Search

Using the methods from topological dynamics, H. Furstenberg introduced the notion of a central set and proved the famous Central Sets Theorem. Later D. De, Neil Hindman, and D. Strauss [Fund. Math.199 (2008), 155-175.] established a stronger version of the Central Sets Theorem and then introduced the notion of $C$-sets satisfying the Central Sets Theorem and studied the properties of these sets. For any weak mixing system $\left(X, \mathcal{B},\mu, T\right),$ and $A_{0},A_{1}\in\mathcal{B}$, with $\mu\left(A_{0}\right)\mu\left(A_{1}\right)>0$, R. Kung and X.Ye [Disc. Cont. Dyn. sys., 18 (2007) 817-827.] proved that the set $N\left(A,B\right)= \left\{n:\mu\left(A_{0}\cap T^{-n}A_{1}\right)>0\right\}$ intersects all sets of positive upper Banach density. However, later N. Hindman and D. Strauss [New York J. Math. 26 (2020) 230-260.] proved that there exist $C$-sets having zero upper Banach density. Inspired by this result, in this article, we prove that $N\left(A, B \right)$ intersects with all $C$-sets. Then we introduce the notion of a dynamical $C^{\star}$-set and then we study their combinatorial properties., Comment: 8 pages

In this article, we explore the properties of hybrid star composed of deconfined quarks and dark energy considering finite value of mass of strange quark ($m_s\neq0$). We have studied the various properties of such stars assuming a linear relation between dark energy pressure and density as $p^{de}=\omega\rho^{de}$, where $-1<\omega<-\frac{1}{3}$, within the framework of Finch-Skea ansatz of $g_{rr}$ component of line element by varying the dark energy coupling parameter ($\beta$). In this model, $\frac{\beta}{1+\beta}$ represents the percentage of dark energy. Following the relation $\rho^{de}=\beta\rho^Q$, we have noted some restriction on the coupling parameter $\beta$ as $0<\beta<-\frac{1}{3\omega}$. It is interesting to note that with the change of percentage composition of dark energy, there is a prominent change of phase within in such stars. Solving TOV equations, the maximum mass attainable in this model is $\approx2~M_{\odot}$ and radius $11.37~km$. Both mass and radius decrease with the increase of $m_s$ and $\beta$ for constant $\omega$. On the other hand, maximum mass increases with the decrease of $\omega$. Various stability conditions along with causality and energy conditions are studied and found to be in agreement with the conditions of a viable stellar model. We have predicted the radii of recently observed compact stars and lighter component of the GW event $170817$ and it is interesting to note that the predicted radius of the model is close to the estimated value of the radius from observations., Comment: 25 pages, 20 figures

Raw nanopore signal analysis is a common approach in genomics to provide fast and resource-efficient analysis without translating the signals to bases (i.e., without basecalling). However, existing solutions cannot interpret raw signals directly if a reference genome is unknown due to a lack of accurate mechanisms to handle increased noise in pairwise raw signal comparison. Our goal is to enable the direct analysis of raw signals without a reference genome. To this end, we propose Rawsamble, the first mechanism that can 1) identify regions of similarity between all raw signal pairs, known as all-vs-all overlapping, using a hash-based search mechanism and 2) use these to construct genomes from scratch, called de novo assembly. Our extensive evaluations across multiple genomes of varying sizes show that Rawsamble provides a significant speedup (on average by 16.36x and up to 41.59x) and reduces peak memory usage (on average by 11.73x and up to by 41.99x) compared to a conventional genome assembly pipeline using the state-of-the-art tools for basecalling (Dorado's fastest mode) and overlapping (minimap2) on a CPU. We find that 36.57% of overlapping pairs generated by Rawsamble are identical to those generated by minimap2. Using the overlaps from Rawsamble, we construct the first de novo assemblies directly from raw signals without basecalling. We show that we can construct contiguous assembly segments (unitigs) up to 2.7 million bases in length (half the genome length of E. coli). We identify previously unexplored directions that can be enabled by finding overlaps and constructing de novo assemblies. Rawsamble is available at https://github.com/CMU-SAFARI/RawHash. We also provide the scripts to fully reproduce our results on our GitHub page.

We define two versions of the archimedean height pairing between certain Bloch higher cycles. Both pairings generalize the archimedean height pairing between ordinary cycles. To do this, we introduce the notion of framed mixed Hodge structures and define two heights of a framed mixed Hodge structure. Moreover, we show that, with a pair of properly intersecting refined higher cycles in complementary codimension, we can associate a framed mixed Hodge structure. As an interesting example, we compute both heights for the complex polylogarithm variation of mixed Hodge structures and show that each of them gives rise to a well known version of the single valued polylogarithm function.

A prevalent assumption regarding real-world data is that it lies on or close to a low-dimensional manifold. When deploying a neural network on data manifolds, the required size, i.e., the number of neurons of the network, heavily depends on the intricacy of the underlying latent manifold. While significant advancements have been made in understanding the geometric attributes of manifolds, it's essential to recognize that topology, too, is a fundamental characteristic of manifolds. In this study, we investigate network expressive power in terms of the latent data manifold. Integrating both topological and geometric facets of the data manifold, we present a size upper bound of ReLU neural networks.

