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Fully quantized training (FQT) accelerates the training of deep neural networks by quantizing the activations, weights, and gradients into lower precision. To explore the ultimate limit of FQT (the lowest achievable precision), we make a first attempt to 1-bit FQT. We provide a theoretical analysis of FQT based on Adam and SGD, revealing that the gradient variance influences the convergence of FQT. Building on these theoretical results, we introduce an Activation Gradient Pruning (AGP) strategy. The strategy leverages the heterogeneity of gradients by pruning less informative gradients and enhancing the numerical precision of remaining gradients to mitigate gradient variance. Additionally, we propose Sample Channel joint Quantization (SCQ), which utilizes different quantization strategies in the computation of weight gradients and activation gradients to ensure that the method is friendly to low-bitwidth hardware. Finally, we present a framework to deploy our algorithm. For fine-tuning VGGNet-16 and ResNet-18 on multiple datasets, our algorithm achieves an average accuracy improvement of approximately 6%, compared to per-sample quantization. Moreover, our training speedup can reach a maximum of 5.13x compared to full precision training.
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https://arxiv.org/abs/2408.14267v1
|
To train large models (like BERT and GPT-3) on hundreds of GPUs, communication has become a major bottleneck, especially on commodity systems with limited-bandwidth TCP network. On one side large batch-size optimization such as LAMB algorithm was proposed to reduce the frequency of communication. On the other side, communication compression algorithms such as 1-bit Adam help to reduce the volume of each communication. However, we find that simply using one of the techniques is not sufficient to solve the communication challenge, especially under low network bandwidth. Motivated by this we aim to combine the power of large-batch optimization and communication compression, but we find that existing compression strategies cannot be directly applied to LAMB due to its unique adaptive layerwise learning rates. To this end, we design a new communication-efficient algorithm, 1-bit LAMB, which introduces a novel way to support adaptive layerwise learning rates under compression. In addition, we introduce a new system implementation for compressed communication using the NCCL backend of PyTorch distributed, which improves both usability and performance. For BERT-Large pre-training task with batch sizes from 8K to 64K, our evaluations on up to 256 GPUs demonstrate that 1-bit LAMB with NCCL-based backend is able to achieve up to 4.6x communication volume reduction, up to 2.8x end-to-end time-wise speedup, and the same sample-wise convergence speed (and same fine-tuning task accuracy) compared to uncompressed LAMB.
|
https://arxiv.org/abs/2104.06069v2
|
We present a novel scheme allowing for 2D target localization using highly
quantized 1-bit measurements from a Frequency Modulated Continuous Wave (FMCW)
radar with two receiving antennas. Quantization of radar signals introduces
localization artifacts, we remove this limitation by inserting a dithering on
the unquantized observations. We then adapt the projected back projection
algorithm to estimate both the range and angle of targets from the dithered
quantized radar observations, with provably decaying reconstruction error when
the number of observations increases. Simulations are performed to highlight
the accuracy of the dithered scheme in noiseless conditions when compared to
the non-dithered and full 32-bit resolution under severe bit-rate reduction.
Finally, measurements are performed using a radar sensor to demonstrate the
effectiveness and performances of the proposed quantized dithered scheme in
real conditions.
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http://arxiv.org/abs/1806.05408v2
|
In this paper, we focus on the multiuser massive multiple-input single-output
(MISO) downlink with low-cost 1-bit digital-to-analog converters (DACs) for PSK
modulation, and propose a low-complexity refinement process that is applicable
to any existing 1-bit precoding approaches based on the constructive
interference (CI) formulation. With the decomposition of the signals along the
detection thresholds, we first formulate a simple symbol-scaling method as the
performance metric. The low-complexity refinement approach is subsequently
introduced, where we aim to improve the introduced symbol-scaling performance
metric by modifying the transmit signal on one antenna at a time. Numerical
results validate the effectiveness of the proposed refinement method on
existing approaches for massive MIMO with 1-bit DACs, and the performance
improvements are most significant for the low-complexity quantized zero-forcing
(ZF) method.
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http://arxiv.org/abs/1810.12039v1
|
The deployment of large-scale antenna arrays for cellular base stations (BSs), termed as `Massive MIMO', has been a key enabler for meeting the ever-increasing capacity requirement for 5G communication systems and beyond. Despite their promising performance, fully-digital massive MIMO systems require a vast amount of hardware components including radio frequency chains, power amplifiers, digital-to-analog converters (DACs), etc., resulting in a huge increase in terms of the total power consumption and hardware costs for cellular BSs. Towards both spectrally-efficient and energy-efficient massive MIMO deployment, a number of hardware limited architectures have been proposed, including hybrid analog-digital structures, constant-envelope transmission, and use of low-resolution DACs. In this paper, we overview the recent interest in improving the error-rate performance of massive MIMO systems deployed with 1-bit DACs through precoding at the symbol level. This line of research goes beyond traditional interference suppression or cancellation techniques by managing interference on a symbol-by-symbol basis. This provides unique opportunities for interference-aware precoding tailored for practical massive MIMO systems. Firstly, we characterize constructive interference (CI) and elaborate on how CI can benefit the 1-bit signal design by exploiting the traditionally undesired multi-user interference as well as the interference from imperfect hardware components. Subsequently, we overview several solutions for 1-bit signal design to illustrate the gains achievable by exploiting CI. Finally, we identify some challenges and future research directions for 1-bit massive MIMO systems that are yet to be explored.
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https://arxiv.org/abs/2007.13950v3
|
Due to challenging applications such as collaborative filtering, the matrix
completion problem has been widely studied in the past few years. Different
approaches rely on different structure assumptions on the matrix in hand. Here,
we focus on the completion of a (possibly) low-rank matrix with binary entries,
the so-called 1-bit matrix completion problem. Our approach relies on tools
from machine learning theory: empirical risk minimization and its convex
relaxations. We propose an algorithm to compute a variational approximation of
the pseudo-posterior. Thanks to the convex relaxation, the corresponding
minimization problem is bi-convex, and thus the method behaves well in
practice. We also study the performance of this variational approximation
through PAC-Bayesian learning bounds. On the contrary to previous works that
focused on upper bounds on the estimation error of M with various matrix norms,
we are able to derive from this analysis a PAC bound on the prediction error of
our algorithm.
We focus essentially on convex relaxation through the hinge loss, for which
we present the complete analysis, a complete simulation study and a test on the
MovieLens data set. However, we also discuss a variational approximation to
deal with the logistic loss.
|
http://arxiv.org/abs/1604.04191v1
|
We consider the problem of noisy 1-bit matrix completion under an exact rank
constraint on the true underlying matrix $M^*$. Instead of observing a subset
of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset
of noisy 1-bit (or binary) measurements generated according to a probabilistic
model. We consider constrained maximum likelihood estimation of $M^*$, under a
constraint on the entry-wise infinity-norm of $M^*$ and an exact rank
constraint. This is in contrast to previous work which has used convex
relaxations for the rank. We provide an upper bound on the matrix estimation
error under this model. Compared to the existing results, our bound has faster
convergence rate with matrix dimensions when the fraction of revealed 1-bit
observations is fixed, independent of the matrix dimensions. We also propose an
iterative algorithm for solving our nonconvex optimization with a certificate
of global optimality of the limiting point. This algorithm is based on low rank
factorization of $M^*$. We validate the method on synthetic and real data with
improved performance over existing methods.
|
http://arxiv.org/abs/1502.06689v1
|
Recent advances in large language models have led to specialized models excelling in specific domains, creating a need for efficient model merging techniques. While traditional merging approaches combine parameters into a single static model, they often compromise task-specific performance. However, task-specific routing methods maintain accuracy but introduce substantial storage overhead. We present \texttt{1bit}-Merging, a novel framework that integrates task-specific routing with 1-bit quantized task vectors to balance performance and storage efficiency. Our approach leverages the observation that different task-specific models store knowledge in distinct layers-chat models primarily in attention layers and math/code models in MLP layers-enabling targeted compression strategies. Through extensive experiments with LLaMA2 and Mistral model families across chat, mathematical reasoning, and code generation tasks, we demonstrate that \texttt{1bit}-Merging achieves comparable or superior performance to existing methods while significantly reducing storage requirements. Our framework offers a practical solution for combining specialized models while maintaining their individual strengths and addressing the storage challenges of current approaches.
|
https://arxiv.org/abs/2502.10743v1
|
This paper tackles the problem of single-user multiple-input multiple-output communication with 1-bit digital-to-analog and analog-to-digital converters. With the information-theoretic capacity as benchmark, the complementary strategies of beamforming and equiprobable signaling are contrasted in the regimes of operational interest, and the ensuing spectral efficiencies are characterized. Various canonical channel types are considered, with emphasis on line-of-sight settings under both spherical and planar wavefronts, respectively representative of short and long transmission ranges at mmWave and terahertz frequencies. In all cases, a judicious combination of beamforming and equiprobable signaling is shown to operate within a modest gap from capacity.
|
https://arxiv.org/abs/2109.04390v1
|
Optical Diffraction Neural Networks (DNNs), a subset of Optical Neural Networks (ONNs), show promise in mirroring the prowess of electronic networks. This study introduces the Hybrid Diffraction Neural Network (HDNN), a novel architecture that incorporates matrix multiplication into DNNs, synergizing the benefits of conventional ONNs with those of DNNs to surmount the modulation limitations inherent in optical diffraction neural networks. Utilizing a singular phase modulation layer and an amplitude modulation layer, the trained neural network demonstrated remarkable accuracies of 96.39% and 89% in digit recognition tasks in simulation and experiment, respectively. Additionally, we develop the Binning Design (BD) method, which effectively mitigates the constraints imposed by sampling intervals on diffraction units, substantially streamlining experimental procedures. Furthermore, we propose an on-chip HDNN that not only employs a beam-splitting phase modulation layer for enhanced integration level but also significantly relaxes device fabrication requirements, replacing metasurfaces with relief surfaces designed by 1-bit quantization. Besides, we conceptualized an all-optical HDNN-assisted lesion detection network, achieving detection outcomes that were 100% aligned with simulation predictions. This work not only advances the performance of DNNs but also streamlines the path towards industrial optical neural network production.
|
https://arxiv.org/abs/2404.07443v1
|
Recently we had reported commissioning of a prototype for pulsar observations at low radio frequencies (<100 MHz) using log-periodic dipole antennas (LPDAs) in the Gauribidanur Radio Observatory near Bangalore in India. The aforementioned system (GAuribidanur Pulsar System, GAPS) is currently being augmented to directly digitize the radio frequency signals from the individual antennas in the array. Our initial results using 1-bit raw voltage recording system indicates that such a back-end receiver offers distinct advantages like, (i) simultaneous observations of any set of desired directions in the sky with multiple offline beams and smaller data rate/volume, (ii) archival of the observed data with minimal resources for re-analysis in the future, either in the same or different set of directions in the sky.
|
https://arxiv.org/abs/2404.15031v1
|
In this paper, a proof-of-concept study of a $1$-bit wideband reconfigurable intelligent surface (RIS) comprising planar tightly coupled dipoles (PTCD) is presented. The developed RIS operates at subTHz frequencies and a $3$-dB gain bandwidth of $27.4\%$ with the center frequency at $102$ GHz is shown to be obtainable via full-wave electromagnetic simulations. The binary phase shift offered by each RIS unit element is enabled by changing the polarization of the reflected wave by $180^\circ$. The proposed PTCD-based RIS has a planar configuration with one dielectric layer bonded to a ground plane, and hence, it can be fabricated by using cost-effective printed circuit board (PCB) technology. We analytically calculate the response of the entire designed RIS and showcase that a good agreement between that result and equivalent full-wave simulations is obtained. To efficiently compute the $1$-bit RIS response for different pointing directions, thus, designing a directive beam codebook, we devise a fast approximate beamforming optimization approach, which is compared with time-consuming full-wave simulations. Finally, to prove our concept, we present several passive prototypes with frozen beams for the proposed $1$-bit wideband RIS.
|
https://arxiv.org/abs/2402.08445v1
|
We investigate the singular subspace of an inclusion of tracial von Neumann
algebras. The singular subspace is a canonical N-N subbimodule of L^{2}(M) and
it contains the quasinormalizer introduced by Popa, one-sided quasinormalizer
introduced by Fang-Gao-Smith, and wq-normalizer introduced in Galatan-Popa
(following upon work in Ioana-Peterson-Popa and Popa). We then obtain a weak
notion of regularity (called spectral regularity) by demanding that the
singular subspace of N in M generates M. By abstracting Voiculescu's original
proof of absence of Cartan subalgebras, we show that there can be no diffuse,
hyperfinite subalgebra of L(\FF_{n}) which is spectrally regular. Our
techniques are robust enough to repeat this process by transfinite induction
and rule out chains of spectrally regular inclusions of algebras starting from
a diffuse, hyperfinite algebra and ending in L(\FF_{n}). We use this to prove
some conjectures made by Galatan-Popa in their study of smooth cohomology of
II_{1}-factors. Our results may be regarded as a consistency check for the
possibility of existence of a "good" cohomology theory of II_{1}-factors.
