Exact diffraction calculation from fields specified over arbitrary curved surfaces

Cataloged from PDF version of article.Calculation of the scalar diffraction field over the entire space from a given field over a surface is an important problem in computer generated holography. A straightforward approach to compute the diffraction field from field samples given on a surface is to superpose the emanated fields from each such sample. In this approach, possible mutual interactions between the fields at these samples are omitted and the calculated field may be significantly in error. In the proposed diffraction calculation algorithm, mutual interactions are taken into consideration, and thus the exact diffraction field can be calculated. The algorithm is based on posing the problem as the inverse of a problem whose formulation is straightforward. The problem is then solved by a signal decomposition approach. The computational cost of the proposed method is high, but it yields the exact scalar diffraction field over the entire space from the data on a surface. © 2011 Elsevier B.V. All rights reserved

Diffraction field computation from arbitrarily distributed data points in space

Cataloged from PDF version of article.Computation of the diffraction field from a given set of arbitrarily distributed data points in space is an important signal processing problem arising in digital holographic 3D displays. The field arising from such distributed data points has to be solved simultaneously by considering all mutual couplings to get correct results. In our approach, the discrete form of the plane wave decomposition is used to calculate the diffraction field. Two approaches, based on matrix inversion and on projections on to convex sets (POCS), are studied. Both approaches are able to obtain the desired field when the number of given data points is larger than the number of data points on a transverse cross-section of the space. The POCS-based algorithm outperforms the matrix-inversion-based algorithm when the number of known data points is large. (C) 2006 Elsevier B.V. All rights reserved

Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search

We generalize the monotone local search approach of Fomin, Gaspers,Lokshtanov and Saurabh [J.ACM 2019], by establishing a connection betweenparameterized approximation and exponential-time approximation algorithms formonotone subset minimization problems. In a monotone subset minimizationproblem the input implicitly describes a non-empty set family over a universeof size $n$ which is closed under taking supersets. The task is to find aminimum cardinality set in this family. Broadly speaking, we use approximatemonotone local search to show that a parameterized $\alpha$-approximationalgorithm that runs in $c^k \cdot n^{O(1)}$ time, where $k$ is the solutionsize, can be used to derive an $\alpha$-approximation randomized algorithm thatruns in $d^n \cdot n^{O(1)}$ time, where $d$ is the unique value in $d \in(1,1+\frac{c-1}{\alpha})$ such that$\mathcal{D}(\frac{1}{\alpha}\|\frac{d-1}{c-1})=\frac{\ln c}{\alpha}$ and$\mathcal{D}(a \|b)$ is the Kullback-Leibler divergence. This running timematches that of Fomin et al. for $\alpha=1$, and is strictly better when$\alpha >1$, for any $c > 1$. Furthermore, we also show that this result can bederandomized at the expense of a sub-exponential multiplicative factor in therunning time. We demonstrate the potential of approximate monotone local search by derivingnew and faster exponential approximation algorithms for Vertex Cover,$3$-Hitting Set, Directed Feedback Vertex Set, Directed Subset Feedback VertexSet, Directed Odd Cycle Transversal and Undirected Multicut. For instance, weget a $1.1$-approximation algorithm for Vertex Cover with running time $1.114^n\cdot n^{O(1)}$, improving upon the previously best known $1.1$-approximationrunning in time $1.127^n \cdot n^{O(1)}$ by Bourgeois et al. [DAM 2011].<br

Optimally Repurposing Existing Algorithms to Obtain Exponential-Time Approximations

The goal of this paper is to understand how exponential-time approximationalgorithms can be obtained from existing polynomial-time approximationalgorithms, existing parameterized exact algorithms, and existing parameterizedapproximation algorithms. More formally, we consider a monotone subsetminimization problem over a universe of size $n$ (e.g., Vertex Cover orFeedback Vertex Set). We have access to an algorithm that finds an$\alpha$-approximate solution in time $c^k \cdot n^{O(1)}$ if a solution ofsize $k$ exists (and more generally, an extension algorithm that canapproximate in a similar way if a set can be extended to a solution with $k$further elements). Our goal is to obtain a $d^n \cdot n^{O(1)}$ time$\beta$-approximation algorithm for the problem with $d$ as small as possible.That is, for every fixed $\alpha,c,\beta \geq 1$, we would like to determinethe smallest possible $d$ that can be achieved in a model where ourproblem-specific knowledge is limited to checking the feasibility of a solutionand invoking the $\alpha$-approximate extension algorithm. Our resultscompletely resolve this question: (1) For every fixed $\alpha,c,\beta \geq 1$, a simple algorithm(``approximate monotone local search'') achieves the optimum value of $d$. (2) Given $\alpha,c,\beta \geq 1$, we can efficiently compute the optimum $d$up to any precision $\varepsilon > 0$. Earlier work presented algorithms (but no lower bounds) for the special case$\alpha = \beta = 1$ [Fomin et al., J. ACM 2019] and for the special case$\alpha = \beta > 1$ [Esmer et al., ESA 2022]. Our work generalizes theseresults and in particular confirms that the earlier algorithms are optimal inthese special cases.<br

Approximate Monotone Local Search for Weighted Problems

In a recent work, Esmer et al. describe a simple method - ApproximateMonotone Local Search - to obtain exponential approximation algorithms fromexisting parameterized exact algorithms, polynomial-time approximationalgorithms and, more generally, parameterized approximation algorithms. In thiswork, we generalize those results to the weighted setting. More formally, we consider monotone subset minimization problems over aweighted universe of size $n$ (e.g., Vertex Cover, $d$-Hitting Set and FeedbackVertex Set). We consider a model where the algorithm is only given access to asubroutine that finds a solution of weight at most $\alpha \cdot W$ (and ofarbitrary cardinality) in time $c^k \cdot n^{O(1)}$ where $W$ is the minimumweight of a solution of cardinality at most $k$. In the unweighted setting,Esmer et al. determine the smallest value $d$ for which a $\beta$-approximationalgorithm running in time $d^n \cdot n^{O(1)}$ can be obtained in this model.We show that the same dependencies also hold in a weighted setting in thismodel: for every fixed $\varepsilon>0$ we obtain a $\beta$-approximationalgorithm running in time $O\left((d+\varepsilon)^{n}\right)$, for the same $d$as in the unweighted setting. Similarly, we also extend a $\beta$-approximate brute-force search (in amodel which only provides access to a membership oracle) to the weightedsetting. Using existing approximation algorithms and exact parameterizedalgorithms for weighted problems, we obtain the first exponential-time$\beta$-approximation algorithms that are better than brute force for a varietyof problems including Weighted Vertex Cover, Weighted $d$-Hitting Set, WeightedFeedback Vertex Set and Weighted Multicut.<br

Neurovascular relationship between abducens nerve and anterior inferior cerebellar artery

We aimed to study the neurovascular relationships between the anterior inferior cerebellar artery (AICA) and the abducens nerve to help determine the pathogenesis of abducens nerve palsy which can be caused by arterial compression. Twenty-two cadaveric brains (44 hemispheres) were investigated after injected of coloured latex in to the arterial system. The anterior inferior cerebellar artery originated as a single branch in 75%, duplicate in 22.7%, and triplicate in 2.3% of the hemispheres. Abducens nerves were located between the AICAs in all hemispheres when the AICA duplicated or triplicated. Additionally, we noted that the AICA or its main branches pierced the abducens nerve in five hemispheres (11.4%). The anatomy of the AICA and its relationship with the abducens nerve is very important for diagnosis and treatment. (Folia Morphol 2010; 69, 4: 201-203

A Holistic and Probabilistic Approach to the Ground-based and Spaceborne Data of HAT-P-19 System

We update the main physical and orbital properties of the transiting hot Saturn planet HAT-P-19 b, based on a global modelling of high-precision transit and occultation light curves, taken with ground-based and space telescopes, archive spectra and radial velocity measurements, brightness values from broadband photometry, and Gaia parallax. We collected 65 light curves by amateur and professional observers, measured mid-transit times, analyzed their differences from calculated transit timings based on reference ephemeris information, which we update as a result. We haven’t found any periodicity in the residuals of a linear trend, which we attribute to the accumulation of uncertainties in the reference mid-transit time and the orbital period. We comment on the scenarios describing the formation and migration of this hot-Saturn type exoplanet with a bloated atmosphere yet a small core, although it is orbiting a metal-rich ([Fe/H] = 0.24 dex) host star. Finally, we review the planetary mass-radius, the orbital period-radius and density, and the stellar metallicity-core mass diagrams, based on the parameters we derive for HAT-P-19 b and those of the other seventy transiting Saturn-mass planets from the NASA Exoplanet Archive

Thoracoscopic-assisted repair of a bochdalek hernia in an adult: a case report

<p>Abstract</p> <p>Introduction</p> <p>Bochdalek hernia is a congenital defect of the diaphragm that usually presents in the neonatal period with life-threatening cardiorespiratory distress. It is rare for Bochdalek hernias to remain silent until adulthood. Once a Bochdalek hernia has been diagnosed, surgical treatment is necessary to avoid complications such as perforation and necrosis.</p> <p>Case presentation</p> <p>We present a 17-year-old Japanese boy with left-upper-quadrant pain for two months. Chest radiography showed an elevated left hemidiaphragm. Computed tomography revealed a congenital diaphragmatic hernia. The spleen and left colon had been displaced into the left thoracic cavity through a left posterior diaphragmatic defect. We diagnosed a Bochdalek hernia. Surgical treatment was performed via a thoracoscopic approach. The boy was placed in the reverse Trendelenburg position and intrathoracic pressure was increased by CO₂gas insufflations. This is a very useful procedure for reducing herniated contents and we were able to place the herniated organs safely back in the peritoneal cavity. The diaphragmatic defect was too large to close with thoracoscopic surgery alone. Small incision thoracotomy was required and primary closure was performed. His postoperative course was uneventful and there has been no recurrence of the diaphragmatic hernia to date.</p> <p>Conclusion</p> <p>Thoracoscopic surgery, performed with the boy in the reverse Trendelenburg position and using CO₂gas insufflations in the thoracic cavity, was shown to be useful for Bochdalek hernia repair.</p