اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMarkovian tricks for non-Markovian trees: contour process, extinction and scaling limits
73
0
0.0
(
0
)
تأليف
Bertrand Cloez
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this work, we study a family of non-Markovian trees modeling populations where individuals live and reproduce independently with possibly time-dependent birth-rate and lifetime distribution. To this end, we use the coding process introduced by Lambert. We show that, in our situation, this process is no longer a L{e}vy process but remains a Feller process and we give a complete characterization of its generator. This allows us to study the model through well-known Markov processes techniques. On one hand, introducing a scale function for such processes allows us to get necessary and sufficient conditions for extinction or non-extinction and to characterize the law of such trees conditioned on these events. On the other hand, using Lyapounov drift techniques , we get another set of, easily checkable, sufficient criteria for extinction or non-extinction and some tail estimates for the tree length. Finally, we also study scaling limits of such random trees and observe that the Bessel tree appears naturally.
قيم البحث
اقرأ أيضاً
For a bosonic (fermionic) open system in a bath with many bosons (fermions) modes, we derive the exact non-Markovian master equation in which the memory effect of the bath is reflected in the time dependent decay rates. In this approach, the reduced
density operator is constructed from the formal solution of the corresponding Heisenberg equations. As an application of the exact master equation, we study the active probing of non-Markovianity of the quantum dissipation of a single boson mode of electromagnetic (EM) field in a cavity QED system. The non-Markovianity of the bath of the cavity is explicitly reflected by the atomic decoherence factor.
Characterisation protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devic
es: ones that can surpass classical computers for particular tasks -- but progress in characterisation must keep up with the complexities of intricate device noise. A missing piece in the zoo of characterisation procedures is tomography which can completely describe non-Markovian dynamics. Here, we formally introduce a generalisation of quantum process tomography, which we call process tensor tomography. We detail the experimental requirements, construct the necessary post-processing algorithms for maximum-likelihood estimation, outline the best-practice aspects for accurate results, and make the procedure efficient for low-memory processes. The characterisation is the pathway to diagnostics and informed control of correlated noise. As an example application of the technique, we improve multi-time circuit fidelities on IBM Quantum devices for both standalone qubits and in the presence of crosstalk to a level comparable with the fault-tolerant noise threshold in a variety of different noise conditions. Our methods could form the core for carefully developed software that may help hardware consistently pass the fault-tolerant noise threshold.
Non-Markovian processes are widespread in natural and human-made systems, yet explicit model- ling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy t
ailed Mittag-Leffler distribution for the inter-event times. We derive an analytically and computationally tractable system of Kolmogorov- like forward equations utilising the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law inter-event times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible (SIS) spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excel- lent approximation to the case when the network dynamics is characterised by power-law distributed inter-event times. We further discuss possible generalizations of our result.
We present a computational model to reconstruct trees of ancestors for animals with sexual reproduction. Through a recursive algorithm combined with a random number generator, it is possible to reproduce the number of ancestors for each generation an
d use it to constraint the maximum number of the following generation. This new model allows to consider the reproductive preferences of particular species and combine several trees to simulate the behavior of a population. It is also possible to obtain a description analytically, considering the simulation as a theoretical stochastic process. Such process can be generalized in order to use an algorithm associated with it to simulate other similar processes of stochastic nature. The simulation is based in the theoretical model previously presented before.
We study non-Markovian stochastic epidemic models (SIS, SIR, SIRS, and SEIR), in which the infectious (and latent/exposing, immune) periods have a general distribution. We provide a representation of the evolution dynamics using the time epochs of in
fection (and latency/exposure, immunity). Taking the limit as the size of the population tends to infinity, we prove both a functional law of large number (FLLN) and a functional central limit theorem (FCLT) for the processes of interest in these models. In the FLLN, the limits are a unique solution to a system of deterministic Volterra integral equations, while in the FCLT, the limit processes are multidimensional Gaussian solutions of linear Volterra stochastic integral equations. In the proof of the FCLT, we provide an important Poisson random measures representation of the diffusion-scaled processes converging to Gaussian components driving the limit process.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
