Stability of Affine G-varieties and Irreducibility in Reductive Groups

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it with the numerical criterion of Mumford, and with Richardson and Bate-Martin-R\"ohrle criteria, in the case $X=G^{N}$. Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson-Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions.Comment: 29 pages. To appear in Int. J. Math. Note: this version 4 is identical with version 2 (version 3 is empty

Peer coaching through mHealth targeting physical activity in people with Parkinson disease: feasibility study

BACKGROUND: Long-term engagement in exercise and physical activity mitigates the progression of disability and increases quality of life in people with Parkinson disease (PD). Despite this, the vast majority of individuals with PD are sedentary. There is a critical need for a feasible, safe, acceptable, and effective method to assist those with PD to engage in active lifestyles. Peer coaching through mobile health (mHealth) may be a viable approach. OBJECTIVE: The purpose of this study was to develop a PD-specific peer coach training program and a remote peer-mentored walking program using mHealth technology with the goal of increasing physical activity in persons with PD. We set out to examine the feasibility, safety, and acceptability of the programs along with preliminary evidence of individual-level changes in walking activity, self-efficacy, and disability in the peer mentees. METHODS: A peer coach training program and a remote peer-mentored walking program using mHealth was developed and tested in 10 individuals with PD. We matched physically active persons with PD (peer coaches) with sedentary persons with PD (peer mentees), resulting in 5 dyads. Using both Web-based and in-person delivery methods, we trained the peer coaches in basic knowledge of PD, exercise, active listening, and motivational interviewing. Peer coaches and mentees wore FitBit Zip activity trackers and participated in daily walking over 8 weeks. Peer dyads interacted daily via the FitBit friends mobile app and weekly via telephone calls. Feasibility was determined by examining recruitment, participation, and retention rates. Safety was assessed by monitoring adverse events during the study period. Acceptability was assessed via satisfaction surveys. Individual-level changes in physical activity were examined relative to clinically important differences. RESULTS: Four out of the 5 peer pairs used the FitBit activity tracker and friends function without difficulty. A total of 4 of the 5 pairs completed the 8 weekly phone conversations. There were no adverse events over the course of the study. All peer coaches were "satisfied" or "very satisfied" with the training program, and all participants were "satisfied" or "very satisfied" with the peer-mentored walking program. All participants would recommend this program to others with PD. Increases in average steps per day exceeding the clinically important difference occurred in 4 out of the 5 mentees. CONCLUSIONS: Remote peer coaching using mHealth is feasible, safe, and acceptable for persons with PD. Peer coaching using mHealth technology may be a viable method to increase physical activity in individuals with PD. Larger controlled trials are necessary to examine the effectiveness of this approach.This study is supported by Boston Roybal Center for Active Lifestyle Interventions (RALI Boston), Grant #P30 AG048785, and the American Parkinson Disease Association, Massachusetts chapter. The authors would like to thank Nicole Sullivan, SOT, for her assistance with data management and data collection and Nick Wendel, DPT, for his assistance with data collection. Additionally, the authors would like to thank the participants in this study for their time, effort, and insights. (P30 AG048785 - Boston Roybal Center for Active Lifestyle Interventions (RALI Boston); American Parkinson Disease Association, Massachusetts chapter)Accepted manuscrip

Critical Hysteresis in Random Field XY and Heisenberg Models

We study zero-temperature hysteresis in random-field XY and Heisenberg models in the zero-frequency limit of a cyclic driving field. We consider three distributions of the random field and present exact solutions in the mean field limit. The results show a strong effect of the form of disorder on critical hysteresis as well as the shape of hysteresis loops. A discrepancy with an earlier study based on the renormalization group is resolved.Comment: 10 pages, 6 figures; this is published version (added some text and references

Complications of Cushing's syndrome: state of the art

Cushing's syndrome is a serious endocrine disease caused by chronic, autonomous, and excessive secretion of cortisol. The syndrome is associated with increased mortality and impaired quality of life because of the occurrence of comorbidities. These clinical complications include metabolic syndrome, consisting of systemic arterial hypertension, visceral obesity, impairment of glucose metabolism, and dyslipidaemia; musculoskeletal disorders, such as myopathy, osteoporosis, and skeletal fractures; neuropsychiatric disorders, such as impairment of cognitive function, depression, or mania; impairment of reproductive and sexual function; and dermatological manifestations, mainly represented by acne, hirsutism, and alopecia. Hypertension in patients with Cushing's syndrome has a multifactorial pathogenesis and contributes to the increased risk for myocardial infarction, cardiac failure, or stroke, which are the most common causes of death; risks of these outcomes are exacerbated by a prothrombotic diathesis and hypokalaemia. Neuropsychiatric disorders can be responsible for suicide. Immune disorders are common; immunosuppression during active disease causes susceptibility to infections, possibly complicated by sepsis, an important cause of death, whereas immune rebound after disease remission can exacerbate underlying autoimmune diseases. Prompt treatment of cortisol excess and specific treatments of comorbidities are crucial to prevent serious clinical complications and reduce the mortality associated with Cushing's syndrome

CRLF2 rearrangement in Ph-like acute lymphoblastic leukemia predicts relative glucocorticoid resistance that is overcome with MEK or Akt inhibition.

