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Wire Arc Additive Manufacturing (WAAM) is a metal 3D printing technology that deposits molten metal wire on a substrate to form desired geometries. Articulated robot arms are commonly used in WAAM to produce complex geometric shapes. However, they mostly rely on proprietary robot and weld control software that limits process tuning and customization, incorporation of third-party sensors, implementation on robots and weld controllers from multiple vendors, and customizable user programming. This paper presents a general open-source software architecture for WAAM that addresses these limitations. The foundation of this architecture is Robot Raconteur, an open-source control and communication framework that serves as the middleware for integrating robots and sensors from different vendors. Based on this architecture, we developed an end-to-end robotic WAAM implementation that takes a CAD file to a printed WAAM part and evaluates the accuracy of the result. The major components in the architecture include part slicing, robot motion planning, part metrology, in-process sensing, and process tuning. The current implementation is based on Motoman robots and Fronius weld controller, but the approach is applicable to other industrial robots and weld controllers. The capability of the WAAM tested is demonstrated through the printing of parts of various geometries and acquisition of in-process sensor data for motion adjustment.

This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown scalar coefficient (denoted by $\beta$), and the error is a random operator. In the course of this study, we propose a quantum version of a class of estimators (denoted by $M$ estimator) of $\beta$, and the large sample behaviour of those quantum version of the estimators are derived, given the fact that the true model is also linear and the samples are observed eigenvalue pairs of the operator valued observables.

In this article, we study whether the slope functions of two functional regression models in two samples are associated with any arbitrary transformation (barring constant and linear transformation) or not along the vertical axis. In order to address this issue, a statistical testing of the hypothesis problem is formalized, and the test statistic is formed based on the estimated second derivative of the unknown transformation. The asymptotic properties of the test statistics are investigated using some advanced techniques related to the empirical process. Moreover, to implement the test for small sample size data, a Bootstrap algorithm is proposed, and it is shown that the Bootstrap version of the test is as good as the original test for sufficiently large sample size. Furthermore, the utility of the proposed methodology is shown for simulated data sets, and DTI data is analyzed using this methodology., Comment: Some typos have been fixed

Large language models (LLMs) are very performant connectionist systems, but do they exhibit more compositionality? More importantly, is that part of why they perform so well? We present empirical analyses across four LLM families (12 models) and three task categories, including a novel task introduced below. Our findings reveal a nuanced relationship in learning of compositional strategies by LLMs -- while scaling enhances compositional abilities, instruction tuning often has a reverse effect. Such disparity brings forth some open issues regarding the development and improvement of large language models in alignment with human cognitive capacities., Comment: Accepted to ICML 2024 Workshop on LLMs & Cognition

We report an extensive computational and experimental investigation of droplet impact and subsequent splitting hydrodynamics on superhydrophobic wedges. 2D and necessary 3D simulations using the volume of fluid method, backed with experimentations, have been performed to predict the droplet impact, spreading, split up, retraction against sliding, and daughter droplet lift off events from the SH wedge. In particular, we examine how the wedge angle , wedge asymmetry , Weber number and normalized Bond number influence the post-impact dynamics. We observe that for symmetric wedges, the maximum spread factor of the droplet decreases with an increase in wedge angle at a fixed We. At high wedge angles, the sharp steepness of the wedge causes less contact area for the droplet to spread. For the asymmetric wedges, it has been noted that beta max increases with an increase in the We due to the higher inertial forces of the droplet against sliding. Furthermore, the increases with an increase in Bo at a fixed We due to the dominance of the gravitational force over the capillary force of the droplet. It has been also found that at the same Bo, the increases with an increase in We due to the dominance of inertial forces over the capillary forces. The split volume of daughter droplets during the split up stage for different symmetric and asymmetric wedge angles has been discussed. In general, our 2D simulations agree well with the experiments for a major part of the droplet lifetime. Further, we have conducted a detailed 3D simulation based energy budget analysis to estimate the temporal evolution of the various energy components at different post impact hydrodynamic regimes.

Cloud workloads have dominated generative AI based on large language models (LLM). Specialized hardware accelerators, such as GPUs, NPUs, and TPUs, play a key role in AI adoption due to their superior performance over general-purpose CPUs. The AI models and the data are often highly sensitive and come from mutually distrusting parties. Existing CPU-based TEEs such as Intel SGX or AMD SEV do not provide sufficient protection. Device-centric TEEs like Nvidia-CC only address tightly coupled CPU-GPU systems with a proprietary solution requiring TEE on the host CPU side. On the other hand, existing academic proposals are tailored toward specific CPU-TEE platforms. To address this gap, we propose Ascend-CC, a confidential computing architecture based on discrete NPU devices that requires no trust in the host system. Ascend-CC provides strong security by ensuring data and model encryption that protects not only the data but also the model parameters and operator binaries. Ascend-CC uses delegation-based memory semantics to ensure isolation from the host software stack, and task attestation provides strong model integrity guarantees. Our Ascend-CC implementation and evaluation with state-of-the-art LLMs such as Llama2 and Llama3 shows that Ascend-CC introduces minimal overhead with no changes in the AI software stack.

