To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Gravitational lenses typically consist of either two or four images (doubles and quads) of the background source. However, it has been shown that gravitational lensing by transparent extended matter distributions should produce an odd number of images. An upper limit for the flux of the missing ‘odd image’ can be obtained using high sensitivity radio observations, such as 5GHz MERLIN (Multi-Element Radio Linked Interferometer Network) data. Limits on the ‘odd image’ flux can then be converted into an upper limit on the core radius of the lensing galaxy.
Patients with depression show abnormalities in the neural circuitry supporting working memory. However, it is unclear if these abnormalities are present in unmedicated remitted depressed patients. To address this question, the current study employed functional magnetic resonance imaging (fMRI), in combination with a simple verbal n-back task, in a cohort of unmedicated remitted depressed patients.
We studied 15 healthy control subjects (HC) and 15 unmedicated remitted depressed patients (rMDD). Participants performed a verbal working memory task of varying cognitive load (n-back) while undergoing fMRI. We used multiple regression analyses to assess overall capacity (1-, 2-, 3-back versus 0-back) as well as quadratic modulation of cognitive demand.
Performance accuracy and response latency did not differ between groups, and overall capacity was similar. However, rMDD showed a positive quadratic load response in the bilateral hippocampus; the converse was true for HC.
Our data suggest that remitted depression was associated with a perturbed pattern of activation in the bilateral hippocampus during a verbal working memory task. We propose that a reduced ability to dampen task-irrelevant activity may reflect a neurobiological risk factor for recurrent depression.
Short-term antidepressant administration has been reported to decrease amygdala response to threat in healthy volunteers and depressed patients. Neuroticism (N) is a risk factor for depression but has also been associated with slow or incomplete remission with antidepressant drug treatment. Our aim was to investigate early selective serotonin reuptake inhibitor (SSRI) administration neural effects on implicit processing of fearful facial expressions in volunteers with high levels of N.
Highly neurotic subjects received 20 mg/day citalopram versus placebo for 7 days in a double-blind, between-groups design. On the last day haemoperfusion and functional magnetic resonance imaging (fMRI) data during a gender discrimination task with fearful and happy faces were acquired. A control group of non-neurotic volunteers was also tested.
High-N volunteers had reduced responses to threatening facial expressions across key neural circuits compared to low-N volunteers. SSRI treatment was found to elevate resting perfusion in the right amygdala, increase bilateral amygdalae activation to positive and negative facial expressions and increase activation to fearful versus happy facial expressions in occipital, parietal, temporal and prefrontal cortical areas.
These results suggest that 7 days of SSRI administration can increase neural markers of fear reactivity in subjects at the high end of the N dimension and may be related to early increases in anxiety and agitation seen early in treatment. Such processes may be involved in the later therapeutic effects through decreased avoidance and increased learning about social ‘threat’ cues.
Antidepressant drugs such as selective serotonin re-uptake inhibitors (SSRIs) remediate negative biases in emotional processing in depressed patients in both behavioural and neural outcome measures. However, it is not clear if these effects occur before, or as a consequence of, changes in clinical state.
In the present study, we investigated the effects of short-term SSRI treatment in depressed patients on the neural response to fearful faces prior to clinical improvement in mood. Altogether, 42 unmedicated depressed patients received SSRI treatment (10 mg escitalopram daily) or placebo in a randomised, parallel-group design. The neural response to fearful and happy faces was measured on day 7 of treatment using functional magnetic resonance imaging. A group of healthy controls was imaged in the same way.
Amygdala responses to fearful facial expressions were significantly greater in depressed patients compared to healthy controls. However, this response was normalised in patients receiving 7 days treatment with escitalopram. There was no significant difference in clinical depression ratings at 7 days between the escitalopram and placebo-treated patients.
Our results suggest that short-term SSRI treatment in depressed patients remediates amygdala hyperactivity in response to negative emotional stimuli prior to clinical improvement in depressed mood. This supports the hypothesis that the clinical effects of antidepressant treatment may be mediated in part through early changes in emotional processing. Further studies will be needed to show if these early effects of antidepressant medication predict eventual clinical outcome.
We present a generalisation of the continuous Gronwall inequality and show its use in bounding solutions of discrete inequalities of a form that arise when analysing the convergence of product integration methods for Volterra integral equations. We then use these ideas to prove convergence of a numerical method which is effective in approximating Volterra integral equations of the second kind with weakly singular kernels.
