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Recent observations about the cosmic microwave background evidence a clear discrepancy between the scale of inflation and the Planck scale expected in the conventional inflationary picture, based on simple chaotic inflationary models. This paper explores a possible resolution of this conflict by considering a slight modification of the standard general relativity scenario, which naturally incorporates a cutoff scale consistent with the observations. This last scale of power suppression appears by the combined effect of the preinflationary background dynamics and an associated initial vacuum state for the cosmological perturbations which differs from the conventional Bunch-Davies state of slow-roll inflation. We revise and correct previous discussions in the literature about the relation between this scale and the scale corresponding to the onset of inflation. The mechanism that produces this cutoff is intimately related to the criterion determining a privileged vacuum state for the primordial perturbations. We adhere to a recent proposal based on an asymptotic diagonalization of the Hamiltonian of the perturbations and leading to a non-oscillatory primordial power spectrum. With this choice, we are able to investigate analytically the model, studying in detail some physically interesting cases. These analytic calculations provide further support to our arguments about the relation between the different scales of the system., Comment: 15 pages, 7 figures

Efficient satellite communications play an enormously important role in all of our daily lives. This includes the transmission of data for communication purposes, the operation of IoT applications or the provision of data for ground stations. More and more, AI-based methods are finding their way into these areas. This paper gives an overview of current research in the field of intelligent optimization of satellite communication. For this purpose, a text-mining based literature review was conducted and the identified papers were thematically clustered and analyzed. The identified clusters cover the main topics of routing, resource allocation and, load balancing. Through such a clustering of the literature in overarching topics, a structured analysis of the research papers was enabled, allowing the identification of latest technologies and approaches as well as research needs for intelligent optimization of satellite communication., Comment: 10 pages, 2 figures, 3 tables

The SoccerNet 2024 challenges represent the fourth annual video understanding challenges organized by the SoccerNet team. These challenges aim to advance research across multiple themes in football, including broadcast video understanding, field understanding, and player understanding. This year, the challenges encompass four vision-based tasks. (1) Ball Action Spotting, focusing on precisely localizing when and which soccer actions related to the ball occur, (2) Dense Video Captioning, focusing on describing the broadcast with natural language and anchored timestamps, (3) Multi-View Foul Recognition, a novel task focusing on analyzing multiple viewpoints of a potential foul incident to classify whether a foul occurred and assess its severity, (4) Game State Reconstruction, another novel task focusing on reconstructing the game state from broadcast videos onto a 2D top-view map of the field. Detailed information about the tasks, challenges, and leaderboards can be found at https://www.soccer-net.org, with baselines and development kits available at https://github.com/SoccerNet., Comment: 7 pages, 1 figure

In this article we study a coupled system of differential equations with Allen-Cahn type non-linearity. Motivated by physical phenomena one of the unknowns in the system is accompanied by a singular perturbation parameter {\epsilon}^2 . By employing variational techniques, we establish the existence of solutions for all values of {\epsilon} and get results on their qualitative properties, including regularity. Additionally, we analyse the behaviour of solutions as {\epsilon} {\to} 0, demonstrating their pointwise convergence to the solution of the problem for {\epsilon} = 0. We establish the uniqueness of this solution modulo translations. Additionally, in the final section, through an appropriate change of scale, we relate this problem and the second Painlev\'e equation.

The goal of this paper is to develop a reliable analytical approach to finding the effective elastic-plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to examine the anisotropy induced by regular inhomogeneity arrangements. The proposed framework is based on the idea of Molinari & El Mouden (1996) to improve classical mean-field models of thermoelastic media by taking into account the interactions between each pair of inhomogeneities within the material volume, known as a cluster model. Both elastic and elasto-plastic regimes are examined. A new extension of the original formulation, aimed to account for the non-linear plastic regime, is performed with the use of the modified tangent linearization of the metal matrix constitutive law. The model uses the second stress moment to track the accumulated plastic strain in the matrix. In the examples, arrangements of spherical inhomogeneities in three Bravais lattices of cubic symmetry (Regular Cubic, Body-Centered Cubic and Face-Centered Cubic) are considered for two basic material scenarios: "hard-in-soft" (MMC) and "soft-in-hard" (PM). As a means of verification, the results of micromechanical mean-field modeling are compared with those of numerical homogenization performed using the Finite Element Method (FEM). In the elastic regime, a comparison is also made with several other micromechanical models dedicated to periodic composites. Within both regimes, the results obtained by the cluster model are qualitatively and quantitatively consistent with FEM calculations, especially for volume fractions of inclusions up to 40%., Comment: 36 pages Accepted for publication in Int. J. Engineering Science on 11 July 2024

