51,431 research outputs found
Gravity Waves as a Probe of Hubble Expansion Rate During An Electroweak Scale Phase Transition
Just as big bang nucleosynthesis allows us to probe the expansion rate when
the temperature of the universe was around 1 MeV, the measurement of gravity
waves from electroweak scale first order phase transitions may allow us to
probe the expansion rate when the temperature of the universe was at the
electroweak scale. We compute the simple transformation rule for the gravity
wave spectrum under the scaling transformation of the Hubble expansion rate. We
then apply this directly to the scenario of quintessence kination domination
and show how gravity wave spectra would shift relative to LISA and BBO
projected sensitivities.Comment: 28 pages, 2 figures
Strong laws of large numbers for sub-linear expectations
We investigate three kinds of strong laws of large numbers for capacities
with a new notion of independently and identically distributed (IID) random
variables for sub-linear expectations initiated by Peng. It turns out that
these theorems are natural and fairly neat extensions of the classical
Kolmogorov's strong law of large numbers to the case where probability measures
are no longer additive. An important feature of these strong laws of large
numbers is to provide a frequentist perspective on capacities.Comment: 10 page
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Modeling and simulating of reservoir operation using the artificial neural network, support vector regression, deep learning algorithm
Reservoirs and dams are vital human-built infrastructures that play essential roles in flood control, hydroelectric power generation, water supply, navigation, and other functions. The realization of those functions requires efficient reservoir operation, and the effective controls on the outflow from a reservoir or dam. Over the last decade, artificial intelligence (AI) techniques have become increasingly popular in the field of streamflow forecasts, reservoir operation planning and scheduling approaches. In this study, three AI models, namely, the backpropagation (BP) neural network, support vector regression (SVR) technique, and long short-term memory (LSTM) model, are employed to simulate reservoir operation at monthly, daily, and hourly time scales, using approximately 30 years of historical reservoir operation records. This study aims to summarize the influence of the parameter settings on model performance and to explore the applicability of the LSTM model to reservoir operation simulation. The results show the following: (1) for the BP neural network and LSTM model, the effects of the number of maximum iterations on model performance should be prioritized; for the SVR model, the simulation performance is directly related to the selection of the kernel function, and sigmoid and RBF kernel functions should be prioritized; (2) the BP neural network and SVR are suitable for the model to learn the operation rules of a reservoir from a small amount of data; and (3) the LSTM model is able to effectively reduce the time consumption and memory storage required by other AI models, and demonstrate good capability in simulating low-flow conditions and the outflow curve for the peak operation period
An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation
The classical law of the iterated logarithm (LIL for short)as fundamental
limit theorems in probability theory play an important role in the development
of probability theory and its applications. Strassen (1964) extended LIL to
large classes of functional random variables, it is well known as the
invariance principle for LIL which provide an extremely powerful tool in
probability and statistical inference. But recently many phenomena show that
the linearity of probability is a limit for applications, for example in
finance, statistics. As while a nonlinear expectation--- G-expectation has
attracted extensive attentions of mathematicians and economists, more and more
people began to study the nature of the G-expectation space. A natural question
is: Can the classical invariance principle for LIL be generalized under
G-expectation space? This paper gives a positive answer. We present the
invariance principle of G-Brownian motion for the law of the iterated logarithm
under G-expectation
Multiple G-It\^{o} integral in the G-expectation space
In this paper, motivated by mathematic finance we introduce the multiple
G-It\^{o} integral in the G-expectation space, then investigate how to
calculate. We get the the relationship between Hermite polynomials and multiple
G-It\^{o} integrals which is a natural extension of the classical result
obtained by It\^{o} in 1951.Comment: 9 page
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