title
string | abstract
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string | arxiv_id
string | date
string | category
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2D Convection-Diffusion in Multipolar Flows
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We present a complete analysis of the problem of convection-diffusion in low
Re, 2-dimensional flows with distributions of singularities, such as those
found in open-space microfluidics and in groundwater flows. Using Boussinesq
transformations and solving the problem in streamline coordinates, we obtain
concentration profiles in flows with complex arrangements of sources and sinks
for both high and low Pe. These yield the complete analytical concentration
profile at every point in applications that previously relied on material
surface tracking, local lump models or numerical analysis such as microfluidic
probes, groundwater heat pumps, or diffusive flows in porous media. Using
conformal transforms, we generate families of symmetrical solutions from simple
ones, and provide a general methodology that can be used to analyze any
arrangement of source and sinks. The solutions obtained that contain the
explicit dependence on the various parameters of the problems, such as Pe, the
spacing of the apertures and their relative injection and aspiration rates. In
particular, we show that the high Pe models can model problems with Pe as low
as 1 with a maximum error committed of under $10\%$, and that this error
decreases approximately as $Pe^{-1.5}$.
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http://arxiv.org/abs/2003.05818v1
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2003.05818
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2020-03-12
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computer-graphics
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2D Convolutional Neural Network for Event Reconstruction in IceCube DeepCore
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IceCube DeepCore is an extension of the IceCube Neutrino Observatory designed to measure GeV scale atmospheric neutrino interactions for the purpose of neutrino oscillation studies. Distinguishing muon neutrinos from other flavors and reconstructing inelasticity are especially difficult tasks at GeV scale energies in IceCube DeepCore due to sparse instrumentation. Convolutional neural networks (CNNs) have been found to have better success at neutrino event reconstruction than conventional likelihood-based methods. In this contribution, we present a new CNN model that exploits time and depth translational symmetry in IceCube DeepCore data and present the model's performance, specifically for flavor identification and inelasticity reconstruction.
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https://arxiv.org/abs/2307.16373v1
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2307.16373
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2023-07-31
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computer-graphics
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2D Convolutional Neural Networks for 3D Digital Breast Tomosynthesis Classification
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Automated methods for breast cancer detection have focused on 2D mammography and have largely ignored 3D digital breast tomosynthesis (DBT), which is frequently used in clinical practice. The two key challenges in developing automated methods for DBT classification are handling the variable number of slices and retaining slice-to-slice changes. We propose a novel deep 2D convolutional neural network (CNN) architecture for DBT classification that simultaneously overcomes both challenges. Our approach operates on the full volume, regardless of the number of slices, and allows the use of pre-trained 2D CNNs for feature extraction, which is important given the limited amount of annotated training data. In an extensive evaluation on a real-world clinical dataset, our approach achieves 0.854 auROC, which is 28.80% higher than approaches based on 3D CNNs. We also find that these improvements are stable across a range of model configurations.
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https://arxiv.org/abs/2002.12314v1
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2002.12314
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2020-02-27
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computer-graphics
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2D correlations in the van der Waals ferromagnet CrBr$_{3}$ using high frequency electron spin resonance spectroscopy
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Broadening the knowledge and understanding on the magnetic correlations in
van der Waals layered magnets is critical in realizing their potential
next-generation applications. In this study, we employ high frequency (240 GHz)
electron spin resonance (ESR) spectroscopy on plate-like CrBr$_{3}$ to gain
insight into the magnetic interactions as a function of temperature (200 - 4 K)
and the angle of rotation ${\theta}$. We find that the temperature dependence
of the ESR linewidth is well described by the Ginzberg-Landau critical model as
well as Berezinskii-Kosterlitz-Thouless (BKT) transition model, indicative of
the presence of two-dimensional (2D) correlations. This suggests that the
three-dimensional ferromagnet CrBr$_{3}$, which has been described as an Ising
or Heisenberg ferromagnet, could present 2D magnetic correlations and BKT-like
behavior even in its bulk form; an observation that, to the best of our
knowledge, has not been reported in the literature. Furthermore, our findings
show that the resonance field follows a $(3cos^2{\theta} - 1)$-like angular
dependence, while the linewidth follows a $(3cos^2{\theta} - 1)^2$-like angular
dependence. This observed angular dependence of the resonance field and
linewidth further confirm an unanticipated 2D magnetic behavior in CrBr$_{3}$.
This behavior is likely due to the interaction of the external magnetic field
applied during the ESR experiment that allows for the mediation of long-range
vortex-like correlations between the spin clusters that may have formed due to
magnetic phase separation. This study demonstrates the significance of
employing spin sensitive techniques such as ESR to better understand the
magnetic correlations in similar van der Waals magnets.
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http://arxiv.org/abs/2010.15342v1
|
2010.15342
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2020-10-29
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computer-graphics
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2-D Covariant Affine Integral Quantization(s)
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Covariant affine integral quantization is studied and applied to the motion of a particle in a punctured plane R^2_\ast=R^2\{0}, for which the phase space is R^2_\ast=R^2\{0}X R^2. We examine the consequences of different quantizer operators built from weight functions on this phase space. To illustrate the procedure, we examine two examples of weights. The first one corresponds to 2-D coherent state families, while the second one corresponds to the affine inversion in the punctured plane. The later yields the usual canonical quantization and a quasi-probability distribution (2-D affine Wigner function) which is real, marginal in both position and momentum.
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https://arxiv.org/abs/1911.00578v2
|
1911.00578
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2019-11-01
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computer-graphics
|
2D-CTC for Scene Text Recognition
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Scene text recognition has been an important, active research topic in computer vision for years. Previous approaches mainly consider text as 1D signals and cast scene text recognition as a sequence prediction problem, by feat of CTC or attention based encoder-decoder framework, which is originally designed for speech recognition. However, different from speech voices, which are 1D signals, text instances are essentially distributed in 2D image spaces. To adhere to and make use of the 2D nature of text for higher recognition accuracy, we extend the vanilla CTC model to a second dimension, thus creating 2D-CTC. 2D-CTC can adaptively concentrate on most relevant features while excluding the impact from clutters and noises in the background; It can also naturally handle text instances with various forms (horizontal, oriented and curved) while giving more interpretable intermediate predictions. The experiments on standard benchmarks for scene text recognition, such as IIIT-5K, ICDAR 2015, SVP-Perspective, and CUTE80, demonstrate that the proposed 2D-CTC model outperforms state-of-the-art methods on the text of both regular and irregular shapes. Moreover, 2D-CTC exhibits its superiority over prior art on training and testing speed. Our implementation and models of 2D-CTC will be made publicly available soon later.
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https://arxiv.org/abs/1907.09705v1
|
1907.09705
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2019-07-23
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computer-graphics
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2D-Curri-DPO: Two-Dimensional Curriculum Learning for Direct Preference Optimization
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Aligning large language models with human preferences is crucial for their safe deployment. While Direct Preference Optimization (DPO) offers an efficient alternative to reinforcement learning from human feedback, traditional DPO methods are limited by their reliance on single preference pairs. Recent work like Curriculum-DPO integrates multiple pairs using a one-dimensional difficulty curriculum based on pairwise distinguishability (PD), but overlooks the complexity of the input prompt itself. To address this, we propose 2D-Curri-DPO, a novel framework employing a two-dimensional curriculum that jointly models Prompt Complexity (PC) and Pairwise Distinguishability. This framework introduces dual difficulty metrics to quantify prompt semantic complexity and response preference clarity, defines a curriculum strategy space encompassing multiple selectable strategies for task adaptation, and incorporates a KL-divergence-based adaptive mechanism for dynamic reference model updates to enhance training stability. Comprehensive experiments demonstrate that 2D-Curri-DPO significantly outperforms standard DPO and prior curriculum methods across multiple benchmarks, including MT-Bench, Vicuna Bench, and WizardLM. Our approach achieves state-of-the-art performance on challenging test sets like UltraFeedback. Ablation studies confirm the benefits of the 2D structure and adaptive mechanisms, while analysis provides guidance for strategy selection. These findings demonstrate that effective alignment requires modeling both prompt complexity and pairwise distinguishability, establishing adaptive, multi-dimensional curriculum learning as a powerful and interpretable new paradigm for preference-based language model optimization.
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https://arxiv.org/abs/2504.07856v2
|
2504.07856
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2025-04-10
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computer-graphics
|
2DDATA: 2D Detection Annotations Transmittable Aggregation for Semantic Segmentation on Point Cloud
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Recently, multi-modality models have been introduced because of the complementary information from different sensors such as LiDAR and cameras. It requires paired data along with precise calibrations for all modalities, the complicated calibration among modalities hugely increases the cost of collecting such high-quality datasets, and hinder it from being applied to practical scenarios. Inherit from the previous works, we not only fuse the information from multi-modality without above issues, and also exhaust the information in the RGB modality. We introduced the 2D Detection Annotations Transmittable Aggregation(\textbf{2DDATA}), designing a data-specific branch, called \textbf{Local Object Branch}, which aims to deal with points in a certain bounding box, because of its easiness of acquiring 2D bounding box annotations. We demonstrate that our simple design can transmit bounding box prior information to the 3D encoder model, proving the feasibility of large multi-modality models fused with modality-specific data.
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https://arxiv.org/abs/2309.11755v1
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2309.11755
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2023-09-21
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computer-graphics
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2D-Densely Connected Convolution Neural Networks for automatic Liver and Tumor Segmentation
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In this paper we propose a fully automatic 2-stage cascaded approach for
segmentation of liver and its tumors in CT (Computed Tomography) images using
densely connected fully convolutional neural network (DenseNet). We
independently train liver and tumor segmentation models and cascade them for a
combined segmentation of the liver and its tumor. The first stage involves
segmentation of liver and the second stage uses the first stage's segmentation
results for localization of liver and henceforth tumor segmentations inside
liver region. The liver model was trained on the down-sampled axial slices
$(256 \times 256)$, whereas for the tumor model no down-sampling of slices was
done, but instead it was trained on the CT axial slices windowed at three
different Hounsfield (HU) levels. On the test set our model achieved a global
dice score of 0.923 and 0.625 on liver and tumor respectively. The computed
tumor burden had an rmse of 0.044.
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http://arxiv.org/abs/1802.02182v1
|
1802.02182
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2018-01-05
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computer-graphics
|
2D Density Control of Micro-Particles using Kernel Density Estimation
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We address the problem of 2D particle density control. The particles are immersed in dielectric fluid and acted upon by manipulating an electric field. The electric field is controlled by an array of electrodes and used to bring the particle density to a desired pattern using dielectrophoretic forces. We use a lumped, 2D, capacitive-based, nonlinear model describing the motion of a particle. The spatial dependency of the capacitances is estimated using electrostatic COMSOL simulations. We formulate an optimal control problem, where the loss function is defined in terms of the error between the particle density at some final time and a target density. We use a kernel density estimator (KDE) as a proxy for the true particle density. The KDE is computed using the particle positions that are changed by varying the electrode potentials. We showcase our approach through numerical simulations, where we demonstrate how the particle positions and the electrode potentials vary when shaping the particle positions from a uniform to a Gaussian distribution.
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https://arxiv.org/abs/2209.03550v1
|
2209.03550
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2022-09-08
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computer-graphics
|
2D dilaton gravity and the Weil-Petersson volumes with conical defects
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We derive the Weil-Petersson measure on the moduli space of hyperbolic surfaces with defects of arbitrary opening angles and use this to compute its volume. We conjecture a matrix integral computing the corresponding volumes and confirm agreement in simple cases. We combine this mathematical result with the equivariant localization approach to Jackiw-Teitelboim gravity to justify a proposed exact solution of pure 2d dilaton gravity for a large class of dilaton potentials.