Federated Class Incremental Learning (FCIL) is a new direction in continual learning (CL) for addressing catastrophic forgetting and non-IID data distribution simultaneously. Existing FCIL methods call for high communication costs and exemplars from previous classes. We propose a novel rehearsal-free method for FCIL named prototypes-injected prompt (PIP) that involves 3 main ideas: a) prototype injection on prompt learning, b) prototype augmentation, and c) weighted Gaussian aggregation on the server side. Our experiment result shows that the proposed method outperforms the current state of the arts (SOTAs) with a significant improvement (up to 33%) in CIFAR100, MiniImageNet and TinyImageNet datasets. Our extensive analysis demonstrates the robustness of PIP in different task sizes, and the advantage of requiring smaller participating local clients, and smaller global rounds. For further study, source codes of PIP, baseline, and experimental logs are shared publicly in https://github.com/anwarmaxsum/PIP., Comment: Conference on Information and Knowledge Management (CIKM) 2024 (Accepted)

Let $C$ be an irreducible nonsingular curve over a formally real field $K$ and let $f$ be a regular function which is a sum of squares in the ring of regular functions of the surface $C \times \mathbb{A}_K$. We show that the (sum of squares) length of $f$ is the same in the ring of regular functions of $C \times \mathbb{A}_K$ and in the field of rational functions of $C \times \mathbb{A}_K$. With this we are able to show that the Pythagoras number of the ring of regular functions is the same as the Pythagoras number of the field of rational functions, for some product algebraic surfaces. This shows that the Pythagoras number of the ring of regular functions of the real plane is 4, which was not known before., Comment: 7 pages, comments welcome!

Structural superlubricity is a special frictionless contact in which two crystals are in incommensurate arrangement such that relative in-plane translation is associated with vanishing energy barrier crossing. So far, it has been realized in multilayer graphene and other van der Waals two-dimensional crystals with hexagonal or triangular crystalline symmetries, leading to isotropic frictionless contacts. Directional structural superlubricity, to date unrealized in two-dimensional systems, is possible when the reciprocal lattices of the two crystals coincide in one direction only. Here, we evidence directional structural superlubricity a $\alpha$-bismuthene/graphite van der Waals system, manifested by spontaneous hopping of the islands over hundreds of nanometres at room temperature, resolved by low-energy electron microscopy and supported by registry simulations. Statistical analysis of individual and collective $\alpha$-bismuthene islands populations reveal a heavy-tailed distribution of the hopping lengths and sticking times indicative of L{\'e}vy flight dynamics, largely unobserved in condensed-matter systems., Comment: 14 pages, 10 figures (including Supplementary Information and Supplementary Figures)

A continual learning (CL) model is desired for remote sensing image analysis because of varying camera parameters, spectral ranges, resolutions, etc. There exist some recent initiatives to develop CL techniques in this domain but they still depend on massive labelled samples which do not fully fit remote sensing applications because ground truths are often obtained via field-based surveys. This paper addresses this problem with a proposal of unsupervised flat-wide learning approach (UNISA) for unsupervised few-shot continual learning approaches of remote sensing image scene classifications which do not depend on any labelled samples for its model updates. UNISA is developed from the idea of prototype scattering and positive sampling for learning representations while the catastrophic forgetting problem is tackled with the flat-wide learning approach combined with a ball generator to address the data scarcity problem. Our numerical study with remote sensing image scene datasets and a hyperspectral dataset confirms the advantages of our solution. Source codes of UNISA are shared publicly in \url{https://github.com/anwarmaxsum/UNISA} to allow convenient future studies and reproductions of our numerical results., Comment: Under Review for Publication in IEEE TGRS

