The Covering Canadian Traveller Problem Revisited

In this paper, we consider the k-Covering Canadian Traveller Problem (k-CCTP), which can be seen as a variant of the Travelling Salesperson Problem. The goal of k-CCTP is finding the shortest tour for a traveller to visit a set of locations in a given graph and return to the origin. Crucially, unknown to the traveller, up to k edges of the graph are blocked and the traveller only discovers blocked edges online at one of their respective endpoints. The currently best known upper bound for k-CCTP is O(?k) which was shown in [Huang and Liao, ISAAC \u2712]. We improve this polynomial bound to a logarithmic one by presenting a deterministic O(log k)-competitive algorithm that runs in polynomial time. Further, we demonstrate the tightness of our analysis by giving a lower bound instance for our algorithm

Error bounds for Lie group representations in quantum mechanics

We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated with the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group, and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy-constrained diamond norm distance of any suitably continuous channel representation of the group

Error bounds for Lie Group representations in quantum mechanics

We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated to the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy constrained diamond norm distance of any suitably continuous channel representation of the group.Comment: 31 pages, 2 figure

State-dependent Trotter Limits and their approximations

The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of electromagnetic fields. It is therefore necessary to discretize these variables to make them amenable to digital simulations. Here, we give sufficient conditions to conclude the validity of this approximate discretized physics. Essentially, it depends on the state-dependent Trotter error, for which we establish explicit bounds that are also of independent interest.Comment: 16 pages, 5 figure

Learning-Augmented Online TSP on Rings, Trees, Flowers and (Almost) Everywhere Else

We study the Online Traveling Salesperson Problem (OLTSP) with predictions. In OLTSP, a sequence of initially unknown requests arrive over time at points (locations) of a metric space. The goal is, starting from a particular point of the metric space (the origin), to serve all these requests while minimizing the total time spent. The server moves with unit speed or is "waiting" (zero speed) at some location. We consider two variants: in the open variant, the goal is achieved when the last request is served. In the closed one, the server additionally has to return to the origin. We adopt a prediction model, introduced for OLTSP on the line [Gouleakis et al., 2023], in which the predictions correspond to the locations of the requests and extend it to more general metric spaces. We first propose an oracle-based algorithmic framework, inspired by previous work [Bampis et al., 2023]. This framework allows us to design online algorithms for general metric spaces that provide competitive ratio guarantees which, given perfect predictions, beat the best possible classical guarantee (consistency). Moreover, they degrade gracefully along with the increase in error (smoothness), but always within a constant factor of the best known competitive ratio in the classical case (robustness). Having reduced the problem to designing suitable efficient oracles, we describe how to achieve this for general metric spaces as well as specific metric spaces (rings, trees and flowers), the resulting algorithms being tractable in the latter case. The consistency guarantees of our algorithms are tight in almost all cases, and their smoothness guarantees only suffer a linear dependency on the error, which we show is necessary. Finally, we provide robustness guarantees improving previous results

Mechanisms of action and processes of yoga-based group intervention for inpatients with schizophrenia spectrum disorders–A longitudinal qualitative study