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https://arxiv.org/abs/2304.14948v2
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2304.14948
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2023-04-28
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computer-graphics
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2D dilute Bose mixture at low temperatures
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The thermodynamic and superfluid properties of the dilute two-dimensional
binary Bose mixture at low temperatures are discussed. We also considered the
problem of the emergence of the long-range order in these systems. All
calculations are performed by means of celebrated Popov's path-integral
approach for the Bose gas with a short-range interparticle potential.
|
http://arxiv.org/abs/1708.00432v2
|
1708.00432
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2017-12-19
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computer-graphics
|
2D-Dirac surface states and bulk gap probed via quantum capacitance in a 3D topological insulator
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BiSbTeSe$_2$ is a 3D topological insulator (3D-TI) with Dirac type surface states and low bulk carrier density, as donors and acceptors compensate each other. Dominating low temperature surface transport in this material is heralded by Shubnikov-de Haas oscillations and the quantum Hall effect. Here, we experimentally probe and model the electronic density of states (DOS) in thin layers of BiSbTeSe$_2$ by capacitance experiments both without and in quantizing magnetic fields. By probing the lowest Landau levels, we show that a large fraction of the electrons filled via field effect into the system ends up in (localized) bulk states and appears as a background DOS. The surprisingly strong temperature dependence of such background DOS can be traced back to Coulomb interactions. Our results point at the coexistence and intimate coupling of Dirac surface states with a bulk many-body phase (a Coulomb glass) in 3D-TIs.
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https://arxiv.org/abs/1912.02725v3
|
1912.02725
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2019-12-05
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computer-graphics
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2-D Directed Formation Control Based on Bipolar Coordinates
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This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, a formation maneuvering simulation study verifies the proposed approach.
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https://arxiv.org/abs/2108.00916v3
|
2108.00916
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2021-08-02
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computer-graphics
|
2D disc modelling of the JWST line spectrum of EX Lupi
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We introduce a number of new theoretical approaches and improvements to the thermo-chemical disc modelling code ProDiMo to better predict and analyse the JWST line spectra of protoplanetary discs. We develop a new line escape probability method for disc geometries, a new scheme for dust settling, and discuss how to apply UV molecular shielding factors to photorates in 2D disc geometry. We show that these assumptions are crucial for the determination of the gas heating/cooling rates and discuss how they affect the predicted molecular concentrations and line emissions. We apply our revised 2D models to the protoplanetary disc around the T Tauri star EX Lupi in quiescent state. We calculate infrared line emission spectra between 5 and 20 mic by CO, H2O, OH, CO2, HCN, C2H2 and H2, including lines of atoms and ions, using our full 2D predictions of molecular abundances, dust opacities, gas and dust temperatures. We develop a disc model with a slowly increasing surface density structure around the inner rim that can simultaneously fit the spectral energy distribution, the overall shape of the JWST spectrum of EX Lupi, and the main observed molecular characteristics in terms of column densities, emitting areas and molecular emission temperatures, which all result from one consistent disc model. The spatial structure of the line emitting regions of the different molecules is discussed. High abundances of HCN and C2H2 are caused in the model by stellar X-ray irradiation of the gas around the inner rim.
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https://arxiv.org/abs/2311.18321v1
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2311.18321
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2023-11-30
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computer-graphics
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2D Discrete Fourier Transform with Simultaneous Edge Artifact Removal for Real-Time Applications
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Two-Dimensional (2D) Discrete Fourier Transform (DFT) is a basic and
computationally intensive algorithm, with a vast variety of applications. 2D
images are, in general, non-periodic, but are assumed to be periodic while
calculating their DFTs. This leads to cross-shaped artifacts in the frequency
domain due to spectral leakage. These artifacts can have critical consequences
if the DFTs are being used for further processing. In this paper we present a
novel FPGA-based design to calculate high-throughput 2D DFTs with simultaneous
edge artifact removal. Standard approaches for removing these artifacts using
apodization functions or mirroring, either involve removing critical
frequencies or a surge in computation by increasing image size. We use a
periodic-plus-smooth decomposition based artifact removal algorithm optimized
for FPGA implementation, while still achieving real-time ($\ge$23 frames per
second) performance for a 512$\times$512 size image stream. Our optimization
approach leads to a significant decrease in external memory utilization thereby
avoiding memory conflicts and simplifies the design. We have tested our design
on a PXIe based Xilinx Kintex 7 FPGA system communicating with a host PC which
gives us the advantage to further expand the design for industrial
applications.
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http://arxiv.org/abs/1603.05154v1
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1603.05154
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2016-03-16
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computer-graphics
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2D discrete Hodge-Dirac operator on the torus
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We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of the continuum counterpart are captured. We provide and prove a discrete version of the Hodge decomposition theorem. Special attention has been paid to discrete models on a combinatorial torus. In this particular case, we also define and calculate the cohomology groups.
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https://arxiv.org/abs/2202.03923v1
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2202.03923
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2022-02-08
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computer-graphics
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2D discrete Yang-Mills equations on the torus
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In this paper, we introduce a discretization scheme for the Yang-Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant derivative operator and its adjoint, which capture essential geometric features similar to their continuous counterparts. Our focus is on discrete models defined on a combinatorial torus, where the discrete Yang-Mills equations are presented in the form of both a system of difference equations and a matrix form.
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https://arxiv.org/abs/2405.15315v1
|
2405.15315
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2024-05-24
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computer-graphics
|
2D-Double transition metal MXenes for spintronics applications: surface functionalization induced ferromagnetic half-metallic complexes
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MXenes are rapidly emerging two-dimensional (2D) materials with thickness, composition, and functionalization-dependent outstanding properties having applications in diverse fields. To disclose nano-spintronic applications of 2D-double transition metal (DTM) carbide and nitride-based pristine and surface-functionalized MXenes (M'2M"X2Tx, M' and M" = Cr, Mo, W; X = C/N; T = -F/-OH/=O), a systematic investigation has been performed on structural stability, magnetic properties and electronic structure using spin-polarized first-principles calculations. 36 stables functionalized MXenes were screened from 144 explored DTM based MXenes. The explored materials exhibit striking properties, having wide range of magnetic ground states, from non-magnetic to ferromagnetic, and then to antiferromagnetic, accompanied by metallic to half-metallic or gapless half-metallic properties, depending on transition metal(s) and terminating group. Mo and W-based MXenes are found to be nonmagnetic and metallic, whereas Cr-Mo and Cr-W-based MXenes are magnetic with varying metallic behavior. W2CrN2O2 and Mo2CrN2O2 systems are found to be ferromagnetic half-metallic 2D materials with a direct band gap of 1.35 eV and 0.77 eV respectively, in the minority spin channel. The comprehensive study on DTM MXenes, provide intrinsic half-metallic properties along with robust ferromagnetism, opens up a class of promising new 2D materials with tunable magnetic and electronic properties for potential device applications in nano-spintronics and electronics.
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https://arxiv.org/abs/2211.00846v1
|
2211.00846
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2022-11-02
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computer-graphics
|
2D-DPO: Scaling Direct Preference Optimization with 2-Dimensional Supervision
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Recent advancements in Direct Preference Optimization (DPO) have significantly enhanced the alignment of Large Language Models (LLMs) with human preferences, owing to its simplicity and effectiveness. However, existing methods typically optimize a scalar score or ranking reward, thereby overlooking the multi-dimensional nature of human preferences. In this work, we propose to extend the preference of DPO to two dimensions: segments and aspects. We first introduce a 2D supervision dataset called HelpSteer-2D. For the segment dimension, we divide the response into sentences and assign scores to each segment. For the aspect dimension, we meticulously design several criteria covering the response quality rubrics. With the 2-dimensional signals as feedback, we develop a 2D-DPO framework, decomposing the overall objective into multi-segment and multi-aspect objectives. Extensive experiments on popular benchmarks demonstrate that 2D-DPO performs better than methods that optimize for scalar or 1-dimensional preferences.
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https://arxiv.org/abs/2410.19720v1
|
2410.19720
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2024-10-25
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computer-graphics
|
2D-Driven 3D Object Detection in RGB-D Images
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In this paper, we present a technique that places 3D bounding boxes around objects in an RGB-D scene. Our approach makes best use of the 2D information to quickly reduce the search space in 3D, benefiting from state-of-the-art 2D object detection techniques. We then use the 3D information to orient, place, and score bounding boxes around objects. We independently estimate the orientation for every object, using previous techniques that utilize normal information. Object locations and sizes in 3D are learned using a multilayer perceptron (MLP). In the final step, we refine our detections based on object class relations within a scene. When compared to state-of-the-art detection methods that operate almost entirely in the sparse 3D domain, extensive experiments on the well-known SUN RGB-D dataset show that our proposed method is much faster (4.1s per image) in detecting 3D objects in RGB-D images and performs better (3 mAP higher) than the state-of-the-art method that is 4.7 times slower and comparably to the method that is two orders of magnitude slower. This work hints at the idea that 2D-driven object detection in 3D should be further explored, especially in cases where the 3D input is sparse.
|
http://openaccess.thecvf.com/content_iccv_2017/html/Lahoud_2D-Driven_3D_Object_ICCV_2017_paper.html
| null |
2017-10-01
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computer-graphics
|
2d dualities from 4d
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We find new $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,2)$ dualities through the twisted compactifications of 4d supersymmetric theories on $S^2$. Our findings include dualities for both $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,2)$ non-Abelian gauge theories, as well as $\mathcal{N}=(0,2)$ Gauge/Landau-Ginzburg duality.
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https://arxiv.org/abs/2407.17350v3
|
2407.17350
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2024-07-24
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computer-graphics
|
2D dynamics of the radiative core of low mass stars
|
Understanding the internal rotation of low mass stars all along their
evolution is of primary interest when studying their rotational dynamics,
internal mixing and magnetic field generation. In this context, helio- and
asteroseismology probe angular velocity gradients deep within solar type stars
at different evolutionary stages. Still the rotation close to the center of
such stars on the main sequence is hardly detectable and the dynamical
interaction of the radiative core with the surface convective envelope is not
well understood. For instance, the influence of the differential rotation
profile sustained by convection and applied as a boundary condition to the
radiation zone is very important in the formation of tachoclines. In this work,
we study a 2D hydrodynamical model of a radiative core when an imposed, solar
or anti-solar, differential rotation is applied at the upper boundary. This
model uses the Boussinesq approximation and we find that the shear induces a
cylindrical differential rotation associated with a unique cell of meridional
circulation in each hemisphere (counterclockwise when the shear is solar-like
and clockwise when it is anti-solar). The results are discussed in the
framework of seismic observables (internal rotation rate, core-to-surface
rotation ratio) while perspectives to improve our modeling by including
magnetic field or transport by internal gravity waves will be discussed.
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http://arxiv.org/abs/1610.08798v1
|
1610.08798
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2016-10-27
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computer-graphics
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2D Eddy Current Boundary Value Problems for Power Cables with Helicoidal Symmetry
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Power cables have complex geometries in order to reduce their AC resistance. The cross-section of a cable consists of several conductors that are electrically insulated from each other to counteract the current displacement caused by the skin effect. Furthermore, the individual conductors are twisted over the cable's length. This geometry has a non-standard symmetry - a combination of translation and rotation. Exploiting this property allows formulating a dimensionally reduced boundary value problem. Dimension reduction is desirable, otherwise the electromagnetic modeling of these cables becomes impracticable due to tremendous computational efforts. We investigate 2D eddy current boundary value problems which still allow the analysis of 3D effects, such as the twisting of conductor layers.
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https://arxiv.org/abs/2301.03370v1
|
2301.03370
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2023-01-09
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computer-graphics
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2D Ego-Motion with Yaw Estimation using Only mmWave Radars via Two-Way weighted ICP
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The interest in single-chip mmWave Radar is driven by their compact form factor, cost-effectiveness, and robustness under harsh environmental conditions. Despite its promising attributes, the principal limitation of mmWave radar lies in its capacity for autonomous yaw rate estimation. Conventional solutions have often resorted to integrating inertial measurement unit (IMU) or deploying multiple radar units to circumvent this shortcoming. This paper introduces an innovative methodology for two-dimensional ego-motion estimation, focusing on yaw rate deduction, utilizing solely mmWave radar sensors. By applying a weighted Iterated Closest Point (ICP) algorithm to register processed points derived from heatmap data, our method facilitates 2D ego-motion estimation devoid of prior information. Through experimental validation, we verified the effectiveness and promise of our technique for ego-motion estimation using exclusively radar data.
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https://arxiv.org/abs/2404.00830v1
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2404.00830
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2024-03-31
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computer-graphics
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2DEG on a cylindrical shell with a screw dislocation
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A two dimensional electron gas on a cylindrical surface with a screw
dislocation is considered. More precisely, we investigate how both the geometry
and the deformed potential due to a lattice distortion affect the Landau levels
of such system. The case showing the deformed potential can be thought in the
context of 3D common semiconductors where the electrons are confined on a
cylindrical shell. We will show that important quantitative differences exist
due to this lattice distortion. For instance, the effective cyclotron frequency
is diminished by the deformed potential, which in turn enhances the Hall
conductivity.
