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Kaustav Das

Publications and source records attributed to Kaustav Das.

15 recordsLinked to original sources

Segmenting Low-Contrast XCTs of Concrete: An Unsupervised Approach

X-Ray Computed Tomography (XCT) is a compelling tool in experimental mechanics, capable of non-destructively extracting information pertaining to the internal morphology of materials. For materials with random heterogeneous morphology such as concrete, such information is of particular relevance since it allows for studies of morphology-related behaviour and for predictive modelling. Nevertheless, XCT images require semantic segmentation for practical usage. Here, concrete poses a unique challenge due to the similar X-ray attenuation coefficients of aggregates and mortar, which result in low contrast between the two phases in the ensuing XCT images. As such, purely intensity-dependent semantic segmentation tools remain unfeasible. While vision transformers (ViTs) and convolutional neural networks (CNNs) are proven techniques for semantic segmentation in such challenging cases, they typically require labelled training data, which is often unavailable for concrete or resource-intensive to obtain, thereby limiting their relevance. To address this challenge, a self-annotation technique is presented here that leverages superpixel algorithms to identify perceptually similar local regions in an image and relates them to the global context by utilizing the receptive field of a CNN-based model. This enables the model to learn a global-local relationship in the images and facilitates the identification of semantically similar structures. When evaluated against manually annotated ground truth on out-of-distribution data, the proposed methodology consistently outperformed direct greyscale thresholding across all pertinent metrics, demonstrating improved discernibility between aggregates and mortar, and providing the most favourable balance of sensitivity and precision for aggregate-phase identification.

cs.CV

Scalable method for mean field control with kernel interactions via random Fourier features

We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by linear-time estimates, enabling efficient stochastic gradient descent for training feedback controls in large populations. We provide theoretical complexity bounds and demonstrate through crowd motion and flocking examples that the approach preserves control performance while substantially reducing computational cost. The results indicate that random feature approximations offer an effective and practical tool for high dimensional and large scale mean field control.

math.OC

ZTF25abjmnps (AT2025ulz) and S250818k: A Candidate Superkilonova from a Sub-threshold Sub-Solar Gravitational Wave Trigger

On August 18, 2025, the LIGO-Virgo-KAGRA collaboration reported gravitational waves from a sub-threshold binary neutron star merger. If astrophysical, this event would have a surprisingly low chirp mass, suggesting that at least one neutron star was below a solar mass. The Zwicky Transient Facility mapped the coarse localization and discovered a transient, ZTF25abjmnps (AT2025ulz), that was spatially and temporally coincident with the gravitational wave trigger. The first week of follow-up suggested properties reminiscent of a GW170817-like kilonova. Subsequent follow-up suggests properties most similar to a young, stripped-envelope, Type IIb supernova. Although we cannot statistically rule out chance coincidence, we undertake due diligence analysis to explore the possible association between ZTF25abjmnps and S250818k. Theoretical models have been proposed wherein sub-solar neutron star(s) may form (and subsequently merge) via accretion disk fragmentation or core fission inside a core-collapse supernova i.e. a ``superkilonova". Here, we qualitatively discuss our multi-wavelength dataset in the context of the superkilonova picture. Future higher significance gravitational wave detections of sub-solar neutron star mergers with extensive electromagnetic follow-up would conclusively resolve this tantalizing multi-messenger association.

astro-ph.HE

On the exponential integrability of the derivative of intersection and self-intersection local time for fractional Brownian motion and a limit theorem related to the self-intersection local time for fractional Brownian motion

We give the correct condition for existence of the $k$-th derivative of the intersection local time for fractional Brownian motion, which was originally discussed in [Guo, J., Hu, Y., and Xiao, Y., Higher-order derivative of intersection local time for two independent fractional Brownian motions, Journal of Theoretical Probability 32, (2019), pp. 1190-1201]. We also show that the $k$-th derivative of the intersection and self-intersection local times of fractional Brownian motion are exponentially integrable for certain parameter values. In addition, we show convergence in distribution when the existence condition is violated for the $k$-th derivative of self-intersection local time of fractional Brownian motion under scaling.

