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In this paper, we introduce a hybrid zonotope-based approach for formally verifying the behavior of autonomous systems operating under Linear Temporal Logic (LTL) specifications. In particular, we formally verify the LTL formula by…

Systems and Control · Electrical Eng. & Systems 2024-05-01 Loizos Hadjiloizou , Frank J. Jiang , Amr Alanwar , Karl H. Johansson

We relate a $l$-loop Feynman integral to a sum of phase space integrals, where the integrands are determined by the spanning trees of the original $l$-loop graph. Causality requires that the propagators of the trees have a modified…

High Energy Physics - Phenomenology · Physics 2019-08-07 Robert Runkel , Zoltán Szőr , Juan Pablo Vesga , Stefan Weinzierl

We investigate the perturbative integrability of two-dimensional massive quantum field theories with polynomial-like interactions and show that any theory of such class which is purely elastic at the tree level is also purely elastic at one…

High Energy Physics - Theory · Physics 2025-04-29 Matheus Fabri , Davide Polvara

Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…

Algebraic Geometry · Mathematics 2007-05-23 Zur Izhakian

We present the first application of color-kinematics (CK) duality at the three-loop level in non-supersymmetric pure Yang-Mills (YM) theory. Building on the minimal deformation approach introduced in \cite{Li:2023akg}, we extend its use to…

High Energy Physics - Theory · Physics 2024-10-23 Zeyu Li , Gang Yang , Guorui Zhu

We present the first comprehensive analysis of the unitarity thresholds and anomalous thresholds of scattering amplitudes at two loops and beyond based on the loop-tree duality, and show how non-causal unphysical thresholds are locally…

We present a numerical strategy to efficiently estimate bipartite entanglement measures, and in particular the Entanglement of Formation, for many-body quantum systems on a lattice. Our approach exploits the Tree Tensor Operator tensor…

Quantum Physics · Physics 2022-01-26 Luca Arceci , Pietro Silvi , Simone Montangero

The calculation of higher-order corrections in Quantum Field Theories is a challenging task. In particular, dealing with multiloop and multileg Feynman amplitudes leads to severe bottlenecks and a very fast scaling of the computational…

High Energy Physics - Phenomenology · Physics 2023-05-16 German F. R. Sborlini

Recently, a new construction for complete loop integrands of massless field theories has been proposed, with on-shell tree-level amplitudes delicately incorporated into its algorithm. This new approach reinterprets integrands in a novel…

High Energy Physics - Theory · Physics 2016-04-28 Rijun Huang , Qingjun Jin , Junjie Rao , Kang Zhou , Bo Feng

Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…

High Energy Physics - Phenomenology · Physics 2009-10-31 Francesco Caravaglios

We describe the two-dimensional TreePM method in this paper. The 2d TreePM code is an accurate and efficient technique to carry out large two-dimensional N-body simulations in cosmology. This hybrid code combines the 2d Barnes and Hut Tree…

Astrophysics · Physics 2009-11-10 Suryadeep Ray

Loop closure is necessary for correcting errors accumulated in simultaneous localization and mapping (SLAM) in unknown environments. However, conventional loop closure methods based on low-level geometric or image features may cause high…

Robotics · Computer Science 2023-11-22 Zhentian Qian , Jie Fu , Jing Xiao

We introduce a new framework for perturbatively computing equilibrium thermodynamic properties of cosmological phase transitions to high loop orders, using the full four-dimensional resummed thermal effective potential and avoiding the…

High Energy Physics - Phenomenology · Physics 2025-07-10 Pablo Navarrete , Risto Paatelainen , Kaapo Seppänen , Tuomas V. I. Tenkanen

We study a two-loop contribution to the dark-matter trispectrum and evaluate it numerically using an infrared-safe integrand. The calculation is organized as an expansion around a fixed reference cosmology: the linear matter power spectrum…

Cosmology and Nongalactic Astrophysics · Physics 2026-03-09 Andrea Favorito

I present a few new and recent ideas of the multiloop calculations.

High Energy Physics - Phenomenology · Physics 2014-05-23 Roman N. Lee

For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle…

High Energy Physics - Phenomenology · Physics 2012-01-31 K. Kato , E. de Doncker , N. Hamaguchi , T. Ishikawa , T. Koike , Y. Kurihara , Y. Shimizu , F. Yuasa

Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and…

Information Theory · Computer Science 2024-09-13 Yansheng Wu , Jin Ma , Shandong Yang

A c++ implementation of the D_s-dimensional unitarity cut algorithm for the numerical evaluation of the virtual contribution to NLO QCD amplitudes is presented. The current version includes an arbitrary number of external gluons with…

High Energy Physics - Phenomenology · Physics 2008-12-17 A. Lazopoulos

We discuss the form of the string-loop-corrected effective action obtained by compactification of the heterotic string theory on the manifold $K3\times T^2$ or on its orbifold limit and the loop-corrected magnetic black hole solutions of…

High Energy Physics - Theory · Physics 2009-11-07 Mikhail Z. Iofa

The discovery of colour-kinematics duality has allowed great progress in our understanding of the UV structure of gravity. However, it has proven difficult to find numerators which satisfy colour-kinematics duality in certain cases. We…

High Energy Physics - Theory · Physics 2016-01-27 Gustav Mogull , Donal O'Connell