19 papers · ranked by Valyu relevance
Xianglong Duan, Chaoyu Quan, Jiang Yang, Zijing Zhu
The operator splitting method has been widely used to solve differential equations by splitting the equation into more manageable parts. In this work, we resolves a long-standing problem—how to establish the stability of multi-product expansion (MPE) splitting methods with negative weights. The difficulty occurs…
Andreas Frommer, Michael Günther, Björn Liljegren-Sailer, Nicole Marheineke
'Nicole Marheineke'] Abstract The port-Hamiltonian approach presents an energy-based modeling of dynamical systems with energy-conservative and energy-dissipative parts as well as an interconnection over the so-called ports. In this paper, we apply an operator splitting that treats the energy-conservative and…
Raymond J. Spiteri, Arash Tavassoli, Siqi Wei, A. I. Smolyakov
Operator splitting is a popular divide-and-conquer strategy for solving differential equations. Typically, the right-hand side of the differential equation is split into a number of parts that are then integrated separately. Many methods are known that split the right-hand side into two parts. This approach is…
M. B. Vovchanskyi
The survey is devoted to operator splitting methods in the abstract formulation and their applications in probability. While the survey is focused on multiplicative methods, the BCH formula is used to discuss exponential splitting methods and a short informal introduction to additive splitting is presented. We…
Hideki Kawahara
Method Compared to the Implicit Euler in Autonomous and Non-Autonomous Systems Authors: ['Hideki Kawahara'] In this paper, we compare the effectiveness of the Operator Splitting Method for specific autonomous and non-autonomous Delay Differential Equations (DDEs) with the Implicit Euler Method. While many existing…
Radu Ioan Boţ, David Alexander Hulett
In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator A and a cocoercive operator B. We study the asymptotic behaviour of the trajectories generated by a second order equation with vanishing damping, attached to this problem, and governed by a…
Andrew Simmonett, Bernard Brooks, Thomas Darden
Evaluation of noncovalent electrostatic interactions is the dominant bottleneck in classical molecular dynamics simulations, and evaluation of Coulombic matrix elements similarly limits quantum mechanical self consistent field calculations. These difficulties are a result of the Coulomb operator’s slow decay, which…
Marco Caliari, Fabio Cassini, Lukas Einkemmer, Alexander Ostermann
Splitting the exponential-like ϕ functions, which typically appear in exponential integrators, is attractive in many situations since it can dramatically reduce the computational cost of the procedure. However, depending on the employed splitting, this can result in order reduction. The aim of this paper is to analyze…
Francisco J. Aragón-Artacho, Radu I. Boţ, David Torregrosa-Belén
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Our main contribution is establishing the first primal-dual splitting algorithm…
Rajorshi Paul, Kevin S. Zhang, Myra Kurosu Jalil, Nicolas Castaño + 2 more
Stentor coeruleus, a single-cell ciliated protozoan, is a model organism for wound healing and regeneration studies. Despite Stentor’s large size (up to 2 mm in extended state), microdissection of Stentor remains challenging. In this work, we describe a hydrodynamic cell splitter, consisting of a cross junction…
Gang Xu, Tianai Zhou, Xiu-Bo Chen, Xiaojun Wang + 1 more
Quantum information splitting (QIS) provides an idea for transmitting the quantum state through a classical channel and a preshared quantum entanglement resource. This paper presents a new scheme for QIS based on a five-qubit cluster state and a Bell state. In this scheme, the sender transmits the unknown three-qubit…
Gabriel Ebner, Jasmin Blanchette, Sophie Tourret
AVATAR is an elegant and effective way to split clauses in a saturation prover using a SAT solver. But is it refutationally complete? And how does it relate to other splitting architectures? To answer these questions, we present a unifying framework that extends a saturation calculus (e.g., superposition) with…
Authors not listed
We present a graph-based proof of the size-extensivity of the first-order exchange energy in symmetry-adapted perturbation theory (SAPT). The connectedness of the exchange energy expression can be established via derivatives of chromatic polynomials $\chi'_G(x)$ evaluated at $x=0$. The proof holds to all orders of the…
Fahad Ahmed, Hattan Abutarboush, Naveed Ashraf, Tayeb A. Denidni + 1 more
'Farooq A. Tahir'] A multifunctional beam splitting frequency selective surface (FSS) is modeled, analyzed, and tested in transmission and reflection modes. The proposed FSS comprises a C-shaped split-ring resonator designed and fabricated on an ultrathin, flexible polyimide material. When a linearly polarized incident…
Roman Joeres, David B. Blumenthal, Olga V. Kalinina
Information Leakage is an increasing problem in machine learning research. It is a common practice to report models with benchmarks, comparing them to the state-of-the-art performance on the test splits of datasets. If two or more dataset splits contain identical or highly similar samples, a model risks simply…
Hao Liang, Liang Chen, Haifeng Zhang, Xiaowei Liu + 2 more
Droplet splitting technology on open digital microfluidic platforms still faces significant challenges in terms of process complexity, the degree of automation, and operating conditions, which hinder its further development. This study proposes a fully automated method for precise droplet splitting based on printed…
Kangbien Park, Yonghee Bae
Drift, selection, and mutation are integral evolutionary factors. In this article, operator model is newly suggested to intuitively represent those evolutionary factors into mathematical operators, and to ultimately offer unconventional methodology for understanding evolutionary dynamics. To be specific, each of the…
Shaked Tayouri, Vladislav Kogan, Jacob Beal, Tal Levy + 7 more
Biosecurity screening of synthetic DNA orders is a key defense against malicious actors and careless enthusiasts producing dangerous pathogens or toxins. It is important to evaluate biosecurity screening tools for potential vulnerabilities and to work responsibly with providers to ensure that vulnerabilities can be…
David Ellerman
Logic to Biology Authors: ['David Ellerman'] This is an essay in what might be called "mathematical metaphysics." There is a fundamental duality that run through mathematics and the natural sciences. The duality starts as the logical level; it is represented by the Boolean logic of subsets and the logic of partitions…