Systematic Review of Supported Housing Literature 1993 – 2008

Supported housing for individuals with severe mental illness strives to provide the services necessary to place and keep individuals in independent housing that is integrated into the community and in which the consumer has choice and control over his or her services and supports. Supported housing can be contrasted to an earlier model called the “linear residential approach” in which individuals are moved from the most restrictive settings (e.g., inpatient settings) through a series of more independent settings (e.g., group homes, supervised apartments) and then finally to independent housing. This approach has been criticized as punishing the client due to frequent moves, and as being less likely to result in independent housing. In the supported housing model (Anthony & Blanch, 1988) consumers have choice and control over their living environment, their treatment, and supports (e.g., case management, mental health and substance abuse services). Supports are flexible and faded in and out depending on needs. Results of this systematic review of supported housing suggest that there are several well-controlled studies of supported housing and several studies conducted with less rigorous designs. Overall, our synthesis suggests that supported housing can improve the living situation of individuals who are psychiatrically disabled, homeless and with substance abuse problems. Results show that supported housing can help people stay in apartments or homes up to about 80% of the time over an extended period. These results are contrary to concerns expressed by proponents of the linear residential model and housing models that espoused more restrictive environments. Results also show that housing subsidies or vouchers are helpful in getting and keeping individuals housed. Housing services appear to be cost effective and to reduce the costs of other social and clinical services. In order to be most effective, intensive case management services (rather than traditional case management) are needed and will generally lead to better housing outcomes. Having access to affordable housing and having a service system that is well-integrated is also important. Providing a person with supported housing reduces the likelihood that they will be re-hospitalized, although supported housing does not always lead to reduced psychiatric symptoms. Supported housing can improve clients’ quality of life and satisfaction with their living situation. Providing supported housing options that are of decent quality is important in order to keep people housed and satisfied with their housing. In addition, rapid entry into housing, with the provision of choices is critical. Program and clinical supports may be able to mitigate the social isolation that has sometimes been associated with supported housing.

Task Assignment in a Distributed System: Improving Performance by Unbalancing Load

We consider the problem of task assignment in a distributed system (such as a distributed Web server) in which task sizes are drawn from a heavy-tailed distribution. Many task assignment algorithms are based on the heuristic that balancing the load at the server hosts will result in optimal performance. We show this conventional wisdom is less true when the task size distribution is heavy-tailed (as is the case for Web file sizes). We introduce a new task assignment policy, called Size Interval Task Assignment with Variable Load (SITA-V). SITA-V purposely operates the server hosts at different loads, and directs smaller tasks to the lighter-loaded hosts. The result is that SITA-V provably decreases the mean task slowdown by significant factors (up to 1000 or more) where the more heavy-tailed the workload, the greater the improvement factor. We evaluate the tradeoff between improvement in slowdown and increase in waiting time in a system using SITA-V, and show conditions under which SITA-V represents a particularly appealing policy. We conclude with a discussion of the use of SITA-V in a distributed Web server, and show that it is attractive because it has a simple implementation which requires no communication from the server hosts back to the task router.

Slack Stealing Job Admission Control Scheduling

In this paper, we present Slack Stealing Job Admission Control (SSJAC)---a methodology for scheduling periodic firm-deadline tasks with variable resource requirements, subject to controllable Quality of Service (QoS) constraints. In a system that uses Rate Monotonic Scheduling, SSJAC augments the slack stealing algorithm of Thuel et al with an admission control policy to manage the variability in the resource requirements of the periodic tasks. This enables SSJAC to take advantage of the 31\% of utilization that RMS cannot use, as well as any utilization unclaimed by jobs that are not admitted into the system. Using SSJAC, each task in the system is assigned a resource utilization threshold that guarantees the minimal acceptable QoS for that task (expressed as an upper bound on the rate of missed deadlines). Job admission control is used to ensure that (1) only those jobs that will complete by their deadlines are admitted, and (2) tasks do not interfere with each other, thus a job can only monopolize the slack in the system, but not the time guaranteed to jobs of other tasks. We have evaluated SSJAC against RMS and Statistical RMS (SRMS). Ignoring overhead issues, SSJAC consistently provides better performance than RMS in overload, and, in certain conditions, better performance than SRMS. In addition, to evaluate optimality of SSJAC in an absolute sense, we have characterized the performance of SSJAC by comparing it to an inefficient, yet optimal scheduler for task sets with harmonic periods.

