Number theory, borderline dimension and extensive entropy in distributions of ranked data.

The consideration of an existing stochastic approach for the reproduction of ranked data pointed at a formal equivalence between its key mathematical expression and that for trajectories at the tangent bifurcation. This fact led to a nonlinear dynamical approach for rank distributions that shows similarities with universality classes in critical phenomena. The renormalization group (RG) fixed-point map f*(x) for a tangent bifurcation of arbitrary nonlinearity z > 1 has proved to be a powerful tool into which the formalism can be couched. The source distribution P(N) of the stochastic approach can be linked to f*(x) while the size-rank N(k) and frequency-rank F(k') distributions are obtained, respectively, from the map trajectories xt and the sums of its positions. We provide now an extension to Number Theory as we obtain from the trajectories xt of f*(x) the numbers, or asymptotic approximations of them, for the Factorial, Natural, Prime and Fibonacci sets. A measure of the advance of these numbers towards infinity is given by sums of positions that represent their reciprocals. We specify rank distribution universality classes, already associated with real data, to these number sets. We find that the convergence of the series of number reciprocals occurs first at nonlinearity z = 2, that which corresponds to the classical Zipf law, and link this transition edge to the action of the attractor when it first reduces the fractal dimension of trajectory positions to zero. Furthermore, the search of logarithmic corrections common to borderline dimensions provides a link to the Prime numbers set. Finally, we find corroborating evidence of these logarithmic corrections from the analysis of large data sets for ranked earthquake magnitudes. The formalism links all types of ranked distributions to a generalized extensive entropy.

How, Why and When Tsallis Statistical Mechanics Provides Precise Descriptions of Natural Phenomena.

The limit of validity of ordinary statistical mechanics and the pertinence of Tsallis statistics beyond it is explained considering the most probable evolution of complex systems processes. To this purpose we employ a dissipative Landau-Ginzburg kinetic equation that becomes a generic one-dimensional nonlinear iteration map for discrete time. We focus on the Renormalization Group (RG) fixed-point maps for the three routes to chaos. We show that all fixed-point maps and their trajectories have analytic closed-form expressions, not only (as known) for the intermittency route to chaos but also for the period-doubling and the quasiperiodic routes. These expressions have the form of q-exponentials, while the kinetic equation's Lyapunov function becomes the Tsallis entropy. That is, all processes described by the evolution of the fixed-point trajectories are accompanied by the monotonic progress of the Tsallis entropy. In all cases the action of the fixed-point map attractor imposes a severe impediment to access the system's built-in configurations, leaving only a subset of vanishing measure available. Only those attractors that remain chaotic have ineffective configuration set reduction and display ordinary statistical mechanics. Finally, we provide a brief description of complex system research subjects that illustrates the applicability of our approach.

Distribution of human papillomavirus genotypes by severity of cervical lesions in HPV screened positive women from the ESTAMPA study in Latin America.

The proportion of HPV16 and 18-associated cervical cancer (CC) appears rather constant worldwide (≥70%), but the relative importance of the other HR-HPV differs slightly by geographical region. Here, we studied the HPV genotype distribution of HPV positive Latin American (LA) women by histological grade, in a sub-cohort from the ESTAMPA study; we also explored the association of age-specific HPV genotypes in severe lesions. Cervical samples from 1,252 participants (854 ≤CIN1, 121 CIN2, 194 CIN3 and 83 CC) were genotyped by two PCRs-Reverse Blotting Hybridization strategies: i) Broad-Spectrum General Primers 5+/6+ and ii) PGMY9/11 PCRs. HPV16 was the most frequently found genotype in all histological grades, and increased with the severity of lesions from 14.5% in ≤ CIN1, 19.8% in CIN2, 51.5% in CIN3 to 65.1% in CC (p < 0.001). For the remaining HR-HPVs their frequency in CC did not increase when compared to less severe categories. The nonavalent vaccine HR-types ranked at the top in CC, the dominant ones being HPV16 and HPV45. HR-HPV single infection occurs, respectively, in 57.1% and 57.0% of ≤CIN1 and CIN2, increasing to 72.2% and 91.6% in CIN3 and CC (p<0.001). No association between age and HPV type was observed in CC, although the risk of HPV16 infection in CIN3 cases increased with age. Results confirm the relevance of HPV16 in the whole clinical spectrum, with a strong rise of its proportion in CIN3 and cancer. This information will be relevant in evaluating the impact of HPV vaccination, as a baseline against which to compare genotype changes in HPV type-specific distribution as vaccinated women participate in screening in LA region. Likewise, these data may help select the best HPV testing system for HPV-based efficient, affordable, and sustainable screening programmes.