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

Few-Shot Class-Incremental Learning presents an extension of the Class Incremental Learning problem where a model is faced with the problem of data scarcity while addressing the catastrophic forgetting problem. This problem remains an open problem because all recent works are built upon the convolutional neural networks performing sub-optimally compared to the transformer approaches. Our paper presents Robust Transformer Approach built upon the Compact Convolution Transformer. The issue of overfitting due to few samples is overcome with the notion of the stochastic classifier, where the classifier's weights are sampled from a distribution with mean and variance vectors, thus increasing the likelihood of correct classifications, and the batch-norm layer to stabilize the training process. The issue of CF is dealt with the idea of delta parameters, small task-specific trainable parameters while keeping the backbone networks frozen. A non-parametric approach is developed to infer the delta parameters for the model's predictions. The prototype rectification approach is applied to avoid biased prototype calculations due to the issue of data scarcity. The advantage of ROBUSTA is demonstrated through a series of experiments in the benchmark problems where it is capable of outperforming prior arts with big margins without any data augmentation protocols., Comment: Under Review in Information Sciences

This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori knowledge about the phenomenon under investigation and delivers a model with corresponding non-asymptotic high probability error bounds. Both non-asymptotic analysis of the method and numerical simulation results are presented and discussed in the paper.

Orthogonalization is one of few mathematical methods conforming to mathematical standards for approximation. Finding a consistent PC matrix of a given an inconsistent PC matrix is the main goal of a pairwise comparisons method. We introduce an orthogonalization for pairwise comparisons matrix based on a generalized Frobenius inner matrix product. The proposed theory is supported by numerous examples and visualizations., Comment: online, submitted as 22 pages and 2 figures

We realise an intrinsic optically pumped magnetic gradiometer based on non-linear magneto-optical rotation. We show that our sensor can reach a gradiometric sensitivity of 18 $\text{fT}/\text{cm}/\sqrt{\text{Hz}}$ and can reject common mode homogeneous magnetic field noise with up to 30 dB attenuation. We demonstrate that our magnetic field gradiometer is sufficiently sensitive and resilient to be employed in biomagnetic applications. In particular, we are able to record the auditory evoked response of the human brain, and to perform real-time magnetocardiography in the presence of external magnetic field disturbances. Our gradiometer provides complementary capabilities in human biomagnetic sensing to optically pumped magnetometers, and opens new avenues in the detection of human biomagnetism., Comment: 7 Pages, 6 Figures

Precise identification of spinal nerve rootlets is relevant to delineate spinal levels for the study of functional activity in the spinal cord. The goal of this study was to develop an automatic method for the semantic segmentation of spinal nerve rootlets from T2-weighted magnetic resonance imaging (MRI) scans. Images from two open-access MRI datasets were used to train a 3D multi-class convolutional neural network using an active learning approach to segment C2-C8 dorsal nerve rootlets. Each output class corresponds to a spinal level. The method was tested on 3T T2-weighted images from datasets unseen during training to assess inter-site, inter-session, and inter-resolution variability. The test Dice score was 0.67 +- 0.16 (mean +- standard deviation across testing images and rootlets levels), suggesting a good performance. The method also demonstrated low inter-vendor and inter-site variability (coefficient of variation <= 1.41 %), as well as low inter-session variability (coefficient of variation <= 1.30 %) indicating stable predictions across different MRI vendors, sites, and sessions. The proposed methodology is open-source and readily available in the Spinal Cord Toolbox (SCT) v6.2 and higher.

A reliable long-term time-series forecaster is highly demanded in practice but comes across many challenges such as low computational and memory footprints as well as robustness against dynamic learning environments. This paper proposes Meta-Transformer Networks (MANTRA) to deal with the dynamic long-term time-series forecasting tasks. MANTRA relies on the concept of fast and slow learners where a collection of fast learners learns different aspects of data distributions while adapting quickly to changes. A slow learner tailors suitable representations to fast learners. Fast adaptations to dynamic environments are achieved using the universal representation transformer layers producing task-adapted representations with a small number of parameters. Our experiments using four datasets with different prediction lengths demonstrate the advantage of our approach with at least $3\%$ improvements over the baseline algorithms for both multivariate and univariate settings. Source codes of MANTRA are publicly available in \url{https://github.com/anwarmaxsum/MANTRA}., Comment: Under Consideration in IEEE Transactions on Artificial Intelligence

