Condensation of degrees emerging through a first-order phase transition in classical random graphs

Due to their conceptual and mathematical simplicity, Erd\"os-R\'enyi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely considered in complex network theory, the condensation of degrees has hitherto eluded a careful study. Here we show that the degree statistics of the classical random graph model undergoes a first-order phase transition between a Poisson-like distribution and a condensed phase, the latter characterized by a large fraction of nodes having degrees in a limited sector of their configuration space. The mechanism underlying the first-order transition is discussed in light of standard concepts in statistical physics. We uncover the phase diagram characterizing the ensemble space of the model and we evaluate the rate function governing the probability to observe a condensed state, which shows that condensation of degrees is a rare statistical event akin to similar condensation phenomena recently observed in several other systems. Monte Carlo simulations confirm the exactness of our theoretical results.Comment: 8 pages, 6 figure

Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase

We calculate the level compressibility $\chi(W,L)$ of the energy levels inside $[-L/2,L/2]$ for the Anderson model on infinitely large random regular graphs with on-site potentials distributed uniformly in $[-W/2,W/2]$. We show that $\chi(W,L)$ approaches the limit $\lim_{L \rightarrow 0^+} \chi(W,L) = 0$ for a broad interval of the disorder strength $W$ within the extended phase, including the region of $W$ close to the critical point for the Anderson transition. These results strongly suggest that the energy levels follow the Wigner-Dyson statistics in the extended phase, consistent with earlier analytical predictions for the Anderson model on an Erd\"os-R\'enyi random graph. Our results are obtained from the accurate numerical solution of an exact set of equations valid for infinitely large regular random graphs.Comment: 7 pages, 3 figure

Condensation of degrees emerging through a first-order phase transition in classical random graphs

Due to their conceptual and mathematical simplicity, Erdös-Rényi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely considered in complex network theory, the condensation of degrees has hitherto eluded a careful study. Here we show that the degree statistics of the classical random graph model undergoes a first-order phase transition between a Poisson-like distribution and a condensed phase, the latter characterized by a large fraction of nodes having degrees in a limited sector of their configuration space. The mechanism underlying the first-order transition is discussed in light of standard concepts in statistical physics. We uncover the phase diagram characterizing the ensemble space of the model, and we evaluate the rate function governing the probability to observe a condensed state, which shows that condensation of degrees is a rare statistical event akin to similar condensation phenomena recently observed in several other systems. Monte Carlo simulations confirm the exactness of our theoretical result

Large-deviation theory for dilutedWishart random matrices

Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue fluctuations of dilutedWishart random matrices based on the replica approach of disordered systems.We derive an analytical expression for the cumulant generating function of the number of eigenvalues IN(x) smaller than x ∈ R+, from which all cumulants of IN(x) and the rate function x (k) controlling its large-deviation probability Prob[IN(x) = kN] e −N x (k) follow. Explicit results for themean value and the variance of IN(x), its rate function, and its third cumulant are discussed and thoroughly compared to numerical diagonalization, showing very good agreement. The presentwork establishes the theoretical framework put forward in a recent letter [Phys. Rev. Lett. 117, 104101 (2016)] as an exact and compelling approach to deal with eigenvalue fluctuations of sparse random matrices

Analysis of the social development in isolated rural areas through agent-based simulation

Este documento busca identificar el desarrollo humano y social en áreas rurales donde la energía juega un papel importante en la forma en la cual las personas toman decisiones y su papel en la mejora de la calidad de vida, medida como la satisfacción de las necesidades básicas de Maslow. El modelo de simulación basada en agentes (ABM) descrito, en conjunto con los resultados de simulaciones realizadas permite caracterizar y concluir respecto al impacto de la adopción de la energía en el desarrollo de una región rural. El estudio muestra que las comunidades están en capacidad de adaptarse y generar un incremento en la calidad de vida mediante el uso de la energía en la vida diaria, permitiendo mostrar que la adopción de una energía en la zona es una herramienta que posibilita el desarrollo de la región.The purpose of this research work is to identify the human and social development in rural areas where electric energy plays an important role in the way people make decisions, and its role in the life quality improvement, which is measured as the satisfaction of Maslow’s basic needs. The described simulation model, based on agents (ABM), jointly with the results of performed simulations allow characterizing and concluding with regard to the impact of the incorporation of electric energy in the development of a rural region. The study exhibits that communities have the capability to adapt and generate an increase in the quality of life by means of the use of electric power in the day-to-day life, allowing to show that the incorporation of electric energy in the area is a tool that enables the development of the region

