The need for parameter estimation with massive datasets has reinvigorated interest in stochastic optimization and iterative estimation procedures. Stochastic approximations are at the forefront of this recent development as they yield procedures that...
Finetuning is a critical step for adapting large language models (LLMs) to domain-specific downstream tasks. To mitigate the substantial computational and memory costs of full-model fine-tuning, Parameter-Efficient Finetuning (PEFT) methods have been...
We investigate simulation-based bandpower covariance matrices commonly used in cosmological parameter inferences such as the estimation of the tensor-to-scalar ratio $r$. We find that upper limits on $r$ can be biased low by tens of percent. The unde...
Accurate cosmological parameter estimates using polarization data of the cosmic microwave background (CMB) put stringent requirements on map calibration, as highlighted in the recent results from the Planck satellite. In this paper, we point out that...
This project deals with blind motion deblurring using a combination of Weiner Deconvolution and Deep Learning techniques to estimate the length and angle parameter of the Point-Spread Function (⭐ 22)
In this note a general way to develop a cardinal interpolant for $l^2$-data on the integer lattice $Z^n$ is shown. Further, a parameter is introduced which allows one to recover the original Paley-Weiner function from which the data came....
In this article, we consider the $d$-dimensional mollified stochastic heat equation (SHE) when the mollification parameter is turned off. Here, we concentrate on the high-dimensional case $d \geq 3$. Recently, the limiting higher moments of the two-d...
There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension $d\geq 3$ as the smoothing parameter is switched off, but most of the results did not hold in the full...
We consider the half-line stochastic heat equation (SHE) with Robin boundary parameter $A = -\frac{1}{2}$. Under narrow wedge initial condition, we compute every positive (including non-integer) Lyapunov exponents of the half-line SHE. As a consequen...
Among the widely used parameter-efficient fine-tuning (PEFT) methods, LoRA and its variants have gained considerable popularity because of avoiding additional inference costs. However, there still often exists an accuracy gap between these methods an...
Fine-tuning large-scale pre-trained models is inherently a resource-intensive task. While it can enhance the capabilities of the model, it also incurs substantial computational costs, posing challenges to the practical application of downstream tasks...
Besides magnetic and charge order, regular arrangements of orbital occupation constitute a fundamental order parameter of condensed matter physics. Even though orbital order is difficult to identify directly in experiments, its presence was firmly es...
We discuss the consequences of unique symmetry of de Sitter spacetime, which is invariant under the modified translations, ${\bf r}\rightarrow {\bf r} -e^{Ht}{\bf a}$, where $H$ is the Hubble parameter. Due to this symmetry, all the comoving observer...
The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacet...
It is well known that in the weak coupling regime, quantum field theories in de Sitter space do not have a unique vacuum, but a class of vacua parametrized by a complex parameter $α$, i.e., the so-called $α$-vacua. In this article, using gauge/gr...
It is shown that product BMO of Chang and Fefferman, defined on the product of Euclidean spaces can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of Coifman, Rochberg, and Weis...
In this paper, we first study biplanes $\mathcal{D}$ with parameters $(v,k,2)$, where the block size $k\in\{13,16\}$. These are the smallest parameter values for which a classification is not available. We show that if $k=13$, then either $\mathcal{D...
In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is pos...
Linear-width is a well-known and highly regarded graph parameter. The concept of Single Ideal and Linear obstacle serves as an obstruction to linear-width on a connectivity sysem. In this concise paper, we present an alternative proof for the equival...
The analysis of the broad iron line profile in the X-ray spectra of active galactic nuclei and black hole X-ray binaries allows us to constrain the spin parameter of the black hole. We compare the constraints on the spin value for two X-ray sources...