Search

Let $F$ be a finite extension of $\mathbb{Q}_p$, and let $E$ be a finite Galois extension of $F$ with degree of extension $l$, where $l$ and $p$ are distinct odd primes. Let $\pi_F$ be an integral, $l$-adic generic representation of ${\rm GL}_3(F)$, and let $\pi_E$ be the base change lifting of $\pi_F$ to ${\rm GL}_3(E)$. Let $J_l(\pi_F)$ (resp. $J_l(\pi_E)$) be the unique generic sub-quotient of the mod-$l$ reduction of $\pi_F$ (resp. $\pi_E$). In this article, using the local converse theorem over local Artinian $\overline{\mathbb{F}}_l$-algebras, we prove that the Frobenius twist of $J_l(\pi_F)$ is isomorphic to the Tate cohomology group $\widehat{H}^0({\rm Gal}(E/F),J_l(\pi_E))$. The result of this article removes the hypothesis that the prime $l$ does not divide the pro-order of ${\rm GL}_2(F)$., Comment: 15 pages

We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher dimensional topological features such as connected components and holes (cycles or loops) in the data. In other words, persistent homology is a multiscale version of homology that characterizes sets based on the connected components and holes. We use super-level sets of functions to extract geometric features via persistent homology. In particular, we explore structures in regression curves via the persistent homology of super-level sets of a function, where the function of interest is - the first derivative of the regression function. In the course of this study, we extend an existing procedure of estimating the persistent homology for the first derivative of a regression function and establish its consistency. Moreover, as an application of the proposed methodology, we demonstrate that the persistent homology of the derivative of a function can reveal hidden structures in the function that are not visible from the persistent homology of the function itself. In addition, we also illustrate that the proposed procedure can be used to compare the shapes of two or more regression curves which is not possible merely from the persistent homology of the function itself., Comment: Following modifications have been made: 1) one paragraph is added in the subsection our contribution. 2) Sketch of the proof is modified. 3) An additional subsection has been incorporated in applications namely, comparison of regression curves. 4) Need and interpretation of supporting lemma's has been emphasized in the appendix

We consider the relaxation of an initial non-equilibrium state in a one-dimensional fluid of hard rods. Since it is an interacting integrable system, we expect it to reach the Generalized Gibbs Ensemble (GGE) at long times for generic initial conditions. Here we show that there exist initial conditions for which the system does not reach GGE even at very long times and in the thermodynamic limit. In particular, we consider an initial condition of uniformly distributed hard-rods in a box with the left half having particles with a singular velocity distribution (all moving with unit velocity) and the right half particles in thermal equilibrium. We find that the density profile for the singular component does not spread to the full extent of the box and keeps moving with a fixed effective speed at long times. We show that such density profiles can be well described by the solution of the Euler equations almost everywhere except at the location of the shocks, where we observe slight discrepancies due to dissipation arising from the initial fluctuations of the thermal background. To demonstrate this effect of dissipation analytically, we consider a second initial condition with a single particle at the origin with unit velocity in a thermal background. We find that the probability distribution of the position of the unit velocity quasi-particle has diffusive spreading which can be understood from the solution of the Navier-Stokes equation of the hard rods. Finally, we consider an initial condition with a spread in velocity distribution for which we show convergence to GGE. Our conclusions are based on molecular dynamics simulations supported by analytical arguments.

Accurate teeth segmentation and orientation are fundamental in modern oral healthcare, enabling precise diagnosis, treatment planning, and dental implant design. In this study, we present a comprehensive approach to teeth segmentation and orientation from panoramic X-ray images, leveraging deep learning techniques. We build our model based on FUSegNet, a popular model originally developed for wound segmentation, and introduce modifications by incorporating grid-based attention gates into the skip connections. We introduce oriented bounding box (OBB) generation through principal component analysis (PCA) for precise tooth orientation estimation. Evaluating our approach on the publicly available DNS dataset, comprising 543 panoramic X-ray images, we achieve the highest Intersection-over-Union (IoU) score of 82.43% and Dice Similarity Coefficient (DSC) score of 90.37% among compared models in teeth instance segmentation. In OBB analysis, we obtain the Rotated IoU (RIoU) score of 82.82%. We also conduct detailed analyses of individual tooth labels and categorical performance, shedding light on strengths and weaknesses. The proposed model's accuracy and versatility offer promising prospects for improving dental diagnoses, treatment planning, and personalized healthcare in the oral domain. Our generated OBB coordinates and codes are available at https://github.com/mrinal054/Instance_teeth_segmentation.

