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All definitions of treatment-resistant depression (TRD) require that patients have experienced insufficient benefit from one or more adequate antidepressant trials. Thus, identifying "failed, adequate trials" is key to the assessment of TRD. The Antidepressant Treatment History Form (ATHF) was one of the first and most widely used instruments that provided objective criteria in making these assessments. The original ATHF was updated in 2018 to the ATHF-SF, changing to a checklist format for scoring, and including specific pharmacotherapy, brain stimulation, and psychotherapy interventions as potentially adequate antidepressant treatments. The ATHF-SF2, presented here, is based on the consensus of the ATHF workgroup about the novel interventions introduced since the last revision and which should/should not be considered effective treatments for major depressive episodes. This document describes the rationale for these choices and, for each intervention, the minimal criteria for determining the adequacy of treatment administration. The Supplementary Material that accompanies this article provide the Scoring Checklist, Data Collection Forms (current episode and composite of previous episodes), and Instruction Manual for the ATHF-SF2. [ABSTRACT FROM AUTHOR]

RECOVER is a randomized sham-controlled trial of vagus nerve stimulation and the largest such trial conducted with a psychiatric neuromodulation intervention. To describe pre-implantation baseline clinical characteristics and treatment history of patients with unipolar, major depressive disorder (MDD), overall and as a function of exposure to interventional psychiatric treatments (INTs), including electroconvulsive therapy, transcranial magnetic stimulation, and esketamine. Medical, psychiatric, and treatment records were reviewed by study investigators and an independent Study Eligibility Committee prior to study qualification. Clinical characteristics and treatment history (using Antidepressant Treatment History [Short] Form) were compared in those qualified (N = 493) versus not qualified (N = 228) for RECOVER, and among the qualified group as a function of exposure to INTs during the current major depressive episode (MDE). Unipolar MDD patients who qualified for RECOVER had marked TRD (median of 11.0 lifetime failed antidepressant treatments), severe disability (median WHODAS score of 50.0), and high rate of baseline suicidality (77% suicidal ideation, 40% previous suicide attempts). Overall, 71% had received at least one INT. Compared to the no INT group, INT recipients were younger and more severely depressed (QIDS-C, QIDS-SR), had greater suicidal ideation, earlier diagnosis of MDD, and failed more antidepressant medication trials. RECOVER-qualified unipolar patients had marked TRD and marked treatment resistance with most failing one or more prior INTs. Treatment with ≥1 INTs in the current MDE was associated with earlier age of MDD onset, more severe clinical presentation, and greater treatment resistance relative to patients without a history of INT. ClinicalTrials.gov Identifier NCT03887715. [Display omitted] • 493 well characterized patients with marked unipolar TRD enrolled at multiple sites, after vetting by independent review. • Marked lifetime resistance: 11.0 median antidepressant treatment failures. • Marked disability: a median WHO Disability Assessment Scale (WHODAS) score of 50.0. • High rate of baseline suicidality: 77% reported suicidal ideation and 40% had previous suicide attempts. • ECT, TMS, or ESK use in current episode was associated with greater treatment resistance, symptom severity, and earlier onset age. [ABSTRACT FROM AUTHOR]

Determining when to recommend a change in treatment regimen due to insufficient improvement is a common challenge in therapeutics. In a sample of 7215 patients with major depressive disorder treated with transcranial magnetic stimulation (TMS) and with PHQ-9 scores before, during and after the course, 3 groups were identified based on number of acute course sessions: exactly 36 sessions (N = 3591), more than 36 sessions (N = 975), and less than 36 sessions (N = 2649). Two techniques were used to determine thresholds for percentage change in PHQ-9 scores at assessments after 10, 20, and 30 sessions that optimized prediction of endpoint response status: the Youden index and fixing the false positive rate at 10%. Positive and negative predictive values were calculated to assess the accuracy of identifying final nonresponders and responders, respectively. There was greater accuracy in predicting final response than nonresponse, especially in the groups that had at least 36 sessions. Substantial proportions of patients with low levels of early improvement were classified as responders at the end of treatment. The findings should be validated with clinician ratings using a more comprehensive depression severity scale. Manifesting clinical improvement early in the TMS course is strongly predictive of final status as a responder, while lack of early improvement is a relatively poor indicator of final nonresponse status. The predictive value of lack of early symptomatic improvement is too low to make reliable recommendations regarding changes in treatment regimen. • Signal detection methods were used to determine the power of early clinical improvement to predict TMS outcomes in a sample of 7215 MDD patients. • Novel methods were used to empirically determine improvement cutpoints on the PHQ-9 after 10, 20, and 30 sessions. • In patients who received 36 or more sessions, early improvement was highly predictive of ultimate responder status. • Lack of early improvement was a relatively poor predictor of final nonresponder status. • Clinicians can be confident that early improvement augers ultimate response, but lack of early benefit has considerably lesser predictive value. [ABSTRACT FROM AUTHOR]