Background: Research exploring the effects of yoga therapy (YT) on individuals with schizophrenia spectrum disorders (SSD) is scarce. Therefore, the current study aimed to explore possible mechanisms of actions and processes, as well as adverse effects of a novel yoga-based group intervention (YoGI) for in-patients with SSD in a German university hospital setting. Material and methods: A longitudinal qualitative study was integrated into a rater-blinded randomized controlled trial, exploring the impact of a 4-week YoGI as add-on treatment. In-depth interviews were conducted with participants receiving YoGI (n = 19) in addition to treatment as usual (TAU) and a control group (n = 14) which only received TAU. Interviews were conducted at baseline (n = 33) and 4 weeks post-intervention (N = 28) to assess the participant's experiences and how they changed over time. The interviews (N = 61) were audio-taped, translated, coded, and analyzed by means of inductive thematic analysis. Separate case summaries were prepared for each participant to analyze longitudinal changes within subjects. The research team members collaboratively discussed the final list of themes and subcodes. Rater-based questionnaires, such as the Positive and Negative Syndrome Scale (PANSS), Calgary Depression Scale for Schizophrenia (CDSS), and Personal and Social Performance Scale (PSP) were administered at baseline to assess clinical outcomes. Results: At baseline, participants reported a desire to improve their stress- and symptom management. A minority of participants expressed reservations toward yoga, and several psychosocial barriers were named, including worries about symptom exacerbation. At post-intervention, four mechanisms of change became evident from the interviews: (1) acquiring competence in relaxation, (2) increased interoceptive awareness, (3) feeling connected, and (4) a sense of spiritual wellbeing. A small number of participants reported difficulties with YoGI. Conclusion: Generally, YoGI positively influenced participants' experiences of their inpatient stay, regarding distress, self- and body awareness, social connectedness, and spiritual wellbeing. However, participants also illuminated necessary adjustments to improve the intervention. YoGI will therefore be adapted and further developed in an iterative process based on a participant involvement approach. The efficacy regarding outcomes and processes needs to be investigated in a future larger-scaled randomized controlled trial

Compassion-based approaches: a systematic review of their effectiveness and acceptability in schizophrenia spectrum disorders

The purpose of this systematic literature review is to provide an exhaustive summary of current research to explore the prospects of compassion-based approaches in treating persons with Schizophrenia Spectrum Disorders (SSD). Thereby, studies investigating the relationship between clinical parameters and self-compassion in SSD, as well as the acceptability, feasibility, and effects of compassion-based approaches for individuals with SSD were considered. The review was performed using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines and checklist. Eight studies were included for qualitative synthesis. The results indicate an important role of self-compassion for several clinical parameters, including negative associations to positive symptoms, negative symptoms, cognitive disorganization, and emotional distress. All studies reported good acceptability and feasibility. Regarding the clinical effectiveness of compassion-based approaches, a variety of clinical benefits, such as improvements of mood, affect regulation, positive symptoms, negative symptoms, cognitive disorganization, and variables relating to psychological recovery were found in individuals with SSD. It is concluded that compassion-based approaches are a promising form of intervention in the treatment of SSD. However, further research, especially randomized controlled trials, in this field is needed to understand the full potential of compassion-based approaches for individuals with SSD

Prevalence, predictors and types of unpleasant and adverse effects of meditation in regular meditators: international cross-sectional study

Background: Meditation is commonly implemented in psychological therapies since the ‘third wave’ of cognitive–behavioural therapy has increased the focus on mindfulness-based interventions. Although extensive research literature demonstrates its benefits, little is known about potential adverse effects. Aims: The aim of this study is to report the prevalence, type and severity of particularly unpleasant meditation-related experiences in the largest cross-sectional study on this topic to date, with 1370 regular meditators. Method: The participants were asked whether they ever encountered particularly unpleasant experiences as a result of their meditation experience. For the first time, the type and severity of those experiences were assessed and the association with several predictors, such as pre-existing mental disorders, were explored via logistic and linear regression. Results: Similar to previous studies, 22% of participants (95% CI 20–24) reported having encountered unpleasant meditation-related experiences, and 13% of participants (95% CI 3–5) reported experiences that were categorised as adverse. Those were mostly of affective, somatic and cognitive nature. Unpleasant meditation-related experiences were more likely to occur in participants with pre-existing mental illnesses (P = 0.000, 95% CI 1.25–2.12). Conclusions: This study demonstrates that unpleasant meditation-related experiences are prevalent among meditators and, to a relevant extent, severe enough to warrant further scientific inquiry. Longitudinal studies are needed to examine whether the unpleasant meditation-related experiences are merely negative and thus should be avoided, or are an inherent part of the contemplative path