Lastly, we deduce nonisomorphism results for crossed products of q-deformed
free group factors by Bogoliubov actions, as well as for the continuous core of
q-deformed Free Araki-Woods algebras. This extends work of
Houdayer-Shlyakhtenko as well as Shlyakhtenko.
|
http://arxiv.org/abs/1505.06682v5
|
This paper describes our system for the SemEval2022 task of matching dictionary glosses to word embeddings. We focus on the Reverse Dictionary Track of the competition, which maps multilingual glosses to reconstructed vector representations. More specifically, models convert the input of sentences to three types of embeddings: SGNS, Char, and Electra. We propose several experiments for applying neural network cells, general multilingual and multitask structures, and language-agnostic tricks to the task. We also provide comparisons over different types of word embeddings and ablation studies to suggest helpful strategies. Our initial transformer-based model achieves relatively low performance. However, trials on different retokenization methodologies indicate improved performance. Our proposed Elmobased monolingual model achieves the highest outcome, and its multitask, and multilingual varieties show competitive results as well.
|
https://arxiv.org/abs/2206.03702v1
|
In this paper, we present our approach and empirical observations for Cause-Effect Signal Span Detection -- Subtask 2 of Shared task 3~\cite{tan-etal-2022-event} at CASE 2022. The shared task aims to extract the cause, effect, and signal spans from a given causal sentence. We model the task as a reading comprehension (RC) problem and apply a token-level RC-based span prediction paradigm to the task as the baseline. We explore different training objectives to fine-tune the model, as well as data augmentation (DA) tricks based on the language model (LM) for performance improvement. Additionally, we propose an efficient beam-search post-processing strategy to due with the drawbacks of span detection to obtain a further performance gain. Our approach achieves an average $F_1$ score of 54.15 and ranks \textbf{$1^{st}$} in the CASE competition. Our code is available at \url{https://github.com/Gzhang-umich/1CademyTeamOfCASE}.
|
https://arxiv.org/abs/2210.17157v1
|
This paper details our participation in the Challenges and Applications of Automated Extraction of Socio-political Events from Text (CASE) workshop @ EMNLP 2022, where we take part in Subtask 1 of Shared Task 3. We approach the given task of event causality detection by proposing a self-training pipeline that follows a teacher-student classifier method. More specifically, we initially train a teacher model on the true, original task data, and use that teacher model to self-label data to be used in the training of a separate student model for the final task prediction. We test how restricting the number of positive or negative self-labeled examples in the self-training process affects classification performance. Our final results show that using self-training produces a comprehensive performance improvement across all models and self-labeled training sets tested within the task of event causality sequence classification. On top of that, we find that self-training performance did not diminish even when restricting either positive/negative examples used in training. Our code is be publicly available at https://github.com/Gzhang-umich/1CademyTeamOfCASE.
|
https://arxiv.org/abs/2211.02729v1
|
This work introduces a novel family of boundary conditions for AdS$_3$ General Relativity, constructed through a polynomial expansion in negative integer powers of the Brown-Henneaux central charge. The associated dynamics is governed by the Dym hierarchy of integrable equations. It is shown that the infinite set of Dym conserved charges generates an abelian asymptotic symmetry group. Additionally, these boundary conditions encompass black hole solutions, whose thermodynamic properties are examined.
|
https://arxiv.org/abs/2401.12338v2
|
In this paper, we classify 1-cocycles of the Witt algebra with coefficients in the tensor product of two arbitrary tensor density modules. In a special case, we recover a theorem originally established by Ng and Taft in \cite{NT}. Furthermore, by these 1-cocycles, we determine Lie bialgebra structures over certain infinite-dimensional Lie algebras containing the Witt algebra.
|
https://arxiv.org/abs/2406.12565v1
|
We develop a cohomological method to classify amalgams of groups. We
generalize this to simplicial amalgams in any concrete category. We compute the
non-commutative 1-cohomology for several examples of amalgams defined over
small simplices.
|
http://arxiv.org/abs/1509.04679v1
|
We discuss two approaches to a recent question of Loh: must a 3-colored
transitive tournament on $N$ vertices have a 1-color-\emph{avoiding} path of
vertex-length at least $N^{2/3}$? This question generalizes the
Erd\H{o}s--Szekeres theorem on monotone subsequences.
First, we define three canonical transformations on these tournaments called
Color, Record, and Dual. We use these to establish a reduction to special
tournaments with natural geometric and combinatorial properties. In many cases
(including all known tight examples), these tournaments have recursive Gallai
decompositions. Not all relevant tournaments have Gallai decompositions, but
those that do satisfy the desired $N^{2/3}$ bound by recent work of Wagner,
roughly analogous to earlier work of Fox, Grinshpun, and Pach on a similar
\emph{undirected} problem.
Second, we consider the related geometric problem of bounding
\emph{slice-increasing} sets $S\subseteq [n]^3$, which---under an additional
ordering hypothesis on $S$---was shown by Loh to be equivalent to the original
question. In particular, we establish a rigorous connection from a problem of
Szab\'o and Tardos, raise a stronger $L^2$-question on slice-counts, and
mention a surprising overlap with the joints problem.
|
http://arxiv.org/abs/1608.04153v2
|
The present paper contributes to the ongoing programme of quantification of isomorphic Banach space theory focusing on Pe{\l}czy\'nski's classical work on dual Banach spaces containing $L_{1}$ ($=L_{1}[0,1]$) and the Hagler--Stegall characterisation of dual spaces containing complemented copies of $L_{1}$. We prove the following quantitative version of the Hagler--Stegall theorem asserting that for a Banach space $X$ the following statements are equivalent: $\bullet$ $X$ contains almost isometric copies of $(\bigoplus_{n=1}^{\infty} \ell_{\infty}^{n})_{\ell_1}$, $\bullet$ for all $\varepsilon>0$, $X^{*}$ contains a $(1+\varepsilon)$-complemented, $(1+\varepsilon)$-isomorphic copy of $L_{1}$, $\bullet$ for all $\varepsilon>0$, $X^{*}$ contains a $(1+\varepsilon)$-complemented, $(1+\varepsilon)$-isomorphic copy of $C[0,1]^{*}$. Moreover, if $X$ is separable, one may add the following assertion: $\bullet$ for all $\varepsilon>0$, there exists a $(1+\varepsilon)$-quotient map $T\colon X\rightarrow C(\Delta)$ so that $T^{*}[C(\Delta)^{*}]$ is $(1+\varepsilon)$-complemented in $X^{*}$, where $\Delta$ is the Cantor set.
|
https://arxiv.org/abs/2108.03057v2
|
We first unify all notions of partial injectivity appearing in the literature
---(universal) separable injectivity, (universal) $\aleph$-injectivity --- in
the notion of $(\alpha, \beta)$-injectivity ($(\alpha,
\beta)_\lambda$-injectivity if the parameter $\lambda$ has to be specified).
Then, extend the notion of space of universal disposition to space of universal
$(\alpha, \beta)$-disposition. Finally, we characterize the $1$-complemented
subspaces of spaces of universal $(\alpha, \beta)$-disposition as precisely the
spaces $(\alpha, \beta)_1$-injective.
|
http://arxiv.org/abs/1708.03823v1
|
The model of incomplete cooperative games incorporates uncertainty into the classical model of cooperative games by considering a partial characteristic function. Thus the values for some of the coalitions are not known. The main focus of this paper is the class of 1-convex cooperative games under this framework. We are interested in two heavily intertwined questions. First, given an incomplete game, in which ways can we fill in the missing values to obtain a classical 1-convex game? Such complete games are called \emph{1-convex extensions}. For the class of minimal incomplete games (in which precisely the values of singletons and grand coalitions are known), we provide an answer in terms of a description of the set of 1-convex extensions. The description employs extreme points and extreme rays of the set. Second, how to determine in a rational, fair, and efficient way the payoffs of players based only on the known values of coalitions? Based on the description of the set of 1-convex extensions, we introduce generalisations of three solution concepts (values) for complete games, namely the $\tau$-value, the Shapley value and the nucleolus. We consider two variants where we compute the centre of gravity of either extreme games or of a combination of extreme games and extreme rays. We show that all of the generalised values coincide for minimal incomplete games which allows to introduce the \emph{average value}. For this value, we provide three different axiomatisations based on axiomatic characterisations of the $\tau$-value and the Shapley value for classical cooperative games. Finally, we turn our attention to \emph{incomplete games with defined upper vector}, asking the same questions and this time arriving to different conclusions. This provides a benchmark to test our tools and knowledge of the average value.
|
https://arxiv.org/abs/2107.04679v2
|
We prove results about 1-cycles on certain Fano varieties using techniques
that rely on rational curves. Firstly, we show that Fano weighted complete
intersections with index bigger than half their dimension have trivial first
Griffiths group. Secondly, we prove that the first Chow group of most $2$-Fano
weighted complete intersections, and of $2$-Fano conic-connected varieties in
$\mathbb{P}^n$ of high enough index (with $3$ obvious exceptions), are
generated by lines. Furthermore, if the Fano variety of lines is irreducible,
the first Chow group is isomorphic to $\mathbb{Z}$.
|
http://arxiv.org/abs/1711.09987v1
|
In this letter, we highlight the enhanced functionalization of the electronic and optical properties in the hybrid heterojunction of 1D Tellurene with 2D monolayer of Graphene and MoS2 in both lateral and vertical geometries, having potential applications in the field of photonics and energy harvesting. The structural geometries of the lateral and vertical assemblies are optimized with a comparative and systematic analysis of the energetics of the different positional placement of the 1D system with respect to the hexagonal 2D layer. The 1D/2D coupling of the electronic structure in this unique assembly enables the realization of the four different types of heterojunctions, viz. type I, type II, Z-scheme and Schottky type, with the band-alignments being entirely dependent upon the stacking geometry of 1D Tellurene with respect to the 2D monolayer. With the static and time-dependent first-principles calculations, we indicate the potential applications of these hybrid systems in broadband photo detection and absorption, covering the full range of Infra-red to visible (IR-Vis) spectrum and in green energy harvesting with an effective separation and migration of photo-generated charge carriers.
|
https://arxiv.org/abs/2203.09124v2
|
An important problem in terrain analysis is modeling how water flows across a
terrain creating floods by forming channels and filling depressions. In this
paper we study a number of \emph{flow-query} related problems: Given a terrain
$\Sigma$, represented as a triangulated $xy$-monotone surface with $n$
vertices, a rain distribution $R$ which may vary over time, determine how much
water is flowing over a given edge as a function of time. We develop
internal-memory as well as I/O-efficient algorithms for flow queries.
