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We study the Gateaux differentiability in the Banach space of meromorphic functions and obtain a complete characterization of the same, by using Birkhoff-James orthogonality techniques. We introduce the concept of extended orthogonality covering set (EOCS), which allows us to present refinements of some earlier results on the Gateaux differentiability of analytic functions. We also discuss some related properties of meromorphic functions which follow directly from the said characterization.

Causality is an important factor determining the maximum mass of a neutron star. Previous works studies causality for smooth equation of state. The density at the core of neutron stars can be few times nuclear saturation density, where the occurrence of first-order phase transition has not been ruled out. The causality condition for first-order phase transition is characteristically different from the causality condition of smooth equation of state which can be evident in the mass-radius expression. In this letter we examine the causality condition for first-order phase transition and its observational significance in the mass-radius sequence. We find that equation of state having first-order phase transition, the causality line deviates considerably from the that of smooth equation of state. Depending on the strength of the discontinuity and the onset density of phase transition there is a narrow band in the mass-radius plot which is available only to the stars having smooth equation of state. This can have significant consequence in the sense that if some pulsars are to lie in this band one can rule out equation of state having first-order phase transition occurring at that particular onset density., Comment: 7 pages, 9 figures

This paper addresses the medical imaging problem of joint detection in the upper limbs, viz. elbow, shoulder, wrist and finger joints. Localization of joints from X-Ray and Computerized Tomography (CT) scans is an essential step for the assessment of various bone-related medical conditions like Osteoarthritis, Rheumatoid Arthritis, and can even be used for automated bone fracture detection. Automated joint localization also detects the corresponding bones and can serve as input to deep learning-based models used for the computerized diagnosis of the aforementioned medical disorders. This in-creases the accuracy of prediction and aids the radiologists with analyzing the scans, which is quite a complex and exhausting task. This paper provides a detailed comparative study between diverse Deep Learning (DL) models - YOLOv3, YOLOv7, EfficientDet and CenterNet in multiple bone joint detections in the upper limbs of the human body. The research analyses the performance of different DL models, mathematically, graphically and visually. These models are trained and tested on a portion of the openly available MURA (musculoskeletal radiographs) dataset. The study found that the best Mean Average Precision (mAP at 0.5:0.95) values of YOLOv3, YOLOv7, EfficientDet and CenterNet are 35.3, 48.3, 46.5 and 45.9 respectively. Besides, it has been found YOLOv7 performed the best for accurately predicting the bounding boxes while YOLOv3 performed the worst in the Visual Analysis test. Code available at https://github.com/Sohambasu07/BoneJointsLocalization

The recent mass ($0.77 \pm ^{0.20}_{0.17}M_{\odot}$) and radius ($10.4\pm^{0.86}_{0.78} \text{km}$) measurement of HESS J1731-347 made it one of the most fascinating object if it is indeed a neutron star. In this work, we examine the current status of the dense matter equation of states in the context of this compact object being a neutron star. We use three sets of equation of states corresponding to the three classes - neutron stars, strange stars, and hybrid stars and perform Bayesian model selection on them. Our results show that for hadronic models, the EoS is preferred to be stiff at the intermediate densities. This makes the Brueckner-Hartree-Fock approximation and models based on Effective-interactions deviate from current astrophysical observations on the inclusion of HESS J1731-347. Furthermore, for the strange star family, the equation of states composed of three flavor quarks prefers relatively smaller bag parameters. Analyzing the hybrid family of equation of states consisting of a first-order phase transition revealed preferences for early first-order phase transition. Comparing all the preferred equations of state among each family, it was found that the current astrophysical constraints most prefer the hybrid equation of states., Comment: 15 figures, 19 pages

We perform Monte Carlo simulation to study the effects of random disorder on equilibrium phase transition of three three-dimensional single-site anisotropic XY ferromagnetnet. The disorder is incorporated in two ways; having a randomly distributed anisotropy and presence of a quenched random field. We show that the critical temperature of ferro-para transition increases with an increase in strength of constant anisotropy. In contrast, the system gets ordered at lower temperatures if the anisotropy has random distribution. The effects of quenched random fields are also studied in single-site anisotropic XY ferromagnet. The transition temperature reduces due to the presence of quenched random field. The compensating field (the required amount of field which preserves the critical temperature for isotropic XY ferromagnet) linearly depends on the strength of constant single-site anisotropy. We compute the magnetic and susceptibility exponent ratios for constant single-site anisotropic XY system only via detailed finite-size scaling analysis., Comment: 20 pages, 10 captioned figures