Large Language Models (LLMs) have recently demonstrated a remarkable ability to model time series data. These capabilities can be partly explained if LLMs understand basic time series concepts. However, our knowledge of what these models understand about time series data remains relatively limited. To address this gap, we introduce TimeSeriesExam, a configurable and scalable multiple-choice question exam designed to assess LLMs across five core time series understanding categories: pattern recognition, noise understanding, similarity analysis, anomaly detection, and causality analysis. TimeSeriesExam comprises of over 700 questions, procedurally generated using 104 carefully curated templates and iteratively refined to balance difficulty and their ability to discriminate good from bad models. We test 7 state-of-the-art LLMs on the TimeSeriesExam and provide the first comprehensive evaluation of their time series understanding abilities. Our results suggest that closed-source models such as GPT-4 and Gemini understand simple time series concepts significantly better than their open-source counterparts, while all models struggle with complex concepts such as causality analysis. We believe that the ability to programatically generate questions is fundamental to assessing and improving LLM's ability to understand and reason about time series data., Comment: Accepted at NeurIPS'24 Time Series in the Age of Large Models Workshop

We theoretically investigate a photosystem II-based reaction center modeled as a nonequilibrium quantum junction. We specifically focus on the electron-electron interactions that enable cotunneling events to be captured through quantum mechanical rates due to the inclusion of a negatively charged manybody state. Using a master equation framework with realistic spectral profiles, we analyze the cotunneling assisted current, power, and work. Amplification of the cotunneling assisted current and power occurs over a narrower bias range, reflecting a trade-off where higher flux is compensated by a reduced work window. We further report that the cotunneling-enhanced thermodynamic variables, particularly within specific bias windows, depends on the interplay between cotunneling amplitudes, electron transition rates, and interaction energy. Both attractive and repulsive electronic interactions can enhance cotunneling, but this effect is sensitive to the energy balance between states and the tunneling strength asymmetries., Comment: 21 pages. 21 figures. Suggestions on relevant references are welcome. More details on the derivations shall be added later

Gathering is a fundamental coordination problem in swarm robotics, where the objective is to bring robots together at a point not known to them at the beginning. While most research focuses on continuous domains, some studies also examine the discrete domain. This paper addresses the optimal gathering problem on an infinite grid, aiming to improve the energy efficiency by minimizing the maximum distance any robot must travel. The robots are autonomous, anonymous, homogeneous, identical, and oblivious. We identify all initial configurations where the optimal gathering problem is unsolvable. For the remaining configurations, we introduce a deterministic distributed algorithm that effectively gathers $n$ robots ($n\ge 9$). The algorithm ensures that the robots gathers at one of the designated min-max nodes in the grid. Additionally, we provide a comprehensive characterization of the subgraph formed by the min-max nodes in this infinite grid model.

Enabling robots to autonomously navigate unknown, complex, dynamic environments and perform diverse tasks remains a fundamental challenge in developing robust autonomous physical agents. These agents must effectively perceive their surroundings while leveraging world knowledge for decision-making. Although recent approaches utilize vision-language and large language models for scene understanding and planning, they often rely on offline processing, offboard compute, make simplifying assumptions about the environment and perception, limiting real-world applicability. We present a novel framework for real-time onboard autonomous navigation in unknown environments that change over time by integrating multi-level abstraction in both perception and planning pipelines. Our system fuses data from multiple onboard sensors for localization and mapping and integrates it with open-vocabulary semantics to generate hierarchical scene graphs from continuously updated semantic object map. The LLM-based planner uses these graphs to create multi-step plans that guide low-level controllers in executing navigation tasks specified in natural language. The system's real-time operation enables the LLM to adjust its plans based on updates to the scene graph and task execution status, ensuring continuous adaptation to new situations or when the current plan cannot accomplish the task, a key advantage over static or rule-based systems. We demonstrate our system's efficacy on a quadruped navigating dynamic environments, showcasing its adaptability and robustness in diverse scenarios.

A particle-hole symmetry protected 2D non-Hermitian Su-Schrieffer-Heeger (SSH) model is investigated. This version differs from the usual Hermitian version by the inclusion of gain and/or loss terms which are represented by complex on-site potentials. The exceptional points occur, when the dimensionless potential magnitude and the hopping amplitudes become close to unity, leading to the coalescence of eigenvalues and nontrivial eigenvector degeneracies. Furthermore, the vectored Zak phase quantization has been obtained and a topolectric RLC circuit has been analysed. If realized experimentally (in photonic and acoustic crystals), the quantization is expected to lead to an extended bulk-boundary correspondence., Comment: 22 pages, 6 Figures

Bianchi type III (BIII) metric is an interesting anisotropic model for studying cosmic anisotropy as it has an additional exponential term multiplied to a directional scale factor. Thus, the cosmological parameters obtained for this BIII metric with the conventional energy-momentum tensor within the framework of a modified gravity theory and the estimation of their values with the help of Hubble, Pantheon plus and other observational data may provide some new information in cosmic evolution. In this work, we have studied the BIII metric under the framework of $f(R,T)$ gravity theory and estimated the values of the cosmological parameters for three different models of this gravity theory by using the Bayesian technique. In our study, we found that all the models show consistent results with the current observations but show deviations in the early stage of the Universe. In one model we have found a sharp discontinuity in the matter-dominated phase of the Universe. Hence through this study, we have found that all the $f(R,T)$ gravity models may not be suitable for studying evolutions and early stages of the Universe in the BIII metric even though they show consistent results with the current observations., Comment: 27 pages, 16 figures

