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The restricted Boltzmann machine is a basic machine learning tool able, in principle, to model the distribution of some arbitrary dataset. Its standard training procedure appears however delicate and obscure in many respects. We bring some…
The quantum version of the Boltzmann transport equation (Wigner-Boltzmann equation) is a quite useful tool to investigate the effects of energy dissipation in quantum systems. Numerical approaches uses to be employed in order to stablish a…
In many applied optimization settings, parameters that define the constraints may not guarantee the best possible solution, and superior solutions might exist that are infeasible for the given parameter values. Removing such constraints,…
Radiation therapy with carbon ions is a novel technique of cancer radiotherapy, applicable in particular to treating radioresistant tumours at difficult localisations. Therapy planning, where the medical physicist, following the medical…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…
A tracking type optimal control problem for a nonlinear and nonlocal kinetic Fokker-Planck equation which arises as the mean field limit of an interacting particle systems that is subject to distance dependent random fluctuations is…
Optical techniques have been employed to coherently control the quantum transport through nanojunctions. Conventional works on optical control of quantum transport usually applied a tailored electrical pulses to perform specific tasks. In…
In this paper, we present an application of the optimal control theory to orbital transfer of Low Earth Orbit satellites. The optimal control problem is treated with Dynamic Programming techniques which require solving the…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
We consider optimal transport problems where the cost is optimized over controlled dynamics and the end time is free. Unlike the classical setting, the search for optimal transport plans also requires the identification of optimal "stopping…
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
We derive and solve a Boltzmann equation governing the cosmological evolution of the number density of current carrying cosmic string loops, whose centrifugally supported equilibrium configurations are also referred to as vortons. The phase…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal…
The paper considers a coupled system of linear Boltzmann transport equations (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in…
We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…
We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin…
Radiotherapy planning is a critical aspect of cancer treatment, where the optimal selection of beam directions and dose distributions significantly impacts treatment efficacy and patient outcomes. Traditionally, this process involves…