Here, we report the full-fledged journey towards the material synthesis and characterization of few-layered/thin WSe$_2$ using sputtered W-films on SiO$_2$/Si substrates followed by electrical studies under dark and illumination conditions. Growth temperature 500oC and gas pressure 55 sccm are found to be the optimized parameters for formation of thermodynamically stable WSe$_{2-x}$ with dominant Raman peak at 265 cm-1. XRD and HR-TEM measurement clarify the formation of high crystallinity along the c-axis and quasi-crystallinity along a and b axes respectively. Lower intensities from Raman-measurement and PL-peak at 768 nm (with 532 nm excitation wavelength) infers the thin nature of the grown film, along with strong second harmonic emission with excitation wavelength varying from 350nm to 450 nm. This work also retracks the controlled etching by reactive ions to achieve large area bi/tri-layer films to fabricate advanced devices. We also have fabricated an advanced MOS structure on SiO$_2$/p-Si substrate which shows tremendous performance by means of photo-capacitance under illumination condition where photo-carriers can survive the higher probe frequencies (> 1MHz). Under illumination condition, HfO$_2$/WSe$_2$ embedded MOS shows its dominance showing a huge electron-inversion region over HfO$_2$/ SiO$_2$/p-Si and SiO$_2$/p-Si MOS devices even at high frequencies (1-10 MHz). Thereby, this work also reveals a possible route for capacitance based highly sensitive photodetection using conventional Si-technology with integration of such WSe$_2$/W as an active material., Comment: 23, 7

Clinicians generally diagnose cardiovascular diseases (CVDs) using standard 12-Lead electrocardiogram (ECG). However, for smartphone-based public healthcare systems, a reduced 3-lead system may be preferred because of (i) increased portability, and (ii) reduced requirement for power, storage and bandwidth. Subsequently, clinicians require accurate 3-lead to 12-Lead ECG reconstruction, which has so far been studied only in the personalized setting. When each device is dedicated to one individual, artificial intelligence (AI) methods such as temporal long short-term memory (LSTM) and a further improved spatio-temporal LSTM-UNet combine have proven effective. In contrast, in the current smartphone-based public health setting where a common device is shared by many, developing an AI lead-reconstruction model that caters to the extensive ECG signal variability in the general population appears a far greater challenge. In this direction, we take a first step, and observe that the performance improvement achieved by a generative model, specifically, 1D Pix2Pix GAN (generative adversarial network), over LSTM-UNet is encouraging., Comment: Accepted to IEEE Healthcom 2024 for presentation as a Main Conference Paper

We develop an iterative assistant we call ChatVis that can synthetically generate Python scripts for data analysis and visualization using a large language model (LLM). The assistant allows a user to specify the operations in natural language, attempting to generate a Python script for the desired operations, prompting the LLM to revise the script as needed until it executes correctly. The iterations include an error detection and correction mechanism that extracts error messages from the execution of the script and subsequently prompts LLM to correct the error. Our method demonstrates correct execution on five canonical visualization scenarios, comparing results with ground truth. We also compared our results with scripts generated by several other LLMs without any assistance. In every instance, ChatVis successfully generated the correct script, whereas the unassisted LLMs failed to do so. The code is available on GitHub: https://github.com/tanwimallick/ChatVis/.

We study regularity results for the solutions of quasilinear subelliptic $p$-Laplace type equation in Heisenberg groups. We prove somewhat surprising excess decay estimates for the constant coefficient homogeneous equation. Excess decay estimates, while well known in the Euclidean case, due to the celebrated works of Uraltseva and Uhlenbeck, was not known in the setting of Heisenberg groups until now and this lack of excess decay estimate is often attributed to the noncommutativity of the horizontal vector fields. Our results show that, in spite of the this noncommutative feature, excess decay estimates analogous to the Euclidean case hold. To illustrate the potency of our excess decay estimates, we prove two results. First is a H\"{o}lder continuity result that extends the presently known results to the full range $1< p < \infty.$ The second is a sharp borderline continuity result for the horizontal gradient of the solution. More precisely, we show that if $u \in HW_{\text{loc}}^{1,p}$ satisfies $$\operatorname{div}_{\mathbb{H}} \left( a(x) \lvert \mathfrak X u \rvert^{p-2} \mathfrak X u \right) \in L^{(Q,1)}_{\text{loc}}$$ in a domain of $\mathbb{H}_{n},$ where $\mathbb{H}_{n}$ is the Heisenberg group with homogeneous dimension $Q=2n+2,$ for $1 < p < \infty, $ with uniformly positive, bounded, Dini continuous scalar function $a$, then $\mathfrak X u$ is continuous. This generalizes the classical result by Stein and the work of Kuusi-Mingione for linear and quasilinear equations, respectively, in the Euclidean case and Folland-Stein for the linear case in the Heisenberg group setting. This result is new even when either $a$ is constant or when the equation is homogeneous.

We developed a deep learning feed-forward network for estimating elliptic flow ($v_2$) coefficients in heavy-ion collisions from RHIC to LHC energies. The success of our model is mainly the estimation of $v_2$ from final state particle kinematic information and learning the centrality and the transverse momentum ($p_{\rm T}$) dependence of $v_2$ in wide $p_{\rm T}$ regime. The deep learning model is trained with AMPT-generated Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias events. We present $v_2$ estimates for $\pi^{\pm}$, $\rm K^{\pm}$, and $\rm p+\bar{p}$ in heavy-ion collisions at various LHC energies. These results are compared with the available experimental data wherever possible., Comment: 4 pages, 2 figures

