Stored energies for electric and magnetic current densities

Electric and magnetic current densities are an essential part of electromagnetic theory. The goal of the present paper is to define and investigate stored energies that are valid for structures that can support both electric and magnetic current densities. Stored energies normalized with the dissipated power give us the Q factor, or antenna Q, for the structure. Lower bounds of the Q factor provide information about the available bandwidth for passive antennas that can be realized in the structure. The definition that we propose is valid beyond the leading order small antenna limit. Our starting point is the energy density with subtracted far-field form which we obtain an explicit and numerically attractive current density representation. This representation gives us the insight to propose a coordinate independent stored energy. Furthermore, we find here that lower bounds on antenna Q for structures with e.g. electric dipole radiation can be formulated as convex optimization problems. We determine lower bounds on both open and closed surfaces that support electric and magnetic current densities. The here derived representation of stored energies has in its electrical small limit an associated Q factor that agrees with known small antenna bounds. These stored energies have similarities to earlier efforts to define stored energies. However, one of the advantages with this method is the above mentioned formulation as convex optimization problems, which makes it easy to predict lower bounds for antennas of arbitrary shapes. The present formulation also gives us insight into the components that contribute to Chu's lower bound for spherical shapes. We utilize scalar and vector potentials to obtain a compact direct derivation of these stored energies. Examples and comparisons end the paper.Comment: Minor updates to figures and tex

Stored Electromagnetic Energy and Antenna Q

Decomposition of the electromagnetic energy into its stored and radiated parts is instrumental in the evaluation of antenna Q and the corresponding fundamental limitations on antennas. This decomposition is not unique and there are several proposals in the literature. Here, it is shown that stored energy defined from the difference between the energy density and the far field energy equals the new energy expressions proposed by Vandenbosch for many cases. This also explains the observed cases with negative stored energy and suggests a possible remedy to them. The results are compared with the classical explicit expressions for spherical regions where the results only differ by ka that is interpreted as the far-field energy in the interior of the sphere. Numerical results of the Q-factors for dipole, loop, and inverted L-antennas are also compared with estimates from circuit models and differentiation of the impedance. The results indicate that the stored energy in the field agrees with the stored energy in the Brune synthesized circuit models whereas the differentiated impedance gives a lower value for some cases. The corresponding results for the bandwidth suggest that the inverse proportionality between bandwidth and Q depends on the relative bandwidth or equivalent the threshold of the reflection coefficient. The Q from the differentiated impedance and stored energy are most useful for relative narrow and wide bandwidths, respectively

Stored energies in electric and magnetic current densities for small antennas

Electric and magnetic currents are essential to describe electromagnetic stored energy, as well as the associated quantities of antenna Q and the partial directivity to antenna Q-ratio, D/Q, for general structures. The upper bound of previous D/Q-results for antennas modeled by electric currents is accurate enough to be predictive, this motivates us here to extend the analysis to include magnetic currents. In the present paper we investigate antenna Q bounds and D/Q-bounds for the combination of electric- and magnetic-currents, in the limit of electrically small antennas. This investigation is both analytical and numerical, and we illustrate how the bounds depend on the shape of the antenna. We show that the antenna Q can be associated with the largest eigenvalue of certain combinations of the electric and magnetic polarizability tensors. The results are a fully compatible extension of the electric only currents, which come as a special case. The here proposed method for antenna Q provides the minimum Q-value, and it also yields families of minimizers for optimal electric and magnetic currents that can lend insight into the antenna design.Comment: 27 pages 7 figure

Bayesian detection of periodic mRNA time profiles without use of training examples

BACKGROUND: Detection of periodically expressed genes from microarray data without use of known periodic and non-periodic training examples is an important problem, e.g. for identifying genes regulated by the cell-cycle in poorly characterised organisms. Commonly the investigator is only interested in genes expressed at a particular frequency that characterizes the process under study but this frequency is seldom exactly known. Previously proposed detector designs require access to labelled training examples and do not allow systematic incorporation of diffuse prior knowledge available about the period time. RESULTS: A learning-free Bayesian detector that does not rely on labelled training examples and allows incorporation of prior knowledge about the period time is introduced. It is shown to outperform two recently proposed alternative learning-free detectors on simulated data generated with models that are different from the one used for detector design. Results from applying the detector to mRNA expression time profiles from S. cerevisiae showsthat the genes detected as periodically expressed only contain a small fraction of the cell-cycle genes inferred from mutant phenotype. For example, when the probability of false alarm was equal to 7%, only 12% of the cell-cycle genes were detected. The genes detected as periodically expressed were found to have a statistically significant overrepresentation of known cell-cycle regulated sequence motifs. One known sequence motif and 18 putative motifs, previously not associated with periodic expression, were also over represented. CONCLUSION: In comparison with recently proposed alternative learning-free detectors for periodic gene expression, Bayesian inference allows systematic incorporation of diffuse a priori knowledge about, e.g. the period time. This results in relative performance improvements due to increased robustness against errors in the underlying assumptions. Results from applying the detector to mRNA expression time profiles from S. cerevisiae include several new findings that deserve further experimental studies

Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution.