Intercalation of magnetic atoms into the van der Waals gaps of layered transition metal dichalcogenides offers an excellent platform to produce exotic physical properties. Here, we report a detailed study of magnetic and electrical transport properties of Co$_{0.28}$TaS$_2$. The temperature dependent resistivity measurements display anomalous upturn below 11 K, which persists in presence of magnetic field even up to 14 T. In the low temperature region, the resistivity upturn exhibits a unique $T^{1/2}$ scaling behavior, which remains unchanged when an external magnetic field is applied. The $T^{1/2}$ dependence of resistivity upturn is the hallmark of non-Fermi liquid state in orbital two-channel Kondo effect(2CK). This anomalous resistivity upturn in Co$_{0.28}$TaS$_2$ can be attributed to the orbital two-channel Kondo mechanism., Comment: 7 pages, 5 figures

Motivated by recent research of Krattenthaler and Wang, we propose five new "Borwein-type" conjectures modulo $3$ and two new "Borwein-type" conjectures modulo $5$., Comment: 6 pages. Comments are welcome!

The Orthogonal Polygon Covering with Squares (OPCS) problem takes as input an orthogonal polygon $P$ without holes with $n$ vertices, where vertices have integral coordinates. The aim is to find a minimum number of axis-parallel, possibly overlapping squares which lie completely inside $P$, such that their union covers the entire region inside $P$. Aupperle et. al~\cite{aupperle1988covering} provide an $\mathcal O(N^{1.5})$-time algorithm to solve OPCS for orthogonal polygons without holes, where $N$ is the number of integral lattice points lying in the interior or on the boundary of $P$. Designing algorithms for OPCS with a running time polynomial in $n$ (the number of vertices of $P$) was discussed as an open question in \cite{aupperle1988covering}, since $N$ can be exponentially larger than $n$. In this paper we design a polynomial-time exact algorithm for OPCS with a running time of $\mathcal O(n^{14})$. We also consider the following structural parameterized version of the problem. A knob in an orthogonal polygon is a polygon edge whose both endpoints are convex polygon vertices. Given an input orthogonal polygon with $n$ vertices and $k$ knobs, we design an algorithm for OPCS with running time $\mathcal O(n^2 + k^{14} \cdot n)$. In \cite{aupperle1988covering}, the Orthogonal Polygon with Holes Covering with Squares (OPCSH) problem is also studied where orthogonal polygon could have holes, and the objective is to find a minimum square covering of the input polygon. This is shown to be NP-complete. We think there is an error in the existing proof in \cite{aupperle1988covering}, where a reduction from Planar 3-CNF is shown. We fix this error in the proof with an alternate construction of one of the gadgets used in the reduction, hence completing the proof of NP-completeness of OPCSH.

In this paper we will be classifying some regular upper-triangular subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to conjugacy by matrices in $SL(n, \mathbb C)$. We do so for dimension 2, codimension 1, and codimension 2 subalgebras. We prove some general results for codimension $k$. The approach we use reduces an abstract classification problem to a combinatorial one, which we solve through a mixture of inductive and computational approaches.

Identifying individual tissues, so-called tissue segmentation, in diabetic foot ulcer (DFU) images is a challenging task and little work has been published, largely due to the limited availability of a clinical image dataset. To address this gap, we have created a DFUTissue dataset for the research community to evaluate wound tissue segmentation algorithms. The dataset contains 110 images with tissues labeled by wound experts and 600 unlabeled images. Additionally, we conducted a pilot study on segmenting wound characteristics including fibrin, granulation, and callus using deep learning. Due to the limited amount of annotated data, our framework consists of both supervised learning (SL) and semi-supervised learning (SSL) phases. In the SL phase, we propose a hybrid model featuring a Mix Transformer (MiT-b3) in the encoder and a CNN in the decoder, enhanced by the integration of a parallel spatial and channel squeeze-and-excitation (P-scSE) module known for its efficacy in improving boundary accuracy. The SSL phase employs a pseudo-labeling-based approach, iteratively identifying and incorporating valuable unlabeled images to enhance overall segmentation performance. Comparative evaluations with state-of-the-art methods are conducted for both SL and SSL phases. The SL achieves a Dice Similarity Coefficient (DSC) of 84.89%, which has been improved to 87.64% in the SSL phase. Furthermore, the results are benchmarked against two widely used SSL approaches: Generative Adversarial Networks and Cross-Consistency Training. Additionally, our hybrid model outperforms the state-of-the-art methods with a 92.99% DSC in performing binary segmentation of DFU wound areas when tested on the Chronic Wound dataset. Codes and data are available at https://github.com/uwm-bigdata/DFUTissueSegNet.

Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes geometrically and admits a stability property under the setting of persistent homology. We present a geometric optimization of the cycles that is computable in polynomial time and is stable in an approximate sense. Tailoring our search criterion to different settings, we obtain various optimization problems like optimal homologous cycle, minimum homology basis, and minimum persistent homology basis. In practice, the (trivial) exact algorithm is computationally expensive despite having a worst case polynomial runtime. Therefore, we design approximation algorithms for the above problems and study their performance experimentally. These algorithms have reasonable runtimes for moderate sized datasets and the cycles computed by these algorithms are consistently of high quality as demonstrated via experiments on multiple datasets., Comment: To Appear in CCCG 2024 : Proc. 36th Canadian Conference on Computational Geometry

Learning robust and effective representations of visual data is a fundamental task in computer vision. Traditionally, this is achieved by training models with labeled data which can be expensive to obtain. Self-supervised learning attempts to circumvent the requirement for labeled data by learning representations from raw unlabeled visual data alone. However, unlike humans who obtain rich 3D information from their binocular vision and through motion, the majority of current self-supervised methods are tasked with learning from monocular 2D image collections. This is noteworthy as it has been demonstrated that shape-centric visual processing is more robust compared to texture-biased automated methods. Inspired by this, we propose a new approach for strengthening existing self-supervised methods by explicitly enforcing a strong 3D structural prior directly into the model during training. Through experiments, across a range of datasets, we demonstrate that our 3D aware representations are more robust compared to conventional self-supervised baselines.

We present a fluctuating hydrodynamic description of a non-polar active lattice gas model with excluded volume interactions that exhibits motility-induced phase separation under appropriate conditions. For quasi-one dimension and higher, stability analysis of the noiseless hydrodynamics gives quantitative bounds on the phase boundary of the motility-induced phase separation in terms of spinodal and binodal. Inclusion of the multiplicative noise in the fluctuating hydrodynamics describes the exponentially decaying two-point correlations in the stationary-state homogeneous phase. Our hydrodynamic description and theoretical predictions based on it are in excellent agreement with our Monte-Carlo simulations and pseudo-spectral iteration of the hydrodynamics equations. Our construction of hydrodynamics for this model is not suitable in strictly one-dimension with single-file constraints, and we argue that this breakdown is associated with micro-phase separation., Comment: 6 pages, 6 figures, + 16 supplemental pages

In this article, we propose L-estimators of the unknown parameters in the instrumental variables regression in the presence of censored data under endogeneity. We allow the random errors involved in the model to be dependent. The proposed estimation procedure is a two-stage procedure, and the large sample properties of the proposed estimators are established. The utility of the proposed methodology is demonstrated for various simulated data and a benchmark real data set.

We study the evolution of a classical harmonic chain with nearest-neighbor interactions starting from domain wall initial conditions. The initial state is taken to be either a product of two Gibbs Ensembles (GEs) with unequal temperatures on the two halves of the chain or a product of two Generalized Gibbs Ensembles (GGEs) with different parameters in the two halves. For this system, we construct the Wigner function and demonstrate that its evolution defines the Generalized Hydrodynamics (GHD) describing the evolution of the conserved quantities. We solve the GHD for both finite and infinite chains and compute the evolution of conserved densities and currents. For a finite chain with fixed boundaries, we show that these quantities relax as $\sim 1/\sqrt{t}$ to their respective steady-state values given by the final expected GE or GGE state, depending on the initial conditions. Exact expressions for the Lagrange multipliers of the final expected GGE state are obtained in terms of the steady state densities. In the case of an infinite chain, we find that the conserved densities and currents at any finite time exhibit ballistic scaling while, at infinite time, any finite segment of the system can be described by a current-carrying non-equilibrium steady state (NESS). We compute the scaling functions analytically and show that the relaxation to the NESS occurs as $\sim 1/t$ for the densities and as $\sim 1/t^2$ for the currents. We compare the analytic results from hydrodynamics with those from exact microscopic numerics and find excellent agreement., Comment: 22 pages, 11 figures

