Instructions to use shreyaspullehf/superconductor-search-v2 with libraries, inference providers, notebooks, and local apps. Follow these links to get started.

Libraries

How to use shreyaspullehf/superconductor-search-v2 with sentence-transformers:

from sentence_transformers import SentenceTransformer

model = SentenceTransformer("shreyaspullehf/superconductor-search-v2")

sentences = [
    "magnetic order superconductor",
    "arXiv:0802.4093v2 [cond-mat.str-el] 27 Feb 2009 Meissner eﬀect without superconductivity from a chiral d-density wave P. Kotetes∗and G. Varelogiannis† Department of Physics, National Technical University of Athens, GR-15780 Athens, Greece We demonstrate that the formation of a chiral d-density wave (CDDW) state generates a Topolo- gical Meissner eﬀect (TME) in the absence of any kind of superconductivity. The TME is identical to the usual superconducting Meissner eﬀect but it appears only for magnetic ﬁelds perpendicular to the plane while it is absent for in plane ﬁelds. The observed enhanced diamagnetic signals in the non-superconducting pseudogap regime of the cuprates may ﬁnd an alternative interpretation in terms of a TME, originating from a chiral d-density wave pseudogap. PACS numbers: 75.20.-g, 71.27.+a, 74.72.-h The Meissner eﬀect is considered to be the most direct signature of superconductivity [1]. However, the surpris- ing observations of such enhanced diamagnetic signals [2] well above the superconducting transition tempera- ture in the pseudogap regime of the cuprates [3], con- stitute a fascinating puzzle. There are two proposals for the nature of this regime that appear to dominate. The ﬁrst, associates the pseudogap with a dx2−y2 density wave (DDW) [4, 5], also called orbital antiferromagnet [6, 7], which normally competes with superconductivity. The second associates the pseudogap with spontaneous vortex-antivortex unbinding leading to incoherent super- conductivity [8] that should persist well above the su- perconducting Tc. This theory is reminiscent of the well known Kosterlitz-Thouless transition [9]. The available ARPES [10] and STM [11] experiments cannot diﬀerentiate a SC from a density wave (DW) gap, and therefore appear somehow incapable in settling di- rectly the issue. On the other hand, the unusual Nernst eﬀect and most importantly, the enhanced diamagnetic signal that accompanies it for a very large temperature region above the SC critical temperature [2], has been considered as a major argument in favor of the incoher- ent SC scenario. In fact, the enhanced diamagnetism is viewed as a signature of the usual Meissner eﬀect associ- ated solely with the SC state, and would therefore contra- dict the dx2−y2 density wave scenario since no Meissner eﬀect was expected in that case [7]. In this letter we put forward the Topological Meissner eﬀect (TME), that results from a chiral dxy + idx2−y2 density wave (CDDW) state. In fact, the Nernst region of the pseudogap regime may well be associated with a CDDW. The most intriguing property of a CDDW is that parity (P) and time-reversal (T ) violation induces Chern-Simons terms in the eﬀective action of the elec- tromagnetic ﬁeld, providing the possibility of the TME and the Spontaneous Quantum Hall eﬀect (SQHE) ear- lier discussed [12, 13, 14, 15, 16, 17, 18]. As we shall demonstrate, the TME is described by the same equa- tion we ﬁnd in the usual Meissner eﬀect of a supercon- ∗Electronic address: pkotetes@central.ntua.gr †Electronic address: varelogi@central.ntua.gr ductor. Though, its origin is radically diﬀerent. In our system we encounter the realization of Parity Anomaly [13, 19], with the emerging Chern-Simons terms provi- ding a topological mass to the electromagnetic ﬁeld, in a gauge invariant manner [20, 21]. Moreover, the pos- session of chirality perpendicular to the plane, implies that the TME is strongly anisotropic. Particularly, it takes place for magnetic ﬁelds perpendicular to the plane while it is absent for in plane ﬁelds, in accordance with the experimental observations [2]. Note ﬁnally that a chi- ral d-density wave state has also been shown recently [22] to explain the experimental results concerning the Polar Kerr eﬀect in YBCO [23]. In order to demonstrate how the TME arises, we shall consider the following BCS hamiltonian for the CDDW HCDDW = 1 2 X k \u0010 ∆kc† kck+Q + ∆∗ kc† k+Qck \u0011 , (1) which describes a dxy+idx2−y2 state characterized by the wave-vector Q = (π, π), which is commensurate to the lattice (k + 2Q = k). Since spin degrees of freedom do not get involved we have considered spinless electrons, so that all our results will refer to one spin component. Fur- thermore, we use gµν = (1, −1, −1), ki = k = (kx, ky), kµ = k = (ω, k), qµ = q = (q0, q), µ = 0, 1, 2, i = 1, 2, e > 0, ℏ= 1 and we assume that repeated indices are summed. In the derivation of the Chern-Simons terms we shall restrict ourselves to the zero temperature case while necessary extensions to ﬁnite temperatures will be afterwards performed. In addition, the summation in k−space is all over the whole 1st Brillouin zone rather than the reduced Brillouin zone. This implies that the operators ck and ck+Q do not describe independent de- grees of freedom. In Eq.(1) we have introduced the CDDW order param- eter ∆k = η∆sin kx sin ky+i∆ \u0000cos kx −cos ky \u0001 , where ∆ is the modulus of the idx2−y2 order parameter, η deﬁnes the relative magnitude of the two components and also determines the direction of the chirality of the state. The chiral character of the state implies the existence of an intrinsic angular momentum in k−space, perpendicular to the plane, originating from P −T violation. Speciﬁ- cally, the dx2−y2 component violates T as it is imaginary, 2 while the dxy component is odd under P in two dimen- sions, which is deﬁned as (kx, ky) →(kx, −ky). In order to obtain the total electronic Hamiltonian H, we have to add the corresponding kinetic part Hkin. For the kinetic part we keep only the nearest neighbors hop- ping term ǫk = −t \u0000cos kx + cos ky \u0001 satisfying the nest- ing condition ǫk+Q = −ǫk, while we also set the chem- ical potential equal to zero. Our approximation can be justiﬁed by considering that our system is close to half- ﬁlling. Under these conditions the excitation spectrum consists of two bands which are fully gapped leading to the topological quantization of the Hall conductance [12, 13, 14, 15, 16, 17, 18], which is the coeﬃcient of the Chern-Simons terms. Omitting the next nearest neigh- bors hopping term δk = t′ cos kx cos ky does not alter qualitatively the occurrence of the TME. However, its inclusion would destroy the quantization of the Hall con- ductance, as in this case, the system is not fully gapped. Similar eﬀects would arise in the presence of disorder or by including the z-axis hopping term. Under this conditions, the total Hamiltonian of the system becomes H = 1 2 P k h ǫk \u0010 c† kck −c† k+Qck+Q \u0011 + \u0010 ∆kc† kck+Q + h.c. \u0011i . We obtain a compact representa- tion of H by introducing the spinor Ψ† k = 1 √ 2(c† k c† k+Q), the isospin Pauli matrices τ and the vector gk ≡ (Re∆k, −Im∆k, ǫk). This yields H = P k Ψ† k gk · τ Ψk. The latter indicates that the ground state of the sys- tem depends on the orientation of the g vector in isospin space. As a result, this hamiltonian supports skyrmion solutions which imply the presence of a Chern-Simons action (see e.g. [18]). To reveal the emerging Chern-Simons terms, we have to take into account the ﬂuctuations of the U(1) gauge ﬁeld Aµ. We add to the Hamiltonian the term Hem = R d2q (2π)2 P k Ψ† k+qΓµ k+q,kAµ(q)Ψk − R d2q (2π)2 P k Ψ† k+q e2 2mAi(−q)Ai(q)Ψk, which describes the interaction of the gauge ﬁeld with the electrons. We have introduced the paramagnetic interaction vertex Γµ k+q,k = −(e , e ∂ ∂ki gk · τ), where µ = 0, 1, 2 and i = 1, 2. At one-loop level, the eﬀective action Sem is given by the relation Sem = 1 2 R d3q (2π)3 Aµ(−q)Πµν(q)Aν(q), with the Polarization tensor Πµν, deﬁned as Πµν(q) = i 2 R k T r \u0010 GkΓµ k,k+qGk+qΓν k+q,k \u0011 −e2 m ρeδi,j. ρe is the two- dimensional electronic density (without including spin), T r denotes trace over isospin indices, Gk is the CDDW fermionic propagator and we have used the abbreviation R k = R dω 2π P k. Computing Πµν up to linear order in q, yields the Chern-Simons action SCS = Z d3x σxy 4 εµνλAµF νλ, (2) with Fµν = ∂µAν −∂νAµ. The coeﬃcient of the Chern- Simons action is the Hall conductance σxy. It can be shown that it is a topological invariant, reﬂecting the existence of a topologically non trivial, P −T violating ground state (see e.g. [18]). Using Eq.(2) we obtain σxy = i 2!