Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem

The Cu induced ultraflat band in the Pb10−x_{10-x}Cux_x(PO4_4)6_6O4_4 (x=0,0.5x=0,0.5)

Based on the first principle calculations, we investigate the geometry and the electronic structures of the lead apatite with and without the Cu doped. Our calculations found that without the Cu doping the lead apatite crystal is an insulator with a flat band above the Fermi lever. Furthermore, our results indicate that by introducing the O1 vacancies would results in the disappear of the flat bands in the undopped crystal. While the Cu is doped forming the LK-99, there exist the ultra-flat bands crossing the Fermi level induced by the doped Cu atoms, which is due to the hybridization between the d states of the Cu atoms and the p states of the fully occupied 1/4 occupied O1 atoms. Moreover, we point out that the hybridization maybe the key for the realization of the room temperature superconductivity for the LK-99, and a possible solutions method to improve the quality of the crystal is proposed. Our work provides a foundation for the future studies on the unique electronic and the superconductivity properties of the LK-99 crystal.Comment: 8 pages, 7 figure

Magnetic phase transitions in the triangular-lattice spin-1 dimer compound K2Ni2(SeO3)3

In our study, we conduct magnetization and heat capacity measurements to investigate field-induced magnetic phase transitions within the newly synthesized compound K2Ni2(SeO3)3, a spin-1 dimer system arranged on a triangular lattice. The Ni-Ni dimers exhibit a ferromagnetic intra-dimer interaction, effectively behaving as an ensemble with a total spin of S=2. In contrast, antiferromagnetic interactions manifest between these dimers on the triangular lattice. The trigonal distortion of the NiO6 octahedra introduces easy-axis magnetic anisotropy, accounting for the distinct magnetic phase diagrams observed when applying c-axis directional and in-plnae magnetic fields. Notably, our investigation unveils a two-step phase transition with the magnetic field aligned with the c direction. We propose that the system at the first transition is from a paramagnetic state to an up-up-down state, characterized by the Z3 lattice-symmetry breaking. Subsequently, a Berezinskii-Kosterlitz-Thouless transition, involving the breaking of the c-axis spin-rotation symmetry, leads to the formation of the "Y state" at low temperatures. These findings yield valuable insights into the magnetic phase transitions inherent to geometrically frustrated magnetic systems featuring dimer structures.Comment: 10 pages, 11 figure

All in Tokens: Unifying Output Space of Visual Tasks via Soft Token

Unlike language tasks, where the output space is usually limited to a set of tokens, the output space of visual tasks is more complicated, making it difficult to build a unified visual model for various visual tasks. In this paper, we seek to unify the output space of visual tasks, so that we can also build a unified model for visual tasks. To this end, we demonstrate a single unified model that simultaneously handles two typical visual tasks of instance segmentation and depth estimation, which have discrete/fixed-length and continuous/varied-length outputs, respectively. We propose several new techniques that take into account the particularity of visual tasks: 1) Soft token. We employ soft token to represent the task output. Unlike hard tokens in the common VQ-VAE which are assigned one-hot to discrete codebooks/vocabularies, the soft token is assigned softly to the codebook embeddings. Soft token can improve the accuracy of both the next token inference and decoding of the task output; 2) Mask augmentation. Many visual tasks have corruption, undefined or invalid values in label annotations, i.e., occluded area of depth maps. We show that a mask augmentation technique can greatly benefit these tasks. With these new techniques and other designs, we show that the proposed general-purpose task-solver can perform both instance segmentation and depth estimation well. Particularly, we achieve 0.279 RMSE on the specific task of NYUv2 depth estimation, setting a new record on this benchmark. The general-purpose task-solver, dubbed AiT, is available at \url{https://github.com/SwinTransformer/AiT}

Neurochemical characterization of pERK-expressing spinal neurons in histamine-induced itch

Date of Acceptance: 08/07/2015 Acknowledgements This work was supported by grants from the Ministry of Science and Technology of China (2012CB966904, 2011CB51005), National Natural Science Foundation of China (31271182, 81200692, 91232724, 81200933, 81101026), Shanghai Natural Science Foundation (12ZR1434300), Key Specialty Construction Project of Pudong Health Bureau of Shanghai (PWZz2013-17), Shenzhen Key Laboratory for Molecular Biology of Neural Development (ZDSY20120617112838879), Fundamental Research Funds for the Central Universities (1500219072) and Sino-UK Higher Education Research Partnership for PhD Studies.Peer reviewedPublisher PD