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http://arxiv.org/abs/1504.02968v1
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1504.02968
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2015-04-12
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computer-graphics
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2D Eigenvalue Problem I: Existence and Number of Solutions
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A two dimensional eigenvalue problem (2DEVP) of a Hermitian matrix pair $(A, C)$ is introduced in this paper. The 2DEVP can be viewed as a linear algebraic formulation of the well-known eigenvalue optimization problem of the parameter matrix $H(\mu) = A - \mu C$. We present fundamental properties of the 2DEVP such as the existence, the necessary and sufficient condition for the finite number of 2D-eigenvalues and variational characterizations. We use eigenvalue optimization problems from the minmax of two Rayleigh quotients and the computation of distance to instability to show their connections with the 2DEVP and new insights of these problems derived from the properties of the 2DEVP.
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https://arxiv.org/abs/1911.08109v3
|
1911.08109
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2019-11-19
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computer-graphics
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2D Eigenvalue Problem III: Convergence Analysis of the 2D Rayleigh Quotient Iteration
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In Part I of this paper, we introduced a two dimensional eigenvalue problem (2DEVP) of a matrix pair and investigated its fundamental theory such as existence, variational characterization and number of 2D-eigenvalues. In Part II, we proposed a Rayleigh quotient iteration (RQI)-like algorithm (2DRQI) for computing a 2D-eigentriplet of the 2DEVP near a prescribed point, and discussed applications of 2DEVP and 2DRQI for solving the minimax problem of Rayleigh quotients, and computing the distance to instability. In this third part, we present convergence analysis of the 2DRQI. We show that under some mild conditions, the 2DRQI is locally quadratically convergent for computing a nonsingular 2D-eigentriplet.
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https://arxiv.org/abs/2303.05357v1
|
2303.05357
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2023-03-09
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computer-graphics
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2D Eigenvalue Problem II: Rayleigh Quotient Iteration and Applications
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In Part I of this paper, we introduced a 2D eigenvalue problem (2DEVP) and presented theoretical results of the 2DEVP and its intrinsic connetion with the eigenvalue optimizations. In this part, we devise a Rayleigh quotient iteration (RQI)-like algorithm, 2DRQI in short, for computing a 2D-eigentriplet of the 2DEVP. The 2DRQI performs $2\times$ to $8\times$ faster than the existing algorithms for large scale eigenvalue optimizations arising from the minmax of Rayleigh quotients and the distance to instability of a stable matrix.
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https://arxiv.org/abs/2209.12040v1
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2209.12040
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2022-09-24
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computer-graphics
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2D electromagnetic simulations of RF heating via inductive coupling in the SPIDER device
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SPIDER is the prototype ion source of MITICA, the full-size neutral beam heating system conceived for the ITER tokamak. It includes eight drivers to heat and sustain the inductively coupled plasma (ICP). Owing to their near cylindrical symmetry, the coupling between the radio-frequency (RF) active currents and the source plasma is studied using a 2D electromagnetic approach with simplified expressions for the plasma electrical conductivity taken from the literature. The power absorbed by the plasma and the effect of the induced plasma currents in lowering the inductance of the driver are based on data from the dedicated S16 experimental campaign (y.~2020) of SPIDER: plasma electron densities on the order of $10^{18}$ m$^{-3}$, electron temperatures $\sim 10$ eV; neutral gas pressure $\sim 0.3$ Pa and up to $50$ kW of net power per driver. It is found that the plasma conductivity cannot be explained by the friction forces associated to local collisional processes alone. The inclusion of an effective collisionality associated to non-local processes seems also insufficient to explain the experimental information. Only when the electrical conductivity is reduced where the RF magnetic field is more intense, can the heating power and driver inductance be acceptably reproduced. We present the first 2D electromagnetic ICP calculations in SPIDER for two types of plasma, without and with the addition of a static magnetic field. The power transfer efficiency to the plasma of the first drivers of SPIDER, in view of these models, is around 50%
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https://arxiv.org/abs/2305.09395v1
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2305.09395
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2023-05-16
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computer-graphics
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2D electron density profile evolution during detachment in Super-X divertor L-mode discharges on MAST-U
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2D electron density profiles obtained from coherence imaging spectroscopy in different MAST-U divertor conditions are compared. The data includes variations of strike point position, core electron density, and heating power. The improved performance of the long-legged divertors results in a lower electron density and particle flux at the target compared to configurations with smaller strike point major radius, while also being characterized by lower temperatures and deeper detachment. Comparisons against SOLPS simulations generally show good agreement in profile shape along and across the separatrix. The peaking of the electron density downstream of the detachment front is associated with significant neutral drag acting on the plasma flow.
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https://arxiv.org/abs/2410.00818v1
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2410.00818
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2024-10-01
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computer-graphics
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2D electron gas in chalcogenide multilayers
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Semiconductor interfaces, such as these existing in multilayer structures
(e.g., quantum wells (QWs)), are interesting because of their ability to form
2D electron gases (2DEGs), in which charge carriers behave completely
differently than they do in the bulk. As an example, in the presence of a
strong magnetic field, the Landau quantization of electronic levels in the 2DEG
results in the quantum Hall effect (QHE), in which Hall conductance is
quantized. This chapter is devoted to the properties of such 2DEGs in
multilayer structures made of compound semiconductors belonging to the class of
Se- and Te-based chalcogenides. In particular, we will also discuss the
interesting question of how the QHE phenomenon is affected by the giant Zeeman
splitting characteristic of II-VI-based diluted magnetic semiconductors (DMSs),
especially when the Zeeman splitting and Landau splitting become comparable. We
will also shortly discuss novel topological phases in chalcogenide multilayers.
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http://arxiv.org/abs/1905.08703v1
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1905.08703
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2019-05-21
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computer-graphics
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2D electrons floating on a suspended atomically thin dielectric
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The 2D electrons trapped in vacuum near the atomically thin dielectric (ATD, mono- or $N$-layer film of $h$-BN or transition metal dichalcogenide) are considered. ATD is suspended above the back gate and forms the capacitor which is controlled by the biased voltage determining 2D concentration, $n_{2D}$. It is found that the leakage current through ATD is negligible and effect of the polarizability of ATD is weak if $N\leq 5$. At temperatures $T=0.1\div$15 K and $n_{2D}=5\times 10^8\div 10^{10}$ cm$^{-2}$, one deals with the Boltzmann liquid of the macroscopic thickness $\sim$100 A. Due to bending of ATD the quadratic dispersion law of the flexural vibrations is transformed into the linear one at small wave vectors. The scattering processes of the electrons caused by these phonons or the monolayer islands on ATD are examined and the momentum and energy relaxation rates are analyzed based on the corresponding balance equations. The momentum relaxation times varies over orders of magnitude in the above region ($T$, $n_{2D}$) and $N$. The response may changed from the polaron transport, for a perfect single-layer ATD at low $T$ and high $n_{2D}$, to the high-mobility ($\geq 10^7$ cm$^2$/Vs) regime at high $T$ and low $n_{2D}$. The quasi-elastic energy relaxation due to the phonon-induced scattering is considered and the conditions for heating of electrons by a weak in-plane electric field are found.
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https://arxiv.org/abs/2103.10424v2
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2103.10424
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2021-03-18
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computer-graphics
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2-D Embedding of Large and High-dimensional Data with Minimal Memory and Computational Time Requirements
|
In the advent of big data era, interactive visualization of large data sets
consisting of M*10^5+ high-dimensional feature vectors of length N (N ~ 10^3+),
is an indispensable tool for data exploratory analysis. The state-of-the-art
data embedding (DE) methods of N-D data into 2-D (3-D) visually perceptible
space (e.g., based on t-SNE concept) are too demanding computationally to be
efficiently employed for interactive data analytics of large and
high-dimensional datasets. Herein we present a simple method, ivhd (interactive
visualization of high-dimensional data tool), which radically outperforms the
modern data-embedding algorithms in both computational and memory loads, while
retaining high quality of N-D data embedding in 2-D (3-D). We show that DE
problem is equivalent to the nearest neighbor nn-graph visualization, where
only indices of a few nearest neighbors of each data sample has to be known,
and binary distance between data samples -- 0 to the nearest and 1 to the other
samples -- is defined. These improvements reduce the time-complexity and memory
load from O(M log M) to O(M), and ensure minimal O(M) proportionality
coefficient as well. We demonstrate high efficiency, quality and robustness of
ivhd on popular benchmark datasets such as MNIST, 20NG, NORB and RCV1.
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http://arxiv.org/abs/1902.01108v1
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1902.01108
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2019-02-04
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computer-graphics
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2D Embeddings of Multi-dimensional Partitionings
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Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models, where each segment of the partitioning represents a region of similar model behavior. Having computed a partitioning, one is commonly interested in understanding how large the segments are and which segments lie next to each other. While visual representations of 2D domain partitionings that reveal sizes and neighborhoods are straightforward, this is no longer the case when considering multi-dimensional domains of three or more dimensions. We propose an algorithm for computing 2D embeddings of multi-dimensional partitionings. The embedding shall have the following properties: It shall maintain the topology of the partitioning and optimize the area sizes and joint boundary lengths of the embedded segments to match the respective sizes and lengths in the multi-dimensional domain. We demonstrate the effectiveness of our approach by applying it to different use cases, including the visual exploration of 3D spatial domain segmentations and multi-dimensional parameter space partitionings of simulation ensembles. We numerically evaluate our algorithm with respect to how well sizes and lengths are preserved depending on the dimensionality of the domain and the number of segments.
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https://arxiv.org/abs/2408.03641v2
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2408.03641
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2024-08-07
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computer-graphics
|
2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited
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A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to 2D signals (images). We revisit some well-known transforms (tensor wavelets, Littlewood-Paley wavelets, ridgelets and curvelets) and show that it is possible to build their empirical counterpart. We prove that such constructions lead to different adaptive frames which show some promising properties for image analysis and processing.
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https://arxiv.org/abs/2410.23533v1
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2410.23533
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2024-10-31
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computer-graphics
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2D energy-momentum tensor distributions of nucleon in a large-$N_c$ quark model from ultra-relativistic to non-relativistic limit
|
Form factors of the energy-momentum tensor (EMT) can be interpreted in certain frames in terms of spatial distributions of energy, stress, linear and angular momentum, based on 2D or 3D Fourier transforms. This interpretation is in general subject to "relativistic recoil corrections", except when the nucleon moves at the speed of light like e.g. in the infinite-momentum frame. We show that it is possible to formulate a large-$N_c$ limit in which the probabilistic interpretation of the nucleon EMT distributions holds also in other frames. We use the bag model formulated in the large-$N_c$ limit as an internally consistent quark model framework to visualize the information content associated with the 2D EMT distributions. In order to provide more intuition, we present results in the physical situation and in three different limits: by considering a heavy-quark limit, a large system-size limit and a constituent-quark limit. The visualizations of the distributions in these extreme limits will help to interpret the results from experiments, lattice QCD, and other models or effective theories.
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https://arxiv.org/abs/2202.01192v2
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2202.01192
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2022-02-02
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computer-graphics
|
2-derivators
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Introduced independently by Grothendieck and Heller in the 1980s, derivators provide a formal way to study homotopy theories by working in some quotient category such as the homotopy category of a model category. In 2015 Riehl and Verity introduced $\infty$-cosmoi, which are particular $(\infty,2)$-categories where one can develop $(\infty,1)$-category theory in a synthetic way. They noticed that much of the theory of $\infty$-cosmoi can be developed inside a quotient, the homotopy $2$-category. In the following, we begin a program that aims to formalise the $\infty$-cosmological approach to $\infty$-category theory in a derivator-like framework. In this paper we introduce some axioms and demonstrate they hold in a variety of models, including common models related to $\infty$-category theory. We also prove that these axioms are stable under a particular shift operation.
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https://arxiv.org/abs/2309.05216v1
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2309.05216
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2023-09-11
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computer-graphics
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2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I
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This paper introduces explicit Galois cohomological methods for determining the ranks of Bloch--Kato Selmer groups associated to the Tate twists of the 2-adic second \'etale cohomology of the Jacobian of a hyperelliptic curve with a rational Weierstrass point. In particular, this can give a method to determine the rational points on such curves via the Chabauty--Coleman--Kim method. This is applied to answer a question of Bugeaud, Mignotte, Siksek, Stoll and Tengely.
