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5 results for “exponential function”
Beyond the exponential horn: a bush-cricket with ear-canals which function as coupled resonators
<p>Bush-crickets have dual-input, tympanal ears located in the tibia of their forelegs. The sound will, first of all, reach the external sides of the tympana, before arriving to the internal sides through the bush-cricket ear-canal, the acoustic trachea (AT), with a phase lapse and pressure gain. It has been shown that for many bush-crickets, the AT has an exponential horn-shaped morphology and function, producing a significant pressure gain above a certain cut-off frequency. However, the underlying mechanism of different AT designs remains elusive. In this study, we demonstrate that the AT of the duetting bush-cricket <em>Pterodichopetala</em> <em>cieloi</em> function as coupled resonators, producing sound pressure gains at the sex-specific conspecific calling song frequency, and attenuating the remainder – a functioning mechanism significantly different than an exponential horn. Furthermore, it is demonstrated that despite the sexual dimorphism between the <em>P</em>. <em>cieloi</em> AT, both male and female AT have a similar biophysical mechanism. The analysis was carried out using an interdisciplinary approach, where micro-computed tomography was used for the morphological properties of the <em>P</em>. <em>cieloi</em> AT, and a finite-element analysis was applied on the precise tracheal geometry to further justify the experimental results and to go beyond experimental limitations.</p>
Beyond the exponential horn: a bush-cricket with ear-canals which function as coupled resonators
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Coefficients for Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials
<p>This is a supplementary dataset for the publication:</p> <p>I. M. Tanash and T. Riihonen, "Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials," in <em>IEEE Transactions on Communications</em>, vol. 68, no. 10, pp. 6514-6524, Oct. 2020, doi: 10.1109/TCOMM.2020.3006902.</p> <p>The dataset contains the sets of the optimized coefficients for the novel minimax approximations and bounds of the Gaussian Q-function, its first four integer powers and for the case of average symbol error probability (SEP) in optimal detection of 4-QAM that is actually a polynomial of the Q-function. The proposed approximations and bounds have the form of a weighted sum of exponential functions. The corresponding optimized coefficients are found up to twenty-five exponential terms with the right boundary of the finite interval on the x-axis (x_K+1) ranging from 1 to 10 in steps of 0.1 for the relative error.</p> <p>The Matlab function (func_extract_coef.m) extracts the required set of optimal coefficients from the provided dataset according to the selected error type, variation, number of terms and the right end-point in case of relative error. See help func_extract_coef for more information.</p> <p>A Matlab script (Example.m) is also provided as an example to illustrate the use of the provided Matlab function in extracting the required coefficients from the dataset, to calculate and plot the corresponding relative error which is shown by figure Example.jpg.</p> <p> </p>
Error curves of finite completely monotonic functions associated with inverse power functions by exponential sum approximations
<p>Each figure of page <span class="math-tex">\(M=1,\ldots,17\)</span> in each PDF file represents the error curve of a finite completely monotonic function <span class="math-tex">\(f(x) = \int_a^b \mathrm{e}^{-xt} \frac{t^{\eta - 1}}{\Gamma(\eta)} \mathrm{d}t\)</span> by an <span class="math-tex">\(M\)</span>-term exponential sum approximation. Each PDF file corresponds to the following parameters:</p> <p>inverse_power0.5_a0.5_b1_EMx.pdf for <span class="math-tex">\(\eta = 0.5, a = 2^{-1}, b = 1\)</span><br> inverse_power0.5_a0.0009765625_b1_EMx.pdf for <span class="math-tex">\(\eta = 0.5, a = 2^{-10}, b = 1\)</span><br> inverse_power1_a0.5_b1_EMx.pdf for <span class="math-tex">\(\eta = 1, a = 2^{-1}, b = 1\)</span><br> inverse_power1_a0.0009765625_b1_EMx.pdf for <span class="math-tex">\(\eta = 1, a = 2^{-10}, b = 1\)</span><br> inverse_power2_a0.5_b1_EMx.pdf for <span class="math-tex">\(\eta = 2, a = 2^{-1}, b = 1\)</span><br> inverse_power2_a0.0009765625_b1_EMx.pdf for <span class="math-tex">\(\eta = 2, a = 2^{-10}, b = 1\)</span></p> <p> </p> <p>Each page includes 6 row figures:<br> Row=1 Best exponential sum approximation<br> Row=2 Approximation by the Gaussian quadrature with the variable transformation <span class="math-tex">\(\Phi_{a/b}(u)\)</span><br> Row=3 Approximation by the Gaussian quadrature with the variable transformation <span class="math-tex">\(\varphi_{\exp, a/b}(u)\)</span><br> Row=4 Approximation by the Gaussian quadrature with the variable transformation <span class="math-tex">\(\varphi_{\mathcal{P}_2, a/b}(u)\)</span><br> Row=5 Approximation by the Gaussian quadrature with the variable transformation <span class="math-tex">\(\varphi_{\mathcal{P}_1, a/b}(u)\)</span><br> Row=6 Approximation by the Gaussian quadrature with the variable transformation <span class="math-tex">\(\varphi_{\mathcal{R}_{0, 1}, a/b}(u)\)</span></p> <p> </p> <p>The figures were generated by</p> <p>https://github.com/ymkoyama/fcmf, commit 17342bf3974eee9b4d6b3d21b06f13b87929a85b on January 21, 2023.</p>
AI-2 does not function as a quorum sensing molecule in Campylobacter jejuni during exponential growth in vitro
GEO Series GSE18455. Campylobacter jejuni subsp. jejuni NCTC 11168 = ATCC 700819; Campylobacter jejuni. 24 samples. Type: Expression profiling by array.
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