This paper contains four main results:
(i) We present an internal-memory algorithm that preprocesses $\Sigma$ into a
linear-size data structure that for a (possibly time varying) rain distribution
$R$ can return the flow-rate functions of all edges of $\Sigma$ in $O(\rho
k+|\phi| \log n)$ time, where $\rho$ is the number of sinks in $\Sigma$, $k$ is
the number of times the rain distribution changes, and $|\phi|$ is the total
complexity of the flow-rate functions that have non-zero values;
(ii) We also present an I/O-efficient algorithm for preprocessing $\Sigma$
into a linear-size data structure so that for a rain distribution $R$, it can
compute the flow-rate function of all edges using $O(\text{Sort}(|\phi|))$ I/Os
and $O(|\phi| \log |\phi|)$ internal computation time.
(iii) $\Sigma$ can be preprocessed into a linear-size data structure so that
for a given rain distribution $R$, the flow-rate function of an edge $(q,r) \in
\Sigma$ under the single-flow direction (SFD) model can be computed more
efficiently.
(iv) We present an algorithm for computing the two-dimensional channel along
which water flows using Manning's equation; a widely used empirical equation
that relates the flow-rate of water in an open channel to the geometry of the
channel along with the height of water in the channel.
|
http://arxiv.org/abs/2009.08014v1
|
Classically, anisotropic surface wave tomography is treated as an optimisation problem where it proceeds through a linearised two-step approach. It involves the construction of 2D group or phase velocity maps for each considered period, followed by the inversion of local dispersion curves inferred from these maps for 1D depth-functions of the elastic parameters. Here, we cast the second step into a fully Bayesian probability framework. Solutions to the inverse problem are thus an ensemble of model parameters (\textit{i.e.} 1D elastic structures) distributed according to a posterior probability density function and their corresponding uncertainty limits. The method is applied to azimuthally-varying synthetic surface wave dispersion curves generated by a 3D-deforming upper mantle. We show that such a procedure captures essential features of the upper mantle structure. The robustness of these features however strongly depend on the wavelength of the wavefield considered and the choice of the model parameterisation. Additional information should therefore be incorporated to regularise the problem such as the imposition of petrological constraints to match the geodynamic predictions.
|
https://arxiv.org/abs/2012.03915v1
|
The atmospheric composition of exoplanets with masses between 2 and 10 M$_\oplus$ is poorly understood. In that regard, the sub-Neptune K2-18b, which is subject to Earth-like stellar irradiation, offers a valuable opportunity for the characterisation of such atmospheres. Previous analyses of its transmission spectrum from the Kepler, Hubble (HST), and Spitzer space telescopes data using both retrieval algorithms and forward-modelling suggest the presence of H$_2$O and an H$_2$--He atmosphere, but have not detected other gases, such as CH$_4$. We present simulations of the atmosphere of K2-18 b using Exo-REM, our self-consistent 1D radiative-equilibrium model, using a large grid of atmospheric parameters to infer constraints on its chemical composition. We show that our simulations favour atmospheric metallicities between 40 and 500 times solar and indicate, in some cases, the formation of H$_2$O-ice clouds, but not liquid H$_2$O clouds. We also confirm the findings of our previous study, which showed that CH$_4$ absorption features nominally dominate the transmission spectrum in the HST spectral range. We compare our results with results from retrieval algorithms and find that the H$_2$O-dominated spectrum interpretation is either due to the omission of CH$_4$ absorptions or a strong overfitting of the data. Finally, we investigated different scenarios that would allow for a CH$_4$-depleted atmosphere. We were able to fit the data to those scenarios, finding, however, that it is very unlikely for K2-18b to have a high internal temperature. A low C/O ratio ($\approx$ 0.01--0.1) allows for H$_2$O to dominate the transmission spectrum and can fit the data but so far, this set-up lacks a physical explanation. Simulations with a C/O ratio $<$ 0.01 are not able to fit the data satisfactorily.
|
https://arxiv.org/abs/2011.10459v1
|
Multi-step stock index forecasting is vital in finance for informed decision-making. Current forecasting methods on this task frequently produce unsatisfactory results due to the inherent data randomness and instability, thereby underscoring the demand for advanced forecasting models. Given the superiority of capsule network (CapsNet) over CNN in various forecasting and classification tasks, this study investigates the potential of integrating a 1D CapsNet with an LSTM network for multi-step stock index forecasting. To this end, a hybrid 1D-CapsNet-LSTM model is introduced, which utilizes a 1D CapsNet to generate high-level capsules from sequential data and a LSTM network to capture temporal dependencies. To maintain stochastic dependencies over different forecasting horizons, a multi-input multi-output (MIMO) strategy is employed. The model's performance is evaluated on real-world stock market indices, including S&P 500, DJIA, IXIC, and NYSE, and compared to baseline models, including LSTM, RNN, and CNN-LSTM, using metrics such as RMSE, MAE, MAPE, and TIC. The proposed 1D-CapsNet-LSTM model consistently outperforms baseline models in two key aspects. It exhibits significant reductions in forecasting errors compared to baseline models. Furthermore, it displays a slower rate of error increase with lengthening forecast horizons, indicating increased robustness for multi-step forecasting tasks.
|
https://arxiv.org/abs/2310.02090v2
|
This paper proposes a 1D residual convolutional neural network (CNN) architecture for music genre classification and compares it with other recent 1D CNN architectures. The 1D CNNs learn a representation and a discriminant directly from the raw audio signal. Several convolutional layers capture the time-frequency characteristics of the audio signal and learn various filters relevant to the music genre recognition task. The proposed approach splits the audio signal into overlapped segments using a sliding window to comply with the fixed-length input constraint of the 1D CNNs. As a result, music genre classification can be carried out on a single audio segment or on the aggregation of the predictions on several audio segments, which improves the final accuracy. The performance of the proposed 1D residual CNN is assessed on a public dataset of 1,000 audio clips. The experimental results have shown that it achieves 80.93% of mean accuracy in classifying music genres and outperforms other 1D CNN architectures.
|
https://arxiv.org/abs/2105.07302v1
|
This paper presents an alternate representation framework to commonly used time-frequency representation for acoustic scene classification (ASC). A raw audio signal is represented using a pre-trained convolutional neural network (CNN) using its various intermediate layers. The study assumes that the representations obtained from the intermediate layers lie in low-dimensions intrinsically. To obtain low-dimensional embeddings, principal component analysis is performed, and the study analyzes that only a few principal components are significant. However, the appropriate number of significant components are not known. To address this, an automatic dictionary learning framework is utilized that approximates the underlying subspace. Further, the low-dimensional embeddings are aggregated in a late-fusion manner in the ensemble framework to incorporate hierarchical information learned at various intermediate layers. The experimental evaluation is performed on publicly available DCASE 2017 and 2018 ASC datasets on a pre-trained 1-D CNN, SoundNet. Empirically, it is observed that deeper layers show more compression ratio than others. At 70% compression ratio across different datasets, the performance is similar to that obtained without performing any dimensionality reduction. The proposed framework outperforms the time-frequency representation based methods.
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https://arxiv.org/abs/2204.00555v1
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Intrusion detection system (IDS) plays an essential role in computer networks protecting computing resources and data from outside attacks. Recent IDS faces challenges improving flexibility and efficiency of the IDS for unexpected and unpredictable attacks. Deep neural network (DNN) is considered popularly for complex systems to abstract features and learn as a machine learning technique. In this paper, we propose a deep learning approach for developing the efficient and flexible IDS using one-dimensional Convolutional Neural Network (1D-CNN). Two-dimensional CNN methods have shown remarkable performance in detecting objects of images in computer vision area. Meanwhile, the 1D-CNN can be used for supervised learning on time-series data. We establish a machine learning model based on the 1D-CNN by serializing Transmission Control Protocol/Internet Protocol (TCP/IP) packets in a predetermined time range as an invasion Internet traffic model for the IDS, where normal and abnormal network traffics are categorized and labeled for supervised learning in the 1D-CNN. We evaluated our model on UNSW\_NB15 IDS dataset to show the effectiveness of our method. For comparison study in performance, machine learning-based Random Forest (RF) and Support Vector Machine (SVM) models in addition to the 1D-CNN with various network parameters and architecture are exploited. In each experiment, the models are run up to 200 epochs with a learning rate in 0.0001 on imbalanced and balanced data. 1D-CNN and its variant architectures have outperformed compared to the classical machine learning classifiers. This is mainly due to the reason that CNN has the capability to extract high-level feature representations that represent the abstract form of low-level feature sets of network traffic connections.
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https://arxiv.org/abs/2003.00476v2
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Online signature verification plays a pivotal role in security infrastructures. However, conventional online signature verification models pose significant risks to data privacy, especially during training processes. To mitigate these concerns, we propose a novel federated learning framework that leverages 1-D Convolutional Neural Networks (CNN) for online signature verification. Furthermore, our experiments demonstrate the effectiveness of our framework regarding 1-D CNN and federated learning. Particularly, the experiment results highlight that our framework 1) minimizes local computational resources; 2) enhances transfer effects with substantial initialization data; 3) presents remarkable scalability. The centralized 1-D CNN model achieves an Equal Error Rate (EER) of 3.33% and an accuracy of 96.25%. Meanwhile, configurations with 2, 5, and 10 agents yield EERs of 5.42%, 5.83%, and 5.63%, along with accuracies of 95.21%, 94.17%, and 94.06%, respectively.
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https://arxiv.org/abs/2406.06597v1
|
The demand of the Internet of Things (IoT) has witnessed exponential growth. These progresses are made possible by the technological advancements in artificial intelligence, cloud computing, and edge computing. However, these advancements exhibit multiple challenges, including cyber threats, security and privacy concerns, and the risk of potential financial losses. For this reason, this study developed a computationally inexpensive one-dimensional convolutional neural network (1DCNN) algorithm for cyber-attack classification. The proposed study achieved an accuracy of 99.90% to classify nine cyber-attacks. Multiple other performance metrices have been evaluated to validate the efficacy of the proposed scheme. In addition, comparison has been done with existing state-of-the-art schemes. The findings of the proposed study can significantly contribute to the development of secure intrusion detection for IIoT systems.
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https://arxiv.org/abs/2409.08529v1
|
Indonesia ranks fourth globally in the number of deaf cases. Individuals with hearing impairments often find communication challenging, necessitating the use of sign language. However, there are limited public services that offer such inclusivity. On the other hand, advancements in artificial intelligence (AI) present promising solutions to overcome communication barriers faced by the deaf. This study aims to explore the application of AI in developing models for a simplified sign language translation app and dictionary, designed for integration into public service facilities, to facilitate communication for individuals with hearing impairments, thereby enhancing inclusivity in public services. The researchers compared the performance of LSTM and 1D CNN + Transformer (1DCNNTrans) models for sign language recognition. Through rigorous testing and validation, it was found that the LSTM model achieved an accuracy of 94.67%, while the 1DCNNTrans model achieved an accuracy of 96.12%. Model performance evaluation indicated that although the LSTM exhibited lower inference latency, it showed weaknesses in classifying classes with similar keypoints. In contrast, the 1DCNNTrans model demonstrated greater stability and higher F1 scores for classes with varying levels of complexity compared to the LSTM model. Both models showed excellent performance, exceeding 90% validation accuracy and demonstrating rapid classification of 50 sign language gestures.
