Disproof of a conjecture on the minimum Wiener index of signed trees

The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices. Sam Spiro [The Wiener index of signed graphs, Appl. Math. Comput., 416(2022)126755] recently introduced the Wiener index for a signed graph and conjectured that the path $P_n$ with alternating signs has the minimum Wiener index among all signed trees with $n$ vertices. By constructing an infinite family of counterexamples, we prove that the conjecture is false whenever $n$ is at least 30.Comment: 7 pages, 2 figure

EFFECTS OF FOUR WEEKS OF HIGH-DEFINITION TRANSCRANIAL DIRECT CURRENT STIMULATION AND FOOT CORE EXERCISE ON FOOT SENSORIMOTOR FUNCTION

Objective: This study aimed to examine the effects of four weeks of high-definition transcranial direct current stimulation (HD-tDCS) and foot core exercise (FCE) on the foot sensorimotor function (i.e., toe flexor strength and passive ankle kinesthesia). Methods: Thirty-six participants were randomly assigned into three groups: HD-tDCS, FCE, and control group. A total of 12 training sessions was performed over 4 weeks (i.e., three sessions per week) in the laboratory. The participants in the HD-tDCS group performed HD-tDCS and the FCE group completed short foot exercise, towel curls, toe spread and squeeze, and balance board training. Foot muscle strength and passive ankle kinesthesia were assessed at baseline and post-intervention. Results: Compared with the control group, HD-tDCS induced a greater decrease in percent change in the passive kinesthesia thresholds of dorsiflexion ( 9.32%), inversion ( 25.15%), and eversion ( 21.46%). A significantly higher increase in percent change in metatarsophalangeal joint flexor strength was existed in HD-tDCS group (13.77%) and a significantly greater increase in percent change in toe flexor strength was observed in the FCE group (13.13%). Conclusion: Four weeks of high-definition transcranial direct current stimulation (HD-tDCS) can improve foot sensorimotor function and foot core exercise can only strengthen toe flexor muscles

¿Bajo la misma Globalización? Desigualdad regional del capital humano en México, 1895-1930

Màster Oficial d'Història Econòmica, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2018-2019, Tutor: Marc Badia-MiróEn este trabajo se analiza la posible relación entre la evolución de la actividad económica en diferentes regiones y la desigualdad regional del nivel del capital humano en México, durante la Primera Globalización. En primer lugar, observamos como el export-led growth model en México, comportaría un periodo caracterizado por un aumento de la divergencia regional. En segundo lugar, analizando las tasas de alfabetización, encontraríamos un aumento del nivel del capital humano a escala nacional, aunque con un crecimiento asimétrico. Finalmente, comprobaríamos la posible influencia de la evolución de distintas actividades económicas exportadoras en la disparidad regional del capital humano, durante este periodo de análisis. Para cerrar el trabajo, se sugerirían futuras investigaciones sobre otros determinantes de la disparidad regional de los niveles del capital humano

Peer attention enhances student learning

Human visual attention is susceptible to social influences. In education, peer effects impact student learning, but their precise role in modulating attention remains unclear. Our experiment (N=311) demonstrates that displaying peer visual attention regions when students watch online course videos enhances their focus and engagement. However, students retain adaptability in following peer attention cues. Overall, guided peer attention improves learning experiences and outcomes. These findings elucidate how peer visual attention shapes students' gaze patterns, deepening understanding of peer influence on learning. They also offer insights into designing adaptive online learning interventions leveraging peer attention modelling to optimize student attentiveness and success

The Applications and Obstacles of Metabonomics in Traditional Chinese Medicine

In the recent years, a wide range of metabonomic technologies are widely used in the modern research of traditional chinese medicine (TCM). At present, the most prevailing methods for TCM research are mainly nuclear magnetic resonance (NMR), gas chromatography-mass spectrometry (GC-MS), and liquid chromatography-mass spectrometry (LC-MS). With these techniques, metabonomics will help to understand syndromes, efficacy and toxicity of TCM. However, every analytical technique has its advantages and drawbacks, and there exist some obstacles of its applications on TCM. So, we discuss metabonomics in TCM and analyze some problems of its applications to study TCM in recent years. We believe that with the further development of metabonomic analytical technology, especially multianalysed techniques, metabonomics will greatly promote TCM research and be beneficial to the modernization of TCM