282 research outputs found
A variational approach to path estimation and parameter inference of hidden diffusion processes
We consider a hidden Markov model, where the signal process, given by a
diffusion, is only indirectly observed through some noisy measurements. The
article develops a variational method for approximating the hidden states of
the signal process given the full set of observations. This, in particular,
leads to systematic approximations of the smoothing densities of the signal
process. The paper then demonstrates how an efficient inference scheme, based
on this variational approach to the approximation of the hidden states, can be
designed to estimate the unknown parameters of stochastic differential
equations. Two examples at the end illustrate the efficacy and the accuracy of
the presented method.Comment: 37 pages, 2 figures, revise
Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error bounds and Algorithms
Biochemical reactions can happen on different time scales and also the
abundance of species in these reactions can be very different from each other.
Classical approaches, such as deterministic or stochastic approach, fail to
account for or to exploit this multi-scale nature, respectively. In this paper,
we propose a jump-diffusion approximation for multi-scale Markov jump processes
that couples the two modeling approaches. An error bound of the proposed
approximation is derived and used to partition the reactions into fast and slow
sets, where the fast set is simulated by a stochastic differential equation and
the slow set is modeled by a discrete chain. The error bound leads to a very
efficient dynamic partitioning algorithm which has been implemented for several
multi-scale reaction systems. The gain in computational efficiency is
illustrated by a realistically sized model of a signal transduction cascade
coupled to a gene expression dynamics.Comment: 32 pages, 7 figure
Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales
The paper concerns itself with establishing large deviation principles for a
sequence of stochastic integrals and stochastic differential equations driven
by general semimartingales in infinite-dimensional settings. The class of
semimartingales considered is broad enough to cover Banach space-valued
semimartingales and the martingale random measures. Simple usable expressions
for the associated rate functions are given in this abstract setup. As
illustrated through several concrete examples, the results presented here
provide a new systematic approach to the study of large deviation principles
for a sequence of Markov processes.
Keywords: large deviations, stochastic integration, stochastic differential
equations, exponential tightness, Markov processes, infinite dimensional
semimartingales, Banach space-valued semimartingalesComment: 47 page
Coupled fluid-thermal analysis of low-pressure sublimation and condensation with application to freeze-drying
Freeze-drying is a low-pressure, low-temperature condensation pumping process widely used in the manufacture of bio-pharmaceuticals for removal of solvents by sublimation. The goal of the process is to provide a stable dosage form by removing the solvent in such a way that the sensitive molecular structure of the active substance is least disturbed. The vacuum environment presents unique challenges for understanding and controlling heat and mass transfer in the process. As a result, the design of equipment and associated processes has been largely empirical, slow and inefficient.^ A comprehensive simulation framework to predict both, process and equipment performance is critical to improve current practice. A part of the dissertation is aimed at performing coupled fluid-thermal analysis of low-pressure sublimation-condensation processes typical of freeze-drying technologies. Both, experimental and computational models are used to first understand the key heat transfer modes during the process. A modeling and computational framework, validated with experiments for analysis of sublimation, water-vapor flow and condensation in application to pharmaceutical freeze-drying is developed.^ Augmented with computational fluid dynamics modeling, the simulation framework presented here allows to predict for the first time, dynamic product/process conditions taking into consideration specifics of equipment design. Moreover, by applying the modeling framework to process design based on a design-space approach, it has demonstrated that there is a viable alternative to empiricism
Succinct Data Structures for Parameterized Pattern Matching and Related Problems
Let T be a fixed text-string of length n and P be a varying pattern-string of length |P| \u3c= n. Both T and P contain characters from a totally ordered alphabet Sigma of size sigma \u3c= n. Suffix tree is the ubiquitous data structure for answering a pattern matching query: report all the positions i in T such that T[i + k - 1] = P[k], 1 \u3c= k \u3c= |P|. Compressed data structures support pattern matching queries, using much lesser space than the suffix tree, mainly by relying on a crucial property of the leaves in the tree. Unfortunately, in many suffix tree variants (such as parameterized suffix tree, order-preserving suffix tree, and 2-dimensional suffix tree), this property does not hold. Consequently, compressed representations of these suffix tree variants have been elusive. We present the first compressed data structures for two important variants of the pattern matching problem: (1) Parameterized Matching -- report a position i in T if T[i + k - 1] = f(P[k]), 1 \u3c= k \u3c= |P|, for a one-to-one function f that renames the characters in P to the characters in T[i,i+|P|-1], and (2) Order-preserving Matching -- report a position i in T if T[i + j - 1] and T[i + k -1] have the same relative order as that of P[j] and P[k], 1 \u3c= j \u3c k \u3c= |P|. For each of these two problems, the existing suffix tree variant requires O(n*log n) bits of space and answers a query in O(|P|*log sigma + occ) time, where occ is the number of starting positions where a match exists. We present data structures that require O(n*log sigma) bits of space and answer a query in O((|P|+occ) poly(log n)) time. As a byproduct, we obtain compressed data structures for a few other variants, as well as introduce two new techniques (of independent interest) for designing compressed data structures for pattern matching
Large Deviations for Small Noise Diffusions in a Fast Markovian Environment
A large deviation principle is established for a two-scale stochastic system
in which the slow component is a continuous process given by a small noise
finite dimensional It\^{o} stochastic differential equation, and the fast
component is a finite state pure jump process. Previous works have considered
settings where the coupling between the components is weak in a certain sense.
In the current work we study a fully coupled system in which the drift and
diffusion coefficient of the slow component and the jump intensity function and
jump distribution of the fast process depend on the states of both components.
In addition, the diffusion can be degenerate. Our proofs use certain stochastic
control representations for expectations of exponential functionals of finite
dimensional Brownian motions and Poisson random measures together with weak
convergence arguments. A key challenge is in the proof of the large deviation
lower bound where, due to the interplay between the degeneracy of the diffusion
and the full dependence of the coefficients on the two components, the
associated local rate function has poor regularity properties.Comment: 42 page
HI-TECH ENERGY METER WITH AUTOMATIC LOAD CONTROL
Now a day’s automation is in every field, although there are many places automation has been emerged and successfully implemented but still the service provider for energy still uses conventional methods for getting the energy consumed by individual customer. This method is very time consuming and un- economical and may lead to human error. Our proposed system (AMR) will automatically send the data of the digital energy meter to the service provider with the help the help of the GSM modem once in a day and hence the system will report the service provider once in a through SMS. The same system can be used to check the last reading consumed by the consumer, when demanded by user through the same GSM modem .The device can also be used to control the load from both the ends that is (user –service provider) with the help of relay circuit and system will also be provided with an LCD display which will update the consumers with different information’s regarding tariff change or sudden power cut
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