Greenhouse climate control is concerned with maximizing performance in terms of crop yield and resource efficiency. One promising approach is model predictive control (MPC), which leverages a model of the system to optimize the control inputs, while enforcing physical constraints. However, prediction models for greenhouse systems are inherently inaccurate due to the complexity of the real system and the uncertainty in predicted weather profiles. For model-based control approaches such as MPC, this can degrade performance and lead to constraint violations. Existing approaches address uncertainty in the prediction model with robust or stochastic MPC methodology; however, these necessarily reduce crop yield due to conservatism and often bear higher computational loads. In contrast, learning-based control approaches, such as reinforcement learning (RL), can handle uncertainty naturally by leveraging data to improve performance. This work proposes an MPC-based RL control framework to optimize the climate control performance in the presence of prediction uncertainty. The approach employs a parametrized MPC scheme that learns directly from data, in an online fashion, the parametrization of the constraints, prediction model, and optimization cost that minimizes constraint violations and maximizes climate control performance. Simulations show that the approach can learn an MPC controller that significantly outperforms the current state-of-the-art in terms of constraint violations and efficient crop growth., Comment: 12 pages, 6 figures, code available at https://github.com/SamuelMallick/mpcrl-greenhouse, submitted to Computers and Electronics in Agriculture

We consider tight-binding models on Bravais lattices with anisotropic onsite potentials that vary along a given direction and are constant along the transverse one. Inspired by our previous work on flatbands in anti-$\mathcal{PT}$ symmetric Hamiltonians [Phys. Rev. A 105, L021305 (2022)], we construct an anti-$\mathcal{PT}$ symmetric Hamiltonians with an $E=0$ flatband by tuning the hoppings and the shapes of potentials. This construction is illustrated for the square lattice with bounded and unbounded potentials. Unlike flatbands in short-ranged translationally invariant Hamiltonians, we conjecture that the considered $E=0$ flatbands do not host compact localized states. Instead the flatband eigenstates exhibit a localization transition along the potential direction upon increasing the potential strength for bounded potentials. For unbounded potentials flatband eigenstates are always localized irrespective of the potential strength., Comment: 10 pages, 13 figures. Comments are welcome

We introduce a method to detect exotic surfaces without explicitly using a smooth 4-manifold invariant or an invariant of a 4-manifold-surface pair in the construction. Our main tools are two versions of families (Seiberg-Witten) generalizations of Donaldson's diagonalization theorem, including a real and families version of the diagonalization. This leads to an example of a pair of exotically knotted $\mathbb{R}P^2$'s embedded in a closed 4-manifold whose complements are diffeomorphic, making it the first example of a non-orientable surface with this property. In particular, any invariant of a 4-manifold-surface pair (including invariants from real Seiberg-Witten theory such as Miyazawa's invariant) fails to detect such an exotic $\mathbb{R} P^2$. One consequence of our construction reveals that non-effective embeddings of corks can still be useful in pursuit of exotica. Precisely, starting with an embedding of a cork $C$ in certain a 4-manifold $X$ where the cork-twist does not change the diffeomorphism type of $X$, we give a construction that provides examples of exotically knotted spheres and $\mathbb{R}P^2$'s with diffeomorphic complements in $ C \# S^2 \times S^2 \subset X \# S^2 \times S^2$ or $C \# \mathbb{C}P^2 \subset X \# \mathbb{C}P^2 $. In another direction, we provide infinitely many exotically knotted embeddings of orientable surfaces, closed surface links, and 3-spheres with diffeomorphic complements in once stabilized corks, and show some of these surfaces survive arbitrarily many internal stabilizations. By combining similar methods with Gabai's 4D light-bulb theorem, we also exhibit arbitrarily large difference between algebraic and geometric intersections of certain family of 2-spheres, embedded in a 4-manifold., Comment: 28 pages, 5 figures

We study large fluctuations of the current in a Dyson gas, a 1D system of particles interacting through a logarithmic potential and subjected to random noise. We adapt the macroscopic fluctuation theory to the Dyson gas and derive two coupled partial differential equations describing the evolution of the density and momentum. These equations are nonlinear and non-local, and the `boundary' conditions are mixed: some at the initial time and others at the final time. If the initial condition can fluctuate (annealed setting), this boundary-value problem is tractable. We compute the cumulant generating function encoding all the cumulants of the current., Comment: 18 pages

In relativistic heavy-ion collisions, the formation of a deconfined and thermalized state of partons, known as quark-gluon plasma, leads to enhanced production of strange hadrons in contrast to proton-proton (pp) collisions, which are taken as baseline. This observation is known as strangeness enhancement in heavy-ion collisions and is considered one of the important signatures that can signify the formation of QGP. However, in addition to strangeness enhancement, recent measurements hint at observing several heavy-ion-like features in high-multiplicity pp collisions at the LHC energies. Alternatively, event shape observables, such as charged particle multiplicity, transverse spherocity, transverse sphericity, charged particle flattenicity, and relative transverse activity classifiers, can fundamentally separate hard interaction-dominated jetty events from soft isotropic events. These features of event shape observables can probe the observed heavy-ion-like features in pp collisions with significantly reduced selection bias and can bring all collision systems on equal footing. In this article, we present an extensive summary of the strange particle ratios to pions as a function of different event classifiers using the PYTHIA~8 model with color reconnection and rope hadronization mechanisms to understand the microscopic origin of strangeness enhancement in pp collisions and also prescribe the applicability of these event classifiers in the context of strangeness enhancement. Charged-particle flattenicity is found to be most suited for the study of strangeness enhancement, and it shows a similar quantitative enhancement as seen for the analysis based on the number of multi-parton interactions., Comment: 14 pages and 12 captioned figures. Submitted for publication

