The genetic architecture of ADHD is complex, with rare and common variants involved. Common genetic variants (as indexed by a composite risk score) associated with clinical ADHD significantly predict ADHD and autistic-like behavioural traits in children from the general population, suggesting that ADHD lies at the extreme of normal trait variation. ADHD and other neurodevelopmental disorders share neurocognitive difficulties in several domains (e.g. impaired cognitive ability and executive functions). We hypothesised that ADHD composite genetic risk scores derived from clinical ADHD cases would also contribute to variation in neurocognitive abilities in the general population.N = 6,832) from a UK population cohort, the Avon Longitudinal Study of Parents and Children (ALSPAC), underwent neurocognitive testing. Parent-reported measures of their children's ADHD and autistic-like traits were used to construct a behavioural latent variable of ‘neurodevelopmental traits’. Composite genetic risk scores for ADHD were calculated for ALSPAC children based on findings from an independent ADHD case–control genome-wide association study. Structural equation modelling was used to assess associations between ADHD composite genetic risk scores and IQ, working memory, inhibitory control and facial emotion recognition, as well as the latent ‘neurodevelopmental trait’ measure.Children  and working memory performance , even after accounting for the relationship with latent neurodevelopmental behavioural trait scores. No associations were found between composite genetic risk scores and inhibitory control or emotion recognition (p > .05).The results confirmed that neurocognitive and neurodevelopmental traits are correlated in children in the general population. Composite genetic risk scores for ADHD were independently associated with lower IQ (These findings suggest that common genetic variants relevant to clinically diagnosed ADHD have pleiotropic effects on neurocognitive traits as well as behavioural dimensions in the general population. This further suggests that the well-recognised association between cognition and neurodevelopmental behavioural traits is underpinned at a biological level. Attention-deficit hyperactivity disorder (ADHD) is a highly heritable neurodevelopmental disorder  in ADHD, which overlap more than expected by chance with regions implicated in other neurodevelopmental conditions, such as ASD or schizophrenia , common risk alleles defined from a clinical ADHD case-control genome-wide association study (GWAS) are higher in an independent set of ADHD cases than controls  contains details of all available data. Ethical approval for the study was obtained from the ALSPAC Ethics and Law Committee and the Local Research Ethics Committees. Full data (phenotypic and genotypic) were available for up to N = 6,832 children, depending on the outcome variables.The Avon Longitudinal Study of Parents and Children (ALSPAC) is a large, well-characterised longitudinal dataset , the Counting Span Task, another measure of working memory, was administered at age ∽10.5 years. The measure used was a computer-generated normally distributed ‘global score’, corresponding to the number of correct trials.Measures of ADHD and social-communication assessed at a similar time to the neurocognitive measures were included in analyses as these were previously found to be associated with ADHD composite genetic risk scores  were male. Details of QC procedures have been reported previously , genome-wide data for 500,527 single nucleotide polymorphisms (SNPs) were available for N = 727) and population controls  were utilised as the primary discovery sample. The QC procedures, ascertainment of these samples and GWAS results have been described in detail previously  in ADHD cases in the discovery GWAS. This list of risk alleles was used to calculate a composite risk score for each individual in ALSPAC, corresponding to the mean number of score alleles (weighted by odds ratio) across the set of SNPs, using the PLINK command (–score). Composite risk scores were also calculated at a variety of other p-value thresholds to test the sensitivity of observed results. The composite genetic scores were standardised using z-score transformations.The results of a published GWAS of British and Irish children with a diagnosis of ADHD  was used to test a model of ADHD composite genetic risk score effects on neurocognitive measures and the latent variable of neurodevelopmental difficulties. SEM has the potential to simultaneously estimate the relationships of multiple manifest/observed and latent predictor and outcome variables. For the purpose of this study, the SEM models combine regression, path and factor analyses. Given that neurodevelopmental and neurocognitive measures are related, modelling the association of composite genetic risk scores with both measures simultaneously can be used to determine the unique effect of composite genetic scores on each of these measures. On figures, manifest variables are represented by squares, latent variables are represented by circles, single direction arrows indicate regression paths, double direction arrows indicate correlations and numbers indicate regression/correlation coefficients.p-values presented are two-tailed. Given the non-independence of the four neurocognitive measures and the structured analytic approach, all results are interpreted using a significance threshold of p < .05.Model goodness of fit was assessed as above. The model estimator used was ‘MLR’, which is robust to non-normality and provides full information maximum likelihood estimation with robust standard errors, using all available data for each model. SEM was performed using Mplus version 7 . This second sample consisted of the published international Psychiatric Genomics Consortium (PGC) meta-analysis of ADHD case-control GWAS , although coefficients are low to modest, with the highest correlation being between IQ and the Digit Span subtest (r = .39).Tablet = −6.79, p < .001; age 10.5 years: t = −2.30, p = .022) and made more emotion recognition errors  than females. They did not differ from females in terms of inhibitory control  or IQ .Males had lower working memory scores  and lower working memory abilities . There were no associations with inhibitory control  or emotion recognition .After adjusting for gender, ADHD composite genetic risk scores, derived from the primary discovery sample  and working memory  and no associations with inhibitory control and facial emotion recognition (p > .05). Model diagrams are displayed in FigureThe confirmatory factor analytic/latent variable model of inattentive, hyperactive-impulsive, social-cognitive and pragmatic language traits showed moderately good fit , as assessed using the global score of the Counting Span Task at the approximate age of 10.5 years. SEM with the neurodevelopmental difficulties latent variable showed a consistent result ; see FigureADHD composite risk scores also predicted lower working memory abilities (SEM including both IQ and working memory (at age 8.5 years) as correlated outcomes showed that these outcomes are independently predicted by ADHD composite genetic risk scores see .To test the sensitivity of the results with regards to inclusion of the latent neurodevelopmental variable, analyses were re-run with ADHD inattentive and hyperactive-impulsive traits as manifest outcome variables and omitting the measures of social-communication. The pattern of results was the same as before see .To look at the effect of population stratification, analyses were co-varied for 10 EIGENSTRAT covariates. This did not affect the results see . The patβ = −.060, p = .0011, R2 = .0038) and males , whereas the association with working memory at age 8 was only seen in females  and not males .Gender was entered as a covariate for all models. When analyses were instead stratified by gender, the association between composite genetic risk scores and IQ was seen separately for both females , but no association with working memory at either time point . SEM testing showed the same pattern of results , albeit they are comparable to those reported in other studies using the composite genetic risk score method , were not specifically selected for previously showing familial effects with ADHD. Previous family and twin studies have suggested that there are shared genetic effects between ADHD and measures of IQ, working memory (as assessed by the WISC Digit Span test), inhibitory control  and other cognitive measures not examined in the current study  and other neurodevelopmental disorders (e.g. autism spectrum disorder (ASD) and schizophrenia) are highly heritable and may overlap in genetic risks.They are also associated with general cognitive delay and difficulties with executive functions and social cognition.A composite measure of common genetic risk variants relevant to a clinical diagnosis of ADHD has previously been found to predict traits of ADHD and social-communication difficulties in the general population.This study suggests that common genetic variants relevant to ADHD diagnosis may also play a role in normal variation in IQ and working memory abilities, independent of their effect on ADHD and ASD-like/social-communication traits in the general population.


Attention-deficit/hyperactivity disorder (ADHD) has been often found to be comorbid with other disorders, including anxiety, depression, and unhealthy behaviors such as drinking alcohol and smoking. These factors were often discussed separately, and the mediating effects of mental health on substance use are unknown. To study the mediating effects of anxiety and depression on the relationship between ADHD and drinking/smoking behaviors, we conducted a cross-sectional study of 1870 college students from Shanghai, China. The Adult ADHD Self-Report Scale (ASRS-v1.1) and Wender Utah Rating Scale (WURS) were used to identify the current and past ADHD. Structural Equation Modeling was carried out to clarify the mediating effect of anxiety and depression on the relationship between core ADHD symptoms and smoking/drinking behaviors. We found that inattention as one of the core symptoms of ADHD was associated with an increased risk of depression as a direct effect, as well as slightly increased risk of smoking/drinking behaviors by an indirect effect of depression. Hyperactivity-impulsivity, as another core symptom of ADHD had a robust impact on smoking and drinking behaviors, while being mediated by anxiety and depression. In conclusion, anxiety and depression was associated with further increased risk behaviors of smoking/drinking alcohol among those students with ADHD. Attention-deficit/hyperactivity disorder (ADHD) is a common neuropsychiatric disorder among children and adults, worldwide26et al. (1999) compared college students with and without ADHD on the self-report symptom inventory  and found the overall score was significantly higher for students with ADHD than for non-ADHD studentsADHD also has a close relationship with mental health. For instance, in an ADHD treatment-seeking group, 18% had major depressive disorder and 32% had general anxiety disorder12As mentioned above, ADHD comorbid with substance use and anxiety and depression were broadly discussed. Among these, anxiety and depression were closely related with substance use, but the results were mixed. Whether substance use is causally associated with depression and anxiety, or opposite causality, consistent and robust genetic polymorphisms had been found by an approach of Mendelian randomization. It suggested that in fact this relationship is more consistent with a self-medication hypothesis than with tobacco use being a risk factor for depression and anxiety17One study suggested that anxiety and depression is closely related with substance use independent of ADHDADHD symptoms may change over the age span. Hyperactive motor behavior typically observed in childhood diminishes among adolescents and young adults, and is replaced by a sense of mental or internal restlessness, according to another study2628Furthermore, for clarifying the mediating effect of anxiety and depression on the relationship between ADHD symptoms and smoking/drinking, the interaction effect of ADHD symptoms and stressful life events on anxiety and depression needs to be discussed. People with ADHD may be vulnerable to stressful environment, as ADHD often comorbid with many emotional and behavioral problems, including anxiety and depressionAmong a total of 1872 participations, 303 participants (16.19%) had the inattention sub-score ≥17, and 193 participants (10.31%) had the hyperactivity-impulsivity sub-score of the ASRS ≥17. There were 180 participants (9.62%) with a WURS score of 46 or above. These participants were placed into either ADHD symptomatic or non-symptomatic groups according to the criteria above, thus 7.75% of the sample were symptomatic, scoring above the cut-off point for ADHD. No significant gender difference was found between the two groups, even though male students showed a slightly higher rate of ADHD (8.78%) than female students (6.63%). Additionally, students in advanced grades showed increased rates of ADHD than those in lower grades. β = 0.58, P < 0.001), smoking  and drinking behaviors . Meanwhile, the symptom of hyperactivity-impulsivity also indirectly predicted smoking  and drinking behaviors  through anxiety. It suggests that anxiety mediated hyperactivity-impulsivity and smoking/drinking behaviors, with the indirect effect of ADHD on smoking/drinking behaviors of 0.13  and 0.15 , respectively. In contrast, inattention was found to negatively predict smoking  and drinking behaviors , and is not associated with anxiety. The proposed Model 1 represents an excellent fit to the data . The loading factors for 9 observed variables of inattention range from 0.64 to 0.75, for 9 observed variables of hyperactivity was 0.68–0.75. The loading factors for 4 variables of smoking ranged from 0.62 to 0.89, for 10 variables of anxiety is 0.66–0.79, for 3 variables of drinking ranged from 0.53 to 0.86.In β = 0.47, P < 0.001) and drinking behaviors . Alternatively inattention was negatively associated with smoking  and drinking . Both ADHD symptoms of hyperactivity-impulsivity  and inattention  were positively associated with depression. Depression also played an important role in mediating the effect pathway between ADHD symptoms and substance use. The indirect effect of hyperactivity-impulsivity on smoking and drinking behaviors was 0.1 . The indirect effect of inattention on smoking and drinking behaviors was 0.05 . Model 2 demonstrated an excellent fit to the data . The loading factors for 9 observed variables of inattention range from 0.64 to 0.75, for 9 observed variables of hyperactivity was 0.68–0.75. The loading factors for 4 variables of smoking ranged from 0.60 to 0.91, for 13 variables of depression was 0.57–0.78, for 3 variables of drinking was 0.53–0.86.In β = 0.152, P < 0.001) and hyperactivity-impulsivity , and SLE  significantly contributed to anxiety. Only the interactions between SLE and inattention symptoms significantly contributed to anxiety . Similar results were found for depression. To be specific, inattention , hyperactivity-impulsivity , and SLE  were significantly associated with depression. Only the interaction between SLE and inattentive symptoms significantly contributed to depression .The interactive effects of SLE and two ADHD core symptoms on anxiety and depression were shown in R2 values in F values in The No study has included mental health as mediator for assessing the effect of ADHD on substance abuse. Our study tested a conceptual model in which two ADHD symptom domains have different effect pathways on college students’ smoking and drinking behaviors, and found that their relationships may be mediated by the presence of anxiety or depression. The findings of the current study are consistent with previous studies showing adults have more prominent inattention (IN) than hyperactivity-impulsivity (HI) symptomsAnother interesting finding of our study is that two ADHD core symptoms have different associations with anxiety and depression. HI is closely related to both anxiety and depression, whereas IN is only related to depression. These associations are supported by a study showing increased episodes of major depression in the inattentive and combined ADHD subtypeDepression and IN often work closely to affect college student’s development. For example, a study carried out in the United States and China showed that both depression and IN were associated with college students’ adjustment, and that the association was cross-cultural and not specific to the United StatesThe above finding may explain the contradictory findings about the relationship between inattention and smoking/drinking in previous studies. The relationship between ADHD symptoms and smoking is complex42In contrast, two studies have found no difference in the number of cigarettes smoked or level of nicotine dependence in adult smokers with ADHD compared with non-ADHD control groups46In addition, except for the mediating effect of depression on the relationship between IN and smoking/drinking, the interaction between IN and SLE may explain the complex association partially. The current study found that IN may affect mental health through an interaction with SLE, no such interaction was found with HI. This may be because young adults with more symptoms of IN experience higher levels of stress, and are at greater risk of developing mental health problemset al employed an adolescent sample, whereas the study by Kollins et al was a cross-sectional analysis of smoking in a young adult sample31Finally, the different findings across these studies may relate to the sampling strategies used. The separate domains of ADHD symptoms may be differentially related to outcomes among both clinical and nonclinical populations. The differences may also reflect variances in the relationship between ADHD symptoms and smoking at various points in the life-course. For instance, Burke This study was approved by the medical ethics committee of Fudan University. The corresponding author confirms that this study was performed in accordance with the approved social experiments guidelines and regulations. Informed consent was obtained from all participants. The totals of 1872 college students were recruited from two high educational institutions in Shanghai, China. One of them is a high professional-technology college which is a three-year College, and students with relatively poor academic achievement in high school will enter this kind of college in China. Another one is a four-year comprehensive university, and students in this university had a relatively good academic achievement in high school. The method of stratified cluster sampling was used. Firstly, six majors were selected randomly from each educational institution; secondly, all grades of the six majors from the high professional-technology college (grade one to three) and the comprehensive university (grade one to four) were selected; lastly, students were recruited randomly from each grade, and they were asked to fill a questionnaire in a health care class by school doctors who were trained to collect the data. Finally, the participants included 980 males (52.38%) and 892 females (47.62%), and their ages ranged from 16 to 25 years with a mean age of 19.13 (SD = 1.30). There were only 39 (2.0%) students younger than 18 years old and 6 (0.32%) students older than 23 years old.All participants were asked to complete a questionnaire consisting of the instruments for assessing ADHD, anxiety, depression, and health risk behaviors including smoking and drinking alcohol. The specific instruments were as follows:Current ADHD: We used the Chinese version of Adult ADHD Self-Report Scale (ASRS)52Childhood ADHD: This study used the Wender Utah Rating Scale (WURS) to assess Childhood ADHD. The WURS is a 25-item scale designed to retrospectively question childhood symptoms of ADHDAnxiety and Depression: Symptom Checklist -90-Revised (SCL-90-R) was used to assess depression and anxiety. The SCL-90-R is a screening measure of general psychiatric symptomatologyTobacco and alcohol use behaviors: Four items on the questionnaire were included regarding participants’ smoking experience and smoking frequency in the last 30 days, and onset of smoking to assess participators’ tobacco use. Similarly, five questions regarding participants’ use of alcohol in the past year; alcohol use over the last 30 days; and if they had been intoxicated in the past year, were asked to reflect participators’ behavior of alcohol use. For instance, “In the past 30 days, how many days have you drunk over 5 cups in two hours” was asked to figure out the alcohol use frequency. These items were selected from the National Health Risk Behavior Investigation Questionnaire for adolescents in ChinaStressful life events: A 15-items scale was used to cover stressful life events that regarding family, school and personal problems in the last half year. The scale was revised based on the College Student’s Stressful Event ChecklistA participant was classified as having significant symptoms of ADHD if his /her score was greater than the clinical cut-off points on both the ASRS (a measure of current ADHD symptoms) and WURS (a retrospective childhood measure of ADHD symptoms). One necessary criterion to diagnose an adult with ADHD is that he/she should have the symptoms in childhood. For ASRS scores, individuals with sum score on either subscale of 17 or greater were considered likely to have ADHD for reducing false negative rate, because one more criterion was added to screen ADHD-symptomatic students in the current study. Ward, Wender, and Reimherr (1993) cited a cut-off score for the WURS of 46, thus participants with a score of 46 or above would be classified as having ADHD as a childThe total score of anxiety ranged from 0 to 40, and participants with scores over 20 were considered to have anxiety symptoms. The total score of depression ranged from 0 to 52, and the participants with scores over 26 were considered to have depression symptoms based on a study which suggested a new norm of SCL-90 for college student in China58The relationship between ADHD symptoms, anxiety and depression and smoking/drinking was analyzed by using Structural Equation Modeling (SEM) by LISREL 8.7. Considering symptoms displayed in college students are different in inattention and hyperactivity-impulsivity symptoms, the structural equation model is constructed with each symptom separately. For exploring the mediating effect of anxiety and depression, two independent structural equation models were performed, and the results are shown in Z-score. Analyses were carried out in three steps which are shown in the three blocks in We also conducted hierarchical regression analyses by SPSS 17.0 to explore the predictors of anxiety and depression . BecauseHow to cite this article: Tong, L. et al. Mediating effect of anxiety and depression on the relationship between Attention-deficit/hyperactivity disorder symptoms and smoking/drinking. Sci. Rep.6, 21609; doi: 10.1038/srep21609 (2016).


