Preference for biological motion is reduced in ASD: implications for clinical trials and the search for biomarkers

BACKGROUND

The neurocognitive mechanisms underlying autism spectrum disorder (ASD) remain unclear. Progress has been largely hampered by small sample sizes, variable age ranges and resulting inconsistent findings. There is a pressing need for large definitive studies to delineate the nature and extent of key case/control differences to direct research towards fruitful areas for future investigation. Here we focus on perception of biological motion, a promising index of social brain function which may be altered in ASD. In a large sample ranging from childhood to adulthood, we assess whether biological motion preference differs in ASD compared to neurotypical participants (NT), how differences are modulated by age and sex and whether they are associated with dimensional variation in concurrent or later symptomatology.

METHODS

Eye-tracking data were collected from 486 6-to-30-year-old autistic (N = 282) and non-autistic control (N = 204) participants whilst they viewed 28 trials pairing biological (BM) and control (non-biological, CTRL) motion. Preference for the biological motion stimulus was calculated as (1) proportion looking time difference (BM-CTRL) and (2) peak look duration difference (BM-CTRL).

RESULTS

The ASD group showed a present but weaker preference for biological motion than the NT group. The nature of the control stimulus modulated preference for biological motion in both groups. Biological motion preference did not vary with age, gender, or concurrent or prospective social communicative skill within the ASD group, although a lack of clear preference for either stimulus was associated with higher social-communicative symptoms at baseline.

LIMITATIONS

The paired visual preference we used may underestimate preference for a stimulus in younger and lower IQ individuals. Our ASD group had a lower average IQ by approximately seven points. 18% of our sample was not analysed for various technical and behavioural reasons.

CONCLUSIONS

Biological motion preference elicits small-to-medium-sized case-control effects, but individual differences do not strongly relate to core social autism associated symptomatology. We interpret this as an autistic difference (as opposed to a deficit) likely manifest in social brain regions. The extent to which this is an innate difference present from birth and central to the autistic phenotype, or the consequence of a life lived with ASD, is unclear.

The architecture of the Gram-positive bacterial cell wall

The primary structural component of the bacterial cell wall is peptidoglycan, which is essential for viability and the synthesis of which is the target for crucial antibiotics1,2. Peptidoglycan is a single macromolecule made of glycan chains crosslinked by peptide side branches that surrounds the cell, acting as a constraint to internal turgor1,3. In Gram-positive bacteria, peptidoglycan is tens of nanometres thick, generally portrayed as a homogeneous structure that provides mechanical strength4-6. Here we applied atomic force microscopy7-12 to interrogate the morphologically distinct Staphylococcus aureus and Bacillus subtilis species, using live cells and purified peptidoglycan. The mature surface of live cells is characterized by a landscape of large (up to 60 nm in diameter), deep (up to 23 nm) pores constituting a disordered gel of peptidoglycan. The inner peptidoglycan surface, consisting of more nascent material, is much denser, with glycan strand spacing typically less than 7 nm. The inner surface architecture is location dependent; the cylinder of B. subtilis has dense circumferential orientation, while in S. aureus and division septa for both species, peptidoglycan is dense but randomly oriented. Revealing the molecular architecture of the cell envelope frames our understanding of its mechanical properties and role as the environmental interface13,14, providing information complementary to traditional structural biology approaches.

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases - due to their repulsion - the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For N interacting bosons, a splitting into an N-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that this splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

Interplay of phosphorus doses, cyanobacterial inoculation, and elevated carbon dioxide on yield and phosphorus dynamics in cowpea

