Genetic optical design for a compressive sensing task

We present a sophisticated optical design method for reducing the number of photodetectors for a specific sensing task. The chosen design parameter is the point spread function, and the selected task is object recognition. The point spread function is optimized iteratively with a genetic algorithm for object recognition based on a neural network. In the experimental demonstration, binary classification of face and non-face datasets was performed with a single measurement using two photodetectors. A spatial light modulator operating in the amplitude modulation mode was provided in the imaging optics and was used to modulate the point spread function. In each generation of the genetic algorithm, the classification accuracy with a pattern displayed on the spatial light modulator was fed-back to the next generation to find better patterns. The proposed method increased the accuracy by about 30 % compared with a conventional imaging system in which the point spread function was the delta function. This approach is practically useful for compressing the cost, size, and observation time of optical sensors in specific applications, and robust for imperfections in optical elements.     

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127–146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator \({\mathscr{A}}\) which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator \({\mathscr{A}}\) to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.     

Prospective trial of a navigator setting under left hepatic lobe on magnetic resonance cholangiopancreatography using a free-breathing prospective acquisition correction technique

PURPOSE: To prospectively compare the image acquisition time and image quality obtained by navigator setting under the left hepatic lobe vs. on the right diaphragm on magnetic resonance cholangiopancreatography (MRCP) using a free-breathing navigator-triggered prospective acquisition correction technique (PACE). MATERIALS AND METHODS: Fifty consecutive patients prospectively underwent three-dimensional T2-weighted turbo spin-echo MRCP using PACE with the navigator randomly set either under the left hepatic lobe or on top of the right diaphragm. Image acquisition time and subjective image quality were compared on a five-point scale using Student's t-test and Mann-Whitney's U test, respectively. RESULTS: There was no significant difference for mean acquisition time (6.1+/-1.6 vs. 6.3+/-1.2 min, P=.689) between the left hepatic lobe group and right diaphragm group. Mean subjective image quality was significantly worse in the left hepatic lobe group than in the right diaphragm group (4.1 vs. 4.7, P=.044). CONCLUSION: Setting the navigator under the left hepatic lobe for MRCP using PACE causes the data processing to be more difficult. As well, under current circumstances, it does not contribute to reducing acquisition time or improving the image quality.     

Multiple Ca(2+) environments in silicate glasses by high-resolution (43)Ca MQMAS NMR technique at high and ultra-high (21.8 T) magnetic fields

We here show the (43)Ca 5QMAS NMR spectra at high field (16.4 T) and the first 7QMAS spectrum at ultra-high field (21.8 T) for geologically important Ca-containing glasses. The high-resolution MQMAS spectra present a clear evidence of multiple Ca sites in the amorphous structures that have never been identified by other analytical methods. The present study suggests that the Ca(2+) ions are mainly in 7- and 8-fold coordination sites. This will offer valuable insights for dynamic properties of magmatic liquids. The MQMAS NMR technique at high magnetic field is a unique tool to understand the detailed structural information on a specific element in solids including organic and inorganic compounds.     

An intense terahertz radiation source at the Compact ERL

The Compact ERL is an energy recovery LINAC (ERL) test facility that is planned for KEK. The circumference of the recirculation path will be 70 m. Initially, the beam energy will be about 65 MeV and the current about 10 mA. Although the primary purpose of the machine is to aid the development of the key technologies that are essential for building an ultra-brilliant new synchrotron light source based on an ERL, the Compact ERL itself has great potential as an intense source of terahertz radiation. To generate the intense terahertz radiation, an electron bunch of a very short bunch length is required and bunch compression is inevitable. We discuss the parameters of the Compact ERL, present the results of a simulation of bunch compression, and make an estimate of the generated coherent synchrotron radiation.     

Angle-resolved photoemission of the c(2 × 2) and c(3 × 1) oxygen overlayers on Fe(110)

Angle-resolved photoemission spectroscopy utilizing synchrotron radiation has been used to study the band structure of the c(2×2) and (3×1) oxygen overlayers on Fe(110). The symmetries of the O-2p-derived states at the center of the surface Brillouin zone $\text{(}\text{Γ}\text{)}$ were identified using polarized light. At $\text{Γ}$ the p_xp_y- and p_z-derived levels are at about 5.5 and 7.0 eV below the Fermi level, respectively, for both ordered overlayers. The p-states of the c(2×2)-O structure show very little dispersion (?0.1 eV) with $\text{k}{}_{\mathrm{}}$. On the other hand, the c(3×1)-O overlayer exhibits considerable dispersion of ～1.6 eV. The essential features of the measured dispersion are reproduced well by the dispersion predicted in a qualitative way for an isolated c(3×1) oxygen monolayer.     

A study of Feynman integrals by micro-differential equations

We use the holonomic character of Feynman integrals to describe their singularity structure explicitly in some simple cases. The results in §1 show that under moderate conditions Feynman amplitudes can be locally expressed essentially in terms of Legendre functions near the points where two positive- Landau-Nakanishi surfaces meet. Related topics such as hierarchical principle in perturbation theory are also discussed in terms of holonomic systems involved. In §4 we use the concrete expressions for Feynman amplitudes obtained in §1 to discuss the validity of Sato's conjecture.Supported in part by NSF MCS 75-2333Supported in part by NSF GP 36269     

Extremal Self-Dual [50, 25, 10] Codes with Automorphisms of Order 3 and Quasi-Symmetric 2-(49, 9,6) Designs

Five non-isomorphic quasi-symmetric 2-(49, 9, 6) designs are known. They arise from extremal self-dual [50, 25, 10] codes with a certain weight enumerator. Four of them have an automorphism of order 3 fixing two points. In this paper, it is shown that there are exactly 48 inequivalent extremal self-dual [50, 25, 10] code with this weight enumerator and an automorphism of order 3 fixing two points. 44 new quasi-symmetric 2-(49, 9, 6) designs with an automorphism of order 3 are constructed from these codes.