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https://arxiv.org/abs/2312.04996v2
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2312.04996
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2023-12-08
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computer-graphics
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2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves II
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We give refined methods for proving finiteness of the Chabauty--Coleman--Kim set $X(\mathbb{Q}_2 )_2 $, when $X$ is a hyperelliptic curve with a rational Weierstrass point. The main developments are methods for computing Selmer conditions at $2$ and $\infty$ for the mod 2 Bloch--Kato Selmer group associated to the higher Chow group $\mathrm{CH}^2 (\mathrm{Jac}(X),1)$. As a result we show that most genus 2 curves in the LMFDB of Mordell--Weil rank 2 with exactly one rational Weierstrass point satsify $\# X(\mathbb{Q}_2 )_2 <\infty $. We also obtain a field-theoretic description of second descent on the Jacobian of a hyperelliptic curve (under some conditions).
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https://arxiv.org/abs/2403.07476v1
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2403.07476
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2024-03-12
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computer-graphics
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2-Designs and Redundant Syndrome Extraction for Quantum Error Correction
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Imperfect measurement can degrade a quantum error correction scheme. A
solution that restores fault tolerance is to add redundancy to the process of
syndrome extraction. In this work, we show how to optimize this process for an
arbitrary ratio of data qubit error probability to measurement error
probability. The key is to design the measurements so that syndromes that
correspond to different errors are separated by the maximum distance in the
signal space, in close analogy to classical error correction codes. We find
that the mathematical theory of 2-designs, appropriately modified, is the right
tool for this. Analytical and simulation results for the bit-flip code, the
5-qubit code, and the Steane code are presented. The results show that
design-based redundancy protocols show improvement in both cost and performance
relative to conventional fault-tolerant error-correction schemes in situations,
quite important in practice, where measure errors are common. In the near term,
the construction of a fault-tolerant logical qubit with a small number of noisy
physical qubits will benefit from targeted redundancy in syndrome extraction.
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http://arxiv.org/abs/1907.04497v2
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1907.04497
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2019-07-11
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computer-graphics
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2DeteCT -- A large 2D expandable, trainable, experimental Computed Tomography dataset for machine learning
|
Recent research in computational imaging largely focuses on developing machine learning (ML) techniques for image reconstruction, which requires large-scale training datasets consisting of measurement data and ground-truth images. However, suitable experimental datasets for X-ray Computed Tomography (CT) are scarce, and methods are often developed and evaluated only on simulated data. We fill this gap by providing the community with a versatile, open 2D fan-beam CT dataset suitable for developing ML techniques for a range of image reconstruction tasks. To acquire it, we designed a sophisticated, semi-automatic scan procedure that utilizes a highly-flexible laboratory X-ray CT setup. A diverse mix of samples with high natural variability in shape and density was scanned slice-by-slice (5000 slices in total) with high angular and spatial resolution and three different beam characteristics: A high-fidelity, a low-dose and a beam-hardening-inflicted mode. In addition, 750 out-of-distribution slices were scanned with sample and beam variations to accommodate robustness and segmentation tasks. We provide raw projection data, reference reconstructions and segmentations based on an open-source data processing pipeline.
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https://arxiv.org/abs/2306.05907v1
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2306.05907
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2023-06-09
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computer-graphics
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2D Euler equations with Stratonovich transport noise as a large scale stochastic model reduction
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The limit from an Euler type system to the 2D Euler equations with Stratonovich transport noise is investigated. A weak convergence result for the vorticity field and a strong convergence result for the velocity field are proved. Our results aim to provide a stochastic reduction of fluid-dynamics models with three different time scales.
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https://arxiv.org/abs/2101.03096v1
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2101.03096
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2021-01-08
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computer-graphics
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2D excitation information by MPS method on infinite helixes
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Understanding the excitation spectrum in two-dimensional quantum many-body systems has long been a challenging task. We present an approach by introducing an excitation ansatz based on an infinite matrix product state (MPS) on a helix structure. With the canonical form of MPS states, we can accurately extract key properties such as energy, degeneracy, spectrum weight, and scaling behavior of low-energy excited states simultaneously. To validate the effectiveness of this method, we begin by applying it to the critical point of the transverse-field Ising model. The extracted scaling exponent of the energy gap closely aligns with the conformal bootstrap results. Subsequently, we apply this approach to the $J_1$-$J_2$ Heisenberg model on a square lattice. We discover that the degeneracy of lowest-energy excitations serves as a reliable metric for distinguishing different phases. The phase boundary identified by our method is consistent with some of the previous findings. The present method provides a promising avenue for studying the excitation spectrum of two-dimensional quantum many-body systems.
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https://arxiv.org/abs/2310.15759v2
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2310.15759
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2023-10-24
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computer-graphics
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2dF-AAOmega spectroscopy of massive stars in the Magellanic Clouds: The north-eastern region of the Large Magellanic Cloud
|
We present spectral classifications from optical spectroscopy of 263 massive
stars in the north-eastern region of the Large Magellanic Cloud. The observed
two-degree field includes the massive 30 Doradus star-forming region, the
environs of SN1987A, and a number of star-forming complexes to the south of 30
Dor. These are the first classifications for the majority (203) of the stars
and include eleven double-lined spectroscopic binaries. The sample also
includes the first examples of early OC-type spectra (AAOmega 30 Dor 248 and
280), distinguished by the weakness of their nitrogen spectra and by C IV 4658
emission. We propose that these stars have relatively unprocessed CNO
abundances compared to morphologically normal O-type stars, indicative of an
earlier evolutionary phase. From analysis of observations obtained on two
consecutive nights, we present radial-velocity estimates for 233 stars, finding
one apparent single-lined binary and nine (>3sigma) outliers compared to the
systemic velocity; the latter objects could be runaway stars or large-amplitude
binary systems and further spectroscopy is required to investigate their
nature.
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http://arxiv.org/abs/1508.03490v1
|
1508.03490
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2015-08-14
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computer-graphics
|
2D Face Recognition System Based on Selected Gabor Filters and Linear Discriminant Analysis LDA
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We present a new approach for face recognition system. The method is based on
2D face image features using subset of non-correlated and Orthogonal Gabor
Filters instead of using the whole Gabor Filter Bank, then compressing the
output feature vector using Linear Discriminant Analysis (LDA). The face image
has been enhanced using multi stage image processing technique to normalize it
and compensate for illumination variation. Experimental results show that the
proposed system is effective for both dimension reduction and good recognition
performance when compared to the complete Gabor filter bank. The system has
been tested using CASIA, ORL and Cropped YaleB 2D face images Databases and
achieved average recognition rate of 98.9 %.
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http://arxiv.org/abs/1503.03741v1
|
1503.03741
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2015-03-12
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computer-graphics
|
2D Feature Distillation for Weakly- and Semi-Supervised 3D Semantic Segmentation
|
As 3D perception problems grow in popularity and the need for large-scale labeled datasets for LiDAR semantic segmentation increase, new methods arise that aim to reduce the necessity for dense annotations by employing weakly-supervised training. However these methods continue to show weak boundary estimation and high false negative rates for small objects and distant sparse regions. We argue that such weaknesses can be compensated by using RGB images which provide a denser representation of the scene. We propose an image-guidance network (IGNet) which builds upon the idea of distilling high level feature information from a domain adapted synthetically trained 2D semantic segmentation network. We further utilize a one-way contrastive learning scheme alongside a novel mixing strategy called FOVMix, to combat the horizontal field-of-view mismatch between the two sensors and enhance the effects of image guidance. IGNet achieves state-of-the-art results for weakly-supervised LiDAR semantic segmentation on ScribbleKITTI, boasting up to 98% relative performance to fully supervised training with only 8% labeled points, while introducing no additional annotation burden or computational/memory cost during inference. Furthermore, we show that our contributions also prove effective for semi-supervised training, where IGNet claims state-of-the-art results on both ScribbleKITTI and SemanticKITTI.
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https://arxiv.org/abs/2311.15605v1
|
2311.15605
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2023-11-27
|
computer-graphics
|
2-d Fermionic SPT with CRT symmetry
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An invariant of SPT-phases with on-site finite group $G$ symmetry for two-dimensional Fermion systems was derived in [O]. This invariant is doubled compared to the conjectured one from the invertible quantum field theory. We show that if we require CRT-symmetry (which holds automatically in quantum field theory) in addition, then our invariant reduces to the conjectured one.
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https://arxiv.org/abs/2212.09038v2
|
2212.09038
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2022-12-18
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computer-graphics
|
2D Fermion on the Strip with Boundary Defects as a CFT with Excited Spin Fields
|
We consider a two-dimensional fermion on the strip in the presence of an
arbitrary number of zero-dimensional boundary changing defects. We show that
the theory is still conformal with time dependent stress-energy tensor and that
the allowed defects can be understood as excited spin fields. Finally we
compute correlation functions involving these excited spin fields without using
bosonization.
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http://arxiv.org/abs/1912.07617v1
|
1912.07617
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2019-12-16
|
computer-graphics
|
2D Fermions and Statistical Mechanics: Critical Dimers and Dirac Fermions in a background gauge field
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In the limit of the lattice spacing going to zero, we consider the dimer model on isoradial graphs in the presence of singular $SL(N,\mathbb{C})$ gauge fields flat away from a set of punctures. We consider the cluster expansion of this twisted dimer partition function show it matches an analogous cluster expansion of the 2D Dirac partition function in the presence of this gauge field. The latter is often referred to as a tau function. This reproduces and generalizes various computations of Dub\'edat (J. Eur. Math. Soc. 21 (2019), no. 1, pp. 1-54). In particular, both sides' cluster expansion are matched up term-by-term and each term is shown to equal a sum of a particular holomorphic integral and its conjugate. On the dimer side, we evaluate the terms in the expansion using various exact lattice-level identities of discrete exponential functions and the inverse Kasteleyn matrix. On the fermion side, the cluster expansion leads us to two novel series expansions of tau functions, one involving the Fuschian representation and one involving the monodromy representation.
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https://arxiv.org/abs/2208.10640v2
|
2208.10640
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2022-08-22
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computer-graphics
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007: Democratically Finding The Cause of Packet Drops
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Network failures continue to plague datacenter operators as their symptoms
may not have direct correlation with where or why they occur. We introduce 007,
a lightweight, always-on diagnosis application that can find problematic links
and also pinpoint problems for each TCP connection. 007 is completely contained
within the end host. During its two month deployment in a tier-1 datacenter, it
detected every problem found by previously deployed monitoring tools while also
finding the sources of other problems previously undetected.
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http://arxiv.org/abs/1802.07222v1
|
1802.07222
|
2018-02-20
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cybersecurity
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0.08 fF, 0.72 nA dark current, 91% Quantum Efficiency, 38 Gb/s Nano-photodetector on a 45 nm CMOS Silicon-Photonic Platform
|
We demonstrated a Germanium-on-Silicon photodetector utilizing an asymmetric-Fabry-Perot resonator with 0.08 fF capacitance. The measurements at 1315.5 nm show 0.72 nA (3.40 nA) dark current, 0.93 A/W (0.96 A/W) responsivity, 36 Gb/s (38 Gb/s) operation at -1V (-2V) bias.
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https://arxiv.org/abs/2401.03527v1
|
2401.03527
|
2024-01-07
|
cybersecurity
|
0/1 Constrained Optimization Solving Sample Average Approximation for Chance Constrained Programming
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Sample average approximation (SAA) is a tractable approach for dealing with chance constrained programming, a challenging stochastic optimization problem. The constraint of SAA is characterized by the $0/1$ loss function which results in considerable complexities in devising numerical algorithms. Most existing methods have been devised based on reformulations of SAA, such as binary integer programming or relaxed problems. However, the development of viable methods to directly tackle SAA remains elusive, let alone providing theoretical guarantees. In this paper, we investigate a general $0/1$ constrained optimization, providing a new way to address SAA rather than its reformulations. Specifically, starting with deriving the Bouligand tangent and Fr$\acute{e}$chet normal cones of the $0/1$ constraint, we establish several optimality conditions. One of them can be equivalently expressed by a system of equations, enabling the development of a semismooth Newton-type algorithm. The algorithm demonstrates a locally superlinear or quadratic convergence rate under standard assumptions, along with nice numerical performance compared to several leading solvers.