The study of temporal coherence in a Bose-Einstein condensate of photons can be challenging, especially in the presence of correlations between the photonic modes. In this work, we use a microscopic, multimode model of photonic condensation inside a dye-filled microcavity and the quantum regression theorem, to derive an analytical expression for the equation of motion of the photon-photon correlation function. This allows us to derive the coherence time of the photonic modes and identify a nonmonotonic dependence of the temporal coherence of the condensed light with the cutoff frequency of the microcavity., Comment: 12 pages, 5 figures

The temporal coherence of an ideal Bose gas increases as the system approaches the Bose-Einstein condensation threshold from below, with coherence time diverging at the critical point. However, counter-examples have been observed for condensates of photons formed in an externally pumped, dye-filled microcavity, wherein the coherence time decreases rapidly for increasing particle number above threshold. This paper establishes intermode correlations as the central explanation for the experimentally observed dramatic decrease in the coherence time beyond critical pump power., Comment: 5 pages, 4 figures

We consider a Klein-Gordon chain that is periodically driven at one end and has dissipation at one or both boundaries. An interesting numerical observation in a recent study~[arXiv:2209.03977] was that for driving frequency in the phonon band, there is a range of values of the driving amplitude $F_d\in (F_1, F_2)$ over which the energy current remains constant. In this range, the system exhibits a "resonant nonlinear wave" (RNW) mode of energy transmission which is a time and space periodic solution. It was noted that the range $(F_1,F_2)$, for which the RNW mode occurs, shrinks with increasing system size $N$ and disappears eventually. Remarkably, we find that the RNW mode is in fact a stable solution even for $F_d$ much larger than $F_2$ and quite large $N$ ($\approx 1000$). For $F_d>F_{2}$, there exists a second attractor which is chaotic. Both attractors have finite basins of attraction and can be reached by appropriate choice of initial conditions. Corresponding to the two attractors for large $F_d$, the system can now be in two nonequilibrium steady states. We improve the perturbative treatment of [arXiv:2209.03977] for the RNW mode by including the contributions of the third harmonics. We also consider the effect of thermal noise at the boundaries and find that the RNW mode is stable for small temperatures. Finally, we present results for a different driving protocol studied in [arXiv:2205.03839] where $F_d$ is taken to scale with system size as $N^{-1/2}$ and there is dissipation only at the non-driven end. We find that the steady state can be characterized by Fourier's law as in [arXiv:2205.03839] for a stochastic model. We point out interesting differences that occur since our dynamics is nonlinear and Hamiltonian. Our results suggest the intriguing possibility of observing the high current carrying RNW phase in experiments by careful preparation of initial conditions., Comment: 11 pages, 14 figures

The recently-emerging field of higher order MDS codes has sought to unify a number of concepts in coding theory. Such areas captured by higher order MDS codes include maximally recoverable (MR) tensor codes, codes with optimal list-decoding guarantees, and codes with constrained generator matrices (as in the GM-MDS theorem). By proving these equivalences, Brakensiek-Gopi-Makam showed the existence of optimally list-decodable Reed-Solomon codes over exponential sized fields. Building on this, recent breakthroughs by Guo-Zhang and Alrabiah-Guruswami-Li have shown that randomly punctured Reed-Solomon codes achieve list-decoding capacity (which is a relaxation of optimal list-decodability) over linear size fields. We extend these works by developing a formal theory of relaxed higher order MDS codes. In particular, we show that there are two inequivalent relaxations which we call lower and upper relaxations. The lower relaxation is equivalent to relaxed optimal list-decodable codes and the upper relaxation is equivalent to relaxed MR tensor codes with a single parity check per column. We then generalize the techniques of GZ and AGL to show that both these relaxations can be constructed over constant size fields by randomly puncturing suitable algebraic-geometric codes. For this, we crucially use the generalized GM-MDS theorem for polynomial codes recently proved by Brakensiek-Dhar-Gopi. We obtain the following corollaries from our main result. First, randomly punctured AG codes of rate $R$ achieve list-decoding capacity with list size $O(1/\epsilon)$ and field size $\exp(O(1/\epsilon^2))$. Prior to this work, AG codes were not even known to achieve list-decoding capacity. Second, by randomly puncturing AG codes, we can construct relaxed MR tensor codes with a single parity check per column over constant-sized fields, whereas (non-relaxed) MR tensor codes require exponential field size., Comment: 38 pages, STOC 2024

