Figurate primes and Hilbert's 8th problem

In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures related with figurate primes and Hilbert's 8th problem, including Goldbach's conjecture, twin primes conjecture and Catalan's conjecture as well.Comment: 7 pages, 1 figur

Surgical treatment of primary hepatic neuroendocrine tumor diagnosed by Al18F-NOTA-Octreotide PET/CT: a case report

Neuroendocrine tumors (NETs) are a heterogeneous group of tumors originating from peptide-producing neurons and neuroendocrine cells. The liver is the most common site of metastasis for NETs, while primary hepatic neuroendocrine tumors (PHNETs) are exceedingly rare. While somatostatin receptor scintigraphy (SRS) has demonstrated superior efficacy compared to [18F]FDG PET imaging in the diagnosis of neuroendocrine tumors, [18F]AlF-NOTA-Octreotide ([18F]AlF-OC) PET/CT also exhibits specific advantages over SRS. This article presents a case study of a patient with a liver mass who underwent sequential [18F]FDG and [18F]AlF-OC PET/CT scans, ruling out hepatocellular carcinoma and confirming the diagnosis of PHNETs. Subsequently, the patient underwent surgical treatment. From another perspective, [18F]AlF-OC exhibits distinct advantages. The postoperative pathology revealed a PHNETs, which further emphasizes its clinical rarity

Explore postgraduate biomedical engineering course integration between medical signal processing and drug development: example for drug development in brain disease

Medical signal processing is a compulsory course in our university’s undergraduate biomedical engineering programme. Recently, application of medical signal processing in supporting new drug development has emerged as a promising strategy in neurosciences. Here, we discuss the curriculum reformation in biomedical signal processing course in the context of drug development and application in central nervous system, with a particular emphasis in knowledge integration

Specific frequency bands of amplitude low-frequency fluctuations in memory-related cognitive impairment: predicting Alzheimer’s disease

Resting-state functional magnetic resonance imaging was utilized to measure the amplitude low frequency fluctuations (ALFF) in human subjects with Alzheimer’s disease (AD) and normal control (NC). Two specific frequency bands (Slow5: 0.01-0.027Hz and Slow4: 0.027-0.073Hz) were analysed in the main cognitive control related four subregions of the right ventral lateral prefrontal cortex (VLPFC), i.e. IFJ, posterior-VLPFC, mid-VLPFC, and anterior-VLPFC. Differences in ALFF values between the AD and the NC group were found throughout the subregions of the right VLPFC. Compared to normal control group, decreased ALFF values were observed in AD patients in the IFJ (in two given frequency bands), and the mid-VLPFC (in Slow5). In contrast, increased ALFF valued were observed in AD patients in the posterior- and anterior-VLPFC (in both Slow5 and Slow4), and also in the mid-VLPFC in Slow4. Moreover, significant ALFF differences between the IFJ and three other subregions of the right VLPFC were found. Furthermore, ALFF values in the right VLPFC showed significant correlations with the time course of disease. Taken together, our findings suggest that AD patients have largely abnormalities in intrinsic neural oscillations which are in line with the AD pathophysiology, and further reveal that the abnormalities are dependent on specific frequency bands. Thus, frequency-domain analyses of the ALFF may provide a useful tool to investigate the AD pathophysiology

Onset of nonlinear electroosmotic flow under AC electric field

Nonlinearity of electroosmotic flows (EOFs) is ubiquitous and plays a crucial role in the mass and energy transfer in ion transport, specimen mixing, electrochemistry reaction, and electric energy storage and utilizing. When and how the transition from a linear regime to a nonlinear one is essential for understanding, prohibiting or utilizing nonlinear EOF. However, suffers the lacking of reliable experimental instruments with high spatial and temporal resolutions, the investigation of the onset of nonlinear EOF still stays in theory. Herein, we experimentally studied the velocity fluctuations of EOFs driven by AC electric field via ultra-sensitive fluorescent blinking tricks. The linear and nonlinear AC EOFs are successfully identified from both the time trace and energy spectra of velocity fluctuations. The critical electric field ($E_{A,C}$) separating the two statuses is determined and is discovered by defining a generalized scaling law with respect to the convection velocity ($U$) and AC frequency ($f_f$) as $E_{A,C}$~${f_f}^{0.48-0.027U}$. The universal control parameters are determined with surprising accuracy for governing the status of AC EOFs. We hope the current investigation could be essential in the development of both theory and applications of nonlinear EOF