Disordered structures such as liquids and glasses, grains and foams, galaxies, etc. are often represented as polyhedral tilings. Characterizing the associated polyhedral tiling is a promising strategy to understand the disordered structure. However, since a variety of polyhedra are arranged in complex ways, it is challenging to describe what polyhedra are tiled in what way. Here, to solve this problem, we create the theory of how the polyhedra are tiled. We first formulate an algorithm to convert a polyhedron into a codeword that instructs how to construct the polyhedron from its building-block polygons. By generalizing the method to polyhedral tilings, we describe the arrangements of polyhedra. Our theory allows us to characterize polyhedral tilings, and thereby paves the way to study from short- to long-range order of disordered structures in a systematic way. Disordered structures are often represented as polyhedral tilings1234567891012345671111213141517p3-code), and then generalize it to polychora. The code for polychora (p4-code) allows us to describe what polyhedra are tiled in what way.In this work, we create the theory of how the polyhedra are tiled. For this purpose, we use the hierarchy of structures of polytopes19contribute to the vertex. We also say that a polygon (side) contributes to a vertex if one of its corners (endpoints) contributes to the vertex. Similarly, the edge is a line segment on the polyhedron along which the sides of polygons meet  instructs how to construct it from its building-block polygons. For this purpose, we combine a polygon-sequence codeword (ps2) and a side-pairing codeword (sp) as p3 = ps2;sp, where “;” is a separator.We first deal with simple polyhedra, where every vertex is degree three. Here, the degree of a vertex is the number of edges connected to that vertexps2-codeword is denoted asThe p2(i) is the number of sides on the polygon i, where i is the identification number (ID). F is the number of faces on the polyhedron. Generating ps2 thus reduces to assigning polygon IDs. To visually distinguish already-encoded polygons from to-be-encoded ones, we assume that all polygons are coloured at first, and make each polygon transparent when encoded. We call a side of a transparent polygon glued to a coloured one a dangling side. To identify each side, we introduce the side-ID ij. Here, the side ij means the jth side of the polygon i, and the side-ID ij represents an integer: ij = j + ij are the corners ij + 1 and ij for 1 ≤ j < p2(i) (s-side) plays a key role in encoding. The ps2-codeword is generated as follows ((a) Choose a side as the initial side, and the polygon 1 is the one having that side.1, 12, 13, ···, (b) Assign IDs (1(c) Make the polygon 1 transparent except for the corners and sides.i (2 ≤ i ≤ F) is the coloured one glued to the s-side.(a) The next polygon i1, i2, i3, ···, i from the side glued to the s-side in a CW direction.(b) Assign IDs (i transparent except for the corners and sides.(c) Make the polygon (a) Repeat the procedure 2 until all polygons get transparent.Here,  < p2(i) . The sma follows :(a) Chop4-code, we assign edge IDs as follows. First we tentatively assign the smaller side ID to the edge, and then relabel the IDs so that the edge i is the one with the ith smallest tentative ID as illustrated in ps2 can be used to assign face, edge and vertex IDs not only to simple polyhedra, but also to non-simple ones.For latter convenience in formulating the p2(F − 1) and p2(F) can be deduced from p2(1) p2(2) p2(3) ··· p2(F −2)  see . Howeversp and the decoding algorithm, we first introduce the zeroth tentative side-pairing codeword (tsp(0)). We then formulate an algorithm to recover the original polyhedron from ps2;tsp(0). Finally, we remove redundancy in tsp(0) step-by-step to obtain sp.To formulate plot as follows. A plot consists of a single dangling side or a chain of dangling sides. Here, two dangling sides are considered to be chained when they contribute to the same vertex contributed by two transparent polygons. Let x be the smallest side ID of a plot. We define the ID of that plot as x  gets transparent, the coloured polygon i is glued to the s-side, so that the s-plot is glued to the polygon i. For example, in encoding the polyhedron shown in P1 is glued to the s-plot 11  asBy collecting the a-pairs, we define ya(i) and xa(i) form the a-pair ya(i)xa(i), where ya(i) > xa(i), and ya(i) < ya(i + 1). Na is the number of a-pairs. For example, tsp(0) of the polyhedron shown in 55610454.Here, the sides D1D2D3 ··· DF, where Di is the partial polyhedron obtained when the polygon i is decoded. For the encoding process, we also consider the sequence E1E2E3 ··· EF. Here, Ei is the partial polyhedron obtained by removing the coloured polygons from Pi  so as to satisfy Di = Ei at any i. If we assign side IDs -gon, then the resultant object D1 is identical with E1. Assume Di − 1 = Ei − 1 for 2 ≤ i ≤ F. To construct Di (=Ei) from Di − 1 and ps2;tsp(0), we introduce a rectification mechanism as follows. Since Di is the partial polyhedron of a simple polyhedron, Di must not have any degree-four vertex contributed by three polygons. We call such a vertex an illegal vertex (i-vertex). However, we allow intermediate products to transiently have i-vertices. When an i-vertex is generated, we rectify it by gluing together the two dangling sides contributing to it  (1 ≤ n ≤ Na) is the side ID of the polygon i, then we glue the side ya(n) to the side xa(n) of Di − 1  of Ei − 1  as follows (p2(1)-gon.(a) The polygon 1 is a 1, 12, 13, ···, D1.(b) Assign IDs (1i (2 ≤ i ≤ F) is a p2(i)-gon.(a) The next polygon i1, i2, i3, ···, (b) Assign IDs (i1 of the polygon i to the s-side of Di − 1.(c) Glue the side ya(n) (1 ≤ n ≤ Na) is the side ID of the polygon i, then glue the side ya(n) to the side xa(n) of Di − 1.(d) If Di.(e) If i-vertices are generated, then rectify them, and repeat this procedure until no i-vertices remain. The resultant object is (a) Repeat the procedure 2 until all polygons are placed.To summarize, the original polyhedron can be recovered from  follows :(a) Thps2;tsp(0), Di = Ei at any i. However, what we need is just DF = EF. By allowing Di ≠ Ei for 1 ≤ i ≤ F − 1, we can make the more compact sp as described below.In decoding tsp(0) step-by-step. To examine ya(Na)xa(Na) for necessity, we consider the first test codeword denoted asWe remove redundancy in ya(Na)xa(Na) off from tsp(0). Then we attempt to decode ps2;test(1). When the polygon having the side ya(Na) is decoded, we will fail to glue the sides ya(Na) and xa(Na) together, because the a-pair ya(Na)xa(Na) is missing in test(1). However, we can proceed decoding. If the missing a-pair is cured and the original polyhedron is successfully reproduced in the subsequent decoding process, then we call the a-pair the curable a-pair. Otherwise, we call it the non-curable a-pair. If the a-pair is curable, then we can remove ya(Na)xa(Na) from tsp(0). We therefore set the first tentative side-pairing codeword as tsp(1) = test(1). On the other hand, if the a-pair is non-curable, then tsp(1) = tsp(0).which is obtained by stripping ya(Na+1 − i)xa(Na + 1 − i) (2 ≤ i ≤ Na) for curability, we consider the ith test codeword testi)xa(Na + 1 − i) off from tspi − 1)( = testi)( = tspi − 1) of the polyhedron shown in 55610454. The a-pair 10454 is non-curable 25274752432;10454-polyhedron for short.We repeat the above-mentioned procedure, and -curable , while t curable . As a rep3-codeword. There are 2E possible initial sides for a polyhedron. Here, E is the number of edges on the polyhedron. We also examine the mirror-image polyhedron, which gives additional 2E possibilities. A maximum of 4E different codewords can be obtained from a polyhedron and its mirror image. To determine the representative one, we introduce the lexicographical number Lex(p3). Given that ps2 and sp can be read as positive F- and 2Nna-digit integers, we define Lex(p3) as the concatenation of the two numbers. Here, Nna is the number of non-curable a-pairs. We use the codeword with the smallest Lex(p3) as the representative one.Our encoding starts with choosing an initial side. A different initial side for the same polyhedron may give a different n-regular graphn the n-regular polyhedron. 3-regular polyhedra are simple, while, for n > 3, n-regular polyhedra are non-simple. In encoding [decoding], if we regard that two dangling sides are chained when they contribute to the same vertex contributed by (n − 1) transparent polygons [polygons] and modify an i-vertex to be a vertex contributed by a pair of two dangling sides and n transparent polygons [polygons], our p3-code is straightforwardly applicable to n-regular polyhedra. For example, the octahedron is encoded as “4-regular 38”. The icosahedron is “5-regular 320”. However, if a non-simple polyhedron is non-regular, this method cannot be used. To deal with all non-simple polyhedra, we formulate a method that uses a one-to-one correspondence between a non-simple polyhedron and its associated simple one as described below.On the analogy of the d (>3) and replacing it with a d-gonal cross sectionp3-codeword of a non-simple polyhedron is generated as follows:Choose a side of a non-simple polyhedron as an initial side.d (>3) and replacing it with a d-gonal cross section.Construct its associated simple polyhedron by cutting every vertex of degree Encode the associated simple polyhedron from the initial side corresponding to the one determined in the procedure 1.p2(i) if the polygon i is the cross section; for example, a codeword for the pentagonal pyramid is Put a dot on The edge and face IDs can be assigned as illustrated in Any non-simple polyhedron can be transformed into its associated simple polyhedron by cutting every vertex of degree ps2 contains dots, it is not a number. We therefore define Lex(ps2) as the concatenation of two numbers ps2(1) and ps2(2). Here, ps2(1) is a number obtained from ps2 by replacing every number without a dot to 0 and then by removing all dots, while ps2(2) is obtained by removing all dots from ps2. For example, LexSince Note that, if a vertex is concave, cutting the vertex may not be well defined. However, by assuming that a polyhedron is flexible, we can inflate it so that a concave vertex becomes a convex one. Then we can cut the vertex.Decoding is achieved easily. We first construct the associated simple polyhedron, and then shrink the cutting sections to the vertices.vi* of the dual polyhedron on each face fi of the original polyhedron.Draw a vertex eij* of the dual, if the faces fi and fj share an edge e, to connect the vertices vi* and vj* such that eij* crosses e, but does not cross the other edges.Draw an edge The duality of polyhedra can be used to make a codeword more compact. Every polyhedron has its associated dual, which is constructed as followsp3-codeword for the octahedron is 66 as the concatenation of Lex (★), which we define as 1, and Lex(46). Therefore, Lex (★46) is 1444444. On the other hand, Lex(66(6) is 0040404040404066464646464646. Since Lex (★46) is the smallest, the representative p3 for the octahedron is ★46, which is more compact than 66 any pair of polyhedra meet only at their faces, edges, or vertices and that (2) each face of each polyhedron meets exactly one other polyhedron along a ridge. The 0-face, peak, and ridge are a point, line segment, and area on the polychoron, where the vertices, edges, and faces of polyhedra meet, respectively . The intp4-codeword consists of a polyhedron-sequence codeword (ps3) and a face-pairing codeword (fp), and is denoted as p4 = ps3;fp.We first deal with polychora whose peaks are all contributed by three polyhedra. Afterwards, the method will be generalized to polychora in general. The ps3-codeword is denoted asThe C is the number of cells on the polychoron, and p3(i) is the p3-codeword for the polyhedron i. To assign IDs to the polyhedra, we use edge (face) IDs ij. Here, the edge (face) ij is the jth edge (face) of the polyhedron i. In encoding, each polyhedron is coloured at first, but gets transparent when encoded. We call a face of a transparent polyhedron glued to a coloured one a dangling face. The smallest-ID dangling face (s-face) plays a key role in encoding. The ps3-codeword is generated as follows ((a) Choose a face of a polyhedron and an edge of that face as the initial face and edge, respectively; the polyhedron 1 is the one having the initial face.p3(1) by encoding the polyhedron 1 in such a way that the face 11 (edge 11) becomes the initial face (edge).(b) Determine (c) Make the polyhedron 1 transparent except for the vertices and edges.i (2 ≤ i ≤ C) is the coloured one glued to the s-face.(a) The next polyhedron p3(i) by encoding the polyhedron i in such a way that the face i1 (edge i1) is glued to the s-face .