Proto-neutron stars have both high-density and relatively high-temperature in them. This study analyses how the equation of state changes with temperature, which is relevant for proto-neutron stars. We determine an equation of state for the proto-neutron stars in the relativistic mean field model in which the coupling parameters are density-dependent. The equation of state considerably affects the mass-radius curve, thereby affecting the f-mode oscillation frequency. Temperature makes the equation of state stiffer at relatively low and intermediate densities, thereby making the star less compact and the mass-radius curve flatter. The f-mode frequency for low and intermediate-mass neutron stars decreases with temperature and thus should be easier to detect. The universal relation (connecting f-mode frequency, mass and radius) changes non-linearly with temperature. The parameters defining the universal relation ($\omega M = a(T) \left(\frac{M}{R}\right) + b(T)$) becomes temperature dependent with the coefficients following a parabolic relation with temperature., Comment: 11 pages, 5 figures

We prove a formula for the involutive concordance invariants of the cabled knots in terms of that of the companion knot and the pattern knot. As a consequence, we show that any iterated cable of a knot with parameters of the form (odd,1) is not smoothly slice as long as either of the involutive concordance invariants of the knot is nonzero. Our formula also gives new bounds for the unknotting number of a cabled knot, which are sometimes stronger than other known bounds coming from knot Floer homology., Comment: Ten pages, one figure. Comments welcome!

Large Language Model (LLM) workloads have distinct prefill and decode phases with different compute and memory requirements which should ideally be accounted for when scheduling input queries across different LLM instances in a cluster. However existing scheduling algorithms treat LLM workloads as monolithic jobs without considering the distinct characteristics of the two phases in each workload. This leads to sub-optimal scheduling and increased response latency. In this work, we propose a heuristic-guided reinforcement learning-based intelligent router for data-driven and workload-aware scheduling. Our router leverages a trainable response-length predictor, and a novel formulation for estimating the impact of mixing different workloads to schedule queries across LLM instances and achieve over 11\% lower end-to-end latency than existing approaches., Comment: 16 pages, 8 figures

This paper presents results from Kepler photometric light curves and high-resolution spectroscopic study of a super Li-rich giant KIC11087027. Using the light curve analysis, we measured the star's rotational period P$_{\rm rot}$=30.4$\pm$0.1~days, which translates to rotational velocity V$_{\rm rot}$=19.5 $\pm$ 1.7~km s$^{-1}$. Star's location in the HR-diagram, derived values of $^{12}C/^{13}C$ = 7$\pm$1 and $[C/N]=-0.95\pm 0.2$, and the inferred asteroseismic parameters from secondary calibration based on spectra suggest star is a low-mass red clump giant in the He-core burning phase. Using Gaia data, we found evidence of variation in radial velocity and proper motion, indicative of presence of an unresolved binary. The large V$_{\rm rot}$ is probably a result of tidal synchronization combined with the after-effects of He-flash, in which the size of the star is reduced significantly. The simultaneous presence of features like high rotation, very high Li abundance, strong dust shell, and strong flares in a single star is relatively uncommon, suggesting that the star experiencing tidal synchronization has recently undergone He-flash. The results pose a question whether the binary interaction, hence the high rotation, is a prerequisite for dredging-up of the high amounts of Li from the interior to the photosphere during or immediately after the He-flash event., Comment: 9 pages, 3 figures, 2 tables, accepted

Nuclei having $4n$ number of nucleons are theorized to possess clusters of $\alpha$ particles ($^4$He nucleus). The Oxygen nucleus ($^{16}$O) is a doubly magic nucleus, where the presence of an $\alpha$-clustered nuclear structure grants additional nuclear stability. In this study, we exploit the anisotropic flow coefficients to discern the effects of an $\alpha$-clustered nuclear geometry w.r.t. a Woods-Saxon nuclear distribution in O--O collisions at $\sqrt{s_{\rm NN}}=7$ TeV using a hybrid of IP-Glasma + MUSIC + iSS + UrQMD models. In addition, we use the multi-particle cumulants method to measure anisotropic flow coefficients, such as elliptic flow ($v_{2}$) and triangular flow ($v_{3}$), as a function of collision centrality. Anisotropic flow fluctuations, which are expected to be larger in small collision systems, are also studied for the first time in O--O collisions. It is found that an $\alpha$-clustered nuclear distribution gives rise to an enhanced value of $v_{2}$ and $v_3$ towards the highest multiplicity classes. Consequently, a rise in $v_3/v_2$ is also observed for the (0-10)\% centrality class. Further, for $\alpha$-clustered O--O collisions, fluctuations of $v_{2}$ are larger for the most central collisions, which decrease towards the mid-central collisions. In contrast, for a Woods-Saxon $^{16}$O nucleus, $v_{2}$ fluctuations show an opposite behavior with centrality. This study, when confronted with experimental data may reveal the importance of nuclear density profile on the discussed observables., Comment: 13 pages and 10 captioned figures, submitted for publication

