Recovering zeros of polynomials modulo a prime

Let $p$ be a prime and $\mathbb{F}_p$ the finite field with $p$ elements. We show how, when given an irreducible bivariate polynomial $F \in \mathbb{F}_p[X,Y]$ and an approximation to a zero, one can recover the root efficiently, if the approximation is good enough. The strategy can be generalized to polynomials in the variables $X_1,\ldots ,X_m$ over the field $\mathbb{F}_p$. These results have been motivated by the predictability problem for nonlinear pseudorandom number generators and other potential applications to cryptography

Generalized explicit inversive generators of small p-weight degree

Using rational functions to generate pseudorandom number sequences is a popular research topic. In this paper, we study bounds on additive character sums of a new explicit generator based on rational functions with small p-weight degree. This extends the class of functions where a nontrivial character sum bound is known

Cayley digraphs of finite abelian groups and monomial ideals

In the study of double-loop computer networks, the diagrams known as L-shapes arise as a graphical representation of an optimal routing for every graph’s node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with a finite abelian group as vertex set, we define a monomial ideal and consider its representations via its minimal system of generators or its irredundant irreducible decomposition. From this last piece of information, we can compute the graph’s diameter and average minimum distance. That monomial ideal is the initial ideal of a certain lattice with respect to a graded monomial ordering. This result permits the use of Gr¨obner bases for computing the ideal and finding an optimal routing. Finally, we present a family of Cayley digraphs parametrized by their diameter d, all of them associated to irreducible monomial ideals

The Role of Lipids During Embryonic Development of the Euphausiids Euphausia Pacifica and Thysanoessa Spinifera

To understand the role of lipids during early embryogenesis, major lipid classes together with individual fatty acid and sterol composition were determined in embryos from multiple developmental stages of the euphausiids Euphausia pacifica and Thysanoessa spinifera. Average lipid content in embryos of E. pacifica and T. spiniferafrom the earliest stage (multicell) were 4.45 and 3.69 µg embryo-1,respectively. During development, the lipid content decreased at similar rates in the embryos of both species. In contrast to many crustacean eggs, phospholipids were the dominant lipid class in all embryonic stages, with decreasing concentrations seen during development. Individual fatty acids and sterols showed selective utilization during early developmental stages. The dominant fatty acids were 16:0 and 16:1ω7 and 20:5ω3, with most polyunsaturated fatty acids preferentially metabolized throughout early stages. An exception was 22:6ω3, which remained near constant through all stages. Cholesterol was the dominant sterol (\u3e82% of total sterols) in embryos, with only minor changes during development. The appearance of algal sterols and fatty alcohols, including phytol, in T. spinifera embryos suggests that considerable amounts of algal lipids are directly allocated to eggs during vitellogenesis. Despite the substantial changes in lipid amount and composition during embryo development, the presence of phospholipids as the dominate lipid store acts to moderate changes in egg-sinking rate for both species until the late (early and late limb-bud) stages of development

Enhanced dielectric constant resolution of thin insulating films by electrostatic force microscopy

This is the author’s version of a work that was accepted for publication in Journal of Physics: Condensed Matter. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Physics: Condensed Matter 24.15 (2012) 10.1088/0953-8984/24/15/155303Electrostatic Force Microscopy has been shown to be a useful tool to determine the dielectric constant of insulating films of nanometer thicknesses that play a key role in many electrical, optical and biological phenomena. Previous approaches make use of simple analytical formulae to analyse the experimental data for thin insulating films deposited directly on a metallic substrate. Here we show that the sensitivity of the EFM signal to changes in the dielectric constant of the thin film can be enhanced by using dielectric substrates with low dielectric constants. We present detailed numerical calculations of the tip-sample electrostatic interaction in the following set-up: the insulating thin film, a dielectric substrate (or spacing layer) of known low dielectric constant and a metallic electrode. The EFM sensitivity to the dielectric constant increases with the thickness of the spacing layer and saturates for thicknesses above 100-300 nm, when it is close to that of an infinite medium.Authors acknowledge C. Gómez-Navarro, J. Gómez-Herrero, P. Varona and F. Rodríguez for insightful discussions. This work was supported by TIN2010-19607, the Spanish MICINN ( Grant No: FIS2009 − 13430 −C02 − 02 ) and by the Comunidad de Madrid Microseres Program (Grant No: S2009/T IC − 1476). GMS acknowledges support from the Spanish Ramón y Cajal Program

Medicina científica y filosofía natural : dos aportes de José Celestino Mutis al desarrollo integral de las ciencias en Colombia

La historia de la ciencia en nuestro país ha sido elaborada a manera de crónica para el gran público o bien a manera de rigurosos trabajos académicos dirigidos a un público restringido. Entre estos dos extremos, y con el propósito de documentar los pilares fundamentales de la ciencia en Colombia, hemos optado por una aproximación intermedia, a la vez atractiva y rigurosa, en torno a 2 manuscritos de José Celestino Mutis en el período colonial en los años que precedieron lo que se ha llamado la “independencia” de nuestro país.74-7