Phosphorus (P) demand is likely to increase especially in legumes to harness greater benefits of nitrogen fixation under elevated CO₂ condition. In the following study, seed yield and seed P uptake in cowpea increased by 26.8% and 20.9%, respectively, under elevated CO₂ level. With an increase in phosphorus dose up to 12 mg kg^-1, seed yield enhanced from 2.6 to 5.4 g plant^-1. P application and cyanobacterial inoculation increased the microbial activity of soil, leading to increased availability of P. Under elevated CO₂ condition, microbial activity, measured as dehydrogenase, acid phosphatase, and alkaline phosphatase activities showed stimulation. Soil available P also increased under elevated CO₂ condition and was stimulated by both P application and cyanobacterial inoculation. Higher P uptake in elevated CO₂ condition led to lower values of inorganic P in soil. Stepwise regression analysis showed that aboveground P uptake, soil available P, and alkaline phosphatase activity of soil influenced the yield while available P, and organic and inorganic P influenced the aboveground P uptake of the crop. This study revealed that under elevated CO₂ condition, P application and cyanobacterial inoculation facilitated P uptake and yield, mediated through enhanced availability of nutrients, in cowpea crop.

Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits

The progress in the field of neural computation hinges on the use of hardware more efficient than the conventional microprocessors. Recent works have shown that mixed-signal integrated memristive circuits, especially their passive (0T1R) variety, may increase the neuromorphic network performance dramatically, leaving far behind their digital counterparts. The major obstacle, however, is immature memristor technology so that only limited functionality has been reported. Here we demonstrate operation of one-hidden layer perceptron classifier entirely in the mixed-signal integrated hardware, comprised of two passive 20 × 20 metal-oxide memristive crossbar arrays, board-integrated with discrete conventional components. The demonstrated network, whose hardware complexity is almost 10× higher as compared to previously reported functional classifier circuits based on passive memristive crossbars, achieves classification fidelity within 3% of that obtained in simulations, when using ex-situ training. The successful demonstration was facilitated by improvements in fabrication technology of memristors, specifically by lowering variations in their I-V characteristics.

Sex differences in frontal lobe connectivity in adults with autism spectrum conditions

Autism spectrum conditions (ASC) are more prevalent in males than females. The biological basis of this difference remains unclear. It has been postulated that one of the primary causes of ASC is a partial disconnection of the frontal lobe from higher-order association areas during development (that is, a frontal 'disconnection syndrome'). Therefore, in the current study we investigated whether frontal connectivity differs between males and females with ASC. We recruited 98 adults with a confirmed high-functioning ASC diagnosis (61 males: aged 18-41 years; 37 females: aged 18-37 years) and 115 neurotypical controls (61 males: aged 18-45 years; 54 females: aged 18-52 years). Current ASC symptoms were evaluated using the Autism Diagnostic Observation Schedule (ADOS). Diffusion tensor imaging was performed and fractional anisotropy (FA) maps were created. Mean FA values were determined for five frontal fiber bundles and two non-frontal fiber tracts. Between-group differences in mean tract FA, as well as sex-by-diagnosis interactions were assessed. Additional analyses including ADOS scores informed us on the influence of current ASC symptom severity on frontal connectivity. We found that males with ASC had higher scores of current symptom severity than females, and had significantly lower mean FA values for all but one tract compared to controls. No differences were found between females with or without ASC. Significant sex-by-diagnosis effects were limited to the frontal tracts. Taking current ASC symptom severity scores into account did not alter the findings, although the observed power for these analyses varied. We suggest these findings of frontal connectivity abnormalities in males with ASC, but not in females with ASC, have the potential to inform us on some of the sex differences reported in the behavioral phenotype of ASC.

A multiply-add engine with monolithically integrated 3D memristor crossbar/CMOS hybrid circuit

Silicon (Si) based complementary metal-oxide semiconductor (CMOS) technology has been the driving force of the information-technology revolution. However, scaling of CMOS technology as per Moore’s law has reached a serious bottleneck. Among the emerging technologies memristive devices can be promising for both memory as well as computing applications. Hybrid CMOS/memristor circuits with CMOL (CMOS + “Molecular”) architecture have been proposed to combine the extremely high density of the memristive devices with the robustness of CMOS technology, leading to terabit-scale memory and extremely efficient computing paradigm. In this work, we demonstrate a hybrid 3D CMOL circuit with 2 layers of memristive crossbars monolithically integrated on a pre-fabricated CMOS substrate. The integrated crossbars can be fully operated through the underlying CMOS circuitry. The memristive devices in both layers exhibit analog switching behavior with controlled tunability and stable multi-level operation. We perform dot-product operations with the 2D and 3D memristive crossbars to demonstrate the applicability of such 3D CMOL hybrid circuits as a multiply-add engine. To the best of our knowledge this is the first demonstration of a functional 3D CMOL hybrid circuit.

