須鎗 弘樹

Fractional flow reserve derived from coronary CT (FFR-CT) is a noninvasive physiological technique that has shown a good correlation with invasive FFR. However, the use of FFR-CT is restricted by strict application standards, and the diagnostic accuracy of FFR-CT analysis may potentially be decreased by severely calcified coronary arteries because of blooming and beam hardening artifacts. The aim of this study was to evaluate the utility of deep learning (DL)-based coronary computed tomography (CT) data analysis in predicting invasive fractional flow reserve (FFR), especially in cases with severely calcified coronary arteries. We analyzed 184 consecutive cases (241 coronary arteries) which underwent coronary CT and invasive coronary angiography, including invasive FFR, within a three-month period. Mean coronary artery calcium scores were 963 ± 1226. We evaluated and compared the vessel-based diagnostic accuracy of our proposed DL model and a visual assessment to evaluate functionally significant coronary artery stenosis (invasive FFR < 0.80). A deep neural network was trained with consecutive short axial images of coronary arteries on coronary CT. Ninety-one coronary arteries of 89 cases (48%) had FFR-positive functionally significant stenosis. On receiver operating characteristics (ROC) analysis to predict FFR-positive stenosis using the trained DL model, average area under the curve (AUC) of the ROC curve was 0.756, which was superior to the AUC of visual assessment of significant (≥ 70%) coronary artery stenosis on CT (0.574, P = 0.011). The sensitivity, specificity, positive and negative predictive value (PPV and NPV), and accuracy of the DL model and visual assessment for detecting FFR-positive stenosis were 82 and 36%, 68 and 78%, 59 and 48%, 87 and 69%, and 73 and 63%, respectively. Sensitivity and NPV for the prediction of FFR-positive stenosis were significantly higher with our DL model than visual assessment (P = 0.0004, and P = 0.024). DL-based coronary CT data analysis has a higher diagnostic accuracy for functionally significant coronary artery stenosis than visual assessment.

Abstract To perform setup procedures including both positional and dosimetric information, we developed a CT–CT rigid image registration algorithm utilizing water equivalent pathlength (WEPL)-based image registration and compared the resulting dose distribution with those of two other algorithms, intensity-based image registration and target-based image registration, in prostate cancer radiotherapy using the carbon-ion pencil beam scanning technique. We used the data of the carbon ion therapy planning CT and the four-weekly treatment CTs of 19 prostate cancer cases. Three CT–CT registration algorithms were used to register the treatment CTs to the planning CT. Intensity-based image registration uses CT voxel intensity information. Target-based image registration uses target position on the treatment CTs to register it to that on the planning CT. WEPL-based image registration registers the treatment CTs to the planning CT using WEPL values. Initial dose distributions were calculated using the planning CT with the lateral beam angles. The treatment plan parameters were optimized to administer the prescribed dose to the PTV on the planning CT. Weekly dose distributions using the three different algorithms were calculated by applying the treatment plan parameters to the weekly CT data. Dosimetry, including the dose received by 95% of the clinical target volume (CTV-D95), rectal volumes receiving &gt; 20 Gy (RBE) (V20), &gt; 30 Gy (RBE) (V30), and &gt; 40 Gy (RBE) (V40), were calculated. Statistical significance was assessed using the Wilcoxon signed-rank test. Interfractional CTV displacement over all patients was 6.0 ± 2.7 mm (19.3 mm maximum standard amount). WEPL differences between the planning CT and the treatment CT were 1.2 ± 0.6 mm-H₂O (&lt; 3.9 mm-H₂O), 1.7 ± 0.9 mm-H₂O (&lt; 5.7 mm-H₂O) and 1.5 ± 0.7 mm-H₂O (&lt; 3.6 mm-H₂O maxima) with the intensity-based image registration, target-based image registration, and WEPL-based image registration, respectively. For CTV coverage, the D95 values on the planning CT were &gt; 95% of the prescribed dose in all cases. The mean CTV-D95 values were 95.8 ± 11.5% and 98.8 ± 1.7% with the intensity-based image registration and target-based image registration, respectively. The WEPL-based image registration was CTV-D95 to 99.0 ± 0.4% and rectal Dmax to 51.9 ± 1.9 Gy (RBE) compared to 49.4 ± 9.1 Gy (RBE) with intensity-based image registration and 52.2 ± 1.8 Gy (RBE) with target-based image registration. The WEPL-based image registration algorithm improved the target coverage from the other algorithms and reduced rectal dose from the target-based image registration, even though the magnitude of the interfractional variation was increased.