Dynamical analogues of rank distributions.

We present an equivalence between stochastic and deterministic variable approaches to represent ranked data and find the expressions obtained to be suggestive of statistical-mechanical meanings. We first reproduce size-rank distributions N(k) from real data sets by straightforward considerations based on the assumed knowledge of the background probability distribution P(N) that generates samples of random variable values similar to real data. The choice of different functional expressions for P(N): power law, exponential, Gaussian, etc., leads to different classes of distributions N(k) for which we find examples in nature. Then we show that all of these types of functions can be alternatively obtained from deterministic dynamical systems. These correspond to one-dimensional nonlinear iterated maps near a tangent bifurcation whose trajectories are proved to be precise analogues of the N(k). We provide explicit expressions for the maps and their trajectories and find they operate under conditions of vanishing or small Lyapunov exponent, therefore at or near a transition to or out of chaos. We give explicit examples ranging from exponential to logarithmic behavior, including Zipf's law. Adoption of the nonlinear map as the formalism central character is a useful viewpoint, as variation of its few parameters, that modify its tangency property, translate into the different classes for N(k).

Rank distributions: Frequency vs. magnitude.

We examine the relationship between two different types of ranked data, frequencies and magnitudes. We consider data that can be sorted out either way, through numbers of occurrences or size of the measures, as it is the case, say, of moon craters, earthquakes, billionaires, etc. We indicate that these two types of distributions are functional inverses of each other, and specify this link, first in terms of the assumed parent probability distribution that generates the data samples, and then in terms of an analog (deterministic) nonlinear iterated map that reproduces them. For the particular case of hyperbolic decay with rank the distributions are identical, that is, the classical Zipf plot, a pure power law. But their difference is largest when one displays logarithmic decay and its counterpart shows the inverse exponential decay, as it is the case of Benford law, or viceversa. For all intermediate decay rates generic differences appear not only between the power-law exponents for the midway rank decline but also for small and large rank. We extend the theoretical framework to include thermodynamic and statistical-mechanical concepts, such as entropies and configuration.

Recurrencia/persistencia de neoplasia intraepitelial cervical posterior a cono LEEP en el Instituto Nacional de Enfermedades Neoplásicas / Recurrence/persistence of cervical intraepithelial neoplasia after undergoing a LEEP conization at Instituto Nacional de Enfermedades Neoplásicas

Objetivo: Determinar la incidencia de recurrencia/persistencia de neoplasia intraepitelial cervical (NIC) en pacientes sometidos a procedimiento de escisión electroquirúrgica en asa (cono LEEP) en el Servicio de Ginecología Oncológica del Instituto Nacional de Enfermedades Neoplásicas (INEN). Materiales y métodos: Estudio de cohorte, retrospectivo en el cual se revisaron las historias clínicas de pacientes sometidos a cono LEEP durante el periodo de enero del 2002 a diciembre del 2003. Los pacientes fueron divididos en un grupo con margen comprometido y otro con margen negativo después del procedimiento de cono LEEP. El seguimiento de los pacientes se realizó cada 3 meses con examen físico, PAP y colposcopía. El desenlace fue la recurrencia de NIC. Para valorar el riesgo de recurrencia de NIC entre los grupos de estudio se calculó el riesgo relativo (RR) con su respectivo intervalo de confianza (IC) al 95%. Resultados: En total 451 pacientes fueron sometidos a cono LEEP durante el periodo de estudio. La edad promedio fue 35.32 años, el promedio de parejas sexuales fue 2.1 y el promedio de hijos fue 2.7. Presentaron margen comprometido 109 (25%) y margen negativo 342 (75%). De ellos solo 94 y 102, respectivamente, cumplían los criterios de elegibilidad y fueron seguidos. La media de seguimiento fue de 21.74 meses. La incidencia de recurrencia/persistencia dentro de los pacientes con margen comprometido fue 5.5% mientras que la incidencia de recurrencia en un grupo de pacientes con margen negativo fue 1.96% No encontramos diferencias significativas en el riesgo de padecer recurrencia de NIC en el grupo de pacientes con margen comprometido versus los pacientes con margen negativo. RR= 2.7; IC 95% (0.41 a 33.8). Conclusión: No se encontró diferencia significativa en la incidencia de neoplasia intracervical para pacientes con margen comprometido y los pacientes con margen negativo.

