We wish to verify that the mortality deceleration (or decrease) is a consequence of the bending of the shape parameter at old ages. This investigation is based upon the Weon model (the Weibull model with an age-dependent shape parameter) for human survival and mortality curves. According to the Weon model, we are well able to describe the mortality decrease after the mortality plateau, including the mortality deceleration. Furthermore, we are able to simply define the mathematical limit of longevity by the mortality decrease. From the demographic analysis of the historical trends in Switzerland (1876-2001) and Sweden (1861-2001), and the most recent trends in the other eleven developed countries (1996-2001), we confirm that the bending of the shape parameter after characteristic life is correlated with the mortality deceleration (or decrease). As a consequence, this bending of the shape parameters and the mortality deceleration is associated with the mathematical limit on longevity. These results suggest that the mathematical limit of longevity can be induced by the mortality deceleration (or decrease) in nature. These findings will give us a breakthrough for studying the mortality
Index-based hedging solutions are used to transfer the longevity risk to the capital markets. However, mismatches between the liability of the hedger and the hedging instrument cause longevity basis risk. Therefore, an appropriate two-population model to measure and assess the longevity basis risk is required. In this paper, we aim to construct a two-population mortality model to provide an effective hedge against the longevity basis risk. The reference population is modelled by using the Lee-Carter model with the renewal process and exponential jumps proposed by Özen and Şahin (2020) and the dynamics of the book population are specified. The analysis based on the UK mortality data indicates that the proposed model for the reference population and the common age effect model for the book population provide a better fit compared to the other models considered in the paper. Different two-population models are used to investigate the impact of the sampling risk on the index-based hedge as well as to analyse the risk reduction regarding hedge effectiveness. The results show that the proposed model provides a significant risk reduction when mortality jumps and the sampling risk are take
Human longevity leaders with remarkably long lifespan play a crucial role in the advancement of longevity research. In this paper, we propose a stochastic model to describe the evolution of the age of the oldest person in the world by a Markov process, in which we assume that the births of the individuals follow a Poisson process with increasing intensity, lifespans of individuals are independent and can be characterized by a gamma-Gompertz distribution with time-dependent parameters. We utilize a dataset of the world's oldest person title holders since 1955, and we compute the maximum likelihood estimate for the parameters iteratively by numerical integration. Based on our preliminary estimates, the model provides a good fit to the data and shows that the age of the oldest person alive increases over time in the future. The estimated parameters enable us to describe the distribution of the age of the record holder process at a future time point.
A typical galactic disc has a finite thickness and in addition to stars it also contains a finite amount of interstellar gas. Here, we investigate the physical impact of the finite thickness of a galactic disc on the disc stability against the non-axisymmetric perturbations and on the longevity of the spiral density waves, with and without the presence of gas. The longevity is quantified via group velocity of density wavepackets. The galactic disc is first modelled as a collisionless stellar disc with finite height and then more realistically as a gravitationally-coupled stars plus gas system (with different thickness for stars and gas). For each case, we derive the appropriate dispersion relation in the WKB approximation, and study the dynamical effect of the disc thickness on the life-time of spiral density waves via a parametric approach. We find the generic trend that the effective reduction in disc self-gravity due to disc thickness makes it more stable against the non-axisymmetric perturbations, and shortens the life-span of the spiral density waves. Further, the interstellar gas and the disc thickness are shown to have a mutually opposite dynamical effect on the disc stabili
Are there limits to human longevity? We suggest a new demographic model to describe human demographic trajectories. Specifically, the model mathematically defines the limits of longevity. Through the demographic analysis of trends for Sweden (between 1751 and 2002), Switzerland (between 1876 and 2002) and Japan (between 1950 and 1999), which are the longest-lived countries, we would like to demonstrate whether or not there is the ultimate limit to longevity. We analyse the trends of new demographic indicators, the characteristic life and the shape parameter, and calculate the mathematical limits of longevity. We find out the surprising phenomenon that the mathematical limits of longevity decrease as the longevity tendency increases in recent decades. These paradoxical trends will be explained by the complementarity of longevity, which is attributable to the nature of biological systems for longevity. According to the regression analysis, the ultimate limit for humans is estimated to be approximately 124 years, which may be considered to be the biological limit for humans.