The number of sessions in an acute TMS course for major depressive disorder (MDD) is greater than in the earlier randomized controlled trials. To compare clinical outcomes in groups that received differing numbers of TMS sessions. From a registry sample (N = 13,732), data were extracted for 7215 patients treated for MDD with PHQ-9 assessments before and after their TMS course. Groups were defined by number of acute course treatment sessions: 1–19 (N = 658), 20–29 (N = 616), 30–35 (N = 1375), 36 (N = 3591), 37–41 (N = 626), or >41 (N = 349) and compared in clinical outcomes at endpoint and at fixed intervals (after 10, 20, 30, and 36 sessions). The impact of additional treatments beyond 36 sessions was also examined. Groups that received fewer than 30 sessions had inferior endpoint outcomes than all other groups. PHQ-9 symptom reduction was greatest in the group that ended treatment at 36 sessions. The extended treatment groups (>36 sessions) differed from all other groups by manifesting less antidepressant response early in the course and had a slower but steady rate of improvement over time. Extending treatment beyond 36 sessions was associated with further improvement without evidence of a plateau. In real-world practice, there are strong relations between the number of TMS sessions in a course and the magnitude of symptom reduction. Courses with less than 30 sessions are associated with diminished benefit. Patients with longer than standard courses typically show less initial improvement and a more gradual trajectory, but meaningful benefit accrues with treatment beyond 36 sessions. • In a study of 7215 MDD patients, there were powerful associations between number of TMS sessions and effectiveness. • The average trajectory was rapid improvement over the first 10 sessions then a markedly slower but steady rate. • Patients with long TMS courses had reduced benefit after 10 sessions but steady improvement thereafter. • There was no evidence in group data that the antidepressant effects of TMS plateau with additional treatment. • The additional treatments given to patients with long TMS courses were associated with substantial clinical improvement. [ABSTRACT FROM AUTHOR]

It has been suggested that sequential bilateral (SBL) TMS, combining high frequency, left dorsolateral prefrontal cortex (DLPFC) stimulation and low frequency, right DLPFC stimulation, is more effective than unilateral TMS. To contrast treatment outcomes of left unilateral (LUL) and SBL protocols. Registry data were collected at 111 practice sites. Of 10,099 patients, 3,871 comprised a modified intent-to-treat (mITT) sample, defined as a primary MDD diagnosis, age ≥18, and PHQ-9 completion before TMS and at least one PHQ-9 assessment after baseline. The mITT sample received high frequency (10 Hz) LUL TMS exclusively (N = 3,327) or SBL TMS in at least 90% of sessions (N = 544). Completers (N = 3,049) were responders or had received ≥20 sessions and had an end of acute treatment PHQ-9 assessment. To control for site effects, a Matched sample (N = 653) included Completers at sites that used both protocols. To control for selection bias, the SBL group was also compared to a Restricted LUL group, drawn from sites where no patient switched to SBL after substantial exposure to LUL TMS. Secondary analyses were conducted on CGI-S ratings. The LUL group had superior outcomes compared to the SBL group for multiple PHQ-9 and CGI-S continuous and categorical measures in the mITT, Completer and Matched samples, including in the specified primary analyses. However, outcome differences were not observed when comparing the Restricted LUL and SBL groups. Within SBL protocols, the LUL-RUL order had superior outcomes compared to the RUL-LUL order in all CGI-S, but not PHQ-9, measures. While limited by the naturalistic design, there was no evidence that SBL TMS was superior to LUL TMS. The sequential order of RUL TMS followed by LUL TMS may have reduced efficacy compared to LUL TMS followed by RUL TMS. • Sequential bilateral (SBL) TMS is frequently used in routine clinical practice despite the lack of an evidence base. • High frequency left unilateral (HF-LUL) treatment was compared to SBL across several treatment cohorts to minimize site/selection bias. • There was no evidence of that SBL TMS was superior to LUL TMS in any analysis. • Sequential low frequency right unilateral followed by HF-LUL may have reduced efficacy compared to left followed by right. [ABSTRACT FROM AUTHOR]