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https://arxiv.org/abs/2409.01975v1
|
Topological materials confined in one-dimension (1D) can transform computing technologies, such as 1D topological semimetals for nanoscale interconnects and 1D topological superconductors for fault-tolerant quantum computing. As such, understanding crystallization of 1D-confined topological materials is critical. Here, we demonstrate 1D-confined crystallization routes during template-assisted nanowire synthesis where we observe diameter-dependent phase selectivity for topological metal tungsten phosphides. A phase bifurcation occurs to produce tungsten monophosphide and tungsten diphosphide at the cross-over nanowire diameter of ~ 35 nm. Four-dimensional scanning transmission electron microscopy was used to identify the two phases and to map crystallographic orientations of grains at a few nm resolution. The 1D-confined phase selectivity is attributed to the minimization of the total surface energy, which depends on the nanowire diameter and chemical potentials of precursors. Theoretical calculations were carried out to construct the diameter-dependent phase diagram, which agrees with experimental observations. Our find-ings suggest a new crystallization route to stabilize topological materials confined in 1D.
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https://arxiv.org/abs/2309.11314v1
|
We study conformal field theory in $d=1$ space-time dimensions. We derive a dispersion relation for the 4-point correlation function of identical bosons and fermions, in terms of the double discontinuity. This extends the conformal dispersion relation of arXiv:1910.12123, which holds for CFTs in dimensions $d\geq 2$, to the case of $d=1$. The dispersion relation is obtained by combining the Lorentzian inversion formula with the operator product expansion of the 4-point correlator. We perform checks of the dispersion relation using correlators of generalised free fields and derive an integral relation between the kernel of the dispersion relation and that of the Lorentzian inversion formula. Finally, for $1$-$d$ holographic conformal theories, we analytically compute scalar Witten diagrams in $AdS_2$ at tree-level and $1$-loop.
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https://arxiv.org/abs/2408.09870v2
|
It is well known that a systematic analysis of the pupil size variations, recorded by means of an eye-tracker, is a rich source of information about a subject's arousal and cognitive state. Current methods for pupil analysis are limited to descriptive statistics, struggle in handling the wide inter-subjects variability and must be coupled with a long series of pre-processing signal operations. In this we present a data-driven approach in which 1-D Convolutional Neural Networks are applied directly to the raw pupil size data. To test its effectiveness, we apply our method in a binary classification task with two different groups of subjects: a group of elderly patients with Parkinson disease (PDs), a condition in which pupil abnormalities have been extensively reported, and a group of healthy adults subjects (HCs). Long-range registration (10 minutes) of the pupil size were collected in scotopic conditions (complete darkness, 0 lux). 1-D convolutional neural network models are trained for classification of short-range sequences (10 to 60 seconds of registration). The model provides prediction with high average accuracy on a hold out test set. Dataset and codes are released for reproducibility and benchmarking purposes.
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https://arxiv.org/abs/2002.02383v2
|
Recently, convolutional neural networks (CNNs) have achieved excellent
performances in many computer vision tasks. Specifically, for hyperspectral
images (HSIs) classification, CNNs often require very complex structure due to
the high dimension of HSIs. The complex structure of CNNs results in
prohibitive training efforts. Moreover, the common situation in HSIs
classification task is the lack of labeled samples, which results in accuracy
deterioration of CNNs. In this work, we develop an easy-to-implement capsule
network to alleviate the aforementioned problems, i.e., 1D-convolution capsule
network (1D-ConvCapsNet). Firstly, 1D-ConvCapsNet separately extracts spatial
and spectral information on spatial and spectral domains, which is more
lightweight than 3D-convolution due to fewer parameters. Secondly,
1D-ConvCapsNet utilizes the capsule-wise constraint window method to reduce
parameter amount and computational complexity of conventional capsule network.
Finally, 1D-ConvCapsNet obtains accurate predictions with respect to input
samples via dynamic routing. The effectiveness of the 1D-ConvCapsNet is
verified by three representative HSI datasets. Experimental results demonstrate
that 1D-ConvCapsNet is superior to state-of-the-art methods in both the
accuracy and training effort.
|
http://arxiv.org/abs/1903.09834v1
|
This paper presents a 1-D convolutional graph neural network for fault detection in microgrids. The combination of 1-D convolutional neural networks (1D-CNN) and graph convolutional networks (GCN) helps extract both spatial-temporal correlations from the voltage measurements in microgrids. The fault detection scheme includes fault event detection, fault type and phase classification, and fault location. There are five neural network model training to handle these tasks. Transfer learning and fine-tuning are applied to reduce training efforts. The combined recurrent graph convolutional neural networks (1D-CGCN) is compared with the traditional ANN structure on the Potsdam 13-bus microgrid dataset. The achievable accuracy of 99.27%, 98.1%, 98.75%, and 95.6% for fault detection, fault type classification, fault phase identification, and fault location respectively.
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https://arxiv.org/abs/2211.02930v1
|
Sleep arousals transition the depth of sleep to a more superficial stage. The
occurrence of such events is often considered as a protective mechanism to
alert the body of harmful stimuli. Thus, accurate sleep arousal detection can
lead to an enhanced understanding of the underlying causes and influencing the
assessment of sleep quality. Previous studies and guidelines have suggested
that sleep arousals are linked mainly to abrupt frequency shifts in EEG
signals, but the proposed rules are shown to be insufficient for a
comprehensive characterization of arousals. This study investigates the
application of five recent convolutional neural networks (CNNs) for sleep
arousal detection and performs comparative evaluations to determine the best
model for this task. The investigated state-of-the-art CNN models have
originally been designed for image or speech processing. A detailed set of
evaluations is performed on the benchmark dataset provided by
PhysioNet/Computing in Cardiology Challenge 2018, and the results show that the
best 1D CNN model has achieved an average of 0.31 and 0.84 for the area under
the precision-recall and area under the ROC curves, respectively.
|
http://arxiv.org/abs/1903.01552v1
|
During the last decade, Convolutional Neural Networks (CNNs) have become the de facto standard for various Computer Vision and Machine Learning operations. CNNs are feed-forward Artificial Neural Networks (ANNs) with alternating convolutional and subsampling layers. Deep 2D CNNs with many hidden layers and millions of parameters have the ability to learn complex objects and patterns providing that they can be trained on a massive size visual database with ground-truth labels. With a proper training, this unique ability makes them the primary tool for various engineering applications for 2D signals such as images and video frames. Yet, this may not be a viable option in numerous applications over 1D signals especially when the training data is scarce or application-specific. To address this issue, 1D CNNs have recently been proposed and immediately achieved the state-of-the-art performance levels in several applications such as personalized biomedical data classification and early diagnosis, structural health monitoring, anomaly detection and identification in power electronics and motor-fault detection. Another major advantage is that a real-time and low-cost hardware implementation is feasible due to the simple and compact configuration of 1D CNNs that perform only 1D convolutions (scalar multiplications and additions). This paper presents a comprehensive review of the general architecture and principals of 1D CNNs along with their major engineering applications, especially focused on the recent progress in this field. Their state-of-the-art performance is highlighted concluding with their unique properties. The benchmark datasets and the principal 1D CNN software used in those applications are also publically shared in a dedicated website.
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https://arxiv.org/abs/1905.03554v1
|
Machine and deep learning algorithms have increasingly been applied to solve problems in various areas of knowledge. Among these areas, Chemometrics has been benefited from the application of these algorithms in spectral data analysis. Commonly, algorithms such as Support Vector Machines and Partial Least Squares are applied to spectral datasets to perform classification and regression tasks. In this paper, we present a 1D convolutional neural networks (1D-CNN) to evaluate the effectiveness on spectral data obtained from spectroscopy. In most cases, the spectrum signals are noisy and present overlap among classes. Firstly, we perform extensive experiments including 1D-CNN compared to machine learning algorithms and standard algorithms used in Chemometrics on spectral data classification for the most known datasets available in the literature. Next, spectral samples of the SARS-COV2 virus, which causes the COVID-19, have recently been collected via spectroscopy was used as a case study. Experimental results indicate superior performance of 1D-CNN over machine learning algorithms and standard algorithms, obtaining an average accuracy of 96.5%, specificity of 98%, and sensitivity of 94%. The promissing obtained results indicate the feasibility to use 1D-CNN in automated systems to diagnose COVID-19 and other viral diseases in the future.
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https://arxiv.org/abs/2301.10746v1
|
This paper presents an efficient deep neural network model for diagnosing Parkinson's disease from gait. More specifically, we introduce a hybrid ConvNet-Transformer architecture to accurately diagnose the disease by detecting the severity stage. The proposed architecture exploits the strengths of both Convolutional Neural Networks and Transformers in a single end-to-end model, where the former is able to extract relevant local features from Vertical Ground Reaction Force (VGRF) signal, while the latter allows to capture long-term spatio-temporal dependencies in data. In this manner, our hybrid architecture achieves an improved performance compared to using either models individually. Our experimental results show that our approach is effective for detecting the different stages of Parkinson's disease from gait data, with a final accuracy of 88%, outperforming other state-of-the-art AI methods on the Physionet gait dataset. Moreover, our method can be generalized and adapted for other classification problems to jointly address the feature relevance and spatio-temporal dependency problems in 1D signals. Our source code and pre-trained models are publicly available at https://github.com/SafwenNaimi/1D-Convolutional-transformer-for-Parkinson-disease-diagnosis-from-gait.
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https://arxiv.org/abs/2311.03177v1
|
We apply the supervariable approach to derive the proper quantum Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries for the 1D diffeomorphism invariant model of a free scalar relativistic particle by exploiting the infinitesimal classical reparameterization (i.e. 1D diffeomorphism) symmetry of this theory. We derive the conserved and off-shell nilpotent (anti-)BRST charges and prove their absolute anticommutativity property by using the virtues of Curci-Ferrari (CF)-type restriction of our present theory. We establish the sanctity of the existence of CF-type restriction (i) by considering the (anti-)BRST symmetry transformations of the coupled (but equivalent) Lagrangians, and (ii) by proving the symmetry invariance of the Lagrangians within the framework of supervariable approach. We capture the nilpotency and absolute anticommutativity of the conserved (anti-)BRST charges within the framework of (anti-)chiral supervariable approach (ACSA) to BRST formalism. One of the novel observations of our present endeavor is the derivation of CF-type restriction by using the modified Bonora-Tonin (BT) supervariable approach (while deriving the (anti-)BRST symmetries for the target spacetime and/or momenta variables) and by symmetry considerations of the Lagrangians of the theory. The rest of the (anti-)BRST symmetries, for the other variables, are derived by using the newly proposed ACSA. We also demonstrate the existence of CF-type restriction in the proof of absolute anticommutativity of the (anti-)BRST charges.