Store Working Memory Networks for Storage and Recall of Arbitrary Temporal Sequences

Neural network models of working memory, called Sustained Temporal Order REcurrent (STORE) models, are described. They encode the invariant temporal order of sequential events in short term memory (STM) in a way that mimics cognitive data about working memory, including primacy, recency, and bowed order and error gradients. As new items are presented, the pattern of previously stored items is invariant in the sense that, relative activations remain constant through time. This invariant temporal order code enables all possible groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such a competence is needed to design self-organizing temporal recognition and planning systems in which any subsequence of events may need to be categorized in order to to control and predict future behavior or external events. STORE models show how arbitrary event sequences may be invariantly stored, including repeated events. A preprocessor interacts with the working memory to represent event repeats in spatially separate locations. It is shown why at least two processing levels are needed to invariantly store events presented with variable durations and interstimulus intervals. It is also shown how network parameters control the type and shape of primacy, recency, or bowed temporal order gradients that will be stored.

Nanostructured ferroelectric materials

Nanostructured materials are central to the evolution of future electronics and information technologies. Ferroelectrics have already been established as a dominant branch in the electronics sector because of their diverse application range such as ferroelectric memories, ferroelectric tunnel junctions, etc. The on-going dimensional downscaling of materials to allow packing of increased numbers of components onto integrated circuits provides the momentum for the evolution of nanostructured ferroelectric materials and devices. Nanoscaling of ferroelectric materials can result in a modification of their functionality, such as phase transition temperature or Curie temperature (TC), domain dynamics, dielectric constant, coercive field, spontaneous polarisation and piezoelectric response. Furthermore, nanoscaling can be used to form high density arrays of monodomain ferroelectric nanostructures, which is desirable for the miniaturisation of memory devices. This thesis details the use of various types of nanostructuring approaches to fabricate arrays of ferroelectric nanostructures, particularly non-oxide based systems. The introductory chapter reviews some exemplary research breakthroughs in the synthesis, characterisation and applications of nanoscale ferroelectric materials over the last decade, with priority given to novel synthetic strategies. Chapter 2 provides an overview of the experimental methods and characterisation tools used to produce and probe the properties of nanostructured antimony sulphide (Sb2S3), antimony sulpho iodide (SbSI) and lead titanate zirconate (PZT). In particular, Chapter 2 details the general principles of piezoresponse microscopy (PFM). Chapter 3 highlights the fabrication of arrays of Sb2S3 nanowires with variable diameters using newly developed solventless template-based approach. A detailed account of domain imaging and polarisation switching of these nanowire arrays is also provided. Chapter 4 details the preparation of vertically aligned arrays of SbSI nanorods and nanowires using a surface-roughness assisted vapour-phase deposition method. The qualitative and quantitative nanoscale ferroelectric properties of these nanostructures are also discussed. Chapter 5 highlights the fabrication of highly ordered arrays of PZT nanodots using block copolymer self-assembled templates and their ferroelectric characterisation using PFM. Chapter 6 summarises the conclusions drawn from the results reported in chapters 3, 4 and 5 and the future work.

A knowledge management system to optimise comfort throughout the building life-cycle

