Related papers: Pegasus: Sound Continuous Invariant Generation
Audio generation has attracted significant attention. Despite remarkable enhancement in audio quality, existing models overlook diversity evaluation. This is partially due to the lack of a systematic sound class diversity framework and a…
This paper presents a novel approach to including non-instantaneous discrete control transitions in the linear hybrid automaton approach to simulation and verification of hybrid control systems. In this paper we study the control of a…
A new procedure for the global construction of the Casimir invariants and Darboux canonical form for finite-dimensional Poisson systems is developed. This approach is based on the concept of matrix congruence and can be applied without the…
We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems -- that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities).…
Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…
Complex systems are naturally hybrid: their dynamic behavior is both continuous and discrete. For these systems, maintenance and repair are an increasing part of the total cost of final product. Efficient diagnosis and prognosis techniques…
We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of…
We investigate a variant of the fuel-based approach to modeling diverging computation in type theories and use it to abstractly capture the essence of oracle Turing machines. The resulting objects we call continuous machines. We prove that…
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…
We propose an incremental approach for safety proofs that decomposes a proof with a complex inductive invariant into a sequence of simpler proof steps. Our proof system combines rules for (i) forward reasoning using inductive invariants,…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
While diffusion models have achieved great success in generating continuous signals such as images and audio, it remains elusive for diffusion models in learning discrete sequence data like natural languages. Although recent advances…
Constructing a control invariant set with an appropriate shape that fits within a given state constraint is a fundamental problem in safety-critical control but is known to be difficult, especially for large or complex spaces. This paper…
Sound synthesis is a complex field that requires domain expertise. Manual tuning of synthesizer parameters to match a specific sound can be an exhaustive task, even for experienced sound engineers. In this paper, we introduce InverSynth -…
Experiments and simulations in solid-state high harmonic generation often make use of the distinction between interband and intraband currents. These two contributions to the total current have been associated with qualitatively different…
Neural audio synthesis methods now allow specifying ideas in natural language. However, these methods produce results that cannot be easily tweaked, as they are based on large latent spaces and up to billions of uninterpretable parameters.…