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https://arxiv.org/abs/1912.12909v2
|
This study proposed a novel robotic gripper that can achieve grasping and infinite wrist twisting motions using a single actuator. The gripper is equipped with a differential gear mechanism that allows switching between the grasping and twisting motions according to the magnitude of the tip force applied to the finger. The grasping motion is activated when the tip force is below a set value, and the wrist twisting motion is activated when the tip force exceeds this value. "Twist grasping," a special grasping mode that allows the wrapping of a flexible thin object around the fingers of the gripper, can be achieved by the twisting motion. Twist grasping is effective for handling objects with flexible thin parts, such as laminated packaging pouches, that are difficult to grasp using conventional antipodal grasping. In this study, the gripper design is presented, and twist grasping is analyzed. The gripper performance is experimentally validated.
|
https://arxiv.org/abs/2211.05303v1
|
Although Majorana platforms are promising avenues to realizing topological
quantum computing, they are still susceptible to errors from thermal noise and
other sources. We show that the error rate of Majorana qubits can be
drastically reduced using a 1D repetition code. The success of the code is due
the imbalance between the phase error rate and the flip error rate. We
demonstrate how a repetition code can be naturally constructed from segments of
Majorana nanowires. We find the optimal lifetime may be extended from a
millisecond to over one second.
|
http://arxiv.org/abs/1906.01658v3
|
Graphene is the first truly two-dimensional (2D) material, possessing a cone-like energy spectrum near the Fermi energy and treated as a gapless semiconductor. Its unique properties trigger researchers to find more applications of it, such as high carrier mobility at room temperature, superior thermoconductivity, high modulus and tensile strength, high transparency, and anomalous quantum Hall effect. However, the gapless feature limits the development of graphene nanoelectronics. Making one-dimensional (1D) strips of graphene (i.e., graphene nanoribbons (GNRs)) could be one of the most promising approaches to modulating the electronic and optical properties of graphene. The electronic and optical properties have been theoretically predicted and experimentally verified highly sensitive to the edge and width. The tunable electronic and optical properties further imply the possibilities of GNR application. Recently, the dangling bond problem is under consideration in the GNR system. Various passivation at the ribbon edge might change the physical properties. In this work, some passivation conditions are studied, such as alkalization and hydrogenation.
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https://arxiv.org/abs/2206.11162v1
|
Materials with flat bands can serve as a promising platform to investigate strongly interacting phenomena. However, experimental realization of ideal flat bands is mostly limited to artificial lattices or moir\'e systems. Here we report a general way to construct one-dimensional (1D) flat bands in phosphorene nanoribbons (PNRs) with pentagonal nature: penta-hexa-PNRs and penta-dodeca-PNRs, wherein the corresponding 1D flat bands are directly verified by using angle-resolved photoemission spectroscopy. We confirm that the observed 1D flat bands originate from the electronic 1D zigzag and Lieb lattices, respectively, as revealed by the combination of bond-resolved scanning tunneling microscopy, scanning tunneling spectroscopy, tight-binding models, and first-principles calculations. Our study demonstrates a general way to construct 1D flat bands in 1D solid materials system, which provides a robust platform to explore strongly interacting phases of matter.
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https://arxiv.org/abs/2407.08353v2
|
A limited number of 2D and 3D materials under a constant pressure contract in volume upon heating isobarically; this anomalous phenomenon is known as the negative thermal expansion (NTE). In this paper, the NTE anomaly is observed in 1D fluids of classical particles interacting pairwisely with two competing length scales: the hard-core diameter $a$ and the finite range $a'>a$ of a soft repulsive potential component. If $a'\le 2a$, the pair interactions reduce themselves to nearest neighbours which permits a closed-form solution of thermodynamics in the isothermal-isobaric ensemble characterized by temperature $T$ and pressure $p$. We focus on the equation of state (EoS) which relates the average distance between particles (reciprocal density) $l$ to $T$ and $p\ge 0$. The EoS is expressible explicitly in terms of elementary or special functions for specific, already known and new, cases like the square shoulder, the linear and quadratic ramps as well as certain types of logarithmic interaction potentials. The emphasis is put on low-$T$ anomalies of the EoS. Firstly, the equidistant ground state as the function of the pressure can exhibit, at some ``compressibility'' pressures, a jump in chain spacing from $a'$ to $a$. Secondly, the analytical structure of the low-$T$ expansion of $l(T,p)$ depends on ranges of $p$-values. Thirdly, the presence of the NTE anomaly depends very much on the shape of the core-softened potential.
|
https://arxiv.org/abs/2503.11310v1
|
Recently, heatmap regression methods based on 1D landmark representations have shown prominent performance on locating facial landmarks. However, previous methods ignored to make deep explorations on the good potentials of 1D landmark representations for sequential and structural modeling of multiple landmarks to track facial landmarks. To address this limitation, we propose a Transformer architecture, namely 1DFormer, which learns informative 1D landmark representations by capturing the dynamic and the geometric patterns of landmarks via token communications in both temporal and spatial dimensions for facial landmark tracking. For temporal modeling, we propose a recurrent token mixing mechanism, an axis-landmark-positional embedding mechanism, as well as a confidence-enhanced multi-head attention mechanism to adaptively and robustly embed long-term landmark dynamics into their 1D representations; for structure modeling, we design intra-group and inter-group structure modeling mechanisms to encode the component-level as well as global-level facial structure patterns as a refinement for the 1D representations of landmarks through token communications in the spatial dimension via 1D convolutional layers. Experimental results on the 300VW and the TF databases show that 1DFormer successfully models the long-range sequential patterns as well as the inherent facial structures to learn informative 1D representations of landmark sequences, and achieves state-of-the-art performance on facial landmark tracking.
|
https://arxiv.org/abs/2311.00241v2
|
In the absence of a sufficient amount of plasma injection into the black hole (BH) magnetosphere, the force-free state of the magnetosphere cannot be maintained, leading to the emergence of strong, time-dependent, longitudinal electric field (spark gap). Recent studies of supermassive BH magnetospheres by using analytical methods and particle-in-cell (PIC) simulations propose the possibility of the efficient particle acceleration and consequent gamma-ray emissions in the spark gap. In this work, we perform one-dimensional general relativistic PIC simulations to examine the gamma-ray emission from stellar-mass BH magnetospheres. We find that intermittent spark gaps emerge and particles are efficiently accelerated, in a similar manner to the supermassive BH case. We build a semi-analytic model of the plasma dynamics and radiative processes which reproduces the maximum electron energies and peak gamma-ray luminosities in the simulation results. Based on this model, we show that gamma-ray signals from stellar-mass BHs wandering through the interstellar medium could be detected by gamma-ray telescopes such as the Fermi Large Area Telescope, or the Cherenkov Telescope Array.
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https://arxiv.org/abs/2310.12532v2
|
We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions under which continuous or $L^2$-generalized solutions stabilize to zero in a finite time. Our criteria are expressed in terms of a propagation operator along characteristic curves.
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https://arxiv.org/abs/2208.00858v1
|
The study of privacy-preserving Natural Language Processing (NLP) has gained rising attention in recent years. One promising avenue studies the integration of Differential Privacy in NLP, which has brought about innovative methods in a variety of application settings. Of particular note are $\textit{word-level Metric Local Differential Privacy (MLDP)}$ mechanisms, which work to obfuscate potentially sensitive input text by performing word-by-word $\textit{perturbations}$. Although these methods have shown promising results in empirical tests, there are two major drawbacks: (1) the inevitable loss of utility due to addition of noise, and (2) the computational expensiveness of running these mechanisms on high-dimensional word embeddings. In this work, we aim to address these challenges by proposing $\texttt{1-Diffractor}$, a new mechanism that boasts high speedups in comparison to previous mechanisms, while still demonstrating strong utility- and privacy-preserving capabilities. We evaluate $\texttt{1-Diffractor}$ for utility on several NLP tasks, for theoretical and task-based privacy, and for efficiency in terms of speed and memory. $\texttt{1-Diffractor}$ shows significant improvements in efficiency, while still maintaining competitive utility and privacy scores across all conducted comparative tests against previous MLDP mechanisms. Our code is made available at: https://github.com/sjmeis/Diffractor.
|
https://arxiv.org/abs/2405.01678v1
|
Let $u$ be a non-negative super-solution to a $1$-dimensional singular
parabolic equation of $p$-Laplacian type ($1<p<2$). If $u$ is bounded below on
a time-segment $\{y\}\times(0,T]$ by a positive number $M$, then it has a
power-like decay of order $\frac p{2-p}$ with respect to the space variable $x$
in $\mathbb R\times[T/2,T]$. This fact, stated quantitatively in Proposition
1.1, is a "sidewise spreading of positivity" of solutions to such singular
equations, and can be considered as a form of Harnack inequality. The proof of
such an effect is based on geometrical ideas.
|
http://arxiv.org/abs/1503.07448v1
|
Given a compact geodesic space $X$ we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or \v{C}ech filtration of $X$ to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their precise relationship to the size of holes, the structure of persistence and the relationship between open and close, Rips and \v{C}ech induced persistences. Amongst other results we prove that a Rips critical point $c$ corresponds to an isometrically embedded circle of length $3c$, that a homology persistence of a locally contractible space with coefficients in a field encodes the lengths of the lexicographically smallest base and that Rips and \v{C}ech induced persistences are isomorphic up to a factor $3/4$. The theory describes geometric properties of the underlying space encoded and extractable from persistence.
|
https://arxiv.org/abs/1709.05164v4
|
We introduce a new microeconomics foundation of a specific type of competitive market equilibrium that can be used to study several markets with information asymmetry such as commodity market, credit market, and insurance market.
|
https://arxiv.org/abs/2505.08425v1
|
In addition to being extremely non-linear, modern problems require millions if not billions of parameters to solve or at least to get a good approximation of the solution, and neural networks are known to assimilate that complexity by deepening and widening their topology in order to increase the level of non-linearity needed for a better approximation. However, compact topologies are always preferred to deeper ones as they offer the advantage of using less computational units and less parameters. This compacity comes at the price of reduced non-linearity and thus, of limited solution search space. We propose the 1-Dimensional Polynomial Neural Network (1DPNN) model that uses automatic polynomial kernel estimation for 1-Dimensional Convolutional Neural Networks (1DCNNs) and that introduces a high degree of non-linearity from the first layer which can compensate the need for deep and/or wide topologies. We show that this non-linearity enables the model to yield better results with less computational and spatial complexity than a regular 1DCNN on various classification and regression problems related to audio signals, even though it introduces more computational and spatial complexity on a neuronal level. The experiments were conducted on three publicly available datasets and demonstrate that, on the problems that were tackled, the proposed model can extract more relevant information from the data than a 1DCNN in less time and with less memory.
|
https://arxiv.org/abs/2009.04077v2
|
We consider one-dimensional self-similar solutions to the isentropic Euler system when the initial data are at vacuum to the left of the origin. For $x>0$ the initial velocity and sound speed are of form $u_0(x)=u_+x^{1-\lambda}$ and $c_0(x)=c_+x^{1-\lambda}$, for constants $u_+\in\RR$, $c_+>0$, $\lambda\in\RR$. We analyze the resulting solutions in terms of the similarity parameter $\lambda$, the adiabatic exponent $\gamma$, and the initial (signed) Mach number $\text{Ma}=u_+/c_+$. Restricting attention to locally bounded data, we find that when the sound speed initially decays to zero in a H\"older manner ($0<\lambda<1$), the resulting flow is always defined globally. Furthermore, there are three regimes depending on $\text{Ma}$: for sufficiently large positive $\text{Ma}$-values, the solution is continuous and the initial H\"older decay is immediately replaced by $C^1$-decay to vacuum along a stationary vacuum interface; for moderate values of $\text{Ma}$, the solution is again continuous and with an accelerating vacuum interface along which $c^2$ decays linearly to zero (i.e., a "physical singularity''); for sufficiently large negative $\text{Ma}$-values, the solution contains a shock wave emanating from the initial vacuum interface and propagating into the fluid, together with a physical singularity along an accelerating vacuum interface. In contrast, when the sound speed initially decays to zero in a $C^1$ manner ($\lambda<0$), a global flow exists only for sufficiently large positive values of $\text{Ma}$. Non-existence of global solutions for smaller $\text{Ma}$-values is due to rapid growth of the data at infinity and is unrelated to the presence of a vacuum.
