相关论文: Invertible Program Restructurings for Continuing M…
Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the…
In this work, we consider the dynamics of repairable systems characterized by three distinct states: one signifying normal operational states, another representing degraded conditions and a third denoting failed conditions. These systems…
Modular exponentiation is crucial to number theory and cryptography, yet remains largely unexplored from a mechanistic interpretability standpoint. We train a 4-layer encoder-decoder Transformer model to perform this operation and…
We study a class of nonlinear elliptic problems driven by a double-phase operator with variable exponents, arising in the modeling of heterogeneous materials undergoing phase transitions. The associated Poisson problem features a…
The dynamics of real-world applications and systems require efficient methods for improving infeasible solutions or restoring corrupted ones by making modifications to the current state of a system in a restricted way. We propose a new…
The paper describes development (improvement/extension) approaches for composite (modular) systems (as combinatorial reengineering). The following system improvement/extension actions are considered: (a) improvement of systems component(s)…
Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
Systems and machines undergo various failure modes that result in machine health degradation, so maintenance actions are required to restore them back to a state where they can perform their expected functions. Since maintenance tasks are…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Machine learning systems may encounter unexpected problems when the data distribution changes in the deployment environment. A major reason is that certain combinations of domains and labels are not observed during training but appear in…
Principal component analysis is a ubiquitous tool in exploratory data analysis. It is widely used by applied scientists for visualization and interpretability purposes. We raise an important issue (the curse of isotropy) about the…
The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
The Transformer model has a tendency to overfit various aspects of the training data, such as the overall sequence length. We study elementary string edit functions using a defined set of error indicators to interpret the behaviour of the…
In this article, we give a geometric description for any invertible operator on a finite dimensional inner--product space. With the aid of such a description, we are able to decompose any given conformal transformation as a product of…
The Harland document management system implements a data model in which document (object) structure can be altered by mixin-style multiple inheritance at any time. This kind of structural fluidity has long been supported by knowledge-base…
With the proliferation of mobile devices, the need for an efficient model to restore any degraded image has become increasingly significant and impactful. Traditional approaches typically involve training dedicated models for each specific…
Software frequently converts data from one representation to another and vice versa. Naively specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming…