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Consideration is given to three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly well suited to describe evolutions of the total number of customers in (in)homogeneous M/M/S queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared with those known from the literature) under which the methods are applicable are being formulated. Two numerical examples are given. It is also shown that, for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound.

In this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics (the idle probability and the mean number of customers in the system) of the systems considered with a given approximation error.

BACKGROUND: Resurgent psychedelic research has largely supported the safety and efficacy of psychedelic therapy for the treatment of various psychiatric disorders. As psychedelic use and therapy increase in prevalence, so does the importance of understanding associated risks. Cases of prolonged negative psychological responses to psychedelic therapy seem to be rare; however, studies are limited by biases and small sample sizes. The current analytical approach was motivated by the question of whether rare but significant adverse effects have been under-sampled in psychedelic research studies. METHODS: A bottom margin analysis approach was taken to focus on negative responders to psychedelic use in a pool of naturalistic, observational prospective studies (N = 807). We define negative response by a clinically meaningful decline in a generic index of mental health, that is, one standard error from the mean decrease in psychological well-being 4 weeks post-psychedelic use (vs pre-use baseline). We then assessed whether a history of diagnosed mental illness can predict negative responses. RESULTS: We find that 16% of the cohort falls into the negative responder subset. Parsing the sample by self-reported history of psychiatric diagnoses, results revealed a disproportionate prevalence of negative responses among those reporting a prior personality disorder diagnosis (31%). One multivariate regression model indicated a greater than four-fold elevated risk of adverse psychological responses to psychedelics in the personality disorder subsample (b = 1.425, p

Psilocybin, a serotonergic psychedelic, is being increasingly researched in clinical studies for the treatment of psychiatric disorders. The relatively lengthy duration of oral psilocybins acute effects (4-6 h) may have pragmatic and cost-effectiveness limitations. Here, we explored the effects of intravenous (IV) N,N-Dimethyltryptamine (DMT), a closely related, but faster-acting psychedelic intervention, on mental health outcomes in healthy volunteers. Data is reported from two separate analyses: (1) A comparison of mental health-related variables 1 week after 7, 14, 18, and 20 mg of IV DMT versus IV saline placebo (n = 13) and, (2) A prospective dataset assessing effects before versus 2 weeks after 20 mg of IV DMT (n = 17). Mental health outcomes included measures of depression severity (QIDS-SR16), trait anxiety (STAI-T), Neuroticism (NEO-FFI), wellbeing (WHO-5), meaning in life (MLQ), optimism (LOT-R), and gratitude (GQ-6). In both the prospective and placebo-controlled datasets, significant improvements in scores of depression were found 1-2 weeks after DMT administration. Significant reductions in trait Neuroticism were only found for the placebo-controlled sample. Finally, changes in depression and trait anxiety correlated with acute peak experiences (assessed via Oceanic Boundlessness). While the use of two separate cohorts in pooled analysis limits the generalizability of these correlational findings, these results suggest that DMT may reduce depressive symptomatology by inducing peak experiences. The short half-life of IV DMT and its potential for flexible dosing via controlled infusions makes it an appealing candidate for psychedelic medicine. Further research in clinical samples is needed to corroborate the therapeutic potential of DMT.

Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, time-dependent analysis is more meaningful. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.