Philadelphia chromosome-like (Ph-like) acute lymphoblastic leukemia (ALL) is a genetically heterogeneous subtype of B-cell ALL characterized by chromosomal rearrangements and mutations that result in aberrant cytokine receptor and kinase signaling. In particular, chromosomal rearrangements resulting in the overexpression of cytokine receptor-like factor 2 (CRLF2) occur in 50% of Ph-like ALL cases. CRLF2 overexpression is associated with particularly poor clinical outcomes, though the molecular basis for this is currently unknown. Glucocorticoids (GCs) are integral to the treatment of ALL and GC resistance at diagnosis is an important negative prognostic factor. Given the importance of GCs in ALL therapy and the poor outcomes for patients with CRLF2 overexpression, we hypothesized that the aberrant signal transduction associated with CRLF2 overexpression might mediate intrinsic GC insensitivity. To test this hypothesis, we exposed Ph-like ALL cells from patient-derived xenografts to GCs and found that CRLF2 rearranged (CRLF2R) leukemias uniformly demonstrated reduced GC sensitivity in vitro. Furthermore, targeted inhibition of signal transduction with the MEK inhibitor trametinib and the Akt inhibitor MK2206, but not the JAK inhibitor ruxolitinib, was sufficient to augment GC sensitivity. These data suggest that suboptimal GC responses may in part underlie the poor clinical outcomes for patients with CRLF2 overexpression and provide rationale for combination therapy involving GCs and signal transduction inhibitors as a means of enhancing GC efficacy

Clear detection of dusty torus signatures in a Weak-Line Radio Galaxy: the case of PKS 0043-42

We report the clearest detection to date of dusty torus signatures in a Weak-Line Radio Galaxy (WLRG). The deep Spitzer InfraRed Spectrograph (IRS) rest-frame mid-infrared (MIR) spectrum of the WLRG PKS 0043-42 (z=0.116) shows a clear spectral turnover at wavelengths longer than ~20 micron suggestive of warm dust, as well as a 9.7 micron silicate absorption feature. In addition, the hard X-ray results, based on Chandra data, strongly support a picture in which PKS 0043-42 has a torus and accretion disc more typical of Strong-Line Radio Galaxies (SLRGs). The MIR and X-ray spectra are markedly different from those of other WLRGs at similar redshifts, and here we show that the former can be successfully fitted with clumpy torus models with parameters characteristic of Type-2 AGN tori: close to edge-on (i=74 deg) and relatively broad (torus angular width=60 deg), with an outer radius of 2 pc, hydrogen column density ~1.6x10^(23) cm^(-2), and AGN bolometric luminosity ~1.6x10^(44) erg s^(-1). The presence of a compact torus in PKS 0043-42 provides evidence that this WLRG is fuelled by cold, rather than hot, gas accretion. We suggest that WLRGs are a diverse population, and PKS 0043-42 may represent a type of radio galaxy in which the AGN activity has been recently re-triggered as a consequence of intermittent gas supply, or in which the covering factor of the Narrow-Line Region (NLR) clouds is relatively low.Comment: 7 pages, 6 figures, 1 table. Accepted by MNRA

Finite size effects in the dynamics of glass-forming liquids

We present a comprehensive theoretical study of finite size effects in the relaxation dynamics of glass-forming liquids. Our analysis is motivated by recent theoretical progress regarding the understanding of relevant correlation length scales in liquids approaching the glass transition. We obtain predictions both from general theoretical arguments and from a variety of specific perspectives: mode-coupling theory, kinetically constrained and defect models, and random first order transition theory. In the latter approach, we predict in particular a non-monotonic evolution of finite size effects across the mode-coupling crossover due to the competition between mode-coupling and activated relaxation. We study the role of competing relaxation mechanisms in giving rise to non-monotonic finite size effects by devising a kinetically constrained model where the proximity to the mode-coupling singularity can be continuously tuned by changing the lattice topology. We use our theoretical findings to interpret the results of extensive molecular dynamics studies of four model liquids with distinct structures and kinetic fragilities. While the less fragile model only displays modest finite size effects, we find a more significant size dependence evolving with temperature for more fragile models, such as Lennard-Jones particles and soft spheres. Finally, for a binary mixture of harmonic spheres we observe the predicted non-monotonic temperature evolution of finite size effects near the fitted mode-coupling singularity, suggesting that the crossover from mode-coupling to activated dynamics is more pronounced for this model. Finally, we discuss the close connection between our results and the recent report of a non-monotonic temperature evolution of a dynamic length scale near the mode-coupling crossover in harmonic spheres.Comment: 19 pages, 10 figures. V2: response to referees + refs added (close to published version

State estimation in quantum homodyne tomography with noisy data

In the framework of noisy quantum homodyne tomography with efficiency parameter $0 < \eta \leq 1$, we propose two estimators of a quantum state whose density matrix elements $\rho_{m,n}$ decrease like $e^{-B(m+n)^{r/ 2}}$, for fixed known $B>0$ and $0<r\leq 2$. The first procedure estimates the matrix coefficients by a projection method on the pattern functions (that we introduce here for $0<\eta \leq 1/2$), the second procedure is a kernel estimator of the associated Wigner function. We compute the convergence rates of these estimators, in $\mathbb{L}_2$ risk