Concentration points on two and three dimensional modular hyperbolas and applications

Let $p$ be a large prime number, $K,L,M,\lambda$ be integers with $1\le M\le p$ and ${\color{red}\gcd}(\lambda,p)=1.$ The aim of our paper is to obtain sharp upper bound estimates for the number $I_2(M; K,L)$ of solutions of the congruence $$xy\equiv\lambda \pmod p, \qquad K+1\le x\le K+M,\quad L+1\le y\le L+M$$ and for the number $I_3(M;L)$ of solutions of the congruence $$xyz\equiv\lambda\pmod p, \quad L+1\le x,y,z\le L+M.$$ We obtain a bound for $I_2(M;K,L),$ which improves several recent results of Chan and Shparlinski. For instance, we prove that if $M<p^{1/4},$ then $I_2(M;K,L)\le M^{o(1)}.$ For $I_3(M;L)$ we prove that if $M<p^{1/8}$ then $I_3(M;L)\le M^{o(1)}.$ Our results have applications to some other problems as well. For instance, it follows that if $\mathcal{I}_1, \mathcal{I}_2, \mathcal{I}_3$ are intervals in \F^*_p of length $|\mathcal{I}_i|< p^{1/8},$ then $$|\mathcal{I}_1\cdot \mathcal{I}_2\cdot \mathcal{I}_3|= (|\mathcal{I}_1|\cdot |\mathcal{I}_2|\cdot |\mathcal{I}_3|)^{1-o(1)}.$$Comment: 12 page

Dense infinite Bh sequences

For h = 3 and h = 4 we prove the existence of infinite Bh sequences B with counting function B(x) = x√(h−1)2+1−(h−1)+o(1). This result extends a construction of I. Ruzsa for B2 sequences

On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus

The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We prove a variety of results on the width, some having stronger versions assuming a conjecture of Cilleruelo and Granville asserting a uniform bound for the number of lattice points on the circle lying in short arcs.Comment: 4 figures. Added some comments about total curvature and other detail

Analysis of technological knowledge flows in the Basque Country

[EN] Knowledge flow of technology is important for continuous growth and extension of science. Patent data analysis has facilitated this knowledge acquisition. The available patent information crosses borders, corresponds and interacts with new inventions to give new strength and dimension to the technology. Therefore, the patent citation information functions as a key indicator of the knowledge flow providing relevant information. It can be identified to which extent a region is a relevant technological knowledge generator to other regions. As an illustrative case, we present a study to determine the role played by the Basque Country region as a generator of technological innovation during the period 1991-2011.Gavilanes-Trapote, J.; Etxeberria-Agiriano, I.; Cilleruelo, E.; Garechana, G. (2019). Analysis of technological knowledge flows in the Basque Country. International Journal of Production Management and Engineering. 7(Número Especial):73-79. https://doi.org/10.4995/ijpme.2019.10572SWORD73797Número EspecialAcs ZJ, Anselin L, Varga A (2002) Patents and innovation counts as measures of regional production of new knowledge Res. Policy 31:1069-1085. https://doi.org/10.1016/S0048-7333(01)00184-6Balland, P., & Rigby, D. (2017). The geography of complex knowledge. Economic Geography, 93(1), 1-23. https://doi.org/10.1080/00130095.2016.1205947Galvez, C., and Moya-Anegon, F. (2007). Standardizing formats of corporate source data. Scientometrics, 70(1), 3-26. https://doi.org/10.1007/s11192-007-0101-0Gavilanes-Trapote, J., Cilleruelo-Carrasco, E., Etxeberria-Agiriano, I., Garechana, G., Rodríguez Andara, A. (2019). Qualitative Patents Evaluation Through the Analysis of Their Citations. Case of the Technological Sectors in the Basque Country. In: Ortiz, Á., Andrés Romano, C., Poler, R., García-Sabater, J.P. (eds) Engineering Digital Transformation. Lecture Notes in Management and Industrial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-96005-0_28Gavilanes-Trapote, J., Río-Belver, R. M., Cilleruelo, E., Garechana G., and Larruscain J. (2015). Patent overlay maps: Spain and the basque country. International Journal of Technology Management (IJTM), 69(3/4), 261. https://doi.org/10.1504/IJTM.2015.072976Harhoff, D., Scherer, F., and Vopel, K. (2004). Citations, family size, opposition and the value of patent rights (vol 32, pg 1343, 2003). Research Policy, 33(2), 363-364. https://doi.org/10.1016/j.respol.2003.10.001Higham, K.W., Governale, M., Jaffe, A.B., and Zülicke, U. (2017) Fame and obsolescence: Disentangling growth and aging dynamics of patent citations. Phys. Rev. E 95, 042309. https://doi.org/10.1103/PhysRevE.95.042309Jaffe, A., Trajtenberg, M., and Fogarty, M. (2000). Knowledge spillovers and patent citations: Evidence from a survey of inventors. American Economic Review, 90(2), 215-218. https://doi.org/10.1257/aer.90.2.215Krugman, P. (1995). Development, geography, and economic Theory. Cambridge-Massachusetts: The MIT Press.Malerba, F., and Orsenigo, L. (1995). Schumpeterian patterns of innovation. Cambridge Journal of Economics, 19(1), 47-65. https://doi.org/10.1093/oxfordjournals.cje.a035308Malmberg, A., and Maskell, P. (1997). Towards an explanation of regional specialization and industry agglomeration. European Planning Studies, 5(1), 25-41. https://doi.org/10.1080/09654319708720382Murata, Y., Nakajima, R., Okamoto, R., and Tamura, R. (2014). Localized knowledge spillovers and patent citations: A distance-based approach. Review of Economics and Statistics, 96(5), 967-985. https://doi.org/10.1162/REST_a_00422Organisation for Economic Co-operation and Development (OECD). (2009). OECD patent statistics manual OECD.Podolny, J., Stuart, T., and Hannan, M. (1996). Networks, knowledge, and niches: Competition in the worldwide semiconductor industry, 1984-1991. American Journal of Sociology, 102(3), 659-689. https://doi.org/10.1086/230994Schmoch, U. (2003). Service marks as novel innovation indicator. Research Evaluation, 12(2), 149-156. https://doi.org/10.3152/147154403781776708Simmie, J. (2003). Innovation and urban regions as national and international nodes for the transfer and sharing of knowledge. Regional Studies, 37(6-7), 607-620. https://doi.org/10.1080/0034340032000108714Stek, P.E., and van Geenhuizen, M.S. (2016). The influence of international research interaction on national innovation performance: A bibliometric approach. Technological Forecasting and Social Change, 110, 61-70. https://doi.org/10.1016/j.techfore.2015.09.017Thompson, P., and Fox-Kean, M. (2005). Patent citations and the geography of knowledge spill-overs: A reassessment. American Economic Review, 95(1), 450-460. https://doi.org/10.1257/0002828053828509Thompsori, P. (2006). Patent citations and the geography of knowledge spillovers: Evidence from inventor- and examiner-added citations. Review of Economics and Statistics, 88(2), 383-388. https://doi.org/10.1162/rest.88.2.383You, H., Li, M., Hipel, K.W., Jiang, J., Ge, B., and Duan, H. (2017) Development trend forecasting for coherent light generator technology based on patent citation network analysis. Scientometrics 111(1), 297-315. https://doi.org/10.1007/s11192-017-2252-