Psilocybin and lysergic acid diethylamide (LSD) experiences can range from very positive to highly challenging (e.g., fear, grief, and paranoia). These challenging experiences contribute to hesitancy toward psychedelic-assisted psychotherapy among health care providers and patients. Co-use of 3,4-Methylenedioxy methamphetamine (MDMA) with psilocybin/LSD anecdotally reduces challenging experiences and enhances positive experiences associated with psilocybin/LSD. However, limited research has investigated the acute effects of co-use of MDMA and psilocybin/LSD. In a prospective convenience sample (N = 698) of individuals with plans to use psilocybin/LSD, we examined whether co-use of MDMA with psilocybin/LSD (n = 27) is associated with differences in challenging or positive experiences. Challenging experiences were measured using the Challenging Experiences Questionnaire and positive experiences were measured using the Mystical Experience Questionnaire and single-item measures of self-compassion, compassion, love, and gratitude. Potentially confounding variables were identified and included as covariates. Relative to psilocybin/LSD alone, co-use of psilocybin/LSD with a self-reported low (but not medium-high) dose of MDMA was associated with significantly less intense total challenging experiences, grief, and fear, as well as increased self-compassion, love and gratitude. Co-use of psilocybin/LSD and MDMA was not associated with differences in mystical-type experiences or compassion. Findings suggest co-use of MDMA with psilocybin/LSD may buffer against some aspects of challenging experiences and enhance certain positive experiences. Limitations include use of a convenience sample, small sample size, and non-experimental design. Additional studies (including controlled dose-response studies) that examine the effects and safety of co-administering MDMA with psilocybin/LSD (in healthy controls and clinical samples) are warranted and may assist the development of personalized treatments.

We investigate a class of exponentially weakly ergodic inhomogeneous birth and death processes. We consider special transformations of the reduced intensity matrix of the process and obtain uniform (in time) error bounds of truncations. Our approach also guarantees that we can find limiting characteristics approximately with an arbitrarily fixed error. As an example, we obtain the respective bounds of the truncation error for an Mt/Mt/S queue for any number of servers S. Arbitrary intensity functions instead of periodic ones can be considered in the same manner.

Abstract Several phase II studies have demonstrated that psilocybin-assisted therapy shows therapeutic potential across a spectrum of neuropsychiatric conditions, including major depressive disorder (MDD). However, the mechanisms underlying its often persisting beneficial effects remain unclear. Observational research suggests that improvements in psychological flexibility may mediate therapeutic effects. However, no psychedelic trials to date have substantiated this finding in a clinical sample. In an exploratory placebo-controlled, within-subject, fixed-order study, individuals with moderate to severe MDD were administered placebo (n = 19) followed by psilocybin (0.3 mg/kg) (n = 15) 4 weeks later. Dosing sessions were embedded within a manualized psychotherapy that incorporated principles of Acceptance and Commitment Therapy. Depression severity, psychological flexibility, mindfulness, and values-congruent living were measured over a 16-weeks study period. Psychological flexibility, several facets of mindfulness, and values-congruent living significantly improved following psilocybin and were maintained through week 16. Additionally, improvements in psychological flexibility and experiential acceptance were strongly associated with reductions in depression severity following psilocybin. These findings support the theoretical premise of integrating psilocybin treatment with psychotherapeutic platforms that target psychological flexibility and add to emerging evidence that increasing psychological flexibility may be an important putative mechanism of change in psilocybin-assisted therapy for MDD and potentially, other mental health conditions.

Abstract Psilocybin, a serotonergic psychedelic, is being increasingly researched in clinical studies for the treatment of psychiatric disorders. The relatively lengthy duration of oral psilocybin’s acute effects (4–6 h) may have pragmatic and cost-effectiveness limitations. Here, we explored the effects of intravenous (IV) N,N-Dimethyltryptamine (DMT), a closely related, but faster-acting psychedelic intervention, on mental health outcomes in healthy volunteers. Data is reported from two separate analyses: (1) A comparison of mental health-related variables 1 week after 7, 14, 18, and 20 mg of IV DMT versus IV saline placebo (n = 13) and, (2) A prospective dataset assessing effects before versus 2 weeks after 20 mg of IV DMT (n = 17). Mental health outcomes included measures of depression severity (QIDS-SR16), trait anxiety (STAI-T), Neuroticism (NEO-FFI), wellbeing (WHO-5), meaning in life (MLQ), optimism (LOT-R), and gratitude (GQ-6). In both the prospective and placebo-controlled datasets, significant improvements in scores of depression were found 1–2 weeks after DMT administration. Significant reductions in trait Neuroticism were only found for the placebo-controlled sample. Finally, changes in depression and trait anxiety correlated with acute peak experiences (assessed via ‘Oceanic Boundlessness’). While the use of two separate cohorts in pooled analysis limits the generalizability of these correlational findings, these results suggest that DMT may reduce depressive symptomatology by inducing peak experiences. The short half-life of IV DMT and its potential for flexible dosing via controlled infusions makes it an appealing candidate for psychedelic medicine. Further research in clinical samples is needed to corroborate the therapeutic potential of DMT.