We present the results of an asteroseismic study of HD 118660 (TIC 171729860), being a chemically peculiar (mild Am) star exhibiting $\delta$ Scuti ($\delta$ Sct) pulsations. It is based on the analysis of two sectors of time-series photometry from the space mission TESS and seismic modelling. It yielded the detection of 15 and 16 frequencies for TESS sectors 23 and 50, respectively. The identified pulsation modes include four radial ($\ell=0$) and five dipolar ($\ell=1$) ones. The radial modes are overtones with order $n$ ranging from $3$ and $6$. Such high values of $n$ are theoretically not expected for stars with the effective temperature of HD 118660 ($\rm T_{\rm eff}\approx 7550 \rm K$ ) located near the red edge of the $\delta$ Sct instability strip. To estimate the asteroseismic parameters, we have generated a grid of stellar models assuming a solar metallicity ($Z=0.014$) and different values for the convective overshooting parameter ($0.1\leq \alpha_{\rm ov}\leq 0.3$). We conclude that the analysis of the radial modes is insufficient to constrain $\alpha_{\rm ov}$ and $Z$ for $\delta$ Sct stars. The value for the equatorial velocity of HD 118660 derived from the seismic radius and the rotational frequency is consistent with values found in the literature., Comment: 10 pages, 7 figures, Accepted for publication in MNRAS

What would be a reasonable definition of the conditional entropy of bipartite quantum processes, and what novel insight would it provide? We develop this notion using four information-theoretic axioms and define the corresponding quantitative formulas. Our definitions of the conditional entropies of channels are based on the generalized state and channel divergences, such as quantum relative entropy, min- and max-relative entropy, etc. We show that the conditional entropy of quantum channels can potentially reveal important features of the channel, such as its underlying causal structure, which cannot be captured by the entropy of quantum channels or the conditional entropy of bipartite states. Specifically, if the von Neumann conditional entropy $S[A|B]_{\mathcal{N}}$ of a quantum channel $\mathcal{N}_{A'B'\to AB}$ is strictly less than $-\log|A|$, then the channel necessarily has causal influence from $A'$ to $B$. Furthermore, we show that our definition of conditional entropy establishes the strong subadditivity of the entropy for quantum channels. We study the total amount of correlations possible due to quantum processes by defining the multipartite mutual information of quantum channels., Comment: 41 pages, 2 figures, 2 tables

Neutrinos described as an open quantum system may interact with the environment which introduces stochastic perturbations to their quantum phase. This mechanism leads to a loss of coherence along the propagation of the neutrino $-$ a phenomenon commonly referred to as decoherence $-$ and ultimately, to a modification of the oscillation probabilities. Fluctuations in space-time, as envisaged by various theories of quantum gravity, are a potential candidate for a decoherence-inducing environment. Consequently, the search for decoherence provides a rare opportunity to investigate quantum gravitational effects which are usually beyond the reach of current experiments. In this work, quantum decoherence effects are searched for in neutrino data collected by the KM3NeT/ORCA detector from January 2020 to November 2021. The analysis focuses on atmospheric neutrinos within the energy range of a few GeV to $100\,\mathrm{GeV}$. Adopting the open quantum system framework, decoherence is described in a phenomenological manner with the strength of the effect given by the parameters $\Gamma_{21}$ and $\Gamma_{31}$. Following previous studies, a dependence of the type $\Gamma_{ij} \propto (E/E_0)^n$ on the neutrino energy is assumed and the cases $n = -2,-1$ are explored. No significant deviation with respect to the standard oscillation hypothesis is observed. Therefore, $90\,\%$ CL upper limits are estimated as $\Gamma_{21} < 4.6\cdot 10^{-21}\,$GeV and $\Gamma_{31} < 8.4\cdot 10^{-21}\,$GeV for $n = -2$, and $\Gamma_{21} < 1.9\cdot 10^{-22}\,$GeV and $\Gamma_{31} < 2.7\cdot 10^{-22}\,$GeV for $n = -1$, respectively., Comment: 17 pages, 5 figures

A chain of quantum dots (QDs) coupled via semiconductor-superconductor hybrid regions can form an artificial Kitaev chain hosting Majorana bound states (MBSs). These zero-energy states are expected to be localised on the edges of the chain, at the outermost QDs. The remaining QDs, comprising the bulk, are predicted to host an excitation gap that protects the MBSs at the edges from local on-site perturbations. In this work, we demonstrate this connection between the bulk and edges in a minimal system, by engineering a three-site Kitaev chain in a two-dimensional electron gas. Through direct tunneling spectroscopy on each site, we show that the appearance of stable zero-bias conductance peaks at the outer QDs is correlated with the presence of an excitation gap in the middle QD. Furthermore, we show that this gap can be controlled by applying a superconducting phase difference between the two hybrid segments, and that the MBSs are robust only when the excitation gap is present. We find a close agreement between experiments and the original Kitaev model, thus confirming key predictions for MBSs in a three-site chain., Comment: 26 pages, 15 figures

The purpose of this note is to pose a question that, when answered, would directly imply the Cohen Structure Theorem. We provide a solution to this question for a specific class of local rings (not necessarily complete). We also explore how this question connects to the Gelfand-Mazur Theorem and, more broadly, to a fundamental theorem in Gelfand theory. Finally, we provide a categorical reformulation of the question.