Comfort is, in essence, satisfaction with the environment, and with respect to the indoor environment it is primarily satisfaction with the thermal conditions and air quality. Improving comfort has social, health and economic benefits, and is more financially significant than any other building cost. Despite this, comfort is not strictly managed throughout the building lifecycle. This is mainly due to the lack of an appropriate system to adequately manage comfort knowledge through the construction process into operation. Previous proposals to improve knowledge management have not been successfully adopted by the construction industry. To address this, the BabySteps approach was devised. BabySteps is an approach, proposed by this research, which states that for an innovation to be adopted into the industry it must be implementable through a number of small changes. This research proposes that improving the management of comfort knowledge will improve comfort. ComMet is a new methodology proposed by this research that manages comfort knowledge. It enables comfort knowledge to be captured, stored and accessed throughout the building life-cycle and so allowing it to be re-used in future stages of the building project and in future projects. It does this using the following: Comfort Performances – These are simplified numerical representations of the comfort of the indoor environment. Comfort Performances quantify the comfort at each stage of the building life-cycle using standard comfort metrics. Comfort Ratings - These are a means of classifying the comfort conditions of the indoor environment according to an appropriate standard. Comfort Ratings are generated by comparing different Comfort Performances. Comfort Ratings provide additional information relating to the comfort conditions of the indoor environment, which is not readily determined from the individual Comfort Performances. Comfort History – This is a continuous descriptive record of the comfort throughout the project, with a focus on documenting the items and activities, proposed and implemented, which could potentially affect comfort. Each aspect of the Comfort History is linked to the relevant comfort entity it references. These three components create a comprehensive record of the comfort throughout the building lifecycle. They are then stored and made available in a common format in a central location which allows them to be re-used ad infinitum. The LCMS System was developed to implement the ComMet methodology. It uses current and emerging technologies to capture, store and allow easy access to comfort knowledge as specified by ComMet. LCMS is an IT system that is a combination of the following six components: Building Standards; Modelling & Simulation; Physical Measurement through the specially developed Egg-Whisk (Wireless Sensor) Network; Data Manipulation; Information Recording; Knowledge Storage and Access.Results from a test case application of the LCMS system - an existing office room at a research facility - highlighted that while some aspects of comfort were being maintained, the building’s environment was not in compliance with the acceptable levels as stipulated by the relevant building standards. The implementation of ComMet, through LCMS, demonstrates how comfort, typically only considered during early design, can be measured and managed appropriately through systematic application of the methodology as means of ensuring a healthy internal environment in the building.

The effect of positive psychological interventions on psychological and physical well-being during pregnancy

Prenatal well-being can have significant effects on the mother and developing foetus. Positive psychological interventions, including gratitude and mindfulness, consistently demonstrate benefits for well-being in diverse populations. No research has been conducted on gratitude during pregnancy; the few studies of prenatal mindfulness interventions have demonstrated well-being benefits. The current study examined the effects of gratitude and mindfulness interventions on prenatal maternal well-being, cortisol and birth outcomes. Five studies were conducted. Study 1 was a systematic review of mindfulness intervention effects on cortisol; this highlighted potential benefits of mindfulness but the need for rigorous protocols in future research. In Study 2 a gratitude and a mindfulness intervention were developed and evaluated; findings indicate usefulness of two 3 week interventions. Study 3 examined the effects of these interventions in a randomised controlled trial (RCT) of non-pregnant women, before examining a pregnant group. No significant intervention effects were found in this study, potentially due to insufficient power and poor protocol adherence. Changes in expected directions were observed for most outcomes and the potential utility of a combined gratitude and mindfulness intervention was noted. In Study 4 a gratitude during pregnancy (GDP) scale was developed and the reliability of an existing mindfulness measure (MAAS) was examined in a pregnant group. Both scales were found to be suitable and reliable measures in pregnancy. Study 5 incorporated the findings of the previous four studies to examine of the effect of a combined mindfulness and gratitude intervention with a group of pregnant women. Forty-six participants took part in a 5-week RCT that examined intervention effects on prenatal gratitude, mindfulness, happiness, satisfaction with life, social support, prenatal stress, depression and sleep. Findings indicated that the intervention improved sleep quality and that effects for prenatal distress were approaching significance. Issues of attrition and non-compliance to study protocols were problematic and are discussed. In summary, the current thesis highlights the need for robust measurement, and intervention and cortisol sampling protocols in future research, particularly with pregnant groups. Findings also demonstrate tentative benefits of a gratitude and mindfulness intervention during pregnancy.