We revisit the problem of the computation of the limiting characteristics of (in)homogeneous continuous-time Markov chains with the finite state space. In general, it can be performed only numerically. The common rule of thumb is to interrupt calculations after quite some time, hoping that the values at some distant time interval will represent the sought-after solution. Convergence or ergodicity bounds, when available, can be used to answer such questions more accurately; i.e., they can indicate how to choose the position and the length of that distant time interval. The logarithmic norm method is a general technique that may allow one to obtain such bounds. Although it can handle continuous-time Markov chains with both finite and countable state spaces, its downside is the need to guess the proper similarity transformations, which may not exist. In this paper, we introduce a new technique, which broadens the scope of the logarithmic norm method. This is achieved by firstly splitting the generator of a Markov chain and then merging the convergence bounds of each block into a single bound. The proof of concept is illustrated by simple examples of the queueing theory.

ABSTRACTBackground: MDMA-assisted psychotherapy (MDMA-AP) is a combined psychotherapeutic and pharmacologic intervention that shows promise in the treatment of posttraumatic stress disorder (PTSD). Although therapeutic alliance has been established as a key predictor across psychotherapies and is emphasised within MDMA-AP treatment manuals, research has not yet examined the relationship between therapeutic alliance and MDMA-AP treatment outcomes.Objective: Examine whether therapeutic alliance predicts changes in PTSD symptoms following MDMA-AP.Method: Twenty-three individuals with chronic PTSD participated in a MDMA-AP clinical trial that included a randomised (MDMA vs. placebo) and open-label phase. The present analyses focused on participants who were administered MDMA over the course of the randomised and open-label phases (n = 22). Therapeutic alliance was assessed using the Working Alliance Inventory at sessions baseline (pre-session 3) and sessions 4 and 9. PTSD symptoms were assessed using the Clinician Administered PTSD Scale and the Impact of Events Scale-Revised.Results: Controlling for baseline clinician-assessed PTSD severity, therapeutic alliance at sessions 4 and 9 (but not baseline) significantly predicted post-MDMA-AP clinician-assessed PTSD severity. Controlling for baseline self-reported PTSD severity, therapeutic alliance at baseline (although this did not survive correction for multiple comparisons) and sessions 4 and 9 predicted post-MDMA-AP self-reported PTSD severity.Conclusions: The present results provide the first preliminary evidence for the relationship between the therapeutic alliance and treatment outcomes within MDMA-AP for PTSD. These findings highlight the important role of psychotherapy, and common psychotherapeutic factors, within MDMA-AP. Replication in studies with larger and more diverse clinical samples remain necessary.Trial registration: ClinicalTrials.gov identifier: NCT00090064.

[This corrects the article DOI: 10.1021/acsptsci.1c00024.].