Abstract To ensure the safety of railroad operations, it is important to monitor and forecast track geometry irregularities. A higher safety requires forecasting with higher spatiotemporal frequencies, which in turn requires capturing spatial correlations. Additionally, track geometry irregularities are influenced by multiple exogenous factors. In this study, a method is proposed to forecast one type of track geometry irregularity, vertical alignment, by incorporating spatial and exogenous factor calculations. The proposed method embeds exogenous factors and captures spatiotemporal correlations using a convolutional long short-term memory. The proposed method is also experimentally compared with other methods in terms of the forecasting performance. Additionally, an ablation study on exogenous factors is conducted to examine their individual contributions to the forecasting performance. The results reveal that spatial calculations and maintenance record data improve the forecasting of vertical alignment.

Current deep learning-based cerebral aneurysm detection demonstrates high sensitivity, but produces numerous false-positives (FPs), which hampers clinical application of automated detection systems for time-of-flight magnetic resonance angiography. To reduce FPs while maintaining high sensitivity, we developed a multidimensional convolutional neural network (MD-CNN) designed to unite planar and stereoscopic information about aneurysms. This retrospective study enrolled time-of-flight magnetic resonance angiography images of cerebral aneurysms from three institutions from June 2006 to April 2019. In the internal test, 80% of the entire data set was used for model training and 20% for the test, while for the external tests, data from different pairs of the three institutions were used for training and the remaining one for testing. Images containing aneurysms &amp;gt; 15 mm and images without aneurysms were excluded. Three deep learning models [planar information-only (2D-CNN), stereoscopic information-only (3D-CNN), and multidimensional information (MD-CNN)] were trained to classify whether the voxels contained aneurysms, and they were evaluated on each test. The performance of each model was assessed using free-response operating characteristic curves. In total, 732 aneurysms (5.9 ± 2.5 mm) of 559 cases (327, 120, and 112 from institutes A, B, and C; 469 and 263 for 1.5T and 3.0T MRI) were included in this study. In the internal test, the highest sensitivities were 80.4, 87.4, and 82.5%, and the FPs were 6.1, 7.1, and 5.0 FPs/case at a fixed sensitivity of 80% for the 2D-CNN, 3D-CNN, and MD-CNN, respectively. In the external test, the highest sensitivities were 82.1, 86.5, and 89.1%, and 5.9, 7.4, and 4.2 FPs/cases for them, respectively. MD-CNN was a new approach to maintain sensitivity and reduce the FPs simultaneously.

<title>Abstract</title>The selection of genes that are important for obtaining gene expression data is challenging. Here, we developed a deep learning-based feature selection method suitable for gene selection. Our novel deep learning model includes an additional feature-selection layer. After model training, the units in this layer with high weights correspond to the genes that worked effectively in the processing of the networks. Cancer tissue samples and adjacent normal pancreatic tissue samples were collected from 13 patients with pancreatic ductal adenocarcinoma during surgery and subsequently frozen. After processing, gene expression data were extracted from the specimens using RNA sequencing. Task 1 for the model training was to discriminate between cancerous and normal pancreatic tissue in six patients. Task 2 was to discriminate between patients with pancreatic cancer (n = 13) who survived for more than one year after surgery. The most frequently selected genes were <italic>ACACB</italic>, <italic>ADAMTS6</italic>, <italic>NCAM1</italic>, and <italic>CADPS</italic> in Task 1, and <italic>CD1D</italic>, <italic>PLA2G16</italic>, <italic>DACH1</italic>, and <italic>SOWAHA</italic> in Task 2. According to The Cancer Genome Atlas dataset, these genes are all prognostic factors for pancreatic cancer. Thus, the feasibility of using our deep learning-based method for the selection of genes associated with pancreatic cancer development and prognosis was confirmed.

