Related papers: Exploring Repetitiveness Measures for Two-Dimensio…
The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
For $d\geq 2$, we construct a doubling measure $\nu$ on $\R^d$ and a rectifiable curve $\Gamma$ such that $\nu(\Gamma)>0$.
The effectiveness of large language models (LLMs) is often hindered by duplicated data in their extensive pre-training datasets. Current approaches primarily focus on detecting and removing duplicates, which risks the loss of valuable…
This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models. The tensionless limit is used to find a IIB supergravity background generated by a tensionless string.…
We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test…
We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE)…
The sensitivity of a string compression algorithm $C$ asks how much the output size $C(T)$ for an input string $T$ can increase when a single character edit operation is performed on $T$. This notion enables one to measure the robustness of…
The Ward identities of the $W_{\infty}$ symmetry in 2D string theory in the tachyon background are studied in the continuum approach. Comparing the solutions with the matrix model results, it is verified that 2D string amplitudes are…
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently,…
Using the reduced formulation on large-N Quantum Field Theories we study strings in space-time dimensions higher that one. We present results on possible string susceptibilities, macroscopic loop operators, 1/N -corrections and other…
In highly repetitive strings, like collections of genomes from the same species, distinct measures of repetition all grow sublinearly in the length of the text, and indexes targeted to such strings typically depend only on one of these…
Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
Using the reduced formulation of large-N Quantum Field Theories we study strings in space-time dimensions higher than one. Some preliminary results concerning the possible string susceptibilities and general properties of the model are…
R2 score is the standard metric for evaluating regression tasks, offering a normalized magnitude-agnostic measure of accuracy that captures variance. However, R2 has three key limitations: it is limited to at most two dimensional inputs, it…
String theory in two-dimensional spacetime illuminates two main threads of recent development in string theory: (1) Open/closed string duality, and (2) Tachyon condensation. In two dimensions, many aspects of these phenomena can be explored…
We demonstrate that string consistency in four spacetime dimensions leads to a spectrum of string states which satisfies the supertrace constraints Str(M^0)=0 and Str(M^2)=\Lambda at tree level, where \Lambda is the one-loop string…
We continue the study of 2D gravity -- ``matrix model'' duality on the example of $(2,2p+1)$ minimal string. We propose a reformulation of the duality, related to a more conventional one by ``$x-y$ swap'' in the language of topological…
Two-dimensional terahertz spectroscopy (2DTS) is a low-frequency analogue of two-dimensional optical spectroscopy that is rapidly maturing as a probe of a wide variety of condensed matter systems. However, a persistent problem of 2DTS is…