ε0ji ∂Π0i ∂qj = e2 4π b N = e2 2π , (3) where we have introduced the winding number of the unit vector ˆgk = gk/| gk |, b N = 1 4π Z d2k ˆgk · ∂ˆgk ∂kx × ∂ˆgk ∂ky ! , (4) which is equal to 2, because the order parameter com- ponents are eigenfunctions of the angular momentum in k−space with eigenvalue l = 2. In the case of a perfect gap, the Hall conductance origi- nates only from the chirality b N of the lower energy band, E− k = −|gk|, which is fully occupied. In the same time, the upper band, E+ k = +|gk|, is totally empty while it is characterized by opposite chirality. Apparently, if both bands were equally occupied then σxy would be equal to zero. In the general case, the two bands, have diﬀerent occupation numbers n−and n+, yielding a non-quantized Hall conductance σxy = e2 2π(n−−n+). Deviations from nesting, disorder or a chemical potential generally lead to such an eﬀect. It is desirable to comprehend, even crudely, the eﬀect of these parameters on the Hall con- ductance and the TME. For this purpose we consider that a ﬁnite chemical po- tential is added to the system. We shall consider that its magnitude is of the order of min|gk|. This minimum is realized at the points k0 = (± π 2 , ± π 2 ), when η << 1. In this case, we may linearize the spectrum about these points so to obtain an approximate analytical solution. The two energy bands are described by the dispersions E± k = −µ± p m2 + (v0 · δk)2, with m = min|gk| = |gk0|, v0 the velocity at these points and δk = k−k0. If |µ| ≥m and µ < 0, hole-pockets arise in the lower band decreas- ing the full occupancy from n−= 1 to n−= 1−nex, with nex the portion of the empty states. On the other hand, if µ ≥m, electron pockets emerge in the upper band ris- ing its occupancy from zero. However, if we take into consideration that the two bands have opposite chirality, it is evident that in both cases, the eﬀect is the same. Consequently, σxy(µ) = σxy(1 −nex). The portion of the empty states will be determined by the area of the el- lipses deﬁned by the four hole-pockets. Straightforward calculations yield the simple relation nex = (µ2 −m2)/2πt∆. (5) We observe that for small values of |µ|, compared to t and ∆, the eﬀect of doping is negligible. We are now in position to obtain the equations of mo- tion of the gauge ﬁeld which will allow us to discuss the TME in a Hall bar geometry setup. We consider that the 3 FIG. 1: (Color online) (a) Inﬂuence of doping on the Topo- logical Meissner eﬀect. The relative change of magnetization hardly reaches 1% in the presence of a small chemical po- tential (∆= 20meV , t = 500meV ). (b) The magnetic ﬁeld screening as a function of the position on the Hall bar extend- ing from −lx to +lx, for diﬀerent values of the penetration depth λ over lx. The magnetic ﬁeld is totally expelled from the sample when lx/λ >> 1 exactly as in the superconducting case. Hall bar has dimensions Lx = 2lx, Ly >> Lx extending from −lx to lx on the x-axis. The relation Ly >> Lx in- dicates that there is negligible y-dependence of the",
    "QCage - A New Microwave-cavity Sample Holder for High-fidelity Qubit Measurements | In this video, you will learn about a new sample holder system, targeted at superconducting quantum processors with tens of qubits.\n\nThe QCage is a sample holder system for microwave resonator-based quantum devices that encloses the sample chip in an all-surrounding microwave cavity, with a total number of 24 coplanar transmission lines optimized for frequencies up to 18 GHz. The QCage is designed to hold the chip suspended inside the cavity, supported only by four corner pedestals and clamped d",
    "Elastic neutron scattering simultaneously probes both the crystal structure\nand magnetic order in a material. Inelastic neutron scattering measures phonons\nand magnetic excitations. Here, we review the average composition, crystal\nstructure and magnetic order in the 245 family of Fe-based superconductors and\nin related insulating compounds from neutron diffraction works. A\nthree-dimensional phase-diagram summarizes various structural, magnetic and\nelectronic properties as a function of the sample composition. A high pressure\nphase diagram for the superconductor is also provided. Magnetic excitations and\nthe theoretic Heisenberg Hamiltonian are provided for the superconductor.\nIssues for future works are discussed."
]
embeddings = model.encode(sentences)

similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [4, 4]

Notebooks
Google Colab
Kaggle

SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2

This is a sentence-transformers model finetuned from sentence-transformers/all-MiniLM-L6-v2. It maps sentences & paragraphs to a 384-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more.

Model Details

Model Description

Model Type: Sentence Transformer
Base model: sentence-transformers/all-MiniLM-L6-v2
Maximum Sequence Length: 256 tokens
Output Dimensionality: 384 dimensions
Similarity Function: Cosine Similarity

Model Sources

Documentation: Sentence Transformers Documentation
Repository: Sentence Transformers on GitHub
Hugging Face: Sentence Transformers on Hugging Face

Full Model Architecture

SentenceTransformer(
  (0): Transformer({'max_seq_length': 256, 'do_lower_case': False, 'architecture': 'BertModel'})
  (1): Pooling({'word_embedding_dimension': 384, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': True, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
  (2): Normalize()
)

Usage

Direct Usage (Sentence Transformers)

First install the Sentence Transformers library:

pip install -U sentence-transformers

Then you can load this model and run inference.

from sentence_transformers import SentenceTransformer

# Download from the 🤗 Hub
model = SentenceTransformer("sentence_transformers_model_id")
# Run inference
sentences = [
    'superconductivity',
    'We highlight the reproducibility and level of control over the electrical\nproperties of YBa$_2$Cu$_3$O$_7$ Josephson junctions fabricated with\nirradiation from a focused helium ion beam. Specifically, we show the results\nof electrical transport properties for several junctions fabricated using a\nlarge range of irradiation doses. At the lower end of this range, junctions\nexhibit superconductor-normal metal-superconductor (SNS) Josephson junction\nproperties. However, as dose increases there is a transition to electrical\ncharacteristics consistent with superconductor-insulator-superconductor (SIS)\njunctions. To investigate the uniformity of large numbers of helium ion\nJosephson junctions we fabricate arrays of both SNS and SIS Josephson junctions\ncontaining 20 connected in series. Electrical transport properties for these\narrays reveal very uniform junctions with no appreciable spread in critical\ncurrent or resistance.',
    'Non-invasive magnetic field sensing using optically - detected magnetic\nresonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial\ndistribution of the magnetic induction upon penetration and expulsion of weak\nmagnetic fields in several representative superconductors. Vector magnetic\nfields were measured on the surface of conventional, Pb and Nb, and\nunconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$,\nBa(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors,\nwith diffraction - limited spatial resolution using variable - temperature\nconfocal system. Magnetic induction profiles across the crystal edges were\nmeasured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all\nsuperconductors show nearly perfect screening of magnetic fields applied after\ncooling to temperatures well below the superconducting transition, $T_c$, a\nrange of very different behaviors was observed for Meissner expulsion upon\ncooling in static magnetic field from above $T_c$. Substantial conventional\nMeissner expulsion is found in LuNi$_2$B$_2$C, paramagnetic Meissner effect\n(PME) is found in Nb, and virtually no expulsion is observed in iron-based\nsuperconductors. In all cases, good correlation with macroscopic measurements\nof total magnetic moment is found. Our measurements of the spatial distribution\nof magnetic induction provide insight into microscopic physics of the Meissner\neffect.',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities)
# tensor([[1.0000, 0.3505, 0.3544],
#         [0.3505, 1.0000, 0.6777],
#         [0.3544, 0.6777, 1.0000]])