PURPOSE: Computed tomography (CT)-based attenuation correction (CTAC) in single-photon emission computed tomography (SPECT) is highly accurate, but it requires hybrid SPECT/CT instruments and additional radiation exposure. To obtain attenuation correction (AC) without the need for additional CT images, a deep learning method was used to generate pseudo-CT images has previously been reported, but it is limited because of cross-modality transformation, resulting in misalignment and modality-specific artifacts. This study aimed to develop a deep learning-based approach using non-attenuation-corrected (NAC) images and CTAC-based images for training to yield AC images in brain-perfusion SPECT. This study also investigated whether the proposed approach is superior to conventional Chang's AC (ChangAC). METHODS: In total, 236 patients who underwent brain-perfusion SPECT were randomly divided into two groups: the training group (189 patients; 80%) and the test group (47 patients; 20%). Two models were constructed using Autoencoder (AutoencoderAC) and U-Net (U-NetAC), respectively. ChangAC, AutoencoderAC, and U-NetAC approaches were compared with CTAC using qualitative analysis (visual evaluation) and quantitative analysis (normalized mean squared error [NMSE] and the percentage error in each brain region). Statistical analyses were performed using the Wilcoxon signed-rank sum test and Bland-Altman analysis. RESULTS: U-NetAC had the highest visual evaluation score. The NMSE results for the U-NetAC were the lowest, followed by AutoencoderAC and ChangAC (P < 0.001). Bland-Altman analysis showed a fixed bias for ChangAC and AutoencoderAC and a proportional bias for ChangAC. ChangAC underestimated counts by 30-40% in all brain regions. AutoencoderAC and U-NetAC produced mean errors of <1% and maximum errors of 3%, respectively. CONCLUSION: New deep learning-based AC methods for AutoencoderAC and U-NetAC were developed. Their accuracy was higher than that obtained by ChangAC. U-NetAC exhibited higher qualitative and quantitative accuracy than AutoencoderAC. We generated highly accurate AC images directly from NAC images without the need for intermediate pseudo-CT images. To verify our models' generalizability, external validation is required.

<p>鉄道事業者にとって，鉄道の軌道形状の変形である軌道狂いの予測は，安全性の確保や保守計画の管理のために重要である．本論文では，新幹線軌道の高低狂いの時空間予測のために， convolutional long short-term memory (ConvLSTM) に基づく深層予測モデルを提案する．提案モデルは，高速検査列車が測定した軌道狂いや動揺などの時空間データだけでなく，軌道構造や地盤などの静的なカテゴリカルデータ，保守作業有無の２値時系列データを用いて学習される．学習では，回帰タスクでは十分な精度が達成できなかったため，高低狂いを２mm単位に量子化したうえで分類タスクとして定式化し，分類精度の観点から予測精度を評価している．実データを用いた実験評価では，高低狂いが進行している要注意地点において，提案モデルは，軌道構造や地盤などの静的なデータや保守作業日記録の時系列データを用いた方がより高い予測性能を示す結果が得られている．</p>

STUDY DESIGN: Retrospective analysis of magnetic resonance imaging (MRI). OBJECTIVE: The aim of this study was to evaluate the performance of our convolutional neural network (CNN) in differentiating between spinal schwannoma and meningioma on MRI. We compared the performance of the CNN and that of two expert radiologists. SUMMARY OF BACKGROUND DATA: Preoperative discrimination between spinal schwannomas and meningiomas is crucial because different surgical procedures are required for their treatment. A deep-learning approach based on CNNs is gaining interest in the medical imaging field. METHODS: We retrospectively reviewed data from patients with spinal schwannoma and meningioma who had undergone MRI and tumor resection. There were 50 patients with schwannoma and 34 patients with meningioma. Sagittal T2-weighted magnetic resonance imaging (T2WI) and sagittal contrast-enhanced T1-weighted magnetic resonance imaging (T1WI) were used for the CNN training and validation. The deep learning framework Tensorflow was used to construct the CNN architecture. To evaluate the performance of the CNN, we plotted the receiver-operating characteristic (ROC) curve and calculated the area under the curve (AUC). We calculated and compared the sensitivity, specificity, and accuracy of the diagnosis by the CNN and two board-certified radiologists. RESULTS: . The AUC of ROC curves of the CNN based on T2WI and contrast-enhanced T1WI were 0.876 and 0.870, respectively. The sensitivity of the CNN based on T2WI was 78%; 100% for radiologist 1; and 95% for radiologist 2. The specificity was 82%, 26%, and 42%, respectively. The accuracy was 80%, 69%, and 73%, respectively. By contrast, the sensitivity of the CNN based on contrast-enhanced T1WI was 85%; 100% for radiologist 1; and 96% for radiologist 2. The specificity was 75%, 56, and 58%, respectively. The accuracy was 81%, 82%, and 81%, respectively. CONCLUSION: We have successfully differentiated spinal schwannomas and meningiomas using the CNN with high diagnostic accuracy comparable to that of experienced radiologists. LEVEL OF EVIDENCE: 4.

