A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study restrictions on digitally continuous functions and their effects.
Incorrect fixed point assertions in digital topology are discussed.
In this paper, we show how to construct graph theoretical models of n-dimensional continuous objects and manifolds. These models retain topological properties of their continuous counterparts. An LCL collection of n-cells in Euclidean space is introduced and investigated. If an LCL collection of n-cells is a cover of a…
Study on cold and freezing sets in digital images.
The paper highlights issues with fixed point claims in digital images.
The paper addresses flaws in fixed point assertions for digital images.
The paper highlights issues in fixed point claims in digital topology.
Critiques incorrect fixed point assertions in digital topology.
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous…
Study minimal freezing sets in convex digital disks.
Study freezing sets for digital images in a 2D grid.
Study of digital topology concepts like hyperspaces and function graphs.
Numeracy is the ability to understand and work with numbers. It is a necessary skill for composing and understanding documents in clinical, scientific, and other technical domains. In this paper, we explore different strategies for modelling numerals with language models, such as memorisation and digit-by-digit composi…
We continue the work of [10], studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in [10]. We introduce freezing sets and cold sets to show how the existence of a fixed point set for a continuous self-map restricts the map on the c…
We continue the work of [5] and [3], in which are considered papers in the literature that discuss fixed point assertions in digital topology. We discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality under "usual" conditions; or that we improve upon.
A method models continuous-time glucose distributions in children with diabetes.
We investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the uni…
Incorrect fixed point assertions in digital topology are discussed.
Deep RL optimizes sensor placement in digital twins for dynamic data acquisition.
Fixed point assertions in digital topology are often incorrect or poorly stated.
A new Multi-Stream VAE separates multiple sources in images and audio.
New framework explains leading digit patterns without probabilistic assumptions.
There is a concept in digital topology of a shy map. We define an analogous concept for topological spaces: We say a function is shy if it is continuous and the inverse image of every path-connected subset of its image is path-connected. Some basic properties of such maps are presented. For example, every shy map onto …
We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.
We use a control framework to analyze the digital vendor's profit maximization problem. The vendor captures market share by focusing costly effort on post-launch product maintenance, which influences user perception of the product and drives a revenue stream associated with product use. Our theoretical results show nec…
New methods for selecting variables in complex biomedical data.
Study optimal bidding strategies for digital ads targeting purchases and health campaigns.
We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applicable to solutions of stochastic differential equations with locally bounded and continuous coefficients. The limit theorems are subsequently…
Proposes a probabilistic digital twin for dynamical systems using sparse Bayesian learning.
This study provides benchmarks for different implementations of LSTM units between the deep learning frameworks PyTorch, TensorFlow, Lasagne and Keras. The comparison includes cuDNN LSTMs, fused LSTM variants and less optimized, but more flexible LSTM implementations. The benchmarks reflect two typical scenarios for au…
Study small-time CLTs for stochastic Volterra equations with various kernels.
Method calculates function integrals on complex manifolds.
NSR enables neural networks to reason with continuous numbers and extrapolate.
Method discovers symmetries in data with neural networks.
Digital Financial Services continue to expand and replace the delivery of traditional banking services to the customers through innovative technologies to meet the growing complex needs and globalization challenges. These diversified digital products help the organizations (service providers) to improve their firm perf…
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus operators. Lipschitz continuity locally linearizes deformations. Complex classes o…
Enhanced multi-fidelity models improve digital twin accuracy and uncertainty quantification.
We propose a data-driven framework for optimizing privacy-preserving data release mechanisms to attain the information-theoretically optimal tradeoff between minimizing distortion of useful data and concealing specific sensitive information. Our approach employs adversarially-trained neural networks to implement random…
Neural machine learning methods, such as deep neural networks (DNN), have achieved remarkable success in a number of complex data processing tasks. These methods have arguably had their strongest impact on tasks such as image and audio processing - data processing domains in which humans have long held clear advantages…
Digital money could reduce germ spread during coronavirus.
Study shows monetary policy impacts digital assets like BTC and ETH.
We discuss an autoencoder model in which the encoding and decoding functions are implemented by decision trees. We use the soft decision tree where internal nodes realize soft multivariate splits given by a gating function and the overall output is the average of all leaves weighted by the gating values on their path. …
Find limiting sets for digital cones and suspensions.
Corrects incorrect assertions about fixed points in digital topology.
Study AFPP of unions of convex digital disks in 2D.
A digital euro protocol offers complete privacy and offline transactions using Groth-Sahai proofs.
Digital trees have approximate fixed point property, and conditions for products are explored.
Study convexity and AFPP in digital images.