Plastic strain-induced phase transformations (PTs) and chemical reactions under high pressure are broadly spread in modern technologies, friction and wear, geophysics, and astrogeology. However, because of very heterogeneous fields of plastic strain $\mathbf{E}^{p}$ and stress $\mathbf{\sigma}$ tensors and volume fraction $c$ of phases in a sample compressed in a diamond anvil cell (DAC) and impossibility of measurements of $\mathbf{\sigma}$ and $\mathbf{E}^{p}$, there are no strict kinetic equations for them. Here, we develop combined experimental-computational approaches to determine all fields in strongly plastically predeformed Zr and kinetic equation for $\alpha$-$\omega$ PT consistent with experimental data for the entire sample. Kinetic equation depends on accumulated plastic strain (instead of time) and pressure and is independent of plastic strain and deviatoric stress tensors, i.e., it can be applied for various above processes. Our results initiate kinetic studies of strain-induced PTs and provide efforts toward more comprehensive understanding of material behavior in extreme conditions., Comment: 28 pages, 11 figures

In 1797, Pfaff gave a simple proof of a ${}_3F_2$ hypergeometric series summation formula which was much later reproved by Andrews in 1996. In the same paper, Andrews also proved other well-known hypergeometric identities using Pfaff's method. In this paper, we prove a number of terminating $q$-hypergeometric series-product identities using Pfaff's method thereby providing a detailed account of its wide applicability., Comment: 17 pages. Comments are welcome!

In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci polynomials serving as activation functions in the middle layer. The trial solution of the differential equation is treated as the output of the FNN, which involves adjustable parameters (weights). These weights are iteratively updated during the training of the Fibonacci neural network using backpropagation. The efficacy of the proposed method is evaluated by solving five differential problems with known exact solutions, allowing for an assessment of its accuracy. Comparative analyses are conducted against previously established techniques, demonstrating superior accuracy and efficacy in solving the addressed problems.

We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of giving a description of the correctable erasure patterns in a maximally recoverable tensor code with the problem of describing bipartite rigid graphs or low-rank completable matrix patterns. Additionally, we relate dependencies among symmetric products of generic vectors to graph rigidity and symmetric matrix completion. With an eye toward applications to computer science, we study the dependency of these matroids on the characteristic by giving new combinatorial descriptions in several cases, including the first description of the correctable patterns in an (m, n, a=2, b=2) maximally recoverable tensor code.

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in details, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory.

(111)NiO epitaxial films are grown on c-sapphire substrates at various growth temperatures ranging from room-temperature to 600C using pulsed laser deposition (PLD) technique. Two series of samples, where different laser fluences are used to ablate the target, are studied here. Films grown with higher laser fluence, are found to be embedded with Ni-clusters crystallographically aligned with the (111)NiO matrix. While the layers grown with lower laser energy density exhibit p-type conductivity specially at low growth temperatures. X-ray diffraction study shows the coexistence of biaxial compressive and tensile hydrostatic strains in these samples, which results in an expansion of the lattice primarily along the growth direction. This effective uniaxial expansion {epsilon}_perpendicular increases with the reduction of the growth temperature. Band gap of these samples is found to decrease linearly with {epsilon}_perpendicular. This result is validated by density functional theory (DFT) calculations. Experimental findings and the theoretical study further indicate that V_Ni + O_I and V_O + Ni_I complexes exist as the dominant native defects in samples grown with Ni-deficient (low laser fluence) and Ni-rich (high laser fluence) conditions, respectively. P-type conductivity observed in the samples grown in Ni-deficient condition is more likely to be resulting from V_Ni + O_I defects than Ni-vacancies (V_Ni)., Comment: 9 pages and 9 figures (Main manuscript), 4 pages and 4 figures (supplemental material)

Advances in neural sensing technology are making it possible to observe the olfactory process in great detail. In this paper, we conceptualize smell from a Data Science and AI perspective, that relates the properties of odorants to how they are sensed and analyzed in the olfactory system from the nose to the brain. Drawing distinctions to color vision, we argue that smell presents unique measurement challenges, including the complexity of stimuli, the high dimensionality of the sensory apparatus, as well as what constitutes ground truth. In the face of these challenges, we argue for the centrality of odorant-receptor interactions in developing a theory of olfaction. Such a theory is likely to find widespread industrial applications, and enhance our understanding of smell, and in the longer-term, how it relates to other senses and language. As an initial use case of the data, we present results using machine learning-based classification of neural responses to odors as they are recorded in the mouse olfactory bulb with calcium imaging., Comment: 20 pages, 10 Figures, 2 Appendix, 1 Table