<p>継続的な治療における今後の治療方針の決定や治療効果の評価のために，各治療のステップに応じてCT画像を複数の時期で撮影することが一般的に行われている．したがって，現在の状態を写したCT画像中の注目すべきスライスが，過去に撮像したCT画像のどのスライスに対応しているかを特定する必要がある．そこで，深層距離学習を用いて異なる時期に撮影したCT画像中の各スライス間の類似度を測り，注目スライスと最も類似したスライスを特定する方法論を提案することが本研究の目的である． モデルの学習には，クエリー，ポシティブ，ネガティブの3つの画像を1組にしたトリプレットロスを利用した．注目するスライスの上下β枚のスライスは臓器の構造が類似していると仮定し，学習時のポシティブ画像として扱い，それ以外のスライスをネガティブ画像とした．9,062枚のCT画像を利用し学習を行い，テストでは，異なる時期に撮影されたCT画像を利用した．学習結果のモデルを用いて，時期が異なるCTスライスの位置を推定したところ，経験豊富な放射線技師の視覚評価と同等の結果を得ることができた．</p>

<p>核医学検査のひとつにSPECTがある．SPECTにおいて体組織による吸収を減弱と呼び，ノイズの原因となる．現在利用されている，CTを用いた減弱補正は有効性が高い．しかし，CT撮影を行うことによる放射線被ばくは健康への悪影響が懸念される．本論文ではU-Netを用いて，減弱補正を再現する手法を提案する．一人の患者につき，補正を行っていないSPECT，CTAC法によって補正されたSPECT画像のペアを用意する．後者を教師画像，前者を入力画像として学習を行った．作成したモデルによって，CTAC法による減弱補正を十分に再現することができた．</p>

<p>乳がんは、遺伝子の特性によって大きく4つのサブタイプに分けられる。乳がんの治療方針はサブタイプによって異なるため、サブタイプを迅速かつ正確に判断する必要がある。現在、患者からがん細胞を採取する方法によってサブタイプの分類が行われている。この方法では、患者は肉体的・心的苦痛や金銭的なコスト負担などを強いられる。一方で、乳がんの診断の際にはMRIなど画像診断も用いられている。しかしながら、MRI画像から乳がんのサブタイプを同定することは専門医でも難しい。そこで、機械学習によって患者のMRI画像からサブタイプを分類することができれば、患者の負担を軽減することが可能であると考えた。本研究では、Residual Networkを使用し、乳がんのサブタイプ分類を行う手法を提案する。提案したネットワークで、実際の乳がん患者から撮影したMRI画像を分類した結果、67.3%の結果を得た。</p>

<p>脳動脈瘤はくも膜下出血と呼ばれる重大疾患の主要因であり，破裂すると多くの場合死に至るため，医師の診断による早期発見・治療が求められる． 医師の診断を支援する目的として，これまでに，磁気共鳴血管画像（Magnetic Resonance Angiography; MRA）を用いて脳動脈瘤を自動検出する機械学習手法がいくつか提案されている． 近年では，画像認識タスクで広く利用されてる畳み込みニューラルネットワーク（Convolutional Neural Networks; CNN）を用いた脳動脈瘤検出手法が提案されており，高い精度で瘤を検出できることで知られている． これまでに提案されているCNNを用いた脳動脈瘤検出手法は，いずれも2次元画像を入力としたネットワーク構成となっており，動脈の屈折部に隠れた瘤が正確に検出することが難しいという問題があった． そこで本研究では，入力として2次元画像を用いたネットワークと3次元ボクセルを用いたネットワークで検出感度を比較し，その精度を評価する． 実験の結果，2Dネットワークと比較し3Dネットワークでは，高い検出感度で少ない誤検出率を達成した．</p>