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https://arxiv.org/abs/2210.11889v4
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2210.11889
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2022-10-21
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cybersecurity
|
0/1 Deep Neural Networks via Block Coordinate Descent
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The step function is one of the simplest and most natural activation functions for deep neural networks (DNNs). As it counts 1 for positive variables and 0 for others, its intrinsic characteristics (e.g., discontinuity and no viable information of subgradients) impede its development for several decades. Even if there is an impressive body of work on designing DNNs with continuous activation functions that can be deemed as surrogates of the step function, it is still in the possession of some advantageous properties, such as complete robustness to outliers and being capable of attaining the best learning-theoretic guarantee of predictive accuracy. Hence, in this paper, we aim to train DNNs with the step function used as an activation function (dubbed as 0/1 DNNs). We first reformulate 0/1 DNNs as an unconstrained optimization problem and then solve it by a block coordinate descend (BCD) method. Moreover, we acquire closed-form solutions for sub-problems of BCD as well as its convergence properties. Furthermore, we also integrate $\ell_{2,0}$-regularization into 0/1 DNN to accelerate the training process and compress the network scale. As a result, the proposed algorithm has a high performance on classifying MNIST and Fashion-MNIST datasets. As a result, the proposed algorithm has a desirable performance on classifying MNIST, FashionMNIST, Cifar10, and Cifar100 datasets.
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https://arxiv.org/abs/2206.09379v2
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2206.09379
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2022-06-19
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cybersecurity
|
0-1 Knapsack in Nearly Quadratic Time
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We study pseudo-polynomial time algorithms for the fundamental \emph{0-1 Knapsack} problem. Recent research interest has focused on its fine-grained complexity with respect to the number of items $n$ and the \emph{maximum item weight} $w_{\max}$. Under $(\min,+)$-convolution hypothesis, 0-1 Knapsack does not have $O((n+w_{\max})^{2-\delta})$ time algorithms (Cygan-Mucha-W\k{e}grzycki-W\l{}odarczyk 2017 and K\"{u}nnemann-Paturi-Schneider 2017). On the upper bound side, currently the fastest algorithm runs in $\tilde O(n + w_{\max}^{12/5})$ time (Chen, Lian, Mao, and Zhang 2023), improving the earlier $O(n + w_{\max}^3)$-time algorithm by Polak, Rohwedder, and W\k{e}grzycki (2021). In this paper, we close this gap between the upper bound and the conditional lower bound (up to subpolynomial factors): - The 0-1 Knapsack problem has a deterministic algorithm in $O(n + w_{\max}^{2}\log^4w_{\max})$ time. Our algorithm combines and extends several recent structural results and algorithmic techniques from the literature on knapsack-type problems: - We generalize the "fine-grained proximity" technique of Chen, Lian, Mao, and Zhang (2023) derived from the additive-combinatorial results of Bringmann and Wellnitz (2021) on dense subset sums. This allows us to bound the support size of the useful partial solutions in the dynamic program. - To exploit the small support size, our main technical component is a vast extension of the "witness propagation" method, originally designed by Deng, Mao, and Zhong (2023) for speeding up dynamic programming in the easier unbounded knapsack settings. To extend this approach to our 0-1 setting, we use a novel pruning method, as well as the two-level color-coding of Bringmann (2017) and the SMAWK algorithm on tall matrices.
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https://arxiv.org/abs/2308.04093v2
|
2308.04093
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2023-08-08
|
cybersecurity
|
0-1 laws for pattern occurrences in phylogenetic trees and networks
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In a recent paper, the question of determining the fraction of binary trees that contain a fixed pattern known as the snowflake was posed. We show that this fraction goes to 1, providing two very different proofs: a purely combinatorial one that is quantitative and specific to this problem; and a proof using branching process techniques that is less explicit, but also much more general, as it applies to any fixed patterns and can be extended to other trees and networks. In particular, it follows immediately from our second proof that the fraction of $d$-ary trees (resp. level-$k$ networks) that contain a fixed $d$-ary tree (resp. level-$k$ network) tends to $1$ as the number of leaves grows.
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https://arxiv.org/abs/2402.04499v2
|
2402.04499
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2024-02-07
|
cybersecurity
|
0-1 phase transitions in sparse spiked matrix estimation
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We consider statistical models of estimation of a rank-one matrix (the spike) corrupted by an additive gaussian noise matrix in the sparse limit. In this limit the underlying hidden vector (that constructs the rank-one matrix) has a number of non-zero components that scales sub-linearly with the total dimension of the vector, and the signal strength tends to infinity at an appropriate speed. We prove explicit low-dimensional variational formulas for the asymptotic mutual information between the spike and the observed noisy matrix in suitable sparse limits. For Bernoulli and Bernoulli-Rademacher distributed vectors, and when the sparsity and signal strength satisfy an appropriate scaling relation, these formulas imply sharp 0-1 phase transitions for the asymptotic minimum mean-square-error. A similar phase transition was analyzed recently in the context of sparse high-dimensional linear regression (compressive sensing).
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https://arxiv.org/abs/1911.05030v1
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1911.05030
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2019-11-12
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cybersecurity
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(0,2) Dualities and the 4-Simplex
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We propose that a simple, Lagrangian 2d $\mathcal{N}=(0, 2)$ duality
interface between the 3d $\mathcal{N}=2$ XYZ model and 3d $\mathcal{N}=2$ SQED
can be associated to the simplest triangulated 4-manifold: the 4-simplex. We
then begin to flesh out a dictionary between more general triangulated
4-manifolds with boundary and 2d $\mathcal{N}=(0, 2)$ interfaces. In
particular, we identify IR dualities of interfaces associated to local changes
of 4d triangulation, governed by the (3,3), (2,4), and (4,2) Pachner moves. We
check these dualities using supersymmetric half-indices. We also describe how
to produce stand-alone 2d theories (as opposed to interfaces) capturing the
geometry of 4-simplices and Pachner moves by making additional field-theoretic
choices, and find in this context that the Pachner moves recover abelian
$\mathcal{N}=(0,2)$ trialities of Gadde-Gukov-Putrov. Our work provides new,
explicit tools to explore the interplay between 2d dualities and 4-manifold
geometry that has been developed in recent years.
|
http://arxiv.org/abs/1905.05173v2
|
1905.05173
|
2019-08-10
|
cybersecurity
|
(0,2) hybrid models
|
We introduce a class of (0,2) superconformal field theories based on hybrid
geometries, generalizing various known constructions. We develop techniques for
the computation of the complete massless spectrum when the theory can be
interpreted as determining a perturbative heterotic string compactification. We
provide evidence for surprising properties regarding RG flows and IR accidental
symmetries in (0,2) hybrid CFTs. We also study the conditions for embedding a
hybrid theory in a particular class of gauged linear sigma models. This
perspective suggests that our construction generates models which cannot be
realized or analyzed by previously known methods.
|
http://arxiv.org/abs/1712.04976v2
|
1712.04976
|
2018-07-24
|
cybersecurity
|
(0,2) Mirror Symmetry on homogeneous Hopf surfaces
|
In this work we find the first examples of (0,2) mirror symmetry on compact non-K\"ahler complex manifolds. For this we follow Borisov's approach to mirror symmetry using vertex algebras and the chiral de Rham complex. Our examples of (0,2) mirrors are given by pairs of Hopf surfaces endowed with a Bismut-flat pluriclosed metric. Requiring that the geometry is homogeneous, we reduce the problem to the study of Killing spinors on a quadratic Lie algebra and the construction of embeddings of the $N=2$ superconformal vertex algebra in the superaffine vertex algebra, combined with topological T-duality.
|
https://arxiv.org/abs/2012.01851v3
|
2012.01851
|
2020-12-03
|
cybersecurity
|
(0,4) brane box models
|
Two-dimensional $\mathcal{N}=(0,4)$ supersymmetric quiver gauge theories are
realized as D3-brane box configurations (two dimensional intervals) which are
bounded by NS5-branes and intersect with D5-branes. The periodic brane
configuration is mapped to D1-D5-D5$'$ brane system at orbifold singularity via
T-duality. The matter content and interactions are encoded by the
$\mathcal{N}=(0,4)$ quiver diagrams which are determined by the brane
configurations. The Abelian gauge anomaly cancellation indicates the presence
of Fermi multiplets at the NS-NS$'$ junction. We also discuss the brane
construction of $\mathcal{N}=(0,4)$ supersymmetric boundary conditions in 3d
$\mathcal{N}=4$ gauge theories involving two-dimensional boundary degrees of
freedom that cancel gauge anomaly.
|
http://arxiv.org/abs/1811.09117v1
|
1811.09117
|
2018-11-22
|
cybersecurity
|
$(0, 4)$ dualities
|
We study a class of two-dimensional ${\cal N}=(0, 4)$ quiver gauge theories
that flow to superconformal field theories. We find dualities for the
superconformal field theories similar to the 4d ${\cal N}=2$ theories of class
${\cal S}$, labelled by a Riemann surface ${\cal C}$. The dual descriptions
arise from various pair-of-pants decompositions, that involves an analog of the
$T_N$ theory. Especially, we find the superconformal index of such theories can
be written in terms of a topological field theory on ${\cal C}$. We interpret
this class of SCFTs as the ones coming from compactifying 6d ${\cal N}=(2, 0)$
theory on $\mathbb{CP}^1 \times {\cal C}$
|
http://arxiv.org/abs/1505.07110v2
|
1505.07110
|
2015-12-14
|
cybersecurity
|
$(0,4)$ Projective Superspaces I: Interacting Linear Sigma Models
|
We describe the projective superspace approach to supersymmetric models with off-shell $(0,4)$ supersymmetry in two dimensions. In addition to the usual superspace coordinates, projective superspace has extra bosonic variables -- one doublet for each $\text{SU}(2)$ in the R-symmetry $\text{SU}(2) \times \text{SU}(2)$ which are interpreted as homogeneous coordinates on $\mathbf{CP}^1 \times \mathbf{CP}^1$. The superfields are analytic in the $\mathbf{CP}^1$ coordinates and this analyticity plays an important role in our description. For instance, it leads to stringent constraints on the interactions one can write down for a given superfield content of the model. As an example, we describe in projective superspace Witten's ADHM sigma model -- a linear sigma model with non-derivative interactions whose target is $\mathbf{R}^4$ with a Yang-Mills instanton solution. The hyperk\"ahler nature of target space and the twistor description of instantons by Ward, and Atiyah, Hitchin, Drinfeld and Manin are natural outputs of our construction.
|
https://arxiv.org/abs/2303.14675v1
|
2303.14675
|
2023-03-26
|
cybersecurity
|
0.52 V-mm ITO-based Mach-Zehnder Modulator in Silicon Photonics
|
Electro-optic modulators transform electronic signals into the optical domain
and are critical components in modern telecommunication networks, RF photonics,
and emerging applications in quantum photonics and beam steering. All these
applications require integrated and voltage-efficient modulator solutions with
compact formfactors that are seamlessly integratable with Silicon photonics
platforms and feature near-CMOS material processing synergies. However,
existing integrated modulators are challenged to meet these requirements.