The GM-MDS theorem, conjectured by Dau-Song-Dong-Yuen and proved by Lovett and Yildiz-Hassibi, shows that the generator matrices of Reed-Solomon codes can attain every possible configuration of zeros for an MDS code. The recently emerging theory of higher order MDS codes has connected the GM-MDS theorem to other important properties of Reed-Solomon codes, including showing that Reed-Solomon codes can achieve list decoding capacity, even over fields of size linear in the message length. A few works have extended the GM-MDS theorem to other families of codes, including Gabidulin and skew polynomial codes. In this paper, we generalize all these previous results by showing that the GM-MDS theorem applies to any polynomial code, i.e., a code where the columns of the generator matrix are obtained by evaluating linearly independent polynomials at different points. We also show that the GM-MDS theorem applies to dual codes of such polynomial codes, which is non-trivial since the dual of a polynomial code may not be a polynomial code. More generally, we show that GM-MDS theorem also holds for algebraic codes (and their duals) where columns of the generator matrix are chosen to be points on some irreducible variety which is not contained in a hyperplane through the origin. Our generalization has applications to constructing capacity-achieving list-decodable codes as shown in a follow-up work by Brakensiek-Dhar-Gopi-Zhang, where it is proved that randomly punctured algebraic-geometric (AG) codes achieve list-decoding capacity over constant-sized fields., Comment: 34 pages, STOC 2024

Bose-Einstein condensates of ultracold atoms serve as low-entropy sources for a multitude of quantum-science applications, ranging from quantum simulation and quantum many-body physics to proof-of-principle experiments in quantum metrology and quantum computing. For stability reasons, in the majority of cases the energetically lowest-lying atomic spin state is used. Here we report the Bose-Einstein condensation of caesium atoms in the Zeeman-excited mf = 2 state, realizing a non-ground-state Bose-Einstein condensate with tunable interactions and tunable loss. We identify two regions of magnetic field in which the two-body relaxation rate is low enough that condensation is possible. We characterize the phase transition and quantify the loss processes, finding unusually high three-body losses in one of the two regions. Our results open up new possibilities for the mixing of quantum-degenerate gases, for polaron and impurity physics, and in particular for the study of impurity transport in strongly correlated one-dimensional quantum wires.

Speech Command Recognition (SCR), which deals with identification of short uttered speech commands, is crucial for various applications, including IoT devices and assistive technology. Despite the promise shown by Convolutional Neural Networks (CNNs) in SCR tasks, their efficacy relies heavily on hyper-parameter selection, which is typically laborious and time-consuming when done manually. This paper introduces a hyper-parameter selection method for CNNs based on the Differential Evolution (DE) algorithm, aiming to enhance performance in SCR tasks. Training and testing with the Google Speech Command (GSC) dataset, the proposed approach showed effectiveness in classifying speech commands. Moreover, a comparative analysis with Genetic Algorithm based selections and other deep CNN (DCNN) models highlighted the efficiency of the proposed DE algorithm in hyper-parameter selection for CNNs in SCR tasks., Comment: 8 Pages, 7 Figures, 4 Tables, Accepted by the 15th International Joint Conference on Computational Intelligence (IJCCI 2023), November 13-15, 2023, Rome, Italy

Recent efforts to enable visual navigation using large language models have mainly focused on developing complex prompt systems. These systems incorporate instructions, observations, and history into massive text prompts, which are then combined with pre-trained large language models to facilitate visual navigation. In contrast, our approach aims to fine-tune large language models for visual navigation without extensive prompt engineering. Our design involves a simple text prompt, current observations, and a history collector model that gathers information from previous observations as input. For output, our design provides a probability distribution of possible actions that the agent can take during navigation. We train our model using human demonstrations and collision signals from the Habitat-Matterport 3D Dataset (HM3D). Experimental results demonstrate that our method outperforms state-of-the-art behavior cloning methods and effectively reduces collision rates.

Recent advancements in superconducting circuits have enabled the experimental study of collective behavior of precisely controlled intermediate-scale ensembles of qubits. In this work, we demonstrate an atomic frequency comb formed by individual artificial atoms strongly coupled to a single resonator mode. We observe periodic microwave pulses that originate from a single coherent excitation dynamically interacting with the multi-qubit ensemble. We show that this revival dynamics emerges as a consequence of the constructive and periodic rephasing of the five superconducting qubits forming the vacuum Rabi split comb. In the future, similar devices could be used as a memory with in-situ tunable storage time or as an on-chip periodic pulse generator with non-classical photon statistics.