The diverse and intriguing phenomena observed in twisted bilayer systems, such as graphene and transition metal dichalcogenides, prompted new questions about the emergent effects that they may host. However, the practical challenge of realizing these structures on a scale large enough for spectroscopic investigation, remains a significant hurdle, resulting in a scarcity of direct measurements of the electronic band structure of twisted transition metal dichalcogenide bilayers. Here we present a systematic nanoscale angle-resolved photoemission spectroscopy investigation of bulk, single layer, and twisted bilayer WS2 with a small twist angle of 4.4{\deg}. The experimental results are compared with theoretical calculations based on density functional theory along the high-symmetry directions {\Gamma}-K and {\Gamma}-M. Surprisingly, the electronic band structure measurements suggest a structural relaxation occurring at 4.4{\deg} twist angle, and formation of large, untwisted bilayer regions., Comment: 23 pages, 11 figures

Quantum mechanics imposes limits on the statistics of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for the simultaneous violation of multiple Bell inequalities. In the simplest case of three observers, it has been shown that violating one Bell inequality precludes the violation of any other inequality, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signalling principle and the inability of simultaneous violations of all inequalities is regarded as their fundamental property. Here we show that the Bell monogamy does not hold universally and that in fact the only monogamous situation exists only for three observers. Consequently, the nature of quantum nonlocality is truly polygamous. We present a systematic methodology for identifying quantum states and tight Bell inequalities that do not obey the monogamy principle for any number of more than three observers. The identified polygamous inequalities are experimentally violated by the measurement of Bell-type correlations using six-photon Dicke states and may be exploited for quantum cryptography as well as simultaneous self testing of multiple nodes in a quantum network., Comment: Improved version with experiment, data supporting figures and exemplary code available in the source files, 5 pages + appendix

Readout errors contribute significantly to the overall noise affecting present-day quantum computers. However, the complete characterization of generic readout noise is infeasible for devices consisting of a large number of qubits. Here we introduce an appropriately tailored quantum detector tomography protocol, the so called Quantum Detector Overlapping Tomography, which enables efficient characterization of $k-$local cross-talk effects in the readout noise as the sample complexity of the protocol scales logarithmically with the total number of qubits. We show that QDOT data provides information about suitably defined reduced POVM operators, correlations and coherences in the readout noise, as well as allows to reconstruct the correlated clusters and neighbours readout noise model. Benchmarks are introduced to verify utility and accuracy of the reconstructed model. We apply our method to investigate cross-talk effects on 79 qubit Rigetti and 127 qubit IBM devices. We discuss their readout noise characteristics, and demonstrate effectiveness of our approach by showing superior performance of correlated clusters and neighbours over models without cross-talk in model-based readout error mitigation applied to energy estimation of MAX-2-SAT Hamiltonians, with the improvement on the order of 20% for both devices., Comment: comments and suggestions are welcome

We show that the higher Pythagoras numbers for the polynomial ring are infinite $p_{2s}(K[x_1,x_2,\dots,x_n])=\infty$ provided that $K$ is a formally real field, $n\geq2$ and $s\geq 1$. This almost fully solves an old question \cite[Problem 8]{cldr1982}. The remaining open cases are precisely $n=1$ and $s>1$. Moreover, we study in detail the cone of binary octics that are sums of fourth powers of quadratic forms. We determine its facial structure as well as its algebraic boundary. This can also be seen as sums of fourth powers of linear forms on the second Veronese of $\mathbb{P}^1$. As a result, we disprove a conjecture of Reznick \cite[Conjecture 7.1]{reznick2011} which states that if a binary form $f$ is a sum of fourth powers, then it can be written as $f=f_1^2+f_2^2$ for some nonnegative forms $f_1,f_2$., Comment: 24 pages, comments welcome, revised version, title changed

Scanning probe microscopy (SPM) is ubiquitous in nanoscale science allowing the observation of features in real space down to the angstrom resolution. The scanning nature of SPM, wherein a sharp tip rasters the surface during which a physical setpoint is maintained via a control feedback loop, often implies that the image is subject to drift effects, leading to distortion of the resulting image. While there are \emph{in-operando} methods to compensate for the drift, correcting the residual linear drift in obtained images is often neglected. In this paper, we present a reciprocal space-based technique to compensate the linear drift in atomically-resolved scanning probe microscopy images without distinction of the fast and slow scanning directions; furthermore this method does not require the set of SPM images obtained for the different scanning directions. Instead, the compensation is made possible by the a priori knowledge of the lattice parameters. The method can also be used to characterize and calibrate the SPM instrument., Comment: 5 pages, 3 figures (+ 5 pages Supplementary Information)