The Major Atmospheric Cherenkov Experiment (MACE) is a large size (21m) Imaging Atmospheric Cherenkov Telescope (IACT) installed at an altitude of 4270m above sea level at Hanle, Ladakh in northern India. Here we report the detection of Very High Energy (VHE) gamma-ray emission from Crab Nebula above 80 GeV. We analysed ~15 hours of data collected at low zenith angle between November 2022 and February 2023. The energy spectrum is well described by a log-parabola function with a flux of ~(3.46 +/- 0.26stat) x 10-10 TeV-1 cm-2 s-1, at 400 GeV with spectral index of 2.09 +/- 0.06stat and a curvature parameter of 0.08 +/- 0.07stat. The gamma-rays are detected in an energy range spanning from 80 GeV to ~5 TeV. The energy resolution improves from ~34% at an analysis energy threshold of 80 GeV to ~21% above 1 TeV. The daily light curve and the spectral energy distribution obtained for the Crab Nebula is in agreement with previous measurements, considering statistical and systematic uncertainties., Comment: Accepted for publication in Astroparticle Physics

Predicting residual stresses has always been a topic of significance due to its implications in the development of enhanced materials and better processing conditions. In this work, an analytical model for prediction of residual stresses is developed for orthogonal machining. It consists of three component models for force, temperature and stress computation. The Oxley force model and Waldorf's slip-line model are employed for obtaining cutting force, thrust force, and temperatures at the shear zone and tool-chip interface for the given parameters. The Komanduri-Hou two heat source model is used for obtaining the temperature distribution in the workpiece. The effect of coolant with differing mass flow rates has also been incorporated. The residual stresses are obtained by combining the mechanical and thermal components, followed by the loading and relaxation of the stresses. Optimal values for unknown parameters are predicted by leveraging a cost function. The residual stress distributions obtained give a tensile region near the surface for Inconel 718, and a compressive region for Ti6Al4V, which are in line with experimental results found in literature.

We introduce a one-dimensional correlated-hopping model of spinless fermions in which a particle can hop between two neighboring sites only if the sites to the left and right of those two sites have different particle numbers. Using a bond-to-site mapping, this model involving four-site terms can be mapped to an assisted pair-flipping model involving only three-site terms. This model shows strong Hilbert space fragmentation (HSF). We define irreducible strings (IS) to label the different fragments, determine the number of fragments, and the sizes of fragments corresponding to some special IS. In some classes of fragments, the Hamiltonian can be diagonalized completely, and in others it can be seen to have a structure characteristic of models which are not fully integrable. In the largest fragment in our model, the number of states grows exponentially with the system size, but the ratio of this number to the total Hilbert space size tends to zero exponentially in the thermodynamic limit. Within this fragment, we provide numerical evidence that only a weak version of the eigenstate thermalization hypothesis (ETH) remains valid; we call this subspace-restricted ETH. To understand the out-of-equilibrium dynamics of the model, we study the infinite-temperature time-dependent autocorrelation functions starting from a random initial state; we find that these exhibit a different behavior near the boundary compared to the bulk. Finally we propose an experimental setup to realize our correlated-hopping model., Comment: 22 pages, 17 figures; added discussion of typical and atypical fragments, ETH properties of additional typical fragments, and zero energy states; added some references

The dynamic yield stress associated with the flow cessation of cement pastes is measured using a rheometer equipped with various shear geometries such as vane, helical, sandblasted co-axial cylinders, and serrated parallel plates, as well as with the mini-cone spread test. Discrepancies in yield stress values are observed for cement pastes at various volume fractions, with one to two orders of magnitude difference between vane, helical and mini-cone spread measurements on the one hand, and co-axial cylinder and parallel plate measurements on the other hand. To understand this discrepancy, the flow profile of a cement paste in the parallel-plate geometry is investigated with a high-speed camera, revealing the rapid formation of an un-sheared band near the static bottom plate. The width of this band depends upon the rotational velocity of the top plate, and upon the shear time. Recalculation of shear stress shows that the reduced sheared gap alone cannot explain the low measured yield stress. Further exploration suggests the formation of zones with lower particle content, possibly linked to cement particle sedimentation. Here, we argue that the complex nature of cement pastes, composed of negatively buoyant non-Brownian particles with attractive interactions due to highly charged nano-size hydration products, accounts for their complex rheological behavior., Comment: Submitted to Journal Rheologica Acta for the peer review process on 13-March-2024, 11 figures. Also includes supplementary information with 5 figures

The dispersion of a passive colloid immersed in a bath of non-interacting and non-Brownian run-and-tumble microswimmers in two dimensions is analyzed using stochastic simulations and an asymptotic theory, both based on a minimal model of swimmer-colloid collisions characterized solely by frictionless steric interactions. We estimate the effective long-time diffusivity $\mathcal{D}$ of the suspended colloid resulting from its interaction with the active bath, and elucidate its dependence on the level of activity (persistence length of swimmer trajectories), the mobility ratio of the colloid to a swimmer, and the number density of swimmers in the bath. We also propose a semi-analytical model for the colloid diffusivity in terms of the variance and correlation time of the net fluctuating active force on the colloid resulting from swimmer collisions. Quantitative agreement is found between numerical simulations and analytical results in the experimentally-relevant regime of low swimmer density, low mobility ratios, and high activity.