ISO 14006. Experiencias previas de estudios de arquitectura que han adoptado el estándar de ecodiseño UNE 150301:2003

This paper aims to analyze the pioneer UNE 150301 standard, as well as its adoption process and its practical results in the sector of architecture studios. First, the structure, the aim and the scope of norm UNE 150301 have been analysed. Second, the standard's implementation has been examined, concluding that 73% of the companies that have obtained the certificate are architecture studios. A case study has therefore been carried out with the participation of five architecture studios pioneers. These experiences have let us know the main aspects and difficulties of the process. In conclusion, the adoption of the standard UNE 150301 can be a helpful tool in order to reduce the environmental impact of the products and obtain some competitive advantages such as cost reduction, improvement in energy efficiency of the product and a better adaptation to acts and regulations.En este artículo se analiza la experiencia de implantación de la norma UNE 150301 de ecodiseño en el sector de los estudios de arquitectura. Tras el examen de la estructura de norma UNE 150301, de sus objetivos y de su alcance, se analiza su difusión, destacándose que el 73% de las empresas certificadas en España son estudios de arquitectura. A continuación se estudia el proceso de implantación real, mediante el estudio de caso que lo analiza en cinco estudios de arquitectura. El estudio realizado permite conocer de primera mano las principales claves y dificultades del proceso de implantación del estándar, así como los resultados obtenidos, entre los que destaca una reducción del impacto ambiental. Se constata, en suma, que la norma UNE 150301 es una herramienta que puede proporcionar ventajas competitivas interesantes a las empresas del sector de los estudios de arquitectura

Short proofs of some extremal results III

We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short

Trajectory of post-COVID brain fog, memory loss, and concentration loss in previously hospitalized COVID-19 survivors:the LONG-COVID-EXP multicenter study