We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We decompose the task of learning operators into two parts: learning sets of basis functions for both the input and output spaces, and learning a potentially nonlinear mapping between the coefficients of the basis functions. B2B operator learning circumvents many challenges of prior works, such as requiring data to be at fixed locations, by leveraging classic techniques such as least-squares to compute the coefficients. It is especially potent for linear operators, where we compute a mapping between bases as a single matrix transformation with a closed form solution. Furthermore, with minimal modifications and using the deep theoretical connections between function encoders and functional analysis, we derive operator learning algorithms that are directly analogous to eigen-decomposition and singular value decomposition. We empirically validate B2B operator learning on six benchmark operator learning tasks, and show that it demonstrates a two-orders-of-magnitude improvement in accuracy over existing approaches on several benchmark tasks.

Map-free LiDAR localization systems accurately localize within known environments by predicting sensor position and orientation directly from raw point clouds, eliminating the need for large maps and descriptors. However, their long training times hinder rapid adaptation to new environments. To address this, we propose FlashMix, which uses a frozen, scene-agnostic backbone to extract local point descriptors, aggregated with an MLP mixer to predict sensor pose. A buffer of local descriptors is used to accelerate training by orders of magnitude, combined with metric learning or contrastive loss regularization of aggregated descriptors to improve performance and convergence. We evaluate FlashMix on various LiDAR localization benchmarks, examining different regularizations and aggregators, demonstrating its effectiveness for rapid and accurate LiDAR localization in real-world scenarios. The code is available at https://github.com/raktimgg/FlashMix.

This paper introduces the hypothetical track-length fitting algorithm, a novel method for measuring the kinetic energies of ionizing particles in liquid argon time projection chambers (LArTPCs). The algorithm finds the most probable offset in track length for a track-like object by comparing the measured ionization density as a function of position with a theoretical prediction of the energy loss as a function of the energy, including models of electron recombination and detector response. The algorithm can be used to measure the energies of particles that interact before they stop, such as charged pions that are absorbed by argon nuclei. The algorithm's energy measurement resolutions and fractional biases are presented as functions of particle kinetic energy and number of track hits using samples of stopping secondary charged pions in data collected by the ProtoDUNE-SP detector, and also in a detailed simulation. Additional studies describe impact of the dE/dx model on energy measurement performance. The method described in this paper to characterize the energy measurement performance can be repeated in any LArTPC experiment using stopping secondary charged pions.

Large Language Models have advanced clinical Natural Language Generation, creating opportunities to manage the volume of medical text. However, the high-stakes nature of medicine requires reliable evaluation, which remains a challenge. In this narrative review, we assess the current evaluation state for clinical summarization tasks and propose future directions to address the resource constraints of expert human evaluation.

In this study, we present an approach $ f(R, G) $ gravity incorporating power law in $ G $. To study the cosmic evolution of the universe given by the reconstruction of the Hubble parameter given by $ E(z) = \bigg( 1+\frac{z(\alpha+(1+z)^{\beta})}{2 \beta + 1} \bigg)^{\frac{3}{2 \beta}} $. Subsequently, we use various recent observational datasets of OHD, Pantheon, and BAO to estimate the model parameters $ H_0,~\alpha $, and $ \beta $ applying the Markov Chain Monte Carlo (MCMC) technique in the emcee package to establish the validity of the model. In our findings, we observe that our model shows consistency with standard $ \Lambda $CDM, transits from deceleration to acceleration, and enters the quintessence region in late times. The cosmological model satisfies necessary energy constraints, simultaneously violating the strong energy condition (SEC), indicating a repulsive nature and consistent with accelerated expansion. The cosmic evolution of the Hawking temperature and the total entropy for the various observational datasets also show the validity of the model. Thus, our established model demonstrates sufficient potential for explicitly describing cosmological models., Comment: 19 pages, 20 figures

Accurately attributing answer text to its source document is crucial for developing a reliable question-answering system. However, attribution for long documents remains largely unexplored. Post-hoc attribution systems are designed to map answer text back to the source document, yet the granularity of this mapping has not been addressed. Furthermore, a critical question arises: What exactly should be attributed? This involves identifying the specific information units within an answer that require grounding. In this paper, we propose and investigate a novel approach to the factual decomposition of generated answers for attribution, employing template-based in-context learning. To accomplish this, we utilize the question and integrate negative sampling during few-shot in-context learning for decomposition. This approach enhances the semantic understanding of both abstractive and extractive answers. We examine the impact of answer decomposition by providing a thorough examination of various attribution approaches, ranging from retrieval-based techniques to LLM-based attributors.

