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The optimal duration for maintaining antidepressant treatment in individuals with obsessive-compulsive disorder (OCD) who achieve symptom stabilization remains unclear.
Methods
This systematic review and pairwise meta-analysis of double-blind randomized placebo-controlled trials (DBRPCTs) compared antidepressant maintenance and antidepressant discontinuation groups in terms of relapse rate at each DBRPCT study endpoint (primary outcome), OCD symptom improvement, all-cause discontinuation, and adverse event-related discontinuation. Furthermore, relapse rates at 4, 8, 12, 16, 20, and 24 weeks were compared between the groups. Risk ratios (RRs) with 95% confidence intervals (CIs) were calculated. The absolute risk reduction (ARR) and number needed to treat to benefit (NNTB) for relapse rates were also estimated.
Results
Nine trials (n = 1084; mean age: 32.8 years; proportion of males: 53.3%) were included. The antidepressant maintenance group had lower relapse rates at each DBRPCT study endpoint (RR [95% CI] = 0.53 [0.42–0.68]; ARR = 21.0%; NNTB = 5) and lower all-cause and adverse event-related discontinuation rates than the antidepressant discontinuation group. The maintenance group also exhibited lower relapse rates at 4 weeks (RR [95% CI] = 0.47 [0.31–0.70]; ARR: not significant; NNTB: not significant), 8 weeks (0.42 [0.31–0.57]; 12.0%; 8), 12 weeks (0.43 [0.32–0.56]; 18.0%; 6), 16 weeks (0.41 [0.32–0.52]; 25.0%; 4), 20 weeks (0.43 [0.34–0.53]; 26.0%; 4), and 24 weeks (0.42 [0.33–0.52]; 27.0%; 4) than the discontinuation group. Moreover, the maintenance group outperformed the discontinuation group regarding OCD symptom improvement.
Conclusions
Individuals with OCD may benefit from continued antidepressant treatment, provided that it is well tolerated.
This Element in Construction Grammar addresses one of its hottest topics and asks: is the unimodal conception of Construction Grammar as a model of linguistic knowledge at odds with the usage-based thesis and the multimodality of language use? Are constructions verbal, i.e. unimodal form-meaning pairings, or are they, or at least are some of them, multimodal in nature? And, more fundamentally, how do we know? These questions have been debated quite controversially over the past few years. This Element presents the current state of research within the field, paying special attention to the arguments that are put forward in favour and against the uni-/multimodal nature of constructions and the various case studies that have been conducted. Although significant progress has been made over the years, the debate points towards a need for a diversification of the questions asked, the data studied, and the methods used to analyse these data.
A partition is called a t-core if none of its hook lengths is a multiple of t. Let $a_t(n)$ denote the number of t-core partitions of n. Garvan, Kim and Stanton proved that for any $n\geq1$ and $m\geq1$, $a_t\big(t^mn-(t^2-1)/24\big)\equiv0\pmod{t^m}$, where $t\in\{5,7,11\}$. Let $A_{t,k}(n)$ denote the number of partition k-tuples of n with t-cores. Several scholars have been subsequently investigated congruence properties modulo high powers of 5 for $A_{5,k}(n)$ with $k\in\{2,3,4\}$. In this paper, by utilizing a recurrence related to the modular equation of fifth order, we establish dozens of congruence families modulo high powers of 5 satisfied by $A_{5,k}(n)$, where $4\leq k\leq25$. Moreover, we deduce an infinite family of internal congruences modulo high powers of 5 for $A_{5,4}(n)$. In particular, we generalize greatly a recent result on a congruence family modulo high powers of 5 enjoyed by $A_{5,4}(n)$, which was proved by Saikia, Sarma and Talukdar (Indian J. Pure Appl. Math., 2024). Finally, we conjecture that there exists a similar phenomenon for $A_{5,k}(n)$ with $k\geq26$.
We study continuous-time Markov chains on the nonnegative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance equation, we derive an iterative formula for calculating stationary measures. Specifically, a stationary measure $\pi(x)$ evaluated at $x\in\mathbb{N}_0$ is represented as a linear combination of a few generating terms, similarly to the characterization of a stationary measure of a birth–death process, where there is only one generating term, $\pi(0)$. The coefficients of the linear combination are recursively determined in terms of the transition rates of the Markov chain. For the class of Markov chains we consider, there is always at least one stationary measure (up to a scaling constant). We give various results pertaining to uniqueness and nonuniqueness of stationary measures, and show that the dimension of the linear space of signed invariant measures is at most the number of generating terms. A minimization problem is constructed in order to compute stationary measures numerically. Moreover, a heuristic linear approximation scheme is suggested for the same purpose by first approximating the generating terms. The correctness of the linear approximation scheme is justified in some special cases. Furthermore, a decomposition of the state space into different types of states (open and closed irreducible classes, and trapping, escaping and neutral states) is presented. Applications to stochastic reaction networks are well illustrated.