Empathy Modulates the Rewarding Effect of Mimicry

We tend to like those who mimic us. In this study we formally test if mimicry changes the reward value of the mimicker, using gaze bias as a proxy for reward. Previous research has demonstrated that people show gaze bias towards more rewarding targets, suggesting that gaze bias can be considered a proxy for relative reward value. Forty adults participated in a conditioning task, where they were mimicked by one face and 'anti-mimicked' by another. Subsequently, they were found to show gaze-bias towards faces that mimicked them compared to those that did not, in a preferential looking task. The strength of this effect correlated positively with individual levels of trait empathy. In a separate, similar task, these participants showed a gaze bias for faces paired with high vs low monetary rewards, thus validating the use of gaze bias as a proxy for learnt reward. Together, these results demonstrate that mimicry changes the reward value of social stimuli, and empathy influences the extent of this change. This can potentially inform conditions marked by deficits in forming social bonds, such as Autism.

Elevated fetal steroidogenic activity in autism

Autism affects males more than females, giving rise to the idea that the influence of steroid hormones on early fetal brain development may be one important early biological risk factor. Utilizing the Danish Historic Birth Cohort and Danish Psychiatric Central Register, we identified all amniotic fluid samples of males born between 1993 and 1999 who later received ICD-10 (International Classification of Diseases, 10th Revision) diagnoses of autism, Asperger syndrome or PDD-NOS (pervasive developmental disorder not otherwise specified) (n=128) compared with matched typically developing controls. Concentration levels of Δ4 sex steroids (progesterone, 17α-hydroxy-progesterone, androstenedione and testosterone) and cortisol were measured with liquid chromatography tandem mass spectrometry. All hormones were positively associated with each other and principal component analysis confirmed that one generalized latent steroidogenic factor was driving much of the variation in the data. The autism group showed elevations across all hormones on this latent generalized steroidogenic factor (Cohen's d=0.37, P=0.0009) and this elevation was uniform across ICD-10 diagnostic label. These results provide the first direct evidence of elevated fetal steroidogenic activity in autism. Such elevations may be important as epigenetic fetal programming mechanisms and may interact with other important pathophysiological factors in autism.

Oxytocin increases eye contact during a real-time, naturalistic social interaction in males with and without autism

Autism spectrum conditions (autism) affect ~1% of the population and are characterized by deficits in social communication. Oxytocin has been widely reported to affect social-communicative function and its neural underpinnings. Here we report the first evidence that intranasal oxytocin administration improves a core problem that individuals with autism have in using eye contact appropriately in real-world social settings. A randomized double-blind, placebo-controlled, within-subjects design is used to examine how intranasal administration of 24 IU of oxytocin affects gaze behavior for 32 adult males with autism and 34 controls in a real-time interaction with a researcher. This interactive paradigm bypasses many of the limitations encountered with conventional static or computer-based stimuli. Eye movements are recorded using eye tracking, providing an objective measurement of looking patterns. The measure is shown to be sensitive to the reduced eye contact commonly reported in autism, with the autism group spending less time looking to the eye region of the face than controls. Oxytocin administration selectively enhanced gaze to the eyes in both the autism and control groups (transformed mean eye-fixation difference per second=0.082; 95% CI:0.025-0.14, P=0.006). Within the autism group, oxytocin has the most effect on fixation duration in individuals with impaired levels of eye contact at baseline (Cohen's d=0.86). These findings demonstrate that the potential benefits of oxytocin in autism extend to a real-time interaction, providing evidence of a therapeutic effect in a key aspect of social communication.