Incommensurate heterostructures of two-dimensional (2D) materials, despite their attractive electronic behaviour, are challenging to simulate because of the absence of translation symmetry. Experimental investigations of these structures often employ scanning tunneling microscopy (STM), however there is to date no comprehensive theory to simulate an STM image in such systems. In this paper, we present a geometry-based method to generate STM images in incommensurate van der Waals (vdW) heterostructures, which we call the moir\'e plane wave expansion model (MPWEM). We generate the STM images using a weighted sum of three image terms: the non-interacting STM images of (1) the substrate layer, (2) the adsorbate layer, and (3) a semi-empirical Fourier expansion of the moir\'e wavevectors obtained analytically which results from the interaction of (1) and (2). We illustrate and benchmark the model using selected vdW 2D systems composed of structurally and electronically distinct crystals, and show that the method reproduces experimental STM images down to angstrom-scale details. The MPWEM, thanks to its simplicity, can serve as an initial prediction tool prior to more computationally expensive calculations which are often limited by the number of atoms and the requirement of periodic supercells, and thus offers a promising class of computationally-friendly STM simulations, of high relevance in the growing field of twistronics., Comment: 12 pages, 5 figures (+ supplementary information)

In this paper, we present a method that allows to further improve speech enhancement obtained with recently introduced Deep Neural Network (DNN) models. We propose a multi-channel refinement method of time-frequency masks obtained with single-channel DNNs, which consists of an iterative Complex Gaussian Mixture Model (CGMM) based algorithm, followed by optimum spatial filtration. We validate our approach on time-frequency masks estimated with three recent deep learning models, namely DCUnet, DCCRN, and FullSubNet. We show that our method with the proposed mask refinement procedure allows to improve the accuracy of estimated masks, in terms of the Area Under the ROC Curve (AUC) measure, and as a consequence the overall speech quality of the enhanced speech signal, as measured by PESQ improvement, and that the improvement is consistent across all three DNN models.

In this paper, we have investigated, using finite element calculations, the effect of initial texture on the formation of multiple necking patterns in ductile metallic rings subjected to rapid radial expansion. The mechanical behavior of the material has been modeled with the elasto-viscoplastic single crystal constitutive model developed by \citet{marin2006}. The polycrystalline microstructure of the ring has been generated using random Voronoi seeds. Both $5000$ grain and $15000$ grain aggregates have been investigated, and for each polycrystalline aggregate three different spatial distributions of grains have been considered. The calculations have been performed within a wide range of strain rates varying from $1.66 \cdot 10^4 ~ \text{s}^{-1}$ to $3.33 \cdot 10^5 ~ \text{s}^{-1}$, and the rings have been modeled with four different initial textures: isotropic texture, $\left\langle 001\right\rangle\parallel\Theta$ Goss texture, $\left\langle 001\right\rangle\parallel$ R Goss texture and $\left\langle 111\right\rangle\parallel$ Z fiber texture. The finite element results show that: (i) the spatial distribution of grains affects the location of the necks, (ii) the decrease of the grain size delays the formation of the necking pattern and increases the number of necks, (iii) the initial texture affects the number of necks, the location of the necks, and the necking time, (iv) the development of the necks is accompanied by a local increase of the slip activity. This work provides new insights into the effect of crystallographic microstructure on dynamic plastic localization and guidelines to tailor the initial texture in order to delay dynamic necking formation and, thus, to improve the energy absorption capacity of ductile metallic materials at high strain rates., Comment: 40 pages Accepted for publication in Mechanics of Materials on 3 March 2023

The aim of speech enhancement is to improve speech signal quality and intelligibility from a noisy microphone signal. In many applications, it is crucial to enable processing with small computational complexity and minimal requirements regarding access to future signal samples (look-ahead). This paper presents signal-based causal DCCRN that improves online single-channel speech enhancement by reducing the required look-ahead and the number of network parameters. The proposed modifications include complex filtering of the signal, application of overlapped-frame prediction, causal convolutions and deconvolutions, and modification of the loss function. Results of performed experiments indicate that the proposed model with overlapped signal prediction and additional adjustments, achieves similar or better performance than the original DCCRN in terms of various speech enhancement metrics, while it reduces the latency and network parameter number by around 30%.