|
https://arxiv.org/abs/2312.07689v1
|
Calculations in Ising model can be cumbersome and non-intuitive. Here we provide a formulation that addresses these issues for 1-D scenario. We represent the microstates of spin interactions as a diagonal matrix. This is done using two operations: Kronecker sum and Kronecker product. The calculations thus become simple matter of manipulating diagonal matrices. We address the following problems in this work: spins in the magnetic field, open-chain 1-D Ising model, closed-chain 1-D Ising model, 1-D Ising model in an external magnetic field. We believe that this representation will help provide students as well as experts with a simple yet powerful technique to carry out calculations in this model.
|
https://arxiv.org/abs/2011.00760v2
|
We study the 1d Ising model with long-range interactions decaying as $1/r^{1+s}$. The critical model corresponds to a family of 1d conformal field theories (CFTs) whose data depends nontrivially on $s$ in the range $1/2\leq s\leq 1$. The model is known to be described by a generalized free field with quartic interaction, which is weakly coupled near $s=1/2$ but strongly coupled near the short-range crossover at $s=1$. We propose a dual description which becomes weakly coupled at $s=1$. At $s=1$, our model becomes an exactly solvable conformal boundary condition for the 2d free scalar. We perform a number of consistency checks of our proposal and calculate the perturbative CFT data around $s=1$ analytically using both 1) our proposed field theory and 2) the analytic conformal bootstrap. Our results show complete agreement between the two methods.
|
https://arxiv.org/abs/2412.12243v2
|
We present a comparison of the observed, spatially integrated stellar and
ionized gas velocity dispersions of $\sim1000$ massive ($\log
M_{\star}/M_{\odot}\gtrsim\,10.3$) galaxies in the Large Early Galaxy
Astrophysics Census (LEGA-C) survey at $0.6\lesssim\,z\lesssim1.0$. The high
$S/N\sim20{\rm\AA^{-1}}$ afforded by 20 hour VLT/VIMOS spectra allows for joint
modeling of the stellar continuum and emission lines in all galaxies, spanning
the full range of galaxy colors and morphologies. These observed integrated
velocity dispersions (denoted as $\sigma'_{g, int}$ and $\sigma'_{\star, int}$)
are related to the intrinsic velocity dispersions of ionized gas or stars, but
also include rotational motions through beam smearing and spectral extraction.
We find good average agreement between observed velocity dispersions, with
$\langle\log(\sigma'_{g, int}/\sigma'_{\star, int})\rangle=-0.003$. This result
does not depend strongly on stellar population, structural properties, or
alignment with respect to the slit. However, in all regimes we find significant
scatter between $\sigma'_{g, int}$ and $\sigma'_{\star, int}$, with an overall
scatter of 0.13 dex of which 0.05 dex is due to observational uncertainties.
For an individual galaxy, the scatter between $\sigma'_{g, int}$ and
$\sigma'_{\star, int}$ translates to an additional uncertainty of
$\sim0.24\rm{dex}$ on dynamical mass derived from $\sigma'_{g, int}$, on top of
measurement errors and uncertainties from Virial constant or size estimates. We
measure the $z\sim0.8$ stellar mass Faber-Jackson relation and demonstrate that
emission line widths can be used to measure scaling relations. However, these
relations will exhibit increased scatter and slopes that are artificially
steepened by selecting on subsets of galaxies with progressively brighter
emission lines.
|
http://arxiv.org/abs/1811.07900v1
|
Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must admit accurate functional derivatives, so that a minimization procedure can be designed. In this work, symbolic regression is explored as an alternative means to machine-learn the KEDF, which results into analytical expressions, whose functional derivatives are easy to compute. The so-determined semi-local functional forms are investigated as a function of the electron number, and we are able to track the transition from the von Weizs\"acker functional, exact for the one-electron case, to the Thomas-Fermi functional, exact in the homogeneous electron gas limit. A number of separate searches are performed, ranging from totally unconstrained to constrained in the form of an enhancement factor. This work highlights the complexity in constructing semi-local approximations of the KEDF and the potential of symbolic regression to advance the search.
|
https://arxiv.org/abs/2412.08143v1
|
Using the inverse period map of the Gauss-Manin connection associated with $QH^{*}(\mathbb{CP}^2)$ and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of $\mathbb{CP}^2$. In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the j-invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of $QH^{*}(\mathbb{CP}^2)$ in closed form as the composition of the Weierstrass $\wp$-function and the universal coverings of $\mathbb{C} \setminus (\mathbb{Z} \oplus e^{\frac{\pi i}{3}}\mathbb{Z})$ and $\mathbb{C} \setminus (\mathbb{Z} \oplus z\mathbb{Z})$ respectively.
|
https://arxiv.org/abs/2402.09574v1
|
It is well known that symmetry protected topological (SPT) phases host
non-trivial boundaries that cannot be mimicked in a lower-dimensional system
with a conventional realization of symmetry. However, for SPT phases of bosons
(fermions) within the cohomology (supercohomology) classification the boundary
can be recreated without the bulk at the cost of a non-onsite symmetry action.
This raises the question: can one also mimic the boundaries of SPT phases which
lie outside the (super)cohomology classification? In this paper, we study this
question in the context of 2+1D fermion SPTs. We focus on the root SPT phase
for the symmetry group $G =Z_2 \times Z^f_2$. Starting with an exactly solvable
model for the bulk of this phase constructed by Tarantino and Fidkowski, we
derive an effective 1d lattice model for the boundary. Crucially, the Hilbert
space of this 1d model does not have a local tensor product structure, but
rather is obtained by placing a local constraint on a local tensor product
Hilbert space. We derive the action of the $Z_2$ symmetry on this Hilbert space
and find a simple 3-site Hamiltonian that respects this symmetry. We study this
Hamiltonian numerically using exact diagonalization and DMRG and find strong
evidence that it realizes an Ising CFT where the $Z_2$ symmetry acts as the
Kramers-Wannier duality; this is the expected stable gapless boundary state of
the present SPT. A simple modification of our construction realizes the
boundary of the 2+1D topological superconductor protected by time-reversal
symmetry ${\cal T}$ with ${\cal T}^2 = (-1)^{\cal F}$.
|
http://arxiv.org/abs/1902.05957v1
|
We demonstrate a 1D magneto-optical trap of the polar free radical calcium
monohydroxide (CaOH). A quasi-closed cycling transition is established to
scatter $\sim 10^3$ photons per molecule, predominantly limited by interaction
time. This enables radiative laser cooling of CaOH while compressing the
molecular beam, leading to a significant increase in on-axis beam brightness
and reduction in temperature from 8.4 mK to 1.4 mK.
|
http://arxiv.org/abs/2001.10525v2
|
Realizing Majorana modes in topological superconductors, i.e., the condensed-matter counterpart of Majorana fermions in particle physics, may lead to a major advance in the field of topologically-protected quantum computation. Here, we introduce one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partially-overlapping, zero-dimensional Majorana modes in proximitized nanowires via periodically-modulated fields. This system realizes centrally-extended quantum-mechanical supersymmetry with spontaneous partial supersymmetry breaking. The massless Majorana modes are the Nambu-Goldstone fermions (Goldstinos) associated with the spontaneously broken supersymmetry. Their experimental fingerprint is a dip-to-peak transition in the zero-bias conductance, which is generally not expected for Majorana modes overlapping at a finite distance. Moreover, the Majorana modes can slide along the wire by applying a rotating magnetic field, realizing a "Majorana pump". This may suggest new braiding protocols and implementations of topological qubits.
|
https://arxiv.org/abs/2106.09039v4
|
Recent work suggests that a sharp definition of `phase of matter' can be
given for periodically driven `Floquet' quantum systems exhibiting many-body
localization. In this work we propose a classification of the phases of
interacting Floquet localized systems with (completely) spontaneously broken
symmetries -- we focus on the one dimensional case, but our results appear to
generalize to higher dimensions. We find that the different Floquet phases
correspond to elements of $Z(G)$, the centre of the symmetry group in question.
In a previous paper we offered a companion classification of unbroken, i.e.,
paramagnetic phases.
|
http://arxiv.org/abs/1602.06949v2
|
Two-dimensional (2D) lateral heterojunctions of transition metal
dichalcogenides (TMDCs) have become a reality in recent years. Semiconducting
TMDC layers in their common H -structure have a nonzero in-plane electric
polarization, which is a topological invariant. We show by means of
first-principles calculations that lateral 2D heterojunctions between TMDCs
with a different polarization generate one-dimensional (1D) metallic states at
the junction, even in cases where the different materials are joined
epitaxially. The metallicity does not depend upon structural details, and is
explained from the change in topological invariant at the junction.
Nevertheless, these 1D metals are susceptible to 1D instabilities, such as
charge- and spin-density waves, making 2D TMDC heterojunctions ideal systems
for studying 1D physics.
|
http://arxiv.org/abs/2008.06758v1
|
We propose a one-dimensional (1D) model for the three-dimensional(3D) incompressible ideal magnetohydrodynamics. We establish a regularity criterion of the Beale-Kato-Majda type for this 1D model. Without the stretching effect, the model with only transport effect equipped with a proper sign is shown to have global in time strong solution. Some numerical simulations suggest that solutions of this model with smooth periodic initial data do not tend to develop singularities at finite time.
|
https://arxiv.org/abs/2107.02920v2
|
In this paper, we first remodel the line coverage as a 1D discrete problem
with co-linear targets. Then, an order-based greedy algorithm, called OGA, is
proposed to solve the problem optimally. It will be shown that the existing
order in the 1D modeling, and especially the resulted Markov property of the
selected sensors can help design greedy algorithms such as OGA. These
algorithms demonstrate optimal/efficient performance and have lower complexity
compared to the state-of-the-art. Furthermore, it is demonstrated that the
conventional continuous line coverage problem can be converted to an equivalent
discrete problem and solved optimally by OGA. Next, we formulate the well-known
weak barrier coverage problem as an instance of the continuous line coverage
problem (i.e. a 1D problem) as opposed to the conventional 2D graph-based
models. We demonstrate that the equivalent discrete version of this problem can
be solved optimally and faster than the state-of-the-art methods using an
extended version of OGA, called K-OGA. Moreover, an efficient local algorithm,
called LOGM, is proposed to mend barrier gaps due to sensor failure. In the
case of m gaps, LOGM is proved to select at most 2m-1 sensors more than the
optimal while being local and implementable in distributed fashion. We
demonstrate the optimal/efficient performance of the proposed algorithms via
extensive simulations.
|
http://arxiv.org/abs/1704.05576v1
|
A Coupled Natural Circulation Loop (CNCL) consists of two Natural Circulation
Loops (NCL) coupled thermally via a common heat exchanger. The transient
modelling of such systems that have practical relevance has not been reported
in the literature to the best of the author's knowledge. The present work aims
to bridge this gap and investigate the dynamic characteristics of a CNCL system
using a 1-D mathematical model. The validation of the model is accomplished by
comparison of the results obtained via 3-D CFD simulation. Both horizontal and
vertical CNCL systems have been considered for this study and behaviour of the
system for parallel and counter flow configurations in the heat exchanger
section is elaborated. Transient and steady state CFD analysis has been
conducted to analyse CNCL system for different heater and cooler orientations
and flow initialisation. The behaviour of the CNCL system is then examined by
carrying a thorough parametric study employing the validated 1-D single phase
CNCL model with liquid sodium as the operating fluid. The CNCL orientation
(vertical or horizontal) coupled with the heater and cooler configuration
determines the system dynamics and behaviour. The CNCL system also exhibits
chaotic flow oscillations at high heat loads.