Empathy and emotion recognition in people with autism, first-degree relatives, and controls

Empathy is the lens through which we view others' emotion expressions, and respond to them. In this study, empathy and facial emotion recognition were investigated in adults with autism spectrum conditions (ASC; N=314), parents of a child with ASC (N=297) and IQ-matched controls (N=184). Participants completed a self-report measure of empathy (the Empathy Quotient [EQ]) and a modified version of the Karolinska Directed Emotional Faces Task (KDEF) using an online test interface. Results showed that mean scores on the EQ were significantly lower in fathers (p<0.05) but not mothers (p>0.05) of children with ASC compared to controls, whilst both males and females with ASC obtained significantly lower EQ scores (p<0.001) than controls. On the KDEF, statistical analyses revealed poorer overall performance by adults with ASC (p<0.001) compared to the control group. When the 6 distinct basic emotions were analysed separately, the ASC group showed impaired performance across five out of six expressions (happy, sad, angry, afraid and disgusted). Parents of a child with ASC were not significantly worse than controls at recognising any of the basic emotions, after controlling for age and non-verbal IQ (all p>0.05). Finally, results indicated significant differences between males and females with ASC for emotion recognition performance (p<0.05) but not for self-reported empathy (p>0.05). These findings suggest that self-reported empathy deficits in fathers of autistic probands are part of the 'broader autism phenotype'. This study also reports new findings of sex differences amongst people with ASC in emotion recognition, as well as replicating previous work demonstrating empathy difficulties in adults with ASC. The use of empathy measures as quantitative endophenotypes for ASC is discussed.

Biopolymer hairpin loops sustained by polarons

We show that polarons can sustain looplike configurations in flexible biopolymers and that the size of the loops depend on both the flexural rigidity of the polymer and the electron-phonon coupling constant. In particular we show that for single stranded DNA (ssDNA) and polyacetylene such loops can have as few as seven monomers. We also show that these configurations are very stable under thermal fluctuations and so could facilitate the formation of hairpin loops of ssDNA.

The primary somatosensory cortex largely contributes to the early part of the cortical response elicited by nociceptive stimuli

Research on the cortical sources of nociceptive laser-evoked brain potentials (LEPs) began almost two decades ago (Tarkka and Treede, 1993). Whereas there is a large consensus on the sources of the late part of the LEP waveform (N2 and P2 waves), the relative contribution of the primary somatosensory cortex (S1) to the early part of the LEP waveform (N1 wave) is still debated. To address this issue we recorded LEPs elicited by the stimulation of four limbs in a large population (n=35). Early LEP generators were estimated both at single-subject and group level, using three different approaches: distributed source analysis, dipolar source modeling, and probabilistic independent component analysis (ICA). We show that the scalp distribution of the earliest LEP response to hand stimulation was maximal over the central-parietal electrodes contralateral to the stimulated side, while that of the earliest LEP response to foot stimulation was maximal over the central-parietal midline electrodes. Crucially, all three approaches indicated hand and foot S1 areas as generators of the earliest LEP response. Altogether, these findings indicate that the earliest part of the scalp response elicited by a selective nociceptive stimulus is largely explained by activity in the contralateral S1, with negligible contribution from the secondary somatosensory cortex (S2).

Genes related to sex steroids, neural growth, and social-emotional behavior are associated with autistic traits, empathy, and Asperger syndrome

Genetic studies of autism spectrum conditions (ASC) have mostly focused on the "low functioning" severe clinical subgroup, treating it as a rare disorder. However, ASC is now thought to be relatively common ( approximately 1%), and representing one end of a quasi-normal distribution of autistic traits in the general population. Here we report a study of common genetic variation in candidate genes associated with autistic traits and Asperger syndrome (AS). We tested single nucleotide polymorphisms in 68 candidate genes in three functional groups (sex steroid synthesis/transport, neural connectivity, and social-emotional responsivity) in two experiments. These were (a) an association study of relevant behavioral traits (the Empathy Quotient (EQ), the Autism Spectrum Quotient (AQ)) in a population sample (n=349); and (b) a case-control association study on a sample of people with AS, a "high-functioning" subgroup of ASC (n=174). 27 genes showed a nominally significant association with autistic traits and/or ASC diagnosis. Of these, 19 genes showed nominally significant association with AQ/EQ. In the sex steroid group, this included ESR2 and CYP11B1. In the neural connectivity group, this included HOXA1, NTRK1, and NLGN4X. In the socio-responsivity behavior group, this included MAOB, AVPR1B, and WFS1. Fourteen genes showed nominally significant association with AS. In the sex steroid group, this included CYP17A1 and CYP19A1. In the socio-emotional behavior group, this included OXT. Six genes were nominally associated in both experiments, providing a partial replication. Eleven genes survived family wise error rate (FWER) correction using permutations across both experiments, which is greater than would be expected by chance. CYP11B1 and NTRK1 emerged as significantly associated genes in both experiments, after FWER correction (P<0.05). This is the first candidate-gene association study of AS and of autistic traits. The most promising candidate genes require independent replication and fine mapping.