Impact of droplets of varying surface tension and subsequent spreading over a solid surface are inherent features in printing applications. In this regard, an experimental study of impact of two drops of varied surface tension is carried out where the sessile water droplet on a hydrophilic substrate is impacted upon by another droplet of sequentially lowered surface tension. The impacts are studied for different impact velocities and offsets with respect to the mid-plane of the two colliding droplets. Sodium Dodecyl Sulfate (SDS) is used to alter the surface tension without altering the viscosity, to study the various parameters affecting the spreading length viz. the surface tension, offset between the drops, and impact velocity. The spreading lengths are obtained through image processing of the captured footage of the impact dynamics by a high-speed camera. It is found out that upon lowering the surface tension, the maximum and equilibrium spreading length varies to a significant extent also the nature of the spreading dynamics changes. Both side and top-view imaging are performed to understand the overall hydrodynamics. There is also a substantial change in drawback when dissimilarity is surface tension between the impacting droplets exist. Finally, a fit model is obtained to predict the maximum spread length of the various cases., Comment: 38

With the advancement of telemedicine, both researchers and medical practitioners are working hand-in-hand to develop various techniques to automate various medical operations, such as diagnosis report generation. In this paper, we first present a multi-modal clinical conversation summary generation task that takes a clinician-patient interaction (both textual and visual information) and generates a succinct synopsis of the conversation. We propose a knowledge-infused, multi-modal, multi-tasking medical domain identification and clinical conversation summary generation (MM-CliConSummation) framework. It leverages an adapter to infuse knowledge and visual features and unify the fused feature vector using a gated mechanism. Furthermore, we developed a multi-modal, multi-intent clinical conversation summarization corpus annotated with intent, symptom, and summary. The extensive set of experiments, both quantitatively and qualitatively, led to the following findings: (a) critical significance of visuals, (b) more precise and medical entity preserving summary with additional knowledge infusion, and (c) a correlation between medical department identification and clinical synopsis generation. Furthermore, the dataset and source code are available at https://github.com/NLP-RL/MM-CliConSummation.

We revisit the somewhat less studied problem of Yang-Lee zeros of the Ising antiferromagnet. For this purpose, we study two models, the nearest-neighbor model on a square lattice, and the more tractable mean-field model corresponding to infinite-ranged coupling between all sites. In the high-temperature limit, we show that the logarithm of the Yang-Lee zeros can be written as a series in half odd integer powers of the inverse temperature, $k$, with the leading term $\sim k^{1/2}$. This result is true in any dimension and for arbitrary lattices. We also show that the coefficients of the expansion satisfy simple identities (akin to sum rules) for the nearest-neighbor case. These new identities are verified numerically by computing the exact partition function for a 2D square lattice of size $16\times16$. For the mean-field model, we write down the partition function (termed the mean-field polynomials) for the ferromagnetic (FM) and antiferromagnetic (AFM) cases, and derive from them the mean-field equations. We analytically show that at high temperatures the zeros of the AFM mean-field polynomial scale as $\sim k^{1/2}$ as well. Using a simple numerical method, we find the roots lie on certain curves (the root curves), in the thermodynamic limit for the mean-field polynomials for the AFM case as well as for the FM one. Our results show a new root curve, that was not found earlier. Our results also clearly illustrate the phase transition expected for the FM and AFM cases, in the language of Yang-Lee zeros. Moreover, for the AFM case, we observe that the root curves separate two distinct phases of zero and non-zero complex staggered magnetization, and thus depict a complex phase boundary.

The BG-rank BG($\pi$) of an integer partition $\pi$ is defined as $$\text{BG}(\pi) := i-j$$ where $i$ is the number of odd-indexed odd parts and $j$ is the number of even-indexed odd parts of $\pi$. In a recent work, Fu and Tang ask for a direct combinatorial proof of the following identity of Berkovich and Uncu $$B_{2N+\nu}(k,q)=q^{2k^2-k}\left[\begin{matrix}2N+\nu\\N+k\end{matrix}\right]_{q^2}$$ for any integer $k$ and non-negative integer $N$ where $\nu\in \{0,1\}$, $B_N(k,q)$ is the generating function for partitions into distinct parts less than or equal to $N$ with BG-rank equal to $k$ and $\left[\begin{matrix}a+b\\b\end{matrix}\right]_q$ is a Gaussian binomial coefficient. In this paper, we provide a bijective proof of Berkovich and Uncu's identity along the lines of Vandervelde and Fu and Tang's idea., Comment: 18 pages, 8 figures. To appear in S\'eminaire Lotharingien de Combinatoire