Our aim in this paper is to explore semisubtractive ideals of semirings. We prove that they form a complete modular lattice. We introduce Golan closures and prove some of their basic properties. We explore the relations between $Q$-ideals and semisubtractive ideals of semirings, and also study them in $s$-local semirings. We introduce two subclasses of semisubtractive ideals: $s$-strongly irreducible and $s$-irreducible, and provide various representation theorems. By endowing a topology on the set of semisubtractive ideals, we prove that the space is $T_0$, sober, connected, and quasi-compact. We also briefly study continuous maps between semisubtractive spaces. We construct $s$-congruences and prove a bijection between these congruences and semisubtractive ideals., Comment: 13 pages

Building on previous work on de Sitter extremal surfaces anchored at the future boundary, we study no-boundary extremal surfaces in slow-roll inflation models, with perturbations to no-boundary global $dS$ preserving the spatial isometry. While in pure de Sitter space the Euclidean hemisphere gives a real area equalling half de Sitter entropy, the no-boundary extremal surface areas here have nontrivial real and imaginary pieces overall. We evaluate the area integrals in the complex time-plane defining appropriate contours. For the 4-dim case, the real and imaginary finite corrections at leading order in the slow-roll parameter match those in the semiclassical expansion of the Wavefunction (or action), and corroborate the cosmic brane interpretation discussed previously. We also study no-boundary extremal surfaces in other cosmologies including 3-dimensional inflation and Schwarzschild de Sitter spaces with small mass., Comment: Latex, 33pgs, 3 figs

The aim of these notes is to study some of the structural aspects of the ring of arithmetical functions. We prove that this ring is neither Noetherian nor Artinian. Furthermore, we construct various types of prime ideals. We also give an example of a semi-prime ideal that is not prime. We show that the ring of arithmetical functions has infinite Krull dimension., Comment: 13 pages. arXiv admin note: text overlap with arXiv:2302.01072

Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. Traditionally, while constructing the loss function, DeepONet training considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework's performance in modeling complex physical systems.

We study the diffusion properties of an interacting hadron gas and evaluate the diffusion coefficient matrix for the baryon, strange, electric, and charm quantum numbers. For the first time, this study sheds light on the charm current and estimates the diffusion matrix coefficient for the charmed states by treating them as a part of the quasi-thermalized medium. We explore the diffusion matrix coefficient as a function of temperature and center-of-mass energy. A van der Waals-like interaction is assumed between the hadrons, including attractive and repulsive interactions. The calculation of diffusion coefficients is based on relaxation time approximation to the Boltzmann transport equation. A good agreement with available model calculations is observed in the hadronic limit. To conclude the study, we discuss, with a detailed explanation, that charm fluctuation is expected to be a better tool for probing the QCD critical point., Comment: 11 pages and 4 captioned figures. Submitted for publication

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

The present investigation reports the design and development of an advanced material with a high figure of merit (FoM) for beampipe applications in particle accelerators by bringing synergy between computational and experimental approaches. Machine learning algorithms have been used to predict the phase(s), low density, and high radiation length of the designed Al-Ti-V alloys. Al-Ti-V alloys with various compositions for single-phase and dual-phase mixtures, liquidus temperature, and density values are obtained using the Latin hypercube sampling method in TC Python Thermo-Calc software. The obtained dataset is utilized to train the machine-learning algorithms. Classification algorithms such as XGBoost and regression models such as Linear Regression and Random Forest regressor have been used to compute the number of phases, radiation length, and density respectively. The XGBoost algorithms show an accuracy of $98\%$, the Linear regression model shows an accuracy of $94\%$, and the Random Forest regressor model is accurate up to $99\%$. The developed Al-Ti-V alloys exhibit high radiation length as well as a good combination of high elastic modulus and toughness due to the synergistic effect of the presence of hard $Al_3Ti$ phase along with a minor volume fraction of FCC $(Al)_{ss}$ solid solution phase mixture. The comparison of our alloys, alloy-1 ($Al_{75.2}Ti_{22.8}V_{2}$) and alloy-2 ($Al_{89}Ti_{10}V_{1}$) shows an increase in the radiation length by seven-times and a decrease in the density by two to three times as compared to stainless steel 304, the preferred material for constructing beampipes in low-energy particle accelerators. Further, we experimentally verify the elastic modulus of the alloy-1 and compute the FoM equal to 0.416, which is better than other existing materials for beampipes in low-energy experiments., Comment: 9 pages and 4 captioned figures. Submitted for publication

Time series foundation models (TSFMs) promise to be powerful tools for a wide range of applications. However, their internal representations and learned concepts are still not well understood. In this study, we investigate the structure and redundancy of representations across various TSFMs, examining the self-similarity of model layers within and across different model sizes. This analysis reveals block-like redundancy in the representations, which can be utilized for informed pruning to improve inference speed and efficiency. Additionally, we explore the concepts learned by these models - such as periodicity and trends - and how these can be manipulated through latent space steering to influence model behavior. Our experiments show that steering interventions can introduce new features, e.g., adding periodicity or trends to signals that initially lacked them. These findings underscore the value of representational analysis for optimizing models and demonstrate how conceptual steering offers new possibilities for more controlled and efficient time series analysis with TSFMs.

