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Long-term satellite image time series (SITS) analysis in heterogeneous landscapes faces significant challenges, particularly in Mediterranean regions where complex spatial patterns, seasonal variations, and multi-decade environmental…
Time series forecasting plays a significant role in finance, energy, meteorology, and IoT applications. Recent studies have leveraged the generalization capabilities of large language models (LLMs) to adapt to time series forecasting,…
In this work, we present a semi-numerical solution of a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite…
Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with…
Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious…
The Laplace transform theory violates a very fundamental requirement of all engineering systems. We show that this theory assumes that all signals must exist over infinite time interval. Since in engineering this infinite time assumption is…
A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It is constructed from the Pad\'e expansions of the matrix exponential solution of a system of first-order…
We introduce the Byte Latent Transformer (BLT), a new byte-level LLM architecture that, for the first time, matches tokenization-based LLM performance at scale with significant improvements in inference efficiency and robustness. BLT…
The traditional theory of Laplace transformation in its currently prevalent form is unsatisfactory. Its deficiencies can be traced back to a mismatch of the definition intervals of the original function and of the inverse L-transform. A new…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
This paper proposes a new methodology in linear time-periodic (LTP) system identification. In contrast to previous methods that totally separate dynamics at different tag times for identification, the method focuses on imposing appropriate…
The Lorentz Integral Transform (LIT) method is reformulated via the Lanczos algorithm both for inclusive and exclusive reactions. The new technique is tested for the total photoabsorption cross section of 3H and 4He. Due to the rapid…
We first develop systematic and comprehensive interval observer designs for linear time-invariant (LTI) systems, under standard assumptions of observability and interval bounds on the initial condition and uncertainties. Traditionally, such…
Linear time-invariant (LTI) systems appear frequently in natural sciences and engineering contexts. Many LTI systems are described by ordinary differential equations (ODEs). For example, biological gene regulation, analog filter circuits,…
Effectively modeling time information and incorporating it into applications or models involving chronologically occurring events is crucial. Real-world scenarios often involve diverse and complex time patterns, which pose significant…
A new method is introduced which uses higher-order Laplace approximation to evaluate functional integrals much faster than existing methods. An implementation in MATLAB is called SLAM-FIT (Sparse Laplace Approximation Method for Functional…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
Recently, large language models (LLMs) have demonstrated powerful capabilities in performing various tasks and thus are applied by recent studies to time series forecasting (TSF) tasks, which predict future values with the given historical…
We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R^n. Practically all previously proposed differential transformations of LPDOs are particular cases of…
We present a novel probabilistic deep learning approach, the 'Stochastic Latent Transformer' (SLT), designed for the efficient reduced-order modelling of stochastic partial differential equations. Stochastically driven flow models are…