Safety is an essential asset when learning control policies for physical systems, as violating safety constraints during training can lead to expensive hardware damage. In response to this need, the field of safe learning has emerged with algorithms that can provide probabilistic safety guarantees without knowledge of the underlying system dynamics. Those algorithms often rely on Gaussian process inference. Unfortunately, Gaussian process inference scales cubically with the number of data points, limiting applicability to high-dimensional and embedded systems. In this paper, we propose a safe learning algorithm that provides probabilistic safety guarantees but leverages the Nadaraya-Watson estimator instead of Gaussian processes. For the Nadaraya-Watson estimator, we can reach logarithmic scaling with the number of data points. We provide theoretical guarantees for the estimates, embed them into a safe learning algorithm, and show numerical experiments on a simulated seven-degrees-of-freedom robot manipulator., Comment: Accepted final version to appear in: Proc. of the IEEE Conference on Decision and Control

Transition metal dichalcogenides exhibit giant spin-orbit coupling, and intriguing spin-valley effects, which can be harnessed through proximity in van der Waals (vdW) heterostructures. Remarkably, due to the prismatic crystal field, the Zeeman-type band splitting of valence bands reach values of several hundreds of meV. While this effect is suppressed in the commonly studied hexagonal (H)-stacked bilayers due to the presence of inversion symmetry, the recent discovery of sliding ferroelectricity in rhombohedral (R-)stacked MX$_2$ bilayers (M=Mo, W; X=S, Se) suggests that the Zeeman effect could be present in these non-centrosymmetric configurations, making it even more intriguing to investigate how the spin-resolved bands would evolve during the phase transition. Here, we perform density functional theory calculations complemented by symmetry analysis to unveil the evolution of ferroelectricity during sliding and the behavior of Zeeman splitting along the transition path. While the evolution of the out-of-plane component of the electric polarization vector resembles the conventional ferroelectric transition, we observe significant in-plane components parallel to the sliding direction, reaching their maximum at the intermediate state. Moreover, we demonstrate that the R-stacked bilayers exhibit persistent Zeeman-type band splitting throughout the transition path, allowed by the lack of inversion symmetry. Further analysis of different stacking configurations generated by sliding along various directions confirms that the Zeeman effect in MX$_2$, primarily arising from the polarity of prismatic ligand coordination of the metal atom, is remarkably robust and completely governs the spin polarization of bands, independently of the sliding direction. This resilience promises robust spin transport in vdW based MX$_2$ bilayers, opening new opportunities for ferroelectric spintronics.

Our research shows that commercially available graphene on quartz modified with rhenium oxide meets the requirements for its use as a conductive and transparent anode in optoelectronic devices. The cluster growth of rhenium oxide enables an increase in the work function of graphene by 1.3 eV up to 5.2 eV, which guarantees an appropriate adjustment to the energy levels of the organic semiconductors used in OLED devices., Comment: 8 pages, 3 figures

The influence of intrinsic defects of 1T-TaS2 on charge density waves (CDW) is studied using scanning tunneling microscopy and spectroscopy (STM, STS), angle-resolved photoelectron spectroscopy (ARPES), and density functional theory (DFT). We identify several types of structural defects and find that most have a local character limited to the single CDW site, with single exception which effectively behaves as a dopant, leading to band bending and affecting multiple neighboring sites. While only one type of defect can be observed by STM topographic imaging, all defects are easily resolved by local density of states (LDOS) mapping with STS. We correlate atomically-resolved STM periodicity of defect-free 1T-TaS2 to top sulfur atoms and introduce tiling of the surface using equiangular hexagon. DFT calculations (with included Coulomb interactions) are used to investigate the electronic structure by introducing sulfur vacancy or substituting sulfur with oxygen. The sulfur vacancy is characterized by metallic properties and is identified as an origin of one of observed experimentally defects. Whereas in the case of the latter, the oxidation of 1T-TaS2 is found to result in the loss of magnetic properties expected in defect-free material., Comment: 25 pages + 5 pages in SI, 6 figures + 6 figures in SI