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We present a theoretical study of the exchange interaction in a system of spatially disordered magnetic moments. A typical example of such a system is an impurity semiconductor, whose magnetic properties are associated with the exchange interaction of the impurity atoms. In this study, we consider the case of antiferromagnetic exchange interaction, which we describe by the Heisenberg Hamiltonian. To calculate the magnetic properties of the disordered system, we employ the density of states method. Our calculations demonstrate a good quantitative agreement with the dependence of the Si:P magnetic susceptibility on temperature in a wide range of impurity concentrations and temperatures.

The kinetic stability of collisionless, sloshing beam-ion (45{\deg} pitch angle) plasma is studied in a 3D simple magnetic mirror, mimicking the Wisconsin High-temperature superconductor Axisymmetric Mirror (WHAM) experiment. The collisional Fokker-Planck code CQL3D-m provides a slowing-down beam-ion distribution to initialize the kinetic-ion/fluid-electron code Hybrid-VPIC, which then simulates free plasma decay without external heating or fueling. Over 1-10 $\mu$s, drift-cyclotron loss-cone (DCLC) modes grow and saturate in amplitude. DCLC scatters ions to a marginally-stable distribution with gas-dynamic rather than classical-mirror confinement. Sloshing ions can trap cool (low-energy) ions in an electrostatic potential well to stabilize DCLC, but DCLC itself does not scatter sloshing beam-ions into said well. Instead, cool ions must come from external sources such as charge-exchange collisions with a low-density neutral population. Manually adding cool ~1 keV ions improves beam-ion confinement ~2-5x in Hybrid-VPIC simulations, which qualitatively corroborates measurements from real mirror devices with sloshing ions., Comment: Submitted; 35 pages, 14 figures

This paper presents the Hammir tandem mirror design based on Realta Fusion's first-of-a-kind model for axisymmetric magnetic mirror fusion performance. This model uses an integrated end plug simulation model including, heating, equilibrium, and transport combined with a new formulation of the plasma operation contours (POPCONs) technique for the tandem mirror central cell. Using this model, it is shown that an end plug utilizing high temperature superconducting magnets and modern neutral beams enables a classical tandem mirror pilot plant producing a fusion gain Q > 5. The approach here represents an important advance in tandem mirror design. The high fidelity end plug model enables calculations of heating and transport in the highly non-Maxwellian end plug to be made more accurately and the central cell POPCON technique allows consideration of a wide range of parameters in the relatively simple near-Maxwellian central cell, facilitating the selection of more optimal central cell plasmas. These advances make it possible to find more conservative classical tandem mirror fusion pilot plant operating points with lower $\beta$, temperatures, neutral beam energies, and end plug performance than designs in the literature. Despite being more conservative, it is shown that these operating points can still form the basis of a viable fusion pilot plant.

The best way to check the validity of our theories (models) is by direct comparison with the experiment (observations). In this study, we address the numerical inaccuracies intrinsic to the process of comparing theory and observations. To achieve this goal, we built 4D spectra grids for Wolf-Rayet stars (WC and WN spectral classes) and Blue Supergiants (BSGs) characterized by low metallicity similar to that of the Small Magellanic Cloud (SMC). Through rigorous testing on designated `test' models, we demonstrated that the numerical precision of derived stellar parameters (effective temperature, mass-loss rate, luminosity, and wind velocity) is not exceeding 0.05 dex. Moreover, the mean absolute deviation of the numerically derived stellar parameters is consistently below this threshold for objects with both weak (SMC grid) and strong winds (WC and WN grids), even in the presence of Gaussian noise. Furthermore, we explored the influence of unaccounted factors, including variations in the metal abundances, wind acceleration laws, and clumping, on the precision of the derived parameters. We found that the first two factors have the strongest influence on the numerical accuracy of the derived stellar parameters. Variations in abundances predominantly influenced the mass-loss rate for weak-wind scenarios, while effective temperature and luminosity remained robust. We found that the wind acceleration law influence the numerical uncertainty of the derived wind parameters mostly for models with weak winds. Interestingly, different degrees of clumping demonstrated good precision for spectra with strong winds, contrasting with a decrease in the precision for weak-wind cases. We found also that the accuracy of our approach depends on spectral range and the inclusion of ultraviolet spectral range improves the precision of derived parameters, especially for object with weak winds., Comment: 28 pages, 14 figures, 4 tables

Sub-picosecond optical laser processing of metals is actively utilized for modification of a heated surface layer. But for deeper modification of different materials a laser in the hard x-ray range is required. Here, we demonstrate that a single 9-keV x-ray pulse from a free-electron laser can form a um-diameter cylindrical cavity with length of ~1 mm in LiF surrounded by shock-transformed material. The plasma-generated shock wave with TPa-level pressure results in damage, melting and polymorphic transformations of any material, including transparent and non-transparent to conventional optical lasers. Moreover, cylindrical shocks can be utilized to obtain a considerable amount of exotic high-pressure polymorphs. Pressure wave propagation in LiF, radial material flow, formation of cracks and voids are analyzed via continuum and atomistic simulations revealing a sequence of processes leading to the final structure with the long cavity. Similar results can be produced with semiconductors and ceramics, which opens a new pathway for development of laser material processing with hard x-ray pulses.

