A mathematical model of a criminal-prone society

Criminals are common to all societies. To fight against them the community takes different security measures as, for example, to bring about a police. Thus, crime causes a depletion of the common wealth not only by criminal acts but also because the cost of hiring a police force. In this paper, we present a mathematical model of a criminal-prone self-protected society that is divided into socio-economical classes. We study the effect of a non-null crime rate on a free-of-criminals society which is taken as a reference system. As a consequence, we define a criminal-prone society as one whose free-of-criminals steady state is unstable under small perturbations of a certain socio-economical context. Finally, we compare two alternative strategies to control crime: (i) enhancing police efficiency, either by enlarging its size or by updating its technology, against (ii) either reducing criminal appealing or promoting social classes at risk

The Advantage of Arriving First: Characteristic Times in Finite Size Populations of Error-Prone Replicators

We study the evolution of a finite size population formed by mutationally isolated lineages of error-prone replicators in a two-peak fitness landscape. Computer simulations are performed to gain a stochastic description of the system dynamics. More specifically, for different population sizes, we compute the probability of each lineage being selected in terms of their mutation rates and the amplification factors of the fittest phenotypes. We interpret the results as the compromise between the characteristic time a lineage takes to reach its fittest phenotype by crossing the neutral valley and the selective value of the sequences that form the lineages. A main conclusion is drawn: for finite population sizes, the survival probability of the lineage that arrives first to the fittest phenotype rises significantly

Agreement Abstractions in Anonymous and Homonymous Distributed Systems Prone to Failures

The distributed computing models typically assume every process in the system has a distinct identifier (ID) or each process is programmed differently, which is named as eponymous system. In such kind of distributed systems, the unique ID is helpful to solve problems: it can be incorporated into messages to make them trackable (i.e., to or from which process they are sent) to facilitate the message transmission; several problems (leader election, consensus, etc.) can be solved without the information of network property in priori if processes have unique IDs; messages in the register of one process will not be overwritten by others process if this process announces; it is useful to break the symmetry. Hence, eponymous systems have influenced the distributed computing community significantly either in theory or in practice. However, every thing in the world has its own two sides. The unique ID also has disadvantages: it can leak information of the network(size); processes in the system have no privacy; assign unique ID is costly in bulk-production(e.g, sensors). Hence, homonymous system is appeared. If some processes share the same ID and programmed identically is called homonymous system. Furthermore, if all processes shared the same ID or have no ID is named as anonymous system. In homonymous or anonymous distributed systems, the symmetry problem (i.e., how to distinguish messages sent from which process) is the main obstacle in the design of algorithms. This thesis is aimed to propose different symmetry break methods (e.g., random function, counting technique, etc.) to solve agreement problem. Agreement is a fundamental problem in distributed computing including a family of abstractions. In this thesis, we mainly focus on the design of consensus, set agreement, broadcast algorithms in anonymous and homonymous distributed systems. Firstly, the fault-tolerant broadcast abstraction is studied in anonymous systems with reliable or fair lossy communication channels separately. Two classes of anonymous failure detectors AΘ and AP∗ are proposed, and both of them together with a already proposed failure detector ψ are implemented and used to enrich the system model to implement broadcast abstraction. Then, in the study of the consensus abstraction, it is proved the AΩ′ failure detector class is strictly weaker than AΩ and AΩ′ is implementable. The first implementation of consensus in anonymous asynchronous distributed systems augmented with AΩ′ and where a majority of processes does not crash. Finally, a general consensus problem– k-set agreement is researched and the weakest failure detector L used to solve it, in asynchronous message passing systems where processes may crash and recover, with homonyms (i.e., processes may have equal identities), and without a complete initial knowledge of the membership.

Agreement Abstractions in Anonymous and Homonymous Distributed Systems Prone to Failures

The distributed computing models typically assume every process in the system has a distinct identifier (ID) or each process is programmed differently, which is named as eponymous system. In such kind of distributed systems, the unique ID is helpful to solve problems: it can be incorporated into messages to make them trackable (i.e., to or from which process they are sent) to facilitate the message transmission; several problems (leader election, consensus, etc.) can be solved without the information of network property in priori if processes have unique IDs; messages in the register of one process will not be overwritten by others process if this process announces; it is useful to break the symmetry. Hence, eponymous systems have influenced the distributed computing community significantly either in theory or in practice. However, every thing in the world has its own two sides. The unique ID also has disadvantages: it can leak information of the network(size); processes in the system have no privacy; assign unique ID is costly in bulk-production(e.g, sensors). Hence, homonymous system is appeared. If some processes share the same ID and programmed identically is called homonymous system. Furthermore, if all processes shared the same ID or have no ID is named as anonymous system. In homonymous or anonymous distributed systems, the symmetry problem (i.e., how to distinguish messages sent from which process) is the main obstacle in the design of algorithms. This thesis is aimed to propose different symmetry break methods (e.g., random function, counting technique, etc.) to solve agreement problem. Agreement is a fundamental problem in distributed computing including a family of abstractions. In this thesis, we mainly focus on the design of consensus, set agreement, broadcast algorithms in anonymous and homonymous distributed systems. Firstly, the fault-tolerant broadcast abstraction is studied in anonymous systems with reliable or fair lossy communication channels separately. Two classes of anonymous failure detectors AΘ and AP∗ are proposed, and both of them together with a already proposed failure detector ψ are implemented and used to enrich the system model to implement broadcast abstraction. Then, in the study of the consensus abstraction, it is proved the AΩ′ failure detector class is strictly weaker than AΩ and AΩ′ is implementable. The first implementation of consensus in anonymous asynchronous distributed systems augmented with AΩ′ and where a majority of processes does not crash. Finally, a general consensus problem– k-set agreement is researched and the weakest failure detector L used to solve it, in asynchronous message passing systems where processes may crash and recover, with homonyms (i.e., processes may have equal identities), and without a complete initial knowledge of the membership.