Evaluation

Metrics

Information Retrieval

Dataset: superconductor-eval
Evaluated with InformationRetrievalEvaluator

Metric	Value
cosine_accuracy@1	0.7
cosine_accuracy@3	0.8
cosine_accuracy@5	0.9
cosine_accuracy@10	1.0
cosine_precision@1	0.7
cosine_precision@3	0.3667
cosine_precision@5	0.24
cosine_precision@10	0.13
cosine_recall@1	0.5
cosine_recall@3	0.7
cosine_recall@5	0.8
cosine_recall@10	0.9
cosine_ndcg@10	0.7651
cosine_mrr@10	0.7861
cosine_map@100	0.7098

Training Details

Training Dataset

Unnamed Dataset

Size: 4,091 training samples
Columns: sentence_0 and sentence_1
Approximate statistics based on the first 1000 samples:
sentence_0 sentence_1
type string string
details
min: 3 tokens
mean: 7.98 tokens
max: 41 tokens

min: 8 tokens
mean: 160.85 tokens
max: 256 tokens

	sentence_0	sentence_1
type	string	string
details	min: 3 tokens mean: 7.98 tokens max: 41 tokens	min: 8 tokens mean: 160.85 tokens max: 256 tokens

Samples:

sentence_0	sentence_1
`codimension two lump solutions in string field theory and ta`	`We present some solutions for lumps in two dimensions in level-expanded string field theory, as well as in two tachyonic theories: pure tachyonic string field theory and pure $\phi^3$ theory. Much easier to handle, these theories might be used to help understanding solitonic features of string field theory. We compare lump solutions between these theories and we discuss some convergence issues.`
`superconductivity explained`	`We review the current understanding of superconductivity in the quasi-one-dimensional organic conductors of the Bechgaard and Fabre salt families. We discuss the interplay between superconductivity, antiferromagnetism, and charge-density-wave fluctuations. The connection to recent experimental observations supporting unconventional pairing and the possibility of a triplet-spin order parameter for the superconducting phase is also presented.`
`erez berg`	Erez Berg- Theory of Strange Metals \| Understanding "strange metal" phenomena - metallic behavior that deviates from that expected of an ordinary Fermi liquid down to the lowest measurable temperatures - is among the most puzzling open problems in condensed matter physics. Such phenomena are observed across many different strongly correlated materials. They seem tied to other interesting phenomena, such as quantum criticality and unconventional superconductivity. I will describe theoretical advances in understanding the possible or

Loss: MultipleNegativesRankingLoss with these parameters:

{
    "scale": 20.0,
    "similarity_fct": "cos_sim",
    "gather_across_devices": false
}

Training Hyperparameters

Non-Default Hyperparameters

eval_strategy: steps
per_device_train_batch_size: 16
per_device_eval_batch_size: 16
num_train_epochs: 4
multi_dataset_batch_sampler: round_robin

