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This article is the first of an intended series of works on the model theory of Ultrafinitism. It is roughly divided into two parts. The first one addresses some of the issues related to ultrafinitistic programs, as well as some of the core…
Proliferation of defects is a mechanism that allows for topological phase transitions. Such a phase transition is found in two dimensions for the XY-model, which lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. The…
In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model.…
Recent advances in Deep Learning (DL) have boosted data-driven System Identification (SysID), but reliable use requires Uncertainty Quantification (UQ) alongside accurate predictions. Although UQ-capable models such as Fuzzy ODE (FODE) can…
We show NP-completeness for the recognition problem of 2-line-bend graphs.
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field…
We study the fractionalization of space group symmetries in two-dimensional topologically ordered phases. Specifically, we focus on Z2-fractionalized phases in two dimensions whose deconfined topological excitations transform trivially…
Image reconstruction-based anomaly detection has recently been in the spotlight because of the difficulty of constructing anomaly datasets. These approaches work by learning to model normal features without seeing abnormal samples during…
The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy…
As a starting point, this paper develops the system of bipolar fuzzy relational equations (FRE) to the most general case, where bipolar FREs are defined by an arbitrary continuous t-norm. Due to the fact that fuzzy relational equations are…
Changepoint detection is the problem of finding abrupt or gradual changes in time series data when the distribution of the time series changes significantly. There are many sophisticated statistical algorithms for solving changepoint…
We present an image-conditioned point cloud completion approach that treats images as the primary geometric source rather than a secondary guide. To this end, we introduce an Image-to-Point (I2P) module that can reconstruct complete point…
The paper investigates how correlations can completely specify a uniformly discrete point process. The setting is that of uniformly discrete point sets in real space for which the corresponding dynamical hull is ergodic. The first result is…
From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set…
Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they…
Network attacks have become a major security concern for organizations worldwide and have also drawn attention in the academics. Recently, researchers have applied neural networks to detect network attacks with network logs. However, public…
The combination of neural network and fuzzy systems into neuro-fuzzy systems integrates fuzzy reasoning rules into the connectionist networks. However, the existing neuro-fuzzy systems are developed under shallow structures having lower…
In this paper, the fuzzy Hausdorff distance is studied, and also the fuzzy equidistant set for two points of a fuzzy metric space is introduced. Here, the fuzzy metric space has been redefined using recently developed fuzzy geometry, and…
The normalization constraint on probability density poses a significant challenge for solving the Fokker-Planck equation. Normalizing Flow, an invertible generative model leverages the change of variables formula to ensure probability…
We review new aspects of integrable systems discovered recently in N=2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten…