A note on the Zassenhaus product formula

We provide a simple method for the calculation of the terms c_n in the Zassenhaus product $e^{a+b}=e^a e^b \prod_{n=2}^{\infty} e^{c_n}$ for non-commuting a and b. This method has been implemented in a computer program. Furthermore, we formulate a conjecture on how to translate these results into nested commutators. This conjecture was checked up to order n=17 using a computer

Measuring nonlinear signal combination using EEG

Relatively little is known about the processes, both linear and nonlinear, by which signals are combined beyond V1. By presenting two stimulus components simultaneously, flickering at different temporal frequencies (frequency tagging) while measuring steady-state visual evoked potentials, we can assess responses to the individual components, including direct measurements of suppression on each other, and various nonlinear responses to their combination found at intermodulation frequencies. The result is a rather rich dataset of frequencies at which responses can be found. We presented pairs of sinusoidal gratings at different temporal frequencies, forming plaid patterns that were "coherent" (looking like a checkerboard) and "noncoherent" (looking like a pair of transparently overlaid gratings), and found clear intermodulation responses to compound stimuli, indicating nonlinear summation. This might have been attributed to cross-orientation suppression except that the pattern of intermodulation responses differed for coherent and noncoherent patterns, whereas the effects of suppression (measured at the component frequencies) did not. A two-stage model of nonlinear summation involving conjunction detection with a logical AND gate described the data well, capturing the difference between coherent and noncoherent plaids over a wide array of possible response frequencies. Multistimulus frequency-tagged EEG in combination with computational modeling may be a very valuable tool in studying the conjunction of these signals. In the current study the results suggest a second-order mechanism responding selectively to coherent plaid patterns

Steady-State Contrast Response Functions Provide a Sensitive and Objective Index of Amblyopic Deficits

Purpose. Visual deficits in amblyopia are neural in origin, yet are difficult to characterize with functional magnetic resonance imagery (fMRI). Our aim was to develop an objective electroencephalography (EEG) paradigm that can be used to provide a clinically useful index of amblyopic deficits. Methods. We used steady-state visual evoked potentials (SSVEPs) to measure full contrast response functions in both amblyopic (n = 10, strabismic or mixed amblyopia, mean age: 44 years) and control (n = 5, mean age: 31 years) observers, both with and without a dichoptic mask. Results. At the highest target contrast, the ratio of amplitudes across the weaker and stronger eyes was highly correlated (r = 0.76) with the acuity ratio between the eyes. We also found that the contrast response function in the amblyopic eye had both a greatly reduced amplitude and a shallower slope, but that surprisingly dichoptic masking was weaker than in controls. The results were compared with the predictions of a computational model of amblyopia and suggest a modification to the model whereby excitatory (but not suppressive) signals are attenuated in the amblyopic eye. Conclusions. We suggest that SSVEPs offer a sensitive and objective measure of the ocular imbalance in amblyopia and could be used to assess the efficacy of amblyopia therapies currently under development

Dietary modulation of cortical excitation and inhibition

The balance of excitatory and inhibitory neurotransmitters in the brain affects both neural responses and behaviour in humans and animals. Here we investigated whether dietary intervention aimed at increasing levels of the inhibitory neurotransmitter GABA can influence neural responses to basic sensory stimuli. Using a steady-state EEG paradigm, we found that the neural response to visual patterns was reduced in individuals who consumed a yeast-extract product rich in substances associated with the production of GABA (glutamate and B vitamins), but not in a control group who consumed a placebo substance (N=14 per group). This demonstrates that the balance of excitation and inhibition in the brain can be influenced by dietary interventions, suggesting possible clinical benefits in conditions (e.g. epilepsy) where inhibition is abnormal

Virtual target screening to rapidly identify potential protein targets of natural products in drug discovery

Inherent biological viability and diversity of natural products make them a potentially rich source for new therapeutics. However, identification of bioactive compounds with desired therapeutic effects and identification of their protein targets is a laborious, expensive process. Extracts from organism samples may show desired activity in phenotypic assays but specific bioactive compounds must be isolated through further separation methods and protein targets must be identified by more specific phenotypic and in vitro experimental assays. Still, questions remain as to whether all relevant protein targets for a compound have been identified. The desire is to understand breadth of purposing for the compound to maximize its use and intellectual property, and to avoid further development of compounds with insurmountable adverse effects. Previously we developed a Virtual Target Screening system that computationally screens one or more compounds against a collection of virtual protein structures. By scoring each compound-protein interaction, we can compare against averaged scores of synthetic drug-like compounds to determine if a particular protein would be a potential target of a compound of interest. Here we provide examples of natural products screened through our system as we assess advantages and shortcomings of our current system in regards to natural product drug discovery