Abstract There is considerable diversity in how treatment-resistant depression (TRD) is defined. However, every definition incorporates the concept that patients with TRD have not benefited sufficiently from one or more adequate trials of antidepressant treatment. This review examines the issues fundamental to the systematic evaluation of antidepressant treatment adequacy and resistance. These issues include the domains of interventions deemed effective in treatment of major depressive episodes (e.g., pharmacotherapy, brain stimulation, and psychotherapy), the subgroups of patients for whom distinct adequacy criteria are needed (e.g., bipolar vs. unipolar depression, psychotic vs. nonpsychotic depression), whether trials should be rated dichotomously as adequate or inadequate or on a potency continuum, whether combination and augmentation strategies require specific consideration, and the criteria used to evaluate the adequacy of treatment delivery (e.g., dose, duration), trial adherence, and clinical outcome. This review also presents the Antidepressant Treatment History Form: Short-Form (ATHF-SF), a completely revised version of an earlier instrument, and details how these fundamental issues were addressed in the ATHF-SF. [ABSTRACT FROM AUTHOR]

Abstract Background Transcranial direct current stimulation (tDCS) has promising antidepressant effects, however, clinical trials have shown variable efficacy. Pre-treatment neurocognitive functioning has previously been identified as an inter-individual predictor of tDCS antidepressant efficacy. Objective In this international multicentre, sham-controlled study, we investigated this relationship while also assessing the influence of clinical and genotype (BDNF Val66Met and COMT Val158Met polymorphisms) factors as predictors of response to active tDCS. Methods The study was a triple-masked, parallel, randomized, controlled design across 6 international academic medical centers. Participants were randomized to active (2.5 mA) or sham (34 μA) tDCS for 30 min each session for 20 sessions. The anode was centered over the left dorsolateral prefrontal cortex at F3 (10/20 EEG system) and the cathode over the lateral right frontal area at F8. Results Better pre-treatment attentional processing speed on the Ruff 2 & 7 Selective Attention Test (Total Speed: β = 0.25, p <.05) and concurrent antidepressant medication use (β = 0.31, p <.05) predicted antidepressant efficacy with active tDCS. Genotype differences in the BDNF Val66Metand COMT Val158Met polymorphisms were not associated with antidepressant effects. Secondary analyses revealed that only participants in the highest performing Ruff 2 & 7 Total Speed group at pre-treatment in both active and sham tDCS conditions showed significantly greater antidepressant response compared to those with lower performance at both the 2 and 4 week treatment time points (p <.05). Conclusions These results suggest that high pre-treatment attentional processing speed may be relevant for identifying participants more likely to show better tDCS antidepressant response to both high (2.5 mA) and very low (34 μA) current intensity stimulation. Clinical trials registration www.clinicaltrials.gov , NCT01562184. Highlights • A predictor analysis from a multicentre trial of tDCS for depression is reported. • Pre-treatment processing speed and medication use predicted response to active tDCS. • Better cognitive performance predicted mood response in both tDCS conditions. • Processing speed may be an important predictor for tDCS antidepressant response. [ABSTRACT FROM AUTHOR]

Background Evidence suggests that transcranial Direct Current Stimulation (tDCS) has antidepressant effects in unipolar depression, but there is limited information for patients with bipolar depression. Additionally, prior research suggests that brain derived neurotrophic factor (BDNF) Val66Met genotype may moderate response to tDCS. Objective To examine tDCS efficacy in unipolar and bipolar depression and assess if BDNF genotype is associated with antidepressant response to tDCS. Methods 130 participants diagnosed with a major depressive episode were randomized to receive active (2.5 milliamps (mA), 30 min) or sham (0.034 mA and two 60-second current ramps up to 1 and 0.5 mA) tDCS to the left prefrontal cortex, administered in 20 sessions over 4 weeks, in a double-blinded, international multisite study. Mixed effects repeated measures analyses assessed change in mood and neuropsychological scores in participants with at least one post-baseline rating in the unipolar (N = 84) and bipolar (N = 36) samples. Results Mood improved significantly over the 4-week treatment period in both unipolar ( p = 0.001) and bipolar groups ( p < 0.001). Among participants with unipolar depression, there were more remitters in the sham treatment group ( p = 0.03). There was no difference between active and sham stimulation in the bipolar sample. BDNF genotype was unrelated to antidepressant outcome. Conclusions Overall, this study found no antidepressant difference between active and sham stimulation for unipolar or bipolar depression. However, the possibility that the low current delivered in the sham tDCS condition was biologically active cannot be discounted. Moreover, BDNF genotype did not moderate antidepressant outcome. Clinical Trials Registration www.clinicaltrials.gov , NCT01562184. [ABSTRACT FROM AUTHOR]

