Multivalued Discrete Tomography Using Dynamical System That Describes Competition

Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown

Tomographic Image Reconstruction Based on Minimization of Symmetrized Kullback-Leibler Divergence

Iterative reconstruction (IR) algorithms based on the principle of optimization are known for producing better reconstructed images in computed tomography. In this paper, we present an IR algorithm based on minimizing a symmetrized Kullback-Leibler divergence (SKLD) that is called Jeffreys’ J-divergence. The SKLD with iterative steps is guaranteed to decrease in convergence monotonically using a continuous dynamical method for consistent inverse problems. Specifically, we construct an autonomous differential equation for which the proposed iterative formula gives a first-order numerical discretization and demonstrate the stability of a desired solution using Lyapunov’s theorem. We describe a hybrid Euler method combined with additive and multiplicative calculus for constructing an effective and robust discretization method, thereby enabling us to obtain an approximate solution to the differential equation.We performed experiments and found that the IR algorithm derived from the hybrid discretization achieved high performance

Catalogue of epidermal genes: Genes expressed in the epidermis during larval molt of the silkworm Bombyx mori

<p>Abstract</p> <p>Background</p> <p>The insect cuticle is composed of various proteins and formed during the molt under hormonal regulation, although its precise composition and formation mechanism are largely unknown. The exhaustive catalogue of genes expressed in epidermis at the molt constitutes a massive amount of information from which to draw a complete picture of the molt and cuticle formation in insects. Therefore, we have catalogued a library of full-length cDNAs (designated epM) from epidermal cells during the last larval molt of <it>Bombyx mori</it>.</p> <p>Results</p> <p>Of the 10,368 sequences in the library, we isolated 6,653 usable expressed sequence tags (ESTs), which were categorized into 1,451 nonredundant gene clusters. Seventy-one clusters were considered to be isoforms or premature forms of other clusters. Therefore, we have identified 1,380 putative genes. Of the 6,653 expressed sequences, 48% were derived from 92 cuticular protein genes (RR-1, 24; RR-2, 17; glycine-rich, 29; other classes, 22). A comparison of epM with another epidermal EST data set, epV3 (feeding stage: fifth instar, day 3), showed marked differences in cuticular protein gene. Various types of cuticular proteins are expressed in epM but virtually only RR-1 proteins were expressed in epV3. Cuticular protein genes expressed specifically in epidermis, with several types of expression patterns during the molt, suggest different types of responses to the ecdysteroid pulse. Compared with other <it>Bombyx </it>EST libraries, 13 genes were preferentially included in epM data set. We isolated 290 genes for proteins other than cuticular proteins, whose amino acid sequences retain putative signal peptides, suggesting that they play some role in cuticle formation or in other molting events. Several gene groups were also included in this data set: hormone metabolism, P450, modifier of cuticular protein structure, small-ligand-binding protein, transcription factor, and pigmentation genes.</p> <p>Conclusion</p> <p>We have identified 1,380 genes in epM data set and 13 preferentially expressed genes in epidermis at the molt. The comparison of the epM and other EST libraries clarified the totally different gene expression patterns in epidermis between the molting and feeding stages and many novel tissue- and stage-specifically expressed epidermal genes. These data should further our understanding of cuticle formation and the insect molt.</p

Efficient (nonrandom) construction and decoding for non-adaptive group testing

The task of non-adaptive group testing is to identify up to $d$ defective items from $N$ items, where a test is positive if it contains at least one defective item, and negative otherwise. If there are $t$ tests, they can be represented as a $t \times N$ measurement matrix. We have answered the question of whether there exists a scheme such that a larger measurement matrix, built from a given $t\times N$ measurement matrix, can be used to identify up to $d$ defective items in time $O(t \log_2{N})$. In the meantime, a $t \times N$ nonrandom measurement matrix with $t = O \left(\frac{d^2 \log_2^2{N}}{(\log_2(d\log_2{N}) - \log_2{\log_2(d\log_2{N})})^2} \right)$ can be obtained to identify up to $d$ defective items in time $\mathrm{poly}(t)$. This is much better than the best well-known bound, $t = O \left( d^2 \log_2^2{N} \right)$. For the special case $d = 2$, there exists an efficient nonrandom construction in which at most two defective items can be identified in time $4\log_2^2{N}$ using $t = 4\log_2^2{N}$ tests. Numerical results show that our proposed scheme is more practical than existing ones, and experimental results confirm our theoretical analysis. In particular, up to $2^{7} = 128$ defective items can be identified in less than $16$s even for $N = 2^{100}$