Selected problems involving the probability of ruin for an insurance company

In the actuarial science literature, an insurance company is said to be ruined if, at some time t \u3e 0, the aggregate claims up to time t exceed the sum of the initial surplus and the total premium collected up to time t. The calculation and/or estimation of the probability of ruin is of fundamental importance. In this paper we use computer simulation to estimate the probabilities of ruin over a finite horizon of time when the aggregate claims process is Compound Poisson and the distribution of the claim sizes is: (i) Weibull, and (ii) exponential with a random parameter. The obtained estimates are compared with the case of exponential claim sizes and it is found that, in all but the increasing failure rate Weibull case, the probability of ruin, assuming exponential claims, overestimates the actual probability of ruin. Thus, one should be extremely careful in using the exponential claim formula uncritically

Dynamics of methane ebullition from a peat monolith revealed from a dynamic flux chamber system

Methane (CH4) ebullition in northern peatlands is poorly quantified in part due to its high spatiotemporal variability. In this study, a dynamic flux chamber (DFC) system was used to continuously measure CH4 fluxes from a monolith of near‐surface Sphagnum peat at the laboratory scale to understand the complex behavior of CH4 ebullition. Coincident transmission ground penetrating radar measurements of gas content were also acquired at three depths within the monolith. A graphical method was developed to separate diffusion, steady ebullition, and episodic ebullition fluxes from the total CH4 flux recorded and to identify the timing and CH4 content of individual ebullition events. The results show that the application of the DFC had minimal disturbance on air‐peat CH4 exchange and estimated ebullition fluxes were not sensitive to the uncertainties associated with the graphical model. Steady and episodic ebullition fluxes were estimated to be averagely 36 ± 24% and 38 ± 24% of the total fluxes over the study period, respectively. The coupling between episodic CH4 ebullition and gas content within the three layers supports the existence of a threshold gas content regulating CH4 ebullition. However, the threshold at which active ebullition commenced varied between peat layers with a larger threshold (0.14 m3 m−3) observed in the deeper layers, suggesting that the peat physical structure controls gas bubble dynamics in peat. Temperature variation (23°C to 27°C) was likely only responsible for small episodic ebullition events from the upper peat layer, while large ebullition events from the deeper layers were most likely triggered by drops in atmospheric pressure

How to Optimally Constrain Galaxy Assembly Bias: Supplement Projected Correlation Functions with Count-in-cells Statistics

Most models for the connection between galaxies and their haloes ignore the possibility that galaxy properties may be correlated with halo properties other than mass, a phenomenon known as galaxy assembly bias. Yet, it is known that such correlations can lead to systematic errors in the interpretation of survey data. At present, the degree to which galaxy assembly bias may be present in the real Universe, and the best strategies for constraining it remain uncertain. We study the ability of several observables to constrain galaxy assembly bias from redshift survey data using the decorated halo occupation distribution (dHOD), an empirical model of the galaxy--halo connection that incorporates assembly bias. We cover an expansive set of observables, including the projected two-point correlation function $w_{\mathrm{p}}(r_{\mathrm{p}})$, the galaxy--galaxy lensing signal $\Delta \Sigma(r_{\mathrm{p}})$, the void probability function $\mathrm{VPF}(r)$, the distributions of counts-in-cylinders $P(N_{\mathrm{CIC}})$, and counts-in-annuli $P(N_{\mathrm{CIA}})$, and the distribution of the ratio of counts in cylinders of different sizes $P(N_2/N_5)$. We find that despite the frequent use of the combination $w_{\mathrm{p}}(r_{\mathrm{p}})+\Delta \Sigma(r_{\mathrm{p}})$ in interpreting galaxy data, the count statistics, $P(N_{\mathrm{CIC}})$ and $P(N_{\mathrm{CIA}})$, are generally more efficient in constraining galaxy assembly bias when combined with $w_{\mathrm{p}}(r_{\mathrm{p}})$. Constraints based upon $w_{\mathrm{p}}(r_{\mathrm{p}})$ and $\Delta \Sigma(r_{\mathrm{p}})$ share common degeneracy directions in the parameter space, while combinations of $w_{\mathrm{p}}(r_{\mathrm{p}})$ with the count statistics are more complementary. Therefore, we strongly suggest that count statistics should be used to complement the canonical observables in future studies of the galaxy--halo connection.Comment: Figures 3 and 4 show the main results. Published in Monthly Notices of the Royal Astronomical Societ

