associated with lower odds of having a detectable VL, and black race was associated with higher odds (OR, 1.68 [CI, 1.57 to 1.80]) (P < 0.001 for each). Similar patterns were seen with continuous VL levels; when analyses were limited to 2010 to 2015; and with adjustment for adherence, substance use, or depression. Limitation: Results are limited to PLWH receiving clinical care. Conclusion: HIV viral suppression rates have improved dramatically across the United States, which is likely partially attributable to improved ART, including ISTI-based regimens. However, disparities among younger and black PLWH merit attention

Drug and alcohol use among people living with HIV in care in the United States by geographic region

Substance use in the U.S. varies by geographic region. Opioid prescribing practices and marijuana, heroin, and methamphetamine availability are evolving differently across regions. We examined self-reported substance use among people living with HIV (PLWH) in care at seven sites from 2017–2019 to understand current regional substance use patterns. We calculated the percentage and standardized percentage of PLWH reporting current drug use and at-risk and binge alcohol use by U.S. Census Bureau geographic region and examined associations in adjusted logistic regression analyses. Among 7,686 PLWH, marijuana use was the most prevalent drug (30%), followed by methamphetamine/crystal (8%), cocaine/crack (7%), and illicit opioids (3%). One-third reported binge alcohol use (32%). Differences in percent of current use by region were seen for marijuana (24–41%) and methamphetamine/crystal (2–15%), with more use in the West and Northeast, and binge alcohol use (26–40%). In adjusted analyses, PLWH in the Midwest were significantly less likely to use methamphetamine/crystal (aOR: 0.13;0.06–0.25) or illicit opioids (aOR:0.16;0.05–0.53), and PLWH in the Northeast were more likely to use cocaine/crack (aOR:1.59;1.16–2.17), compared to PLWH in the West. Understanding differences in substance use patterns in the current era, as policies continue to evolve, will enable more targeted interventions in clinical settings among PLWH

Vaporized Nicotine (E-Cigarette) and Tobacco Smoking among People with HIV: Use Patterns and Associations with Depression and Panic Symptoms

Background: Vaporized nicotine (VN) use is increasing among people with HIV (PWH). We examined demographics, patterns of use, depression, and panic symptoms associated with VN and combustible cigarette (CC) use among PWH. Methods: We analyzed VN use among PWH in care at 7 US sites. PWH completed a set of patient-reported outcomes, including substance use and mental health. We categorized VN use as never vs. ever with the frequency of use (days/month) and CC use as never, former, or current. We used relative risk regression to associate VN and CC use, depression, and panic symptoms. Linear regression estimated each relationship with VN frequency. Models were adjusted for demographics. Results: Among 7431 PWH, 812 (11%) reported ever-using VN, and 264 (4%) reported daily use. Half (51%) of VN users concurrently used CC. VN users were more likely than those without use to be younger, to be White, and to report ever-using CC. PWH reporting former CC use reported ≥8.5 more days per month of VN use compared with never CC use [95% confidence interval (95% CI): 5.5 to 11.5 days/month] or current CC use (95% CI: 6.6 to 10.5 days/month). Depression (relative risk: 1.20 [95% CI: 1.02 to 1.42]) and panic disorder (1.71 [95% CI: 1.43 to 2.05]) were more common among PWH ever-using VN. Depression was common among PWH using VN (27%) and CC (22%), as was panic disorder (21% for VN and 16% for CC). Conclusion: Our study elucidated demographic associations with VN use among PWH, revealed the overlap of VN and CC use, and associations with depression/panic symptoms, suggesting roles of VN in self-medication and CC substitution, warranting further longitudinal/qualitative research

Associations between alcohol and cigarette use and type 1 and 2 myocardial infarction among people with HIV

Objectives: People with HIV have a higher risk of myocardial infarction (MI) than the general population, with a greater proportion of type 2 MI (T2MI) due to oxygen demand–supply mismatch compared with type 1 (T1MI) resulting from atherothrombotic plaque disruption. People living with HIV report a greater prevalence of cigarette and alcohol use than do the general population. Alcohol use and smoking as risk factors for MI by type are not well studied among people living with HIV. We examined longitudinal associations between smoking and alcohol use patterns and MI by type among people living with HIV. Design and Methods: Using longitudinal data from the Centers for AIDS Research Network of Integrated Clinical Systems cohort, we conducted time-updated Cox proportional hazards models to determine the impact of smoking and alcohol consumption on adjudicated T1MI and T2MI. Results: Among 13 506 people living with HIV, with a median 4 years of follow-up, we observed 177 T1MI and 141 T2MI. Current smoking was associated with a 60% increase in risk of both T1MI and T2MI. In addition, every cigarette smoked per day was associated with a 4% increase in risk of T1MI, with a suggestive, but not significant, 2% increase for T2MI. Cigarette use had a greater impact on T1MI for men than for women and on T2MI for women than for men. Increasing alcohol use was associated with a lower risk of T1MI but not T2MI. Frequency of heavy episodic alcohol use was not associated with MI. Conclusions: Our findings reinforce the prioritization of smoking reduction, even without cessation, and cessation among people living with HIV for MI prevention and highlight the different impacts on MI type by gender