Time Course of Dichoptic Masking in Normals and Suppression in Amblyopes

Purpose: To better understand the relationship between dichoptic masking in normal vision and suppression in amblyopia we address three questions: First, what is the time course of dichoptic masking in normals and amblyopes? Second, is interocular suppression low-pass or band-pass in its spatial dependence? And third, in the above two regards, is dichoptic masking in normals different from amblyopic suppression? Methods: We measured the dependence of dichoptic masking in normal controls and amblyopes on the temporal duration of presentation under three conditions; monocular (the nontested eye—i.e., dominant eye of normals or nonamblyopic eye of amblyopes, being patched), dichoptic-luminance (the nontested eye seeing a mean luminance—i.e., a DC component) and dichoptic-contrast (the nontested eye seeing high-contrast visual noise). The subject had to detect a letter in the other eye, the contrast of which was varied. Results: We found that threshold elevation relative to the patched condition occurred in both normals and amblyopes when the nontested eye saw either 1/f or band-pass filtered noise, but not just mean luminance (i.e., there was no masking from the DC component that corresponds to a channel responsive to a spatial frequency of 0 cyc/deg); longer presentation of the target (corresponding to lower temporal frequencies) produced greater threshold elevation. Conclusions: Dichoptic masking exhibits similar properties in both subject groups, being low-pass temporally and band-pass spatially, so that masking was greatest at the longest presentation durations and was not greatly affected by mean luminance in the nontested eye

Revision rates after primary hip and knee replacement in England between 2003 and 2006

<b>Background</b>: Hip and knee replacement are some of the most frequently performed surgical procedures in the world. Resurfacing of the hip and unicondylar knee replacement are increasingly being used. There is relatively little evidence on their performance. To study performance of joint replacement in England, we investigated revision rates in the first 3 y after hip or knee replacement according to prosthesis type. <b>Methods and Findings</b>: We linked records of the National Joint Registry for England and Wales and the Hospital Episode Statistics for patients with a primary hip or knee replacement in the National Health Service in England between April 2003 and September 2006. Hospital Episode Statistics records of succeeding admissions were used to identify revisions for any reason. 76,576 patients with a primary hip replacement and 80,697 with a primary knee replacement were included (51% of all primary hip and knee replacements done in the English National Health Service). In hip patients, 3-y revision rates were 0.9% (95% confidence interval [CI] 0.8%–1.1%) with cemented, 2.0% (1.7%–2.3%) with cementless, 1.5% (1.1%–2.0% CI) with “hybrid” prostheses, and 2.6% (2.1%–3.1%) with hip resurfacing (p < 0.0001). Revision rates after hip resurfacing were increased especially in women. In knee patients, 3-y revision rates were 1.4% (1.2%–1.5% CI) with cemented, 1.5% (1.1%–2.1% CI) with cementless, and 2.8% (1.8%–4.5% CI) with unicondylar prostheses (p < 0.0001). Revision rates after knee replacement strongly decreased with age. <b>Interpretation</b>: Overall, about one in 75 patients needed a revision of their prosthesis within 3 y. On the basis of our data, consideration should be given to using hip resurfacing only in male patients and unicondylar knee replacement only in elderly patients

MESSENGER: Exploring Mercury's Magnetosphere

The MESSENGER mission to Mercury offers our first opportunity to explore this planet s miniature magnetosphere since the brief flybys of Mariner 10. Mercury s magnetosphere is unique in many respects. The magnetosphere of Mercury is among the smallest in the solar system; its magnetic field typically stands off the solar wind only - 1000 to 2000 km above the surface. For this reason there are no closed drift paths for energetic particles and, hence, no radiation belts. The characteristic time scales for wave propagation and convective transport are short and kinetic and fluid modes may be coupled. Magnetic reconnection at the dayside magnetopause may erode the subsolar magnetosphere allowing solar wind ions to impact directly the regolith. Inductive currents in Mercury s interior may act to modify the solar wind interaction by resisting changes due to solar wind pressure variations. Indeed, observations of these induction effects may be an important source of information on the state of Mercury s interior. In addition, Mercury s magnetosphere is the only one with its defining magnetic flux tubes rooted in a planetary regolith as opposed to an atmosphere with a conductive ionospheric layer. This lack of an ionosphere is probably the underlying reason for the brevity of the very intense, but short-lived, - 1-2 min, substorm-like energetic particle events observed by Mariner 10 during its first traversal of Mercury s magnetic tail. Because of Mercury s proximity to the sun, 0.3 - 0.5 AU, this magnetosphere experiences the most extreme driving forces in the solar system. All of these factors are expected to produce complicated interactions involving the exchange and re-cycling of neutrals and ions between the solar wind, magnetosphere, and regolith. The electrodynamics of Mercury s magnetosphere are expected to be equally complex, with strong forcing by the solar wind, magnetic reconnection at the magnetopause and in the tail, and the pick-up of planetary ions all driving field-aligned electric currents. However, these field-aligned currents do not close in an ionosphere, but in some other manner. In addition to the insights- into magnetospheric physics offered by study of the solar wind - Mercury system, quantitative specification of the "external" magnetic field generated by magnetospheric currents is necessary for accurate determination of the strength and multi-polar decomposition of Mercury s intrinsic magnetic field. MESSENGER S highly capable instrumentation and broad orbital coverage will greatly advance our understanding of both the origin of Mercury s magnetic field and the acceleration of charged particles in small magnetospheres. In. this article, we review what is known about Mercury s magnetosphere and describe the MESSENGER science team s strategy for obtaining answers to the outstanding science questions surrounding the interaction of the solar wind with Mercury and its small, but dynamic, magnetosphere