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We clarify the notion of Wilsonian renormalization group (RG) invariance in supersymmetric gauge theories, which states that the low-energy physics can be kept fixed when one changes the ultraviolet cutoff, provided appropriate changes are…

The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as…

Scientific algorithm discovery is iterative: hypotheses are proposed, implemented, stress-tested, and revised. Current LLM-guided search systems accelerate proposal generation, but often under-represent scientific structure by optimizing…

According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the…

The reaction center consists of atoms in the product whose local properties are not identical to the corresponding atoms in the reactants. Prior studies on reaction center identification are mainly on semi-templated retrosynthesis methods.…

Reservoir computing is a type of a recurrent neural network, mapping the inputs into higher dimensional space using fixed and nonlinear dynamical systems, called reservoirs. In the literature, there are various types of reservoirs ranging…

Most state of the art decision systems based on Reinforcement Learning (RL) are data-driven black-box neural models, where it is often difficult to incorporate expert knowledge into the models or let experts review and validate the learned…

Vector quantization is a fundamental operation for data compression and vector search. To obtain high accuracy, multi-codebook methods represent each vector using codewords across several codebooks. Residual quantization (RQ) is one such…

We introduce RGFlow, a deep neural network-based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns…

The Renormalisation Group (RG) provides a framework in which it is possible to assess whether a deep-learning network is sensitive to small changes in the input data and hence prone to error, or susceptible to adversarial attack. Distinct…

On the basis of the classical theory of envelopes, we formulate the renormalization group (RG) method for global analysis, recently proposed by Goldenfeld et al. It is clarified why the RG equation improves things.

We introduce DiFfRG (Discretisation Framework for functional Renormalisation Group flows), a comprehensive computational C++ framework for solving functional Renormalisation Group flows in very general truncation schemes. Its central…

We have developed a new tool for numerical work in General Relativity: GRworkbench. While past tools have been ad hoc, GRworkbench closely follows the framework of Differential Geometry to provide a robust and general way of computing on…

In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on…

Let $k$ be a field, let $G$ be a reductive group, and let $V$ be a linear representation of $G$. Let $V//G = Spec(Sym(V^*))^G$ denote the geometric quotient and let $\pi: V \to V//G$ denote the quotient map. Arithmetic invariant theory…

We report on results about a study of algebraic graph invariants, based on computer exploration, and motivated by graph-isomorphism and reconstruction problems.

This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called IR Tools, serves two related purposes: we provide implementations…

In this work, a constant time Quantum searching algorithm over a datasets is proposed and subsequently the algorithm is executed in real chip quantum computer developed by IBM Quantum experience (IBMQ). QISKit, the software platform…

In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…

Modern DNA sequencing technologies enable geneticists to rapidly identify genetic variation among many human genomes. However, isolating the minority of variants underlying disease remains an important, yet formidable challenge for medical…