Return times, recurrence densities and entropy for actions of some discrete amenable groups

Results of Wyner and Ziv and of Ornstein and Weiss show that if one observes the first k outputs of a finite-valued ergodic process, then the waiting time until this block appears again is almost surely asymptotic to $2^{hk}$, where $h$ is the entropy of the process. We examine this phenomenon when the allowed return times are restricted to some subset of times, and generalize the results to processes parameterized by other discrete amenable groups. We also obtain a uniform density version of the waiting time results: For a process on $s$ symbols, within a given realization, the density of the initial $k$-block within larger $n$-blocks approaches $2^{-hk}$, uniformly in $n>s^k$, as $k$ tends to infinity. Again, similar results hold for processes with other indexing groups.Comment: To appear in Journal d'Analyse Mathematiqu

Solution of the Percus-Yevick equation for hard discs

We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure

Device for producing and enclosing a hot plasma

1391103 High-frequency discharge tubes EUROPEAN ATOMIC ENERGY COM- MUNITY 24 July 1972 [23 July 1971] 34566/72 Heading H1D A device for producing and enclosing a hot plasma comprises a toroidal vessel 1 having means 2 for generating a magnetic field along the azimuthal axis 3 of the torus to induce annular electric currents along said axis, and means 6, 7 for generating an oscillating electric field in the vessel having a component parallel to the magnetic field and a frequency at or near the bounce frequency (i.e. about ten times the collison frequency of ions.) A second toroidal vessel or liner 4 is disposed in the first vessel 1, and the diameter of the plasma is limited by annular discs 5. The electric field is generated by annular electrodes 6 and 7 disposed above and below the axis 3 and connected through insulated ducts 8 to a generator producing oscillations having a fre- quency between 10 and 100 KHz. The electric field may alternatively be produced by an aerial disposed in an aperture in the vessel wall and fed with a signal having a fundamental frequency corresponding to the plasma frequency which is amplitude modulated at the bounce frequency

The Heterogeneous Course of Depressive Symptoms for the Dementia Caregiver

Caregiving may be burdensome to caregivers, negatively affecting health and impacting decisions to institutionalize patients. It is unclear how caregiver depression changes over longer periods or whether heterogeneous trajectories for caregivers are apparent. The goals of this article are to characterize the course of depressive symptoms among caregivers over time and to examine the impact of baseline patient and caregiver characteristics on these trajectories. Patients with dementia and their caregivers were followed every 6 months for up to 6 years or until death (n = 133). Growth mixture modeling identified trajectories of caregiver depression over time. Most caregivers had stable trajectories of symptoms, with a smaller subset showing evidence of wear-and-tear. Patient clinical characteristics had no impact on symptom course for caregivers. Future work should utilize a longitudinal perspective and consider that there may be heterogeneous trajectories for caregivers. Those caregivers who follow a wear-and-tear trajectory may require targeted interventions to improve outcomes

Takotsubo cardiomyopathy associated with anesthesia: three case reports

Takotsubo cardiomyopathy is a form of transient, reversible left ventricular dysfunction that can mimic an acute coronary event. However, cardiac catheterization often reveals normal coronary arteries. Patients are often postmenopausal women who experience acute physical or emotional distress. The prognosis for this entity is quite favorable. In this report, we present three cases of Takotsubo cardiomyopathy in patients having procedures involving anesthesia. Each case illustrates a different etiology for the syndrome: Patient, procedure, and anesthetic management

The Differential Impact of Unique Behavioral and Psychological Symptoms for the Dementia Caregiver: How and Why Do Patients' Individual Symptom Clusters Impact Caregiver Depressive Symptoms?