Background Therapeutic repetitive Transcranial Magnetic Stimulation (rTMS) has emerged as a standard of care for individuals with major depressive disorder (MDD) who do not benefit from, or are unable to tolerate, antidepressant pharmacotherapy. Depth of stimulation is limited with currently approved figure-eight coils and larger coils capable of deeper penetration may be associated with loss of stimulation focality and undesired recruitment of motor cortex. A second generation 2-coil array rTMS system was designed to target converging brain pathways for potentially deeper prefrontal cortex stimulation. Methods A randomized, double-blind, sham-controlled trial examined the safety and efficacy of an investigational 2-coil rTMS device. Antidepressant treatment-resistant or treatment-intolerant MDD patients (n = 92) received 20 daily rTMS treatments with coil centers positioned over left dorsolateral prefrontal cortex (dlPFC) and dorsomedial prefrontal cortex (dmPFC). 10 Hz stimulation (maximum summated power for both coils ≤ 120% motor threshold) was delivered. Primary efficacy endpoint was change in HAMD-24 score from baseline to the conclusion of treatments. Results Data from n = 75 (per-protocol sample) showed significantly greater improvement (mean HAMD-24 change) over time for the active (n = 38) versus sham (n = 37) group after 20 sessions (F = 7.174; p = 0.008) and also at the one-month follow-up (F = 6.748; p = 0.010). Response rates were 55.3% (active) versus 32.4% (sham) (p = 0.063); remission rates were 26.3% versus 18.9% (p > 0.05). Other secondary outcomes were generally supportive. Conclusions The results confirmed safety and acute efficacy of the 2-coil rTMS device. Despite modest sample size, primary outcome was clinically and statistically significant, and the effect size was comparable with those reported for regulatory trials with FDA-cleared devices. [ABSTRACT FROM AUTHOR]

Transcranial Direct Current Stimulation (tDCS) is a new, non-invasive neuromodulation approach for treating depression that has shown promising efficacy. The aim of this trial was to conduct the first international, multicentre randomised controlled trial of tDCS as a treatment for unipolar and bipolar depression. The study recruited 120 participants across 6 sites in the USA and Australia. Participants received active or sham tDCS (2.5 mA, 20 sessions of 30 min duration over 4 weeks), followed by a 4-week open label active treatment phase and a 4-week taper phase. Mood and neuropsychological outcomes were assessed with the primary antidepressant outcome measure being the Montgomery-Asberg Depression Rating Scale (MADRS). A neuropsychological battery was administered to assess safety and examine cognitive effects. The study also investigated the possible influence of genetic polymorphisms on outcomes. The trial was triple-blinded. Participants, tDCS treaters and study raters were blinded to each participant's tDCS group allocation in the sham-controlled phase. Specific aspects of tDCS administration, device operation and group allocation were designed to optimise the integrity of blinding. Outcome measures will be tested using a mixed effects repeated measures analysis with the primary factors being Time as a repeated measure, tDCS condition (sham or active) and Diagnosis (unipolar or bipolar). A restricted number of random and fixed factors will be included as required to account for extraneous differences. As a promising treatment, tDCS has excellent potential for translation into widespread clinical use, being cost effective, portable, easy to operate and well tolerated. [ABSTRACT FROM AUTHOR]