William (Bill) Peterson's contributions to ocean science, management, and policy

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Schwing, F. B., Sissenwine, M. J., Batchelder, H., Dam, H. G., Gomez-Gutierrez, J., Keister, J. E., Liu, H., & Peterson, J. O. William (Bill) Peterson's contributions to ocean science, management, and policy. Progress in Oceanography, 182, (2020): 102241, doi:10.1016/j.pocean.2019.102241.In addition to being an esteemed marine ecologist and oceanographer, William T. (Bill) Peterson was a dedicated public servant, a leader in the ocean science community, and a mentor to a generation of scientists. Bill recognized the importance of applied science and the need for integrated “big science” programs to advance our understanding of ecosystems and to guide their management. As the first US GLOBEC program manager, he was pivotal in transitioning the concept of understanding how climate change impacts marine ecosystems to an operational national research program. The scientific insight and knowledge generated by US GLOBEC informed and advanced the ecosystem-based management approaches now being implemented for fishery management in the US. Bill held significant leadership roles in numerous international efforts to understand global and regional ecological processes, and organized and chaired a number of influential scientific conferences and their proceedings. He was passionate about working with and training young researchers. Bill’s academic affiliations, notably at Stony Brook and Oregon State Universities, enabled him to advise, train, and mentor a host of students, post-doctoral researchers, and laboratory technicians. Under his collegial guidance they became critical independent thinkers and diligent investigators. His former students and colleagues carry on Bill Peterson’s legacy of research that helps us understand marine ecosystems and informs more effective resource stewardship and conservation

Prostatic cyst: An unusual cause of hemospermia

A 31-year-old man was referred to our service because of recurrent hemospermia over the last 4 years, there were no other symptoms like perineal pain, fever, dysuria, nocturia or urgency; this patient only presented hemospermia with clots. Genital examination was normal. Semen analysis showed no change in volume and pH; however, hemospermia and asthenozoospermia were observed. The semen culture was normal. Ultrasonography only revealed the presence of a cystic lesion adjoining the prostate gland, next to the bladder neck. The retrograde urethrogram was normal. The CT scan revealed only a small calcification in the right seminal vesicle. Endoscopic cistourethroscopy demonstrated 2 cystic dilatations arising on both sides of the prostate gland adjacent to the bladder neck, behind the verumontanum with vessels running over the surface prostatic cyst dilatation. The diagnosis of prostatic gland cystic dilatation was reached and confirmed by pathology that reported fibroconnective tissue with fibrosis and hyalinization. Transurethral unroofing of the cyst was performed separately with a successful outcome

Prostatic cyst: An unusual cause of hemospermia

AbstractA 31-year-old man was referred to our service because of recurrent hemospermia over the last 4 years, there were no other symptoms like perineal pain, fever, dysuria, nocturia or urgency; this patient only presented hemospermia with clots. Genital examination was normal. Semen analysis showed no change in volume and pH; however, hemospermia and asthenozoospermia were observed. The semen culture was normal. Ultrasonography only revealed the presence of a cystic lesion adjoining the prostate gland, next to the bladder neck. The retrograde urethrogram was normal. The CT scan revealed only a small calcification in the right seminal vesicle. Endoscopic cistourethroscopy demonstrated 2 cystic dilatations arising on both sides of the prostate gland adjacent to the bladder neck, behind the verumontanum with vessels running over the surface prostatic cyst dilatation. The diagnosis of prostatic gland cystic dilatation was reached and confirmed by pathology that reported fibroconnective tissue with fibrosis and hyalinization. Transurethral unroofing of the cyst was performed separately with a successful outcome

Descripción de la presencia de un caso de teniasis en nuestro medio

Introducción del caso clínico: Varón, de origen español, de 35 años, que refiere prurito anal en la consulta médica de la cárcel donde cumple condena y que lo relaciona con episodios previos diagnosticados de “lombrices”. Estos fueron tratados con Lomper (Mebendazol) de modo empírico. Se le solicitan estudios parasitológicos en heces frescas al servicio de Microbiología del Hospital Virgen de las Nieves de Granada, hallándose la presencia de huevos de Taenia spp. Para ello, la muestra fue concentrada y visualizada en fresco de acuerdo con el procedimiento estándar previamente publicado por nosotros (1). También se observó a 1000X mediante la tinción de ácido alcohol resistencia (Figuras 1 y 2). Se le puso tratamiento para teniasis con Praziquantel. El estudio de control a los tres meses fue negativo. En la anamnesis posterior este negó haber salido del país ni haber tenido contacto con personas de áreas endémicas. Los episodios de prurito anal los sufre desde la adolescencia habiendo sido tratados siempre. Refiere que cuando era adolescente tuvo contacto con un familiar que también tenía lombrices, una tía que tenía cerdos y gallinas y que acudía a matanzas de cerdos en la localidad de Cenes de la Vega (Granada). En su historia clínica constan que los estudios serológicos del VIH, VHA, VHB, VHC y lúes, así como la prueba de Mantoux fueron negativas