In this article, I discuss the motion of $N$ point masses in non-relativistic mechanics, when the interaction between them is purely the Newtonian gravitational interaction, with $N$ greater than or equal to 2. The dynamical equations of motion cannot be solved in closed form, for general initial conditions, for any $N$ greater than 2. However, the qualitative behavior of the solutions can be understood from general considerations. I discuss in particular motion the three masses on a line, and the counter-intuitive case of four masses on a line that leads to all particles escaping to infinity in a finite time., Comment: Submitted to Physics News

Today, malware is one of the primary cyberthreats to organizations. Malware has pervaded almost every type of computing device including the ones having limited memory, battery and computation power such as mobile phones, tablets and embedded devices like Internet-of-Things (IoT) devices. Consequently, the privacy and security of the malware infected systems and devices have been heavily jeopardized. In recent years, researchers have leveraged machine learning based strategies for malware detection and classification. Malware analysis approaches can only be employed in resource constrained environments if the methods are lightweight in nature. In this paper, we present MALITE, a lightweight malware analysis system, that can classify various malware families and distinguish between benign and malicious binaries. MALITE converts a binary into a gray scale or an RGB image and employs low memory and battery power consuming as well as computationally inexpensive malware analysis strategies. We have designed MALITE-MN, a lightweight neural network based architecture and MALITE-HRF, an ultra lightweight random forest based method that uses histogram features extracted by a sliding window. We evaluate the performance of both on six publicly available datasets (Malimg, Microsoft BIG, Dumpware10, MOTIF, Drebin and CICAndMal2017), and compare them to four state-of-the-art malware classification techniques. The results show that MALITE-MN and MALITE-HRF not only accurately identify and classify malware but also respectively consume several orders of magnitude lower resources (in terms of both memory as well as computation capabilities), making them much more suitable for resource constrained environments.

Weather forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of weather systems remains a challenge for traditional statistical models. Apart from Auto Regressive time forecasting models like ARIMA, deep learning techniques (Vanilla ANNs, LSTM and GRU networks), have shown promise in improving forecasting accuracy by capturing temporal dependencies. This paper explores the application of metaheuristic algorithms, namely Genetic Algorithm (GA), Differential Evolution (DE), and Particle Swarm Optimization (PSO), to automate the search for optimal hyperparameters in these model architectures. Metaheuristic algorithms excel in global optimization, offering robustness, versatility, and scalability in handling non-linear problems. We present a comparative analysis of different model architectures integrated with metaheuristic optimization, evaluating their performance in weather forecasting based on metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). The results demonstrate the potential of metaheuristic algorithms in enhancing weather forecasting accuracy \& helps in determining the optimal set of hyper-parameters for each model. The paper underscores the importance of harnessing advanced optimization techniques to select the most suitable metaheuristic algorithm for the given weather forecasting task., Comment: 8 pages, 3 figures, 2 Tables, Accepted by the 15th International Conference on Evolutionary Computation Theory and Applications (ECTA 2023) to be held as part of IJCCI 2023, November 13-15, 2023, Rome, Italy

The global burden of acute and chronic wounds presents a compelling case for enhancing wound classification methods, a vital step in diagnosing and determining optimal treatments. Recognizing this need, we introduce an innovative multi-modal network based on a deep convolutional neural network for categorizing wounds into four categories: diabetic, pressure, surgical, and venous ulcers. Our multi-modal network uses wound images and their corresponding body locations for more precise classification. A unique aspect of our methodology is incorporating a body map system that facilitates accurate wound location tagging, improving upon traditional wound image classification techniques. A distinctive feature of our approach is the integration of models such as VGG16, ResNet152, and EfficientNet within a novel architecture. This architecture includes elements like spatial and channel-wise Squeeze-and-Excitation modules, Axial Attention, and an Adaptive Gated Multi-Layer Perceptron, providing a robust foundation for classification. Our multi-modal network was trained and evaluated on two distinct datasets comprising relevant images and corresponding location information. Notably, our proposed network outperformed traditional methods, reaching an accuracy range of 74.79% to 100% for Region of Interest (ROI) without location classifications, 73.98% to 100% for ROI with location classifications, and 78.10% to 100% for whole image classifications. This marks a significant enhancement over previously reported performance metrics in the literature. Our results indicate the potential of our multi-modal network as an effective decision-support tool for wound image classification, paving the way for its application in various clinical contexts.