Transformer-based recommender systems, such as BERT4Rec or SASRec, achieve state-of-the-art results in sequential recommendation. However, it is challenging to use these models in production environments with catalogues of millions of items: scaling Transformers beyond a few thousand items is problematic for several reasons, including high model memory consumption and slow inference. In this respect, RecJPQ is a state-of-the-art method of reducing the models' memory consumption; RecJPQ compresses item catalogues by decomposing item IDs into a small number of shared sub-item IDs. Despite reporting the reduction of memory consumption by a factor of up to 50x, the original RecJPQ paper did not report inference efficiency improvements over the baseline Transformer-based models. Upon analysing RecJPQ's scoring algorithm, we find that its efficiency is limited by its use of score accumulators for each item, which prevents parallelisation. In contrast, LightRec (a non-sequential method that uses a similar idea of sub-ids) reported large inference efficiency improvements using an algorithm we call PQTopK. We show that it is also possible to improve RecJPQ-based models' inference efficiency using the PQTopK algorithm. In particular, we speed up RecJPQ-enhanced SASRec by a factor of 4.5 x compared to the original SASRec's inference method and by a factor of 1.56 x compared to the method implemented in RecJPQ code on a large-scale Gowalla dataset with more than a million items. Further, using simulated data, we show that PQTopK remains efficient with catalogues of up to tens of millions of items, removing one of the last obstacles to using Transformer-based models in production environments with large catalogues., Comment: Accepted by RecSys 2024

Transformer-based Cross-Encoders achieve state-of-the-art effectiveness in text retrieval. However, Cross-Encoders based on large transformer models (such as BERT or T5) are computationally expensive and allow for scoring only a small number of documents within a reasonably small latency window. However, keeping search latencies low is important for user satisfaction and energy usage. In this paper, we show that weaker shallow transformer models (i.e., transformers with a limited number of layers) actually perform better than full-scale models when constrained to these practical low-latency settings since they can estimate the relevance of more documents in the same time budget. We further show that shallow transformers may benefit from the generalized Binary Cross-Entropy (gBCE) training scheme, which has recently demonstrated success for recommendation tasks. Our experiments with TREC Deep Learning passage ranking query sets demonstrate significant improvements in shallow and full-scale models in low-latency scenarios. For example, when the latency limit is 25ms per query, MonoBERT-Large (a cross-encoder based on a full-scale BERT model) is only able to achieve NDCG@10 of 0.431 on TREC DL 2019, while TinyBERT-gBCE (a cross-encoder based on TinyBERT trained with gBCE) reaches NDCG@10 of 0.652, a +51% gain over MonoBERT-Large. We also show that shallow Cross-Encoders are effective even when used without a GPU (e.g., with CPU inference, NDCG@10 decreases only by 3% compared to GPU inference with 50ms latency), which makes Cross-Encoders practical to run even without specialized hardware acceleration., Comment: Accepted by ECIR2024

Sequential Recommendation is a popular recommendation task that uses the order of user-item interaction to model evolving users' interests and sequential patterns in their behaviour. Current state-of-the-art Transformer-based models for sequential recommendation, such as BERT4Rec and SASRec, generate sequence embeddings and compute scores for catalogue items, but the increasing catalogue size makes training these models costly. The Joint Product Quantisation (JPQ) method, originally proposed for passage retrieval, markedly reduces the size of the retrieval index with minimal effect on model effectiveness, by replacing passage embeddings with a limited number of shared sub-embeddings. This paper introduces RecJPQ, a novel adaptation of JPQ for sequential recommendations, which takes the place of item embeddings tensor and replaces item embeddings with a concatenation of a limited number of shared sub-embeddings and, therefore, limits the number of learnable model parameters. The main idea of RecJPQ is to split items into sub-item entities before training the main recommendation model, which is inspired by splitting words into tokens and training tokenisers in language models. We apply RecJPQ to SASRec, BERT4Rec, and GRU4rec models on three large-scale sequential datasets. Our results showed that RecJPQ could notably reduce the model size (e.g., 48% reduction for the Gowalla dataset with no effectiveness degradation). RecJPQ can also improve model performance through a regularisation effect (e.g. +0.96% NDCG@10 improvement on the Booking.com dataset). Overall, RecJPQ allows the training of state-of-the-art transformer recommenders in industrial applications, where datasets with millions of items are common., Comment: Accepted by ACM WSDM 2024

We study the theoretical model of a ferromagnetic semiconductor as a system of randomly distributed Ising spins with a long-range exchange interaction. Using the density-of-states approach, we analytically obtain the magnetic susceptibility and heat capacity over a wide range of temperatures and magnetic fields. It is shown that the finite system of spins in magnetic field less than a certain critical field is in a superparamagnetic state due to thermodynamic fluctuations. The complex phase structure of a ferromagnetic semiconductor is discussed.