Simultaneous measurement of mass and radius with high precision is essential to unravel the equation of state of matter at the centre of neutron stars. Measurement of massive pulsars indicates that the equation of state has to be stiff at low densities. The radius measurement of PSR J0030+0451 has rejected several relatively softer equations of state. In this work, an ensemble of agnostically constructed EoS was studied for the mass and radius measurement. The range of radius of neutron stars obtained from the ensemble was confined within a radius bound from 10.5 - 14.5 km. It is seen that higher masses prefer stiffer EoS. However, the slope of the speed of sound (the stiffness of the EoS) is very sensitive to the radius measurement. Assuming the radius measurement to be precise up to 2 km, then a higher radius indicates sharp stiffening of the equation of state at low density; however, it also indicates a sharp fall after the peak, indicating a relatively softer core for massive neutron stars. On the other hand, for the same precision, a lower radius measurement indicates a relatively softer equation of state., Comment: 11 pages, 7 figures

We introduce a novel family of translationally-invariant su$(m|n)$ supersymmetric spin chains with long-range interaction not directly associated to a root system. We study the symmetries of these models, establishing in particular the existence of a boson-fermion duality characteristic of this type of systems. Taking advantage of the relation of the new chains with an associated many-body supersymmetric spin dynamical model, we are able to compute their partition function in closed form for all values of $m$ and $n$ and for an arbitrary number of spins. When both $m$ and $n$ are even, we show that the partition function factorizes as the product of the partition functions of two supersymmetric Haldane-Shastry spin chains, which in turn leads to a simple expression for the thermodynamic free energy per spin in terms of the Perron eigenvalue of a suitable transfer matrix. We use this expression to study the thermodynamics of a large class of these chains, showing in particular that the specific heat presents a single Schottky peak at approximately the same temperature as a suitable $k$-level model. We also analyze the critical behavior of the new chains, and in particular the ground state degeneracy and the existence of low energy excitations with a linear energy-momentum dispersion relation. In this way we are able to show that the only possible critical chains are the ones with $m=0,1,2$. In addition, using the explicit formula for the partition function we are able to establish the criticality of the su$(0|n)$ and su$(2|n)$ chains with even $n$, and to evaluate the central charge of their associated conformal field theory., Comment: 44 pages, 6 figures. Minor changes, 2 appendices and 3 new references added

Quasi-normal modes of NSs are an exciting prospect for analyzing the internal composition of NSs and studying matter at high densities. In this work, we focus on studying the $f$- and $p$- quadrupolar oscillation modes, which couple with gravitational waves. We construct two different EOS ensembles, one without and one with a first-order phase transition, and examine how $f$- and $p$-modes might help us differentiate them. We find ensemble specific exclusion regions in the $65\%$ and $95\%$ confidence contours of the frequency-damping time relations. The exclusion regions become more prominent for the higher-order oscillation modes. However, these modes have higher frequencies, which are beyond the detection capabilities of present gravitational wave detectors. The quasi-universal relations of dimensionless quantities prove to be ineffective in differentiating the EOS ensembles, as they obscure the details of the EOS., Comment: 12 pages, 7 figures

States with negative Wigner function, a significant subclass of non-classical states, serve as a valuable resource for various quantum information processing tasks. Here, we provide a criterion for detecting such quantum states exhibiting negative Wigner function. Our method relies on evaluating moments of the Wigner function which involves computing simple functionals and can be implemented in a real experiment without the need for full state tomography or Wigner function reconstruction. We then provide explicit examples to support our detection scheme. Further, we propose an experimental method utilizing the continuous variable SWAP operator to realize these moments in a real experiment., Comment: 10 pages, 2 figures

Long-range multi-particle correlations in heavy-ion collisions have shown conclusive evidence of the hydrodynamic behavior of strongly interacting matter, and are associated with the final-state azimuthal momentum anisotropy. In small collision systems, azimuthal anisotropy can be influenced by the hadronization mechanism and residual jet-like correlations. Thus, one of the motives of the planned p--O and O--O collisions at the LHC and RHIC is to understand the origin of small system collectivity. As the anisotropic flow coefficients ($v_n$) are sensitive to the initial-state effects including nuclear shape, deformation, and charge density profiles, studies involving $^{12}$C and $^{16}$O nuclei are transpiring due to the presence of exotic $\alpha$ ($^{4}$He) clusters in such nuclei. In this study, for the first time, we investigate the effects of nuclear $\alpha$--clusters on the azimuthal anisotropy of the final-state hadrons in p--C and p--O collisions at $\sqrt{s_{\rm NN}}= 9.9$ TeV within a multi-phase transport model framework. We report the transverse momentum ($p_{\rm T}$) and pseudorapidity ($\eta$) spectra, participant eccentricity ($\epsilon_2$) and triangularity ($\epsilon_3$), and estimate the elliptic flow ($v_2$) and triangular flow ($v_3$) of the final-state hadrons using the two-particle cumulant method. These results are compared with a model-independent Sum of Gaussians (SOG) type nuclear density profile for $^{12}$C and $^{16}$O nuclei., Comment: 16 pages and 10 captioned figures. Submitted for publication