We consider nonlinear singular Volterra integral equations of the second kind. We generalise the transformation method introduced in Part I of this paper  to cope with both the nonlinearity and slightly more general singular kernels. We also consider a particular class of nonlinear equation for which the solution behaviour is known. Using this a priori knowledge, we propose a modification of the transformation technique which results in a numerical method with good asymptotic stability properties. Applying the general theory of Part I of this paper, we prove convergence of this scheme.
Processing emotional facial expressions is of interest in eating disorders (EDs) as impairments in recognizing and understanding social cues might underlie the interpersonal difficulties experienced by these patients. Disgust and anger are of particular theoretical and clinical interest. The current study investigated the neural response to facial expressions of anger and disgust in bulimia nervosa (BN).
Participants were 12 medication-free women with BN in an acute episode (mean age 24 years), and 16 age-, gender- and IQ-matched healthy volunteers (HVs). Functional magnetic resonance imaging (fMRI) was used to examine neural responses to angry and disgusted facial expressions.
Compared with HVs, patients with BN had a decreased neural response in the precuneus to facial expressions of both anger and disgust and a decreased neural response to angry facial expressions in the right amygdala.
The neural response to emotional facial expressions in BN differs from that found in HVs. The precuneus response may be consistent with the application of mentalization theory to EDs, and the amygdala response with relevant ED theory. The findings are preliminary, but novel, and require replication in a larger sample.
Previous imaging studies have revealed that acute major depression is characterized by altered neural responses to negative emotional stimuli. Typically, responses in limbic regions such as the amygdala are increased while activity in cortical regulatory regions such as the dorsolateral prefrontal cortex (DLPFC) is diminished. Whether these changes persist in unmedicated recovered patients is unclear.
We used functional magnetic resonance imaging to examine neural responses to emotional faces in a facial expression-matching task in 16 unmedicated recovered depressed patients and 21 healthy controls.
Compared with controls, recovered depressed patients had increased responses bilaterally to fearful faces in the DLPFC and right caudate. Responses in the amygdala did not distinguish the groups.
Our findings indicate that clinical recovery from depression is associated with increased activity in the DLPFC to negative emotional stimuli. We suggest that this increase may reflect a compensatory cortical control mechanism with the effect of limiting emotional dysregulation in limbic regions such as the amygdala.
Selective serotonin reuptake inhibitors (SSRIs) are typically thought to
have a delay of several weeks in the onset of their clinical effects.
However, recent reports suggest they may have a much earlier therapeutic
onset. A reduction in amygdala responsivity has been implicated in the
therapeutic action of SSRIs.
To investigate the effect of a single dose of an SSRI on the amygdala
response to emotional faces.
Twenty-six healthy volunteers were randomised to receive a single oral
dose of citalopram (20 mg) or placebo. Effects on the processing of
facial expressions were assessed 3 h later using functional magnetic
Volunteers treated with citalopram displayed a significantly reduced
amygdala response to fearful facial expressions compared with
Such an immediate effect of an SSRI on amygdala responses to threat
supports the idea that antidepressants have an earlier onset of
therapeutically relevant effects than conventionally thought.
Depression is associated with neural abnormalities in emotional processing.
This study explored whether these abnormalities underlie risk for depression.
We compared the neural responses of volunteers who were at high and low-risk for the development of depression (by virtue of high and low neuroticism scores; high-N group and low-N group respectively) during the presentation of fearful and happy faces using functional magnetic resonance imaging (fMRI).
The high-N group demonstrated linear increases in response in the right fusiform gyrus and left middle temporal gyrus to expressions of increasing fear, whereas the low-N group demonstrated the opposite effect. The high-N group also displayed greater responses in the right amygdala, cerebellum, left middle frontal and bilateral parietal gyri to medium levels of fearful v. happy expressions.
Risk for depression is associated with enhanced neural responses to fearful facial expressions similar to those observed in acute depression.
Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst–Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current–voltage (I–V) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I–V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).
We previously found that children of parents with depression showed
impaired performance on a task of emotional categorisation.
To test the hypothesis that children of parents with depression would
show abnormal neural responses in the anterior cingulate cortex, a brain
region involved in the integration of emotional and cognitive
Eighteen young people (mean age 19.8 years) with no personal history of
depression but with a biological parent with a history of major
depression (FH+ participants) and 16 controls (mean age 19.9
years) underwent functional magnetic resonance imaging while completing
an emotional counting Stroop task.