Nivel de Cumplimiento del protocolo MINSA, en el abordaje del embarazo prolongado en el Hospital Bertha Calderón Roque en el periodo Septiembre–Octubre 2014

Embarazo postérmino (EP) es aquel que se extiende más allá de las 42 semanas de amenorrea completa o 294 días del último periodo menstrual. Se considera que un embarazo prolongado se asocia a mayor morbi-mortalidad perinatal. El riesgo de mortalidad fetal aumenta en 2,5 veces en gestaciones de 41 a 42 semanas, así mismo está asociado con distocia de labor y cesárea. Se estima que de 4 a 19% de los embarazos alcanzan las 42 semanas y del 2 a 7% completan 43 semanas. En otros estudios la incidencia varía entre el 5 y 8% de los partos y es considerado de alto riesgo por condicionar una mayor morbimortalidad. La mortalidad fetal aumenta después de las 42 semanas y se duplica a las 43 semanas. Aproximadamente un tercio de las muertes se deben a asfixia intrauterina por insuficiencia placentaria, contribuyendo además con la mayor incidencia de malformaciones, especialmente del sistema nervioso central. A la asfixia perinatal se agrega además, la compresión del cordón umbilical y el síndrome de aspiración meconial. El retardo del crecimiento y la macrosomía fetal son condiciones que se observan con mayor frecuencia en el embarazo prolongado. La macrosomía constituye factor de riesgo para traumatismo obstétrico (fractura de clavícula, parálisis braquial, céfalo hematoma). Otros riesgos son la dificultad para regular la temperatura y complicaciones metabólicas como hipoglucemia y policitemia. El 20 a 25% de los recién nacidos postérmino concentra el alto riesgo perinatal. En el momento actual, tomando en cuenta los elementos biofísicos y teniendo una buena clínica obstétrica de base: anamnesis, altura uterina, circunferencia abdominal, volumen del líquido amniótico, ganancia de peso materno y la prueba de movimientos fetales, permiten un seguimiento clínico adecuado de estos pacientes

Gradient-Descent Quantum Process Tomography by Learning Kraus Operators

We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive. To make the process trace preserving, we use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. Our ansatz uses a few Kraus operators to avoid direct estimation of large process matrices, e.g., the Choi matrix, for low-rank quantum processes. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes, but shines by combining the best features of these two methods. Similar to CS (but unlike PLS), GD-QPT can reconstruct a process from just a small number of random measurements, and similar to PLS (but unlike CS) it also works for larger system sizes, up to at least five qubits. We envisage that the data-driven approach of GD-QPT can become a practical tool that greatly reduces the cost and computational effort for QPT in intermediate-scale quantum systems

Strengthening patients’ triage in community pharmacies: A cluster randomised controlled trial to evaluate the clinical impact of a minor ailment service

Background Self-perceived minor ailments might conceal other health conditions if patients are not appropriately assisted by health care professionals. The aim of the study was to evaluate the patient-related outcomes of a community pharmacy Minor Ailment Service (MAS) compared to usual pharmacist care (UC). Methods A cluster randomised controlled trial was conducted over six months in community pharmacy in the province of Valencia (Spain). Patients seeking care or requesting a product for a minor ailments considered in the study (dermatological problems, gastrointestinal disturbance, pain and upper respiratory tract related symptoms) were included. The intervention consisted of a standardised pharmacist-patient consultation guided by a web-based program using co-developed management protocols and patients’ educational material. Patients were followed up by phone ten days later. Primary clinical outcomes were appropriate medical referral and modification of direct product request. Secondary outcomes were symptom resolution and reconsultation rates. Results A total of 808 patients (323 MAS and 485 UC) were recruited in 27 pharmacies of 21 municipalities. Patients visiting MAS pharmacies had higher odds for being referred to a physician (OR = 2.343, CI95% = [1.146–4.792]) and higher reconsultation rates (OR = 1.833, CI95% = [1.151–2.919]) compared to UC. No significant differences between groups were observed for modification of direct product request and symptom resolution. Conclusions The use of management protocols through the MAS strengthened the identification of referral criteria such as red flags in patients suffering minor ailments. These patients with symptoms of minor ailments possibly due to more severe illness were to be referred and evaluated by physicians. Results reinforce that MAS increases safety for those patients consulting in community pharmacy for minor ailments.Spanish Society of Community PharmacyPharmaceutical Association of Valenci