Comments on 1/16 BPS Quantum States and Classical Configurations

We formulate the problem of counting 1/16 BPS states of N = 4 Yang Mills theory as the enumeration of the local cohomology of an operator acting on holomorphic fields on C^2. We study aspects of the enumeration of this cohomology at finite N, especially for operators constructed only out of products of covariant derivatives of scalar fields, and compare our results to the states obtained from the quantization of giant gravitons and dual giants. We physically interpret the holomorphic fields that enter our conditions for supersymmetry semi-classically by deriving a set of Bogomolnyi equations for 1/16-BPS bosonic field configurations in N = 4 Yang Mills theory on R^4 with reality properties and boundary conditions appropriate to radial quantization. An arbitrary solution to these equations in the free theory is parameterized by holomorphic data on C^2 and lifts to a nearby solution of the interacting Bogomolnyi equations only when the constraints equivalent to Q cohomology are obeyed.Comment: 61 page

Impact of neuroanatomical variations and electrode orientation on stimulus current in a device for migraine: a computational study

Objective. Conventional treatment methods for migraine often have side effects. One treatment involves a wearable neuromodulator targeting frontal nerves. Studies based on this technique have shown limited efficacy and the existing setting can cause pain. These may be associated with neuroanatomical variations which lead to high levels of required stimulus current. The aim of this paper is to study the effect of such variations on the activation currents of the Cefaly neuromodulator. Also, using a different electrode orientation, the possibility of reducing activation current levels to avoid painful side-effects and improve efficacy, is explored. Approach. This paper investigates the effect of neuroanatomical variations and electrode orientation on the stimulus current thresholds using a computational hybrid model involving a volume conductor and an advanced nerve model. Ten human head models are developed considering statistical variations of key neuroanatomical features, to model a representative population. Main results. By simulating the required stimulus current level in the head models, it is shown that neuroanatomical variations have a significant impact on the outcome, which is not solely a function of one specific neuroanatomical feature. The stimulus current thresholds based on the conventional Cefaly system vary from 4.4 mA to 25.1 mA across all head models. By altering the electrode orientation to align with the nerve branches, the stimulus current thresholds are substantially reduced to between 0.28 mA and 15 mA, reducing current density near pain-sensitive structures which may lead to a higher level of patient acceptance, further improving the efficacy. Significance. Computational modeling based on statistically valid neuroanatomical parameters, covering a representative adult population, offers a powerful tool for quantitative comparison of the effect of the position of stimulating electrodes which is otherwise not possible in clinical studies

Dictionary selection for Compressed Sensing of EEG signals using sparse binary matrix and spatiotemporal sparse Bayesian learning

Online monitoring of electroencephalogram (EEG) signals is challenging due to the high volume of data and power requirements. Compressed sensing (CS) may be employed to address these issues. Compressed sensing using sparse binary matrix, owing to its low power features, and reconstruction/decompression using spatiotemporal sparse Bayesian learning have been shown to constitute a robust framework for fast, energy efficient and accurate multichannel bio-signal monitoring. EEG signal, however, does not show a strong temporal correlation. Therefore, the use of sparsifying dictionaries has been proposed to exploit the sparsity in a transformed domain instead. Assuming sparsification adds values, a challenge, therefore, in employing this CS framework for the EEG signal is to identify the suitable dictionary. Using real multichannel EEG data from 15 subjects, in this paper, we systematically evaluated the performance of the framework when using various wavelet bases while considering their key attributes of number of vanishing moments and coherence with sensing matrix. We identified Beylkin as the wavelet dictionary leading to the best performance. Using the same dataset, we then compared the performance of Beylkin with discrete cosine basis, often used in the literature, and the case of using no sparsifying dictionary. We further demonstrate that using dictionaries (Beylkin and DCT) may improve performance tangibly only for a high compression ratio (CR) of 80% and with smaller block sizes; as compared to when using no dictionaries

Development of complexity induced frameworks for charged cylindrical polytropes

The main theme of this work is the development of complexity induced generalized frameworks for static cylindrical polytropes. We consider two different definitions of generalized polytopes with charged anisotropic inner fluid distribution. A new methodology based on complexity factor for the generation of consistent sets of differential equations will be presented. We conclude our work by carrying out graphical analysis of developed frameworks.Comment: 21 pages, 6 figure

Minimizing Stimulus Current in a Wearable Pudendal Nerve Stimulator Using Computational Models.

After spinal cord injury, functions of the lower urinary tract may be disrupted. A wearable device with surface electrodes which can effectively control the bladder functions would be highly beneficial to the patients. A trans-rectal pudendal nerve stimulator may provide such a solution. However, the major limiting factor in such a stimulator is the high level of current it requires to recruit the nerve fibers. Also, the variability of the trajectory of the nerve in different individuals should be considered. Using computational models and an approximate trajectory of the nerve derived from an MRI study, it is demonstrated in this paper that it may be possible to considerably reduce the required current levels for trans-rectal stimulation of the pudendal nerve compared to the values previously reported in the literature. This was corroborated by considering an ensemble of possible and probable variations of the trajectory. The outcome of this study suggests that trans-rectal stimulation of the pudendal nerve is a plausible long term solution for treating lower urinary tract dysfunctions after spinal cord injury

Design of a wearable device for conditional neuromodulation of the pudendal nerve