Sleep disturbances and circadian CLOCK genes in borderline personality disorder

Borderline personality disorder (BPD) is characterised by a deep-reaching pattern of affective instability, incoherent identity, self-injury, suicide attempts, and disturbed interpersonal relations and lifestyle. The daily activities of BPD patients are often chaotic and disorganized, with patients often staying up late while sleeping during the day. These behavioural patterns suggest that altered circadian rhythms may be associated with BPD. Furthermore, BPD patients frequently report suffering from sleep disturbances. In this review, we overview the evidence that circadian rhythms and sleep are disturbed in BPD, and we explore the possibility that personality traits that are pertinent for BPD may be associated with circadian typology, and perhaps to circadian genotypes. With regards to sleep architecture, we review the evidence that BPD patients display altered non-REM and REM sleep. A possible cue to a deeper understanding of this temporal dysregulation might be an analysis of the circadian clock at the molecular and cellular level, as well as behavioural studies using actigraphy and we suggest avenues for further exploration of these factors

How Grading for Equity Changed the Way I Teach

If you are anything like us, you are likely frustrated with the amount of time you spend both grading and then quibbling with students about grades - oftentimes in situations that have no real connection with classroom learning. Members of the computer science department at UNI have been discussing teaching and learning together for years and we were thrilled to discover the 2019 book Grading for Equity by author and educator Joe Feldman. In it he writes There is growing awareness that traditional grading practices have become a barrier to meaningful student learning. From this belief he presents a style of classroom management and grading built on three pillars: that grades should be accurate, bias-resistant, and provide intrinsic student motivation. For the last three years we have been using this style of grading in a variety of computer science and education courses and it has fundamentally changed the way we teach. In this session we will present on the WHAT and WHY of Grading for Equity and share with you the HOW as we discuss the ways we have used this grading structure in our own classrooms

Logic and Theory Repair in Legal Modification

The complexities involved in adapting current traffic regulations to accommodate autonomous vehicles (AVs) arise from the intricate legal rules and the changes in the traditional roles of drivers and legal responsibility. We argue that revising the law during the legal reform process can be seen as an effort to rectify the legal reasoning that is no longer suitable for the new circumstance. In this paper, we propose to apply an automatic theory repair system, called ABC, to assist legal professionals in making changes to legal rules more efficiently

A legal system to modify autonomous vehicle designs in transnational contexts

Autonomous vehicles, one of the signature technologies of the rapid development of artificial intelligence, have brought about a rapid change in the relevant legal norms and legal mandates. This change makes it more challenging for manufacturers and designers of autonomous vehicles to ensure the legal compliance of their product designs in a more dynamic way. Therefore, rather than approaching the issue from the perspective of judges or the cars themselves, we propose a legal reasoning system applicable to the adjustment of autonomous vehicle design options from the designer’s perspective, building on a series of previous studies. Focusing on the circulation of autonomous vehicles between different countries, the system attempts to help designers accomplish the adjustment of design solutions between different legal systems instead of designing new prototypes

Charge Neutrality of the Color-Flavor Locked Phase from the Low Energy Effective Theory

We investigate the issue of charge neutrality of the CFL$K^0$ phase of dense quark matter using the low energy effective theory of high density QCD. We show that the local electric and color charge neutrality of the ground state in a homogeneous color superconducting medium follows from its dynamics. We also consider the situation of a spatially inhomogeneous medium, such as may be found in a neutron star core. We find that spatial inhomogeneity results in the generation of electric fields, and positrons/electrons may be present in the ground state. We estimate the concentration of charged leptons in the ground state to be $n_{e}\sim{10^2}{cm}^{-3}$ and consider their influence on the opacity of the medium with respect to the modified photons.Comment: typos corrected, this version to appear in PR