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Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
We introduce and analyze a **memory-weighted velocity operator** \(\mathscr{V}_{\alpha,\beta}\) as a mathematical framework for describing rates of change in systems with time-varying, power-law memory. The operator employs two independent…
Episodic control has been proposed as a third approach to reinforcement learning, besides model-free and model-based control, by analogy with the three types of human memory. i.e. episodic, procedural and semantic memory. But the…
We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…
We analyze the motion of a pressure control system described by a differential equation with nonlocal dissipative force. This system is composed by an oscillator, a membrane and a constant force. We consider the dissipative memory kernel…
Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such…
We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…
This work introduces a time-adaptive strategy that uses a refinement estimator based on the first Frenet curvature. In dynamics, a time-adaptive strategy is a mechanism that interactively proposes changes to the time step used in iterative…
In recent years, adaptive identification methods that can achieve the true value convergence of parameters without requiring persistent excitation (PE) have been widely studied, and concurrent learning has been intensively studied. However,…
This note provides a detailed algorithm to the application of local (perturbation) analysis of differential equations which is normally taught at graduate math courses. Exercise books often present more abstract and simplified versions of…
Biological brains are inherently limited in their capacity to process and store information, but are nevertheless capable of solving complex tasks with apparent ease. Intelligent behavior is related to these limitations, since resource…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that…
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…
Hardware accelerators for neural networks have shown great promise for both performance and power. These accelerators are at their most efficient when optimized for a fixed functionality. But this inflexibility limits the longevity of the…
In this paper we will study some interesting properties of modifications of the Euler-Poincar\'e equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism.…
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…
Model predictive control (MPC) is a promising technique for motion cueing in driving simulators, but its high computation time limits widespread real-time application. This paper proposes a hybrid algorithm that combines filter-based and…
General-purpose trajectory planning algorithms for automated driving utilize complex reward functions to perform a combined optimization of strategic, behavioral, and kinematic features. The specification and tuning of a single reward…
We study optimal dynamic persuasion in a bandit experimentation model where a principal, unlike in standard settings, has a single-peaked preference over the agent's stopping time. This non-monotonic preference arises because maximizing the…