(b) Determine i transparent except for the vertices and edges.(c) Make the polyhedron (a) Repeat the procedure 2 until all polyhedra get transparent.where  follows :(a) ChAs with the case of polyhedra, this method can be used to assign cell, ridge, peak, and 0-face IDs to polychora in general.zeroth tentative face-pairing codeword tfp(0), we explain plots for polychora. If a pair of two dangling faces contribute to a peak contributed by two transparent polyhedra, the dangling faces are considered to be chained. A single dangling face or chained dangling faces form a plot; the plot here is a two-dimensional object. We assign plot IDs so that the smallest-ID face of the plot x is the face x. If the polyhedron i in Pi − 1 is glued to plots other than the s-plot, we call them a-plots. By the a-pair wzv, we mean that the face w (of the polyhedron i) is glued to the face v of the a-plot v in such a way that the edge z (of the face w) is glued to the smallest-ID edge of the face v. By collecting the a-pairs, tfp(0) is denoted asTo define wa(i) > va(i) and wa(i) < wa(i + 1).Here, dangling face, we mean a face that is not glued to the other polyhedron. If a pair of dangling faces contribute to a peak that is also contributed by three polyhedra, we call that peak an illegal peak (i-peak). The i-peak can be rectified by gluing together the two dangling faces contributing to it. The original polychoron can be recovered from its ps3;tfp(0) as follows :In decoding, by a p3(1) to obtain the polyhedron 1, assigning face and edge IDs.(a) Decode 1.p3(i) to obtain the next polyhedron i (2 ≤ i ≤ C), assigning face and edge IDs.(a) Decode i1 of the polyhedron i to the s-face of Di−1 in such a way that the edge i1 is glued to the smallest-ID edge of the s-face.(b) Glue the face wa(n) (1 ≤ n ≤ Na) is the face ID of the polyhedron i, then glue the face wa(n) to the face va(n) of Di−1 in such a way that the edge za(n) is glued to the smallest-ID edge of the face va(n).(c) If (d) If i-peaks are generated, then rectify them, and repeat this procedure until no i-peaks remain.2.(a) Repeat the procedure 2 until all polyhedra are placed.3.sp, the redundancy in tfp(0) can be removed step-by-step with generating tfp(1), tfp(2), tfp(3), ···, and tfpNa) as the concatenation of the two numbers. We use the lexicographically smallest p4 as the representative one.A maximum of 12degree of a peak as the number of polyhedra contributing to that peak. We call a peak of degree more than three an affected peak. We say a polychoron without an affected peak to be non-affected. Reversely, an affected polychoron has one or more affected peaks. The p4-code for non-affected polychora formulated above can be generalized to affected ones by using a one-to-one correspondence between an affected polychoron and its associated non-affected one as described below.We first define the Any affected polychora can be transformed into a non-affected one by cutting its affected peaks. However, when different affected peaks are incident to the same 0-face, different non-affected polychora are obtained depending on the order of cutting. Therefore, we first assign peak IDs, and then cut the affected peaks in the ascending order of peak ID.XY, connecting the 0-faces X and Y. We say its 0-face to be type-X (type-Y), if it is the cross section of a peak incident to X (Y). The ridges of the cs-cell are classified into three types: type-X ridges consisting of only type-X 0-faces, type-XY ridges consisting of both type-X and type-Y 0-faces, and type-Y ridges consisting of only type-Y 0-faces. In other words, by cutting a peak XY, it is mapped to a cs-cell in such a way that its endpoints are mapped to either type-X or type-Y ridges. Note that the type-X and -Y ridges do not adjoin each other because the type-XY ridges separate them, and that the number of the type-XY ridges is the same as the degree of the peak XY. In the example shown in XY of degree four, the 0-faces X and Y are mapped to the cross-section ridges a′b′c′d′ and e′f′g′h′, respectively. Four cross-section ridges a′d′h′e′, b′a′e′f′, c′b′f′g′, and d′c′g′h′ are type-XY.Suppose that we create a cross-section cell (cs-cell) by cutting an affected peak Choose a face and an edge of an affected polychoron as an initial face and edge, and then assign peak IDs.Cut the affected peaks in the ascending order of peak ID.Encode the associated non-affected polychoron from the initial face and edge corresponding to the ones used in procedure (1).p3-codeword for a cs-hexahedron as XY ridges.To identify the cs-cell that is created when we cut an affected peak, we denote, for example, the Based on the above discussion, an affected polychoron can be encoded as follows:p4-codeword for a polychoron shown in 6 and For example, a Decoding is achieved easily. We first reproduce the associated non-affected polychoron, and then shrink the cs-cells to the corresponding affected peaks.p4), we define Lex(ps3) for a non-simple polychoron as the concatenation of Lex(ps3(1)) and Lex(ps3(2)). Here, ps3(1) is the codeword obtained from ps3 as follows. We first replace every p3 with 0 except p3s for the cs-cells corresponding to the affected peaks. We then deal with the p3s for the affected peaks, and replace the digits without double lines with 0 and remove the double lines. The ps3(2)-codeword is the one obtained by removing double lines from ps3. For example, Lex is defined as the concatenation of Lex (★) and Lex(p4).As in the case of polyhedra, the duality of polychorap4-code can be used to describe the arrangement of polyhedra in polyhedral tilings. The complex of polyhedra shown in p4-codeword OtHG3rd4(HG3rd)4H. Here, by a partial p4, we mean that decoding it results in a partial polychoron. Ot (=464(46)44) and H (=46) are the representative p3s of the truncated octahedron and hexahedron, respectively. G3rd (=6(48)3(64)6(84)36) is the third smallest p3 of the great rhombicuboctahedron.Since a complex of polyhedra can be regarded as a partial polychoron, the p4-codeword that represents what polyhedra are tiled in what way. Traditionally, the index c3c4c5∙∙∙ has been used to classify polyhedra in polyhedral tilings of liquids, glasses, grains and foams, where ci is the number of i-gons on the polyhedron1234569p3 code, the same polyhedron is encoded as “356645445”. We also note that when the Voronoi polyhedron associated with an atom is encoded as 356645445, the atom is surrounded by neighbouring atoms forming a ★356645445-polyhedron. Our method thus allows us to describe polyhedral tilings succinctly, which is essential to understand disordered structures. In addition, although the short-range order can be studied by the previous methods, the long-range order cannot. Only our theory allows us to characterize what polyhedra are tiled in what way, and thereby paves the way to study from short- to long-range order of disordered structures in a systematic way. Moreover, our theory can be generalized to higher-dimensional polytopes to study disordered structures of any dimension.In this work, we have created the theory of polyhedral tilings, which allows us to convert a local arrangement of polyhedra into a partial How to cite this article: Nishio, K. and Miyazaki, T. How to describe disordered structures. Sci. Rep.6, 23455; doi: 10.1038/srep23455 (2016).


ADHD is prevalent in adults and frequently associated with impairment and distress. While medication is often the first line of treatment a high proportion of people with the condition are not fully treated by medication alone, cannot tolerate medication or do not wish to take it. Preliminary studies suggest that psychosocial approaches are a promising adjunctive or alternative treatment option. To date, individual cognitive-behaviour therapy (CBT) has been found to be efficacious in three randomized controlled trials (RCTs). There is a need for more RCTs to be carried out in order to replicate these results in different sites, to further investigate the acceptability and feasibility of CBT in this population and to further develop CBT approaches based on a psychological model. This randomized controlled trial investigates the efficacy of individual, formulation-based CBT when added to treatment-as-usual as compared with treatment as usual alone.Sixty patients with a diagnosis of adult ADHD attending a specialist clinic are randomly allocated to 1 of 2 treatments, ‘Treatment as Usual’ (TAU) or TAU plus 16 sessions individual CBT (TAU + CBT). In the TAU + CBT, the first 15 sessions take place over 30 weeks with a 16th ‘follow-up’ session at 42 weeks. Outcomes are assessed at 30 weeks and 42 weeks following randomization. The two primary outcomes are self-rated ADHD symptoms and functioning . Secondary outcomes include distress, mood, ADHD-related cognitions, ADHD-related behaviours and informant-rated ADHD symptoms.The primary analysis will include all participants for whom data is available and will use longitudinal regression models to compare treatments. Secondary outcomes will be analysed similarly.The results of the study will provide information about a) whether CBT adds benefit over and above TAU for ADHD and, b) if CBT is found to be efficacious, potential mechanisms of change and predictors of efficacy.ISRCTN03732556, assigned 04/11/2010Current Controlled Trials  Although Attention Deficit Hyperactivity Disorder (ADHD) was originally identified in children, it is increasingly recognised that symptoms may persist into adulthood. The disorder is frequently associated with impairment, distress and psychiatric co-morbidity ,2. EstimMedication is the first line treatment for ADHD in adults. However, approximately 50% of individuals with adult ADHD are not able to tolerate, do not respond to, or fail to reach optimal outcomes on medication alone . The NICThere is promising preliminary evidence suggesting that psychological treatment approaches are of benefit for individuals with Adult ADHD ,7. A ranSome of these results are from open-label uncontrolled studies -13 whichOther studies have compared potentially efficacious treatments with a control group using a non-randomized design. The studies include group treatments of psychoeducation ,15and moThere have been seven RCTs of group treatments and these include cognitive remediation programmes ,18 metacSo far, to the authors’ knowledge, there have been only three RCTs of individual CBT -26. SafrSimilarly the study by Virta et al. investigated a manualised approach which was not formulation driven, although the topics of a few sessions were chosen by the participants. CBT was compared with cognitive training and no treatment/waitlist conditions. More participants in the CBT condition improved compared with the other two conditions. Both active conditions showed a significant decrease in ADHD symptoms but CBT was superior in efficacy for decreasing ADHD symptoms.In their 2010 review, Knouse and Safren noted that the treatments with the largest effect sizes commonly comprise short-term, highly structured programmes with an emphasis on teaching specific skills and strategies and practice outside the session .The psychological treatments developed and evaluated thus far by RCTs have tended to be skills-based i.e. sessions focused on teaching specific skills to combat the symptoms of ADHD such as training in organising and planning. However, the emotional and behavioural problems experienced by adults with ADHD often extend far beyond the impact of the core symptoms themselves.ADHD in adulthood is the persistence of a childhood condition which has often had a wide-ranging effect on an individual’s emotional, social and cognitive development. For example children with ADHD commonly experience difficulties at school related to their symptoms and may receive negative feedback from parents, teachers and peers. This may lead to the development of negative self-beliefs which persist into adulthood. Consistent with this, it is not uncommon to encounter in adults with ADHD emotional problems such as depression, anxiety and low self-esteem and concurrent maladaptive coping responses .Individual cognitive behavioural therapy is recommended in NICE and other guidelines for ‘common mental health problems’ such as anxiety and depression. At the heart of individual CBT is the development of an individual formulation (the formulation-based approach) in collaboration with the client. Although disorder-specific CBT protocols exist for certain emotional disorders of mild-moderate severity, individual formulation is still important and particularly so for more complex cases or conditions of greater severity.The formulation is essentially a shared hypothesis as to the relationships between the individual’s predisposition , their experiences, and how these have contributed to the development of certain beliefs, behaviours, emotions