Architectural Knowledge Management (AKM) involves the organized handling of information related to architectural decisions and design within a project or organization. An essential artifact of AKM is the Architecture Decision Records (ADR), which documents key design decisions. ADRs are documents that capture decision context, decision made and various aspects related to a design decision, thereby promoting transparency, collaboration, and understanding. Despite their benefits, ADR adoption in software development has been slow due to challenges like time constraints and inconsistent uptake. Recent advancements in Large Language Models (LLMs) may help bridge this adoption gap by facilitating ADR generation. However, the effectiveness of LLM for ADR generation or understanding is something that has not been explored. To this end, in this work, we perform an exploratory study that aims to investigate the feasibility of using LLM for the generation of ADRs given the decision context. In our exploratory study, we utilize GPT and T5-based models with 0-shot, few-shot, and fine-tuning approaches to generate the Decision of an ADR given its Context. Our results indicate that in a 0-shot setting, state-of-the-art models such as GPT-4 generate relevant and accurate Design Decisions, although they fall short of human-level performance. Additionally, we observe that more cost-effective models like GPT-3.5 can achieve similar outcomes in a few-shot setting, and smaller models such as Flan-T5 can yield comparable results after fine-tuning. To conclude, this exploratory study suggests that LLM can generate Design Decisions, but further research is required to attain human-level generation and establish standardized widespread adoption., Comment: This paper has been accepted to IEEE ICSA 2024 (Main Track - Research Track)

Motif finding is an important step for the detection of rare events occurring in a set of DNA or protein sequences. Extraction of information about these rare events can lead to new biological discoveries. Motifs are some important patterns that have numerous applications including the identification of transcription factors and their binding sites, composite regulatory patterns, similarity between families of proteins, etc. Although several flavors of motif searching algorithms have been studied in the literature, we study the version known as $ (l, d) $-motif search or Planted Motif Search (PMS). In PMS, given two integers $ l $, $ d $ and $ n $ input sequences we try to find all the patterns of length $ l $ that appear in each of the $ n $ input sequences with at most $ d $ mismatches. We also discuss the quorum version of PMS in our work that finds motifs that are not planted in all the input sequences but at least in $ q $ of the sequences. Our algorithm is mainly based on the algorithms qPMSPrune, qPMS7, TraverStringRef and PMS8. We introduce some techniques to compress the input strings and make faster comparison between strings with bitwise operations. Our algorithm performs a little better than the existing exact algorithms to solve the qPMS problem in DNA sequence. We have also proposed an idea for parallel implementation of our algorithm.

Atomic superfluids formed using Bose-Einstein condensates (BECs) in a ring trap are currently being investigated in the context of superfluid hydrodynamics, quantum sensing and matter-wave interferometry. The characterization of the rotational properties of such superfluids is important, but can presently only be performed by using optical absorption imaging, which completely destroys the condensate. Recent studies have proposed coupling the ring BEC to optical cavity modes carrying orbital angular momentum to make minimally destructive measurements of the condensate rotation. The sensitivity of these proposals, however, is bounded below by the standard quantum limit set by the combination of laser shot noise and radiation pressure noise. In this work, we provide a theoretical framework that exploits the fact that the interaction between the scattered modes of the condensate and the light reduces to effective optomechanical equations of motion. We present a detailed theoretical analysis to demonstrate that the use of squeezed light and backaction evasion techniques allows the angular momentum of the condensate to be sensed with noise well below the standard quantum limit. Our proposal is relevant to atomtronics, quantum sensing and quantum information., Comment: 16 pages, 13 figures

We consider an analytically tractable model that exhibits the main features of the Page curve characterizing the evolution of entanglement entropy during evaporation of a black hole. Our model is a gas of non-interacting fermions on a lattice that is released from a box into the vacuum. More precisely, our Hamiltonian is a tight-binding model with a defect at the junction between the filled box and the vacuum. In addition to the entanglement entropy we consider several other observables, such as the spatial density profile and current, and show that the semiclassical approach of generalized hydrodynamics provides a remarkably accurate description of the quantum dynamics including that of the entanglement entropy at all times. Our hydrodynamic results agree closely with those obtained via exact microscopic numerics. We find that the growth of entanglement is linear and universal, i.e, independent of the details of the defect. The decay shows $1/t$ scaling for conformal defect while for non-conformal defects, it is slower. Our study shows the power of the semiclassical approach and could be relevant for discussions on the resolution of the black hole information paradox.