Non-adenomatous non-epithelial carcinoma (hemangiopericytoma) of prostate treated with conservative surgery followed by adjuvant chemoradiation

Hemangiopericytoma is a malignant vascular tumour of soft tissue. Microscopically, the tumour shows tightly packed cellular areas surrounding thin-walled branching blood vessels. Traditionally these tumours are treated using wide surgical excision. Only a very few cases of hemangiopericytoma of the prostate have been described worldwide. The feasibility of managing such a case with a combination of conservative surgery and adjuvant anti-malignancy treatment is unexplored. Here, we report a case of hemangiopericytoma of the prostate treated with local excision, with preservation of prostate, followed by adjuvant radiotherapy (40 Gy in 20 fractions to pelvis followed by 24 Gy in 12 fractions as boost to prostate) and chemotherapy (doxorubicin and iphosphamide). Post-treatment computed tomography scan after 4 weeks showed regression of pelvic lymph nodes and a normal-appearing prostate. Levels of serum prostate-specific and carcinogenic embryonic antigen were normal throughout the period of treatment. To date, followup has been uneventful, except for occasional bouts of diarrhea.We conclude that conservative surgery followed by adjuvant radiation and chemotherapy, with subsequent close follow-up, may adequately control localized disease in selected cases of hemangiopericytoma of the prostate. The role of conservative surgery in tumours located at other sites has yet to be defined.

Hyperglycaemia as a predictor of outcome during non-invasive ventilation in decompensated COPD

RATIONALE

Hyperglycaemia predicts a poor outcome in Intensive Care Unit (ICU) patients. Whether this is true for respiratory failure necessitating non-invasive ventilation (NIV) is not known.

OBJECTIVES

To determine whether hyperglycaemia within 24 h of admission independently predicts outcome of NIV during acute decompensated ventilatory failure complicating chronic obstructive pulmonary disease (COPD) exacerbations.

METHODS

Patients with COPD presenting with acute hypercapnic respiratory failure at University Hospital Aintree between June 2006 and September 2007 and receiving NIV within 24 h of admission were studied prospectively. Random blood glucose levels were measured before NIV administration.

RESULTS

88 patients (mean baseline pH 7.25, PaCO(2) 10.20 kPa, and PaO(2) 8.19 kPa) met the inclusion criteria, with NIV normalising arterial pH off therapy in 79 (90%). After multivariate logistic regression, the following predicted outcome: baseline respiratory rate (OR 0.91; 95% CI 0.84 to 0.99), random glucose > or = 7 mmol/l (OR 0.07; 95% CI 0.007 to 0.63) and admission APACHE II (Acute Physiology and Chronic Health Evaluation II) score (OR 0.75; 95% CI 0.62 to 0.90). The combination of baseline respiratory rate (RR) <30 breaths/min and random glucose <7 mmol/l increased prediction of NIV success to 97%, whilst use of all three factors was 100% predictive.

CONCLUSIONS

In acute decompensated ventilatory failure complicating COPD, hyperglycaemia upon presentation was associated with a poor outcome. Baseline RR and hyperglycaemia are as good at predicting clinical outcomes as the APACHE II score. Combining these variables increases predictive accuracy, providing a simple method of early risk stratification.