math.PR

An optical to infrared study of type II SN2024ggi at nebular times

We present 0.3-21mic observations at ~275d and ~400d for Type II supernova (SN) 2024ggi, combining ground-based optical and near-infrared data from the Keck I/II telescopes and space-based infrared data from the James Webb Space Telescope. Although the optical regions dominate the observed flux, SN2024ggi is bright at infrared wavelengths (65%/35% falls each side of 1mic). SN2024ggi exhibits a plethora of emission lines from H, He, intermediate-mass elements (O, Na, Mg, S, Ar, Ca), and iron-group elements (IGEs; Fe, Co, and Ni) -- all lines have essentially the same width, suggesting efficient macroscopic chemical mixing of the inner ejecta at <~2000km/s and little mixing of 56Ni at larger velocities. Molecular emission in the infrared range is dominated by the CO fundamental, which radiates about 5% of the total SN luminosity. A molecule-free radiative-transfer model based on a standard red-supergiant star explosion (i.e., ~1e51erg, 0.06Msun of 56Ni from a 15.2Msun progenitor) yields a satisfactory match throughout the optical and infrared at both epochs. The SN2024ggi CO luminosity is comparable to the fractional decay-power absorbed in the model C/O-rich shell -- accounting for CO cooling would likely resolve the model overestimate of the [OI]0.632mic flux. The relative weakness of the molecular emission in SN2024ggi and the good overall match obtained with our molecule-free model suggests negligible microscopic mixing -- about 95% of the SN luminosity is radiated by atoms and ions. Lines from IGEs, which form from explosion ashes at such late times, are ideal diagnostics of the magnitude of 56Ni mixing in core-collapse SN ejecta. Stable Ni, clearly identified in SN2024ggi (e.g., [NiII]6.634mic), is probably a common product of massive-star explosions.

astro-ph.SR

SN 2023gpw: exploring the diversity and power sources of hydrogen-rich superluminous supernovae

We present our observations and analysis of SN 2023gpw, a hydrogen-rich superluminous supernova (SLSN II) with broad emission lines in its post-peak spectra. Unlike previously observed SLSNe II, its light curve suggests an abrupt drop during a solar conjunction between ~80 and ~180 d after the light-curve peak, possibly analogous to a normal hydrogen-rich supernova (SN). Spectra taken at and before the peak show hydrogen and helium `flash' emission lines attributed to early interaction with a dense confined circumstellar medium (CSM). A well-observed ultraviolet excess appears as these lines disappear, also as a result of CSM interaction. The blackbody photosphere expands roughly at the same velocity throughout the observations, indicating little or no bulk deceleration. This velocity is much higher than what is seen in spectral lines, suggesting asymmetry in the ejecta. The high total radiated energy ($\gtrsim9\times10^{50}$ erg) and aforementioned lack of bulk deceleration in SN 2023gpw are difficult to reconcile with a neutrino-driven SN simply combined with efficient conversion from kinetic energy to emission through interaction. This suggests an additional energy source such as a central engine. While magnetar-powered models qualitatively similar to SN 2023gpw exist, more modeling work is required to determine if they can reproduce the observed properties in combination with early interaction. The required energy might alternatively be provided by accretion onto a black hole created in the collapse of a massive progenitor star.

astro-ph.HE

Inferring CSM Properties of Type II SNe Using a Magnitude-Limited ZTF Sample

Although all Type II supernovae (SNe) originate from massive stars possessing a hydrogen-rich envelope, their light curve morphology is diverse, reflecting poorly characterised heterogeneity in the physical properties of their progenitor systems. Here, we present a detailed light curve analysis of a magnitude-limited sample of 639 Type II SNe from the Zwicky Transient Facility Bright Transient Survey. Using Gaussian processes, we systematically measure empirical light curve features (e.g. rise times, peak colours and luminosities) in a robust sampling-independent manner. We focus on rise times as they are highly sensitive to pre-explosion progenitor properties, especially the presence of a dense circumstellar medium (CSM) shed by the progenitor in the years immediately pre-explosion. By correlating our feature measurements with physical parameters from an extensive grid of STELLA hydrodynamical models with varying progenitor properties (CSM structure, $\dot M$, $R_{CSM}$ and $M_{ZAMS}$), we quantify the proportion of events with sufficient pre-explosion mass-loss to significantly alter the initial light curve (roughly $M_{CSM} \geq 10^{-2.5} M_{\odot}$) in a highly complete sample of 377 spectroscopically classified Type II SNe. We find that 67 $\pm$ 6\% of observed SNe in our magnitude-limited sample show evidence for substantial CSM ($M_{CSM} \geq 10^{-2.5} M_{\odot}$) close to the progenitor ($R_{CSM} <10^{15}$ cm) at the time of explosion. After applying a volumetric-correction, we find 36$^{+5}_{-7}$\% of all Type II SN progenitors possess substantial CSM within $10^{15}$ cm at the time of explosion. This high fraction of progenitors with dense CSM, supported by photometric and spectroscopic evidence of previous SNe, reveals mass-loss rates significantly exceeding those measured in local group red supergiants or predicted by current theoretical models.

