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Quantum annealers conventionally use forward annealing to generate heuristic solutions. Reverse annealing can potentially generate better solutions but necessitates an appropriate initial state. Ways to find such states are generally unknown or highly problem dependent, offer limited success, and severely restrict the scope of reverse annealing. We use a general method that improves the overall solution quality and quantity by feeding reverse annealing with low-quality solutions obtained from forward annealing. An experimental demonstration of solving the graph coloring problem using the D-Wave quantum annealers shows that our method is able to convert invalid solutions obtained from forward annealing to at least one valid solution obtained after assisted reverse annealing for $57\%$ of $459$ random Erd\H{o}s-R\'enyi graphs. Our method significantly outperforms random initial states, obtains more unique solutions on average, and widens the applicability of reverse annealing. Although the average number of valid solutions obtained drops exponentially with the problem size, a scaling analysis for the graph coloring problem shows that our method effectively extends the computational reach of conventional forward annealing using reverse annealing.

The analysis of empirical data through model-free inequalities leads to the conclusion that violations of Bell-type inequalities by empirical data cannot have any significance unless one believes that the universe operates according to the rules of a mathematical model., Comment: Expanded version of the paper published in Annals of Physics 469 (2024) 169742. arXiv admin note: text overlap with arXiv:2304.03962

Hybrid algorithms that combine quantum and classical resources have become commonplace in quantum computing. The variational quantum eigensolver (VQE) is routinely used to solve prototype problems. Currently, hybrid algorithms use no more than one kind of quantum computer connected to a classical computer. In this work, a novel triple-hybrid algorithm combines the effective use of a classical computer, a gate-based quantum computer, and a quantum annealer. The solution of a graph coloring problem found using a quantum annealer reduces the resources needed from a gate-based quantum computer to accelerate VQE by allowing simultaneous measurements within commuting groups of Pauli operators. We experimentally validate our algorithm by evaluating the ground state energy of H$_2$ using different IBM Q devices and the DWave Advantage system requiring only half the resources of standard VQE. Other larger problems we consider exhibit even more significant VQE acceleration. Several examples of algorithms are provided to further motivate a new field of multi-hybrid algorithms that leverage different kinds of quantum computers to gain performance improvements.

One of the most critical tasks of Microsoft sellers is to meticulously track and nurture potential business opportunities through proactive engagement and tailored solutions. Recommender systems play a central role to help sellers achieve their goals. In this paper, we present a content recommendation model which surfaces various types of content (technical documentation, comparison with competitor products, customer success stories etc.) that sellers can share with their customers or use for their own self-learning. The model operates at the opportunity level which is the lowest possible granularity and the most relevant one for sellers. It is based on semantic matching between metadata from the contents and carefully selected attributes of the opportunities. Considering the volume of seller-managed opportunities in organizations such as Microsoft, we show how to perform efficient semantic matching over a very large number of opportunity-content combinations. The main challenge is to ensure that the top-5 relevant contents for each opportunity are recommended out of a total of $\approx 40,000$ published contents. We achieve this target through an extensive comparison of different model architectures and feature selection. Finally, we further examine the quality of the recommendations in a quantitative manner using a combination of human domain experts as well as by using the recently proposed "LLM as a judge" framework.

This paper provides a detailed analysis of the important performance metrics like effective capacity and symbol error rate over fluctuating Nakagami-m fading channel. This distribution is obtained from the ratio of two random variables, following the Nakagami-m distribution and the uniform distribution. Our study derives exact analytical expressions for the EC and SER under different modulation schemes, considering the effect of channel parameters. Recognising the importance of additive Laplacian noise in today scenario, it has been considered for the error performance analysis of the system. This work may be utilised for the design and optimization of the systems operating in environments characterized by fluctuating Nakagami-m fading., Comment: 18 pages

In this paper, we design a real-time question-answering system specifically targeted for helping sellers get relevant material/documentation they can share live with their customers or refer to during a call. Taking the Seismic content repository as a relatively large scale example of a diverse dataset of sales material, we demonstrate how LLM embeddings of sellers' queries can be matched with the relevant content. We achieve this by engineering prompts in an elaborate fashion that makes use of the rich set of meta-features available for documents and sellers. Using a bi-encoder with cross-encoder re-ranker architecture, we show how the solution returns the most relevant content recommendations in just a few seconds even for large datasets. Our recommender system is deployed as an AML endpoint for real-time inferencing and has been integrated into a Copilot interface that is now deployed in the production version of the Dynamics CRM, known as MSX, used daily by Microsoft sellers.