OBJECTIVE: The behavioral and psychological symptoms associated with dementia (BPSD) are highly burdensome to caregivers. While BPSD consist of a wide variety of patient behaviors including depression, physical aggression, and paranoid delusions, it remains unclear whether specific symptoms have a differential impact on caregivers. The aims of this study were 1) to assess how individual BPSD, categorized based on how they may affect caregivers, impact depressive symptoms for dementia patient caregivers and 2) to test the pathways by which BPSD clusters impact caregiver depressive symptoms. DESIGN: Cross-sectional analysis of data from a longitudinal study of patients with Alzheimer disease and dementia with Lewy bodies. SETTING: Multiple U.S. dementia clinics. PARTICIPANTS: One hundred sixty patient-caregiver dyads. METHODS: Using multivariate generalized estimating equation logistic models, we analyzed the relationship between four BPSD clusters (patient depressive symptoms, accusatory/aggressive behaviors, nonthreatening psychotic symptoms, and difficult to manage behaviors) and caregiver depressive symptoms and assessed mediators of these relationships. RESULTS: Only the presence of patient depressive symptoms was associated with caregiver depression (odds ratio: 1.55; 95% confidence interval: 1.14-2.1). This relationship was mediated by caregiver report of both the symptom's impact on the patient and perceived burden to caregivers. CONCLUSION: Patient depressive symptoms may be the most important driver of the relationship between BPSD and caregiver depression. Research in this field should further test the effects of individual BPSD and also consider how symptoms may negatively impact caregivers by increasing burden and evoking empathy for the patient

Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions

We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the possibility of phase coexistence between two phases of colloidal suspensions, one being rich and the other being poor in colloidal particles. The reliability of this effective approach is discussed

Are There Sensitive Time Periods for Dementia Caregivers? The Occurrence of Behavioral and Psychological Symptoms in the Early Stages of Dementia

ABSTRACT Background: The behavioral and psychological symptoms associated with dementia (BPSD) can be burdensome to informal/family caregivers, negatively affecting mental health and expediting the institutionalization of patients. Because the dementia patient-caregiver relationship extends over long periods of time, it is useful to examine how BPSD impact caregiver depressive symptoms at varied stages of illness. The goal of this study was to assess the association of BPSD that occur during early stage dementia with subsequent caregiver depressive symptoms. Methods: Patients were followed from the early stages of dementia every six months for up to 12 years or until death (n = 160). Caregiver symptoms were assessed on average 4.5 years following patient's early dementia behaviors. A generalized estimating equation (GEE) extension of the logistic regression model was used to determine the association between informal caregiver depressive symptoms and BPSD symptoms that occurred at the earliest stages dementia, including those persistent during the first year of dementia diagnosis. Results: BPSD were common in early dementia. None of the individual symptoms observed during the first year of early stage dementia significantly impacted subsequent caregiver depressive symptoms. Only patient agitation/aggression was associated with subsequent caregiver depressive symptoms (OR = 1.76; 95% CI = 1.04-2.97) after controlling for concurrent BPSD, although not in fully adjusted models. Conclusions: Persistent agitation/aggression early in dementia diagnosis may be associated with subsequent depressive symptoms in caregivers. Future longitudinal analyses of the dementia caregiving relationship should continue to examine the negative impact of persistent agitation/aggression in the diagnosis of early stage dementia on caregivers

Scale-free networks as preasymptotic regimes of superlinear preferential attachment

We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing network models that perfectly match the structure of some real scale-free networks, such as the Internet. We obtain an analytic solution, supported by extensive simulations, for the degree distribution in superlinearly growing networks with arbitrary average degree, and confirm that in the true thermodynamic limit these networks are indeed degenerate, i.e., almost all nodes have low degrees. We then show that superlinear growth has vast preasymptotic regimes whose depths depend both on the average degree in the network and on how superlinear the preference kernel is. We demonstrate that a superlinearly growing network model can reproduce, in its preasymptotic regime, the structure of a real network, if the model captures some sufficiently strong structural constraints -- rich-club connectivity, for example. These findings suggest that real scale-free networks of finite size may exist in preasymptotic regimes of network evolution processes that lead to degenerate network formations in the thermodynamic limit