Related papers: Deep learning complete intersection Calabi-Yau man…
In this note, we propose a new approach to solving the Calabi problem on manifolds with edge-cone singularities of prescribed angles along complex hypersurfaces. It is shown how the classical approach of Aubin-Yau in derving {\it a priori}…
These are lecture notes on non-K\"ahler complex threefolds presented at the MATRIX program ``The geometry of moduli spaces in string theory''. We review some basics of Calabi-Yau geometry in Section 1, describe topological features of the…
We introduce ABC-Dataset, a collection of one million Computer-Aided Design (CAD) models for research of geometric deep learning methods and applications. Each model is a collection of explicitly parametrized curves and surfaces, providing…
We study nodal complete intersection threefolds of type $(2,4)$ in $\PP^5$ which contain an Enriques surface in its Fano embedding. We completely determine Calabi-Yau birational models of a generic such threefold. These models have Hodge…
Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data…
We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete…
Understanding and predicting the human visual attentional mechanism is an active area of research in the fields of neuroscience and computer vision. In this work, we propose DeepFix, a first-of-its-kind fully convolutional neural network…
3D building models with facade details are playing an important role in many applications now. Classifying point clouds at facade-level is key to create such digital replicas of the real world. However, few studies have focused on such…
Cross-subject motor-imagery decoding remains a major challenge in EEG-based brain-computer interfaces. To mitigate strong inter-subject variability, recent work has emphasized manifold-based approaches operating on covariance…
We explore the distribution of topological numbers in Calabi-Yau manifolds, using the Kreuzer-Skarke dataset of hypersurfaces in toric varieties as a testing ground. While the Hodge numbers are well-known to exhibit mirror symmetry,…
Computed Tomography (CT) is widely used in healthcare for detailed imaging. However, Low-dose CT, despite reducing radiation exposure, often results in images with compromised quality due to increased noise. Traditional methods, including…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
Providing an efficient strategy to navigate safely through unsignaled intersections is a difficult task that requires determining the intent of other drivers. We explore the effectiveness of Deep Reinforcement Learning to handle…
It has been shown by Batyrev and Borisov that nef partitions of reflexive polyhedra can be used to construct mirror pairs of complete intersection Calabi--Yau manifolds in toric ambient spaces. We construct a number of such spaces and…
Deep hedging uses recurrent neural networks to hedge financial products that cannot be fully hedged in incomplete markets. Previous work in this area focuses on minimizing some measure of quadratic hedging error by calculating pathwise…
Using the algebraic geometric approach of Berenstein et {\it al} (hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with discrete torsion.…
Breaking the diffraction limit in optical imaging is crucial for resolving subwavelength details in a wide range of applications, where superoscillatory imaging and subtraction imaging are two common strategies for surpassing conventional…
For responsible decision making in safety-critical settings, machine learning models must effectively detect and process edge-case data. Although existing works show that predictive uncertainty is useful for these tasks, it is not evident…
Deep learning has become a powerful tool in computational biology, revolutionising the analysis and interpretation of biological data over time. In our article review, we delve into various aspects of deep learning in computational biology.…
We provide a set of tools for analyzing the geometry of elliptically fibered Calabi-Yau manifolds, starting with a description of the total space rather than with a Weierstrass model or a specified type of fiber/base. Such an approach to…