Contrary to the well known diffraction limit, the fluorescence microscope is in principle capable of unlimited resolution. The necessary elements are spatially structured illumination light and a nonlinear dependence of the fluorescence emission rate on the illumination intensity. As an example of this concept, this article experimentally demonstrates saturated structured-illumination microscopy, a recently proposed method in which the nonlinearity arises from saturation of the excited state. This method can be used in a simple, wide-field (nonscanning) microscope, uses only a single, inexpensive laser, and requires no unusual photophysical properties of the fluorophore. The practical resolving power is determined by the signal-to-noise ratio, which in turn is limited by photobleaching. Experimental results show that a 2D point resolution of <50 nm is possible on sufficiently bright and photostable samples. super resolution ͉ moiré ͉ resolution extension ͉ saturation T he fluorescence microscope has become a ubiquitous imaging tool in cell biology through its unique ability to image the 3D interior of a living specimen with multicolor molecular labels of extreme specificity, a combination of strengths not shared by higher-resolution techniques such as electron microscopy and scanned-probe methods. It is therefore unfortunate that its spatial resolution is subject to a hard limit caused by diffraction. Recently, ways have been found to bypass the diffraction limit. 2D resolution in the 30-nm range has been realized by using stimulated emission depletion (STED) (1). STED is based on saturated stimulated emission using two synchronized ultrafast laser sources (2, 3); the underlying concept has been generalized to encompass a class of reversible saturable phenomena (4). STED and other proposed methods (5-7) were conceived in the context of laser-scanning microscopy and are designed to directly minimize the size of a scanned focal point. This article demonstrates an alternative approach that brings theoretically unlimited resolution to a wide-field (nonscanning) microscope by using a nonlinear fluorescence response together with a periodic illumination pattern that fills the field of view. Both structured illumination light and optical nonlinearity, of course, are established ideas. Patterned light, for example, has been used for measuring surface shapes (8) and deformations The reason that structured illumination can provide resolution extension is that it can render otherwise unresolvable highresolution information visible in the form of low-resolution moiré fringes Because the nonlinearity does not have to sharpen a focal spot, a larger class of physical phenomena can be exploited. In fact, it was pointed out recently (25) that the method can even use simple saturation of the excited state itself. This well known effect (the fact that once the illumination is intense enough to raise most fluorophore molecules to the excited state, additional intensity increases will not yield proportionate increases in the emission rate) occurs in all fluorophores and can be induced with a single, inexpensive light source. It is ill-suited for point scanning because it would broaden, not sharpen, the focal spot, but that is not a problem in the extended-pattern approach. The following sections experimentally demonstrate saturated structured-illumination microscopy (SSIM), as an example of the more general concept of nonlinear structured-illumination microscopy, and show that it can achieve 2D resolution of Ͻ50 nm. Principle The classical resolution limit specifies a maximum spatial frequency k 0 that can be observed through the microscope. For a light microscope, k 0 ϭ 2NA͞ em , where em is the observation wavelength and NA is the numerical aperture of the objective lens Structured-illumination microscopy extends resolution beyond the cutoff by moving information into the observable region, from elsewhere in frequency space, in the form of moiré fringes. Moiré fringes are produced by frequency mixing whenever two signals are multiplied. In this case, the multiplication is the one inherent in fluorescence: the observed emission intensity is the product of the local density of fluorescent dye (i.e., the sample) and the local intensity of excitation light. If the illumination contains a spatial frequency k 1 , then each sample frequency k gives rise to moiré fringes at the difference frequency k Ϫ k 1 . Those fringes will be observable in the microscope if k Ϫ k 1 Ͻ k 0 , that is, if k lies within a circle of radius k 0 around k 1 Abbreviations: SSIM, saturated structured-illumination microscopy; FWHM, full width at half maximum

Optimal Planar Electric Dipole Antenna

Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on radiation Q-factor (maximizing single resonance fractional bandwidth), but are far from reaching the associated physical bounds on efficiency. The relative performance of other canonical antenna designs is compared in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design.Comment: 10 pages, 15 figures, 2 tables, 4 boxe

Fundamental bounds on transmission through periodically perforated metal screens with experimental validation

This paper presents a study of transmission through arrays of periodic sub-wavelength apertures. Fundamental limitations for this phenomenon are formulated as a sum rule, relating the transmission coefficient over a bandwidth to the static polarizability. The sum rule is rigorously derived for arbitrary periodic apertures in thin screens. By this sum rule we establish a physical bound on the transmission bandwidth which is verified numerically for a number of aperture array designs. We utilize the sum rule to design and optimize sub-wavelength frequency selective surfaces with a bandwidth close to the physically attainable. Finally, we verify the sum rule and simulations by measurements of an array of horseshoe-shaped slots milled in aluminum foil.Comment: 10 pages, 11 figures. Updated Introduction and Conclusion

Improved variance estimation of classification performance via reduction of bias caused by small sample size

BACKGROUND: Supervised learning for classification of cancer employs a set of design examples to learn how to discriminate between tumors. In practice it is crucial to confirm that the classifier is robust with good generalization performance to new examples, or at least that it performs better than random guessing. A suggested alternative is to obtain a confidence interval of the error rate using repeated design and test sets selected from available examples. However, it is known that even in the ideal situation of repeated designs and tests with completely novel samples in each cycle, a small test set size leads to a large bias in the estimate of the true variance between design sets. Therefore different methods for small sample performance estimation such as a recently proposed procedure called Repeated Random Sampling (RSS) is also expected to result in heavily biased estimates, which in turn translates into biased confidence intervals. Here we explore such biases and develop a refined algorithm called Repeated Independent Design and Test (RIDT). RESULTS: Our simulations reveal that repeated designs and tests based on resampling in a fixed bag of samples yield a biased variance estimate. We also demonstrate that it is possible to obtain an improved variance estimate by means of a procedure that explicitly models how this bias depends on the number of samples used for testing. For the special case of repeated designs and tests using new samples for each design and test, we present an exact analytical expression for how the expected value of the bias decreases with the size of the test set. CONCLUSION: We show that via modeling and subsequent reduction of the small sample bias, it is possible to obtain an improved estimate of the variance of classifier performance between design sets. However, the uncertainty of the variance estimate is large in the simulations performed indicating that the method in its present form cannot be directly applied to small data sets

Revealing cell cycle control by combining model-based detection of periodic expression with novel cis-regulatory descriptors

<p>Abstract</p> <p>Background</p> <p>We address the issue of explaining the presence or absence of phase-specific transcription in budding yeast cultures under different conditions. To this end we use a model-based detector of gene expression periodicity to divide genes into classes depending on their behavior in experiments using different synchronization methods. While computational inference of gene regulatory circuits typically relies on expression similarity (clustering) in order to find classes of potentially co-regulated genes, this method instead takes advantage of known time profile signatures related to the studied process.</p> <p>Results</p> <p>We explain the regulatory mechanisms of the inferred periodic classes with <it>cis</it>-regulatory descriptors that combine upstream sequence motifs with experimentally determined binding of transcription factors. By systematic statistical analysis we show that periodic classes are best explained by combinations of descriptors rather than single descriptors, and that different combinations correspond to periodic expression in different classes. We also find evidence for additive regulation in that the combinations of <it>cis</it>-regulatory descriptors associated with genes periodically expressed in fewer conditions are frequently subsets of combinations associated with genes periodically expression in more conditions. Finally, we demonstrate that our approach retrieves combinations that are more specific towards known cell-cycle related regulators than the frequently used clustering approach.</p> <p>Conclusion</p> <p>The results illustrate how a model-based approach to expression analysis may be particularly well suited to detect biologically relevant mechanisms. Our new approach makes it possible to provide more refined hypotheses about regulatory mechanisms of the cell cycle and it can easily be adjusted to reveal regulation of other, non-periodic, cellular processes.</p

Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal

In the present paper an iterative time-reversal algorithm, that retrofocuses an acoustic wave field to its controllable part is established. For a fixed temporal support, i.e., transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm reduces the temporal support of the excitation from the requirement of negligible remaining energy to the requirement of controllability. The timereversal retrofocusing is analyzed from a boundary control perspective where time reversal is used to steer the acoustic wave field towards a desired state. The wave field is controlled by transducers located at subsets of the boundary, i.e., the controllable part of the boundary. The time-reversal cavity and time-reversal mirror cases are analyzed. In the cavity case, the transducers generate a locally plane wave in the fundamental mode through a set of ducts. Numerical examples are given to illustrate the convergence of the iterative time-reversal algorithm. In the mirror case, a homogeneous half space is considered. For this case the analytic expression for the retrofocused wave field is given for finite temporal support. It is shown that the mirror case does not have the same degree of steering as the cavity case. It is also shown that the pressure can be perfectly retrofocused for infinite temporal support. Two examples are given that indicate that the influence of the evanescent part of the wave field is small