Design Optimization and Security For Communication Networks

In this work we introduce a new mathematical tool for optimization of routes, topology design, and energy efficiency in wireless sensor networks. We introduce a vector field formulation that models communication in the network, and routing is performed in the direction of this vector field at every location of the network. The magnitude of the vector field at every location represents the density of amount of data that is being transited through that location. We define the total communication cost in the network as the integral of a quadratic form of the vector field over the network area. With the above formulation, we introduce a mathematical machinery based on partial differential equations very similar to the Maxwell's equations in electrostatic theory. We show that in order to minimize the cost, the routes should be found based on the solution of these partial differential equations. In our formulation, the sensors are sources of information, and they are similar to the positive charges in electrostatics, the destinations are sinks of information and they are similar to negative charges, and the network is similar to a non-homogeneous dielectric media with variable dielectric constant (or permittivity coefficient). In one of the applications of our mathematical model based on the vector fields, we offer a scheme for energy efficient routing. Our routing scheme is based on changing the permittivity coefficient to a higher value in the places of the network where nodes have high residual energy, and setting it to a low value in the places of the network where the nodes do not have much energy left. Our simulations show that our method gives a significant increase in the network life compared to the shortest path and weighted shortest path schemes. Our initial focus is on the case where there is only one destination in the network, and later we extend our approach to the case where there are multiple destinations in the network. In the case of having multiple destinations, we need to partition the network into several areas known as regions of attraction of the destinations. Each destination is responsible for collecting all messages being generated in its region of attraction. The complexity of the optimization problem in this case is how to define regions of attraction for the destinations and how much communication load to assign to each destination to optimize the performance of the network. We use our vector field model to solve the optimization problem for this case. We define a vector field, which is conservative, and hence it can be written as the gradient of a scalar field (also known as a potential field). Then we show that in the optimal assignment of the communication load of the network to the destinations, the value of that potential field should be equal at the locations of all the destinations. Another application of our vector field model is to find the optimal locations of the destinations in the network. We show that the vector field gives the gradient of the cost function with respect to the locations of the destinations. Based on this fact, we suggest an algorithm to be applied during the design phase of a network to relocate the destinations for reducing the communication cost function. The performance of our proposed schemes is confirmed by several examples and simulation experiments. In another part of this work we focus on the notions of responsiveness and conformance of TCP traffic in communication networks. We introduce the notion of responsiveness for TCP aggregates and define it as the degree to which a TCP aggregate reduces its sending rate to the network as a response to packet drops. We define metrics that describe the responsiveness of TCP aggregates, and suggest two methods for determining the values of these quantities. The first method is based on a test in which we drop a few packets from the aggregate intentionally and measure the resulting rate decrease of that aggregate. This kind of test is not robust to multiple simultaneous tests performed at different routers. We make the test robust to multiple simultaneous tests by using ideas from the CDMA approach to multiple access channels in communication theory. Based on this approach, we introduce tests of responsiveness for aggregates, and call it CDMA based Aggregate Perturbation Method (CAPM). We use CAPM to perform congestion control. A distinguishing feature of our congestion control scheme is that it maintains a degree of fairness among different aggregates. In the next step we modify CAPM to offer methods for estimating the proportion of an aggregate of TCP traffic that does not conform to protocol specifications, and hence may belong to a DDoS attack. Our methods work by intentionally perturbing the aggregate by dropping a very small number of packets from it and observing the response of the aggregate. We offer two methods for conformance testing. In the first method, we apply the perturbation tests to SYN packets being sent at the start of the TCP 3-way handshake, and we use the fact that the rate of ACK packets being exchanged in the handshake should follow the rate of perturbations. In the second method, we apply the perturbation tests to the TCP data packets and use the fact that the rate of retransmitted data packets should follow the rate of perturbations. In both methods, we use signature based perturbations, which means packet drops are performed with a rate given by a function of time. We use analogy of our problem with multiple access communication to find signatures. Specifically, we assign orthogonal CDMA based signatures to different routers in a distributed implementation of our methods. As a result of orthogonality, the performance does not degrade because of cross interference made by simultaneously testing routers. We have shown efficacy of our methods through mathematical analysis and extensive simulation experiments.

Rapid ratiometric determination of hemoglobin concentration using UV-VIS diffuse reflectance at isosbestic wavelengths.

We developed a ratiometric method capable of estimating total hemoglobin concentration from optically measured diffuse reflectance spectra. The three isosbestic wavelength ratio pairs that best correlated to total hemoglobin concentration independent of saturation and scattering were 545/390, 452/390, and 529/390 nm. These wavelength pairs were selected using forward Monte Carlo simulations which were used to extract hemoglobin concentration from experimental phantom measurements. Linear regression coefficients from the simulated data were directly applied to the phantom data, by calibrating for instrument throughput using a single phantom. Phantoms with variable scattering and hemoglobin saturation were tested with two different instruments, and the average percent errors between the expected and ratiometrically-extracted hemoglobin concentration were as low as 6.3%. A correlation of r = 0.88 between hemoglobin concentration extracted using the 529/390 nm isosbestic ratio and a scalable inverse Monte Carlo model was achieved for in vivo dysplastic cervical measurements (hemoglobin concentrations have been shown to be diagnostic for the detection of cervical pre-cancer by our group). These results indicate that use of such a simple ratiometric method has the potential to be used in clinical applications where tissue hemoglobin concentrations need to be rapidly quantified in vivo.