Background Repetitive transcranial magnetic stimulation (TMS) is efficacious for acute treatment of resistant major depressive disorder (MDD), but there is little information on maintenance TMS after acute response. Objective/hypothesis This pilot feasibility study investigated 12-month outcomes comparing two maintenance TMS approaches – a scheduled, single TMS session delivered monthly (SCH) vs. observation only (OBS). Methods Antidepressant-free patients with unipolar, non-psychotic, treatment-resistant MDD participated in a randomized, open-label, multisite trial. Patients meeting protocol-defined criteria for improvement after six weeks of acute TMS were randomized to SCH or OBS regimens. TMS reintroduction was available for symptomatic worsening; all patients remained antidepressant-free during the trial. Results Sixty-seven patients enrolled in the acute phase, and 49 (73%) met randomization criteria. Groups were matched, although more patients in the SCH group had failed ≥2 antidepressants (p = .035). There were no significant group differences on any outcome measure. SCH patients had nonsignificantly longer time to first TMS reintroduction, 91 ± 66 days, vs. OBS, 77 ± 52 days; OBS patients were nonsignificantly more likely to need reintroduction (odds ratio = 1.21, 95% CI .38–3.89). Reintroduction lasted 14.3 ± 17.8 days (SCH) and 16.9 ± 18.9 days (OBS); 14/18 (78%) SCH and 17/27 (63%) OBS responded to reintroduction. Sixteen patients (32.7%) completed all 53 weeks of the study. Conclusions Maintaining treatment-resistant depressed patients off medications with periodic TMS appears feasible in some cases. There was no statistical advantage of SCH vs. OBS, although SCH was associated with a nonsignificantly longer time to relapse. Those who initially respond to TMS have a strong chance of re-responding if relapse occurs. [ABSTRACT FROM AUTHOR]

Background Transcranial Magnetic Stimulation (TMS) customarily uses high-field electromagnets to achieve therapeutic efficacy in Major Depressive Disorder (MDD). Low-field magnetic stimulation also may be useful for treatment of MDD, with fewer treatment-emergent adverse events. Objective/Hypothesis To examine efficacy, safety, and tolerability of low-field magnetic stimulation synchronized to an individual's alpha frequency (IAF) (synchronized TMS, or sTMS) for treatment of MDD. Methods Six-week double-blind sham-controlled treatment trial of a novel device that used three rotating neodymium magnets to deliver sTMS treatment. IAF was determined from a single-channel EEG prior to first treatment. Subjects had baseline 17-item Hamilton Depression Rating Scale (HamD 17 ) ≥ 17. Results 202 subjects comprised the intent-to-treat (ITT) sample, and 120 subjects completed treatment per-protocol (PP). There was no difference in efficacy between active and sham in the ITT sample. Subjects in the PP sample ( N = 59), however, had significantly greater mean decrease in HamD 17 than sham ( N = 60) (−9.00 vs. −6.56, P = 0.033). PP subjects with a history of poor response or intolerance to medication showed greater improvement with sTMS than did treatment-naïve subjects (−8.58 vs. −4.25, P = 0.017). Efficacy in the PP sample reflects exclusion of subjects who received fewer than 80% of scheduled treatments or were inadvertently treated at the incorrect IAF; these subgroups failed to separate from sham. There was no difference in adverse events between sTMS and sham, and no serious adverse events attributable to sTMS. Conclusions Results suggest that sTMS may be effective, safe, and well tolerated for treating MDD when administered as intended. [ABSTRACT FROM AUTHOR]

Abstract: Background: Major depressive disorder is a prevalent, disabling, and often chronic or recurrent psychiatric condition. About 35% of patients fail to respond to conventional treatment approaches and are considered to have treatment-resistant depression (TRD). Objective: We compared the safety and effectiveness of different stimulation levels of adjunctive vagus nerve stimulation (VNS) therapy for the treatment of TRD. Methods: In a multicenter, double blind study, 331 patients with TRD were randomized to one of three dose groups: LOW (0.25 mA current, 130 μs pulse width), MEDIUM (0.5–1.0 mA, 250 μs), or HIGH (1.25–1.5 mA, 250 μs). A highly treatment-resistant population (>97% had failed to respond to ≥6 previous treatments) was enrolled. Response and adverse effects were assessed for 22 weeks (end of acute phase), after which output current could be increased, if clinically warranted. Assessments then continued until Week 50 (end of long-term phase). Results: VNS therapy was well tolerated. During the acute phase, all groups showed statistically significant improvement on the primary efficacy endpoint (change in Inventory of Depressive Symptomatology-Clinician Administered Version [IDS-C]), but not for any between-treatment group comparisons. In the long-term phase, mean change in IDS-C scores showed continued improvement. Post-hoc analyses demonstrated a statistically significant correlation between total charge delivered per day and decreasing depressive symptoms; and analysis of acute phase responders demonstrated significantly greater durability of response at MEDIUM and HIGH doses than at the LOW dose. Conclusions: TRD patients who received adjunctive VNS showed significant improvement at study endpoint compared with baseline, and the effect was durable over 1 year. Higher electrical dose parameters were associated with response durability. [Copyright &y& Elsevier]