Abstract Psilocybin and lysergic acid diethylamide (LSD) experiences can range from very positive to highly challenging (e.g., fear, grief, and paranoia). These challenging experiences contribute to hesitancy toward psychedelic-assisted psychotherapy among health care providers and patients. Co-use of 3,4-Methylenedioxy methamphetamine (MDMA) with psilocybin/LSD anecdotally reduces challenging experiences and enhances positive experiences associated with psilocybin/LSD. However, limited research has investigated the acute effects of co-use of MDMA and psilocybin/LSD. In a prospective convenience sample (N = 698) of individuals with plans to use psilocybin/LSD, we examined whether co-use of MDMA with psilocybin/LSD (n = 27) is associated with differences in challenging or positive experiences. Challenging experiences were measured using the Challenging Experiences Questionnaire and positive experiences were measured using the Mystical Experience Questionnaire and single-item measures of self-compassion, compassion, love, and gratitude. Potentially confounding variables were identified and included as covariates. Relative to psilocybin/LSD alone, co-use of psilocybin/LSD with a self-reported low (but not medium–high) dose of MDMA was associated with significantly less intense total challenging experiences, grief, and fear, as well as increased self-compassion, love and gratitude. Co-use of psilocybin/LSD and MDMA was not associated with differences in mystical-type experiences or compassion. Findings suggest co-use of MDMA with psilocybin/LSD may buffer against some aspects of challenging experiences and enhance certain positive experiences. Limitations include use of a convenience sample, small sample size, and non-experimental design. Additional studies (including controlled dose–response studies) that examine the effects and safety of co-administering MDMA with psilocybin/LSD (in healthy controls and clinical samples) are warranted and may assist the development of personalized treatments.

Background: Across psychotherapeutic frameworks, the strength of the therapeutic alliance has been found to correlate with treatment outcomes; however, its role has never been formally assessed in a trial of psychedelic-assisted therapy. We aimed to investigate the relationships between therapeutic alliance and rapport, the quality of the acute psychedelic experience and treatment outcomes. Methods: This 2-arm double-blind randomized controlled trial compared escitalopram with psychedelic-assisted therapy for moderate-severe depressive disorder (N = 59). This analysis focused on the psilocybin condition (n = 30), who received two oral doses of 25 mg psilocybin, 3-weeks apart, with psychological preparation, in-session support, and integration therapy. A new psychedelic therapy model, called "Accept-Connect-Embody" (ACE), was developed in this trial. The primary outcome was depression severity 6 weeks post treatment (Quick Inventory of Depressive Symptomatology, QIDS-SR-16). Path analyses tested the hypothesis that therapeutic alliance (Scale To Assess the Therapeutic Relationship Patient Version, STAR-P) would predict depression outcomes via its influence on the acute psychedelic experience, specifically emotional-breakthrough (EBI) and mystical-type experiences (MEQ). The same analysis was performed on the escitalopram arm to test specificity. Results: The strength of therapeutic alliance predicted pre-session rapport, greater emotional-breakthrough and mystical-type experience (maximum EBI and MEQ scores across the two psilocybin sessions) and final QIDS scores (β = -0.22, R 2 = 0.42 for EBIMax; β = -0.19, R 2 = 0.32 for MEQMax). Exploratory path models revealed that final depression outcomes were more strongly affected by emotional breakthrough during the first, and mystical experience during the second session. Emotional breakthrough, but not mystical experience, during the first session had a positive effect on therapeutic alliance ahead of the second session (β = 0.79, p < 0.0001). Therapeutic alliance ahead of the second session had a direct impact on final depression scores, not mediated by the acute experience, with a weaker alliance ahead of the second psilocybin session predicting higher absolute depression scores at endpoint (β = -0.49, p < 0.001) Discussion: Future research could consider therapist training and characteristics; specific participant factors, e.g., attachment style or interpersonal trauma, which may underlie the quality of the therapeutic relationship, the psychedelic experience and clinical outcomes; and consider how therapeutic approaches might adapt in cases of weaker therapeutic alliance. Clinical Trial Registration: This trial is registered at http://clinicaltrials.gov, identifier (NCT03429075).

Psychedelic therapy shows promise as a novel intervention for a wide range of mental health concerns but its therapeutic action is incompletely understood. In line with acceptance and commitment therapy's (ACT's) transdiagnostic model, qualitative research has suggested that reductions in experiential avoidance are an important component of therapeutic outcomes associated with psychedelics. However, limited research has quantitatively explored the association between decreases in experiential avoidance and therapeutic outcomes associated with psychedelics. Therefore, in two prospective studies, using convenience samples of individuals with plans to use a psychedelic, we explored the impact of psychedelic use on experiential avoidance, depression severity, and suicidal ideation, as well as relationships between changes in these outcomes. Participants (Study 1, N=104; Study 2, N=254) completed self-report questionnaires of depression severity, suicidal ideation, and experiential avoidance: 1) before using a psychedelic (in ceremonial and non-ceremonial contexts), as well as 2) 2-weeks and 3) 4-weeks after psychedelic use. Across both studies, repeated measures ANOVAs indicated significant decreases in experiential avoidance, depression severity, and suicidal ideation after psychedelic use. Furthermore, decreases in experiential avoidance were significantly associated with decreases in depression severity and suicidal ideation. These results suggest that psychedelics may lead to significant decreases in experiential avoidance, depression severity, and suicidal ideation. Additionally, these findings imply that reduced experiential avoidance may be a transdiagnostic mechanism mediating treatment success within psychedelic therapy. We conclude that integrating psychedelics with psychotherapeutic interventions that target experiential avoidance (e.g. ACT) may enhance therapeutic outcomes.

In this paper it is shown, that if a possibly inhomogeneous Markov chain with continuous time and finite state space is weakly ergodic and all the entries of its intensity matrix are locally integrable, then, using available results from the perturbation theory, its time-dependent probability characteristics can be approximately obtained from another Markov chain, having piecewise constant intensities and the same state space. The approximation error (the taxicab distance between the state probability distributions) is provided. It is shown how the Cauchy operator and the state probability distribution for an arbitrary initial condition can be calculated. The findings are illustrated with the numerical examples.

We revisit the problem of the computation of the limiting characteristics of (in)homogeneous continuous-time Markov chains with the finite state space. In general, it can be performed only numerically. The common rule of thumb is to interrupt calculations after quite some time, hoping that the values at some distant time interval will represent the sought-after solution. Convergence or ergodicity bounds, when available, can be used to answer such questions more accurately; i.e., they can indicate how to choose the position and the length of that distant time interval. The logarithmic norm method is a general technique that may allow one to obtain such bounds. Although it can handle continuous-time Markov chains with both finite and countable state spaces, its downside is the need to guess the proper similarity transformations, which may not exist. In this paper, we introduce a new technique, which broadens the scope of the logarithmic norm method. This is achieved by firstly splitting the generator of a Markov chain and then merging the convergence bounds of each block into a single bound. The proof of concept is illustrated by simple examples of the queueing theory. [ABSTRACT FROM AUTHOR]

In this paper, the representability of the generalized Student’s distribution as uniform and normal-scale mixtures is considered. It is also shown that the generalized Burr and the Snedecor–Fisher distributions can be represented as the scale mixtures of uniform, folded normal, exponential, Weibull or Fréchet distributions. New multiplication-type theorems are proven for these and related distributions. The relation between the generalized Student and generalized Burr distribution is studied. It is shown that the Snedecor–Fisher distribution is a special case of the generalized Burr distribution. Based on these mixture representations, some limit theorems are proven for random sums in which the symmetric and asymmetric generalized Student or symmetric and asymmetric two-sided generalized Burr distributions are limit laws. Also, limit theorems are proven for maximum and minimum random sums and absolute values of random sums in which the generalized Burr distributions are limit laws.

In the paper, quasi-exponentiated normal distributions are introduced for any real power (exponent) no less than two. With natural exponents, the quasi-exponentiated normal distributions coincide with the distributions of the corresponding powers of normal random variables with zero mean. Their representability as scale mixtures of normal and exponential distributions is proved. The mixing distributions are written out in the closed form. Two approaches to the construction of asymmetric quasi-exponentiated normal distributions are described. A limit theorem is proved for sums of a random number of independent random variables in which the asymmetric quasi-exponentiated normal distribution is the limit law.