Controls showed significant activation in the pregenual anterior
cingulate cortex to both positive and negative words during the emotional
Stroop task. This activation was absent in FH+
Our findings show that people at increased familial risk of depression
demonstrate impaired modulation of the anterior cingulate cortex in
response to emotionally valenced stimuli.
We used functional magnetic resonance imaging to investigate the effects of short-term treatment with reboxetine, a selective noradrenaline reuptake inhibitor, on emotional facial processing in healthy volunteers. Reboxetine was associated with a reduced amygdala response to fearful faces and increased activation to happy v. neutral facial expressions in the right fusiform gyrus, relative to placebo treatment and in the absence of changes in mood. Our results show that reboxetine modulates the neural substrates of emotional processing, highlighting a mechanism by which drug treatment could normalise negative bias in depression and anxiety.
We consider the following system of equations:
where the spatial average ⟨ B ⟩ = 0 and μ > σ > 0. This system plays an important role as a Ginzburg-Landau equation with a mean field in several areas of the applied sciences and the steady-states of this system extend to periodic steady-states with period L on the real line which are observed in experiments. Our approach is by combining methods of nonlinear functional analysis such as nonlocal eigenvalue problems and the variational characterization of eigenvalues with Jacobi elliptic integrals. This enables us to give a complete classification of all stable steady-states for any positive L.
Because of the importance and excitement of recent developments in research on large scale atmosphere-ocean dynamics, in 1996 an intense programme was held at the Isaac Newton Institute in Cambridge bringing together about 300 scientists from a wide range of specialisms. The articles in these two volumes consist of reviews, up to date research findings, and challenging statements about problems for future research. These are based on presentations made during the programme and more recent developments in the research, resulting from the vigorous and continuing interactions between many of the participants.
Numerical weather prediction and ocean modelling are successful applications of mathematical physics and numerical analysis. Their scientific methodology is essentially reductionist, because it involves reducing the calculations of a complex environmental process into constituent parts, each of which can be understood scientifically and modelled (Hunt 1999). This involves combining quantitative representation at every point in space and time of physical processes, governing phase changes, radiation and molecular diffusion, with the mathematical modelling of fluid mechanics on a wide range of scales from thousands of kilometres to centimetres. In order that the predictions cover all the aspects of practical importance, as well as increasing their accuracy year on year, regular improvements are needed in the models of key processes and mechanisms; some are well understood such as phase changes and low amplitude waves, but others such as radiation and turbulence can only be approximately parameterised or modelled, using the latest research as it develops.
The aim of this chapter is to introduce a probabilistic approach to defining balance for geophysical flows. Geophysical flows are split into fast and slow components where the slow component describes some ‘average’ or ‘macroscopic’ large scale evolution, whereas the fast component describes the more rapid fluctuations of particle positions on a ‘microscopic’ fine or very local scale. We will treat the fast variables as random variables and, in the spirit of statistical physics, we will identify fluid microstates as measure-preserving maps, and fluid macrostates as probability distributions on the set of microstates. A balanced flow will then be characterised by a particular macrostate (i.e. probability distribution), which is, in a sense to be defined later, the most likely for the observed macroscopic properties of the fluid. We will characterise semigeostrophic flow as the most likely evolution of minimum energy states consistent with the large-scale constraints of the system.
Like many other physical systems, the atmosphere has both fast and slow dynamics. The slow dynamics describe the macroscopic or averaged evolution of the air ‘parcels’ (say approximately 10 km by 10 km in the horizontal, by 100m in the vertical, or more), whereas the fast dynamics describes the microscopic or fine scale rapid movement of air ‘particles’ (of sizes about 10–100 m3) that are 108–109 × smaller. To the synoptic large scale modeller these fast microscale motions are mostly irrelevant and a nuisance. First, these (often unstable) motions do not usually provide information relevant to the largescale model; secondly they are often associated with unwanted phenomena, such as gravity waves; and thirdly they often lead to instabilities that plague numerical calculations.
In the paper King , a new class of source solutions was derived for the nonlinear diffusion equation for diffusivities of the form D(c) = D0cm/(l - vc)m+2. Here we extend this method for the nonlinear diffusion and convection equation
to obtain mass-conserving source solutions for a nonlinear conductivity function K(c) = K0cm+2/(l - vc)m+1. In particular we consider the cases m = -1,0, and 1, where fully analytical solutions are available. Furthermore we provide source solutions for the exponential forms of the diffusivity and conductivity as given by D(c) = D0c−2e−n/c and K(c) = K0ce−n/c.