Conversely, emerging electro-optic materials heterogeneously integrated with Si
photonics open a new avenue for device engineering. Indium tin oxide (ITO) is
one such compelling material for heterogeneous integration in Si exhibiting
formidable electro-optic effect characterized by unity order index at
telecommunication frequencies. Here we overcome these limitations and
demonstrate a monolithically integrated ITO electro- optic modulator based on a
Mach Zehnder interferometer (MZI) featuring a high-performance half-wave
voltage and active device length product, VpL = 0.52 V-mm. We show, how that
the unity-strong index change enables a 30 micrometer-short pi-phase shifter
operating ITO in the index-dominated region away from the epsilon-bear-zero ENZ
point. This device experimentally confirms electrical phase shifting in ITO
enabling its use in multifaceted applications including dense on-chip
communication networks, nonlinearity for activation functions in photonic
neural networks, and phased array applications for LiDAR.
|
http://arxiv.org/abs/1809.03544v1
|
1809.03544
|
2018-08-16
|
cybersecurity
|
0.5 Petabyte Simulation of a 45-Qubit Quantum Circuit
|
Near-term quantum computers will soon reach sizes that are challenging to directly simulate, even when employing the most powerful supercomputers. Yet, the ability to simulate these early devices using classical computers is crucial for calibration, validation, and benchmarking. In order to make use of the full potential of systems featuring multi- and many-core processors, we use automatic code generation and optimization of compute kernels, which also enables performance portability. We apply a scheduling algorithm to quantum supremacy circuits in order to reduce the required communication and simulate a 45-qubit circuit on the Cori II supercomputer using 8,192 nodes and 0.5 petabytes of memory. To our knowledge, this constitutes the largest quantum circuit simulation to this date. Our highly-tuned kernels in combination with the reduced communication requirements allow an improvement in time-to-solution over state-of-the-art simulations by more than an order of magnitude at every scale.
|
https://arxiv.org/abs/1704.01127v2
|
1704.01127
|
2017-04-04
|
cybersecurity
|
($0,6$) AdS$_3$/CFT$_2$ and surface defects
|
We explore a new class of AdS$_3$ solutions in massive type IIA supergravity preserving $\mathcal{N} = (0,6)$ supersymmetry and realising an $\mathfrak{osp}(6|2)$ superconformal algebra. These solutions exhibit an SO(6)-symmetric internal space constructed from a $\mathbb{CP}^3$, and are fully specified by a single cubic function controlling the fluxes and warping. We propose a brane box configuration underlying the solutions from which we construct a two-dimensional quiver gauge theory whose anomaly structure and central charge we analyse, and from which we can realise Seiberg-like dualities as large gauge transformations. The brane box configuration suggests an interpretation of the solutions as dual to surface defects within the ABJ(M) theory. Our findings provide a concrete setting for exploring holography beyond the ABJM vacuum. Remarkably, no explicit field theories are currently known to realise $\mathcal{N} = (0,6)$ supersymmetry in two dimensions, making our setup a promising and largely unexplored direction for field-theoretic investigations.
|
https://arxiv.org/abs/2504.20864v1
|
2504.20864
|
2025-04-29
|
cybersecurity
|
0.71-{\AA} resolution electron tomography enabled by deep learning aided information recovery
|
Electron tomography, as an important 3D imaging method, offers a powerful
method to probe the 3D structure of materials from the nano- to the
atomic-scale. However, as a grant challenge, radiation intolerance of the
nanoscale samples and the missing-wedge-induced information loss and artifacts
greatly hindered us from obtaining 3D atomic structures with high fidelity.
Here, for the first time, by combining generative adversarial models with
state-of-the-art network architectures, we demonstrate the resolution of
electron tomography can be improved to 0.71 angstrom which is the highest
three-dimensional imaging resolution that has been reported thus far. We also
show it is possible to recover the lost information and remove artifacts in the
reconstructed tomograms by only acquiring data from -50 to +50 degrees (44%
reduction of dosage compared to -90 to +90 degrees full tilt series). In
contrast to conventional methods, the deep learning model shows outstanding
performance for both macroscopic objects and atomic features solving the
long-standing dosage and missing-wedge problems in electron tomography. Our
work provides important guidance for the application of machine learning
methods to tomographic imaging and sheds light on its applications in other 3D
imaging techniques.
|
http://arxiv.org/abs/2003.12259v1
|
2003.12259
|
2020-03-27
|
cybersecurity
|
$0.7-2.5~\mu$m spectra of Hilda asteroids
|
The Hilda asteroids are primitive bodies in resonance with Jupiter whose
origin and physical properties are not well understood. Current models posit
that these asteroids formed in the outer Solar System and were scattered along
with the Jupiter Trojans into their present-day positions during a chaotic
episode of dynamical restructuring. In order to explore the surface composition
of these enigmatic objects in comparison with an analogous study of Trojans
(Emery et al. 2011), we present new near-infrared spectra (0.7-2.5 $\mu$m) of
25 Hilda asteroids. No discernible absorption features are apparent in the
data. Synthesizing the bimodalities in optical color and infrared reflectivity
reported in previous studies, we classify 26 of the 28 Hildas in our spectral
sample into the so-called less-red and red sub-populations and find that the
two sub-populations have distinct average spectral shapes. Combining our
results with visible spectra, we find that Trojans and Hildas possess similar
overall spectral shapes, suggesting that the two minor body populations share a
common progenitor population. A more detailed examination reveals that while
the red Trojans and Hildas have nearly identical spectra, less-red Hildas are
systematically bluer in the visible and redder in the near-infrared than
less-red Trojans, indicating a putative broad, shallow absorption feature
between 0.5 and 1.0 $\mu$m. We argue that the less-red and red objects found in
both Hildas and Trojans represent two distinct surface chemistries and
attribute the small discrepancy between less-red Hildas and Trojans to the
difference in surface temperatures between the two regions.
|
http://arxiv.org/abs/1707.09064v1
|
1707.09064
|
2017-07-27
|
cybersecurity
|
0.75 atoms improve the clock signal of 10,000 atoms
|
Since the pioneering work of Ramsey, atom interferometers are employed for
precision metrology, in particular to measure time and to realize the second.
In a classical interferometer, an ensemble of atoms is prepared in one of the
two input states, whereas the second one is left empty. In this case, the
vacuum noise restricts the precision of the interferometer to the standard
quantum limit (SQL). Here, we propose and experimentally demonstrate a novel
clock configuration that surpasses the SQL by squeezing the vacuum in the empty
input state. We create a squeezed vacuum state containing an average of 0.75
atoms to improve the clock sensitivity of 10,000 atoms by 2.05 dB. The SQL
poses a significant limitation for today's microwave fountain clocks, which
serve as the main time reference. We evaluate the major technical limitations
and challenges for devising a next generation of fountain clocks based on
atomic squeezed vacuum.
|
http://arxiv.org/abs/1605.07754v1
|
1605.07754
|
2016-05-25
|
cybersecurity
|
0.75 Gbit/s high-speed classical key distribution with mode-shift keying chaos synchronization of Fabry-Perot lasers
|
High-speed physical key distribution is diligently pursued for secure communication. In this paper, we propose and experimentally demonstrate a scheme of high-speed key distribution using mode-shift keying chaos synchronization between two multi-longitudinal-mode Fabry-Perot lasers commonly driven by a super-luminescent diode. Legitimate users dynamically select one of the longitudinal modes according to private control codes to achieve mode-shift keying chaos synchronization. The two remote chaotic light waveforms are quantized to generate two raw random bit streams, and then those bits corresponding to chaos synchronization are sifted as shared keys by comparing the control codes. In this method, the transition time, i.e., the chaos synchronization recovery time is determined by the rising time of the control codes rather than the laser transition response time, so the key distribution rate is improved greatly. Our experiment achieved 0.75-Gbit/s key distribution rate with a bit error rate of 3.8*10-3 over 160-km fiber transmission with dispersion compensation. The entropy rate of the laser chaos is evaluated as 16 Gbit/s, which determines the ultimate final key rate together with key generation ratio. It is therefore believed that the method pays a way for Gbit/s physical key distribution.
|
https://arxiv.org/abs/2004.08586v3
|
2004.08586
|
2020-04-18
|
cybersecurity
|
0.7 MW Yb:YAG pumped degenerate optical parametric oscillator at 2.06 μm
|
Frequency comb and field-resolved broadband absorption spectroscopy are promising techniques for rapid, precise, and sensitive detection of short-lived atmospheric pollutants on-site. Enhancing detection sensitivity in absorption spectroscopy hinges on bright sources that cover molecular resonances and fast signal modulation techniques to implement lock-in detection schemes efficiently. Yb:YAG thin-disk lasers, combined with optical parametric oscillators (OPO), present a compelling solution to fulfill these requirements. In this work, we report on a bright OPO pumped by a Yb:YAG thin-disk Kerr-lens mode-locked oscillator delivering 2.8 W, 114 fs pulses at 2.06 {\mu}m with an averaged energy of 90 nJ. The OPO cavity operates at 30.9 MHz pulse repetition rates, the second harmonic of the pump cavity, allowing for broadband, efficient, and dispersion-free modulation of the OPO output pulses at 15.45 MHz rate. With 13% optical-to-optical conversion efficiency and a high-frequency intra-cavity modulation, this scalable scheme holds promise to advance the detection sensitivity and frontiers of field-resolved spectroscopic techniques.
|
https://arxiv.org/abs/2407.13371v1
|
2407.13371
|
2024-07-18
|
cybersecurity
|
0.82 um 105 W diode-pumped thulium-doped all silica fiber laser
|
An all-silica-fiber thulium-doped fiber laser emitting at 0.82 um on the transition from 3H4 to the ground state 3H6 outputs 105 W continuous-wave (CW) power and 555 W quasi-continuous-wave (QCW) instantaneous power with 0.96% duty cycle in 240-us rectangular pulses. The TDFL comprises a double-clad thulium-doped fiber (TDF) which is designed and fabricated in-house and is incorporated into an all-fiber cavity and cladding-pumped by five pigtailed diode lasers at 0.79 um. Co-lasing at 1.9 um counteracts population trapping in 3F4. The slope efficiency relative to absorbed pump power reaches 64% QCW and 77.5% CW. QCW, the beam quality M2 becomes 2.2 (beam parameter product BPP 0.57 mm mrad) and 2.45 (BPP 0.64) in orthogonal directions at ~250 W of instantaneous output power. Additionally, a modified QCW setup is continuously wavelength-tunable from 812 nm to 835 nm. We believe this is the first reported demonstration of high-power laser operation of the 3H4 to 3H6 transition in a TDF. Given also the simplicity and other attractions of an all-silica-fiber laser with direct-diode cladding-pumping, we believe our demonstration is valuable for applications ranging from laser machining of aluminum (benefitting from an absorption peak at 0.83 um) to scientific applications including strontium-based atomic clocks and cesium-based quantum metrology.
|
https://arxiv.org/abs/2505.09582v1
|
2505.09582
|
2025-05-14
|
cybersecurity
|
0.8% Nyquist computational ghost imaging via non-experimental deep learning
|
We present a framework for computational ghost imaging based on deep learning and customized pink noise speckle patterns. The deep neural network in this work, which can learn the sensing model and enhance image reconstruction quality, is trained merely by simulation. To demonstrate the sub-Nyquist level in our work, the conventional computational ghost imaging results, reconstructed imaging results using white noise and pink noise via deep learning are compared under multiple sampling rates at different noise conditions. We show that the proposed scheme can provide high-quality images with a sampling rate of 0.8% even when the object is outside the training dataset, and it is robust to noisy environments. This method is excellent for various applications, particularly those that require a low sampling rate, fast reconstruction efficiency, or experience strong noise interference.
|
https://arxiv.org/abs/2108.07673v1
|
2108.07673
|
2021-08-17
|
cybersecurity
|
0+ and 1+ heavy-light exotic mesons at N2LO in the chiral limit
|
We use QCD spectral sum rules (QSSR) and the factorization properties of
molecule and four-quark currents to estimate the masses and couplings of the 0+
and 1+ molecules and four-quark at N2LO of PT QCD. We include in the OPE the
contributions of non-perturbative condensates up to dimension-six. Within the
Laplace sum rules approach (LSR) and in the MS-scheme, we summarize our results
in Table 2, which agree within the errors with some of the observed XZ-like
molecules or/and four-quark. Couplings of these states to the currents are also
extracted. Our results are improvements of the LO ones in the existing
literature.
|
http://arxiv.org/abs/1801.09110v1
|
1801.09110
|
2018-01-27
|
cybersecurity
|
0-Auslander correspondence
|
In this short note we prove an analogue of Auslander correspondence for exact dg categories whose $H^0$-category is $0$-Auslander in the sense of Gorsky--Nakaoka--Palu.
|
https://arxiv.org/abs/2306.15958v2
|
2306.15958
|
2023-06-28
|
cybersecurity
|
0-Concordance of 2-knots
|
In this paper we investigate the 0-concordance classes of 2-knots in $S^4$,
an equivalence relation that is related to understanding smooth structures on
4-manifolds. Using Rochlin's invariant, and invariants arising from
Heegaard-Floer homology, we will prove that there are infinitely many
0-concordance classes of 2-knots.