We introduce twisted set-theoretic Yang-Baxter solutions and develop an associated cohomology theory, which extends the standard cohomology theory of Yang-Baxter solutions. By employing cocycles of twisted biquandles along with Alexander numbering, we construct state-sum invariants for knots and knotted surfaces. As an application, we use our approach to distinguish the $2$-twist spun trefoil from its reverse orientation, in line with prior findings., Comment: 24 pages, 19 figures, calculations and examples added

A biquandle is a solution to the set-theoretical Yang-Baxter equation, which yields invariants for virtual knots such as the coloring number and the state-sum invariant. A virtual biquandle enriches the structure of a biquandle by incorporating an invertible unary map. This unary operator plays a crucial role in defining the action of virtual crossings on the labels of incoming arcs in a virtual link diagram. This leads to extensions of invariants from biquandles to virtual biquandles, thereby enhancing their strength. In this article, we establish a connection between the coloring invariant derived from biquandles and virtual biquandles. We prove that the number of colorings of a virtual link $L$ by virtual biquandles can be recovered from colorings by biquandles. We achieve this by proving the equivalence between two different representations of virtual braid groups. Furthermore, we introduce a new set of labeling rules using which one can construct a presentation of the associated fundamental virtual biquandle of $L$ using only the relations coming from the classical crossings. This is an improvement to the traditional method, where writing down a presentation of the associated fundamental virtual biquandle necessitates noting down the relations arising from the classical and virtual crossings., Comment: 12 pages, title changed, references updated

Segmenting a moving needle in ultrasound images is challenging due to the presence of artifacts, noise, and needle occlusion. This task becomes even more demanding in scenarios where data availability is limited. In this paper, we present a novel approach for needle segmentation for 2D ultrasound that combines classical Kalman Filter (KF) techniques with data-driven learning, incorporating both needle features and needle motion. Our method offers three key contributions. First, we propose a compatible framework that seamlessly integrates into commonly used encoder-decoder style architectures. Second, we demonstrate superior performance compared to recent state-of-the-art needle segmentation models using our novel convolutional neural network (CNN) based KF-inspired block, achieving a 15\% reduction in pixel-wise needle tip error and an 8\% reduction in length error. Third, to our knowledge we are the first to implement a learnable filter to incorporate non-linear needle motion for improving needle segmentation., Comment: 7 pages, 4 figures, accepted at ISBI 2024

Given the imperative for advanced wireless networks in the next generation and the rise of real-time applications within wireless communication, there is a notable focus on investigating data rate performance across various fading scenarios. This research delved into analyzing the effective throughput of the shadowed Beaulieu-Xie (SBX) composite fading channel using the PDF-based approach. To get the simplified relationship between the performance parameter and channel parameters, the low-SNR and the high-SNR approximation of the effective rate are also provided. The proposed formulations are evaluated for different values of system parameters to study their impact on the effective throughput. Also, the impact of the delay parameter on the EC is investigated. Monte-Carlo simulations are used to verify the facticity of the deduced equations., Comment: 18 pages

We explore residually finite and profinite quandles. We prove that the endomorphism monoid and the automorphism group of finitely generated residually finite quandles are residually finite. In fact, we establish the similar result for a broad class of residually finite quandles. We provide a topological characterization of profinite quandles. We establish necessary and sufficient conditions for profinite quandles ensuring that their endomorphism monoids and automorphism groups are profinite., Comment: 14 pages

Resection and whole brain radiotherapy (WBRT) are the standards of care for the treatment of patients with brain metastases (BM) but are often associated with cognitive side effects. Stereotactic radiosurgery (SRS) involves a more targeted treatment approach and has been shown to avoid the side effects associated with WBRT. However, SRS requires precise identification and delineation of BM. While many AI algorithms have been developed for this purpose, their clinical adoption has been limited due to poor model performance in the clinical setting. Major reasons for non-generalizable algorithms are the limitations in the datasets used for training the AI network. The purpose of this study was to create a large, heterogenous, annotated BM dataset for training and validation of AI models to improve generalizability. We present a BM dataset of 200 patients with pretreatment T1, T1 post-contrast, T2, and FLAIR MR images. The dataset includes contrast-enhancing and necrotic 3D segmentations on T1 post-contrast and whole tumor (including peritumoral edema) 3D segmentations on FLAIR. Our dataset contains 975 contrast-enhancing lesions, many of which are sub centimeter, along with clinical and imaging feature information. We used a streamlined approach to database-building leveraging a PACS-integrated segmentation workflow., Comment: 12 pages, 2 figures, 1 table

Entanglement is a valuable resource in quantum information technologies. The practical implementation of entangled photon sources faces obstacles from imperfections and defects inherent in physical systems, resulting in a loss or degradation of entanglement. The topological photonic insulators, however, have emerged as promising candidates, demonstrating an exceptional capability to resist defect-induced scattering, thus enabling the development of robust entangled sources. Despite their inherent advantages, building programmable topologically protected entangled sources remains challenging due to complex device designs and weak material nonlinearity. Here we present a development in entangled photon pair generation achieved through a non-magnetic and tunable anomalous Floquet insulator, utilizing an optical spontaneous four-wave mixing process. We verify the non-classicality and time-energy entanglement of the photons generated by our topological system. Our experiment demonstrates a substantial enhancement in nonclassical photon pair generation compared to devices reliant only on topological edge states. Our result could lead to the development of resilient quantum sources with potential applications in quantum technology., Comment: 24 pages, 14 figures

Peripheral nerve blocks are crucial to treatment of post-surgical pain and are associated with reduction in perioperative opioid use and hospital stay. Accurate interpretation of sono-anatomy is critical for the success of ultrasound (US) guided peripheral nerve blocks and can be challenging to the new operators. This prospective study enrolled 227 subjects who were systematically scanned for supraclavicular and interscalene brachial plexus in various settings using three different US machines to create a dataset of 227 unique videos. In total, 41,000 video frames were annotated by experienced anaesthesiologists using partial automation with object tracking and active contour algorithms. Four baseline neural network models were trained on the dataset and their performance was evaluated for object detection and segmentation tasks. Generalizability of the best suited model was then tested on the datasets constructed from separate US scanners with and without fine-tuning. The results demonstrate that deep learning models can be leveraged for real time segmentation of supraclavicular brachial plexus in neck ultrasonography videos with high accuracy and reliability. Model was also tested for its ability to differentiate between supraclavicular and adjoining interscalene brachial plexus. The entire dataset has been released publicly for further study by the research community.

We introduce PyRCA, an open-source Python machine learning library of Root Cause Analysis (RCA) for Artificial Intelligence for IT Operations (AIOps). It provides a holistic framework to uncover the complicated metric causal dependencies and automatically locate root causes of incidents. It offers a unified interface for multiple commonly used RCA models, encompassing both graph construction and scoring tasks. This library aims to provide IT operations staff, data scientists, and researchers a one-step solution to rapid model development, model evaluation and deployment to online applications. In particular, our library includes various causal discovery methods to support causal graph construction, and multiple types of root cause scoring methods inspired by Bayesian analysis, graph analysis and causal analysis, etc. Our GUI dashboard offers practitioners an intuitive point-and-click interface, empowering them to easily inject expert knowledge through human interaction. With the ability to visualize causal graphs and the root cause of incidents, practitioners can quickly gain insights and improve their workflow efficiency. This technical report introduces PyRCA's architecture and major functionalities, while also presenting benchmark performance numbers in comparison to various baseline models. Additionally, we demonstrate PyRCA's capabilities through several example use cases., Comment: Github repo: https://github.com/salesforce/PyRCA

The translation of AI-generated brain metastases (BM) segmentation into clinical practice relies heavily on diverse, high-quality annotated medical imaging datasets. The BraTS-METS 2023 challenge has gained momentum for testing and benchmarking algorithms using rigorously annotated internationally compiled real-world datasets. This study presents the results of the segmentation challenge and characterizes the challenging cases that impacted the performance of the winning algorithms. Untreated brain metastases on standard anatomic MRI sequences (T1, T2, FLAIR, T1PG) from eight contributed international datasets were annotated in stepwise method: published UNET algorithms, student, neuroradiologist, final approver neuroradiologist. Segmentations were ranked based on lesion-wise Dice and Hausdorff distance (HD95) scores. False positives (FP) and false negatives (FN) were rigorously penalized, receiving a score of 0 for Dice and a fixed penalty of 374 for HD95. Eight datasets comprising 1303 studies were annotated, with 402 studies (3076 lesions) released on Synapse as publicly available datasets to challenge competitors. Additionally, 31 studies (139 lesions) were held out for validation, and 59 studies (218 lesions) were used for testing. Segmentation accuracy was measured as rank across subjects, with the winning team achieving a LesionWise mean score of 7.9. Common errors among the leading teams included false negatives for small lesions and misregistration of masks in space.The BraTS-METS 2023 challenge successfully curated well-annotated, diverse datasets and identified common errors, facilitating the translation of BM segmentation across varied clinical environments and providing personalized volumetric reports to patients undergoing BM treatment.

Efficient artificial photosynthesis systems are currently realized as catalyst- and surfacefunctionalized photovoltaic tandem- and triple-junction devices, enabling photoelectrochemical (PEC) water oxidation while simultaneously recycling CO2 and generating hydrogen as a solar fuel for storable renewable energy. Although PEC systems also bear advantages for the activation of dinitrogen - such as a high system tunability with respect to the electrocatalyst integration and a directly controllable electron flux to the anchoring catalyst through the adjustability of incoming irradiation - only a few PEC devices have been developed and investigated for this purpose. We have developed a series of photoelectrodeposition procedures to deposit mixed-metal electrocatalyst nanostructures directly on the semiconductor surface for light-assisted dinitrogen activation. These electrocatalyst compositions containing Co, Mo and Ru in different atomic ratios follow previously made recommendations of metal compositions for dinitrogen reduction and exhibit different physical properties. XPS studies of the photoelectrode surfaces reveal that our electrocatalyst films are to a large degree nitrogen-free after their fabrication, which is generally difficult to achieve with traditional magnetron sputtering or e-beam evaporation techniques. Initial chronoamperometric measurements of the p-InP photoelectrode coated with the Co-Mo alloy electrocatalyst show higher photocurrent densities in the presence of N2(g) than in the presence of Ar at -0.09 V vs RHE. Indications of successful dinitrogen activation have also been found in consecutive XPS studies, where both, N 1s and Mo 3d spectra, reveal evidence of nitrogen-metal interactions.

Artificial Intelligence for IT operations (AIOps) aims to combine the power of AI with the big data generated by IT Operations processes, particularly in cloud infrastructures, to provide actionable insights with the primary goal of maximizing availability. There are a wide variety of problems to address, and multiple use-cases, where AI capabilities can be leveraged to enhance operational efficiency. Here we provide a review of the AIOps vision, trends challenges and opportunities, specifically focusing on the underlying AI techniques. We discuss in depth the key types of data emitted by IT Operations activities, the scale and challenges in analyzing them, and where they can be helpful. We categorize the key AIOps tasks as - incident detection, failure prediction, root cause analysis and automated actions. We discuss the problem formulation for each task, and then present a taxonomy of techniques to solve these problems. We also identify relatively under explored topics, especially those that could significantly benefit from advances in AI literature. We also provide insights into the trends in this field, and what are the key investment opportunities.

We take the point of view that building a one-way bridge from experimental data to mathematical models instead of the other way around avoids running into controversies resulting from attaching meaning to the symbols used in the latter. In particular, we show that adopting this view offers new perspectives for constructing mathematical models for and interpreting the results of Einstein-Podolsky-Rosen-Bohm experiments. We first prove new Bell-type inequalities constraining the values of the four correlations obtained by performing Einstein-Podolsky-Rosen-Bohm experiments under four different conditions. The proof is ``model-free'' in the sense that it does not refer to any mathematical model that one imagines to have produced the data. The constraints only depend on the number of quadruples obtained by reshuffling the data in the four data sets without changing the values of the correlations. These new inequalities reduce to model-free versions of the well-known Bell-type inequalities if the maximum fraction of quadruples is equal to one. Being model-free, a violation of the latter by experimental data implies that not all the data in the four data sets can be reshuffled to form quadruples. Furthermore, being model-free inequalities, a violation of the latter by experimental data only implies that any mathematical model assumed to produce this data does not apply. Starting from the data obtained by performing Einstein-Podolsky-Rosen-Bohm experiments, we construct instead of postulate mathematical models that describe the main features of these data. The mathematical framework of plausible reasoning is applied to reproducible and robust data, yielding without using any concept of quantum theory, the expression of the correlation for a system of two spin-1/2 objects in the singlet state. (truncated here), Comment: Corrected typo's, minor corrections in appendix B.3, major correction in section 11.4.2

A transparent polarisation sensitive phase pattern exhibits a position and polarisation dependent phase shift of transmitted light and it represents a unitary transformation. A quantum ghost image of this pattern is produced with hyper-entangled photons consisting of Einstein-Podolsky-Rosen (EPR) and polarisation entanglement. In quantum ghost imaging, a single photon interacts with the pattern and is detected by a stationary detector and a non-interacting photon is imaged on a coincidence camera. EPR entanglement manifests spatial correlations between an object plane and a ghost image plane, whereas a polarisation dependent phase shift exhibited by the pattern is detected with polarisation entanglement. In this quantum ghost imaging, the which-position-polarisation information of a photon interacting with the pattern is not present in the experiment. A quantum ghost image is constructed by measuring correlations of the polarisation-momentum of an interacting photon with polarisation-position of a non-interacting photon. The experiment is performed with a coincidence single photon detection camera, where a non-interacting photon travels a long optical path length of 17.83~$m$ from source to camera and a pattern is positioned at an optical distance of 19.16~$m$ from the camera., Comment: 10 pages, 4 figures

We present a new inequality constraining correlations obtained when performing Einstein-Podolsky-Rosen-Bohm experiments. The proof does not rely on mathematical models that are imagined to have produced the data and is therefore ``model-free''. The new inequality contains the model-free version of the well-known Bell-CHSH inequality as a special case. A violation of the latter implies that not all the data pairs in four data sets can be reshuffled to create quadruples. This conclusion provides a new perspective on the implications of the violation of Bell-type inequalities by experimental data., Comment: Extended version of Annals of Physics, Volume 453, 169314, 2023 (https://doi.org/10.1016/j.aop.2023.169314)

Over the last few decades, different types of plasma waves (e.g., the ion acoustic waves (IAWs), electrostatic solitary waves (ESWs), upper/lower hybrid waves, the Langmuir waves etc.) have been observed in the upstream, downstream and ramp regions of the collisionless interplanetary (IP) shocks. These waves appear as short duration (only a few milliseconds at 1 au) electric field signatures in the in-situ measurements, with typical frequencies $\sim1-10$ kHz. A number of IAW features at the IP shocks seem to be unexplained by kinetic models and requires a new modeling effort. Thus, this paper is dedicated to bridge this gap. In this paper, we model the linear IAWs inside the shock ramp, by devising a novel linearization method of the two-fluid magnetohydrodynamic equations with spatially dependent shock parameters. It is found that, for parallel propagating waves, the linear dispersion relation leads to a finite growth rate dependent on the the shock density compression ratio, as Wind data suggest. Further analysis reveals that the wave frequency grows towards the downstream within the shock ramp, and the wave growth rate is independent of the electron-to-ion temperature ratio, as Magnetospheric Multiscale (MMS) in-situ measurements suggest, and uniform within the shock ramp. Thus, this study help understand the characteristics of the IAWs at the collisionless IP shocks., Comment: 16 pages, 4 figures, Accepted for publication in ApJ

Quandles are self-distributive, right-invertible, idempotent algebras. A group with conjugation for binary operation is an example of a quandle. Given a quandle $(Q, \ast)$ and a positive integer $n$, define $a\ast_n b = (\cdots (a\ast \underbrace{b)\ast \cdots )\ast b}_{n}$, where $a, b \in Q$. Then, $(Q, \ast_n)$ is again a quandle. We set forth the following problem. ``Find $(Q, \ast)$ such that the sequence $\{(Q, \ast_n)\, :\, n\in \mathbb{Z}^+ \}$ is made up of pairwise non-isomorphic quandles.'' In this article we find such a quandle $(Q, \ast)$. We study the general linear group of $2$-by-$2$ matrices over $\mathbb{C}$ as a quandle under conjugation. Its (algebraically) connected components, that is, its conjugacy classes, are subquandles of it. We show the latter are connected as quandles and prove rigidity results about them such as the dihedral quandle of order $3$ is not a subquandle for most of them. Then we consider the quandle which is the projective linear group of $2$-by-$2$ matrices over $\mathbb{C}$ with conjugation, and prove it solves the problem above. In the course of this work we prove a sufficient and necessary condition for a quandle to be latin. This will reduce significantly the complexity of algorithms for ascertaining if a quandle is latin., Comment: 25 pages

We report on two major hybrid applications of quantum computing, namely, the quantum approximate optimisation algorithm (QAOA) and the variational quantum eigensolver (VQE). Both are hybrid quantum classical algorithms as they require incremental communication between a classical central processing unit and a quantum processing unit to solve a problem. We find that the QAOA scales much better to larger problems than random guessing, but requires significant computational resources. In contrast, a coarsely discretised version of quantum annealing called approximate quantum annealing (AQA) can reach the same promising scaling behaviour using much less computational resources. For the VQE, we find reasonable results in approximating the ground state energy of the Heisenberg model when suitable choices of initial states and parameters are used. Our design and implementation of a general quasi-dynamical evolution further improves these results., Comment: This article is a book contribution. The book is freely available at http://hdl.handle.net/2128/31840

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There are problems with VQE that forbid a favourable scaling towards quantum advantage. In order to alleviate the problems, we propose and extensively test a quantum annealing inspired heuristic that supplements VQE. The improved VQE enables an efficient initial state preparation mechanism, in a recursive manner, for a quasi-dynamical unitary evolution. We conduct an in-depth scaling analysis of finding the ground state energies with increasing lattice sizes of the Heisenberg model, employing simulations of up to $40$ qubits that manipulate the complete state vector. For the current devices, we further propose a benchmarking toolkit using a mean-field model and test it on IBM Q devices. The improved VQE avoids barren plateaus, exits local minima, and works with low-depth circuits. Realistic gate execution times estimate a longer computational time to complete the same computation on a fully functional error-free quantum computer than on a quantum computer emulator implemented on a classical computer. However, our proposal can be expected to help accurate estimations of the ground state energies beyond $50$ qubits when the complete state vector can no longer be stored on a classical computer, thus enabling quantum advantage.

We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. Using a massively parallel universal quantum computer simulator, we observe that a low-depth-circuit ansatz advantageously exploits the efficiently preparable N\'{e}el initial state, avoids potential barren plateaus, and works for both one- and two-dimensional lattices. The analysis reflects the decisive ingredients required for a simulation by comparing different ans\"{a}tze, initial parameters, and gradient-based versus gradient-free optimizers. Extrapolation to the thermodynamic limit accurately yields the analytical value for the ground state energy, given by the Bethe ansatz. We predict that a fully functional quantum computer with 100 qubits can calculate the ground state energy with a relatively small error.

A transparent polarisation sensitive phase pattern makes a polarisation dependent transformation of quantum state of photons without absorbing them. Such an invisible pattern can be imaged with quantum entangled photons by making joint quantum measurements on photons. This paper shows a long path experiment to quantum image a transparent polarisation sensitive phase pattern with hyper-entangled photon pairs involving momentum and polarisation degrees of freedom. In the imaging configuration, a single photon interacts with the pattern while the other photon, which has never interacted with the pattern, is measured jointly in a chosen polarisation basis and in a quantum superposition basis of its position which is equivalent to measuring its momentum. Individual photons of each hyper-entangled pair cannot provide a complete image information. The image is constructed by measuring the polarisation state and position of the interacting photon corresponding to a measurement outcome of the non-interacting photon. This paper presents a detailed concept, theory and free space long path experiments on quantum imaging of polarisation sensitive phase patterns., Comment: 13 pages, 7 figures

We investigate pairing and superconductivity in the attractive Fermi Hubbard model on the one-dimensional sawtooth lattice, which exhibits a flat band by fine-tuning the hopping rates. We first solve the two-body problem, both analytically and numerically, to extract the binding energy and the effective mass of the pairs. Based on the DMRG method, we address the ground-state properties of the many-body system, assuming equal spin populations. We compare our results with those available for a linear chain, where the model is integrable by Bethe ansatz, and show that the multiband nature of the system substantially modifies the physics of the BCS-BEC crossover. Near a flat band, the chemical potential remains always close to its zero-density limit predicted by the two-body physics. In contrast, the pairing gap exhibits a remarkably strong density dependence and, differently from the pair binding energy, it is no longer peaked at the flat-band point. We show that these results can be interpreted in terms of polarization screening effects, due to an anomalous attraction between pairs in the medium and single fermions. Importantly, we unveil that three-body bound states (trimers) exist in the sawtooth lattice, in sharp contrast with the linear chain geometry, and we compute their binding energy. The nature of these states is investigated via a strong coupling variational approach, revealing that they originate from tunneling-induced exchange processes., Comment: Revised version: title modified and new section with more results on trimers

We introduce Merlion, an open-source machine learning library for time series. It features a unified interface for many commonly used models and datasets for anomaly detection and forecasting on both univariate and multivariate time series, along with standard pre/post-processing layers. It has several modules to improve ease-of-use, including visualization, anomaly score calibration to improve interpetability, AutoML for hyperparameter tuning and model selection, and model ensembling. Merlion also provides a unique evaluation framework that simulates the live deployment and re-training of a model in production. This library aims to provide engineers and researchers a one-stop solution to rapidly develop models for their specific time series needs and benchmark them across multiple time series datasets. In this technical report, we highlight Merlion's architecture and major functionalities, and we report benchmark numbers across different baseline models and ensembles., Comment: 22 pages, 1 figure, 14 tables

The seamless forecast approach of subseasonal to seasonal scale variability has been succeeding in the forecast of multiple meteorological scales in a uniform framework. In this paradigm, it is hypothesized that reduction in initial error in dynamical forecast would help to reduce forecast error in extended lead-time up to 2-3 weeks. This is tested in a version of operational extended range forecasts based on Climate Forecast System version 2 (CFSv2) developed at Indian Institute of Tropical Meteorology (IITM), Pune. Forecast skills are assessed to understand the role of initial errors on the prediction skill for MJO. A set of lowest and highest initial day error (LIDE & HIDE) cases are defined and the error-growth for these categories are analysed for the strong MJO events during May to September (MJJAS). The MJO forecast initial errors are categorized and defined using the well-known multivariate MJO index introduced by Wheeler &Hendon (2004). The probability distribution of bivariate RMSE and error growth evolution (first order difference of index error for each successive lead days) with respect to extended range lead-time are used as metrics in this analysis. The result showed that initial error is not showing any influence in the skill of model after a lead time of 7-10 days and the error growth remains the same for both set of errors. A rapid error growth evolution of same order is seen for both the classified cases. Further the physical attribution of these errors is studied and found that the errors originate from the events with initial phase in Western Pacific and Indian Ocean. The spatial distribution of OLR and the zonal winds also confirms the same. The study emphasises the importance of better representation of MJO phases especially over Indian ocean in the model to improve the MJO prediction rather than focusing primarily on the initial condition, Comment: 27 pages, 9 figures

We consider flows $(X,T)$, given by actions $(t, x) \to tx$, on a compact metric space $X$ with a discrete $T$ as an acting group. We study a new class of flows - the \textsc{Strongly Rigid} ($ \mathbf {SR} $) \ flows, that are properly contained in the class of distal ($ \mathbf D $) flows and properly contain the class of all equicontinuous ($ \mathbf {EQ} $) flows. Thus, $\mathbf {EQ} \ \text{flows} \subsetneqq \mathbf {SR} \ \text{flows} \subsetneqq \mathbf{ D} \ \text{flows}$. The concepts of equicontinuity, strong rigidity and distality coincide for the induced flow $(2^X,T)$. We observe that strongly rigid $(X,T)$ gives distinct properties for the induced flow $(2^X,T)$ and its enveloping semigroup $E(2^X)$. We further study strong rigidity in case of particular semiflows $(X,S)$, with $S$ being a discrete acting semigroup.

A general method to mitigate the effect of errors in quantum circuits is outlined. The method is developed in sight of characteristics that an ideal method should possess and to ameliorate an existing method which only mitigates state preparation and measurement errors. The method is tested on different IBM Q quantum devices, using randomly generated circuits with up to four qubits. A large majority of results show significant error mitigation.

The paper develops a general theory of orderability of quandles with a focus on link quandles of tame links and gives some general constructions of orderable quandles. We prove that knot quandles of many fibered prime knots are right-orderable, whereas link quandles of most non-trivial torus links are not right-orderable. As a consequence, we deduce that the knot quandle of the trefoil is neither left nor right orderable. Further, it is proved that link quandles of certain non-trivial positive (or negative) links are not bi-orderable, which includes some alternating knots of prime determinant and alternating Montesinos links. The paper also explores interconnections between orderability of quandles and that of their enveloping groups. The results establish that orderability of link quandles behave quite differently than that of corresponding link groups., Comment: 25 pages, to appear in Proceedings of the Edinburgh Mathematical Society

This paper investigates the Cyber-Physical behavior of users in a large indoor shopping mall by leveraging anonymized (opt in) Wi-Fi association and browsing logs recorded by the mall operators. Our analysis shows that many users exhibit a high correlation between their cyber activities and their physical context. To find this correlation, we propose a mechanism to semantically label a physical space with rich categorical information from DBPedia concepts and compute a contextual similarity that represents a user's activities with the mall context. We demonstrate the application of cyber-physical contextual similarity in two situations: user visit intent classification and future location prediction. The experimental results demonstrate that exploitation of contextual similarity significantly improves the accuracy of such applications., Comment: Accepted in ACM Transactions on Sensor Networks, 2020

The ground-state properties of the Hubbard chain with on-site repulsion and anisotropic nearest-neighbor attraction are investigated by means of density matrix renormalization group calculations. The non-local attraction acts between fermions of one spin component only, mimicking the effect of p-wave Feshbach resonances in cold-atom systems. We analyze the onset of itinerant ferromagnetism, pinpointing the critical attraction strength where partially and fully ferromagnetic states occur. In the cold-atom setup, where the two (pseudo) spin populations are separately conserved, ferromagnetism occurs with the nucleation of a fully imbalanced band-insulating domain hosting the attractive component only. The size of this domain grows with the attraction strength, therefore increasing the (opposite) imbalance of the other domain, until the two spin components are fully separated. In the presence of a harmonic trap, the ferromagnetic state hosts a partially imbalanced domain in the center with an excess of the attractive component and filling lower than one. This central region is surrounded by fully imbalanced domains, located in the trap tails, hosting only fermions belonging to the other component., Comment: 8 pages, 7 figures

In this paper, we define the notion of a virtually symmetric representation of representations of virtual braid groups and prove that many known representations are equivalent to virtually symmetric. Using one such representation, we define the notion of virtual link groups which is an extension of virtual link groups defined by Kauffman. Moreover, we introduce the concept of marked Gauss diagrams as a generalisation of Gauss diagrams and their interpretation in terms of knot-like diagrams. We extend the definition of virtual link groups to marked Gauss diagrams and define their peripheral structure. We define $C_m$-groups and prove that every group presented by a $1$-irreducible $C_1$-presentation of deficiency $1$ or $2$ can be realized as the group of a marked Gauss diagram., Comment: 27 pages, 13 figures. Minor change in the structure of the paper, symbols, figures, accepted in Topology and its Applications

We use discrete-event simulation to construct a subquantum model that can reproduce the quantum-theoretical prediction for the statistics of data produced by the Einstein-Podolsky-Rosen-Bohm experiment and an extension thereof. This model satisfies Einstein's criterion of locality and generates data in an event-by-event and cause-and-effect manner. We show that quantum theory can describe the statistics of the simulation data for a certain range of model parameters only.

It is a widely accepted view that COVID 19 is either transmitted via surface contamination or via close contact of an un-infected person with an infected person. Surface contamination usually happens when infected water droplets from exhalation/sneeze/cough of COVID sick person settle on nearby surfaces. To curb this, social distancing and good hand hygiene advise is advocated by World health Organization (WHO). We argue that COVID 19 coronovirus can also be airborne in a puff cloud loaded with infected droplets generated by COVID sick person. An elementary calculation shows that a $5~\mu m$ respiratory infected droplet can remain suspended for about 9.0 minutes and a $2~\mu m$ droplet can remain suspended for about an hour! And social distancing advise of 3 feet by WHO and 6 feet by CDC (Centers for Disease Control and Prevention) may not be sufficient in some circumstances as discussed in the text., Comment: 6 pages and 1 figure

We obtained a density-dependent analytical expression of binding energy per nucleon for different neutron-proton asymmetry of the nuclear matter (NM) with a polynomial fitting, which manifests the results of effective field theory motivated relativistic mean-field (E-RMF) model. This expression has the edge over the Br$\ddot{u}$ckner energy density functional [Phys. Rev. {\bf 171}, 1188 (1968)] since it resolves the Coster-Band problem. The NM parameters like incompressibility, neutron pressure, symmetry energy, and its derivatives are calculated using the acquired expression of energy per nucleon. Further, the weight function calculated by E-RMF densities are folded with calculated NM parameters within coherent density fluctuation model to find the properties of closed/semi-closed-shell even-even $^{16}$O, $^{40}$Ca, $^{48}$Ca, $^{56}$Ni, $^{90}$Zr, $^{116}$Sn, and $^{208}$Pb nuclei. The values obtained for the neutron pressure $P^{A}$, symmetry energy $S^{A}$ and its derivative $L_{sym}^A$ known as slope parameter, lie within a narrow domain whereas there is a large variation in isoscalar incompressibility $K^{A}$ and surface incompressibility $K_{sym}^{A}$ while moving from light to heavy nuclei. The sizable variation in $K^{A}$ and $K_{sym}^{A}$ for light and heavy nuclei depicts their structural dependence due to the peculiar density distribution of each nucleus. A comparison of surface quantities calculated in the present work has also been made with ones obtained via Br$\ddot{u}$ckner energy density functional., Comment: 8 pages, 5 figures, 3 tables. Published in Phys. Rev. C 103 , 024305 (2021)

