Computing graph gonality is hard

There are several notions of gonality for graphs. The divisorial gonality dgon(G) of a graph G is the smallest degree of a divisor of positive rank in the sense of Baker-Norine. The stable gonality sgon(G) of a graph G is the minimum degree of a finite harmonic morphism from a refinement of G to a tree, as defined by Cornelissen, Kato and Kool. We show that computing dgon(G) and sgon(G) are NP-hard by a reduction from the maximum independent set problem and the vertex cover problem, respectively. Both constructions show that computing gonality is moreover APX-hard.Comment: The previous version only dealt with hardness of the divisorial gonality. The current version also shows hardness of stable gonality and discusses the relation between the two graph parameter

Simulating Induced Interdigitation in Membranes

AbstractIn this study we introduce a mesoscopic lipid-water-alcohol model. Dissipative particle dynamics (DPD) simulations have been used to investigate the induced interdigitation of bilayers consisting of double-tail lipids by adding alcohol molecules to the bilayer. Our simulations nicely reproduce the experimental phase diagrams. We find that alcohol can induce an interdigitated structure where the common bilayer structure changes into monolayer in which the alcohol molecules screen the hydrophobic tails from the water phase. At low concentrations of alcohol the membrane has domains of the interdigitated phase that are in coexistence with the common membrane phase. We compute the effect of the chain length of the alcohol on the phase behavior of the membrane and show that the stability of the interdigitated phase depends on the length of the alcohol. We show that we can reproduce the experimental hydrophobic thickness of the bilayer for various combinations of lipids and alcohols. We use our model to clarify some of the experimental questions related to the structure of the interdigitated phase and put forward a simple model that explains the alcohol chain length dependence of the stability of this interdigitated phase

Early Warning Signals Based on Momentary Affect Dynamics can Expose Nearby Transitions in Depression:A Confirmatory Single-Subject Time-Series Study

Background: In complex systems early warning signals such as rising autocorrelation, variance and network connectivity are hypothesized to anticipate relevant shifts in a system. For direct evidence hereof in depression, designs are needed in which early warning signals and symptom transitions are prospectively assessed within an individual. Therefore, this study aimed to detect personalized early warning signals preceding the occurrence of a major symptom transition. Methods: Six single-subject time-series studies were conducted, collecting frequent observations of momentary affective states during a time-period when participants were at increased risk of a symptom transition. Momentary affect states were reported three times a day over three to six months (95-183 days). Depressive symptoms were measured weekly using the Symptom CheckList-90. Presence of sudden symptom transitions was assessed using change point analysis. Early warning signals were analysed using moving window techniques. Results: As change point analysis revealed a significant and sudden symptom transition in one participant in the studied period, early warning signals were examined in this person. Autocorrelation (r=0·51; p<2.2e-16), and variance (r=0·53; p<2.2e-16) in 'feeling down', and network connectivity (r=0·42; p<2.2e-16) significantly increased a month before this transition occurred. These early warnings also preceded the rise in absolute levels of 'feeling down' and the participant's personal indication of risk for transition. Conclusions: This study replicated the findings of a previous study and confirmed the presence of rising early warning signals a month before the symptom transition occurred. Results show the potential of early warning signals to improve personalized risk assessment in the field of psychiatry

Detecting impending symptom transitions using early warning signals in individuals receiving treatment for depression

Background: The path to depressive symptom improvement during therapy is often complex, as many individuals experience periods of instability and discontinuous symptom change. If the process of remission follows complex dynamic systems principles, early warning signals (EWS) may precede such depressive symptom transitions. Aims: We aimed to test whether EWS, in the form of rises in lag-1 autocorrelation and variance, occur in momentary affect time series preceding transitions towards lower levels of depressive symptoms during therapy. We also investigated the presence of EWS in patients without symptom transitions. Methods: In a sample of 41 depressed individuals who were starting psychological treatment, positive affect and negative affect (high and low arousal) were measured five times a day using ecological momentary assessments (EMA) for four months (521 observations per individual on average; yielding 25,197 observations in total), and depressive symptoms were assessed weekly over six months. We used a moving window method and time-varying autoregressive generalized additive modeling (TV-AR GAM) to determine whether EWS occurred in these momentary affect measures, within-persons. Results: For the moving-window autocorrelation, 89% of individuals with transitions showed at least one EWS in one of the variables (versus 62.5% in the no-transition group), and the proportion of EWS in the separate variables was consistently higher (~44% across affect measures) than for individuals without transitions (~27%). Rising variance was found for few individuals, both preceding transitions (~11%) and for individuals without a transition (~12%). Conclusions: The process of symptom remission showed critical slowing down in at least part of our sample. Our findings indicate that EWS are not generic across all affect measures and may have limited value as a personalized prediction method

Early warning signals and critical transitions in psychopathology:challenges and recommendations