Terremoto 2010 en Chile y vivienda social: resultados y aprendizajes para recomendación de políticas públicas

El territorio chileno esta propenso, desde antes que se constituyera como nación, al impacto del comportamiento de la naturaleza que le es inherente y que también le produce daños. Está representado en los seísmos, los más dañinos. Todavía, la sociedad chilena no termina de comprender que esos daños, son parte de un desequilibrio de una convivencia armoniosa entre ella y esa naturaleza, puesto que el ser humano que vive y habita sobre ella, también lo es. Así entonces, cada vez que el territorio y su espacio son remecidos por los seísmos, la naturaleza, manifestada en la sociedad, adquiere nuevos aprendizajes para mejorar la respuesta al próximo evento. El terremoto 2010 de 8.8° Richter, fue el segundo de mayor magnitud después del otro que hasta ahora, es el más grande del planeta, y que pudo ser medido. Aquel, fue el terremoto de Valdivia de 9,5° Richter, ocurrido el 22 de mayo de 1960. Las sociedades no son estáticas, cambian, son dinámicas. Esta vez el seísmo del 2010, ocurrió en una sociedad que hace ya 35 años, adoptó un modelo de economía de libre mercado. La pobreza que tenía a 1990, era de aproximadamente, un 40%. La del 2010, de un 14%. Durante la dictadura militar hubo otro seísmo de 7,8° Richter, recién instalándose el modelo aludido. El del 2010, permite sacar conclusiones en el contexto de este modelo económico. Los resultados aparentemente son interesantes en cuanto a que hubo pocas víctimas pero por otra parte, hubo un gran daño económico. La tesis profundiza en el impacto del seísmo en la dimensión del parque habitacional construido y de la vivienda social y en los habitantes más pobres y vulnerables. Es la primera investigación sobre seísmos y vivienda social en Chile. Se asume la hipótesis que ciertas variables por una parte, y una cultura antisísmica por otra, están presentes y han penetrado en los sectores populares durante los últimos 50 años y que ello, podría estar en la base de los resultados obtenidos. Se plantea una suerte de “matrimonio bien avenido” entre el habitante y políticas públicas en vivienda. De ello, se derivan recomendaciones para mejorar los avances en el problema investigado que se contextualizan en referencia al marco teórico elaborado. Sin embargo, y no obstante lo investigado, lo ya avanzado no garantiza buenos resultados en el próximo evento, Por ello, los aprendizajes nutren a otros, nuevos, que acompañarán a la sociedad chilena en su esencia e identidad como nación. ABSTRACT Long before its establishment as an independent nation, the Chilean territory has been prone to the impact of nature, which is an inherent and damaging feature of this land. Such an impact is represented by earthquakes, which are regarded as the most damaging natural disasters. Today, the Chilean society is still unable to understand that these impacts are part of an unbalanced coexistence between individuals and nature since human beings, who live and inhabit this space, are also an element of nature. Therefore, each time this territory is hit by earthquakes, nature —represented by society— learns new lessons in order to provide a better response to future events. The 2010 earthquake, which rated 8.8 on the Richter scale, was the second largest earthquake after the most powerful earthquake ever recorded. Such an event was the Valdivia earthquake of May 22, 1960, which rated 9.5 on the Richter scale. Societies are not static as they are changing and dynamic. The 2010 earthquake took place within a context in which society operated under a free market economy model that had been running for 35 years. As of 1990, 40 per cent of the population lived in poverty; in 2010, such a figure was reduced to 14 per cent. Likewise, a magnitude 7.8 quake struck the country during the military regime period in the early days of the above model. The 2010 earthquake allows us to draw some conclusions within the context of this economic model. Results are interesting since there were few fatalities but significant economic loss. This thesis provides insights into the impact of the 2010 earthquake on the housing stock, social housing and those living in poverty and vulnerability. This is the first research on earthquakes and social housing conducted in Chile. The hypothesis is that certain variables and anti-seismic culture have permeated popular segments of the population over the last 50 years. The latter may be at the basis of the results obtained during this research. Likewise, this study proposes a certain “happy marriage” between the inhabitant and public policies on housing. The above offers some recommendations intended to further explore this issue; these suggestions are contextualized according to the theoretical framework developed in this research. However, current progress on this matter does not ensure positive results in the event of an earthquake. This is why these lessons will serve as models for future events, which are intrinsically tied to local society and Chilean identity.