<p>高精度かつ高速な医療画像のセグメンテーションは，多くの医療現場において重要な課題である．現在ではその手法の一つとして，エネルギー最小化問題に基づくグラフカットが利用されている．しかし，グラフカットでは，隣接するピクセル値が類似している場合，完全かつ自動的にセグメンテーションを行うことは困難である．この問題には多くの対策があるが，そのほとんどは実行速度という点で適していない．それに対し，深層学習による手法は，複雑な特徴を獲得することができるため，自動セグメンテーションが可能である．本研究では，Residual Unitによって拡張した3D U-Netと，セグメンテーション結果を修正する3DCNNを組み込んだモデルを提案する．</p>

We study large deviation properties of probability distributions with either a compact support or a fat tail by comparing them with q-deformed exponential distributions. Our main result is a large deviation property for probability distributions with a fat tail. (C) 2015 Elsevier B.V. All rights reserved.

Stirling approximation of the factorials and multinominal coefficients are generalized based on the κ-generalized functions introduced by Kaniadakis. We have related the κ-generalized multinominal coefficients to the κ-entropy by introducing a new κ-product operation, which exists only when κ ≠ 0.

The law of multiplicative error is presented for independent observations and correlated observations represented by the q-product, respectively. We obtain the standard log-normal distribution in the former case and the log-q-normal distribution in the latter case. Queiros' q-log normal distribution is also reconsidered in the framework of the law of error. These results are presented with mathematical conditions to give rise to these distributions.

An axiomatic definition is given for the q-gamma function Gamma(q)(x), q is an element of R, q &gt; 0, x is an element of R of Tsallis (non-extensive) statistical physics, the continuous analogue of the q-factorial of Suyari [H. Suyari, Physica A 368 (1) (2006) 63], and the q-analogue of the gamma function Gamma(x) of Euler and Gauss. A working definition in closed form, based oil the Hurwitz and Riemann zeta functions (including their analytic continuous), is shown to Satisfy this definition. Several relations involving the q-gamma and other functions are obtained. The (q,q)-polygamma functions psi((m))(q,q) (x), m is an element of N, defined by successive derivatives of In(q) Gamma(q)(x), where In(q) a = (1 - q)(-1)(a(1-q) - 1), a &gt; 0 is the q-logarithmic function, are also reported. The new functions are used to calculate the inferred probabilities and multipliers for Tsallis systems with finite numbers of particles N &lt;&lt; infinity. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

We reformulate the Gauss' law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.

One of the promising approaches to how to derive a non-Gaussian distribution is generalizing the log-likelihood function in Gauss' law of error. In this contribution, it is shown that a generalization of the log-likelihood function in Gauss' law of error is equivalent to a generalization of the average. The proof is given for the case of the two-parameter generalized likelihood function, which unifies some known one-parameter generalizations.

Based on the one-parameter generalization of Shannon-Khinchin (SK) axioms presented by one of the authors, and utilizing a tree-graphical representation, we have developed for the first time a two-parameter generalization of the SK axioms in accordance with the two-parameter entropy introduced by Sharma, Taneja, and Mittal. The corresponding unique theorem is also proved. It is found that our two-parameter generalization of Shannon additivity is a natural consequence from the Leibniz product rule of the two-parameter Chakrabarti-Jagannathan difference operator. (c) 2007 Elsevier B.V. All rights reserved.

Shannon additivity one of the Shannon-Khinchin axioms, determines a lower bound of average code length of a D-ary code tree. As its generalization, the generalized Shannon additivity is applied to determining a lower bound of average description length of a rooted tree which we call "q-generalized D-ary code tree ". The generalized Shannon additivity is one of the generalized Shannon-Khinchin axioms for Tsallis entropy. This reveals that Tsallis entropy is a lower bound of average description length for the q-generalized D-ary code tree.