There is little disagreement among insurance actuaries and financial economists about the societal benefits of longevity-risk pooling in the form of life annuities, defined benefit pensions, self-annuitization funds, and even tontine schemes. Indeed, the discounted value or cost of providing an income for life is lower -- in other words, the amount of upfront capital required to generate a similar income stream with the same level of statistical safety is lower -- when participants pool their financial resources versus going it alone. Moreover, when participants' financial circumstances and lifespans are homogenous, there is consensus on how to share the "winnings" among survivors, namely by distributing them equally among survivors, a.k.a. a uniform rule. Alas, what is lesser-known and much more problematic is allocating the winnings in such a pool when participants differ in wealth (contributions) and health (longevity), especially when the pools are relatively small in size. The same problems arise when viewed from the dual perspective of decentralized risk sharing (DRS). The positive correlation between health and income and the fact that wealthier participants are likely to li
We use a two-sex partial differential equation (PDE) model based on the Grandmother Hypothesis. We build on an earlier model by Kim et al. [27] by allowing for evolution in both longevity and age at last birth, and also assuming that post-fertile females support only their daughters' fertility. Similarly to Kim et al. [27], we find that only two locally stable equilibria exist: one corresponding to great ape-like longevities and the other corresponding to hunter-gatherer longevities. Our results show that grandmothering enables the transition between these two equilibria, without extending the end of fertility. Moreover, sensitivity analyses of the model show that male competition, arising from a skew in the mating sex ratio towards males, plays a significant role in determining whether the transition from great ape-like longevities to higher longevities is possible and the equilibrium value of the average adult lifespan. Whereas grandmothering effects have a significant impact on the equilibrium value of the average age at last birth and enable the transition to higher longevities, they have an insignificant impact on the equilibrium value of the average adult lifespan.
This paper statistically analysed pensioner longevity in Ghana. It fundamentally sought to ascertain the significant determinants of longevity amongst Ghanaian pensioners, specifically, SSNIT pensioners by estimating the mortality rate of SSNIT pensioners, determining the factors that significantly affect the longevity of the average SSNIT pensioner and constructing a predictive model for predicting the longevity of SSNIT pensioners in Ghana. Secondary data was obtained from the leading pension provider in Ghana, SSNIT. The results of the study revealed that the total number of male deaths was significantly greater, about four times more, than the total number of female deaths. There was sufficient evidence that there exists a lower rate of death among female pensioners as compared to male pensioners. Furthermore, a significant number of the SSNIT pensioners used in the analysis survived less than 8 years after retirement before their death and the average basic salary of the pensioners who lived less than 8 years after retirement was GH 7741.827 cedis and served for 35.65 years on average. On the contrary, it was observed that pensioners who lived more than 8 years after retiremen
In the framework of the supersymmetric standard model, the lighter stau often becomes long-lived. Such longevity of the stau is realized in three well-motivated scenarios: (A) the stau is the next-to-lightest supersymmetric particle (NLSP) and the gravitino is the lightest supersymmetric particle (LSP), (B) the stau is the LSP and R-parity is slightly violated, and (C) the stau is NLSP, the neutralino is the LSP, and the their masses are degenerate. We study the event topology and the decay of the stopping stau at the hadron calorimeter at the LHC, and show that it is possible to identify the reason why the stau becomes long-lived.
In recent we introduced, developed and established a new concept, model, methodology and principle for studying human longevity in terms of demographic basis. We call the new model the "Weon model", which is a general model modified from the Weibull model with an age-dependent shape parameter to describe human survival and mortality curves. We demonstrate the application of the Weon model to the mortality dynamics and the mathematical limit of longevity (the mortality rate to be mathematically zero, implying a maximum longevity) in the Section I. The mathematical limit of longevity can be induced by the mortality dynamics in nature. As a result, we put forward the complementarity principle, which explains the recent paradoxical trends that the mathematical limit decreases as the longevity increases, in the Section II. Our findings suggest that the human longevity can be limited by the complementarity principle.
