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Einstein's Special Theory of Relativity was proposed a little over a hundred years back. It remained a bedrock of twentieth century physics right up to Quantum Field Theory. However, the failure over several decades to provide a unified description of Electromagnetism and Gravitation or alternatively, Quantum Theory and General Relativity has finally lead researchers to abandon the differentiable spacetime manifold on which all of the above was based. In the most recent approaches we consider a spacetime that is discretized or is noncommutative. This immediately leads to corrections to the Special Theory of Relativity, more specifically to Lorentz Symmetry. It is quite significant that there are observational indicators, particularly in ultra high energy cosmic rays which suggest that such corrections are indeed there. We examine the whole issue in this paper.

We report an error found during independent review of the NuTauSim publicly available code \url{https://github.com/harmscho/NuTauSim} that forms the basis of this publication. The error in the code was in tracking the density of the medium during particle propagation. After the first interaction, the code was referencing the depth of penetration back to the surface of the Earth rather than the location of the last interaction. The results were obtained using densities that were systematically underestimated when the particle was traversing the inner layers of the Earth by assigning the density of either ice or bedrock, depending on the particle energy or ice thickness of the simulation. This error was fixed and the repository updated on September 29, 2018.

This paper presents a method for mathematical modelling of surfaces conditioned on empirical data. It is based on solving a discrete biharmonic equation over a domain with given inner point and inner curve data. The inner curve data is used to model boundary values while the inner point data is used for modeling a load vector with the goal to generate a smooth surface. The construction of boundary data is an ill-posed problem, for which a special regularization approach is suggested. The method is designed for surface construction problems with a very limited amount of measured data. In the paper we apply the method by using empirical data of soil thickness and geological maps indicating exposed bedrock regions.

Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance in edge computing, we introduce a low-power Multi-layer Perceptron (MLP) accelerator based on a pipelined matrix multiplication scheme and a nonuniform quantization methodology. The implementation is running on Field-programmable Gate Array (FPGA) devices and tested its performance on handwritten digit classification and Q-learning tasks. Results show that our method can achieve better performance with fewer power consumption.

Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic approach to accurately compute the kinetic energy density in such contexts. In our recent work, we introduced an analytical Green's function-based framework to address this issue. Majority of the existing efforts to construct an approximate kinetic energy density for atomic systems uses homogeneous electron gas as the bedrock of their formalism. In this work, we have shown by using a Pöschl-Teller potential that for realistic atomic potentials such model yields improper results emphasizing the need to change the leading-order term for the quest of kinetic energy densities of atoms and molecules.

In this study, we integrate the established obstacle problem formulation from ice sheet modeling with cutting-edge deep learning methodologies to enhance ice thickness predictions, specifically targeting the Greenland ice sheet. By harmonizing the mathematical structure with an energy minimization framework tailored for neural network approximations, our method's efficacy is confirmed through both 1D and 2D numerical simulations. Utilizing the NSIDC-0092 dataset for Greenland and incorporating bedrock topography for model pre-training, we register notable advances in prediction accuracy. Our research underscores the potent combination of traditional mathematical models and advanced computational techniques in delivering precise ice thickness estimations.

Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics. Such is its influence that whenever cut-elimination is not provable in a sequent calculus the invariable response has been a move to a richer proof system to regain it. In this paper we investigate a radically different approach to the latter: adapting age-old cut-elimination to restrict the shape of the cut-formulas when elimination is not possible. We tackle the "first level" above cut-free: analytic cuts. Our methodology is applied to the sequent calculi for bi-intuitionistic logic and S5 where analytic cuts are already known to be required. This marks the first steps in a theory of cut-restriction.

The State of Tripura lies in northeast India which is considered to be one of the most seismically active regions of the world. In the present study, a realistic Probabilistic Seismic Hazard Assessment (PSHA) of Tripura State based on improved seismogenic sources considering layered polygonal sources corresponding to hypo-central depth range of 0 to 25 km, 25 to 70 km and 70 to 180 km, respectively and data driven selection of suitable Ground Motion Prediction Equations (GMPEs) in a logic tree framework is presented. Analyses have been carried out by formulating a layered seismogenic source zonation together with smooth-gridded seismicity. Using the limited accelerogram records available, most suitable GMPEs have been selected after performing a thorough quantitative assessment and thus the uncertainty in selecting appropriate GMPEs in PSHA has been addressed by combining them with proper weight factor. The computations of seismic hazard are carried out in a higher resolution of grid interval of 0.05 $\degree$ X 0.05 $\degree$. The probabilistic seismic hazard distribution in terms of Peak Ground Acceleration (PGA) and 5% damped Pseudo Spectral Acceleration (PSA) at different time

The regularity of earthquakes, their destructive power, and the nuisance of ground vibration in urban environments, all motivate designs of defence structures to lessen the impact of seismic and ground vibration waves on buildings. Low frequency waves, in the range $1$ to $10$ Hz for earthquakes and up to a few tens of Hz for vibrations generated by human activities, cause a large amount of damage, or inconvenience, depending on the geological conditions they can travel considerable distances and may match the resonant fundamental frequency of buildings. The ultimate aim of any seismic metamaterial, or any other seismic shield, is to protect over this entire range of frequencies, the long wavelengths involved, and low frequency, have meant this has been unachievable to date. Elastic flexural waves, applicable in the mechanical vibrations of thin elastic plates, can be designed to have a broad zero-frequency stop-band using a periodic array of very small clamped circles. Inspired by this experimental and theoretical observation, all be it in a situation far removed from seismic waves, we demonstrate that it is possible to achieve elastic surface (Rayleigh) and body (pressure P and s

AI agents powered by large language models (LLMs) have shown strong capabilities in problem solving. Through combining many intelligent agents, multi-agent collaboration has emerged as a promising approach to tackle complex, multi-faceted problems that exceed the capabilities of single AI agents. However, designing the collaboration protocols and evaluating the effectiveness of these systems remains a significant challenge, especially for enterprise applications. This report addresses these challenges by presenting a comprehensive evaluation of coordination and routing capabilities in a novel multi-agent collaboration framework. We evaluate two key operational modes: (1) a coordination mode enabling complex task completion through parallel communication and payload referencing, and (2) a routing mode for efficient message forwarding between agents. We benchmark on a set of handcrafted scenarios from three enterprise domains, which are publicly released with the report. For coordination capabilities, we demonstrate the effectiveness of inter-agent communication and payload referencing mechanisms, achieving end-to-end goal success rates of 90%. Our analysis yields several key finding