|
http://arxiv.org/abs/1907.06524v1
|
1907.06524
|
2019-07-15
|
cybersecurity
|
0-concordance of knotted surfaces and Alexander ideals
|
In this paper we provide a new obstruction to 0-concordance of knotted
surfaces in $S^4$ in terms of Alexander ideals. We use this to prove the
existence of infinitely many linearly independent 0-concordance classes and to
provide the first proof that the submonoid of 2-knots is not a group. The main
result is that the Alexander ideal induces a homomorphism from the
0-concordance monoid $\mathscr{C}_0$ of oriented surface knots in $S^4$ to the
ideal class monoid of $\mathbb{Z}[t^{\pm1}]$. Consequently, any surface knot
with nonprincipal Alexander ideal is not 0-slice and in fact, not invertible in
$\mathscr{C}_0$. Many examples are given. We also characterize which ideals are
the ideals of surface knots, generalizing a theorem of Kinoshita, and
generalize the knot determinant to the case of nonprincipal ideals. Lastly, we
show that under a mild condition on the knot group, the peripheral subgroup of
a knotted surface is also a 0-concordance invariant.
|
http://arxiv.org/abs/1911.13112v1
|
1911.13112
|
2019-11-29
|
cybersecurity
|
0-cycles on Grassmannians as representations of projective groups
|
Let $F$ be an infinite division ring, $V$ be a left $F$-vector space, $r>0$
be an integer. We study the structure of the representation of the linear group
$\mathrm{GL}_F(V)$ in the vector space of formal finite linear combinations of
$r$-dimensional vector subspaces of $V$ with coefficients in a field $K$. This
gives a series of natural examples of irreducible infinite-dimensional
representations of projective groups. These representations are non-smooth if
$F$ is locally compact and non-discrete.
|
http://arxiv.org/abs/1811.08675v3
|
1811.08675
|
2019-09-12
|
cybersecurity
|
0D-2D Heterostructure for making very Large Quantum Registers using itinerant Bose-Einstein Condensate of Excitons
|
Presence of coherent resonant tunneling in quantum dot (zero-dimensional) - quantum well (two-dimensional) heterostructure is necessary to explain the collective oscillations of average electrical polarization of excitonic dipoles over a macroscopically large area. This was measured using photo excited capacitance as a function of applied voltage bias. Resonant tunneling in this heterostructure definitely requires momentum space narrowing of charge carriers inside the quantum well and that of associated indirect excitons, which indicates bias dependent itinerant Bose-Einstein condensation of excitons. Observation of periodic variations in negative quantum capacitance points to in-plane coulomb correlations mediated by long range spatial ordering of indirect, dipolar excitons. Enhanced contrast of quantum interference beats of excitonic polarization waves even under white light and observed Rabi oscillations over a macroscopically large area also support the presence of density driven excitonic condensation having long range order. Periodic presence (absence) of splitting of excitonic peaks in photocapacitance spectra even demonstrate collective coupling (decoupling) between energy levels of the quantum well and quantum dots with applied biases, which can potentially be used for quantum gate operations. All these observations point to experimental control of macroscopically large, quantum state of a two-component Bose-Einstein condensate of excitons in this quantum dot - quantum well heterostructure. Therefore, in principle, millions of two-level excitonic qubits can be intertwined to fabricate large quantum registers using such hybrid heterostructure by controlling the local electric fields and also by varying photoexcitation intensities of overlapping light spots.
|
https://arxiv.org/abs/2107.13518v3
|
2107.13518
|
2021-07-28
|
cybersecurity
|
0-dimensional Homology Preserving Dimensionality Reduction with TopoMap
|
This note presents TopoMap, a novel dimensionality reduction technique which provides topological guarantees during the mapping process. In particular, TopoMap performs the mapping from a high-dimensional space to a visual space, while preserving the 0-dimensional persistence diagram of the Rips filtration of the high-dimensional data, ensuring that the filtrations generate the same connected components when applied to the original as well as projected data. The presented case studies show that the topological guarantee provided by TopoMap not only brings confidence to the visual analytic process but also can be used to assist in the assessment of other projection methods.
|
https://openreview.net/forum?id=zrDNDWjOGwH
| null |
2020-10-10
|
cybersecurity
|
0-Dimensional Ideal Approximation Theory
|
We propose axioms for 0-dimensional ideal approximation theory and note that extriangulated categories satisfy these axioms.
|
https://arxiv.org/abs/2502.04665v1
|
2502.04665
|
2025-02-07
|
cybersecurity
|
0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
|
Orbifold singularities of M-theory constitute the building blocks of a broad class of supersymmetric quantum field theories (SQFTs). In this paper we show how the local data of these geometries determines global data on the resulting higher symmetries of these systems. In particular, via a process of cutting and gluing, we show how local orbifold singularities encode the 0-form, 1-form and 2-group symmetries of the resulting SQFTs. Geometrically, this is obtained from the possible singularities which extend to the boundary of the non-compact geometry. The resulting category of boundary conditions then captures these symmetries, and is equivalently specified by the orbifold homology of the boundary geometry. We illustrate these general points in the context of a number of examples, including 5D superconformal field theories engineered via orbifold singularities, 5D gauge theories engineered via singular elliptically fibered Calabi-Yau threefolds, as well as 4D SQCD-like theories engineered via M-theory on non-compact $G_2$ spaces.
|
https://arxiv.org/abs/2203.10102v4
|
2203.10102
|
2022-03-18
|
cybersecurity
|
$0^{+}$ fully-charmed tetraquark states
|
Motivated by the LHCb's new observation of structures in the $J/\psi$-pair
invariant mass spectrum, for which could be classified as possible
$cc\bar{c}\bar{c}$ tetraquark candidates, we systematically study $0^{+}$
fully-charmed tetraquark states through QCD sum rules. Making the development
of calculation techniques to fourfold heavy hadronic systems, four different
configuration currents with $0^{+}$ are considered and vacuum condensates up to
dimension $6$ are included in the operator product expansion (OPE). Finally,
mass values acquired for $0^{+}$ $cc\bar{c}\bar{c}$ tetraquark states agree
well with the experimental data of the broad structure, which supports that it
could be a $0^{+}$ fully-charmed tetraquark state.
|
http://arxiv.org/abs/2010.07719v1
|
2010.07719
|
2020-10-15
|
cybersecurity
|
0-Gaps on 3D Digital Curves
|
In Digital Geometry, gaps are some basic portion of a digital object that a discrete ray can cross without intersecting any voxel of the object itself. Such a notion is quite important in combinatorial image analysis and it is strictly connected with some applications in fields as CAD and Computer graphics. In this paper we prove that the number of $0$-gaps of a $3$D digital curve can be expressed as a linear combination of the number of its $i$-cells (with $i = 0, \ldots, 3$).
|
https://arxiv.org/abs/2109.13341v1
|
2109.13341
|
2021-09-16
|
cybersecurity
|
0-Hecke Modules, Domino Tableaux, and Type-$B$ Quasisymmetric Functions
|
We extend the notion of ascent-compatibility from symmetric groups to all Coxeter groups, thereby providing a type-independent framework for constructing families of modules of $0$-Hecke algebras. We apply this framework in type $B$ to give representation-theoretic interpretations of a number of noteworthy families of type-$B$ quasisymmetric functions. Next, we construct modules of the type-$B$ $0$-Hecke algebra corresponding to type-$B$ analogues of Schur functions and introduce a type-$B$ analogue of Schur $Q$-functions; we prove that these shifted domino functions expand positively in the type-$B$ peak functions. We define a type-$B$ analogue of the $0$-Hecke--Clifford algebra, and we use this to provide representation-theoretic interpretations for both the type-$B$ peak functions and the shifted domino functions. We consider the modules of this algebra induced from type-$B$ $0$-Hecke modules constructed via ascent-compatibility and prove a general formula, in terms of type-$B$ peak functions, for the type-$B$ quasisymmetric characteristics of the restrictions of these modules.
|
https://arxiv.org/abs/2404.04961v1
|
2404.04961
|
2024-04-07
|
cybersecurity
|
0-Hecke modules for row-strict dual immaculate functions
|
We introduce a new basis of quasisymmetric functions, the row-strict dual immaculate functions. We construct a cyclic, indecomposable 0-Hecke algebra module for these functions. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution $\psi$ on the ring of quasisymmetric functions. We give an explicit description of the effect of $\psi$ on the associated 0-Hecke modules, via the poset induced by the 0-Hecke action on standard immaculate tableaux. This remarkable poset reveals other 0-Hecke submodules and quotient modules, often cyclic and indecomposable, notably for a row-strict analogue of the extended Schur functions studied in Assaf-Searles (2019). Like the dual immaculate function, the row-strict dual immaculate function is the generating function of a suitable set of tableaux, corresponding to a specific descent set. We give a complete combinatorial and representation-theoretic picture by constructing 0-Hecke modules for the remaining variations on descent sets, and showing that \emph{all} the possible variations for generating functions of tableaux occur as characteristics of the 0-Hecke modules determined by these descent sets.
|
https://arxiv.org/abs/2202.00708v3
|
2202.00708
|
2022-02-01
|
cybersecurity
|
0-MMS: Zero-Shot Multi-Motion Segmentation With A Monocular Event Camera
|
Segmentation of moving objects in dynamic scenes is a key process in scene understanding for navigation tasks. Classical cameras suffer from motion blur in such scenarios rendering them effete. On the contrary, event cameras, because of their high temporal resolution and lack of motion blur, are tailor-made for this problem. We present an approach for monocular multi-motion segmentation, which combines bottom-up feature tracking and top-down motion compensation into a unified pipeline, which is the first of its kind to our knowledge. Using the events within a time-interval, our method segments the scene into multiple motions by splitting and merging. We further speed up our method by using the concept of motion propagation and cluster keyslices. The approach was successfully evaluated on both challenging real-world and synthetic scenarios from the EV-IMO, EED, and MOD datasets and outperformed the state-of-the-art detection rate by 12\%, achieving a new state-of-the-art average detection rate of 81.06%, 94.2% and 82.35% on the aforementioned datasets. To enable further research and systematic evaluation of multi-motion segmentation, we present and open-source a new dataset/benchmark called MOD++, which includes challenging sequences and extensive data stratification in-terms of camera and object motion, velocity magnitudes, direction, and rotational speeds.
|
https://arxiv.org/abs/2006.06158v2
|
2006.06158
|
2020-06-11
|
cybersecurity
|
$[0,n]\cup \{ω\}$ is a spectrum of a non-disintegrated flat strongly minimal model complete theory in a language with finite signature
|
We build a new spectrum of recursive models (SRM(T)) of a strongly minimal theory. This theory is non-disintegrated, flat, model complete, and in a language with a finite signature.
|
https://arxiv.org/abs/1908.09387v2
|
1908.09387
|
2019-08-25
|
cybersecurity
|
$0\nu\beta\beta$ and $2\nu\beta\beta$ nuclear matrix elements in the interacting boson model with isospin restoration
|
We introduce a method for isospin restoration in the calculation of nuclear
matrix elements (NME) for $0\nu\beta\beta$ and $2\nu\beta\beta$ decay within
the framework of interacting boson model (IBM-2). With this method, we
calculate NME for all processes of interest in $0\nu\beta^-\beta^-$,
$2\nu\beta^-\beta^-$, and in $0\nu\beta^+\beta^+$, $0\nu\beta^+ EC^+$, $R0\nu
ECEC$, $2\nu\beta^+\beta^+$, $2\nu\beta^+EC$, and $2\nu ECEC$. With this
method, the Fermi (F) matrix elements for $2\nu\beta\beta$ vanish, and those
for $0\nu\beta\beta$ are considerably reduced.
|
http://arxiv.org/abs/1506.08530v1
|
1506.08530
|
2015-06-29
|
cybersecurity
|
$0\nu\beta\beta$ in left-right theories with Higgs doublets and gauge coupling unification
|
We consider a version of Left-Right Symmetric Model in which the scalar
sector consists of a Higgs bidoublet ($\Phi$) with $B-L=0$, Higgs doublets
($H_{L,R}$) with $B-L=1$ and a charged scalar ($\delta^+$) with $B-L=2$ leading
to radiatively generated Majorana masses for neutrinos and thereby, leads to
new physics contributions to neutrinoless double beta decay ($0\nu \beta
\beta$). We show that such a novel framework can be embedded in a non-SUSY
$SO(10)$ GUT leading to successful gauge coupling unification at around
$10^{16}$ GeV with the scale of left-right symmetry breaking around $10^{10}$
GeV. The model can also be extended to have left-right symmetry breaking at TeV
scale, enabling detection of $W_R, Z_R$ bosons in LHC and future collider
searches. In the context of neutrinoless double beta decay, this model can
saturate the present bound from GERDA and KamLAND-Zen experiments. Also, we
briefly explain how keV-MeV range RH neutrino arising from our model can
saturate various astrophysical and cosmological constraints and can be
considered as warm Dark Matter (DM) candidate to address various cosmological
issues. We also discuss on left-right theories with Higgs doublets without
having scalar bidoublet leading to fermion masses and mixings by inclusion of
vector like fermions.