We present q-Stirling's formula, q-multinomial coefficient, one-to-one correspondence between q-multinominal coefficient and Tsallis entropy, q-Pascal's triangle and a conjecture on the q-central limit theorem in Tsallis statistics for the generalization of the well-known fundamental formulas to systems exhibiting power-law behaviors. The main approach is based on the q-product, uniquely determined by Tsallis entropy, which has already been successfully applied to our recent proof of the law of error in Tsallis statistics. (c) 2006 Elsevier B.V. All rights reserved.

In order to theoretically explain the ubiquitous existence of power-law behavior such as chaos and fractals in nature, Tsallis entropy has been successfully applied to the generalization of the traditional Boltzmann-Gibbs statistics, the fundamental information measure of which is Shannon entropy. Tsallis entropy S-q is a one-parameter generalization of Shannon entropy S-1 in the sense that lim(q--&gt;1) S-q = S-1. The generalized statistics using Tsallis entropy are referred to as Tsallis statistics. In order to present the law of error in Tsallis statistics as a generalization of Gauss' law of error and prove it mathematically, we apply the new multiplication operation determined by q-logarithm and q-exponential, the fundamental functions in Tsallis statistics, to the definition of the likelihood function in Gauss' law of error. The present maximum-likelihood principle (MLP) leads us to determine the so-called q-Gaussian distribution, which coincides with one of the Tsallis distributions derived from the maximum entropy principle for Tsallis entropy under the second moment constraint.

For a unified description of power-law behaviors such as chaos, fractal and scale-free network, Tsallis entropy has been applied to the generalization of the traditional Boltzmann-Gibbs statistics as a fundamental information measure. Tsallis entropy S, is an one-parameter generalization of Shannon entropy S, in the sense that lim(q -&gt; 1) S-q = S-1. The generalized Boltzmann-Gibbs statistics by means of Tsallis entropy is nowadays called Tsallis statistics. The main approach in Tsallis statistics has been the maximum entropy principle, but there have been missing some fundamental mathematical formulae such as law of error, q-Stirling's formula and q-multinomial coefficient. Recently, we have succeeded in proving law of error in Tsallis statistics using the q-product uniquely determined by Tsallis entropy. Along the same lines as the proof, we present q-Stirling's formula, q-multinomial coefficient and a conjecture on the q-central limit theorem in Tsallis statistics.

Tsallis entropy, one-parameter generalization of Shannon entropy, has been often discussed in statistical physics as a new information measure. This new information measure has provided many satisfactory physical interpretations in nonextensive systems exhibiting chaos or fractal. We present the generalized Shannon-Khinchin axioms to nonextensive systems and prove the uniqueness theorem rigorously. Our results show that Tsallis entropy is the simplest among all nonextensive entropies. By the detailed comparisons of our axioms with the previously presented two sets of axioms, we reveal the peculiarity of pseudoadditivity as an axiom. In this correspondence, the most fundamental basis for Tsallis entropy as information measure is established in the information-theoretic framework.

The 1/f spectra that appear in electroencephalogram data are among the characteristics that appear in the wide range of self-organizing phenomena encompassing both physical and sociological phenomena. The fact that they appear across the various objects suggests that the underlying cause of the 1/f spectra can be elucidated by using a simplified model that does not depend on the detailed structure of the objects. This paper, treating the electroencephalogram as a macro-quantity of neuron activities, demonstrates the existence of a self-similar solution through the spatial-temporal coarse-graining of a neural network, which is a simplified model of the brain. The self-similar solution in fact leads to the derivation of a 1/f spectrum. (C) 2003 Wiley Periodicals, Inc.

K work Sau Fa (1998 J. Phys. A: Math. Gen. 318159) has shown an inequality 'S(AB) less than or equal to S(A) + S(B) + (1 - q)S(A)S(B)' for two interacting systems A and B. A typical example of S(A) is the Tsallis entropy as stated in his paper. However, there exist many counterexamples to the above inequality. The reason leading to the incorrect result is also presented.

We present the most concise set of axioms for Tsallis entropy, and rigorously prove the uniqueness theorem. This set of axioms consists of only two distinct additivities: pseudoadditivity and Shannon additivity. We then compare our axioms with the axioms presented by Santos. The peculiarity of pseudoadditivity as an axiom for Tsallis entropy is also discussed.