and physical reactions. In addition to this developmental aspect, the formulation specifies the possible influence of these beliefs and behaviours on maintaining ADHD symptoms, impairments in daily functioning and distress. Treatment is then tailored to the individual and focuses on the idiosyncratic problematic behaviours and thoughts identified in the detailed assessment, while drawing on a range of evidence-based strategies.In relation to ADHD, a formulation-based approach may be structured and teach specific skills and strategies, but it would also entail a detailed assessment to identify the main problems experienced by the individual patient which then allows them to be targeted directly. The formulation allows the client and therapist to collaboratively address the core symptoms of ADHD using education, adaptations to the client’s environment and repetition of adaptive skills in order to compensate for executive dysfunction. In addition it allows for the identification and modification of beliefs (e.g. ‘I cannot concentrate so there is no point trying’) and behaviours (e.g. procrastination) that may be serving to maintain problems and associated distress. The therapist can help the client make links between their beliefs and pertinent early life experiences in a compassionate and understanding way and this minimises the possibility of provoking shame or a defensive reaction. This individualised approach improves the client’s understanding of their difficulties and reduces the potential for relapse. This approach would also make it likely that some of the co-morbidities would be addressed during treatment such as anxiety and low mood.While the RCTs of individual CBT so far have used treatment models, to the authors’ knowledge none has used a formulation-based approach in order to identify and modify idiosyncratic underlying beliefs  and compensatory strategies. Formulation-based approaches to ADHD have been described and found to be helpful in previous uncontrolled studies ,10,12 buThe current study therefore aims to develop and evaluate a collaborative, formulation-based approach to treating adult ADHD. A group of individuals receiving CBT combined with treatment as usual for adults with ADHD will be compared with a group receiving treatment as usual only, employing a randomized design. Detailed cognitive-behavioural assessments as well as information about cognitions and behaviours from a measure developed in a concurrent study will inform the content of the intervention. Therapists will also have access to a range of skills-based approaches, as have been used in previous studies, as and when indicated by the formulation, and a treatment manual is being produced which will be updated iteratively.While common elements of the most effective treatments have been noted, previous studies have not formally investigated mechanisms of change. For example, do symptoms and distress improve because people have learned more effective skills in managing their symptoms? Do negative automatic thoughts about the condition (for example ‘my ADHD will stop me from doing the things I want to do’), underlying beliefs about the self (for example ‘I am a failure’) and associated compensatory strategies need to be changed for CBT to be effective? It is hoped the current study will shed light on the mechanisms of successful CBT for adult ADHD.We will assess demographics, co-morbidity and other clinical factors at baseline to examine whether they are associated with a poorer outcome.To investigate efficacy, patient acceptability and feasibility of a formulation-based cognitive-behavioural therapy for adults with attention deficit hyperactivity disorder (ADHD).A secondary aim is to investigate the predictors of outcome and mechanisms of change.CBT plus treatment as usual will be more effective than treatment as usual alone in i) reducing ADHD symptoms ii) improving functioning.A two-arm randomized controlled trial of patients who meet DSM IV criteria for adult ADHD. Participants will be randomly assigned to one of two treatment arms. The first condition is treatment as usual (TAU). TAU will often but not always be pharmacotherapy, overseen either by the ADHD service in which the research is being carried out, the participant’s local adult ADHD Service, a community mental health team or a general practitioner. The second condition is TAU and in addition sixteen sessions of CBT.NB for brevity, the rest of protocol will refer to the two treatments as CBT and TAU rather than CBT plus TAU and TAU alone.Each participant will be assessed and participants who give informed consent will be randomly allocated to one of two treatments. Treatment will start as soon as possible after randomization. The final outcome measure will be at 42 weeks after randomization.See Figure We will study 60 participants over approximately three years. All will have received a diagnosis of adult ADHD, either in the Adult ADHD Service or elsewhere . Participants will either already be attending follow-up clinics in the Service, including psychoeducation workshops, or will have been recently referred to the service for medication follow-up or psychological treatment.The psychoeducation workshops include group discussion, didactic teaching and provision of written materials and cover topics such as what it means to have ADHD, relationships, emotions  and ADHD, time management, problem-solving, relationships and the future with ADHD. Broadly they follow the format described in a previous study  with somBoth clinician and participant agree that randomization is acceptable.The participant has given written informed consent.The participant is aged 18 to 65.The participant is diagnosed with adult ADHD by a mental health professional.The participant’s score on the inattentive or hyperactive/impulsive subscale of the Adult Barkley Current Behaviour Scale (self-rated) is 6 or more.The participant is rated to have clinical severity of at least a moderate level .The research psychologist will use a standardized psychiatric interview  under supervision by the PI or nominated deputy to exclude those who have a clinically significant anxiety disorder and current episode of major depression, significant risk of self harm and active substance misuse/dependence in last three months. Participants will also be excluded if they have an acquired brain injury, a primary diagnosis of psychosis or bipolar disorder, a pervasive developmental disorder, a diagnosis of a personality disorder or any other primary clinical diagnosis whereby participation in the trial would be inappropriate to their clinical needs.Participants with a Verbal IQ of less than 80 will be excluded from taking part owing to the verbal and cognitive elements of the intervention.Patients who are considered by the research psychologist in discussion with the PI to be unable to comply with the requirements of an RCT (e.g. are not able to attend regularly and reliably for assessment and treatment sessions), who are currently undergoing another talking therapy for adult ADHD or any other psychiatric disorder, who are unable to speak English at an adequate level to participate in the trial will be excluded.Eligibility will be established according to the inclusion and exclusion criteria. For pragmatic reasons, to maximize recruitment, it was decided not to have inclusion/exclusion criteria related to the use or otherwise of medication or the stabilisation or otherwise of the dose. Use of medication will be routinely recorded and it is anticipated that any variation in use of medication will be accounted for controlled for in the randomized design.Individuals likely to meet eligibility criteria for the study will be given an information sheet about the treatment trial by their doctor and invited to take part. Potential participants will attend an assessment appointment with a research psychologist to ascertain eligibility for the study. If the patient understands the purpose of the trial and is willing to give informed consent to be randomized, treated and followed up, they will sign the consent form to participate in the trial.A battery of self-report measures and two structured diagnostic interviews will be administered. The Mini-International Neuropsychiatric Interview (M.I.N.I.) assesses for co-morbid psychiatric diagnoses and takes approximately 15 minutes . ConnersParticipants will be randomly allocated to one of the two treatments. Randomization will be performed by an independent group in another service in the same NHS Trust using a concealed sequence. The sequence will be generated using randomization tables and fixed-length blocks , stratified for gender. The sequence will be generated by one named individual and put into numbered sealed envelopes. The envelopes will be kept by another named individual (the independent researcher) in a locked drawer to which only she has access. When a participant is suitable for randomization the ADHD assistant will email the independent researcher giving the participant number and gender. The independent researcher will reply by email with the allocation and will record this along with the participant number and gender in an electronic secured access file.The individual assignments will be available to the Adult ADHD team on a need to know basis. The local statistician/s will be independent and will not have access to the treatment allocations.All participants in the trial will receive TAU. This will include visits to their clinic doctor in the Service, if they have one, or visits to their local Specialist ADHD Service, CMHT or GP for management of their ADHD. They may be given some general advice but no specific advice with regard to strategies they may use to manage their ADHD symptoms. There will be no additional therapist involvement. The number of outpatient sessions will be recorded along with any treatments given to participants by the clinic doctor.In addition to treatment as usual, participants will also attend up to 15 weekly 50-minute CBT sessions over a period of 30 weeks as well as their treatment as usual sessions at the clinic. They will have a sixteenth, follow-up CBT session at 42 weeks.During the early stages of treatment a shared formulation will be derived by patient and therapist. In the formulation links will be made between the individual’s predisposition, their early life experiences and current behavioural coping and cognitions. Treatment will then focus on the problematic cognitions and behaviours identified in the assessment and agreed in the formulation, while drawing on a range of evidence-based strategies such as thought records and behavioural experiments. Therapists will also have access to a range of skills-based approaches as have been used in previous studies, as and when they are indicated by the formulation (e.g. time management). A CBT manual has been developed but will be updated iteratively.The aim will be to complete up to 15 sessions within 30 weeks. These will be scheduled approximately weekly several weeks ahead. If the patient is not able to attend an appointment because of ill health, the appointment will be rescheduled to within one week’s time. If it is not possible to rearrange the session within this timeframe, a session may be held over the phone. Ideally no more than three sessions in a row should take place over the phone. However if the choice is between not having a session and offering a telephone session, a telephone session will always be offered, even if three consecutive phone sessions have already taken place.Wherever possible, assessments will be carried out at the adult ADHD Service. If the participant is unable to attend an appointment, an alternative appointment may be offered either at the participant’s convenience if not yet randomized, or within the two weeks of the post-assessment due date. If it is not possible for the participant to attend then questionnaires will be posted to them and the remainder of the assessment will be carried out over the phone.Participants who drop out of treatment early will be assessed for outcomes as soon as possible rather than waiting for the normal follow-up.It will not be practicable for the assistant psychologist to remain blind to the treatment group allocation and so we will not attempt this.See Table Adult Barkley Current Symptoms Scale The Barkley Current Symptoms Scale includes questions that assess the frequency of the 18 DSM–IV symptoms for ADHD. Items assess the frequency of 9 inattentive and 9 hyperactive/impulsive symptoms on a scale ranging from 0 = “never or rarely” to 3 = “often” with a score of 2 or above indicating the presence of a symptom. The presence of six or more symptoms for each subtype is considered clinically significant, in line with the recommended threshold of six out of nine