Bis(μ2-4-amino-3-nitro­benzoato)bis­(4-amino-3-nitro­benzoato)octa­butyldi-μ3-oxido-tetra­tin(IV)

The tetranuclear molecules of the title compound, [Sn4(C4H9)8(C7H5N2O4)4O2], reside on a crystallographic inversion center. Both the two independent Sn atoms are five-coordinate, with distorted trigonal–bipyramidal geometries. One Sn atom is coordinated by two O atoms of the carboxyl­ate anions, one bridging O atom and two butyl groups and the other Sn atom is coordinated by an O atom of the carboxyl­ate anion, two bridging O atoms and two butyl groups. All the butyl groups are equatorial with respect to the SnO3 trigonal plane. The mol­ecular structure is stabilized by intra­molecular N—H⋯O hydrogen bonds. In the crystal, pairs of inter­molecular bifurcated acceptor N—H⋯O and C—H⋯O hydrogen bonds link the mol­ecules into chains along [10]. Weak inter­molecular C—H⋯π and π–π inter­actions [centroid–centroid distance = 3.713 (2) Å] are also observed

Modified Glucose-Insulin-Potassium Regimen Provides Cardioprotection With Improved Tissue Perfusion in Patients Undergoing Cardiopulmonary Bypass Surgery

Background Laboratory studies demonstrate glucose-insulin-potassium (GIK) as a potent cardioprotective intervention, but clinical trials have yielded mixed results, likely because of varying formulas and timing of GIK treatment and different clinical settings. This study sought to evaluate the effects of modified GIK regimen given perioperatively with an insulin-glucose ratio of 1:3 in patients undergoing cardiopulmonary bypass surgery. Methods and Results In this prospective, randomized, double-blinded trial with 930 patients referred for cardiac surgery with cardiopulmonary bypass, GIK (200 g/L glucose, 66.7 U/L insulin, and 80 mmol/L KCl) or placebo treatment was administered intravenously at 1 mL/kg per hour 10 minutes before anesthesia and continuously for 12.5 hours. The primary outcome was the incidence of in-hospital major adverse cardiac events including all-cause death, low cardiac output syndrome, acute myocardial infarction, cardiac arrest with successful resuscitation, congestive heart failure, and arrhythmia. GIK therapy reduced the incidence of major adverse cardiac events and enhanced cardiac function recovery without increasing perioperative blood glucose compared with the control group. Mechanistically, this treatment resulted in increased glucose uptake and less lactate excretion calculated by the differences between arterial and coronary sinus, and increased phosphorylation of insulin receptor substrate-1 and protein kinase B in the hearts of GIK-treated patients. Systemic blood lactate was also reduced in GIK-treated patients during cardiopulmonary bypass surgery. Conclusions A modified GIK regimen administered perioperatively reduces the incidence of in-hospital major adverse cardiac events in patients undergoing cardiopulmonary bypass surgery. These benefits are likely a result of enhanced systemic tissue perfusion and improved myocardial metabolism via activation of insulin signaling by GIK. Clinical Trial Registration URL: clinicaltrials.gov. Identifier: NCT01516138

Power-Law Decay of Standing Waves on the Surface of Topological Insulators

We propose a general theory on the standing waves (quasiparticle interference pattern) caused by the scattering of surface states off step edges in topological insulators, in which the extremal points on the constant energy contour of surface band play the dominant role. Experimentally we image the interference patterns on both Bi$_2$Te$_3$ and Bi$_2$Se$_3$ films by measuring the local density of states using a scanning tunneling microscope. The observed decay indices of the standing waves agree excellently with the theoretical prediction: In Bi$_2$Se$_3$, only a single decay index of -3/2 exists; while in Bi$_2$Te$_3$ with strongly warped surface band, it varies from -3/2 to -1/2 and finally to -1 as the energy increases. The -1/2 decay indicates that the suppression of backscattering due to time-reversal symmetry does not necessarily lead to a spatial decay rate faster than that in the conventional two-dimensional electron system. Our formalism can also explain the characteristic scattering wave vectors of the standing wave caused by non-magnetic impurities on Bi$_2$Te$_3$.Comment: 4 pages, 3 figure