Faster point compression for elliptic curves of $j$-invariant $0$

Предлагается новый метод сжатия двух точек (до $2\lceil\log_2(q)\rceil + 4$ битов) для эллиптической кривой $E_b : y^2 = x^3 + b$ с $j$-инвариантом $0$ над конечным полем $\mathbb{F}_q$ при $q\equiv 1\pmod 3$. Точнее, получены простые явные формулы преобразования координат $x_0, y_0, x_1, y_1$ двух точек $P_0, P_1 \in E_b(\mathbb{F}_q)$ в два элемента $\mathbb{F}_q$, дополненные четырьмя битами. Для восстановления (на этапе разжатия) точек $P_0, P_1$ предлагается извлекать корень шестой степени $\sqrt[6]{Z} \in \mathbb{F}_q$ из некоторого элемента $Z \in \mathbb{F}_q$. Известно, что при $q\equiv 3\pmod 4$, $q\not\equiv 1\pmod {27}$ это можно сделать с использованием только одного возведения в степень в $\mathbb{F}_q$. Таким образом, новый метод сжатия оказывается значительно быстрее классического метода для координат $x_0, x_1$, в котором разжатие использует два возведения в степень в $\mathbb{F}_q$. Показано, что новый метод можно использовать для сжатия одной $\mathbb{F}_{q^2}$-точки на кривой $E_b$ с $b \in \mathbb{F}_{q^2}^*$.

Efficacy of the acupressure wrist-ankle strap in mild insomnia patients with anxiety disorders: study protocol for a randomized controlled trial

Background Insomnia is very common in current society, and patients are often accompanied by a certain degree of anxiety, depression, etc. Recent studies have found that the hypothalamic-pituitary-adrenal (HPA) axis excitement-inhibition state is an important indicator of sleep quality. Wrist-ankle acupuncture (WAA) is safe and effective for insomnia. Based on WAA theory, the acupressure wrist-ankle straps are portable WAA point compression straps that can treat diseases by automatically applying pressure to the treatment location and being operated by patients themselves. We design this trial to evaluate the clinical effect of the acupressure wrist-ankle strap in the treatment of mild insomnia patients with anxiety disorders. Methods/design This trial is a parallel-design, patients-assessor blinded, randomized, sham-controlled. In total, 114 patients diagnosed with mild insomnia and anxiety disorders will be randomly assigned into two groups, the acupressure wrist-ankle strap group or the non-acupressure wrist-ankle strap group; they will receive treatments for eight weeks with five sessions each week. Rating scales, sleep monitors, and laboratory tests will be used to observe the clinical effect. From the perspective of the circadian secretion of peripheral blood-related hormones in the hypothalamic-pituitary-adrenal (HPA) axis, the possible mechanism of acupressure wrist-ankle straps for treating insomnia is studied. Discussion The results of this study will confirm the efficacy of acupressure wrist-ankle strap in treating mild insomnia patients with anxiety disorder and whether its mechanism is related to the HPA axis. The acupressure wrist-ankle strap may become a pure physical, no side effect treatment of mild insomnia. Trial registration Chinese Clinical Trial Registry ChiCTR2000039352. Registered on 24 October 2020.

Efficacy of The Acupressure Wrist-Ankle Strap Combined With CBTI In Mild Insomnia Patients With Anxiety Disorders: Study Protocol For A Randomized Controlled Trial

Background: Insomnia is very common in current society, and patients are often accompanied by a certain degree of anxiety, depression, etc. Recent studies have found that the hypothalamic-pituitary-adrenal (HPA) axis excitement-inhibition state is an important indicator of sleep quality. Wrist-ankle acupuncture (WAA) is safe and effective for insomnia. The acupressure wrist-ankle straps, based on WAA theory, is a portable WAA point compression strap, which can treat diseases by automatically applying pressure to the treatment location and be operated by patients themselves. We design this trial to evaluate the clinical effect of the acupressure wrist-ankle strap in the treatment of mild insomnia patients with anxiety disorders. Methods/design: This trial is a parallel-design, patients-assessor blinded, randomized, sham-controlled. In total, 108 patients diagnosed with mild insomnia patients with anxiety disorders will be randomly equally assigned into two groups, acupressure wrist-ankle strap group or non-acupressure wrist-ankle strap group; they will receive treatments for 8 weeks with 5 sessions each week. Rating scales, sleep monitor and laboratory tests will be used to observe the clinical effect. From the perspective of the circadian secretion of peripheral blood-related hormones in the hypothalamic- pituitary- adrenal (HPA) axis, the possible mechanism of acupressure wrist-ankle straps for treating insomnia is studied.Discussion: The results of this study will confirm the efficacy of acupressure wrist-ankle strap combined with CBTI in the treatment of mild insomnia patients with anxiety disorder and whether its mechanism is related to HPA axis. The acupressure wrist-ankle strap may become a pure physical, no side effect treatment of mild insomnia.Trial registration: Chinese Clinical Trial Registry (identifier: ChiCTR2000039352; registration date: 24 October 2020).

Diagnostic Dilemma of Recurrent Pulmonary Embolism

Popliteal venous aneurysms are rare vascular disorders associated with a high risk of pulmonary embolism. We present the case of a 56-year-old woman hospitalized for a third episode of unprovoked pulmonary embolism. Venous ultrasonography identified a popliteal aneurysm, repeatedly missed by two-point compression venous ultrasonography, which was eventually confirmed by a magnetic resonance examination. Because of its highly symptomatic nature despite optimal anticoagulant treatment, the decision was made to undergo surgery, consisting of aneurysmectomy followed by patch angioplasty. The goal of this paper is to report a rare case of popliteal venous aneurysm and its treatment strategies and postoperative evolution.