symptoms in DSM- IV. This measure has strong reliability and validity and has been widely used in ADHD research.Work and Social Adjustment Scale This is a reliable and valid measure  that has3.Clinical Outcomes in Routine Evaluation Outcome measure (CORE-OM) . This is4.Hospital Anxiety and Depression Scale (HADS) This is a 14-item scale with two subscales measuring anxiety and depression respectively. It has been found to reliably and validly assess the symptom severity and caseness of anxiety disorders and depression in psychiatric and primary care patients and in the general population .5.ADHD Cognitions Questionnaire Participants will rate various beliefs in relation to their ADHD. The reliability and validity of this scale is being evaluated in a parallel study.6.ADHD Behaviours Questionnaire Participants will rate the extent to which they engage in certain behaviours in relation to their ADHD. The reliability and validity of this scale is also being evaluated in a parallel study.7.The Rosenberg Self-Esteem Scale .This is a 10-item uni-dimensional measure of global self esteem, self-worth or acceptance that has been shown to be reliable and valid including in psychiatric outpatients .8.The Autism Spectrum Quotient  *†This is a 50-item questionnaire designed to assess autism spectrum symptoms in the general population. Results so far show good reliability. Studies in adults show that the scale can distinguish between ASD and controls as well as between ASD and psychiatric conditions such as OCD and social anxiety -42. The 9.Global Impression scales (improvement** and satisfaction**)  prov10.Frost Multidimensional Perfectionism Scale, Unhealthy Perfectionism subscale , The ori11.Beliefs about Emotions Questionnaire This is a 12-item scale that assesses beliefs about experiencing or expressing negative thoughts and emotions. It was validated using participants with chronic fatigue syndrome and healthy controls and shows good internal reliability, validity and sensitivity to change. Responses are rated on a seven point Likert scale where 6 = “totally agree” and 0 = “Totally disagree”.12.Adult Barkley Current Symptoms Scale – Other Report Form. This is an informant version of the Adult Barkley Current Symptoms Scale.13.Global Impression Scales (improvement)**. Global measure of improvement (see 9) rated by the nominated informant.14.Global Impression scales (severity and improvement)**. Global measures of severity and improvement (See 9) rated by the independent evaluator.15.Global Assessment of Functioning . A gener16.The independent evaluator will also be asked to say which group they thought the participant was in and why .17.Ratings of CBT compliance and adherence**. Number of CBT sessions attended, whether they were face-to-face or telephone, their duration and percentage completion of homework will be recorded. At the end of CBT treatment, the therapist will also score how well the participant adhered to the CBT approach, the extent to which the participant accepted the model of therapy and the therapeutic alliance on a five-point scale ranging from “not at all” to “completely”. They will also rate homework compliance on a scale of 0% to 100% completion on a session-by-session basis. These measures were adapted from a previous RCT . A new m18.Global Impression scales (severity and improvement) ** Global measures of severity and improvement rated by the therapist (See 9). For practical reasons these will be administered in the CBT condition only.19.Medications and doses. At the each assessment point the assistant psychologist will take a record of current medications and doses, any changes, compliance with medication. They will also ask about any adverse events/reactions that may not yet have come to the attention of the trial personnel.20.The details of TAU for all participants i.e. number of sessions with the service managing their ADHD  will be recorded.* baseline only.** 30 weeks and 42 weeks only.† This is routinely administered during clinic assessments. This will only be included in the questionnaire pack if, for any reason, it has not already been completed.The trial will be conducted in compliance with ethical approval  and R&D approval (reference R&D2009/051).The study opened to recruitment February 2010.The main Sponsor is South London and Maudsley NHS Foundation Trust.There will be a combined Trial Steering Committee (TSC) and Data monitoring and ethics committee (DMEC). They will be responsible for monitoring progress of the trial and serious adverse events or reactions. A trial management group will meet more regularly to discuss the day-to-day running and management of the trial. The combined TSC and DMEC will aim to meet at least three times over the course of the trial.Therapists’ compliance with treatment manuals will be monitored in two ways. All therapists will receive a minimum of monthly face to face group supervision sessions. All sessions will be audio-recorded and some recordings will be used to provide feedback to therapists on competence and treatment fidelity. Although the patient manual will be developed iteratively, the broad approach and content of therapy will be agreed by the principal investigator and the clinicians involved in the study  at the outset of the trial. Deviations from this will be noted and feedback given to the therapist. Following completion of the treatment sessions and of the patient and therapist manuals, 10% recorded sessions will be rated by two independent raters in order to assess adherence to the manual-defined therapy.The following power analysis is based on a previous study by Safren et al.  which cot-test with a 0.050 two-sided significance level.A sample size of 23 in each group will have 90% power to detect a difference in means of 9.000. This is the difference between the change score of the Group 1 mean of 14.200 (SD = 7.2 assuming a correlation between pre and post measure of r = 0.5) and the Group 2 mean of 5.200 . This is also assuming that the common standard deviation is 9.050 (conservative estimate) using a two group The intention to treat number is 23, however we will try to recruit 30 to each group to allow for dropouts.Between group effect sizes will be computed for the outcome measures.The two conditions i) CBT and ii) TAU will be compared using random effects modelling. Intention to treat analysis will be used. It is predicted that the CBT group, covarying for baseline levels, will have better results than the TAU group on the primary outcome  and secondary outcome measures. A more detailed analytic structure will be written before data analysis begins.This is a randomized controlled trial to further investigate the feasibility and acceptability of CBT in addition to TAU as compared with TAU alone. This is the first study to investigate individualized formulation-based CBT for adults with ADHD using a randomized controlled design. It is hoped it will provide important information about the efficacy of this approach in this client group. It will also provide information as to the feasibility of conducting a larger better-powered study in the future, potential effect sizes and acceptability of the approach to patients. Finally it will provide some preliminary information about mechanisms of change as well as predictors of successful CBT outcome.A limitation of this study is that it is not designed to match for therapist time and attention and so it will not be possible to say whether any changes seen in the CBT group are specific to the CBT. Future studies should evaluate this formulation-based approach alongside an active control condition.It is hoped this study will provide further information for people with ADHD, healthcare providers and commissioners as to which treatments are most useful for ADHD in adulthood. It will also provide some preliminary information about the mechanisms of change and predictors of outcome in terms of symptoms and functioning.


Firstly, associations were explored between WM microstructure and ADHD severity in the subgenual cingulum. Secondly, to ensure that tract-specific approaches afforded enhanced rather than differential sensitivity, associations were measured between WM microstructure and autistic traits in the right corticospinal tract based on results of a previously-published voxelwise analysis.This analysis examined hypothesised associations between microstructural attributes in specific white matter (WM) tracts selected 40 right-handed males aged 14–18 years  underwent a 60 direction diffusion MRI scan. Clinical ADHD and autism variation were assessed by validated questionnaires. Deterministic tractography based on spherical deconvolution methods was used to map the subgenual cingulum and corticospinal tract.Fractional anisotropy was positively correlated and radial diffusivity was negatively correlated with a) ADHD severity in the left subgenual cingulum and b) autistic traits in the inferior segment of the right corticospinal tract. No case–control differences were found.Results shed light on possible anatomical correlates of ADHD severity and autistic symptoms in pathways which may be involved in the ADHD phenotype. They provide further evidence that tract-specific approaches may a) reveal associations between microstructural metrics and indices of phenotypic variability which would not be detected using voxelwise approaches, and b) provide improved rather than differential sensitivity compared to voxelwise approaches. •Adolescents with ADHD and controls underwent a diffusion MRI scan.•ADHD severity was associated with microstructure in the left subgenual cingulum.•Autistic traits in were associated with microstructure in the right corticospinal tract.•No case–control differences were found.•Use of tract-specific approaches may improve sensitivity to detect associations. It is cHeterogeneity in imaging findings is analogous to the clinical heterogeneity in ADHD. There is increasing evidence from structural and functional imaging studies of ADHD that aberrant neurodevelopment and brain function is widespread and broadly distributed . Using dDimensional measures of clinical variability in ADHD (e.g. questionnaire-based measures of ADHD severity and cognitive test measures) have been shown to correlate with white matter (WM) microstructure, but findings here have also been mixed . Some stWhilst voxel-based global search techniques have their advantages, they do not allow a search to be constrained to a specific anatomical pathway of interest and effectively assume that the properties of neighbouring voxels are independent, even though this will not be the case if they are contained within the same white matter pathway. Diffusion MRI-based tractography  scan with diffusion encoded along 60 non-collinear optimally ordered directions  with a bn = 2 from each group).ExploreDTI version 4.8.2  was usedLmax. was 8 and tracking was terminated when the angle threshold of the pathway changed through >45°. Regions of interest (ROIs) based on Boolean logical operations  were drawn to define the subgenual cingulum bilaterally and the right corticospinal tract, which were drawn in each subject's native space on directionally encoded colour maps based on the principal eigenvector of the diffusion tensor. Fibres of the contralateral hemisphere were excluded by the placement of a NOT gate in the sagittal plane two slices (3.75 mm) lateral to the mid-sagittal plane in the hemisphere that was not of interest. Once tracts were drawn, fibres inconsistent with known anatomy were excluded by NOT gates. The corticospinal tract was split into superior and inferior segments on the basis of the previous TBSS results  were seen for FA or MD, AD and RD were explored to further investigate the nature of these results.The Robust Estimation of the Tensor by Outlier Rejection (RESTORE) algorithm , which aU tests.Analyses were carried out in SPSS, version 18.0 . Group dShapiro–Wilk tests were used to check normality (Shapiro–Wilk statistic >0.05) of the distributions of total ADHD/SCQ scores in the ADHD group. Total ADHD scores were normally distributed but total SCQ scores were not. Total SCQ scores were transformed to normality using ln(score + 1).For each tract, the distributions of FA and MD  were also checked for normality (Shapiro–Wilk statistic >0.05). The majority were normally distributed. Those which were not  were not amenable to transformation.For the correlation analyses, where both symptom scores and diffusion parameters were normally distributed, Pearson's coefficient was used, otherwise, Spearman's coefficient was used. Correlations were tested between diffusion parameters and the following phenotypic variables: a) total ADHD score, in the subgenual cingulum bilaterally and b) SCQ score, in the right corticospinal tract (including superior and inferior sections).Logistic regressions were used to test for case–control differences in microstructure, with case/control status as the outcome and diffusion parameters as the predictor variables. Regressions were then re-run with age as a covariate. As logistic regressions do not have a formal requirement for normality of the independent variable , regress3n = 17. Two of the remaining controls had high reported levels of inattentive/hyperactive–impulsive symptoms and were thus excluded from the case–control analyses, meaning these were run with 17 ADHD and 17 controls. Two participants in the ADHD group had low endorsement of current ADHD symptom scores, they were considered ‘remitted’ and the case–control analyses were subsequently re-run with them excluded i.e. with 15 ADHD and 17 controls.Two participants were excluded from each group due to scan artefact, leaving 17 in the ADHD group and 19 in the control group. Therefore correlation analyses in the ADHD group were carried out with n = 17 ADHD and n = 17 controls), and Mann Whitney U test statistic results for differences in the distributions of these variables. In both the ADHD and control groups, neither total ADHD nor SCQ scores were correlated with age. All controls had an SDQ total difficulties score within in the normal range and none had any SDQ subscale score in the abnormal range. 