3D Gaussian Splatting (3DGS) has transformed novel-view synthesis with its fast, interpretable, and high-fidelity rendering. However, its resource requirements limit its usability. Especially on constrained devices, training performance degrades quickly and often cannot complete due to excessive memory consumption of the model. The method converges with an indefinite number of Gaussians -- many of them redundant -- making rendering unnecessarily slow and preventing its usage in downstream tasks that expect fixed-size inputs. To address these issues, we tackle the challenges of training and rendering 3DGS models on a budget. We use a guided, purely constructive densification process that steers densification toward Gaussians that raise the reconstruction quality. Model size continuously increases in a controlled manner towards an exact budget, using score-based densification of Gaussians with training-time priors that measure their contribution. We further address training speed obstacles: following a careful analysis of 3DGS' original pipeline, we derive faster, numerically equivalent solutions for gradient computation and attribute updates, including an alternative parallelization for efficient backpropagation. We also propose quality-preserving approximations where suitable to reduce training time even further. Taken together, these enhancements yield a robust, scalable solution with reduced training times, lower compute and memory requirements, and high quality. Our evaluation shows that in a budgeted setting, we obtain competitive quality metrics with 3DGS while achieving a 4--5x reduction in both model size and training time. With more generous budgets, our measured quality surpasses theirs. These advances open the door for novel-view synthesis in constrained environments, e.g., mobile devices.

Ruberman in the 90's showed that the group of exotic diffeomorphisms of closed 4-manifolds can be infinitely generated. We provide various results on the question of when such infinite generation can localize to a smaller embedded submanifold of the original manifold. Our results include: (1) All known infinitely generated groups of exotic diffeomorphisms of 4-manifolds detected by families Seiberg-Witten theory do not localize to any topologically (locally-flatly) embedded rational homology balls in the ambient 4-manifold. (2) Many exotic diffeomorphisms cannot be obtained as Dehn twists along homology spheres (under mild assumptions). (3) There is no contractible 4-manifolds with Seifert fibered boundary that have a universal property for exotic diffeomorphisms analogous to a universal cork. In addition, there is no universal compact 4-manifold $W$ such that the set of exotic diffeomorphisms of a 4-manifold can localize to an embedding of $W$. (4) Certain infinite generations of exotic diffeomorphism groups do localize to a non-compact subset $V$ with a small Betti number, but not to any compact subset of $V$. (5) An analogous result holds for mapping class groups of 4-manifolds., Comment: 26 pages, 3 figures, Corollary 1.7 is added

This study introduces a hypothesis-testing framework to assess whether large language models (LLMs) possess genuine reasoning abilities or primarily depend on token bias. We go beyond evaluating LLMs on accuracy; rather, we aim to investigate their token bias in solving logical reasoning tasks. Specifically, we develop carefully controlled synthetic datasets, featuring conjunction fallacy and syllogistic problems. Our framework outlines a list of hypotheses where token biases are readily identifiable, with all null hypotheses assuming genuine reasoning capabilities of LLMs. The findings in this study suggest, with statistical guarantee, that most LLMs still struggle with logical reasoning. While they may perform well on classic problems, their success largely depends on recognizing superficial patterns with strong token bias, thereby raising concerns about their actual reasoning and generalization abilities. Codes and data are open-sourced at https://github.com/bowen-upenn/llm_token_bias., Comment: This paper has been accepted at EMNLP 2024

We aim to investigate the global star formation scenario in star-forming sites AFGL 5157, [FSR2007] 0807 (hereafter FSR0807), [HKS2019] E70 (hereafter E70), [KPS2012] MWSC 0620 (hereafter KPS0620), and IRAS 05331+3115 in the outer galactic arm. The distribution of young stellar objects in these sites coincides with a higher extinction and H2 column density, which agrees with the notion that star formation occurs inside the dense molecular cloud cores. We have found two molecular structures at different velocities in this direction; one contains AFGL 5157 and FSR0807, and the other contains E70, [KPS2012] MWSC 0620, and IRAS 05331+3115. All these clusters in our target region are in different evolutionary stages and might form stars through different mechanisms. The E70 cluster seems to be the oldest in our sample; AFGL 5157 and FSR0807 formed later, and KPS0620 and IRAS 05331+3115 are the youngest sites. AFGL 5157 and FSR0807 are physically connected and have cold filamentary structures and dense hub regions. Additionally, the near-infrared photometric analysis shows signatures of massive star formation in these sites. KPS0620 also seems to have cold filamentary structures with the central hub but lacks signatures of massive stars. Our analysis suggests molecular gas flow and the hub filamentary star formation scenario in these regions. IRAS 05331+3115 is a single clump of molecular gas favoring low-mass star formation. Our study suggests that the selected area is a menagerie of star-forming sites where the formation of the stars happens through different processes., Comment: 19 pages, 13 figures, and 3 tables; Accepted for publication in AJ