This chapter presents the current state of research in multimodal Construction Grammar with a focus on co-speech gestures. We trace the origins of the idea that constructions may have to be (re-)conceptualized as multimodal form–meaning pairs, deriving from the inherently multimodal nature of language use and the usage-based model, which attributes to language use a primordial role in language acquisition. The issue of whether constructions are actually multimodal is contested. We present two current positions in the field. The first one argues that a construction should only count as multimodal if gestures are mandatory parts of that construction. Other, more meaning-centered, approaches rely less on obligatoriness and frequency of gestural (co-)occurrences and either depart from a recurrent gesture to explore the verbal constructions it combines with or focus on a given meaning, for example, negation, and explore its multimodal conceptualization in discourse. The chapter concludes with a plea for more case studies and for the need to develop large-scale annotated corpora and apply statistical methods beyond measuring mere frequency of co-occurrence.
This article explores the notions of $\mathcal {F}$-transitivity and topological $\mathcal {F}$-recurrence for backward shift operators on weighted $\ell ^p$-spaces and $c_0$-spaces on directed trees, where $\mathcal {F}$ represents a Furstenberg family of subsets of $\mathbb {N}_0$. In particular, we establish the equivalence between recurrence and hypercyclicity of these operators on unrooted directed trees. For rooted directed trees, a backward shift operator is hypercyclic if and only if it possesses an orbit of a bounded subset that is weakly dense.
Late-life depression (LLD) is characterized by repeated recurrent depressive episodes even with maintenance treatment. It is unclear what clinical and cognitive phenotypic characteristics present during remission predict future recurrence.
Methods:
Participants (135 with remitted LLD and 69 comparison subjects across three institutions) completed baseline phenotyping, including psychiatric, medical, and social history, psychiatric symptom and personality trait assessment, and neuropsychological testing. Participants were clinically assessed every two months for two years while receiving standard antidepressant treatment. Analyses examined group differences in phenotypic measure using general linear models. Concurrent associations between phenotypic measures and diagnostic groups were examined using LASSO logistic regression.
Results:
Sixty (44%) LLD participants experienced a relapse over the two-year period. Numerous phenotypic measures across all domains differed between remitted LLD and comparison participants. Only residual depressive symptom severity, rumination, medical comorbidity, and executive dysfunction significantly predicted LLD classification. Fewer measures differed between relapsing and sustained remission LLD subgroups, with the relapsing group exhibiting greater antidepressant treatment intensity, greater fatigue, rumination, and disability, higher systolic blood pressure, greater life stress and lower instrumental social support. Relapsing group classification was informed by antidepressant treatment intensity, lower instrumental social support, and greater life stress.
Conclusions:
A wide range of phenotypic factors differed between remitted LLD and comparison groups. Fewer measures differed between relapsing and sustained remission LLD subgroups, with less social support and greater stress informing vulnerability to subsequent relapse. This research suggests potential targets for relapse prevention and emphasizes the need for clinically translatable relapse biomarkers to inform care.
The aim of this study was to evaluate the rate of dysplasia and carcinoma-ex-papillomatosis in patients with recurrent respiratory papillomatosis and assess for any risk factors.
Methods
A 15-year retrospective observational cohort study was performed from a single centre. Data on patient demographics, treatment history and pathology results were extracted from clinical records.
Results
Of the 123 patients identified, nine had juvenile-onset recurrent respiratory papillomatosis and 114 had adult-onset recurrent respiratory papillomatosis. Thirteen (11 per cent) of patients with adult-onset recurrent respiratory papillomatosis had dysplasia, and one patient progressed to carcinoma-ex-papillomatosis. Patients with evidence of dysplasia had an average older age of disease onset compared to those without dysplasia (49 years vs 39 years, p = 0.03).
Conclusion
An older age of recurrent respiratory papillomatosis onset was the only risk factor for dysplasia. Gender, tobacco use, subglottic or tracheal involvement, number of surgeries and cidofovir were not prognostic factors in this series.