16/17 of the ADHD group had a medication history, of treatment with short/long acting stimulants and/or atomoxetine. Six of these had discontinued their medication prior to the scan.Examples of tractography reconstructions are shown in p = 0.021), accompanied by trend significant negative correlation with RD  (p = 0.859) or MD (p = 0.704) were found in the right subgenual cingulum.Significant positive correlation was found between current ADHD severity  and FA in the left subgenual cingulum  , Fig. 2.p = 0.158) and autistic trait score and MD  in the right corticospinal tract. When this tract was divided into inferior and superior segments, significant associations were found in the inferior corticospinal tract only, for FA  and RD  (p = 0.658) or MD (p = 0.183).A weak trend towards association was seen between autistic trait score and FA  , Fig. 3.n = 17/17). Results were unchanged with the exclusion of the two ADHD subjects considered as remitted (n = 15/17).In line with the previous global voxelwise analysis of the same subjects, no case–control differences in FA or MD were found for the subgenual cingulum or total right corticospinal tract, and no case–control differences were revealed with the addition of age as a covariate , which had not been evident in the previous voxelwise analysis of the same sample of young people with ADHD. Also, the same pattern of microstructure  was found to be associated with increasing autistic traits in the right inferior corticospinal tract as it was in the voxelwise analysis, confirming that tractography does indeed provide enhanced, rather than differential, sensitivity. Results based on anatomically-defined reconstructions of specific tracts potentially have more biological plausibility: in neurodevelopmental disorders, it is more likely that an entire pathway will be affected rather than just an isolated piece of tissue contained in a voxel. These analyses highlight pathways which merit further investigation in future research into clinical variability of the ADHD phenotype.The associations between WM microstructure and ADHD severity in the subgenual cingulum are in keeping with previous literature implicating both the anterior cingulate and the cingulum in the pathophysiology of ADHD. However these results are the first to demonstrate correlation between microstructure and ADHD symptom severity specifically in the anterior  portion of the cingulum, which directly underlies the anterior cingulate. The fact that the association was seen in the left hemisphere is at odds with a meta-analysis of fMRI studies which found that the right rather than the left anterior cingulate cortex was one of the areas with dysfunction during tasks of inhibition , althougThe associations between autistic traits and WM microstructure in the right corticospinal tract support the TBSS findings from the same sample , confirmincreased FA and decreasing MD . Total ASD score was negatively correlated with RD, and there was a trend towards a negative association between total ADHD score and RD. Although ADHD case status and increasing symptom severity have tended to be associated with decreased FA e.g. , there iasing MD , and theasing MD . The useasing MD  magnetisasing MD , quantitasing MD  and multasing MD . HoweverIn line with the previous TBSS findings from this sample, no case-control differences in microstructure were found in the tracts examined, despite the use of rigorous methodology to examine microstructure in specific tracts and the increased power to detect effects afforded by an extended ROI approach i.e. the tractography method reported here. It is not possible to rule this out as being an effect of medication. It remains unclear as to whether stimulants and atomoxetine may have a role in normalising microstructure as studies have not yet been set up to investigate this question explicitly. However there is evidence to suggest that stimulants may attenuate alterations in a) macrostructure , b) braiStrengths of these analyses are as follows. The ADHD group was a thoroughly assessed clinical group, all with a lifetime diagnosis of DSM-IV ADHD-C to decrease heterogeneity in the phenotype. All were right-handed males to remove the confounding influence of gender and handedness. The age range included only older adolescents to try to minimise the effect of age on brain structure. The lack of a prerequisite to stop medication will have helped even out group differences in movement during scans. The combination of 60 direction diffusion imaging, cardiac gating and the RESTORE algorithm will have improved robustness in the estimates of diffusion parameters. The use of an SD algorithm will have improved specificity of fibre tracking compared to models based on the tensor alone.Limitations are as follows. There was a statistically significant group difference in the distribution of age, and although age was not found to exert any influence as a covariate in the case–control analyses, this difference should be considered a limitation to the group comparisons. Many of the correlations would not have survived a correction for multiple testing, but might have been of greater strength in a larger sample. Nonetheless, the risk of results being ascribable to type 1 errors was reduced by adopting a hypothesis-driven approach with regards to the few tracts under study. By virtue of how they are calculated, the diffusivity measures reported here are not mutually independent of each other as they are all computed from the three eigenvalues of the diffusion tensor. Thus it was not appropriate to apply a multiple testing correction in these regards. Data are cross-sectional so no inference can be made about direction of effects or causality. Also, whilst SD methods afford better anatomical specificity and veracity of pathway reconstruction over tenser-based tracking approaches, they cannot in themselves improve quantification of the underlying microstructural characteristics . These tenser-based parameters, which are projected onto the SD-derived tracts, will still be subject to the tensor's inability to resolve complex architecture. This problem could be resolved, for example, by using parameters derived directly from the fibre orientation distribution function, such as the hindrance modulated orientational anisotropy HMOA,  or the aIn summary, this study investigated associations between ADHD severity and autistic traits and WM microstructure in ADHD, using tractography in combination with SD methods to help improve the anatomical fidelity of pathway reconstruction through areas of complex fibre architecture. Results suggest that certain patterns of WM microstructure are correlates of ADHD severity and autistic traits and provide clues on pathways to investigate further in future research. They also highlight the benefit of adopting tract-specific approaches to improve power to detect effects, and suggest that such approaches indeed provide improved rather than differential sensitivity.The authors have no conflicts of interest to report.


The routine procedure of GISH using genomic DNA of rye as a probe is time-consuming and labor-intensive because of the preparation and labeling of genomic DNA of rye and denaturing of chromosomes and probes. In this study, new oligonucleotide probes Oligo-1162, Oligo-pSc200 and Oligo-pSc250 were developed. The three new probes can be used for non-denaturing fluorescence in situ hybridization (ND-FISH) assays and replace genomic DNA of rye as a probe to discriminate rye chromosomes in wheat backgrounds. In addition, previously developed oligonucleotide probes Oligo-pSc119.2-1, Oligo-pSc119.2-2, Oligo-pTa535-1, Oligo-pTa535-2, Oligo-pTa71-2, Oligo-pAWRC.1 and Oligo-CCS1 can also be used for ND-FISH of wheat and rye. These probes have provided an easier, faster and more cost-effective method for the FISH analysis of wheat and hybrids derived from wheat × rye.Genomic  S. cereale L.) has been used in wheat (T. aestivum L.) breeding programs as a source of genes for resistance to abiotic stress, diseases and insects1234in situ hybridization, and the use of PCR-based markers have been exploited with great success. However, the application of C-banding technology in breeding programs is limited because of its time consuming nature and a required high skill level in interpreting resultsin situ hybridization have been widely used to detect rye chromatin in wheat-rye hybrids. The PCR-based markers are convenient for identifying rye chromatin, however, they do not show the physical size of the rye translocations. Fluorescence in situ hybridization (FISH) and genomic in situ hybridization (GISH) have been most useful for investigating wheat-rye hybrids891089131589Rye  and T. aestivum L. Mianyang11 × S. cereale L. Kustro (MK) were analyzed by ND-FISH using oligonucleotides Oligo-1162, Oligo-pSc200 and Oligo-pSc250 as probes  × S. cereale L. AR106BONE (genome RR) and Mianyang11 × S. cereale L. Kustro (genome RR), respectively. The wheat-rye 1R disomic addition line 14T-71, the wheat-rye 1BL·1RS translocation line 14T-78 and the wheat-rye 5DS-4RS·4RL and 4RS-5DS·5DL translocation line 14T-267 were also used. Lines 14T-71 and 14T-78 were slected from the progeny that were derived form MK × Mianyang11. Some MK seeds were irradiated with fast neutron. Then the irradiated MK was used as recipient to cross with common wheat cultivar CN27 (genomes AABBDD) and line 14T-267 was selected form the progeny of this cross combination. The detailed information of these materials are listed in The plant materials used in this study included octoploid triticales MA and MK, derived from S. cereale L. Kustro was sequenced by using the Specific Length Amplified Fragment Sequencing (SLAF-seq) method . The sequencing procedure was performed as described by Chen et al.T. aestivum L. Chinese Spring. Then, a lot of reads, which were 60 bp long and had low wheat homology were obtained. One read with a sequence depth of 85 was randomly selected to use as an oligonucleotide probe. This probe was named Oligo-1162 , 6-carboxytetramethylrhodamine (Tamra) or Cy5. The signals of probes labeled with 6-FAM, Tamra and Cy5 were displayed in the colors green, red and white, respectively. Oligonucleotide probes were synthesized by Shanghai Invitrogen Biotechnology Co. Ltd. . These synthesized probes were diluted by using 1×TE solution (pH7.0). For Oligo-1162, Oligo-pSc200 and Oligo-pSc250, probe amounts per slide are listed in in situ hybridization were conducted with the methods described by Han et al.Probes Oligo-1162, Oligo-pSc200 and Oligo-pSc250 were hybridized together to mitotic metaphase chromosomes of octoploid triticales MA and MK in the ND-FISH method. After rinsing the chromosome preparations of MA and MK, GISH was carried out on the same slides with the genomic DNA probe of Kustro. Genomic DNA of rye was labeled with Texas Red-5-dUTP (Invitrogen). Probe labeling and Images were taken using an epifluorescence microscope  equipped with a cooled charge-coupled device camera operated with HCIMAGE Live software (version 2.0.1.5) and processed with photoshop CS 3.0.S.F. and Z.T. designed the study, analyzed the data and wrote the manuscript. L.C., Y.W., M.L., L.Q. and B.Y. performed the experiments. Z.Y. and Z.R. discussed the manuscript.How to cite this article: Fu, S. et al. Oligonucleotide Probes for ND-FISH Analysis to Identify Rye and Wheat Chromosomes. Sci. Rep.5, 10552; doi: 10.1038/srep10552 (2015).


