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Humans can often count unfamiliar objects by observing visual repetition and composition, rather than relying only on object categories. However, many exemplar-free counting models struggle in such situations and may overcount when objects…
Force detectors rely on resonators to transduce forces into a readable signal. Usually these resonators operate in the linear regime and their signal appears amidst a competing background comprising thermal or quantum fluctuations as well…
We perform a complete analytical reduction of general one-loop Feynman integrals with five and six external legs for tensors up to rank R=3 and 4, respectively. An elegant formalism with extensive use of signed minors is developed for the…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
In this paper we discuss different recursion relations (BCFW and all-line shift) for the form factors of the operators from the $\mathcal{N}=4$ SYM stress-tensor current supermultiplet $T^{AB}$ in momentum twistor space. We show that…
Among the unitarity cuts of 4-loop massless propagators two kinds are currently fully known: the 2-particle cuts with 3 loops corresponding to form-factors, and the 5-particle phase-space integrals. In this paper we calculate master…
Recent advances in fMRI-based visual decoding have enabled compelling reconstructions of perceived images. However, most approaches rely on subject-specific training, limiting scalability and practical deployment. We introduce…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
Integration-by-parts (IBP) reduction of Feynman integrals to master integrals is a key computational bottleneck in precision calculations in high-energy physics. Traditional approaches based on the Laporta algorithm require solving large…
Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical…
Formation control of autonomous agents can be seen as a physical system of individuals interacting with local potentials, and whose evolution can be described by a Lagrangian function. In this paper, we construct and implement forced…
We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant…
The wide adoption of deep neural networks has been accompanied by ever-increasing energy and performance demands due to the expensive nature of training them. Numerous special-purpose architectures have been proposed to accelerate training:…
We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm starts with…
This paper proposes an automatic power factor correction for variable inductive loads, most dominantly induction motors (IM) utilizing the Programmable Logic Controllers (PLC). This hardware implementation of a 3{\O} Inductive load system…
We introduce the simplest minimal subtraction method for massive $\lambda \phi^{4}$ field theory with $O(N)$ internal symmetry, which resembles the same method applied to massless fields by using two steps. First, the utilization of the…
In this paper we present the implementation of a Control Barrier Function (CBF) using a quadratic program (QP) formulation that provides obstacle avoidance for a robotic manipulator arm system. CBF is a control technique that has emerged…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. However, the absence of an inherent iterative structure in the transformer architecture…
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…