The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of Shannon entropy. Information content in a nonextensive system is obtained uniquely from generalized axioms by replacing the usual additivity with pseudoadditivity. The satisfaction of the form invariance of the pseudoadditivity of nonextensive entropy and its information content is found to require the normalization of nonextensive entropies. The proposed principle requires the same normalization as that derived previously [A.K. Rajagopal and S. Abe, Phys. Rev. Lett. 83, 1711 (1999)], but is simpler and establishes a basis for the systematic definition of various entropies in nonextensive systems.

The behavior of atoms in the Jaynes-Cummings model has been discussed and analyzed extensively to date in terms of transition probability and entropy. In this paper, the Jaynes-Cummings model is described in terms of a quantum-mechanical channel expressing the state transition. For this channel, von Neumann entropy and quantum mutual entropy are derived. By means of these quantities, the variation of the atomic state and its nonreciprocity in this model are discussed. (C) 2000 Scripta Technica.

The concrete mathematical formula of the average generalization errors and their learning curves of a simple perceptron are derived as rigorously as possible, which means rigorous derivation except for using one approximation called "self-averaging" in statistical physics. These learning curves can be plotted by numerically computing the obtained formulas and the behavior of their learning curves are easily found. In particular, it is shown that in case of binary weights as the number of examples increases, the student perceptron suddenly freezes into the state of reference perceptron at a certain number of examples per weight and above that point the average generalization error is constantly zero. This phenomena is called "perfect generalization". Our results are in good agreement with those by the statistical method.

We describe the practical implementation of the nonlinear (chaos) time series analysis based on the paradigm of deterministic chaos. Some important techniques of statistical test for nonlinearity, phase space reconstruction, and nonlinear prediction are discussed with some applications to finance. The use of the nonlinear time series analysis is illustrated with particular emphasis on issues of choices of time delay coordinate and embedding parameters. Finally, we propose the weighted embedding method which is found to work well in financial applications.

The general quantum communication process, with the optical communication process as its actual model, is strictly formulated mathematically in terms of Ohya's quantum mechanics channel, which describes the state change. Until recently the decay process and the amplifier process have been described as actual communication processes, using the concepts of the channel and its extension, lifting. Based on that description, the error probability and SNP are derived. This paper introduces a new system called the control system into the communication process, and provides the squeezed vacuum state as the quantum state of the system. We examine how conventional communication efficiency can be improved by the squeezed vacuum state, using the error probability. (C) 1998 Scripta Technica.

1994年, Bell研のShorは公開鍵暗号の基礎である素因数分解を量子コンピュータ上で多項式時間で解くことのできるアルゴリズムを発見した.この発見を機に, 量子コンピュータの研究が一躍脚光をあびることとなった.そして, 今日まで多くの研究者が「古典的な計算機では膨大な計算量を要する問題を量子コンピュータで解くと, どれほどその計算量が減少するか」という問題に挑んでいる.本論文では, 組合せ最適化問題を解くために, その組合せ最適化問題の目的関数の値すべてを多項式時間で計算できる量子回路を構成する.

1994年, Bell研のShorは公開鍵暗号の基礎である素因数分解を量子コンピュータ上で多項式時間で解くことのできるアルゴリズムを発見した.この発見を機に, 量子コンピュータの研究が一躍脚光をあびることとなった.そして, 今日まで多くの研究者が「古典的な計算機では膨大な計算量を要する問題を量子コンピュータで解くと, どれほどその計算量が減少するか」という問題に挑んでいる.本論文では, 組合せ最適化問題を解くために, その組合せ最適化問題の目的関数の値すべてを多項式時間で計算できる量子回路を構成する.

Jaynes-Cummingsモデルにおける原子の振舞いは, これまでに遷移確率やエントロピー等を用いて多くの解析や議論がなされてきた.本論文では, 状態変換を表す量子力学的チャネルを用いてJaynes-Cummingsモデルを記述し, そのチャネルに対して, von Neumannエントロピー及び量子相互エントロピーを導出し, これらを用いてこのモデルにおける原子の状態の変化及び非可逆性について議論する.