After spinal cord injury, the normal functions of the lower urinary tract may be disrupted. Namely, incontinence and concurrent voiding problems may ensue. The troublesome side effects of the drugs, infection due to catheterisation, and the costs and risks associated with more invasive treatments indicate the need for alternative forms of treatment. The pudendal nerve neuromodulation may provide such an alternative. The unique aspect of this technique is that depending on the stimulus frequency it may result in micturition-like or continence-like reflexes. Also, the stimulus current can be applied trans-rectally, meaning that a minimally-invasive wearable solution may be developed. The major limitation of such a solution is the high level of the required stimulus current to activate the nerve trans-rectally. The efficacy of the trans-rectal neuromodulation of the pudendal may be increased by only applying the stimulus when needed, when employed to tackle incontinence. The electromyogram signal from the external anal sphincter may be used to detect the onset of hyper-reflexive contractions of the bladder. The ability of recording this signal can be readily incorporated in the neuromodulation device due to the proximity of the structures. However, the recording electrodes should be designed for an efficacious and chronic recording. Thus, the main objective of this thesis was to design and optimise the neuromodulation and recording electrodes on the said device. A volume conductor model of such a device in situ was developed and used in tandem with a double layer cable model of nerve fibres to minimise the stimulus current. It was demonstrated that a considerable reduction in the stimulus current may be achieved even when the variations of the nerve trajectory in different individuals are considered. Using computational models and experimental measurements, a recording assembly was identified for an efficacious recording of the electromyogram from the external anal sphincter

Coverage and predictors of vaccination among children of 1-4 years of age in a rural sub-district of Sindh

OBJECTIVE: To estimate the proportion of children 1-4 years of age vaccinated in the first year of their life and determine socio-demographic factors associated with vaccination in the rural sub-district Khairpur, Sindh, Pakistan.STUDY DESIGN: Cross-sectional study.PLACE AND DURATION OF STUDY: The study was conducted in 9 Union Councils of sub-district Gambat, district Khairpur, Sindh, from August to October 2008.METHODOLOGY: A questionnaire based representative multi-stage cluster survey was conducted. A total of 549 children aged 1-4 years were assessed for coverage and predictors of vaccination. Univariate and multivariate analysis was done using logistic regression to determine the unadjusted and adjusted relationship between socio-demographic predictor and outcome (vaccination status).RESULTS: The coverage for complete vaccination was 71.9% (95%CI=68.1%-75.7%). Educational level of mother (p=0.042), father (p=0.001) and child birth at hospital (p=0.006) were significantly associated with the vaccination status. Mother\u27s educational level of intermediate and above was the strongest predictor (OR=12.19, 95%CI=1.57-94.3) for vaccination.CONCLUSION: Education of parents, particularly mother\u27s education was important determinant of vaccination status of the children. In addition, distance from taluka health facility and misconception of parents were among the main reasons of not getting the children vaccinated. There is a need to educate the parents especially mothers about the importance of vaccination and organize EPI services at Basic Health Unit level to improve the vaccination coverage in rural areas of Pakistan

Supersymmetric States in M5/M2 CFTs

We propose an exact, finite $N$ formula for the partition function over $1/4^{th}$ BPS states in the conformal field theory on the world volume of $N$ coincident M5 branes and $1/8^{th}$ BPS states in the theory of $N$ coincident M2 branes. We obtain our partition function by performing the radial quantization of the Coulomb Branches of these theories, and rederive the same formula from the quantization of supersymmetric giant and dual giant gravitons in $AdS_7 \times S^4$ and $AdS_4 \times S^7$. Our partition function is qualitatively similar to the analogous quantity in ${\cal N}=4$ Yang Mills. It reduces to the sum over supersymmetric multi gravitons at low energies, but deviates from this supergravity formula at energies that scale like a positive power of $N$.Comment: 24 pages, harvmac; v2 reference adde

Detecting colorectal cancer using electrical impedance spectroscopy: an ex vivo feasibility study

Objective: Colorectal cancer is the fourth most common cancer worldwide, with a lifetime risk of around 20%. Current solutions do not allow clinicians to objectively assess tissue abnormality during endoscopy and perioperatively. A solution capable of objectively assessing samples in real time could greatly improve the treatment process. A solution that can be integrated in minimally invasive diagnostics and management strategies to provide real-time point-of-care information would be greatly transformative. Electrical impedance spectroscopy (EIS) may provide such a solution. In this paper, we present a feasibility study on using EIS in assessing colorectal tissue. Approach: We performed tetrapolar EIS using ZedScan on excised human colorectal tumour tissue and the matched normal colonic mucosa in 22 freshly resected specimens following elective surgery for colorectal cancer. Histopathological examination was used to confirm the final diagnosis. Statistical significance was assessed with Wilcoxon signed rank test. Main results: Tetrapolar EIS could discriminate cancer with statistically significant results when applying frequencies between 305 Hz – 625 kHz (p < 0.05). 300 Ω was set as the transfer impedance threshold to detect cancer. Thus, the area under the corresponding receiver operating characteristic curve for this threshold was 0.7105. Significance: This feasibility study demonstrates that impedance spectra changes in colorectal cancer tissue are detectable and may be statistically significant, suggesting that EIS has the potential to be the core technology in a novel non-invasive point of care test for detecting colorectal cancer. These results warrant further development and increasing the size of the study with a device specificity designed for colorectal cancer

Effect of Model Complexity on Fiber Activation Estimates in a Wearable Neuromodulator for Migraine

Migraine is a prevalent and highly disabling disorder. The pharmaceutical and invasive treatment methods have trouble-some side effects and associated risks, hence undesirable. Transcutaneous supraorbital neuromodulation has been shown to potentially suppress episodic migraine attacks yet results have low efficacy. This inconclusive response may be associated with neuroanatomical variations of patients which may be investigated using computational models. Model complexity is a limiting factor in implementing such techniques. This paper investigates the effect of model complexity on fiber activation estimates in transcutaneous frontal nerve stimulation. It is shown that the model can be simplified while minimally affecting the outcome