In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative $q$-series identities which are interesting examples of our proposed conjecture and Bressoud's generalized conjecture. Finally, using certain positivity-preserving transformations for $q$-binomial coefficients, we prove the non-negativity of the infinite families., Comment: 17 pages, 2 figures. Dedicated to George E. Andrews and Bruce C. Berndt in celebration of their 85th birthdays. Comments are welcome!

We explore the dynamics of a tracer in an active particle harmonic chain, investigating the influence of interactions. Our analysis involves calculating mean-squared displacements (MSD) and space-time correlations through Green's function techniques and numerical simulations. Depending on chain characteristics, i.e., different time scales determined by interaction stiffness and persistence of activity, tagged-particle MSD exhibit ballistic, diffusive, and single-file diffusion (SFD) scaling over time, with crossovers explained by our analytic expressions. Our results reveal transitions in bulk particle displacement distributions from an early-time bimodal to late-time Gaussian, passing through regimes of unimodal distributions with finite support and negative excess kurtosis and longer-tailed distributions with positive excess kurtosis. The distributions exhibit data collapse, aligning with ballistic, diffusive, and SFD scaling in the appropriate time regimes. However, at much longer times, the distributions become Gaussian. Finally, we derive expressions for steady-state static and dynamic two-point displacement correlations, consistent with simulations and converging to equilibrium results for small persistence. Additionally, the two-time stretch correlation extends to longer separation at later times, while the autocorrelation for the bulk particle shows diffusive scaling beyond the persistence time.

Let $p$ and $l$ be distinct odd primes, and let $F$ be a $p$-adic field. Let $\pi$ be a generic smooth integral representation of ${\rm GL}_n(F)$ over an $\overline{\mathbb{Q}}_l$-vector space. Let $E$ be a finite Galois extension of $F$ with $[E:F]=l$. Let $\Pi$ be the base change lift of $\pi$ to the group ${\rm GL}_n(E)$. Let $\mathbb{W}^0(\Pi, \psi_E)$ be the lattice of $\overline{\mathbb{Z}}_l$-valued functions in the Whittaker model of $\Pi$, with respect to a standard ${\rm Gal}(E/F)$-equivaraint additive character $\psi_E:E\rightarrow \overline{\mathbb{Q}}_l^\times$. We show that the unique generic sub-quotient of the zero-th Tate cohomology group of $\mathbb{W}^0(\Pi, \psi_E)$ is isomorphic to the Frobenius twist of the unique generic sub-quotient of the mod-$l$ reduction of $\pi$. We first prove a version of this result for a family of smooth generic representations of ${\rm GL}_n(E)$ over the integral Bernstein center of ${\rm GL}_n(F)$. Our methods use the theory of Rankin-selberg convolutions and simple identities of local $\gamma$-factors. The results of this article remove the hypothesis that $l$ does not divide the pro-order of ${\rm GL}_{n-1}(F)$ in our previous work., Comment: Preliminary version, comments are welcome

In our contribution we study stochastic models in one space dimension with two conservation laws. One model is the coupled continuum stochastic Burgers equation, for which each current is a sum of quadratic non-linearities, linear diffusion, and spacetime white noise. The second model is a two-lane stochastic lattice gas. As distinct from previous studies, the two conserved densities are tuned such that the flux Jacobian, a $2 \times 2$ matrix, has coinciding eigenvalues. In the steady state, investigated are spacetime correlations of the conserved fields and the time-integrated currents at the origin. For a particular choice of couplings the dynamical exponent 3/2 is confirmed. Furthermore, at these couplings, continuum stochastic Burgers equation and lattice gas are demonstrated to be in the same universality class., Comment: 34 pages, 9 figures