This study investigates the association between a history of previous cancers and the subsequent risk of developing head and neck cancer.
Method
A retrospective case–control design was employed, analysing 561 patient records from two National Health Service hospitals, with 273 patients diagnosed with head and neck cancer and 288 patients serving as controls.
Results
Statistical analysis revealed a significant association between prior cancer history, particularly squamous cell carcinoma (SCC), and increased risk of developing head and neck cancer (p < 0.05). Subtype analysis highlighted specific head and neck cancers, such as oropharyngeal and laryngeal cancers, as particularly associated with a history of SCC.
Conclusion
The findings suggest that previous cancer diagnoses, especially SCC, may predispose individuals to head and neck cancer, challenging the traditional focus on tobacco, alcohol and human papillomavirus as primary risk factors. These results underscore the need for incorporating prior cancer history into risk assessment protocols and surveillance strategies to improve early detection and patient outcomes.
For $E \subset \mathbb {N}$, a subset $R \subset \mathbb {N}$ is E-intersective if for every $A \subset E$ having positive relative density, $R \cap (A - A) \neq \varnothing $. We say that R is chromatically E-intersective if for every finite partition $E=\bigcup _{i=1}^k E_i$, there exists i such that $R\cap (E_i-E_i)\neq \varnothing $. When $E=\mathbb {N}$, we recover the usual notions of intersectivity and chromatic intersectivity. We investigate to what extent the known intersectivity results hold in the relative setting when $E = \mathbb {P}$, the set of primes, or other sparse subsets of $\mathbb {N}$. Among other things, we prove the following: (1) the set of shifted Chen primes $\mathbb {P}_{\mathrm {Chen}} + 1$ is both intersective and $\mathbb {P}$-intersective; (2) there exists an intersective set that is not $\mathbb {P}$-intersective; (3) every $\mathbb {P}$-intersective set is intersective; (4) there exists a chromatically $\mathbb {P}$-intersective set which is not intersective (and therefore not $\mathbb {P}$-intersective).
This study aimed to investigate the impact of vitamin D deficiency on vestibular function and recurrence in patients with benign paroxysmal positional vertigo.
Methods
This study enrolled 138 patients diagnosed with benign paroxysmal positional vertigo. Vestibular function was evaluated, including ocular vestibular evoked myogenic potentials, cervical vestibular evoked myogenic potentials and caloric tests. Vitamin D levels were recorded.
Results
There was a significant difference in mean vitamin D levels between the normal and abnormal groups of the caloric test, cervical vestibular evoked myogenic potentials, and ocular vestibular evoked myogenic potentials. The likelihood of abnormal vestibular function was lower in patients with normal vitamin D levels than those with deficient levels (< 10 ng/ml). Vitamin D levels were the only predictive factor for recurrence among patients with benign paroxysmal positional vertigo.
Conclusion
A deficiency in vitamin D is more likely to result in abnormalities in the caloric test, cervical vestibular evoked myogenic potentials, and ocular vestibular evoked myogenic potentials in benign paroxysmal positional vertigo patients. The interaction among these factors may contribute to the recurrence.
We consider an $\mathrm{M}/\mathrm{G}/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state n if there are n customers being served), observing also that here (unlike irreducible Markov chains, for example) it is possible for recurrent and transient states to coexist. We also prove a lower bound on the growth speed in the transient case.
We consider two continuous-time generalizations of conservative random walks introduced in Englander and Volkov (2022), an orthogonal and a spherically symmetrical one; the latter model is also known as random flights. For both models, we show the transience of the walks when $d\ge 2$ and that the rate of direction changing follows a power law $t^{-\alpha}$, $0<\alpha\le 1$, or the law $(\!\ln t)^{-\beta}$ where $\beta>2$.
Let $(X,\mu ,T,d)$ be a metric measure-preserving dynamical system such that three-fold correlations decay exponentially for Lipschitz continuous observables. Given a sequence $(M_k)$ that converges to $0$ slowly enough, we obtain a strong dynamical Borel–Cantelli result for recurrence, that is, for $\mu $-almost every $x\in X$,
where $\mu (B_k(x)) = M_k$. In particular, we show that this result holds for Axiom A diffeomorphisms and equilibrium states under certain assumptions.
Benign paroxysmal positional vertigo is the most common episodic vestibular disorder, although it is often quiescent by the time patients visit a specialist clinic, making the diagnosis difficult to confirm. Patients fear the consequences of a relapse and it is not clear what follow up should be provided.