Crossing the cultural divide: assessing the needs of a local immigrant community

Gemstone Team CARE (Community Assessment of Resident Experiences)

Nutritional Control of L1 Arrest and Recovery in Caenorhabditis elegans by Insulin-like Peptides and Signaling

Animals must coordinate development with fluctuating nutrient availability. Nutrient availability governs post-embryonic development in Caenorhabditis elegans: larvae that hatch in the absence of food do not initiate post-embryonic development but enter "L1 arrest" (or "L1 diapause") and can survive starvation for weeks, while rapidly resume normal development once get fed. Insulin-like signaling (IIS) has been shown to be a key regulator of L1 arrest and recovery. However, the C. elegans genome encodes 40 insulin-like peptides (ILPs), and it is unknown which peptides participate in nutritional control of L1 arrest and recovery. Work in other contexts has identified putative receptor agonists and antagonists, but the extent of specificity versus redundancy is unclear beyond this distinction.

We measured mRNA expression dynamics with high temporal resolution for all 40 insulin-like genes during entry into and recovery from L1 arrest. Nutrient availability influences expression of the majority of insulin-like genes, with variable dynamics suggesting complex regulation. We identified 13 candidate agonists and 8 candidate antagonists based on expression in response to nutrient availability. We selected ten candidate agonists (daf-28, ins-3, ins-4, ins-5, ins-6, ins-7, ins-9, ins-26, ins-33 and ins-35) for further characterization in L1 stage larvae. We used destabilized reporter genes to determine spatial expression patterns. Expression of candidate agonists was largely overlapping in L1 stage larvae, suggesting a role of the intestine, chemosensory neurons ASI and ASJ, and the interneuron PVT in systemic control of L1 development. Transcriptional regulation of candidate agonists was most significant in the intestine, as if nutrient uptake was a more important influence on transcription than sensory perception. Scanning in the 5' upstream promoter region of these 40 ILPs, We found that transcription factor PQM-1 and GATA putative binding sites are depleted in the promoter region of antagonists. A novel motif was also found to be over-represented in ILPs.

Phenotypic analysis of single and compound deletion mutants did not reveal effects on L1 recovery/developmental dynamics, though simultaneous disruption of ins-4 and daf-28 extended survival of L1 arrest without enhancing thermal tolerance, while overexpression of ins-4, ins-6 or daf-28 shortened L1 survival. Simultaneous disruption of several ILPs showed a temperature independent, transient dauer phenotype. These results revealed the relative redundancy and specificity among agonistic ILPs.

TGF- β and steroid hormone (SH) signaling have been reported to control the dauer formation along with IIS. Our preliminary results suggest they may also mediate the IIS control of L1 arrest and recovery, as the expression of several key components of TGF-β and SH signaling pathway genes are negatively regulated by DAF-16, and loss-of-function of these genes partially represses daf-16 null phenotype in L1 arrest, and causes a retardation in L1 development.

In summary, my dissertation study focused on the IIS, characterized the dynamics and sites of ILPs expression in response to nutrient availability, revealed the function of specific agonistic ILPs in L1 arrest, and suggested potential cross-regulation among IIS, TGF-β signaling and SH signaling in controlling L1 arrest and recovery. These findings provide insights into how post-embryonic development is governed by insulin-like signaling and nutrient availability.

