16 papers
Vanishing Moment Dilations and Applications to Balanced and Graph Frames
Deguang Han, Shankhadeep Mondal, Kai Liu +1
Given a matrix we examine finite frames with vanishing -moments and investigate their connections with the frame dilation proper…
Jensen-type inequalities on pairs of measure spaces and their applications
Shankhadeep Mondal, P. D. Johnson, R. N. Mohapatra +1
We develop applications of a Jensen-type inequality for pairs of positive measure spaces. The framework yields and operator inequalities for positive integral operators, norm…
Hybrid Neural-Classical Correction for Frozen Time Series Foundation Models: A Comprehensive Ablation Study on High-Frequency Stock Prediction
Kasun Dewage, Suranadi De Silva, Shankhadeep Mondal
Foundation models for time series forecasting demonstrate impressive zero-shot generalization but often underperform on specialized domains such as high-frequency finance. We prese…
The structure of optimal dual frames for probabilistic erasures under Hilbert--Schmidt norm
Shankhadeep Mondal, R. N. Mohapatra, Jen-Chih Yao
Frames provide redundant representations that enable stable signal reconstruction under coefficient losses. In this paper, we study optimal dual frames for probabilistic erasures u…
Inequalities for Pairs of Measure Spaces and Applications
P. D. Johnson, R. N. Mohapatra, Shankhadeep Mondal
We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general pr…
Refined upper bounds for the numerical radius via weighted operator means
Shankhadeep Mondal, Ram Narayan Mohapatra, Kasun Tharuka Dewage
We establish a parameterized family of upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space, based on weighted expressions involving the mod…
When Mathematics Meets Painting: Fibonacci Geometry, Cubism and Visual Abstraction
Shankhadeep Mondal, R. N. Mohapatra
This paper explores the Fibonacci sequence and the Golden Ratio as organizing principles for visual composition and abstraction in painting. The author shows how recursive proporti…
Designing optimal dual frames for average error optimization
Shankhadeep Mondal, Deguang Han, R. N. Mohapatra
In this paper, we investigates the problem of optimal dual frame selection for signal reconstruction in the presence of erasures. Unlike traditional approaches relying on left inve…
Optimal K dual frames and pairs in the presence of erasures
Shankhadeep Mondal, Deguang Han, R. N. Mohapatra
This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame…
Optimal Dual Frame Pairs: A Synergy with Graph Theory
Shankhadeep Mondal, Ram Narayan Mohapatra
This paper investigates the optimization of dual frame pairs in the context of erasure problems in data transmission, using a graph theoretical approach. Frames are essential for m…
On the paper Optimal dual frames of probabilistic erasures
Shankhadeep Mondal, Ram Narayan Mohapatra
In the paper Optimal Dual Frames for Probabilistic Erasures, the authors have given conditions under which the canonical dual is claimed to be the unique probability optimal dual f…
Robustness of infinite frames and Besselian structures
Shankhadeep Mondal, Geetika Verma, Ram Narayan Mohapatra
This paper extends the concepts of Minimal Redundancy Condition (MRC) and robustness of erasures for infinite frames in Hilbert spaces. We begin by establishing a comprehensive fra…
Optimal dual pairs of frames for erasures
S. Arati, P. Devaraj, Shankhadeep Mondal
The study involves characterizations of dual pairs of frames which are optimal to handle erasures among all dual pairs for a finite dimensional Hilbert space. A new optimality meas…
Optimal dual frames and dual pairs for probability modelled erasures using weighted average of operator norm and spectral radius
S. Arati, P. Devaraj, Shankhadeep Mondal
The prime focus of this paper is the study of optimal duals of a given finite frame as well as optimal dual pairs, in the context of probability modelled erasures of frame coeffici…
Probability Modelled Averaged Spectrally Optimal Dual Frame and Dual Pair for Erasure
Shankhadeep Mondal
Finding the optimal dual frame and optimal dual pair for signal reconstruction, which can minimize the reconstruction error when erasure occurs during data transmission, is a deep…
Probabilistic Modelled Optimal Frame for Erasures under Spectral and Operator Norm
Shankhadeep Mondal
Error occurs in data transmission process when some data are missing at the time of reconstruction. Finding the best dual frame or a dual pair that minimizes the reconstruction err…