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Articles 1 - 20 of 20
Full-Text Articles in Physical Sciences and Mathematics
From Mathematics To Medicine: A Practical Primer On Topological Data Analysis (Tda) And The Development Of Related Analytic Tools For The Functional Discovery Of Latent Structure In Fmri Data, Andrew Salch, Adam Regalski, Hassan Abdallah, Raviteja Suryadevara, Michael J. Catanzaro, Vaibhav A. Diwadkar
From Mathematics To Medicine: A Practical Primer On Topological Data Analysis (Tda) And The Development Of Related Analytic Tools For The Functional Discovery Of Latent Structure In Fmri Data, Andrew Salch, Adam Regalski, Hassan Abdallah, Raviteja Suryadevara, Michael J. Catanzaro, Vaibhav A. Diwadkar
Mathematics Faculty Research Publications
fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent. …
Stochastic Processes And Integrals, Jose L. Menaldi
Stochastic Processes And Integrals, Jose L. Menaldi
Mathematics Faculty Research Publications
Stochastic integrals with respect to Wiener process and Poisson measures are discusses, beginning from stochastic processes.
Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin
Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin
Mathematics Faculty Research Publications
Singular control for multidimensional Gaussian-Poisson processes with a long-run (or ergodic) and a discounted criteria are discussed. The dynamic programming yields the corresponding Hamilton-Jacobi-Bellman equations, which are discussed. Full details on the proofs and further extensions are left for coming works.
A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia
A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia
Mathematics Faculty Research Publications
We study the asymptotic behavior of an optimal distributed control problem where the state is given by the heat equation with mixed boundary conditions. The parameter α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion Γ1 of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes the internal energy g. It is proven that the optimal control ĝα with optimal state uĝαα and optimal adjoint state pĝαα are convergent as α → 1 …
Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro
Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro
Mathematics Faculty Research Publications
We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-di erential operator with Wentzell boundary conditions.
Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin
Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If uα(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that limα→0αuα(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem.
Penalty Approximation And Analytical Characterization Of The Problem Of Super-Replication Under Portfolio Constraints, Alain Bensoussan, Nizar Touzi, José Luis Menaldi
Penalty Approximation And Analytical Characterization Of The Problem Of Super-Replication Under Portfolio Constraints, Alain Bensoussan, Nizar Touzi, José Luis Menaldi
Mathematics Faculty Research Publications
In this paper, we consider the problem of super-replication under portfolio constraints in a Markov framework. More specifically, we assume that the portfolio is restricted to lie in a convex subset, and we show that the super-replication value is the smallest function which lies above the Black-Scholes price function and which is stable for the so-called face lifting operator. A natural approach to this problem is the penalty approximation, which not only provides a constructive smooth approximation, but also a way to proceed analytically.
Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan
Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan
Mathematics Faculty Research Publications
In this paper we study stopping time and impulse control problems for stochastic Navier-Stokes equation. Exploiting a local monotonicity property of the nonlinearity, we establish existence and uniqueness of strong solutions in two dimensions which gives a Markov-Feller process. The variational inequality associated with the stopping time problem and the quasi-variational inequality associated with the impulse control problem are resolved in a weak sense, using semigroup approach with a convergence uniform over path.
Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan
Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan
Mathematics Faculty Research Publications
In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this signi cantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.
Stochastic Hybrid Control, A. Bensoussan, J. L. Menaldi
Stochastic Hybrid Control, A. Bensoussan, J. L. Menaldi
Mathematics Faculty Research Publications
The objective of this paper is to study the stochastic version of a previous paper of the authors, in which hybrid control for deterministic systems was considered. The modelling is quite similar to the deterministic case. We have a system whose state is composed of a continuous part and a discrete part. They are affected by a continuous type control and an impulse control. The dynamics is moreover perturbed by noise, also a continuous and a discrete noise process. The Markovian character of the state process is preserved. We develop the model and show how the dynamic programming approach leads …
Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin
Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.
Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi
Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi
Mathematics Faculty Research Publications
We consider the strong solution of a semi linear HJB equation associated with a stochastic optimal control in a Hilbert space H: By strong solution we mean a solution in a L2(μ,H)-Sobolev space setting. Within this framework, the present problem can be treated in a similar fashion to that of a finite-dimensional case. Of independent interest, a related linear problem with unbounded coefficient is studied and an application to the stochastic control of a reaction-diffusion equation will be given.
Ergodic Control Of Reflected Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin
Ergodic Control Of Reflected Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
No abstract provided.
On An Investment-Consumption Model With Transaction Costs, Marianne Akian, José Luis Menaldi, Agnès Sulem
On An Investment-Consumption Model With Transaction Costs, Marianne Akian, José Luis Menaldi, Agnès Sulem
Mathematics Faculty Research Publications
This paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a variational inequality for the value function. Existence and uniqueness of a viscosity solution are proved. The variational inequality is solved by using a numerical algorithm based on policies, iterations, and multigrid methods. Numerical results are displayed …
Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi
Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi
Mathematics Faculty Research Publications
We consider control problems with trajectories which involve ordinary measureable control functions and controls which are measures. The payoff involves a running cost in time and a running cost against the control measures. In the optimal control problem we are trying to minimize this payoff with both controls. In the differential game problem we are trying to minimize the cost with the ordinary controls assuming that the measure controls are chosen to maximize the cost. We will characterize the value functions in both cases using viscosity solution theory by deriving the Bellman and Isaacs equations.
Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar
Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar
Mathematics Faculty Research Publications
A multidimensional Wiener process is controlled by an additive process of bounded variation. A convex nonnegative function measures the cost associated with the position of the state process, and the cost of controlling is proportional to the displacement induced. We minimize a limiting time-average expected (ergodic) criterion. Under reasonable assumptions, we prove that the optimal discounted cost converges to the optimal ergodic cost. Moreover, under some additional conditions there exists a convex Lipschitz continuous function solution to the corresponding Hamilton-Jacobi-Bellman equation which provides an optimal stationary feedback control.
On The Optimal Reward Function Of The Continuous Time Multiarmed Bandit Problem, José Luis Menaldi, Maurice Robin
On The Optimal Reward Function Of The Continuous Time Multiarmed Bandit Problem, José Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
The optimal reward function associated with the so-called "multiarmed bandit problem" for general Markov-Feller processes is considered. It is shown that this optimal reward function has a simple expression (product form) in terms of individual stopping problems, without any smoothness properties of the optimal reward function neither for the global problem nor for the individual stopping problems. Some results relative to a related problem with switching cost are obtained.
Some Estimates For Finite Difference Approximations, José-Luis Menaldi
Some Estimates For Finite Difference Approximations, José-Luis Menaldi
Mathematics Faculty Research Publications
Some estimates for the approximation of optimal stochastic control problems by discrete time problems are obtained. In particular an estimate for the solutions of the continuous time versus the discrete time Hamilton-Jacobi-Bellman equations is given. The technique used is more analytic than probabilistic.
On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin
On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
No abstract provided.
Reflected Diffusion Processes With Jumps, José-Luis Menaldi, Maurice Robin
Reflected Diffusion Processes With Jumps, José-Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
A stochastic differential equation of Wiener-Poisson type is considered in a d-dimensional bounded region. By using a penalization argument on the domain, we are able to prove the existence and uniqueness of solutions in the strong sense. The main assumptions are Lipschitzian coefficients, either convex or smooth domains and a regular outward reflecting direction. As a direct consequence, it is verified that the reflected diffusion process with jumps depends on the initial date in a Lipschitz fashion.