|
http://arxiv.org/abs/1804.10051v1
|
Mott variable-range hopping is a fundamental mechanism for electron transport
in disordered solids in the regime of strong Anderson localization. We give a
brief description of this mechanism, recall some results concerning the
behavior of the conductivity at low temperature and describe in more detail
recent results (obtained in collaboration with N. Gantert and M. Salvi)
concerning the one-dimensional Mott variable-range hopping under an external
field.
|
http://arxiv.org/abs/1803.05166v2
|
Detailed chemical abundances of very metal-poor (VMP, [Fe/H] < -2) stars are important for better understanding the First Stars, early star formation and chemical enrichment of galaxies. Big on-going and coming high-resolution spectroscopic surveys provide a wealth of material that needs to be carefully analysed. For VMP stars, their elemental abundances should be derived based on the non-local thermodynamic equilibrium (non-LTE = NLTE) line formation because low metal abundances and low electron number density in the atmosphere produce the physical conditions favorable for the departures from LTE. The galactic archaeology research requires homogeneous determinations of chemical abundances. For this purpose, we present grids of the 1D-NLTE abundance corrections for the Na I, Mg I, Ca I, Ca II, Ti II, Fe I, Zn I, Zn II, Sr II, and Ba II lines, which are used in the galactic archaeology research. The range of atmospheric parameters represents VMP stars on various evolutionary stages and covers effective temperatures from 4000 to 6500~K, surface gravities from log g = 0.5 to log g = 5.0, and metallicities $-5.0 \le$ [Fe/H] $\le -2.0$. The data is publicly available, and we provide the tools for interpolating in the grids online.
|
https://arxiv.org/abs/2307.04523v1
|
We say that a knot $k_1$ in the $3$-sphere {\it $1$-dominates} another $k_2$
if there is a proper degree 1 map $E(k_1) \to E(k_2)$ between their exteriors,
and write $k_1 \ge k_2$. When $k_1 \ge k_2$ but $k_1 \ne k_2$ we write $k_1 >
k_2$. One expects in the latter eventuality that $k_1$ is more {\it
complicated}. In this paper we produce various sorts of evidence to support
this philosophy.
|
http://arxiv.org/abs/1511.07073v1
|
Neptune remains a mysterious world that deserves further exploration and is a
high-priority objective for a future planetary mission in order to better
understand the formation and evolution of ice giant planets. We have developed
a coupled ion-neutral 1D photochemical model of Neptune's atmosphere to study
the origin and evolution of the hydrocarbons and the oxygen species. The
up-to-date chemical scheme is derived from one used for Titan's atmosphere,
which led to good agreements with the Cassini-CIRS observations for oxygen
species and the main hydrocarbons. The main results we obtain are the
following: The ion-neutral chemistry coupling produces aromatics (and benzene
in particular) in the atmosphere of Neptune with relatively high abundances.
Our model results are in good agreement with observations (taking model
uncertainties into account). Two ionospheric peaks are present in the
atmosphere located above the pressure level of 10$^{-5}$ mbar and around
10$^{-3}$ mbar. The influx of oxygen species in the upper atmosphere of Neptune
has an effect on the concentration of many ions. We show that in situ
exploration of Neptune's atmosphere would provide very interesting constraints
for photochemical models concerning in particular the origin of oxygen species
and the contribution of ion chemistry. A precise description of upper
atmospheric chemistry is crucial for a better understanding of the internal
composition and the formation processes of this planet.
|
http://arxiv.org/abs/2011.07984v1
|
The design and development of new photonic devices for technological applications requires a deep understanding of the effect of structural properties on the resulting band gap size and its position. Here, we perform a theoretical study of behavior of the photonic band gap sizes, positions and percentages under variations of the parameters characterizing binary (two materials), ternary (three materials) and linear dielectric grating multilayer structures. The resulting band gap atlas show that binary systems may suffice for most applications but ternary systems may add additional flexibility in design if needed. Linear gratings show a regular pattern for all gaps studied, this regularity was able to be reproduced with only few materials involved. The position of the gaps showed a very monotonous behavior for all calculations performed. Finally, additional extensions of formulas commonly used in the design of Bragg mirrors/reflectors using binary materials were proposed with their corresponding limitations discussed. These results can be seen as a technological horizon for photonic device development.
|
https://arxiv.org/abs/2405.13633v1
|
GeSn alloys have been regarded as a potential lasing material for a complementary metal-oxide-semiconductor (CMOS)-compatible light source. Despite their remarkable progress, all GeSn lasers reported to date have large device footprints and active areas, which prevent the realization of densely integrated on-chip lasers operating at low power consumption. Here, we present a 1D photonic crystal (PC) nanobeam with a very small device footprint of 7 ${\mu}m^2$ and a compact active area of ~1.2 ${\mu}m^2$ on a high-quality GeSn-on-insulator (GeSnOI) substrate. We also report that the improved directness in our strain-free nanobeam lasers leads to a lower threshold density and a higher operating temperature compared to the compressive strained counterparts. The threshold density of the strain-free nanobeam laser is ~18.2 kW cm$^{ -2}$ at 4 K, which is significantly lower than that of the unreleased nanobeam laser (~38.4 kW cm$^{ -2}$ at 4 K). Lasing in the strain-free nanobeam device persists up to 90 K, whereas the unreleased nanobeam shows a quenching of the lasing at a temperature of 70 K. Our demonstration offers a new avenue towards developing practical group-IV light sources with high-density integration and low power consumption.
|
https://arxiv.org/abs/2108.06142v2
|
The space electron-ion-positive dust plasma system containing isothermal
inertialess electron species, cold inertial ion species, and stationary
positive (positivively charged) dust species is considered. The basic features
of one dimensional (1D) planar and nonplanar subsonic solitary waves are
investigated by the pseudo-potential and reductive perturbation methods,
respectively. It is observed that the presence of the positive dust species
reduces the phase speed of the ion-acoustic waves, and consequently supports
the subsonic solitary waves with the positive wave potential in such a space
dusty plasma system. It is observed that the cylindrical and spherical subsonic
solitary waves significantly evolve with time, and that the time evolution of
the spherical solitary waves is faster than that of the cylindrical ones. The
applications of the work in many space dusty plasma systems, particularly in
Earth's mesosphere, cometary tails, Jupiter's magnetosphere, etc. are
addressed.
|
http://arxiv.org/abs/2009.09131v1
|
With increasing miniaturization of diagnostic devices for more effective detection of blood-borne pathogens for example, Poiseuille molecular flow in micro channels has become increasingly relevant. Since continuum mechanics no longer applies for Poiseuille flow when the Knudson number is near or larger than unity, kinetic theory is required to capture the microscopic molecular scattering responsible for channel molecular flow and the velocity profile across a channel. Here, we apply a response matrix solution to the 1D Poiseuille flow with a BGK approximation featuring simplicity with precision by following a consistent numerical formulation leading to high precision, 8-place benchmarks.
|
https://arxiv.org/abs/2406.16954v1
|
We construct explicit measure-valued solutions to the one-dimensional pressureless gas dynamics system in a strip-like domain by introducing a new boundary potential. The constructed solutions satisfy an entropy condition, and depending on the boundary data and the behavior of the potentials, mass accumulation can occur at the boundaries. The approach relies on a systematic treatment of boundary potentials and their interactions with the initial data, providing a more precise understanding of the formation and propagation of singularities in measure-valued solutions.
|
https://arxiv.org/abs/2502.15927v2
|
Magnetic resonance imaging (MRI) is mainly limited by long scanning time and vulnerable to human tissue motion artifacts, in 3D clinical scenarios. Thus, k-space undersampling is used to accelerate the acquisition of MRI while leading to visually poor MR images. Recently, some studies 1) use effective undersampling patterns, or 2) design deep neural networks to improve the quality of resulting images. However, they are considered as two separate optimization strategies. In this paper, we propose a cross-domain network for MR image reconstruction, in a retrospective data-driven manner, under limited sampling rates. Our method can simultaneously obtain the optimal undersampling pattern (in k-space) and the reconstruction model, which are customized to the type of training data, by using an end-to-end learning strategy. We propose a 1D probabilistic undersampling layer, to obtain the optimal undersampling pattern and its probability distribution in a differentiable way. We propose a 1D inverse Fourier transform layer, which connects the Fourier domain and the image domain during the forward pass and the backpropagation. In addition, by training 3D fully-sampled k-space data and MR images with the traditional Euclidean loss, we discover the universal relationship between the probability distribution of the optimal undersampling pattern and its corresponding sampling rate. Experiments show that the quantitative and qualitative results of recovered MR images by our 1D probabilistic undersampling pattern obviously outperform those of several existing sampling strategies.
|
https://arxiv.org/abs/2003.03797v3
|
In this paper we prove an infinite dimensional KAM theorem, in which the
assumptions on the derivatives of perturbation in \cite{GT} are weakened from
polynomial decay to logarithmic decay. As a consequence, we apply it to 1d
quantum harmonic oscillators and prove the reducibility of a linear harmonic
oscillator, $T=- \frac{d^2}{dx^2}+x^2$, on $L^2(\R)$ perturbed by a
quasi-periodic in time potential $V(x,\omega t; \omega)$ with logarithmic
decay. This entails the pure-point nature of the spectrum of the Floquet
operator $K$, where K:=-{\rm i}\sum_{k=1}^n\omega_k\frac{\partial}{\partial
\theta_k}- \frac{d^2}{dx^2}+x^2+\varepsilon V(x,\theta;\omega), is defined on
$L^2(\R) \otimes L^2(\T^n)$ and the potential $V(x,\theta;\omega)$ has
logarithmic decay as well as its gradient in $\omega$.
|
http://arxiv.org/abs/1605.05480v1
|
For a family of 1-d quantum harmonic oscillator with a perturbation which is $C^2$ parametrized by $E\in{\mathcal I}\subset{\Bbb R}$ and quadratic on $x$ and $-{\rm i}\partial_x$ with coefficients quasi-periodically depending on time $t$, we show the reducibility (i.e., conjugation to time-independent) for a.e. $E$. As an application of reducibility, we describe the behaviors of solution in Sobolev space: -- Boundedness w.r.t. $t$ is always true for "most" $E\in{\mathcal I}$. -- For "generic" time-dependent perturbation, polynomial growth and exponential growth to infinity w.r.t. $t$ occur for $E$ in a "small" part of ${\mathcal I}$. Concrete examples are given for which the growths of Sobolev norm do occur.
|
https://arxiv.org/abs/2003.13034v2
|
Local topological markers are effective tools for determining the topological properties of both homogeneous and inhomogeneous systems. The Chern marker is an established topological marker that has previously been shown to effectively reveal the topological properties of 2D systems. In an earlier work, the present authors have developed a marker that can be applied to 1D time-dependent systems which can be used to explore their topological properties, like charge pumping under the presence of disorder. In this paper, we show how to alter the 1D marker so that it can be applied to quasiperiodic and aperiodic systems. We then verify its effectiveness against different quasicrystal Hamiltonians, some which have been addressed in previous studies using existing methods, and others which possess topological structures that have been largely unexplored. We also demonstrate that the altered 1D marker can be productively applied to systems that are fully aperiodic.