In this paper, we work towards extending Audio-Visual Question Answering (AVQA) to multilingual settings. Existing AVQA research has predominantly revolved around English and replicating it for addressing AVQA in other languages requires a substantial allocation of resources. As a scalable solution, we leverage machine translation and present two multilingual AVQA datasets for eight languages created from existing benchmark AVQA datasets. This prevents extra human annotation efforts of collecting questions and answers manually. To this end, we propose, MERA framework, by leveraging state-of-the-art (SOTA) video, audio, and textual foundation models for AVQA in multiple languages. We introduce a suite of models namely MERA-L, MERA-C, MERA-T with varied model architectures to benchmark the proposed datasets. We believe our work will open new research directions and act as a reference benchmark for future works in multilingual AVQA., Comment: Accepted to Interspeech 2024

We present FaithFill, a diffusion-based inpainting object completion approach for realistic generation of missing object parts. Typically, multiple reference images are needed to achieve such realistic generation, otherwise the generation would not faithfully preserve shape, texture, color, and background. In this work, we propose a pipeline that utilizes only a single input reference image -having varying lighting, background, object pose, and/or viewpoint. The singular reference image is used to generate multiple views of the object to be inpainted. We demonstrate that FaithFill produces faithful generation of the object's missing parts, together with background/scene preservation, from a single reference image. This is demonstrated through standard similarity metrics, human judgement, and GPT evaluation. Our results are presented on the DreamBooth dataset, and a novel proposed dataset.

We extend the range of parameters associated with the Gagliardo-Nirenberg interpolation inequalities in the fractional Coulomb-Sobolev spaces for radial functions. We also study the optimality of this newly extended range of parameters.

This article investigates the exceptional set of the boundary for the following problem: \begin{equation*} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal{M}_{\lambda,\Lambda}^+(D^2u) + b(x,t)\cdot Du + c(x,t)u =0 \quad \rm{in} ~ \Omega_{T}, \end{aligned} \end{equation*} We provide a sufficient condition on the exceptional set in terms of the bound of the Hausdorff measure of this boundary portion. This condition ensures that even if the boundary values are not nonnegative on this portion, the supersolution remains nonnegative.

It is increasingly common in a wide variety of applied settings to collect data of multiple different types on the same set of samples. Our particular focus in this article is on studying relationships between such multiview features and responses. A motivating application arises in the context of precision medicine where multi-omics data are collected to correlate with clinical outcomes. It is of interest to infer dependence within and across views while combining multimodal information to improve the prediction of outcomes. The signal-to-noise ratio can vary substantially across views, motivating more nuanced statistical tools beyond standard late and early fusion. This challenge comes with the need to preserve interpretability, select features, and obtain accurate uncertainty quantification. We propose a joint additive factor regression model (JAFAR) with a structured additive design, accounting for shared and view-specific components. We ensure identifiability via a novel dependent cumulative shrinkage process (D-CUSP) prior. We provide an efficient implementation via a partially collapsed Gibbs sampler and extend our approach to allow flexible feature and outcome distributions. Prediction of time-to-labor onset from immunome, metabolome, and proteome data illustrates performance gains against state-of-the-art competitors. Our open-source software (R package) is available at https://github.com/niccoloanceschi/jafar.

Rationality is the quality of being guided by reason, characterized by decision-making that aligns with evidence and logical principles. It plays a crucial role in reliable problem-solving by ensuring well-grounded and consistent solutions. While large language models (LLMs) have made significant progress in generating human-like text, they still exhibit limitations such as bounded knowledge space and inconsistent outputs. In response, recent efforts have shifted toward developing multimodal and multi-agent systems, as well as integrating modules like external tools, programming codes, symbolic reasoners, utility function, and conformal risk controls rather than relying solely on a single LLM for decision-making. This paper surveys the state-of-the-art advancements in language and multimodal agents, evaluates how they contribute to make intelligent agents more rational, and identifies open challenges and future research directions. We maintain an open repository at https://github.com/bowen-upenn/Agent_Rationality., Comment: We maintain an open repository at https://github.com/bowen-upenn/Agent_Rationality

In this article we consider the following boundary value problem \begin{equation*}\label{abs} \left\{ \begin{aligned} F(x,u,Du,D^{2}u)+c(x)u+ p(x)u^{-\alpha}&=0~\text{in}~\Omega\\ u&=0~~\text{on}~~\partial\Omega, \end{aligned} \right. \end{equation*} where $\Omega$ is a bounded and $C^{2}$ smooth domain in $\mathbb{R}^N$ and $F$ has superlinear growth in gradient and $c(c)<-c_{0}$ for some positive constant $c_{0}.$ Here, we studies the boundary behaviour of the solutions to above equation and establishes the global regularity result similar to one established in [12,16] with linear growth in gradient.