Ins-4 and daf-28 function redundantly to regulate C. elegans L1 arrest

© 2014 The Authors.Caenorhabditis elegans larvae reversibly arrest development in the first larval stage in response to starvation (L1 arrest or L1 diapause). Insulin-like signaling is a critical regulator of L1 arrest. However, the C. elegans genome encodes 40 insulin-like peptides, and it is unknown which peptides participate in nutritional control of L1 development. Work in other contexts has revealed that insulin-like genes can promote development ("agonists") or developmental arrest ("antagonists"), suggesting that such agonists promote L1 development in response to feeding. We measured mRNA expression dynamics with high temporal resolution for all 40 insulin-like genes during entry into and recovery from L1 arrest. Nutrient availability influences expression of the majority of insulin-like genes, with variable dynamics suggesting complex regulation. We identified thirteen candidate agonists and eight candidate antagonists based on expression in response to nutrient availability. We selected ten candidate agonists (. daf-28, ins-3, ins-4, ins-5, ins-6, ins-7, ins-9, ins-26, ins-33 and ins-35) for further characterization in L1 stage larvae. We used destabilized reporter genes to determine spatial expression patterns. Expression of candidate agonists is largely overlapping in L1 stage larvae, suggesting a role of the intestine, chemosensory neurons ASI and ASJ, and the interneuron PVT in control of L1 development. Transcriptional regulation of candidate agonists is most significant in the intestine, as if internal nutrient status is a more important influence on transcription than sensory perception. Phenotypic analysis of single and compound deletion mutants did not reveal effects on L1 developmental dynamics, though simultaneous disruption of ins-4 and daf-28 increases survival of L1 arrest. Furthermore, overexpression of ins-4, ins-6 or daf-28 alone decreases survival and promotes cell division during starvation. These results suggest extensive functional overlap among insulin-like genes in nutritional control of L1 development while highlighting the role of ins-4, daf-28 and to a lesser extent ins-6.

A new instrument for measuring anticoagulation-related quality of life: development and preliminary validation.

BACKGROUND: Anticoagulation can reduce quality of life, and different models of anticoagulation management might have different impacts on satisfaction with this component of medical care. Yet, to our knowledge, there are no scales measuring quality of life and satisfaction with anticoagulation that can be generalized across different models of anticoagulation management. We describe the development and preliminary validation of such an instrument - the Duke Anticoagulation Satisfaction Scale (DASS). METHODS: The DASS is a 25-item scale addressing the (a) negative impacts of anticoagulation (limitations, hassles and burdens); and (b) positive impacts of anticoagulation (confidence, reassurance, satisfaction). Each item has 7 possible responses. The DASS was administered to 262 patients currently receiving oral anticoagulation. Scales measuring generic quality of life, satisfaction with medical care, and tendency to provide socially desirable responses were also administered. Statistical analysis included assessment of item variability, internal consistency (Cronbach's alpha), scale structure (factor analysis), and correlations between the DASS and demographic variables, clinical characteristics, and scores on the above scales. A follow-up study of 105 additional patients assessed test-retest reliability. RESULTS: 220 subjects answered all items. Ceiling and floor effects were modest, and 25 of the 27 proposed items grouped into 2 factors (positive impacts, negative impacts, this latter factor being potentially subdivided into limitations versus hassles and burdens). Each factor had a high degree of internal consistency (Cronbach's alpha 0.78-0.91). The limitations and hassles factors consistently correlated with the SF-36 scales measuring generic quality of life, while the positive psychological impact scale correlated with age and time on anticoagulation. The intra-class correlation coefficient for test-retest reliability was 0.80. CONCLUSIONS: The DASS has demonstrated reasonable psychometric properties to date. Further validation is ongoing. To the degree that dissatisfaction with anticoagulation leads to decreased adherence, poorer INR control, and poor clinical outcomes, the DASS has the potential to help identify reasons for dissatisfaction (and positive satisfaction), and thus help to develop interventions to break this cycle. As an instrument designed to be applicable across multiple models of anticoagulation management, the DASS could be crucial in the scientific comparison between those models of care.

Adapting Behavioral Parent Training as an Interactive Computer Game

Behavioral Parent Training (BPT) is a well-established therapy that reduces child externalized behaviors and parent stress. Although BPT was originally developed for parents of children with defiant behaviors, the program’s key concepts are relevant to parenting all children. Since parents might not fully utilize BPT due to cost and program location, we created an online game as a low-cost, easily accessible alternative or complement to BPT. We tested the game with nineteen undergraduate students at the University of Maryland. The experimental group completed pretest survey on core BPT knowledge, played the game, and completed a BPT posttest, while the control group completed a pretest and posttest survey over a three week period. Participants in the experimental group also completed a survey to indicate their satisfaction with the overall program. The experimental group demonstrated significantly higher levels of BPT knowledge than the control group and high levels of satisfaction. This suggests that an interactive, online BPT platform is an engaging and accessible way for parents to learn key concepts.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.