Sensitization patterns and minimum screening panels for aeroallergens in self-reported allergic rhinitis in China

Optimization of skin prick test (SPT) panels, especially in view of significant differences in sensitizations patterns within different geographical areas, is an unmet need within China. Our aim was to assess the patterns and clinical relevance of aeroallergen sensitizations in allergic rhinitis (AR) and define the minimal battery of SPT allergens, classified according to the Koppen-Geiger climate map. Overall, 7148 subjects with self-reported AR completed a standard questionnaire and were assessed for sensitization to relevant allergens by SPT. 6340 (88.7%) patients had at least one positive skin prick reaction, and demonstrated unique sensitization patterns by stratification with age, gender, and geographic region. Sensitization to house dust mites (HDM) was highest in south China, whereas the three most prevalent aeroallergens were mugwort, ragweed and dandelion pollen in north-west China. Higher sensitization rates and multiple sensitizations were associated with AR comorbidities. Eight allergens (Der f, mugwort, Blatella, hazel, goosefoot, Penicillium notatum, animal dander and Der p) allowed identification > 96% of sensitized subjects in central China. Differences in optimal panels were observed between regions, with five to six allergens being sufficient for north-east, north-west and south China. These SPT panels may provide a cost-effective tool for screening sensitized patients in China

Case Report: Camrelizumab combined with gemcitabine and oxaliplatin in the treatment of advanced intrahepatic cholangiocarcinoma: a case report and literature review

Intrahepatic cholangiocarcinoma (ICC) is one of the most common invasive malignant tumors, with a 5-year survival rate of less than 5%. Currently, radical surgical resection is the preferred treatment for ICC. However, most patients are only diagnosed at an advanced stage and are therefore not eligible for surgery. Herein, we present a case of advanced ICC in which radical surgery was not possible due to tumor invasion of the second porta hepatis and right hepatic artery. Six treatment cycles with a gemcitabine and oxaliplatin (GEMOX) regimen combined with camrelizumab immunotherapy achieved a partial response and successful tumor conversion, as tumor invasion of the second porta hepatis and right hepatic artery was no longer evident. The patient subsequently underwent successful radical surgical resection, including hepatectomy, caudate lobe resection, and cholecystectomy combined with lymph node dissection. Cases of patients with advanced ICC undergoing surgical resection after combined immunotherapy and chemotherapy are rare. The GEMOX regimen combined with camrelizumab demonstrated favorable antitumor efficacy and safety, suggesting that it might be a potential feasible and safe conversion therapy strategy for patients with advanced ICC

Development of a Non-invasive Deep Brain Stimulator With Precise Positioning and Real-Time Monitoring of Bioimpedance

Methods by which to achieve non-invasive deep brain stimulation via temporally interfering with electric fields have been proposed, but the precision of the positioning of the stimulation and the reliability and stability of the outputs require improvement. In this study, a temporally interfering electrical stimulator was developed based on a neuromodulation technique using the interference modulation waveform produced by several high-frequency electrical stimuli to treat neurodegenerative diseases. The device and auxiliary software constitute a non-invasive neuromodulation system. The technical problems related to the multichannel high-precision output of the device were solved by an analog phase accumulator and a special driving circuit to reduce crosstalk. The function of measuring bioimpedance in real time was integrated into the stimulator to improve effectiveness. Finite element simulation and phantom measurements were performed to find the functional relations among the target coordinates, current ratio, and electrode position in the simplified model. Then, an appropriate approach was proposed to find electrode configurations for desired target locations in a detailed and realistic mouse model. A mouse validation experiment was carried out under the guidance of a simulation, and the reliability and positioning accuracy of temporally interfering electric stimulators were verified. Stimulator improvement and precision positioning solutions promise opportunities for further studies of temporally interfering electrical stimulation