The symmetric simple exclusion process (SEP), where diffusive particles cannot overtake each other, is a paradigmatic model of transport in the single-file geometry. In this model, the study of currents has attracted a lot of attention, but so far most results are restricted to two geometries: (i) a finite system between two reservoirs, which does not conserve the number of particles but reaches a nonequilibrium steady state, and (ii) an infinite system which conserves the number of particles but never reaches a steady state. Here, we determine the full cumulant generating function of the integrated current in the important intermediate situation of a semi-infinite system connected to a reservoir, which does not conserve the number of particles and never reaches a steady state. This result is obtained thanks to the determination of the full spatial structure of the correlations which remarkably obey the very same closed equation recently obtained in the infinite geometry. Besides their intrinsic interest, these results allow us to solve two open problems: the survival probability of a fixed target in the SEP, and the statistics of the number of particles injected by a localized source., Comment: 6 pages + 13 pages of supplemental material

In this paper, we prove a theorem concerning the existence of three solutions for the following boundary value problem: \begin{equation*} -\mathcal{M}_{\lambda,\Lambda}^+(D^2u)-\Gamma|Du|^2=f(u)~~~\text{in}\ \Omega, u=0~~~\text{on}\ \partial\Omega, \end{equation*} where $f:[0,\infty]\to[0,\infty]$ is a $C^{\alpha}$ function and $\Omega$ denotes a bounded, smooth domain in $\mathbb{R}^N$. By constructing two ordered pairs of sub and supersolutions for a specific class of $f$ exhibiting sublinear growth, we further establish the existence of three positive solutions to the aforementioned boundary value problem.

We give a short overview of recent developments in exact solutions for macroscopic fluctuation theory by using connections to classical integrable systems. A calculation of the cumulant generating function for a tagged particle is also given, agreeing with a previous result obtained from a microscopic analysis., Comment: 20 pages, 1 figure. Proceedings for STATPHYS 28

This paper presents a novel approach for distributed model predictive control (MPC) for piecewise affine (PWA) systems. Existing approaches rely on solving mixed-integer optimization problems, requiring significant computation power or time. We propose a distributed MPC scheme that requires solving only convex optimization problems. The key contribution is a novel method, based on the alternating direction method of multipliers, for solving the non-convex optimal control problem that arises due to the PWA dynamics. We present a distributed MPC scheme, leveraging this method, that explicitly accounts for the coupling between subsystems by reaching agreement on the values of coupled states. Stability and recursive feasibility are shown under additional assumptions on the underlying system. Two numerical examples are provided, in which the proposed controller is shown to significantly improve the CPU time and closed-loop performance over existing state-of-the-art approaches., Comment: 15 pages, 9 figures, submitted to IEEE Transactions on Automatic Control, code available at https://github.com/SamuelMallick/stable-dmpc-pwa/tree/paper_2024 and https://github.com/SamuelMallick/hybrid-vehicle-platoon/tree/paper-2024

Recent developments in artificial intelligence (AI) have permeated through an array of different immersive environments, including virtual, augmented, and mixed realities. AI brings a wealth of potential that centers on its ability to critically analyze environments, identify relevant artifacts to a goal or action, and then autonomously execute decision-making strategies to optimize the reward-to-risk ratio. However, the inherent benefits of AI are not without disadvantages as the autonomy and communication methodology can interfere with the human's awareness of their environment. More specifically in the case of autonomy, the relevant human-computer interaction literature cites that high autonomy results in an "out-of-the-loop" experience for the human such that they are not aware of critical artifacts or situational changes that require their attention. At the same time, low autonomy of an AI system can limit the human's own autonomy with repeated requests to approve its decisions. In these circumstances, humans enter into supervisor roles, which tend to increase their workload and, therefore, decrease their awareness in a multitude of ways. In this position statement, we call for the development of human-centered AI in immersive environments to sustain and promote awareness. It is our position then that we believe with the inherent risk presented in both AI and AR/VR systems, we need to examine the interaction between them when we integrate the two to create a new system for any unforeseen risks, and that it is crucial to do so because of its practical application in many high-risk environments., Comment: This is an accepted position statement of CHI 2024 Workshop (Novel Approaches for Understanding and Mitigating Emerging New Harms in Immersive and Embodied Virtual Spaces: A Workshop at CHI 2024)

In this paper, we introduce "Marking", a novel grading task that enhances automated grading systems by performing an in-depth analysis of student responses and providing students with visual highlights. Unlike traditional systems that provide binary scores, "marking" identifies and categorizes segments of the student response as correct, incorrect, or irrelevant and detects omissions from gold answers. We introduce a new dataset meticulously curated by Subject Matter Experts specifically for this task. We frame "Marking" as an extension of the Natural Language Inference (NLI) task, which is extensively explored in the field of Natural Language Processing. The gold answer and the student response play the roles of premise and hypothesis in NLI, respectively. We subsequently train language models to identify entailment, contradiction, and neutrality from student response, akin to NLI, and with the added dimension of identifying omissions from gold answers. Our experimental setup involves the use of transformer models, specifically BERT and RoBERTa, and an intelligent training step using the e-SNLI dataset. We present extensive baseline results highlighting the complexity of the "Marking" task, which sets a clear trajectory for the upcoming study. Our work not only opens up new avenues for research in AI-powered educational assessment tools, but also provides a valuable benchmark for the AI in education community to engage with and improve upon in the future. The code and dataset can be found at https://github.com/luffycodes/marking.