On the diameter of random planar graphs

We show that the diameter D(G_n) of a random labelled connected planar graph with n vertices is equal to n^{1/4+o(1)}, in probability. More precisely there exists a constant c>0 such that the probability that D(G_n) lies in the interval (n^{1/4-\epsilon},n^{1/4+\epsilon}) is greater than 1-\exp(-n^{c\epsilon}) for {\epsilon} small enough and n>n_0(\epsilon). We prove similar statements for 2-connected and 3-connected planar graphs and maps.Comment: 24 pages, 7 figure

Positioning Verfification in the Context of Software/System Certification

Formal verification applied to software has been seen as an important focus in research for determining the acceptability of that software for use. However, in examining the requirements for determining the safety of a software intensive system for use in critical situations, it is quite clear that verification plays a role,but not necessarily a central role. It is entirely possible that a piece of software satisfies its specification, but is unsafe to use. (The first and foremost reason for this is that the program satisfies an unsafe specification.) In this paper we will address the nature of certification in the context of critical systems, decomposing it,by means of a new philosophical framework, into four aspects: evidence, confidence, determination and certification. Our point of view is that establishing the safety (in a very general sense) of a system is a confidence building exercise much in the same vein as the scientific method; our framework serves as a setting in which we can properly understand and develop such an exercise. We will then place formal verification and assurance cases in this setting, discussing their roles and limitations.Keywords: Software certification, System certification, Formal specification, Verification,Critical systems, Safety, Assurance cases, Safety case

SESSION 6: Innovating the Built Environment Post-COVID-19

ABSTRACT: Innovating the Built Environment for a Post-COVID-19 World It would seem an act of academic malpractice to teach a course titled Innovating the Built Environment: How the Law Responds to Disruptive Change, and host an all-day symposium as an integral part of that course, and not endeavor to address the most-disruptive thing to happen to the built environment in more than 100 years: The coronavirus pandemic. This disruption to real estate is the proverbial elephant in the room. Hopefully, it will maintain a minimum six-foot distance from others as we address how it impacts the four Special Topics addressed above. What should/will our built environment look like in a post-COVID 19 world? This Session 6 discussion begins with two special guests as Featured Speakers and then brings back a few of the panelists from earlier sessions to discuss how today’s Special Topics may be fundamentally altered for a post-COVID 19 world

Growth of high quality InP layers in STI trenches on miscut Si (001) substrates

In this work, we report the selective area epitaxial growth of high quality InP in shallow trench isolation (STI) structures on Si (0 0 1) substrates 6° miscut toward (1 1 1) using a thin Ge buffer layer. We studied the impact of growth rates and steric hindrance effects on the nano-twin formation at the STI side walls. It was found that a too high growth rate induces more nano-twins in the layer and results in InP crystal distortion. The STI side wall tapering angle and the substrate miscut angle induced streric hindrance between the InP facets and the STI side walls also contribute to defect formation. In the [-1 1 0] orientated trenches, when the STI side wall tapering angle is larger than 10°, crystal distortion was observed while the substrate miscut angle has no significant impact on the InP defect formation. In the [-1 1 0] trenches, both the increased STI tapering angle and the substrate miscut angle induce high density of defects. With a small STI tapering angle and a thin Ge layer, we obtained extended defect free InP in the top region of the [1 1 0] trenches with aspect ratio larger than 2

The PACE|AA Protocol for Machine Readable Travel Documents, and its Security

We discuss an efficient combination of the cryptographic protocols adopted by the International Civil Aviation Organization (ICAO) for securing the communication of machine readable travel documents and readers. Roughly, in the original protocol the parties first run the Password-Authenticated Connection Establishment (PACE) protocol to establish a shared key and then the reader (optionally) invokes the Active Authentication (AA) protocol to verify the passport\u27s validity. Here, we show that by carefully re-using some of the secret data of the PACE protocol for the AA protocol one can save one exponentiation on the passports\u27s side. We call this the PACE|AA protocol. We then formally prove that this more efficient combination not only preserves the desirable security properties of the two individual protocols but also increases privacy by preventing misuse of the challenge in the Active Authentication protocol. We finally discuss a solution which allows deniable authentication in the sense that the interaction cannot be used as a proof towards third parties

The role of body height as a co-factor of excess weight in Switzerland

OBJECT: Excess weight (Body Mass Index [BMI] ≥25.0 kg/m2 ) is a major health issue worldwide, including in Switzerland. For high-income countries, little attention has been paid to body height in context of excess weight. The aim of this study is to assess the importance of body height as a co-factor for excess weight in multiple large nationwide data sets. DATA AND METHODS: In this comparative study, we included the largest nationwide and population-based studies in the fields of public health, nutrition and economics for Switzerland, as well as data of the medical examination during conscription for the Swiss Armed Forces, which contained information on BMI and, if possible, waist-to-height-ratio (WHtR) and waist-to-hip-ratio (WHR). RESULTS: The multinomial logistic regressions show that the probability of belonging to the excess weight category (BMI ≥25.0 kg/m2 ) decreased with increasing height in both sexes inall contemporary data sets. This negative association was shown to be constant, only among conscripts measured in the 1870s the association was positive, when increasing height was associated with a higher BMI. The negative association not only emerge in BMI, but also in WHtR and WHR. CONCLUSION: Our results emphasize the importance of body height as a co-factor of excess weight, suggesting a clear negative association between height and BMI, WHtR and WHR. Evidence indicates that both early-life environmental exposures and alleles associated with height may contribute to these associations. This knowledge could serve as further starting points for prevention programs in the field of public health

The role of body height as a co-factor of excess weight in Switzerland.

OBJECT Excess weight (Body Mass Index [BMI] ≥25.0 kg/m2 ) is a major health issue worldwide, including in Switzerland. For high-income countries, little attention has been paid to body height in context of excess weight. The aim of this study is to assess the importance of body height as a co-factor for excess weight in multiple large nationwide data sets. DATA AND METHODS In this comparative study, we included the largest nationwide and population-based studies in the fields of public health, nutrition and economics for Switzerland, as well as data of the medical examination during conscription for the Swiss Armed Forces, which contained information on BMI and, if possible, waist-to-height-ratio (WHtR) and waist-to-hip-ratio (WHR). RESULTS The multinomial logistic regressions show that the probability of belonging to the excess weight category (BMI ≥25.0 kg/m2 ) decreased with increasing height in both sexes inall contemporary data sets. This negative association was shown to be constant, only among conscripts measured in the 1870s the association was positive, when increasing height was associated with a higher BMI. The negative association not only emerge in BMI, but also in WHtR and WHR. CONCLUSION Our results emphasize the importance of body height as a co-factor of excess weight, suggesting a clear negative association between height and BMI, WHtR and WHR. Evidence indicates that both early-life environmental exposures and alleles associated with height may contribute to these associations. This knowledge could serve as further starting points for prevention programs in the field of public health

High Frequency Asymptotics for the Spin-Weighted Spheroidal Equation

We fully determine a uniformly valid asymptotic behaviour for large $a \omega$ and fixed $m$ of the angular solutions and eigenvalues of the spin-weighted spheroidal differential equation. We fully complement the analytic work with a numerical study.Comment: The .tar.gz file should contain 1 tex file, 24 figures in .ps format and 1 bibliography file in .bbl format. All these files are located in the same director