|
http://arxiv.org/abs/1809.10577v2
|
1809.10577
|
2019-12-27
|
cybersecurity
|
$0\nu\beta\beta$ nuclear matrix elements, neutrino potentials and $\mathrm{SU}(4)$ symmetry
|
Intimate relation between the Gamow-Teller part of the matrix element
$M^{0\nu}_\mathrm{GT}$ and the $2\nu\beta\beta$ closure matrix element
$M^{2\nu}_\mathrm{cl}$ is explained and explored. If the corresponding radial
dependence $C^{2\nu}_\mathrm{cl}(r)$ would be known, $M^{0\nu}$ corresponding
to any mechanism responsible for the $0\nu\beta\beta$ decay can be obtained as
a simple integral. However, the $M^{2\nu}_\mathrm{cl}$ values sensitively
depend on the properties of higher lying $1^+$ states in the intermediate
odd-odd nuclei. We show that the $\beta^-$ and $\beta^+$ amplitudes of such
states typically have opposite relative signs, and their contributions reduce
severally the $M^{2\nu}_\mathrm{cl}$ values. Vanishing values of
$M^{2\nu}_\mathrm{cl}$ are signs of a partial restoration of the spin-isospin
$\mathrm{SU}(4)$ symmetry. We suggest that demanding that
$M^{2\nu}_\mathrm{cl}$ = 0 is a sensible way, within the method of the
Quasi-particle Random Phase Approximation (QRPA), of determining the amount of
renormalization of isoscalar particle-particle interaction strength
$g^{T=0}_{pp}$. Using such prescription, the matrix elements $M^{0\nu}$ are
evaluated; their values are not very different ($\le$ 20\%) from the usual QRPA
values when $g^{T=0}_{pp}$ is related to the known $2\nu\beta\beta$ half-lives.
|
http://arxiv.org/abs/1808.05016v1
|
1808.05016
|
2018-08-15
|
cybersecurity
|
0-Pierced Triangles within a Poisson Overlay
|
Let the Euclidean plane be simultaneously and independently endowed with a
Poisson point process and a Poisson line process, each of unit intensity.
Consider a triangle T whose vertices all belong to the point process. The
triangle is 0-pierced if no member of the line process intersects any side of
T. Our starting point is Ambartzumian's 1982 joint density for angles of T; our
exposition is elementary and raises several unanswered questions.
|
http://arxiv.org/abs/1804.01353v2
|
1804.01353
|
2019-04-24
|
cybersecurity
|
0-$\pi$ phase-controllable $thermal$ Josephson junction
|
Two superconductors coupled by a weak link support an equilibrium Josephson
electrical current which depends on the phase difference $\varphi$ between the
superconducting condensates [1]. Yet, when a temperature gradient is imposed
across the junction, the Josephson effect manifests itself through a coherent
component of the heat current that flows oppositely to the thermal gradient for
$ \varphi <\pi/2$ [2-4]. The direction of both the Josephson charge and heat
currents can be inverted by adding a $\pi$ shift to $\varphi$. In the static
electrical case, this effect was obtained in a few systems, e.g. via a
ferromagnetic coupling [5,6] or a non-equilibrium distribution in the weak link
[7]. These structures opened new possibilities for superconducting quantum
logic [6,8] and ultralow power superconducting computers [9]. Here, we report
the first experimental realization of a thermal Josephson junction whose phase
bias can be controlled from $0$ to $\pi$. This is obtained thanks to a
superconducting quantum interferometer that allows to fully control the
direction of the coherent energy transfer through the junction [10]. This
possibility, joined to the completely superconducting nature of our system,
provides temperature modulations with unprecedented amplitude of $\sim$ 100 mK
and transfer coefficients exceeding 1 K per flux quantum at 25 mK. Then, this
quantum structure represents a fundamental step towards the realization of
caloritronic logic components, such as thermal transistors, switches and memory
devices [10,11]. These elements, combined with heat interferometers [3,4,12]
and diodes [13,14], would complete the thermal conversion of the most important
phase-coherent electronic devices and benefit cryogenic microcircuits requiring
energy management, such as quantum computing architectures and radiation
sensors.
|
http://arxiv.org/abs/1607.02428v3
|
1607.02428
|
2016-12-15
|
cybersecurity
|
0-$\pi$ quantum transition in a carbon nanotube Josephson junction: universal phase dependence and orbital degeneracy
|
We investigate experimentally the supercurrent in a clean carbon nanotube
quantum dot, close to orbital degeneracy, connected to superconducting leads in
a regime of strong competition between local electronic correlations and
superconducting proximity effect. For an odd occupancy of the dot and
intermediate coupling to the reservoir, the Kondo effect can develop in the
normal state and screen the local magnetic moment of the dot. This leads to
singlet-doublet transitions that strongly affect the Josephson effect in a
single-level quantum dot: the sign of the supercurrent changes from positive to
negative (0 to $\pi$-junction). In the regime of strongest competition between
the Kondo effect and proximity effect, meaning that the Kondo temperature
equals the superconducting gap, the magnetic state of the dot undergoes a first
order quantum transition induced by the superconducting phase difference across
the junction. This is revealed experimentally by anharmonic current-phase
relations. In addition, the very specific electronic configuration of clean
carbon nanotubes, with two nearly orbitally degenerated states, leads to
different physics depending whether only one or both quasi-degenerate upper
levels of the dots participate to transport, which is determined by their
occupancy and relative widths. When the transport of Cooper pairs takes place
through only one of these levels, we find that the phase diagram of the
phase-dependent 0-$\pi$ transition is a universal characteristic of a
discontinuous level-crossing quantum transition at zero temperature. In the
case were two levels participate to transport, the nanotube Josephson current
exhibits a continuous 0-$\pi$ transition, independent of the superconducting
phase, revealing a different physical mechanism of the transition.
|
http://arxiv.org/abs/1601.03878v1
|
1601.03878
|
2016-01-15
|
cybersecurity
|
0-Pi quantum transition in a carbon nanotube Josephson junction: Universal phase dependence and orbital degeneracy
|
In a quantum dot hybrid superconducting junction, the behavior of the
supercurrent is dominated by Coulomb blockade physics, which determines the
magnetic state of the dot. In particular, in a single level quantum dot singly
occupied, the sign of the supercurrent can be reversed, giving rise to a
pi-junction. This 0-pi transition, corresponding to a singlet-doublet
transition, is then driven by the gate voltage or by the superconducting phase
in the case of strong competition between the superconducting proximity effect
and Kondo correlations. In a two-level quantum dot, such as a clean carbon
nanotube, 0-pi transitions exist as well but, because more cotunneling
processes are allowed, are not necessarily associated to a magnetic state
transition of the dot. In this proceeding, after a review of 0-pi transitions
in Josephson junctions, we present measurements of current-phase relation in a
clean carbon nanotube quantum dot, in the single and two-level regimes. In the
single level regime, close to orbital degeneracy and in a regime of strong
competition between local electronic correlations and superconducting proximity
effect, we find that the phase diagram of the phase-dependent transition is a
universal characteristic of a discontinuous level-crossing quantum transition
at zero temperature. In the case where the two levels are involved, the
nanotube Josephson current exhibits a continuous 0-pi transition, independent
of the superconducting phase, revealing a different physical mechanism of the
transition.
|
http://arxiv.org/abs/1712.08372v1
|
1712.08372
|
2017-12-22
|
cybersecurity
|
0ptical trapping with optical magnetic field and photonic Hall effect forces
|
Optical trapping is having ever-increasing impact in science $-$ particularly biophysics, photonics and most recently in quantum optomechanics $-$ owing to its superior capability for manipulating nanoscale structures and materials. However, essentially all experimental optical trapping studies in the optical dipole regime have, to date, been dominated by the interaction between a material's electric polarizability, $\alpha_{e}$, and the electric part of the incident electromagnetic field, and therefore described by electric field intensity gradient forces. Optical trapping based on optical magnetic light-matter interactions has not been experimentally addressed despite it's immediate extension of the boundaries of optical trapping research and applications. This paper addresses this long-standing deficiency through the realization of optical magnetic trapping of large index of refraction (i.e., Si) nanoparticles and also presents a formalism for quantitative understanding of the experimental findings. Our experimental optical trapping results require including optical magnetic polarizability, $\alpha_{m}$, and electric-magnetic scattering forces associated with the Photonic Hall effect that are qualitatively and quantitatively validated by Maxwell stress tensor calculations. Our findings bring new opportunities for nanoparticle manipulation, potentially relax the limitations Ashkin claimed based on the optical Earnshaw's theorem, motivate optical matter formation by optical magnetic interactions, and suggest new N-body effects and symmetry breaking to drive dynamics of optical matter systems.
|
https://arxiv.org/abs/2408.09707v1
|
2408.09707
|
2024-08-19
|
cybersecurity
|
0-rotatability of classes of rooted symmetric trees. Are rooted symmetric trees 0-rotatable?
|
A graceful labelling of a tree T = (V,E), where V is the set of vertices of the tree and E is its edge set, is a bijective function f from V to the set consisting of the numbers 0, 1, ... |E| inclusive, such that if edge uv is assigned the value |f(u)-f(v)| then the edge labels are distinct numbers of the set consisting of the numbers 1, 2, ..., |E| inclusive. A tree is said to be 0-roratable if for any of its vertices there is a graceful labelling that assigns the label 0 to that vertex. A rooted symmetric tree is a tree in which all vertices at the same level from root vertex have the same degree. It was known since 1979 that rooted symmetric trees are graceful and an algebraic definition of graceful labelling of this class of trees was found by the author. In this paper we prove that rooted symmetric trees with at most 3 levels (including root vertex) are 0-rotatable. We also prove that symmetric spider trees with leg length at most 3 and symmetric banana trees, both of which are classes of rooted symmetric trees with 4 levels, are 0-rotatable. Based on these results, we conjecture that all spiders are 0-rotatable and raise the more general question whether all symmetric rooted trees are 0-rotatable.
|
https://arxiv.org/abs/2312.16235v1
|
2312.16235
|
2023-12-25
|
cybersecurity
|
$0$-Shake Slice Implies Slice
|
Here, we prove that $0-$shake slice knots are slice.
|
https://arxiv.org/abs/2012.11176v2
|
2012.11176
|
2020-12-21
|
cybersecurity
|
0-Shake Slice Knots are Slice
|
A proof that $0-$shake slice knots are slice.
|
https://arxiv.org/abs/2104.00247v2
|
2104.00247
|
2021-04-01
|
cybersecurity
|
0-Step Capturability, Motion Decomposition and Global Feedback Control of the 3D Variable Height-Inverted Pendulum
|
One common method for stabilizing robots after a push is the Instantaneous Capture Point, however, this has the fundamental limitation of assuming constant height. Although there are several works for balancing bipedal robots including height variations in 2D, the amount of literature on 3D models is limited. There are optimization methods using variable Center of Pressure (CoP) and reaction force to the ground, although they do not provide the physical region where a robot can step and require a precomputation for the analysis. This work provides the necessary and sufficient conditions to maintain balance of the 3D Variable Height Inverted Pendulum (VHIP) with both, fixed and variable CoP. We also prove that the 3D VHIP with Fixed CoP is the same as its 2D version, and we generalize controllers working on the 2D VHIP to the 3D VHIP. We also show the generalization of the Divergent Component of Motion to the 3D VHIP and we provide an alternative motion decomposition for the analysis of height and CoP strategies independently. This allow us to generalize previous global feedback controllers done in the 2D VHIP to the 3D VHIP with a Variable CoP.
|
https://arxiv.org/abs/1912.06078v1
|
1912.06078
|
2019-12-12
|
cybersecurity
|
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