Objective: To determine the incidence of recurrence/persistence of cervical intraepithelial neoplasia (CIN) in patients who underwent a loop electrosurgical excision procedure (LEEP) at the Department of Gynecologic Oncology of Instituto Nacional de Enfermedades Neoplásicas (INEN). Materials and methods: A retrospective cohort study in which medical records of patients who underwent a LEEP conization from January 2002 to December 2003 were examined. After the LEEP conization, patients were divided into two groups: one with positive margin and another one with negative margin. Follow-up was performed every 3 months and consisted of a physical examination, Pap test and colposcopy. The outcome was recurrence of CIN. To assess the risk of CIN recurrence among the study groups, relative risk (RR) and its respective 95% confidence interval (CI) were calculated. Results: A total of 451 patients underwent a LEEP conization during the study period. The mean age was 35.32 years old, the mean number of sexual partners was 2.1 and the mean number of children was 2.7. One hundred and nine (109) patients (25%) showed a positive margin and 342 (75%) showed a negative one. Out of these subjects, only 94 and 102, respectively, met the eligibility criteria and were followed. The mean follow-up period was 21.74 months. The incidence of recurrence/persistence in patients with positive margin was 5.5%, while the incidence of recurrence/persistence in the group of patients with negative margin was 1.96%. We found no significant differences in the risk of CIN recurrence in the group of patients with positive margin versus patients with negative margin. RR = 2.7, 95% CI (0.41 to 33.8). Conclusion: There was no significant difference in the incidence of cervical intraepithelial neoplasia between patients with positive margin and patients with negative margin.

Actividad antiinflamatoria in vitro de los polisacáridos sulfatados de Patallus mollis extraídos mediante digestión enzimática / In vitro anti-inflammatory effect of Patallus mollis sulphated polysaccharides extracted by enzymatic digestion

Objetivo: Evaluar la actividad antiinflamatoria in vitro de los polisacáridos (PCs) del tegumento de Patallus mollis mediante la prueba de la estabilidad de la membrana celular del glóbulo rojo y la desnaturalización de la albumina. Materiales y métodos: Los especímenes fueron recolectados en la bahía de Pucusana, se identificaron y los PCs se extrajeron mediante digestión enzimática con bromelina (PBr), papaína (PPa) y pepsina (PPe). Se cuantifico el contenido de azucares, sulfatos y proteínas totales mediante métodos colorimétricos. Para la prueba de estabilidad de la membrana, se preparó una solución de glóbulos rojos [10 % v/v], la cual se mezcló con PBS, NaCl [0,36%], y PCs [2000 ­ 62.5 µg/mL]. Para la prueba de la desnaturalización de la albúmina, la mezcla consistió en suero de albúmina bovina [0,5%] con PCs [2000 ­ 62.5 µg/mL]. Como controles se utilizó diclofenaco sódico y agua destilada. El análisis de resultados fue en base a la absorbancia medida en un espectrofotómetro de placas a 420 y 660 nm, según las pruebas respectivamente. Resultados: Los PCs presentaron niveles elevados de azúcares y proteínas totales, así como presencia de sulfatos totales. Además los PCs exhibieron una capacidad estabilizadora de la membrana, siendo la máxima presentada por PBr a una concentración de 62.5 µg/mL. Solo el PPa presentó inhibición de la desnaturalización de albúmina inducida por calor a una dosis de 2000 µg/mL. Conclusión: Nuestros resultados sugieren que los PCs tiene actividades antiinflamatorias y son candidatos potenciales para la formulación de un ingrediente alimentario funcional y / o fármaco para tratar enfermedades inflamatorias.

[Parametrial involvement in cervical cancer IB1 patients treated with radical hysterectomy in Peru]. / Compromiso parametrial en pacientes con cáncer de cérvix IB-1 tratadas con histerectomía radical en Perú

OBJECTIVES: To assess the frequency and factors associated with parametrial involvement (PI) in patients with cervical cancer IB1 who underwent radical hysterectomy (RH) at the National Institute of Neoplastic Diseases in Peru. MATERIALS AND METHODS: Cross-sectional study of 214 patients with cervical cancer IB1 undergoing RH with pelvic lymphadenectomy between 2007 and 2012. The population was compared with and without clinicopathological variables associated with PI such as age, tumor size, depth of infi histological grade and pelvic lymph node involvement. RESULTS: Ten patients (4.6%) had PI. Multivariate analysis showed that the depth of invasion (OR 8.37, 95% CI 1.24- 56.41, p=0.029) and pelvic node involvement (OR 18.03; 95% CI 3.30-98.44, p=0.001) were all independent predictors of PI. The presence of tumor size = 2 cm, invasion = 10 mm, absence of lymphovascular permeation and absence of nodal involvement identifi 97 patients at low risk of PI, none of whom had PI pathology. CONCLUSIONS: We confi the low frequency of PI in the cervical cancer IB1 subgroup and its association with the depth of invasion and lymph node involvement suggested in previous studies. This information will allow the identifi of a subgroup of patients at low risk of PI for less radical surgery in our institution.

