Fuzzy Functional Differential Equations under Dissipative-Type Conditions

Fuzzy functional differential equations with continuous right-hand sides are studied. The existence and uniqueness of a solution are proved under dissipative-type conditions. The continuous dependence of the solution on the initial conditions is shown. The existence of the solution on an infinite interval and its stability are also analyzed.Вивчаються нєчіткі функціонально-диференціальні рівняння з неперервною правою частиною. Доведено існування та єдиність розв'язку за умов дисипативного типу. Встановлено неперервну залежність розв'язку від початкових умов. Також розглянуто питання про існування розв'язку на нескінченному інтервалі та його стійкість

A study of temperature-related non-linearity at the metal-silicon interface

In this paper, we investigate the temperature dependencies of metal-semiconductor interfaces in an effort to better reproduce the current-voltage-temperature (IVT) characteristics of any Schottky diode, regardless of homogeneity. Four silicon Schottky diodes were fabricated for this work, each displaying different degrees of inhomogeneity; a relatively homogeneous NiV/Si diode, a Ti/Si and Cr/Si diode with double bumps at only the lowest temperatures, and a Nb/Si diode displaying extensive non-linearity. The 77–300 K IVT responses are modelled using a semi-automated implementation of Tung's electron transport model, and each of the diodes are well reproduced. However, in achieving this, it is revealed that each of the three key fitting parameters within the model display a significant temperature dependency. In analysing these dependencies, we reveal how a rise in thermal energy “activates” exponentially more interfacial patches, the activation rate being dependent on the carrier concentration at the patch saddle point (the patch's maximum barrier height), which in turn is linked to the relative homogeneity of each diode. Finally, in a review of Tung's model, problems in the divergence of the current paths at low temperature are explained to be inherent due to the simplification of an interface that will contain competing defects and inhomogeneities

DiLoCo: Distributed Low-Communication Training of Language Models

Large language models (LLM) have become a critical component in many applications of machine learning. However, standard approaches to training LLM require a large number of tightly interconnected accelerators, with devices exchanging gradients and other intermediate states at each optimization step. While it is difficult to build and maintain a single computing cluster hosting many accelerators, it might be easier to find several computing clusters each hosting a smaller number of devices. In this work, we propose a distributed optimization algorithm, Distributed Low-Communication (DiLoCo), that enables training of language models on islands of devices that are poorly connected. The approach is a variant of federated averaging, where the number of inner steps is large, the inner optimizer is AdamW, and the outer optimizer is Nesterov momentum. On the widely used C4 dataset, we show that DiLoCo on 8 workers performs as well as fully synchronous optimization while communicating 500 times less. DiLoCo exhibits great robustness to the data distribution of each worker. It is also robust to resources becoming unavailable over time, and vice versa, it can seamlessly leverage resources that become available during training

Average and extreme multi-atom Van der Waals interactions: Strong coupling of multi-atom Van der Waals interactions with covalent bonding

<p>Abstract</p> <p>Background</p> <p>The prediction of ligand binding or protein structure requires very accurate force field potentials – even small errors in force field potentials can make a 'wrong' structure (from the billions possible) more stable than the single, 'correct' one. However, despite huge efforts to optimize them, currently-used all-atom force fields are still not able, in a vast majority of cases, even to keep a protein molecule in its native conformation in the course of molecular dynamics simulations or to bring an approximate, homology-based model of protein structure closer to its native conformation.</p> <p>Results</p> <p>A strict analysis shows that a specific coupling of multi-atom Van der Waals interactions with covalent bonding can, in extreme cases, increase (or decrease) the interaction energy by about 20–40% at certain angles between the direction of interaction and the covalent bond. It is also shown that on average multi-body effects decrease the total Van der Waals energy in proportion to the square root of the electronic component of dielectric permittivity corresponding to dipole-dipole interactions at small distances, where Van der Waals interactions take place.</p> <p>Conclusion</p> <p>The study shows that currently-ignored multi-atom Van der Waals interactions can, in certain instances, lead to significant energy effects, comparable to those caused by the replacement of atoms (for instance, C by N) in conventional pairwise Van der Waals interactions.</p