OBJECTIVE: This study aimed to apply Sankey plots and exponential bar plots for visualizing the trajectory of post-COVID brain fog, memory loss, and concentration loss in a cohort of previously hospitalized COVID-19 survivors.METHODS: A sample of 1,266 previously hospitalized patients due to COVID-19 during the first wave of the pandemic were assessed at 8.4 (T1), 13.2 (T2), and 18.3 (T3) months after hospital discharge. They were asked about the presence of the following self-reported cognitive symptoms: brain fog (defined as self-perception of sluggish or fuzzy thinking), memory loss (defined as self-perception of unusual forgetfulness), and concentration loss (defined as self-perception of not being able to maintain attention). We asked about symptoms that individuals had not experienced previously, and they attributed them to the acute infection. Clinical and hospitalization data were collected from hospital medical records.RESULTS: The Sankey plots revealed that the prevalence of post-COVID brain fog was 8.37% (n = 106) at T1, 4.7% (n = 60) at T2, and 5.1% (n = 65) at T3, whereas the prevalence of post-COVID memory loss was 14.9% (n = 189) at T1, 11.4% (n = 145) at T2, and 12.12% (n = 154) at T3. Finally, the prevalence of post-COVID concentration loss decreased from 6.86% (n = 87) at T1, to 4.78% (n = 60) at T2, and to 2.63% (n = 33) at T3. The recovery exponential curves show a decreasing trend, indicating that these post-COVID cognitive symptoms recovered in the following years after discharge. The regression models did not reveal any medical record data associated with post-COVID brain fog, memory loss, or concentration loss in the long term.CONCLUSION: The use of Sankey plots shows a fluctuating evolution of post-COVID brain fog, memory loss, or concentration loss during the first years after the infection. In addition, exponential bar plots revealed a decrease in the prevalence of these symptoms during the first years after hospital discharge. No risk factors were identified in this cohort.</p

Associated-Onset Symptoms and Post-COVID-19 Symptoms in Hospitalized COVID-19 Survivors Infected with Wuhan, Alpha or Delta SARS-CoV-2 Variant

This study compared associated-symptoms at the acute phase of infection and post-COVID-19 symptoms between individuals hospitalized with the Wuhan, Alpha or Delta SARS-CoV-2 variant. Non-vaccinated individuals hospitalized because of SARS-CoV-2 infection in one hospital during three different waves of the pandemic (Wuhan, Alpha or Delta) were scheduled for a telephone interview. The presence of post-COVID-19 symptoms was systematically assessed. Hospitalization and clinical data were collected from medical records. A total of 201 patients infected with the Wuhan variant, 211 with the Alpha variant and 202 with Delta variant were assessed six months after hospitalization. Patients infected with the Wuhan variant had a greater number of symptoms at hospital admission (higher prevalence of fever, dyspnea or gastrointestinal problems) than those infected with Alpha or Delta variant (p < 0.01). A greater proportion of patients infected with the Delta variant reported headache, anosmia or ageusia as onset symptoms (p < 0.01). The mean number of post-COVID-19 symptoms was higher (p < 0.001) in individuals infected with the Wuhan variant (mean: 2.7 ± 1.3) than in those infected with the Alpha (mean: 1.8 ± 1.1) or Delta (mean: 2.1 ± 1.5) variant. Post-COVID-19 dyspnea was more prevalent (p < 0.001) in people infected with the Wuhan variant, whereas hair loss was higher in those infected with the Delta variant (p = 0.002). No differences in post-COVID-19 fatigue by SARS-CoV-2 variant were found (p = 0.594). Differences in COVID-19 associated onset symptoms and post-COVID-19 dyspnea were observed depending on the SARS-CoV-2 variant. The presence of fatigue was a common post-COVID-19 symptom to all SARS-CoV-2 variants

Prevalence of Musculoskeletal Post-COVID Pain in Hospitalized COVID-19 Survivors Depending on Infection with the Historical, Alpha or Delta SARS-CoV-2 Variant

We compared the prevalence of musculoskeletal post-COVID pain between previously hospitalized COVID-19 survivors infected with the historical, Alpha or Delta SARS-CoV-2 variant. Data about musculoskeletal post-COVID pain were systematically collected through a telephone interview involving 201 patients who had survived the historical variant, 211 who had survived the Alpha variant and 202 who had survived the Delta variant six months after hospital discharge. Participants were recruited from non-vaccinated individuals hospitalized due to SARS-CoV-2 infection in one hospital of Madrid (Spain) during three different waves of the pandemic (historical, Alpha or Delta variant). Hospitalization and clinical data were collected from hospital medical records. In addition, anxiety/depressive levels and sleep quality were also assessed. The prevalence of musculoskeletal post-COVID pain was higher (p = 0.003) in patients infected with the historical variant (47.7%) than in those infected with the Alpha (38.3%) or Delta (41%) variants. A significantly (p = 0.002) higher proportion of individuals infected with the historical variant reported generalized pain (20.5%) when compared with those infected with the other variants. The prevalence of new-onset post-COVID musculoskeletal pain reached 80.1%, 75.2% and 79.5% of patients infected with the historical, Alpha or Delta variants, respectively. No specific risk factors for developing post-COVID pain were identified depending on the SARS-CoV-2 variant. In conclusion, this study found that musculoskeletal post-COVID pain is highly prevalent in COVID-19 survivors six months after hospital discharge, with the highest prevalence and most generalized pain symptoms in individuals infected with the historical variant. Approximately 50% developed “de novo” post-COVID musculoskeletal pain symptoms