Clinical ADHD cases, including both + comorbidity and non-comorbid groups, performed substantially worse on continuous performance test (CPT), working memory. Comparing ADHD-non-comorbid and ADHD + comorbidity groups, the latter did significantly worse on inhibitory control, time processing, and the level of perseveration response on CPT indexes, as well as on working memory performance and child behavior checklist (CBCL) tests particularly the CBCL-deficient emotional self-regulation test in the ADHD + comorbidity group. Children diagnosed as ODD or with conduct disorder showed close correlations between clinical CBCL profiles and externalized symptoms. Our findings suggest that ADHD + comorbidity and ADHD non-comorbid cases may be differentiated by a number of neuropsychological measures, such as processing speed, inhibitory control, and working memory, that may reflect different levels of involvement of the hot and cool executive domains, which are more impaired in cases of severe symptomatic-externalized behavior and emotional regulation problems. Therefore, profiles based on clinical and behavioral findings can help clinicians select better strategies for detecting neuropsychological impairment in Brazilian children with ADHD.Attention-deficit hyperactivity disorder (ADHD) is a complex neurodevelopmental disorder that implies several-step process, and there is no single test to diagnose both ADHD and associated comorbidities, such as oppositional-defiant disorder (ODD), anxiety disorder, depression, and certain types of learning disabilities. The purpose of the present study was to examine correlations between behavioral and clinical symptoms by administering an extensive neuropsychological battery to a sample of children and adolescents from a developing country. The sample was divided into three groups: non-ADHD, ADHD-non-comorbid, and ADHD + comorbidity. A full neuropsychological battery and clinical assessment found that 105 children met DSM-5 criteria, of whom 46.6% had the predominantly inattentive presentation, 37.3% had combined presentation, and 16% were predominantly hyperactive/impulsive presentation. The internal correlation between neuropsychological tests did not reach statistical significance in the comparison between ADHD and non-ADHD cases ( Attention-deficit hyperactivity disorder (ADHD) affects approximately 5.9 and 7.1% of children and adolescents across different cultures and are characterized by persistent pattern of inattention, hyperactivity, and/or impulsivity . The lacSeveral studies showed a high prevalence of comorbidities of approximately 20–50% , 4, and Convergent data from various sources, including neuroimaging, neuropsychological, genetics, and neurochemical studies, have generally implicated fronto-striatal network abnormalities as contributing to ADHD , 11. StuAbnormal brain networks can be related to this additive substrates of the observed synergistic dysfunctional neuropsychological performance present in the ADHD+ cases. Left dorsolateral prefrontal cortex (DLPFC) and anterior cingulated cortex (ACC) have been associated with interference control assessment, work memory, and EF . It is wA child behavior checklist (CBCL)  profile Child behavior checklist scores may provide useful information for differential diagnosis when used in combination with other clinical data  . BiedermBiederman et al.  and SpenOther behavioral rating scales may also be useful to assess ADHD children in ecological contexts (family and school), including the Conners’ rating scaling , the ADHThus, our primary objective was to examine correlations between behavioral and clinical symptoms by administering an extensive neuropsychological battery to a sample of ADHD children and adolescents with and without comorbidities in a sample of Brazilian children.Ethics committee approval was obtained as was all parents’ informed consent before enrollment.One hundred and twenty-four children aged 6–14 were selected through voluntary enrollment by parents attending the ADHD Outpatient Sector at NANI-UNIFESP following complaints of restlessness, attention difficulties, and/or impulsivity. They were then asked to attend an individual trial interview. Children who met the inclusion (at least 6 DSM-5) for hyperactivity and/or 6 for inattention (starting before the age of 12) were referred to a multidisciplinary assessment schedule, which consisted of medical and neuropsychological evaluations, as well as social, neurological, and psychiatric examinations and family assessment. All the children were not taking medication in the period of evaluation.(1)Intellectual level: Wechsler Intelligence Scale for Children abbreviated WISC-III .(2)EACIP scale : teacher(3)Conners’ CPT : compute(4)Working memory : (a) for(5)Rey figure: assesses visual-constructive functions (Rey copy) as well as visual memory (Rey memory) when subjects draw a complex figure from memory .(6)The widely used CBCL, which takes parent-reported data for 112 behavioral problems and three areas of competency , has beeThe neuropsychological battery included:Using our interdisciplinary criteria, the ADHD diagnosis was based on DSM-5 and neurologic and psychiatric evaluations. The diagnosis of psychiatric comorbidities was based on the CBCL and one structured psychiatric interview. In relation to comorbidities, the assessment was conducted by two board-certified doctors (a psychiatrist and a neuropediatrician) with great experience (over 25 years) in clinical evaluation and research. Data were collected over 2 days of testing. At the end of this evaluation, their cases were discussed by the service team, and the diagnoses were established. All diagnostic uncertainties were resolved by excluding cases in which cognitive and clinical data were non-congruent. Children presenting symptoms of inattention, hyperactive-impulsivity, and ADHD combined with comorbidities (ADHD + comorbidity) or without comorbidities (ADHD-non-comorbid) were included in the study.Clinical and neuropsychological test scores were compared using multivariate analysis of variance, followed by Tukey’s test and Pearson’s correlation coefficient to assess correlations between clinical and neuropsychological variables. Three groups were compared: non-ADHD, ADHD-non-comorbid, and ADHD + comorbidity. All tests were two tailed, and alpha was set at 0.05.Most children were males . The average age was 7 years and 7 months and ranged from 6 to 12 (SD 1.6). In relation to DSM-5 ADHD, 105 (68.1%) children met at least 6 criteria for inattentiveness and/or hyperactivity; 49 cases (46.6%) were predominantly inattentive presentation; 39 (37.3%) showed hyperactivity and inattention symptoms combined (combined presentation); and 17 (16%) showed predominantly hyperactivity plus impulsivity presentation. Of the remainder of the 154 children, those not meeting ADHD criteria were 49 (31.9%), of whom seven presented learning disabilities (14.3%), 10 (20.4%) had altered family dynamics, 16 (32.6%) had adaptive disorders, and 16  had a mental deficit (QI < 85) .In relation to performance on the CPT, ADHD children had more difficulty with omission, commission, reaction time, variability, and perseverance than non-ADHD children. However, the number of omissions was significantly higher for children from the inattentive group than the combined group, which suggests the omission measure may be a differential criterion. In fact, 44% of ADHD+ comorbidity children met the criteria for DESR in ODD (11 patients), CD (3 patients), BD (4 patients), and AD (28 patients).Table Table This study aimed to compare the neuropsychological profile of symptomatic children and adolescents presenting comorbidity with ADHD with those suffering from ADHD without comorbidity.In recent years, the role of multidisciplinary evaluation of ADHD has been constantly reviewed and involved several centers in different countries . TherefoConners’ CPT is widely utilized to test for sustained attention and inhibition due to ease of administration and a broad profile allowing age-group distribution for parameters closely related to attention ability, such as reaction time, omission, and commission errors.Our study showed that Conners’ CPT was sufficiently sensitive to distinguish cases that met the criteria for clinical ADHD from non-ADHD profiles, but not for absolute differentiation between the ADHD modes of clinical presentation, because significant differences were found for omission scores alone Table . ADHD + Conners’ CPT as an isolated paradigm that is not ideal for diagnosing the modes of clinical presentation, but it is useful for assessing the overall impact of ADHD on the cognitive domain and for separating purely contextual cases. It is also particularly sensitive for cases of comorbidities, such as ODD and CD Table .For Rey complex figure visual-constructive and visual-spatial skills, we found a negative correlation between percentile perseveration in Conners’ CPT and drawing a figure from memory. The higher the performance on the memory test, the lower the perseveration on the CPT Table . We contThe negative correlations Table  we obserIn combined ADHD cases (score >6 for hyperactivity), performance correlated positively with more omissions, reaction time, and variability of answers in the CPT Table .Several studies showed a high prevalence of comorbidities of approximately 20–50% , 5. Our Although ADHD has long been conceptualized as a deficient self-regulation disorder, researchers have only recently focused on DESR. DESR refers to (1) deficits in self-regulation of physiological arousal due to strong emotions, (2) difficulties inhibiting inappropriate behavior in response to either positive or negative emotions, (3) problems refocusing attention from strong emotions, and (4) disorganization of coordinated behavior in response to emotional activation . ClinicaROC curve analyses showed close correlations with CBCL scales for ADHD + comorbidity children, particularly ODD and CD cases via Pearson’s test . ODD cases showed CPT score alterations especially for vigilance adaptation (Hit RT), commission, and perseveration. These findings may be related to low inhibitory and impulsivity control in ADHD + comorbidity cases.Although our paper only reassures the known close relation between the severity of neuropsychological profile with behavioral symptoms of children with ADHD , 23, 42,Overall, our study suggests multiple connections between neuropsychological test scores, which are useful for a more detailed delimitation of the clinical profile and outcome signaling comorbidities in ADHD children. Therefore, our study provides evidence regarding the neuropsychological deficits of these patients, so that techniques that might improve low inhibitory and interference control should be included in the rehabilitation techniques in children and adolescents with ADHD + comorbidities. A larger sample will help us to determine clinical and neuropsychological indicators that may lead not only to a more precise diagnosis but early detection of neurocognitive outcome that can also help us to select rehabilitation strategies for better social and cognitive inclusion of ADHD children and adolescents.This study should be considered in the light of its limitations. Data were derived from a limited sample, and as such, our results might not be extrapolated to clinical settings. Co-occurrence of internalized and externalized problems and demographic and clinical heterogeneity of the samples may limit generalization of our findings.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.