1. The owner of the private key does not know the value of m such that C1 = sm(a, b) and C2 = s −m(a, b), and thus he/she can not compute L(C1, C2). 2. If sλ(a, b) = 3 modulo n , then L(a, b) is not invertible modulo n. It follows that the owner of the private key can not decrypt the cipher C = (C1, C2) since he/she can not compute L(C1,C2) L(a,b) . In this short note, in order to decrypt the c...

INTRODUCTION Anomalies in the craniovertebral junction may be a rare cause of syncope. The mechanisms of syncope related to craniovertebral junction anomaly remain unknown.We present an extremely rare case with anomaly in the craniovertebral junction and syncope, and discuss the mechanism of the syncope. CASE PRESENTATION A 10-year-old Japanese boy with a congenital anomaly in the cranioverte...

This note investigates πT,c1,c2(a1,a2)=P(supt∈[0,T](σ1B(t)−c1t)>a1,supt∈[0,T](σ2B(t)−c2t)>a2), where {B(t):t≥0} is a standard Brownian motion, with T>0,σ1,σ2>0,c1,c2∈R. We derive explicit formula for the probability πT,c1,c2(a1,a2) and find its asymptotic behavior both in so called many-source high-threshold regimes.

UNLABELLED Two paintings, O1 and O2, were split into their luminance (grayscale) components L1, L2 and their color components C1, C2. The two color components, C1, C2, were transparently superimposed. Adding the grayscale of the first painting (= C1 + C2 + L1) looked like the original O1, while adding the grayscale of the second painting (= C1 + C2 + L2) looked like the original O2. CONCLUSIO...

Anomalous vertebral artery (VA), commonly the persistent first intersegmental artery (FIA) is often seen with congenital atlantoaxial dislocations (AAD). An unusual redundant/ectatic loop of VA passing below the C1 (upside down VA) has been described below and appears to be different from FIA. The operative technique to protect it while C1-2 joint manipulation has been described. A 35 year old ...

OBJECTIVE  The purpose of this comparison case study is to show a potential complication associated with atlantoaxial fusion, and the preoperative evaluation that could help to avoid it. BACKGROUND DATA  The use of lateral mass screw fixation in atlantoaxial fusion has provided surgeons the ability to create rigid fixation, with a high success rate of fusion. While the use of screws for fixat...

Metrizamide is useful for evaluating both posterior fossa and the cervical spinal canal [1, 2]. Because the contrast material is diluted by spinal fluid enroute from the lumbar region to the cervical spinal canal, the C1-C2 puncture technique has been advocated as the most suitable approach for instillation of contrast material [3]. The procedure is safe and without great technical difficulties...

This paper presents an optimum color conversion from the 3D RGB space into a 2D selected space to the purpose of pattern recognition. The method is based on the Karhunen-Loève transform (KLT), also known as Principal Component Analysis (PCA). The resulted 2D space is defined by the two color components (called C1 and C2), corresponding to the two largest eigenvalues of the RGB pixel covariance ...