Compromiso parametrial en pacientes con cáncer de cérvix IB-1 tratadas con histerectomía radical en Perú / Parametrial involvement in cervical cancer IB1 patients treated with radical hysterectomy in Peru

Objetivos. Evaluar la frecuencia y factores asociados al compromiso parametrial (CP) en pacientes con cáncer de cérvix IB-1 sometidas a histerectomía radical (HR) en el Instituto Nacional de Enfermedades Neoplásicas del Perú. Materiales y métodos. Estudio transversal analítico en 214 pacientes con cáncer de cérvix IB-1 sometidas a HR con linfadenectomía pélvica entre el 2007 y 2012. Se comparó la población con y sin CP según variables clinicopatológicas como edad, tamaño tumoral, profundidad de infiltración, grado histológico y afectación ganglionar pélvica. Resultados. Diez pacientes (4,6%) presentaron CP. El análisis multivariable mostró que la profundidad de la invasión (OR 8,37, IC 95%: 1,24-56,41, p=0,029) y el compromiso de ganglios pélvicos (OR 18,03, IC 95%: 3,30-98,44, p=0,001) resultaron ser predictores independientes del CP. La presencia de tamaño tumoral ≤ 2 cm, invasión ≤ 10 mm, ausencia de permeación linfovascular y ausencia de compromiso ganglionar permitió identificar 97 pacientes de bajo riesgo de CP, de los cuales ninguno tuvo CP en patología. Conclusiones. Confirmamos la baja frecuencia del CP en el subgrupo de cáncer de cervix IB-1 y su asociación con la profundidad de la invasión y con el compromiso ganglionar linfático sugeridos en estudios previos. Esta información permitirá identificar un subgrupo de pacientes con bajo riesgo de CP candidatas a una cirugía menos radical en nuestra institución...

Objectives. To assess the frequency and factors associated with parametrial involvement (PI) in patients with cervical cancer IB1 who underwent radical hysterectomy (RH) at the National Institute of Neoplastic Diseases in Peru. Materials and methods. Cross-sectional study of 214 patients with cervical cancer IB1 undergoing RH with pelvic lymphadenectomy between 2007 and 2012. The population was compared with and without clinicopathological variables associated with PI such as age, tumor size, depth of infiltration, histological grade and pelvic lymph node involvement. Results. Ten patients (4.6%) had PI. Multivariate analysis showed that the depth of invasion (OR 8.37, 95% CI 1.24- 56.41, p=0.029) and pelvic node involvement (OR 18.03; 95% CI 3.30-98.44, p=0.001) were all independent predictors of PI. The presence of tumor size ≤ 2 cm, invasion ≤ 10 mm, absence of lymphovascular permeation and absence of nodal involvement identified 97 patients at low risk of PI, none of whom had PI pathology. Conclusions. We confirmed the low frequency of PI in the cervical cancer IB1 subgroup and its association with the depth of invasion and lymph node involvement suggested in previous studies. This information will allow the identification of a subgroup of patients at low risk of PI for less radical surgery in our institution...

Nocardiosis pulmonar, como causa de imagen radiológica en consolidación pulmonar con área de cavitación / Pulmonary nocardiosis, as a cause of radiological imaging in lung consolidation with cavitation area

La Nocardia es una bacteria aerobia estricta grampositiva. Se adquiere generalmente a través del tracto respiratorio, Comprende varias especies, siendo N. asteroides la que más afecta al hombre (85%). Su diagnóstico se basa en el aislamiento en esputo de Nocardia sp. La nocardiosis pulmonar es una infección infrecuente y debe considerarse en pacientes con estado de inmunodepresión y con patología pulmonar subyacente, como la tuberculosis. El compromiso pulmonar por Nocardia consiste con mayor frecuencia en abscesos necrotizantes. Los hallazgos radiológicos son nódulos pulmonares múltiples de diversos tamaños y las consolidaciones pulmonares son las manifestaciones más frecuentes.(AU)

Valor de la biopsia de endometrio y la ultrasonografía transvaginal en la evaluación prequirúrgica de pacientes con cáncer de endometrio / Value of endometrial biopsy and transvaginal ultrasonography in the presurgical evaluation of patients with endometrial cancer