Empirical evidence is mounting that monitoring momentary experiences for the presence of early warning signals (EWS) may allow for personalized predictions of meaningful symptom shifts in psychopathology. Studies aiming to detect EWS require intensive longitudinal measurement designs that center on individuals undergoing change. We recommend that researchers: (a) define criteria for relevant symptom shifts a priori to allow specific hypothesis testing; (b) balance the observation period length and high-frequency measurements with participant burden by testing ambitious designs with pilot studies; (c) choose variables that are meaningful to their patient group and facilitate replication by others. Thoroughly considered designs are necessary to assess the promise of EWS as a clinical tool to detect, prevent or encourage impending symptom changes in psychopathology

Critical slowing down in momentary affect as early warning signal of impending transitions in depression

Based on dynamical systems theory, the current study aimed to investigate if recurrence of depression is systematically preceded by within-person early warning signals (EWS) in positive and negative affect. Ecological momentary assessments were collected 5 times a day for a period of 4 months (averaging 524 assessments per individual) in 37 formerly depressed individuals discontinuing antidepressant medication. EWS (increases in window autocorrelation and variance) preceded recurrence of depression in 32.9% of the participants across robustness checks. Compared to participants that remained in remission, participants with a recurrence showed (1) significantly more positive trends in the variance, but not in autocorrelation, and (2) the average number of significant EWS was over three times larger across tested affect variables. Although the results provide the first systematic evidence that EWS occur more often before the recurrence of depression, the low sensitivity of EWS poses a substantial challenge for clinical applications

Anticipating Transitions in Mental Health in At-Risk Youths:A 6-Month Daily Diary Study Into Early-Warning Signals

If psychopathology behaves like a complex dynamic system, sudden onset or worsening of symptoms may be preceded by early-warning signals (EWSs). EWSs could thus reflect personalized warning signals for impending psychopathology. We empirically investigated this hypothesis in at-risk youths (N = 122, mean age = 23.6 ± 0.7 years, 57% males) from the clinical cohort of Tracking Adolescents’ Individual Lives Survey (TRAILS-CC), who provided daily emotion assessments for 6 months. We analyzed whether EWSs (rising autocorrelations and standard deviations in emotions) preceded transitions toward psychopathology. Across indicators and a range of analytical options, EWSs had low sensitivity (M = 26%, SD = 11%) and moderate specificity (M = 75%, SD = 14%). Thus, in the present sample, the proposed generic nature and clinical utility of EWSs could not be substantiated. Given this finding, we call for a more nuanced view on the application of complex-dynamic-systems principles to psychopathology and lay out key questions to be addressed in the future

Discrete and metric divisorial gonality can be different

This paper compares the divisorial gonality of a finite graph $G$ to the divisorial gonality of the associated metric graph $\Gamma(G,\mathbb{1})$ with unit lengths. We show that $\text{dgon}(\Gamma(G,\mathbb{1}))$ is equal to the minimal divisorial gonality of all regular subdivisions of $G$, and we provide a class of graphs for which this number is strictly smaller than the divisorial gonality of $G$. This settles a conjecture of M. Baker in the negative.Comment: 15 pages, 4 figures. Changes: improved Lemma 4.4, added Proposition 5.3, changed open question

Factors influencing the implementation of clinical guidelines for health care professionals: A systematic meta-review

BACKGROUND: Nowadays more and more clinical guidelines for health care professionals are being developed. However, this does not automatically mean that these guidelines are actually implemented. The aim of this meta-review is twofold: firstly, to gain a better understanding of which factors affect the implementation of guidelines, and secondly, to provide insight into the "state-of-the-art" regarding research within this field. METHODS: A search of five literature databases and one website was performed to find relevant existing systematic reviews or meta-reviews. Subsequently, a two-step inclusion process was conducted: (1) screening on the basis of references and abstracts and (2) screening based on full-text papers. After that, relevant data from the included reviews were extracted and the methodological quality of the reviews was assessed by using the Quality Assessment Checklist for Reviews. RESULTS: Twelve systematic reviews met our inclusion criteria. No previous systematic meta-reviews meeting all our inclusion criteria were found. Two of the twelve reviews scored high on the checklist used, indicating only "minimal" or "minor flaws". The other ten reviews scored in the lowest of middle ranges, indicating "extensive" or "major" flaws. A substantial proportion (although not all) of the reviews indicates that effective strategies often have multiple components and that the use of one single strategy, such as reminders only or an educational intervention, is less effective. Besides, characteristics of the guidelines themselves affect actual use. For instance, guidelines that are easy to understand, can easily be tried out, and do not require specific resources, have a greater chance of implementation. In addition, characteristics of professionals - e.g., awareness of the existence of the guideline and familiarity with its content - likewise affect implementation. Furthermore, patient characteristics appear to exert influence: for instance, co-morbidity reduces the chance that guidelines are followed. Finally, environmental characteristics may influence guideline implementation. For example, a lack of support from peers or superiors, as well as insufficient staff and time, appear to be the main impediments. CONCLUSIONS: Existing reviews describe various factors that influence whether guidelines are actually used. However, the evidence base is still thin, and future sound research - for instance comparing combinations of implementation strategies versus single strategies - is needed. (aut. ref.