Related papers: Efficient Coalgebraic Partition Refinement
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
Categories of partitions are combinatorial structures arising from the representation theory of certain compact quantum groups and are linked to classical diagram algebras such as the Temperley-Lieb algebra. In this paper, we present…
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive semi-definite Hamiltonians, our method has expected running-time that is almost linear in $(M/(\epsilon_{\rm…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
We propose a family of quantum algorithms for estimating Gowers uniformity norms $ U^k $ over finite abelian groups and demonstrate their applications to testing polynomial structure and counting arithmetic progressions. Building on recent…
A novel simulation strategy is proposed to search for semiconductor quantum devices which are optimized with respect to required performances. Based on evolutionary programming, a tecnique implementing the paradigm of genetic algorithms to…
While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
A recently published paper (Schmid, Rozowski, Silva, and Rot, 2022) offers a (co)algebraic framework for studying processes with algebraic branching structures and recursion operators. The framework captures Milner's algebra of regular…
A quantified Boolean formula (QBF) is a propositional formula extended with universal and existential quantification over propositions. There are two methodologies in CEGAR based QBF solving techniques, one that is based on a refinement…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
Algebraic model counting unifies many inference tasks on logic formulas by exploiting semirings. Rather than focusing on inference, we consider learning, especially in statistical-relational and neurosymbolic AI, which combine logical,…
Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…