Extended Dynamic Mode Decomposition (EDMD) is a widely used data-driven algorithm for estimating the Koopman Operator. EDMD extends Dynamic Mode Decomposition (DMD) by lifting the snapshot data using nonlinear dictionary functions before performing the estimation. This letter investigates how the estimation process is affected when the data is quantized. Specifically, we examine the fundamental connection between estimates of the operator obtained from unquantized data and those from quantized data via EDMD. Furthermore, using the law of large numbers, we demonstrate that, under a large data regime, the quantized estimate can be considered a regularized version of the unquantized estimate. We also explore the relationship between the two estimates in the finite data regime. We further analyze the effect of nonlinear lifting functions on this regularization due to quantization. The theory is validated through repeated numerical experiments conducted on two different dynamical systems., Comment: 6 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2404.02014

This letter presents a Koopman-theoretic lifted linear parameter-varying (LPV) system with countably infinite dimensions to model the nonlinear dynamics of a quadrotor on SE(3) for facilitating control design. The LPV system evolves in time in the space of the observables, called the lifted space. A primary challenge in utilizing the Koopman-based linearization is identifying a set of observables that can adequately span the lifted space, with the majority of the current methods using data to learn these observables. In this study, we analytically derive the observables for the quadrotor dynamics on SE(3) to formulate the lifted LPV system. The lifted LPV system has a countably infinite dimension which is then truncated for practical control design. The truncation is analytically justified by showing vanishing residual property in a bounded trajectory regime. The LPV system is then approximated as a linear time-invariant (LTI) system with a set of virtual control inputs. The controllability of the lifted LTI system is translatable to the true quadrotor system on SE(3). A linear model-predictive control (LMPC) scheme is formulated and implemented in numerical simulations employing this LTI framework for various tracking problems, with attention given to the potential for real-time implementation., Comment: 6 pages, 5 figures

Recently, time series foundation models have shown promising zero-shot forecasting performance on time series from a wide range of domains. However, it remains unclear whether their success stems from a true understanding of temporal dynamics or simply from memorizing the training data. While implicit reasoning in language models has been studied, similar evaluations for time series models have been largely unexplored. This work takes an initial step toward assessing the reasoning abilities of deep time series forecasting models. We find that certain linear, MLP-based, and patch-based Transformer models generalize effectively in systematically orchestrated out-of-distribution scenarios, suggesting underexplored reasoning capabilities beyond simple pattern memorization.

The aim of this series of papers is to study $z$-ideals of semirings. In this article, we introduce some distinguished classes of $z$-ideals of semirings, which include $z$-prime, $z$-semiprime, $z$-irreducible, and $z$-strongly irreducible ideals and study some of their properties. Using a $z$-closure operator, we show the equivalence of these classes of ideals with the corresponding $z$-ideals that are prime, semirprime, irreducible, and strongly irreducible, respectively., Comment: 15 pages

The purpose of this note is to study some algebraic properties of irreducible ideals of monoids. We establish relations between irreducible, prime, and semiprime ideals. We explore some properties of irreducible ideals in local, Noetherian, and Laskerian monoids., Comment: 7 pages

In this paper, we present a data-driven ensemble approach for option price prediction whose derivation is based on the no-arbitrage theory of option pricing. Using the theoretical treatment, we derive a common representation space for achieving domain adaptation. The success of an implementation of this idea is shown using some real data. Then we report several experimental results for critically examining the performance of the derived pricing models., Comment: 24 pages

We study a class polynomials obtained from an enumeration of the number of queen paths. In particular, we find the generating function for the diagonal sequence of this table and the zero distribution of a sequence of related polynomials.

Wind flow can be highly unpredictable and can suffer substantial fluctuations in speed and direction due to the shape and height of hills, mountains, and valleys, making accurate wind speed (WS) forecasting essential in complex terrain. This paper presents a novel and adaptive model for short-term forecasting of WS. The paper's key contributions are as follows: (a) The Partial Auto Correlation Function (PACF) is utilised to minimise the dimension of the set of Intrinsic Mode Functions (IMF), hence reducing training time; (b) The sample entropy (SampEn) was used to calculate the complexity of the reduced set of IMFs. The proposed technique is adaptive since a specific Deep Learning (DL) model-feature combination was chosen based on complexity; (c) A novel bidirectional feature-LSTM framework for complicated IMFs has been suggested, resulting in improved forecasting accuracy; (d) The proposed model shows superior forecasting performance compared to the persistence, hybrid, Ensemble empirical mode decomposition (EEMD), and Variational Mode Decomposition (VMD)-based deep learning models. It has achieved the lowest variance in terms of forecasting accuracy between simple and complex terrain conditions 0.70%. Dimension reduction of IMF's and complexity-based model-feature selection helps reduce the training time by 68.77% and improve forecasting quality by 58.58% on average.

In [Adv. Math., 321 (2017) 269-286], using the theory of ultrafilters, J. H. Johnson Jr., and F. K. Richter proved the nilpotent polynomial Hales-Jewett theorem. Using this result they proved the restricted version of the van der Waerden theorem for nilprogressions of rank $2$ and conjectured that this result must hold for arbitrary rank. In this article, we give an affirmative answer to their conjecture.