Objective
This evaluation reviewed the results of an open access pathway that offered priority appointments to patients with a history of positional vertigo.
Results and conclusion
In total, 664 patients were included in the analysis, 52 per cent of whom had unconfirmed benign paroxysmal positional vertigo. Open follow up improved diagnostic rates by approximately 40 per cent. The rate of benign paroxysmal positional vertigo recurrence was 34 per cent in patients with follow up of at least one year, 41 per cent with follow up of one to two years, and 53 per cent with follow up of two years or more. One in five recurrences occurred in a different semi-circular canal. These results suggest that specialist follow up is required for management of recurrent benign paroxysmal positional vertigo.
In this chapter the basic theory of Markov chains is developed, with a focus on irreducible chains.The transition matrix is introduced as well as the notions of irreducibility, periodicity, recurrence (null and positive), and transience.The theory is applied to the relationship of a random walk on a group to the random walk on a finite-index subgroup induced by the "hitting measure."
The early prediction of adolescent depression recurrence poses a significant challenge in the field. This study aims to investigate and compare the abilities of the general psychopathology factor (p) and the specific internalizing factor, in predicting depression recurrence over a 2-year course, as well as identifying remitted depressed adolescents from healthy adolescents. Longitudinal changes of these two factors in different trajectory groups were also tracked to examine their sensitivity to sustained remission and relapse.
Methods
We included 255 baseline-remitted depressed adolescents and a healthy control group (n = 255) matched in age, sex, and race, sourced from the Adolescent Brain Cognitive Development Study. The linear mixed model was employed for the statistical analysis.
Results
The p factor not only effectively discriminated between remitted depressed adolescents and healthy controls but also robustly predicted the depression recurrence over a subsequent 2-year course. The specific internalizing factor could only differentiate remitted depressed adolescents from healthy controls. Additionally, a noteworthy longitudinal decline of the p factor in the sustained-remission group was observed.
Conclusions
Psychopathology factors serve as the inherent and enduring measurement of long-term mental health aberrations. Longitudinal results indicate that the p factor is more sensitive to respond to sustained remission than the internalizing factor. The ability of the overall p factor to anticipate depression relapse, unlike the specific internalizing factor, suggests the clinical interventions should monitor and mitigate the coincident symptoms across all dimensions to preempt relapse of adolescent depression, rather than an exclusive focus on internalizing symptoms.
In this chapter, we turn to martingales, which play a central role in probability theory. We illustrate their use in a number of applications to the analysis of discrete stochastic processes. After some background on stopping times and a brief review of basic martingale properties and results, we develop two major directions. We show how martingales can be used to derive a substantial generalization of our previous concentration inequalities – from the sums of independent random variables we focused on previously to nonlinear functions with Lipschitz properties. In particular, we give several applications of the method of bounded differences to random graphs. We also discuss bandit problems in machine learning. In the second thread, we give an introduction to potential theory and electrical network theory for Markov chains. This toolkit in particular provides bounds on hitting times for random walks on networks, with important implications in the study of recurrence among other applications. We also introduce Wilson’s remarkable method for generating uniform spanning trees.
We show a new method of estimating the Hausdorff measure of a set from below. The method requires computing the subsequent closest return times of a point to itself.
This study aimed to analyse clinical and radiological features (phenotypes) to predict revision risk after functional endoscopic sinus surgery in patients with chronic rhinosinusitis with nasal polyps.
Method
Phenotype characteristics of the patients with chronic rhinosinusitis with nasal polyps who underwent functional endoscopic sinus surgery were analysed retrospectively.
Results
The rates of asthma, aspirin sensitivity, smoking and a positive prick test result were significantly higher in revision functional endoscopic sinus surgery cases (p < 0.001, 0.001, < 0.001 and < 0.001, respectively). Multivariate analysis demonstrated that only gender, pre-operative nasal steroid use, pre-operative systemic steroid use, intra-operative systemic steroid use and smoking were significant risk factors for revision functional endoscopic sinus surgery (p = 0.034, 0.001, 0.010, 0.007 and 0.001, respectively). In addition, only eosinophilia and aspirin sensitivity were significant risk factors for multiple revision functional endoscopic sinus surgery procedures (p = 0.043 and 0.005, odds ratio = 2.4 and 5.2).
Conclusion
Beyond the endotype of chronic rhinosinusitis with nasal polyps, defining clinical and radiological factors enables a valid prediction of patients at high risk of revision functional endoscopic sinus surgery.