Paradoxical movement of the lower ribcage at rest and during exercise in COPD patients

Paradoxical inward displacement of the costal margin during inspiration is observed in many chronic obstructive pulmonary disease patients at rest but its importance is unclear. The current authors studied 20 patients (forced expiratory volume in one second 32.6+/-11.7, functional residual capacity 186+/-32% predicted) and 10 healthy controls at rest and during symptom-limited incremental exercise. With optoelectronic plethysmography, the phase shift between pulmonary and abdominal ribcage volumes and the percentage of inspiratory time the ribcage compartments moved in opposite directions were quantified, using control data to define the normal range of movement. Eight patients showed lower ribcage inspiratory paradox at rest (P+), while 12 patients did not (P-). This was unrelated to resting lung function or exercise tolerance. Total end-expiratory chest wall volume (EEV(cw)) increased immediately when exercise began in P+ patients, but later in exercise in P- patients. This difference in EEV(cw) was mainly due to a greater increase of end-expiratory pulmonary ribcage volume in P+ patients. During exercise, dyspnoea increased similarly in the two groups, while leg effort increased more markedly in the patients without paradox. In conclusion, lower ribcage paradox at rest is reproducible and associated with early-onset hyperinflation of the chest wall and predominant dyspnoea at end-exercise. When paradox is absent, the sense of leg effort becomes a more important symptom limiting exercise.

Management of acute ventilatory failure

Acute ventilatory failure is a challenging yet increasingly common medical emergency reflecting the growing burden of respiratory disease. It is not a diagnosis in itself but the end result of a diversity of disease processes culminating in arterial hypoxaemia and hypercapnia. This review focuses on key management issues including giving appropriate oxygen therapy, treatment of the underlying aetiology as well as any precipitant factors and provision of assisted ventilation if required. Ventilatory assistance can be provided both invasively and non-invasively and the indications for either or both forms of assisted ventilation are discussed. Further emphasis is needed regarding advanced directives of care and clinicians should be aware of ethical issues regarding assisted ventilation.

Pleural tuberculosis

Pleural effusions in tuberculosis are commonly seen in young adults as an immunological phenomenon occurring soon after primary infection. However, the epidemiology and demographics of tuberculous pleurisy are changing due to the impact of HIV co-infection and the increasing number of pleural effusions seen as part of re-activation disease. Pleural biopsy for histology and culture is the mainstay of diagnosis with closed needle biopsy adequate in the majority of cases. Techniques such as PCR of biopsy specimens and the role of pleural fluid ADA are still being evaluated as a diagnostic aid. Tuberculous empyema is less commonly seen in the western world and the diagnostic yield from pleural fluid here is greater than in "primary" effusions. Treatment with appropriate antituberculous chemotherapy is generally successful though there is currently insufficient evidence to recommend the routine use of corticosteroids in this condition.

Radio-iodine (NaI131) therapy in hyperthyroidism

Iodine131 is well recognised as an ideal isotope for treatment of hyperthyroidism. NaI131 therapy is considered as the simplest, safest, least expensive and most effective form of therapy for most patients. This form of therapy can be applied to all categories of patients except in pregnant and nursing mothers who are not willing to forgo breastfeeding. In contrary to the common belief, this form of therapy can also be used in children and adolescents. One common complication is hypothyroidism which can be easily treated but life long follow-up is essential which is, however, necessary in other modalities of treatment also. NaI131 therapy in hyperthyroidism can be instituted on outpatient basis. This form of therapy is available in several centres of Calcutta.

Calculation of the first excited (1)S(e) state of the He atom using supersymmetric quantum mechanics and extension to the nth excitation

Usually the renormalized Numerov (RN) algorithm is used to solve the set of coupled differential equations of the few-body system, mainly for the ground state. The straightforward approach of this algorithm faces some serious problems of convergence to calculate the excited states. Here we present an alternative method using the supersymmetric quantum mechanics formalism to a multidimensional bound-state problem. The problem of convergence is avoided in this approach by searching for the ground state of the partner potential. Application of this formalism to the first excited (1)S(e) state of the He atom gives excellent results; it is much better than the conventional RN algorithm and the hyperspherical adiabatic approximation. We also indicate how the method can be generalized to the nth excited state.