Related papers: Fast numerical generation of Lie closure
A method is obtained to compute the maximum number of functionally independent invariant functions under the action of a linear algebraic group as long as its Lie algebra admits a base of square-zero matrices. Some applications are also…
This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or…
Virtualization-based obfuscation produces extremely large and structurally complex binaries, posing challenges for LLM-based analysis due to input size limits and the need for large-scale labeled data. We address this by focusing on…
As new Model-X knockoff construction techniques are developed, primarily concerned with determining the correct conditional distribution from which to sample, we focus less on deriving the correct multivariate distribution and instead ask…
We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…
The standard oracle model for matroid algorithms assumes that each independence query can be answered in constant time, regardless of the size of the queried set. While this abstraction has underpinned much of the theoretical progress in…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
The reduction of a large number of scalar integrals to a small set of master integrals via Laporta's algorithm is common practice in multi-loop calculations. It is also a major bottleneck in terms of running time and memory consumption. It…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
In this paper, we show how to use the analysis of the Lie algebra associated with a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to decompose the dynamics and describe their…
Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many…
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…
In the article, we discuss the architecture of the polynomial neural network that corresponds to the matrix representation of Lie transform. The matrix form of Lie transform is an approximation of the general solution of the nonlinear…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…