As the simplest model of interacting-particle transport in a randomly disordered medium, we consider the asymmetric simple exclusion process (ASEP) in which particles with hard-core interactions perform biased random walks, on the supercritical percolation cluster. In this process, the long time trajectory of a marked particle consists of steps on the backbone, punctuated by time spent in side-branches. We study the probability distribution in the steady state of the waiting time $T_w$ of a randomly chosen particle, in a side-branch since its last step along the backbone. Exact numerical evaluation of this on a single side-branch of lengths $L= 1$ to $9$ show that for large fields, the probability distribution of $\log T_w $ has multiple well separated peaks. We extend this result to a random comb, and to the ASEP on the percolation cluster. For the latter problem, we show that in the steady state, the fractional number of particles that have been in the same side-branch for a time interval greater than $T_w$ varies as $exp( - c \sqrt{ln T_w})$ for large $T_w$, where $c$ depends only on the bias field. The system shows dynamical heterogeneity, with particles segregating into pockets of high and low mobilities. These long timescales are not reflected in the eigenvalue spectrum of the Markov evolution matrix., Comment: 10 pages

Lack of diverse perspectives causes neutrality bias in Wikipedia content leading to millions of worldwide readers getting exposed by potentially inaccurate information. Hence, neutrality bias detection and mitigation is a critical problem. Although previous studies have proposed effective solutions for English, no work exists for Indian languages. First, we contribute two large datasets, mWikiBias and mWNC, covering 8 languages, for the bias detection and mitigation tasks respectively. Next, we investigate the effectiveness of popular multilingual Transformer-based models for the two tasks by modeling detection as a binary classification problem and mitigation as a style transfer problem. We make the code and data publicly available.

In 2009, Berkovich and Garvan introduced a new partition statistic called the GBG-rank modulo $t$ which is a generalization of the well-known BG-rank. In this paper, we use the Littlewood decomposition of partitions to study partitions with bounded largest part and fixed integral value of GBG-rank modulo primes. As a consequence, we obtain new elegant generating function formulas for unrestricted partitions, self-conjugate partitions, and partitions whose parts repeat finite number of times., Comment: 16 pages, 2 figures. Comments are welcome!

The quantum kicked rotor is a paradigmatic model system in quantum physics. As a driven quantum system, it is used to study the transition from the classical to the quantum world and to elucidate the emergence of chaos and diffusion. In contrast to its classical counterpart, it features dynamical localization, specifically Anderson localization in momentum space. The interacting many-body kicked rotor is believed to break localization, as recent experiments suggest. Here, we present evidence for many-body dynamical localization for the Lieb-Liniger version of the many-body quantum kicked rotor. After some initial evolution, the momentum distribution of interacting quantum-degenerate bosonic atoms in one-dimensional geometry, kicked hundreds of times by means of a pulsed sinusoidal potential, stops spreading. We quantify the arrested evolution by analysing the energy and the information entropy of the system as the interaction strength is tuned. In the limiting cases of vanishing and strong interactions, the first-order correlation function exhibits a very different decay behavior. Our results shed light on the boundary between the classical, chaotic world and the realm of quantum physics., Comment: 13 pages, 11 figures

The telecloning protocol distributes quantum states from a single sender to multiple receivers via a shared entangled state by exploiting the notions of teleportation and approximate cloning. We investigate the optimal telecloning fidelities obtained using both Gaussian and non-Gaussian shared resources. When the shared non-Gaussian state is created by subtracting photons from both the modes of the Gaussian two-mode squeezed vacuum state, we demonstrate that higher telecloning fidelities can be achieved in comparison with its Gaussian counterpart. To quantify this advantage, we introduce a quadrature-based nonclassicality measure, which is capable of estimating the fidelity of the clones, both with Gaussian and non-Gaussian resource states. We further provide a linear optical setup for asymmetric telecloning of continuous variable states using a multimode entangled state., Comment: v1: 14 pages, 7 figures v2: close to published version

We propose and study M-estimation to estimate the parameters in the censored regression model in the presence of endogeneity, i.e., the Tobit model. In the course of this study, we follow two-stage procedures: the first stage consists of applying control function procedures to address the issue of endogeneity using instrumental variables, and the second stage applies the M-estimation technique to estimate the unknown parameters involved in the model. The large sample properties of the proposed estimators are derived and analyzed. The finite sample properties of the estimators are studied through Monte Carlo simulation and a real data application related to women's labor force participation.

Besicovitch showed that a compact set in $\mathbb{R}^n$ which contains a unit line segment in every direction can have measure $0$. These constructions also work over other metric spaces like the $p$-adics and profinite integers. It is conjectured that it is impossible to construct sets with measure $0$ which contain a unit $2$-disk in every direction in $\mathbb{R}^n$. We prove that over the $p$-adics and profinite integers any set which contains a 2-flat in every direction must have positive measure. The main ingredients are maximal Kakeya estimates for $(\mathbb{Z}/N\mathbb{Z})^n$ proven in [Dha22] and adapting Fourier analytic arguments of Oberlin [Obe05]. In general, we prove $L^{n-1}$ to $L^{n-1}$ estimates for the maximal operator corresponding to $2$-flats.