To maximize value from an EGS system, engineers need to optimize flow rate, well spacing, and well configuration. Numerical simulations yield interesting and surprising results regarding the effect of coupled processes on long term thermal performance. Thermoelastic fracture opening and propagation can have a significant negative effect on the uniformity of flow. On the other hand, interactions between fracture opening and buoyancy driven fluid circulation cause downward fracture propagation during long-term circulation that greatly improves the thermal longevity of the system. Passive inflow control design can significantly mitigate the negative effect of thermoelastic fracture opening on flow uniformity, while maintaining the positive effects of thermoelastic fracture opening and propagation on flow rate and thermal longevity. Overall, simulations suggest that an EGS doublet with 8000 ft laterals at 475' F, using inflow control at the production well, could sustain electricity generation rates of 8 to 10 MWe for more than 30 years. Without inflow control, 6 to 8 MWe over 30 years is possible; however, there is greater risk of uncontrolled thermal breakthrough.
The probability of detecting technosignatures (i.e. evidence of technological activity beyond Earth) increases with their longevity, or the time interval over which they manifest. Therefore, the assumed distribution of longevities has some bearing on the chances of success of technosignature searches, as well as on the inferred age of technosignatures following a first contact. Here, we investigate the possibility that the longevity of technosignatures conforms to the so-called Lindy's law, whereby, at any time, their remaining life expectancy is roughly proportional to their age. We show that, if Lindy's law applies, the general tenet that the first detected technosignature ought to be very long lived may be overruled. We conclude by discussing the number of emitters that had to appear, over the history of the Galaxy, in order for one of them to be detectable today from Earth.
This paper is a contribution to the "BraTS 2023 Local Synthesis of Healthy Brain Tissue via Inpainting Challenge". The task of this challenge is to transform tumor tissue into healthy tissue in brain magnetic resonance (MR) images. This idea originates from the problem that MR images can be evaluated using automatic processing tools, however, many of these tools are optimized for the analysis of healthy tissue. By solving the given inpainting task, we enable the automatic analysis of images featuring lesions, and further downstream tasks. Our approach builds on denoising diffusion probabilistic models. We use a 2D model that is trained using slices in which healthy tissue was cropped out and is learned to be inpainted again. This allows us to use the ground truth healthy tissue during training. In the sampling stage, we replace the slices containing diseased tissue in the original 3D volume with the slices containing the healthy tissue inpainting. With our approach, we achieve comparable results to the competing methods. On the validation set our model achieves a mean SSIM of 0.7804, a PSNR of 20.3525 and a MSE of 0.0113. In future we plan to extend our 2D model to a 3D model, allo
We study I-balls/oscillons, which are long-lived, quasi-periodic, and spatially localized solutions in real scalar field theories. Contrary to the case of Q-balls, there is no evident conserved charge that stabilizes the localized configuration. Nevertheless, in many classical numerical simulations, it has been shown that they are extremely long-lived. In this paper, we clarify the reason for the longevity, and show how the exponential separation of time scales emerges dynamically. Those solutions are time-periodic with a typical frequency of a mass scale of a scalar field. This observation implies that they can be understood by the effective theory after integrating out relativistic modes. We find that the resulting effective theory has an approximate global U(1) symmetry reflecting an approximate number conservation in the non-relativistic regime. As a result, the profile of those solutions is obtained via the bounce method, just like Q-balls, as long as the breaking of the U(1) symmetry is small enough. We then discuss the decay processes of the I-ball/oscillon by the breaking of the U(1) symmetry, namely the production of relativistic modes via number violating processes. We sh
In order to understand the phenomenon of longevity in biological world, the relationship between the potential of longevity and the structural complexity of an organism is analyzed. I. The potential of longevity is the maximum lifespan of an organism if it lives in an ideal environment. The longevity of an organism includes two parts: the time for development (development time) and the time for structure-maintenance (maintenance time). II. The development time of an organism depends on its structural complexity. The maintenance time is related to two factors: the degree of damage-exposure and the potential of functionality for structure-maintenance. The potential of functionality is built in structural complexity. Since both of development time and maintenance time are determined by structural complexity, the potential of longevity of an organism is hidden in structural complexity. III. The individuals of different species have different potentials of longevity because they have different structural complexities. An animal has limited longevity because it has limited structural complexity. Limited structural complexity and limited longevity are essential for the survival of a speci
Who {\em values} life annuities more? Is it the healthy retiree who expects to live long and might become a centenarian, or is the unhealthy retiree with a short life expectancy more likely to appreciate the pooling of longevity risk? What if the unhealthy retiree is pooled with someone who is much healthier and thus forced to pay an implicit loading? To answer these and related questions this paper examines the empirical conditions under which retirees benefit (or may not) from longevity risk pooling by linking the {\em economics} of annuity equivalent wealth (AEW) to {\em actuarially} models of aging. I focus attention on the {\em Compensation Law of Mortality} which implies that individuals with higher relative mortality (e.g. lower income) age more slowly and experience greater longevity uncertainty. Ergo, they place higher utility value on the annuity. The impetus for this research today is the increasing evidence on the growing disparity in longevity expectations between rich and poor.
Pension schemes all over the world are under increasing pressure to efficiently hedge the longevity risk posed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pension scheme which decides to hedge the longevity risk using a mortality-linked security, typically a longevity bond. The pension scheme invests in the risky assets available in the market, including the longevity bond, by using the contributions from a representative scheme member to ensure a minimum guarantee such that the member is able to purchase a lifetime annuity upon retirement. We transform this constrained optimal investment problem into an unconstrained problem by replicating a self-financing portfolio of future contributions from the member and the minimum guarantee provided by the scheme. We solve the resulting optimisation problem using the dynamic programming principle and through a series of numerical studies reveal that the longevity risk has an important impact on the performance of investment strategies. Our results provide mathematical evidence supporting the use of mortality-linked securities for efficient hedging of the longevity risk.
In many cohorts (such as the UK Biobank) on which Mendelian Randomization studies are routinely performed, data on participants' longevity is inadequate as the majority of participants are still living. To nevertheless estimate effects on longevity, it is increasingly common for researchers to substitute participants' `parental attained age', i.e. parental lifespan or current age (which is routinely collected in UK Biobank), as a proxy outcome. The common approach to performing this clever trick appears to be based on a solid understanding of its underlying assumptions. However, we have not seen these assumptions (or the causal effects whose identification they enable) clearly stated anywhere in the literature. In this note, we fill that gap.
Purpose: Trochlear Dysplasia (TD) is a common malformation in adolescents, leading to anterior knee pain and instability. Surgical interventions such as trochleoplasty require precise planning to correct the trochlear groove. However, no standardized preoperative plan exists to guide surgeons in reshaping the femur. This study aims to generate patient-specific, pseudo-healthy MR images of the trochlear region that should theoretically align with the respective patient's patella, potentially supporting the pre-operative planning of trochleoplasty. Methods: We employ a Wavelet Diffusion Model (WDM) to generate personalized pseudo-healthy, anatomically plausible MR scans of the trochlear region. We train our model using knee MR scans of healthy subjects. During inference, we mask out pathological regions around the patella in scans of patients affected by TD, and replace them with their pseudo-healthy counterpart. An orthopedic surgeon measured the sulcus angle (SA), trochlear groove depth (TGD) and Déjour classification in MR scans before and after inpainting. The code is available at https://github.com/wehrlimi/Generate-Pseudo-Healthy-Knee-MRI . Results: The inpainting by our model
Modern science is organized around specialization in training and teamwork. Scientists develop deep expertise within a field and combine complementary knowledge through collaboration to solve complex problems. Yet whether specialization is the most effective path to sustained innovation remains unclear. Here we introduce a quantitative framework that distinguishes generalists from specialists based on scaling patterns of disciplinary mobility while remaining independent of career age and productivity. Applying this framework to 49 million publications produced by 3 million scientists between 1900 and 2020, we examine how research style relates to innovation, learning, collaboration, and productivity. We find that scientists who move across fields are more likely to sustain innovative contributions throughout their careers, whereas those who remain within narrow fields exhibit the age-related decline in innovation. Generalists are less anchored to the literature of their training. They are more likely to pursue research independently, and, when they collaborate, they preferentially partner with other generalists. Teams with a greater share of generalists produce more innovative rese