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A problem which occurs frequently is that of choosing a suitable shape for a duct, such as a wind tunnel contraction or an air intake. Basically similar problems, involving potential flow fields, occur in other branches of engineering, particularly in electrical engineering, and the electrolytic tank is now established as a tool which may usefully be employed in their investigation. The use of the simple shallow tank is limited to those fields which can be treated as two-dimensional or axisymmetric, but many problems fall within these categories.
In forming a duct model for the electrolytic tank the walls of the duct are represented by insulating surfaces, and electrodes are positioned to represent two suitable velocity potential surfaces up- and down-stream of the duct. To represent a sector of an axi-symmetric duct the base of the tank must be inclined at 3°-5° to the horizontal and the water line on the tank base then represents the axis of symmetry.
In a recent technical note Rajaratnam has pointed out the possibility of using the pressure difference measured between two static pressure holes of different diameter as a means of determining skin friction. The device exploits the fact that for any hole there is an error in measurement of static pressure which depends both on the hole diameter and on local skin friction, as Shaw has demonstrated. Consequently the difference in pressure measured between two adjacent holes of different diameter will be a function of the skin friction. In this note the device will be called a “static hole pair”. The larger hole will be referred to as the “test” hole, and the smaller hole as the “reference” hole.
A technique has been devised for measuring the concentration of “Polyox” in dilute aqueous solutions. “Poly-ox”* is one of those polymers whose addition to water in low concentrations causes a reduction in skin friction (if the Reynolds number is sufficiently high) in turbulent flow through a pipe or boundary layer. (See, for example, ref. 1.) The analytical method is probably applicable to other polymers having this property, and it should be generally useful in this field of research. For example, in any experiment in which a polymer solution is injected at a point in a boundary layer, the method could be used to determine the distribution of polymer concentration at downstream sections. It is based on polarography, a well-established tool of chemical analysis of which an excellent account is given in ref. 2.
Accurate representation of a model field in an electrolytic tank requires, among other things, that the electrical conductivity of the liquid should be everywhere constant. Einstein and Sander and Yates have discussed the importance of other possible inaccuracies, and have shown that by correct probe design, circuit design and choice of electrode materials, these may be made very small. This note describes very briefly some experiments, carried out in two shallow electrolytic tanks, which demonstrate that the principal error can be that introduced by variations of conductivity produced by non-uniformity of temperature distribution in the electrolyte. The point is of particular importance since the results also showed that the mechanical design of the tank can have a vital bearing on the achievement of uniform temperature.
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.
Method
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.
Results
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.
Conclusions
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.
Method
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.
Results
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.
Conclusions
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.
Method
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.
Results
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.
Conclusions
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.
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).
Method
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.
Results
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.
Conclusions
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.
Method
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.
Results
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.
Conclusions
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.
Aims
To investigate the effect of a single dose of an SSRI on the amygdala response to emotional faces.
Method
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 resonance imaging.
Results
Volunteers treated with citalopram displayed a significantly reduced amygdala response to fearful facial expressions compared with placebo.
Conclusions
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.
The asymptotic properties of solutions of the non-linear eigenvalue problem, associated with the homogeneoud Dirichlet problem for
are investigated. Here f and g are smooth functions of position in a finite plane region with a smooth boundary. The results for the positive solution are well established, but knowledge of other branches of solutions is scarce. Here positive solutions are pieced together across lines partitioning the domain, and variational arguments are framed, as an effective means of locating the lines, so that the composite function is everywhere a solution of *. Heuristic arguments suggest strongly that there is a close relationship between the nodal lines of * and certain classes of weighted geodesic lines defined by the classical variational problem for the functional
which provides an effective basis for computation. Some results are proved but others remain conjectures. Analogous results are proved for the associated ordinary differential equation. The geometry of the solutions is surprisingly restricted when the coefficients are spatially variable. The arguments are extended to a class of reactive, diffusive systems. It is possible to predict the pattern of domains of different outcomes in terms of properties of the surface on which the reactions occur, without a knowledge of the chemical kinetics. The results appear to provide a basis for stringent testing of the postulated role of reactive-diffusive mechanisms in the formation of complex patterns in biological species.
In the paper King [8], 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.
Depression is associated with neural abnormalities in emotional processing.
Aims
This study explored whether these abnormalities underlie risk for depression.
Method
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).
Results
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.
Conclusions
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.
Aims
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 information.
Method
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.
Results
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+ participants.
Conclusions
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.
A canonical Hamiltonian structure for the semi-geostrophic equations is presented and from this a reduced non-canonical Hamiltonian structure is derived, providing a fully nonlinear version of the approximate linearized vorticity advection representation. The structure of this model is described naturally within the framework of contact geometry. A Hamiltonian approach leading to a symplectic algorithm for calculating solutions to the equations of motion is formulated. Basic necessary functional methods are introduced and the Lagrangian and Eulerian kinematic structures are discussed, together with their relevance to symplectic integrating algorithms.