astro-ph.HE

Switching to a Green and sustainable finance setting: a mean field game approach

We consider a continuum of carbon-emitting firms who seek to maximise their stock price, and a regulator (e.g., Government) who wishes for the economy to flourish, whilst simultaneously punishing firms who behave non-green. Interpreting the regulator as a major player and the firms as the minor players, we model this setting through a mean field game with major and minor players. We extend the stochastic maximum principle derived by Carmona & Zhu [A probabilistic approach to mean field games with major and minor players. Annals of Applied Probability, 2016, 94, 745--788] by relaxing the assumptions on the forms of the minimisers for the Hamiltonians, allowing them to depend on more arguments. This allows the major and representative minor player to interact in a more natural fashion, thereby permitting us to consider more realistic models for our green and sustainable finance problem. Through our stochastic maximum principle, we derive explicit Nash equilibria for a number of examples.

math.PR

A Luminous Red Optical Flare and Hard X-ray Emission in the Tidal Disruption Event AT2024kmq

We present the optical discovery and multiwavelength follow-up observations of AT2024kmq, a likely tidal disruption event (TDE) associated with a supermassive ($M_{\rm BH}\sim 10^{8} M_\odot$) black hole in a massive galaxy at $z=0.192$. The optical light curve of AT2024kmq exhibits two distinct peaks: an early fast (timescale 1 d) and luminous ($M\approx-20$ mag) red peak, then a slower (timescale 1 month) blue peak with a higher optical luminosity ($M\approx-22$ mag) and featureless optical spectra. The second component is similar to the spectroscopic class of "featureless TDEs" in the literature, and during this second component we detect highly variable, luminous ($L_X\approx 10^{44}$ erg s$^{-1}$), and hard ($f_ν\propto ν^{-1.5}$) X-ray emission. Luminous ($10^{29} $erg s$^{-1}$ Hz$^{-1}$ at 10 GHz) but unchanging radio emission likely arises from an underlying active galactic nucleus. The luminosity, timescale, and color of the early red optical peak can be explained by synchrotron emission, or alternatively by thermal emission from material at a large radius ($R\approx\mathrm{few}\times10^{15}$ cm). Possible physical origins for this early red component include an off-axis relativistic jet, and shocks from self-intersecting debris leading to the formation of the accretion disk. Late-time radio observations will help distinguish between the two possibilities.

astro-ph.HE

On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes

We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes the Brownian motion case. We also discuss related results present in the literature for fractional Brownian motion, and in particular give a counter-example to a result in [Guo, J., Hu, Y., and Xiao, Y., Higher-order derivative of intersection local time for two independent fractional Brownian motions, Journal of Theoretical Probability 32, (2019), pp. 1190-1201] related to this question.

math.PR

Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility

We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion around the mean of its argument. The difficulties then faced are simplifying a number of expectations induced by the Taylor expansion. Under the assumption of piecewise-constant parameters, we derive closed-form pricing formulas and devise a fast calibration scheme. Furthermore, we perform a numerical error and sensitivity analysis to investigate the quality of our approximation and show that the errors are well within the acceptable range for application purposes. Lastly, we derive bounds on the remainder term generated by the Taylor expansion.

q-fin.MF

On Stochastic Partial Differential Equations and their applications to Derivative Pricing through a conditional Feynman-Kac formula

The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a 'conditional Feynman-Kac formula'). The problem requires conditioning on a backward filtration generated by the noise of the auxiliary process and enlarged by its terminal value, leading us to search for a backward Brownian motion here. This adds a source of irregularity to the SPDE which we tackle with new techniques. Lastly, we establish a new class of mixed Monte-Carlo PDE numerical methods.

q-fin.MF

Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion

In a recent paper by Yu (arXiv:2008.05633, 2020), higher order derivatives of self-intersection local time of fractional Brownian motion were defined, and existence over certain regions of the Hurst parameter $H$ was proved. Utilizing the Wiener chaos expansion, we provide new proofs of Yu's results, and show how a Varadhan-type renormalization can be used to extend the range of convergence for the even derivatives.

math.PR

Explicit approximations of option prices via Malliavin calculus in a general stochastic volatility framework

We establish an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters. Our methodology is based on expansions of the mixing representation of the put option price as an expectation of the Black-Scholes formula, in which the resulting terms are calculated explicitly by Malliavin calculus. We obtain an explicit representation of the error generated by the expansion procedure, and bound it in terms of moments of functionals of the underlying volatility process. Under the assumption of piecewise-constant parameters, our approximation formulas become closed-form, and compatible with a proposed fast calibration scheme. Finally, we perform a numerical sensitivity analysis to investigate the quality of our approximation formula in the so-called Stochastic Verhulst model, and show that the errors are well within the acceptable range for application purposes.

q-fin.MF