Sequential recommendation is an important recommendation task that aims to predict the next item in a sequence. Recently, adaptations of language models, particularly Transformer-based models such as SASRec and BERT4Rec, have achieved state-of-the-art results in sequential recommendation. In these models, item ids replace tokens in the original language models. However, this approach has limitations. First, the vocabulary of item ids may be many times larger than in language models. Second, the classical Top-K recommendation approach used by these models may not be optimal for complex recommendation objectives, including auxiliary objectives such as diversity, coverage or coherence. Recent progress in generative language models inspires us to revisit generative approaches to address these challenges. This paper presents the GPTRec sequential recommendation model, which is based on the GPT-2 architecture. GPTRec can address large vocabulary issues by splitting item ids into sub-id tokens using a novel SVD Tokenisation algorithm based on quantised item embeddings from an SVD decomposition of the user-item interaction matrix. The paper also presents a novel Next-K recommendation strategy, which generates recommendations item-by-item, considering already recommended items. The Next-K strategy can be used for producing complex interdependent recommendation lists. We experiment with GPTRec on the MovieLens-1M dataset and show that using sub-item tokenisation GPTRec can match the quality of SASRec while reducing the embedding table by 40%. We also show that the recommendations generated by GPTRec on MovieLens-1M using the Next-K recommendation strategy match the quality of SASRec in terms of NDCG@10, meaning that the model can serve as a strong starting point for future research., Comment: Accepted at Gen-IR@SIGIR2023 workshop

This paper classifies all modular data of integral modular fusion categories up to rank 13. Furthermore, it also classifies all integral half-Frobenius fusion rings up to rank 12. We find that each perfect integral modular fusion category up to rank 13, as well as every perfect integral half-Frobenius fusion ring up to rank 12, is trivial. We have also refined the non-pointed odd-dimensional modular data at ranks below 25 to three items, all of rank 17, FPdim 225, and type [[1,3],[3,8],[5,6]], filling gaps in the literature. For rank 25, we have narrowed down the perfect case to 3 types. Our initial key insight is that the Egyptian fractions, which are typically employed to list possible types, can be chosen with squared denominators. We then develop several type criteria as initial filters. In particular, we establish that the number of distinct basic FPdims in a non-trivial perfect fusion ring must be at least 4. To obtain the fusion rings, we solve the dimension and associativity equations using new features on Normaliz created specifically for this purpose. The S-matrices (if they exist) are obtained by self-transposing the character table, while the T-matrices are derived by solving the Anderson-Moore-Vafa equations. Finally, we verify the extended axioms of modular data. From rank 13 onward, the types were further restricted by additional properties unique to the modular case, which involved the universal grading, congruence representations of the modular group and Galois action, leading to critical arithmetic constraints. In particular, we get that, up to rank 21, a prime divisor of the global FPdim does not exceed the rank, and more strongly up to rank 15 in the non-pointed case, does not exceed half the rank. Ultimately, we narrowed down the classification at rank 14 to 35 possible types, 8 of which are non-perfect., Comment: 34 pages. New results involving stronger arithmetic constraints, motivated by new results on the rank of Z(Rep(G)); reduction of the rank 14 case to 35 types; reduction of perfect odd-dim rank 25 to 3 types; the computational proofs are now well documented; new features on Normaliz involving modular grading; new SageMath functions available for classifying constrained types. Comments are welcome!

High-power femtosecond laser radiation propagates nonlinearly in air exhibiting pulse self-focusing and strong multiphoton medium ionization, which leads to the spatial fragmentation of laser pulse into highly-localized light channels usually called the filaments. The filaments are characterized by high optical intensity, reduced (even zero) angular spreading and can contain laser plasma or be plasmaless (postfilaments). The presence of optical turbulence on the propagation path dramatically changes pulse filamentation dynamics and in some cases causes pulse fragmentation enhancement and collapse arrest. For the first time to our knowledge, we experimentally and theoretically investigate the transverse profile of Ti:sapphire femtosecond laser radiation nonlinearly propagating a 65 m air path to the region of postfilament evolution after passing through an artificial localized air turbulence. We show that when a turbulent layer is placed before the filamentation region, the average number of high-intensive local fluence maxima ("hot points") in pulse profile as well as their sizes grow as the turbulence strength increases, and then saturates at some levels. On the contrary, the deposition of a turbulent screen within the filamentation region has almost no effect on both the number and the average diameter of the postfilaments.