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Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
We introduce a novel architecture and computational framework for formal, automated analysis of systems with a broad set of nonlinearities in the feedback loop, such as neural networks, vision controllers, switched systems, and even simple…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
Several Scientific and engineering applications require merging of sampled images for complex perception development. In most cases, for such requirements, images are merged at intensity level. Even though it gives fairly good perception of…
The problem of light waves interaction with charged particles becomes more and more complex starting with the case of plane waves, where the analytical solution is well known, to more natural, though more complicated situations which…
Foundational models with billions of parameters which have been trained on large corpora of data have demonstrated non-trivial skills in a variety of domains. However, due to their monolithic structure, it is challenging and expensive to…
We propose an architecture and process for using the Iterated Learning Model ("ILM") for artificial neural networks. We show that ILM does not lead to the same clear compositionality as observed using DCGs, but does lead to a modest…
Two types of framework for blurred image classification based on adaptive dictionary are proposed. Given a blurred image, instead of image deblurring, the semantic category of the image is determined by blur insensitive sparse coefficients…
Large-scale Vision-Language Models (LVLMs) output text from images and instructions, demonstrating capabilities in text generation and comprehension. However, it has not been clarified to what extent LVLMs possess the ability to understand…
Light adaptation or brightness correction is a key step in improving the contrast and visual appeal of an image. There are multiple light-related tasks (for example, low-light enhancement and exposure correction) and previous studies have…
Light-field microscopy (LFM) is a 3D microscopy technique whereby volumetric information of a sample is gained by simultaneously capturing both the position and momentum (angular) information of light illuminating a scene. Conventional LFM…
Class-incremental learning requires a learning system to continually learn knowledge of new classes and meanwhile try to preserve previously learned knowledge of old classes. As current state-of-the-art methods based on Vision-Language…
Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of…
Large Language Models (LLMs) have demonstrated substantial efficacy in advancing graph-structured data analysis. Prevailing LLM-based graph methods excel in adapting LLMs to text-rich graphs, wherein node attributes are text descriptions.…
Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…
This paper presents a novel network structure with illumination-aware gamma correction and complete image modelling to solve the low-light image enhancement problem. Low-light environments usually lead to less informative large-scale dark…
This paper presents a new method of gray level image enhancement, based on point transforms. In order to define the transform function, it was used a generalization of the homographic function.
We present a new perspective on gravitational lensing. We describe a new extension of the weak lensing formalism capable of describing strongly lensed images. By integrating the non-linear geodesic deviation equation, the amplification…
The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…
A method for the local and global interpretation of a black-box model on the basis of the well-known generalized additive models is proposed. It can be viewed as an extension or a modification of the algorithm using the neural additive…