|
https://arxiv.org/abs/2201.09741v2
|
Filaments are ubiquitous in astronomical data sets. Be it in particle simulations or observations, filaments are always tracers of a perturbation in the equilibrium of the studied system and hold essential information on its history and future evolution. However, the recovery of such structures is often complicated by the presence of a large amount of background and transverse noise in the observation space. While the former is generally detrimental to the analysis, the latter can be attributed to measurement errors and it can hold essential information about the structure. To further complicate the scenario, 1D manifolds (filaments) are generally non-linear and their geometry difficult to extract and model. In order to study hidden manifolds within the dataset, particular care has to be devoted to background noise removal and transverse noise modelling, while still maintaining accuracy in the recovery of their geometrical structure. We propose 1-DREAM: a toolbox composed of five main Machine Learning methodologies whose aim is to facilitate manifold extraction in such cases. Each methodology has been designed to address issues when dealing with complicated low-dimensional structures convoluted with noise and it has been extensively tested in previously published works. In this work all methodologies are presented in detail, joint within a cohesive framework and demonstrated for three interesting astronomical cases: a simulated jellyfish galaxy, a filament extracted from a simulated cosmic web and the stellar stream of Omega-Centauri as observed with the GAIA DR2. Two newly developed visualization techniques are also proposed, that take full advantage of the results obtained with 1-DREAM. The code is made publicly available to benefit the community. The controlled experiments on a purposefully built data set prove the accuracy of the pipeline in recovering the hidden structures.
|
https://arxiv.org/abs/2503.21584v1
|
In this article, we present our contribution to the ICPHM 2023 Data Challenge on Industrial Systems' Health Monitoring using Vibration Analysis. For the task of classifying sun gear faults in a gearbox, we propose a residual Convolutional Neural Network that operates on raw three-channel time-domain vibration signals. In conjunction with data augmentation and regularization techniques, the proposed model yields very good results in a multi-class classification scenario with real-world data despite its relatively small size, i.e., with less than 30,000 trainable parameters. Even when presented with data obtained from multiple operating conditions, the network is still capable to accurately predict the condition of the gearbox under inspection.
|
https://arxiv.org/abs/2304.07305v2
|
The influence of surface constraints on the self-assembly of liquid droplets
is investigated. A semi-quantitative explanation for large scale pattern
formation consisting of small scale closely arranged droplets inside the large
scale distorted ring of droplets is presented in this paper. The scale at which
the influence of constraints become dominant is also determined in this study.
It is seen that the underlying roughness has a larger impact than the nature of
polymer on pore size. Comparative studies of pore patterns formed on smooth and
constrained substrates are reported. The simulated energy minimized shape of
the droplets on smooth and constrained substrates are obtained using
\textit{Surface Evolver}.
|
http://arxiv.org/abs/1605.02942v2
|
On a star graph $G$ with $n = n_+ + n_-$ edges of unit length, we study the operator $-\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_+$ and $\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_-$ edges equipped with Dirichlet boundary conditions at the outer vertices and a Kirchhoff condition at the central vertex. We study the spectral properties of the corresponding indefinite Kirchhoff Laplacian on $G$ and we show that it is similar to a selfadjoint operator in the Hilbert space $L^2(G)$ and that its eigenfunctions form a Riesz basis. Furthermore, we give a complete description of the point spectrum.
|
https://arxiv.org/abs/2505.22901v1
|
We consider a Schr\"odinger operator with complex-valued potentials on the
line. The operator has essential spectrum on the half-line plus eigenvalues
(counted with algebraic multiplicity) in the complex plane without the positive
half-line. We determine series of trace formulas. Here we have the new term: a
singular measure, which is absent for real potentials. Moreover, we estimate of
sum of Im part of eigenvalues plus singular measure in terms of the norm of
potentials. The proof is based on classical results about the Hardy spaces.
|
http://arxiv.org/abs/1909.08454v1
|
Since the first experimental observation of optical Airy beams, various applications ranging from particle and cell micromanipulation to laser micromachining have exploited their non-diffracting and accelerating properties. The later discovery that Airy beams can self-heal after being blocked by an obstacle further proved their robustness to propagate under scattering and disordered environment. Here, we report the generation of Airy beams on an integrated silicon photonic chip and demonstrate that the on-chip 1D Airy beams preserve the same properties as the 2D beams. The 1D meta-optics used to create the Airy beam has the size of only 3 by 16 microns, at least three orders of magnitude smaller than the conventional optic. The on-chip self-healing beams demonstrated here could potentially enable diffraction-free light routing for on-chip optical networks and high-precision micromanipulation of bio-molecules on an integrated photonic chip.
|
https://arxiv.org/abs/2103.12254v1
|
We establish asymptotics of growing one dimensional self-similar fractal graphs, they are networks that allow multiple weighted edges between nodes, in terms of quantum central limit theorems for algebraic probability spaces in pure state. An additional structure is endowed with the repeating units of centro-symmetric Jacobians in the adjacency of a linear graph creating a self-similar fractal. The family of fractals induced by centro-symmetric Jacobians formulated as orthogonal polynomials that satisfy three term recurrence relations support such limits. The construction proceeds with the interacting fock spaces, T-algebras endowed with a quantum probability space, corresponding to the Jacobi coefficients of the recurrence relations and when some elements of the centro-symmetric matrix are constrained in a specific way we obtain, as the same Jacobian structure is repeated, the central limits. The generic formulation of Leonard pairs that form bases of conformal blocks and probablistic laplacians used in physics provide choice of centro-symmetric Jacobians widening the applicability of the result. We establish that the T-algebras of these 1D fractals, as they form a special class of distance-regular graphs, are thin and the induced association schemes are self-duals that lead to anyon systems with modular invariance.
|
https://arxiv.org/abs/2401.15515v1
|
The study of heat exchangers with both the hot and cold fluid sides driven by
buoyancy forces is an area of considerable interest due to their inherent
passivity and non-existence of moving parts. The current study aims to study
such heat exchange devices employing the basic Coupled Natural Circulation Loop
(CNCL) systems. A 1-D Fourier series based semi-analytical model of the basic
CNCL system is proposed. A 3-D CFD validation is performed to validate the
developed 1-D model. The non-dimensional numbers such as Grashof number,
Fourier number, Stanton number and Reynolds number, which determine the system
behavior are identified and a detailed parametric study is performed. Both
vertical and horizontal CNCL systems are considered along with the parallel and
counter flow configurations. The heater-cooler location greatly influences the
behavior of CNCL system. The vertical CNCL always exhibits counter flow
configuration whereas the horizontal CNCL system may exhibit parallel or
counter flow arrangement depending on the heater-cooler location and initial
flow conditions.
|
http://arxiv.org/abs/1811.08074v1
|
Analytical/quasi-analytical solutions are proposed for a steady, compressible, two-phase flow in mechanical equilibrium in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between a variable outlet pressure and an upstream tank. A critical pressure ratio distinguishes subsonic and supersonic outlet regimes: the article proposes a methodology to determine the full flow behaviour, as a function of pressure ratio and heat-flux distribution. Going forward, these analytical reference solutions will help validate numerical codes for more complex industrial applications. Specific results are studied for a mixture of liquid water and water vapour.
|
https://arxiv.org/abs/2404.10345v1
|
A study of the one-dimensional molecular chain (MC) with two single-particle degenerate states is presented. We establish connection of the MC with the Ising model with phononic interactions and investigate properties of the model using a transfer matrix method. The transfer matrix method offers a promising pathway for simulating such materials properties. The role of degeneracy of states and phononic interaction being made explicit. We analyze regimes of the system and parameters of the occurring crossover. Here, we present exact results for the magnetization per spin, the correlation function and the effective volume of the system. We demonstrate possibility of existence of two peaks in the specific heat capacity thermal behavior.
|
https://arxiv.org/abs/2102.13627v2
|
Spontaneous symmetry breaking generally circumvents one-dimensional systems with local interactions in thermal equilibrium. Here, we analyze a category of one-dimensional Hermitian models via local non-Hermitian constructions. Notably, spontaneous symmetry breaking and long-range order may emerge at finite temperatures in such systems under periodic boundary conditions, in sharp contrast to Hermitian constructions. We demonstrate clear numerical evidence, such as order parameters and specific heat, supporting phase diagrams with robust ordered phases. Non-Hermitian physics plays a vital role in prohibiting domain-wall proliferation and promoting spontaneous symmetry breaking. The fermions exhibit an exotic topological nature in their path-integral windings, which uphold nonzero integers -- commonly a non-Hermitian signature -- in the ordered phases, thus offering a novel and spontaneous origin for both symmetry breaking and non-Hermiticity.
|
https://arxiv.org/abs/2410.19052v1
|
Airborne electromagnetic surveys may consist of hundreds of thousands of soundings. In most cases, this makes 3D inversions unfeasible even when the subsurface is characterized by a high level of heterogeneity. Instead, approaches based on 1D forwards are routinely used because of their computational efficiency. However, it is relatively easy to fit 3D responses with 1D forward modelling and retrieve apparently well-resolved conductivity models. However, those detailed features may simply be caused by fitting the modelling error connected to the approximate forward. In addition, it is, in practice, difficult to identify this kind of artifacts as the modeling error is correlated. The present study demonstrates how to assess the modelling error introduced by the 1D approximation and how to include this additional piece of information into a probabilistic inversion. Not surprisingly, it turns out that this simple modification provides not only much better reconstructions of the targets but, maybe, more importantly, guarantees a correct estimation of the corresponding reliability.
|
https://arxiv.org/abs/2109.13780v1
|
We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data, and the initial value problem, covering the cases of both the Wick renormalization of the diffusion and of point-wise multiplication. We provide explicit representations for the solutions in both cases, characterized by the $S$-transform and the Gaussian multiplicative chaos measure.
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https://arxiv.org/abs/2402.09127v1
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We study two homogeneous supersymmetric extensions for the $f(R)$ modified gravity model of Starobinsky with the FLRW metric. The actions are defined in terms of a superfield $\mathcal{R}$ that contains the FLRW scalar curvature. One model has N=1 local supersymmetry, and its bosonic sector is the Starobinsky action; the other action has N=2, its bosonic sector contains, in additional to Starobinsky, a massive scalar field without self-interaction. As expected, the bosonic sectors of these models are consistent with cosmic inflation, as we show by solving numerically the classical dynamics. Inflation is driven by the $R^2$ term during the large curvature regime. In the N=2 case, the additional scalar field remains in a low energy state during inflation. Further, by means of an additional superfield, we write equivalent tensor-scalar-like actions from which we can give the Hamiltonian formulation.
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https://arxiv.org/abs/2110.00556v2
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Objective: Innovative therapies such as thermoembolization are expected to play an important role in improvising care for patients with diseases such as hepatocellular carcinoma. Thermoembolization is a minimally invasive strategy that combines thermal ablation and embolization in a single procedure. This approach exploits an exothermic chemical reaction that occurs when an acid chloride is delivered via an endovascular route. However, comprehension of the complexities of the biophysics of thermoembolization is challenging. Mathematical models can aid in understanding such complex processes and assisting clinicians in making informed decisions. In this study, we used a Hagen Poiseuille 1D blood flow model to predict the mass transport and possible embolization locations in a porcine hepatic artery. Method: The 1D flow model was used on in vivo embolization imaging data of three pigs. The hydrolysis time constant of acid chloride chemical reaction was optimized for each pig, and LOOCV method was used to test the model's predictive ability. Conclusion: This basic model provided a balanced accuracy rate of 66.8% for identifying the possible locations of embolization in the hepatic artery. Use of the model provides an initial understanding of the vascular transport phenomena that are predicted to occur as a result of thermoembolization.
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https://arxiv.org/abs/2409.06811v1
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