Dispersion by mobile agents is a well studied problem in the literature on computing by mobile robots. In this problem, $l$ robots placed arbitrarily on nodes of a network having $n$ nodes are asked to relocate themselves autonomously so that each node contains at most $\lfloor \frac{l}{n}\rfloor$ robots. When $l\le n$, then each node of the network contains at most one robot. Recently, in NETYS'23, Kaur et al. introduced a variant of dispersion called \emph{Distance-2-Dispersion}. In this problem, $l$ robots have to solve dispersion with an extra condition that no two adjacent nodes contain robots. In this work, we generalize the problem of Dispersion and Distance-2-Dispersion by introducing another variant called \emph{Distance-$k$-Dispersion (D-$k$-D)}. In this problem, the robots have to disperse on a network in such a way that shortest distance between any two pair of robots is at least $k$ and there exist at least one pair of robots for which the shortest distance is exactly $k$. Note that, when $k=1$ we have normal dispersion and when $k=2$ we have D-$2$-D. Here, we studied this variant for a dynamic ring (1-interval connected ring) for rooted initial configuration. We have proved the necessity of fully synchronous scheduler to solve this problem and provided an algorithm that solves D-$k$-D in $\Theta(n)$ rounds under a fully synchronous scheduler. So, the presented algorithm is time optimal too. To the best of our knowledge, this is the first work that considers this specific variant.

The international collaboration designing and constructing the Deep Underground Neutrino Experiment (DUNE) at the Long-Baseline Neutrino Facility (LBNF) has developed a two-phase strategy toward the implementation of this leading-edge, large-scale science project. The 2023 report of the US Particle Physics Project Prioritization Panel (P5) reaffirmed this vision and strongly endorsed DUNE Phase I and Phase II, as did the European Strategy for Particle Physics. While the construction of the DUNE Phase I is well underway, this White Paper focuses on DUNE Phase II planning. DUNE Phase-II consists of a third and fourth far detector (FD) module, an upgraded near detector complex, and an enhanced 2.1 MW beam. The fourth FD module is conceived as a "Module of Opportunity", aimed at expanding the physics opportunities, in addition to supporting the core DUNE science program, with more advanced technologies. This document highlights the increased science opportunities offered by the DUNE Phase II near and far detectors, including long-baseline neutrino oscillation physics, neutrino astrophysics, and physics beyond the standard model. It describes the DUNE Phase II near and far detector technologies and detector design concepts that are currently under consideration. A summary of key R&D goals and prototyping phases needed to realize the Phase II detector technical designs is also provided. DUNE's Phase II detectors, along with the increased beam power, will complete the full scope of DUNE, enabling a multi-decadal program of groundbreaking science with neutrinos.

In this work, we present a comparative study between continuous-wave (CW) and pulsed optical tweezers for 250 nm, 500 nm and 1-micron radius polystyrene beads at 5 different laser powers. We have used a Ti:Sapphire (MIRA 900F) laser that can be easily switched from CW to pulsed mode of operation, so there is no change in the experimental conditions in the two cases. We have measured the difference in the trap strength in both cases by fitting the power spectrum curve with Lorentzian. As it turns out, trapping with pulsed tweezers seems to be more effective for the smaller particles and as the particle size is increased both CW and pulsed tweezers appear to be equally effective at lower average laser powers but as the power is increased pulsed tweezers do a better job at stable trapping.

KM3NeT/ORCA is a water Cherenkov neutrino detector under construction and anchored at the bottom of the Mediterranean Sea. The detector is designed to study oscillations of atmospheric neutrinos and determine the neutrino mass ordering. This paper focuses on an initial configuration of ORCA, referred to as ORCA6, which comprises six out of the foreseen 115 detection units of photo-sensors. A high-purity neutrino sample was extracted, corresponding to an exposure of 433 kton-years. The sample of 5828 neutrino candidates is analysed following a binned log-likelihood method in the reconstructed energy and cosine of the zenith angle. The atmospheric oscillation parameters are measured to be $\sin^2\theta_{23}= 0.51^{+0.04}_{-0.05}$, and $ \Delta m^2_{31} = 2.18^{+0.25}_{-0.35}\times 10^{-3}~\mathrm{eV^2} \cup \{-2.25,-1.76\}\times 10^{-3}~\mathrm{eV^2}$ at 68\% CL. The inverted neutrino mass ordering hypothesis is disfavoured with a p-value of 0.25., Comment: 29 pages, 12 figures

In this paper, we revisit the 1979 work of Isbell on subfactors of groups and their projections, which he uses to establish a stronger formulation of the butterfly lemma and its consequence, the refinement theorem for subnormal series of subgroups. We point out an error in the second part of Isbell's refinement theorem, but show that the rest of his results can be extended to the general self-dual context of a noetherian form, which includes in its scope all semi-abelian categories as well as all Grandis exact categories. Furthermore, we show that Isbell's formulations of the butterfly lemma and the refinement theorem amount to canonicity of isomorphisms established in these results.