All Hyperparameters

Click to expand

overwrite_output_dir: False
do_predict: False
eval_strategy: steps
prediction_loss_only: True
per_device_train_batch_size: 16
per_device_eval_batch_size: 16
per_gpu_train_batch_size: None
per_gpu_eval_batch_size: None
gradient_accumulation_steps: 1
eval_accumulation_steps: None
torch_empty_cache_steps: None
learning_rate: 5e-05
weight_decay: 0.0
adam_beta1: 0.9
adam_beta2: 0.999
adam_epsilon: 1e-08
max_grad_norm: 1
num_train_epochs: 4
max_steps: -1
lr_scheduler_type: linear
lr_scheduler_kwargs: {}
warmup_ratio: 0.0
warmup_steps: 0
log_level: passive
log_level_replica: warning
log_on_each_node: True
logging_nan_inf_filter: True
save_safetensors: True
save_on_each_node: False
save_only_model: False
restore_callback_states_from_checkpoint: False
no_cuda: False
use_cpu: False
use_mps_device: False
seed: 42
data_seed: None
jit_mode_eval: False
bf16: False
fp16: False
fp16_opt_level: O1
half_precision_backend: auto
bf16_full_eval: False
fp16_full_eval: False
tf32: None
local_rank: 0
ddp_backend: None
tpu_num_cores: None
tpu_metrics_debug: False
debug: []
dataloader_drop_last: False
dataloader_num_workers: 0
dataloader_prefetch_factor: None
past_index: -1
disable_tqdm: False
remove_unused_columns: True
label_names: None
load_best_model_at_end: False
ignore_data_skip: False
fsdp: []
fsdp_min_num_params: 0
fsdp_config: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
fsdp_transformer_layer_cls_to_wrap: None
accelerator_config: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
parallelism_config: None
deepspeed: None
label_smoothing_factor: 0.0
optim: adamw_torch_fused
optim_args: None
adafactor: False
group_by_length: False
length_column_name: length
project: huggingface
trackio_space_id: trackio
ddp_find_unused_parameters: None
ddp_bucket_cap_mb: None
ddp_broadcast_buffers: False
dataloader_pin_memory: True
dataloader_persistent_workers: False
skip_memory_metrics: True
use_legacy_prediction_loop: False
push_to_hub: False
resume_from_checkpoint: None
hub_model_id: None
hub_strategy: every_save
hub_private_repo: None
hub_always_push: False
hub_revision: None
gradient_checkpointing: False
gradient_checkpointing_kwargs: None
include_inputs_for_metrics: False
include_for_metrics: []
eval_do_concat_batches: True
fp16_backend: auto
push_to_hub_model_id: None
push_to_hub_organization: None
mp_parameters:
auto_find_batch_size: False
full_determinism: False
torchdynamo: None
ray_scope: last
ddp_timeout: 1800
torch_compile: False
torch_compile_backend: None
torch_compile_mode: None
include_tokens_per_second: False
include_num_input_tokens_seen: no
neftune_noise_alpha: None
optim_target_modules: None
batch_eval_metrics: False
eval_on_start: False
use_liger_kernel: False
liger_kernel_config: None
eval_use_gather_object: False
average_tokens_across_devices: True
prompts: None
batch_sampler: batch_sampler
multi_dataset_batch_sampler: round_robin
router_mapping: {}
learning_rate_mapping: {}

Training Logs

Epoch	Step	superconductor-eval_cosine_ndcg@10
1.0	256	0.7651

Framework Versions

Python: 3.9.6
Sentence Transformers: 5.1.2
Transformers: 4.57.1
PyTorch: 2.8.0
Accelerate: 1.10.1
Datasets: 4.3.0
Tokenizers: 0.22.1

Citation

BibTeX

Sentence Transformers

@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}

MultipleNegativesRankingLoss

@misc{henderson2017efficient,
    title={Efficient Natural Language Response Suggestion for Smart Reply},
    author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil},
    year={2017},
    eprint={1705.00652},
    archivePrefix={arXiv},
    primaryClass={cs.CL}
}