Recent studies have demonstrated the promise of psilocybin therapies in creating positive changes for those with poor mental health across multiple diagnostic categories, including major depressive disorder (MDD), end-of-life anxiety, and obsessive-compulsive disorder (OCD). While there may be a large population that is eligible to participate in psilocybin therapy based on psychiatric diagnosis and medical clearance, little attention has been given to intrapersonal and interpersonal factors that might influence patient's readiness (i.e., eligibility and capacity) for psychedelic interventions. This paper proposes that readiness assessment includes both intrapersonal and interpersonal factors in order to improve safety, patient care, and treatment outcomes. While at the present time a reliable and valid instrument has not been developed, we propose that three specific areas of focus – patient presentation, therapeutic alliance, and patient safety – may be used to establish a patient's readiness for psilocybin therapy, thus increasing therapy optimization and personalization. • Psilocybin psychotherapy presents a novel opportunity for positive changes across many difficult to treat psychiatric illness. • Potential psychedelic therapy patients need to be thoughtfully and carefully prepared for optimal benefit. • The development of a novel scale which captures key elements which for positive outcomes would be helpful for the field. • The key elements for success include openness, motivation, affective tolerance, and the quality of the therapeutic alliance. [ABSTRACT FROM AUTHOR]

Few treatment options exist for patients with difficult-to-treat depression (DTD). One potentially efficacious treatment is vagus nerve stimulation (VNS): chronic stimulation of the vagus nerve using an implanted stimulator. Given a series of recent VNS clinical studies, including a large, five-year naturalistic investigation, the Center for Medicare and Medicaid Services (CMS) reconsidered the previous non coverage determination and announced coverage for patients participating in a "coverage with evidence" trial. This study, entitled, A P R ospective, Multi-c E nter, Randomized C ontrolled Blinded Trial Dem O nstrating the Safety and Effectiveness of V NS Therapy® System as Adjunctiv E Therapy Versus a No Stimulation Control in Subjects With Treatment- R esistant Depression (RECOVER), includes DTD patients with at least four unsuccessful antidepressant treatments in the current episode and will randomize both unipolar and bipolar DTD participants, each up to 500 evaluable enrollees. Predetermined interim analyses will define the necessary sample size. All participants will be implanted with VNS devices: half receive active stimulation during year one, and half receive delayed stimulation after year one. Participants will be followed for 5 years. This RCT is unique for DTD studies: 1) large sample size and long study duration (one year of controlled comparison); 2) use of a percent time in response as the primary outcome measure, given the chronic illness and its fluctuating course (vis-à-vis meeting a response criteria at a single time point); 3) inclusion of diverse measures of VNS impact on function, including quality of life, degree of disability, health status, and suicidality. [ABSTRACT FROM AUTHOR]

Abstract When analyzing the computational complexity of well-known puzzles, most papers consider the algorithmic challenge of solving a given instance of (a generalized form of) the puzzle. We take a different approach by analyzing the computational complexity of designing a "good" puzzle. We assume a puzzle maker designs part of an instance, but before publishing it, wants to ensure that the puzzle has a unique solution. Given a puzzle, we introduce the FCP (fewest clues problem) version of the problem: Given an instance to a puzzle, what is the minimum number of clues we must add in order to make the instance uniquely solvable? We analyze this question for the Nikoli puzzles Sudoku, Shakashaka, and Akari. Solving these puzzles is NP -complete, and we show their FCP versions are Σ 2 P -complete. Along the way, we show that the FCP versions of Triangle Partition , Planar 1- in -3 SAT , and Latin Square are all Σ 2 P -complete. We show that even problems in P have difficult FCP versions, sometimes even Σ 2 P -complete, though "closed under cluing" problems are in the (presumably) smaller class NP ; for example, FCP 2 SAT is NP -complete. [ABSTRACT FROM AUTHOR]