We investigate the ground state properties of a non-locally coupled bosonic system in a bilayer optical superlattice by considering bosons in one layer to be of softcore in nature and separately allowing two and three body hardcore constraints on the other layer. We find that the presence of different constraints on bosons in one layer influences the overall phase diagram exhibiting various Mott insulator phases at incommensurate densities due to the presence of the superlattice potential apart from the usual Mott insulators at commensurate densities. Moreover, the presence of two or three-body constraints significantly modifies the Mott insulator-Superfluid phase transition points as a function of the superlattice potential. Due to the various competing interactions, constraints and superlattice potential the phase diagrams exhibit significantly different features. We obtain the complete phase diagrams by using the cluster-mean-field theory approach. We further extend this work to a coupled two-leg ladder superlattice where we obtain similar physics using the density matrix renormalization group method ., Comment: 10 pages, 10 figures

Anomaly detection refers to the task of finding unusual instances that stand out from the normal data. In several applications, these outliers or anomalous instances are of greater interest compared to the normal ones. Specifically in the case of industrial optical inspection and infrastructure asset management, finding these defects (anomalous regions) is of extreme importance. Traditionally and even today this process has been carried out manually. Humans rely on the saliency of the defects in comparison to the normal texture to detect the defects. However, manual inspection is slow, tedious, subjective and susceptible to human biases. Therefore, the automation of defect detection is desirable. But for defect detection lack of availability of a large number of anomalous instances and labelled data is a problem. In this paper, we present a convolutional auto-encoder architecture for anomaly detection that is trained only on the defect-free (normal) instances. For the test images, residual masks that are obtained by subtracting the original image from the auto-encoder output are thresholded to obtain the defect segmentation masks. The approach was tested on two data-sets and achieved an impressive average F1 score of 0.885. The network learnt to detect the actual shape of the defects even though no defected images were used during the training.

Humans can easily detect a defect (anomaly) because it is different or salient when compared to the surface it resides on. Today, manual human visual inspection is still the norm because it is difficult to automate anomaly detection. Neural networks are a useful tool that can teach a machine to find defects. However, they require a lot of training examples to learn what a defect is and it is tedious and expensive to get these samples. We tackle the problem of teaching a network with a low number of training samples with a system we call AnoNet. AnoNet's architecture is similar to CompactCNN with the exceptions that (1) it is a fully convolutional network and does not use strided convolution; (2) it is shallow and compact which minimizes over-fitting by design; (3) the compact design constrains the size of intermediate features which allows training to be done without image downsizing; (4) the model footprint is low making it suitable for edge computation; and (5) the anomaly can be detected and localized despite the weak labelling. AnoNet learns to detect the underlying shape of the anomalies despite the weak annotation as well as preserves the spatial localization of the anomaly. Pre-seeding AnoNet with an engineered filter bank initialization technique reduces the total samples required for training and also achieves state-of-the-art performance. Compared to the CompactCNN, AnoNet achieved a massive 94% reduction of network parameters from 1.13 million to 64 thousand parameters. Experiments were conducted on four data-sets and results were compared against CompactCNN and DeepLabv3. AnoNet improved the performance on an average across all data-sets by 106% to an F1 score of 0.98 and by 13% to an AUROC value of 0.942. AnoNet can learn from a limited number of images. For one of the data-sets, AnoNet learnt to detect anomalies after a single pass through just 53 training images.

Based on the matrix product states method, we investigate numerically the ground state properties of one-dimensional mixtures of repulsive bosons and spin-imbalanced attractive fermions, the latter being in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where Cooper pairs condense at a finite momentum $k=k_{FFLO}$. We find that the visibility of such a state is dramatically enhanced as the repulsive Bose-Fermi mixture is brought close to the phase-separation point. In particular, large amplitude self-induced oscillations with wave-vector $2k_{FFLO}$ appear in both the fermion total density and the boson density profiles, leaving sharp fingerprints in the corresponding static structure factors. We show that these features remain well visible in cold atoms systems trapped longitudinally by a smooth flat-bottom potential. Hence bosons can be used to directly reveal the modulated Fermi superfluid in experiments., Comment: enlarged version, 9 pages, 10 figures, added discussion on attractive Bose-Fermi mixtures

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