El manejo inicial del cáncer de endometrio es quirúrgico, en base a factores pronósticos que se pueden evaluar en los estudios preoperatorios. En el presente estudio evaluamos la exactitud de la biopsia de endometrio para determinar el tipo histológico y grado de diferenciación del cáncer de endometrio; asimismo comparamos la exactitud de la ultrasonografía transvaginal y la resonancia magnética en la determinación de la infiltración del miometrio antes del tratamiento quirúrgico. Material y métodos: 21 pacientes con diagnóstico de cáncer de endometrio, hospitalizadas en Instituto Nacional de Enfermedades Neoplásicas, desde Agosto del 2007 hasta Abril del 2008, fueron evaluadas en el preoperatorio con biopsia de endometrio, ultrasonografia transvaginal y resonancia magnética determinando la infiltración miometrial, comparando estos resultados con los hallazgos histopatológicos de la pieza operatoria. Resultados: La exactitud de la biopsia de endometrio para determinar el tipo histológico y grado de diferenciación del tumor, fue 95% y 72% respectivamente. No se encontraron diferencias estadísticamente significativas entre la exactitud de la ultrasonografia transvaginal y la resonancia magnética para determinar la profundidad de invasión del miometrio (71% vs. 86% p=0,228). Conclusión: Existe una alta correlación entre la biopsia prequirúrgica de endometrio y el estudio anatomopatológico de la pieza operatoria y la ultrasonografía transvaginal es tan efectiva como la resonancia magnética en la evaluación preoperatoria de las pacientes con cáncer de endometrio. La biopsia de endometrio y la ultrasonografia transvaginal en la evaluación preoperatoria pueden ayudarnos a clasificar a los pacientes con cáncer de endometrio en grupos de diferente riesgo para planificar un tratamiento quirúrgico adecuado.

Initial management of endometrial cancer is surgery based on prognostic factors can be evaluated in the preoperative evaluation. In this study we evaluated the accuracy of endometrial biopsy to determine histological type and degree of differentiation of endometrial cancer; also compare the accuracy of transvaginal ultrasonography and magnetic resonance in determining miometral infiltration before surgical treatment. Material and methods: 21 patients diagnosed with endometrial cancer, hospitalized at the Instituto Nacional de Enfermedades Neoplásicas, from August 2007 to April 2008 were evaluated in the preoperative endometrial biopsy, transvaginal ultrasound and magnetic resonance determining miometral infiltration, comparing these results with the histological findings of the surgical specimen. Results: The accuracy of endometrial biopsy to determine the histological type and degree of differentiation of the tumor was 95% and 72% respectively. There are not statistically significant differences between the accuracy of transvaginal ultrasonography and magnetic resonance to determine the depth of miometral invasion (71% vs. 86% p = 0.228). Conclusion: There is a high correlation between preoperative endometrial biopsy and the pathological specimen; and transvaginal ultrasonography is as effective as magnetic resonance in the preoperative evaluation of patients with endometrial cancer. The endometrial biopsy and transvaginal ultrasonography in the preoperative evaluation may help to classify patients with endometrial cancer in different risk groups to plan appropriate surgical treatment.

Quantifying energy dissipation by grazing animals in harsh environments.

Grazing systems in harsh environments are common throughout the world, and animal production is the mainstay of the livelihoods of many resource-poor farmers. The energy cost of the various activities involved in the process of harvesting the pasture to transform it into animal product can be estimated through an energy balance. This cost would be the difference between the metabolizable energy intake (MEI) and the energy expenditures for maintenance (MEm), temperature regulation (MEtr), and the energy for production (MEp). Each of the ME has its own net energy (NE) and its associated efficiency (K). When MEI>MEm+MEtr+MEp, the difference is attributable to the energy dissipated during grazing. The efficiency of converting the energy consumed into animal products depends on the magnitude of the dissipation. The inefficiency is associated with the energy spent in locomotion and the stress produced when there is low availability of energy in the pasture. This paper presents a method to quantify the dissipation of energy by grazing animals by considering it as a function of available energy. Such an understanding is required in order to develop management strategies to increase conversion efficiency.

Perforación rectosigmoide asintomática y extrusión peranal de catéter de derivación ventrículoperitoneal / Perforation rectumsigmoid asymptomatic and extrusion peranal of catheter of derivation ventricleperitoneal

Se estudia la historia clínica de un lactante de 10 meses de edad, quien fue hospitalizado por la expulsión a través del ano de la extremidad distal de un catéter de derivación ventrículoperitoneal que había sido implantado por hidrocefalia congénita. Se discute el mecanismo probable de la reducción espontánea del tubo y la forma de abordar el manejo de esta rara complicación