The parametric optimization for the ultrasound computed tomography system is introduced. It is hypothesized that the pulse characteristic directly affects the information present in the reconstructed profile. The ultrasound excitation modes based on pulse-width modifications are studied to estimate the effect on reconstruction quality. Studies show that the pulse width affects the response of the transducer and, thus, the reconstruction. The ultrasound scanning parameters, mainly pulse width, are assessed and optimally set by an Artificial Intelligence driven process, according to the object without the requirement of a-priori information. The optimization study uses a novel intelligent object placement procedure to ensure repeatability of the same region of interest, a key requirement to minimize the error. Further, Kanpur Theorem 1 is implemented to evaluate the quality of the acquired projection data and discard inferior quality data. Scanning results corresponding to homogeneous and heterogeneous phantoms are presented. The image processing step involves deep learning model evaluating the dice coefficient for estimating the reconstruction quality if prior information about the inner profile is known or a classical error estimate otherwise. The models segmentation accuracy is 95.72 percentage and intersection over union score is 0.8842 on the validation dataset. The article also provides valuable insights about the development and low-level control of the system., Comment: 20 Pages, 13 figures

Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output to the quantum algorithm are classical. In contrast to stand-alone single-core quantum computers, in many distributed scenarios, quantum information might have to be passed on from one quantum information processing system to another one, possibly via noisy quantum communication channels with noise levels above fault-tolerant thresholds. In such situations, quantum information processing devices will have quantum inputs, quantum outputs or even both, which pass qubits among each other. Such a scenario has first been considered in the context of point-to-point communication by Christandl and M{\"u}ller-Hermes, IEEE Trans. Inf. Th. 2024. Working in the fault-tolerant framework of Kitaev we provide general tools for making quantum computation with quantum input and quantum output robust against circuit noise. The framework allows the direct composition of the statements, enabling versatile future application. As concrete applications, we show that encoders and decoders affected by general noise (including coherent errors) can be constructed for arbitrary linear distance communication codes. For the weaker, but standard, model of local stochastic noise, we obtain such encoders and decoders for practical communication codes, which include families of efficient coding circuits., Comment: 69 Pages, 12 Figures

A unique sample independent 3D self calibration methodology is tested on a unique optical coherence tomography and multi-spectral scanning laser ophthalmoscope (OCT-SLO) hybrid system. Operators visual cognition is replaced by computer vision using the proposed novel fully automatic AI-driven system design. Sample specific automatic contrast adjustment of the beam is achieved on the pre-instructed region of interest. The AI model deduces infrared, fluorescence, and visual spectrum optical alignment by estimating pre-instructed features quantitatively. The tested approach, however, is flexible enough to utilize any apt AI model. Relative comparison with classical signal-to-noise-driven automation is shown to be 200 percent inferior and 130 percent slower than the AI-driven approach. The best spatial resolution of the system is found to be (a) 2.41 microns in glass bead eye phantom, 0.76 with STD 0.46 microns in the mouse retina in the axial direction, and (b) better than 228 line pair per millimeter (lp per mm) or 2 microns for all three spectrums, i.e., 488 nm, 840 nm, and 520 to 550 nm emission in coronal, frontal or x-y plane. Intelligent automation reduces the possibility of developing cold cataracts (especially in mouse imaging) and patient-associated discomfort due to delay during manual alignment by facilitating easy handling for swift ocular imaging and better accuracy. The automatic novel tabletop compact system provides true functional 3D images in three different spectrums for dynamic sample profiles. This is especially useful for photodynamic imaging treatment., Comment: 20 Pages, 11 figures

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

X-ray Computed Tomography (CT) is used to recover the true surfaces of fluid channels and fed to simulation tool (ANSYS) to create accurate cyber environment. The simulation tool also receives CT-assisted multiphase fluid profiles (belonging to the instance just before the flow starts) as an initial condition. This unique methodology is made possible by using a novel in-situ compact adaptor design is used to create fluid channels that can be placed inside any industrial X-ray CT and fulfill the above objective. It is integrated with an android based App to control the flow once placed inside CT. It is portable and compact enough: (a) to be placed inside various experimental environments, and (b) modular enough to be mounted with multi-modal systems simultaneously. Two key parameters, (a) spatial distribution and (b) the air volume fraction, are measured using two different non-invasive imaging modalities: (a) Electrical Impedance Tomography (EIT) and (d) X-ray Computed Tomography (CT). Simulated outcomes are correlated with the experimental outcomes from both EIT and X-ray CT, showing an agreement of 85 to 98 percent, respectively. Time-averaged electrically conductive fluid flow profile obtained by EIT shows a match with mass mass-attenuated fluid profile obtained by X-ray CT, justifying the utility of an in-situ adaptor. CT assistance for CFD studies can be replaced by EIT assistance as former techniques: (a) scanning time may be relatively slower than the latter, (b) it does not require rotations, (c) economical, and (d) fluid channels need not be placed inside of shielded compartment thus improving practicality. The data of analysis is shared in this work. Multimodal non-invasive imaging provides multiphase flow information, it also differentiates conductive, and mass-attenuated multiphase profiles at common cross-sections., Comment: 11 Pages, 5 figures