arXiv subjects

Sourav Pal

Publications and source records attributed to Sourav Pal.

At least 19 recordsLinked to original sources

arXiv2026

MnemoDyn: Learning Resting State Dynamics from 40K FMRI sequences

We present a dynamical-systems based model for resting-state functional magnetic resonance imaging (rs-fMRI), trained on a dataset of roughly 40K rs-fMRI sequences covering a wide variety of public and available-by-permission datasets. While most existing proposals use transformer backbones, we utilize multi-resolution temporal modeling of the dynamics across parcellated brain regions. We show that MnemoDyn is compute efficient and generalizes very well across diverse populations and scanning protocols. When benchmarked against current state-of-the-art transformer-based approaches, MnemoDyn consistently delivers superior reconstruction quality. Overall, we find that with such large-scale pre-training on (non-proprietary) rs-fMRI datasets, we get a highly performant model for various downstream tasks. Our results also provide evidence of the efficacy of the model on small sample size studies which has implications for neuroimaging studies at large where resting state fMRI is a commonly acquired imaging modality.

cs.LG↗

arXiv2026

Function theory of the hexablock and applications to the tetrablock and Euclidean biball

The realization, interpolation, extension and Toeplitz corona problems are amongst the central themes in function theory of a domain in $\mathbb{C}^d$. The present work addresses these four problems for the hexablock $\mathbb{H}$, a domain in $\mathbb{C}^4$ arising in connection with a special case of $\mu$-synthesis in $H^{\infty}$ control theory. We determine Schur-Agler class $SA(\mathbb{H})$ for $\mathbb{H}$ and find a realization formula for $\mathbb H$. With the help of this realization formula we state and prove interpolation, extension and Toeplitz corona theorems for the hexablock. As an application, we obtain analogous theorems for the Euclidean unit ball in $\mathbb{C}^2$. Moreover, we recover the existing same results for the tetrablock $\mathbb E$, another domain associated with the $\mu$-synthesis, as consequences of the hexablock theory and in terms of the Schur-Agler class $SA(\mathbb{H})$ and admissible kernels on $\mathbb{H}$.

math.CV↗

arXiv2026

Function theoretic aspects of the symmetrized polydisc and generalization

We introduce Schur-Agler type class for the symmetrized polydisc $\mathbb{G}_d$ and establish a realization theorem for functions in this class. We state and prove an interpolation theorem on $\mathbb{G}_d$ with interpolating functions belonging to the associated Schur-Agler type class. Moreover, Toeplitz corona and extension theorems are established for $\mathbb{G}_d$. We also extend the realization, interpolation, Toeplitz corona and extension theorems to a more general symmetrized family of domains $\Theta_d$.

math.CV↗

arXiv2026

Cosmology with Intensity Mapping via Statistics Beyond the Power Spectrum in the SKAO Era

The cosmological distribution of neutral hydrogen (HI) during the post-reionization era is highly non-Gaussian due to the underlying non-linear structure formation, complex galaxy biasing, and potential primordial non-Gaussianity. One needs higher-order (beyond two-point) statistics to maximally extract the non-Gaussian information out of the 21-cm intensity maps. This chapter summarizes the potential of several higher-order statistics, including voxel intensity distribution, emission line stacking, probability density functions, $\ell_1$-norm, bispectrum, and various marked statistics. Additionally, image-based morphological descriptors, such as the Largest Cluster Statistic, local dimensions, and Minkowski functionals, etc., can potentially characterize the morphology and geometry of the cosmic web encoded in the 21-cm intensity maps. This chapter presents forecasts of the detectability of these higher-order statistics in the context of the future SKAO observations. These forecasts incorporate instrumental noise, observational effects, and, in some cases, foreground removal in their analyses. With its unprecedented sensitivity, the future SKAO 21-cm observations will enable us to measure these higher-order statistics more precisely, possibly helping to break degeneracies between astrophysical and cosmological parameters, and maximizing the science outcome from these surveys.

astro-ph.CO↗

arXiv2026

Tracing Ultra Light Axions in Post-reionization, Lyman-$\alpha$ and CMB Missions

Ultra-light axions (ULAs) are dark matter candidates proposed to resolve the small scale anomalies of the standard cosmological model. Due to their inherent quantum pressure, ULAs result in a distinct, scale-dependent suppression on the matter power spectrum, which can leave imprints on the upcoming observations. We explore such possibilities by forecasting on the post-reionization large scale structure (LSS) surveys and next-generation cosmic microwave background (CMB) missions. By utilizing the cross-correlation between 21-cm intensity mapping (SKA1-MID and PUMA) and the Lyman-$\alpha$ forest (DESI-like), we explore possible signatures of ULAs in post-reionization surveys while mitigating instrument-specific systematics. The Fisher matrix analysis projects uncertainties on the fractional ULA abundance across a wide ULA mass range of $10^{-30}\text{ eV} \le m_a \le 10^{-20}\text{ eV}$, revealing an optimal detection sensitivity at intermediate masses around $m_a \sim 10^{-25}\text{ eV}$. Furthermore, while next-generation CMB mission alone can yield small projected errors on the ULA fraction compared to future LSS missions, a joint analysis of the DESI-like and PUMA cross-spectrum alongside CMB-S4-like missions estimates an error on the ULA fraction to be $\mathcal{O}(10^{-4})$ for $m_a\lesssim 10^{-28}$ eV, highlighting a significant improvement over standalone LSS and CMB missions.

astro-ph.CO↗

arXiv2026

Realization, interpolation, extension on the pentablock and applications to $\mathbb D^2$, $\mathbb G_2$

We introduce Schur-Agler class for the pentablock $\mathbb P$ and establish a realization theorem for functions in this class. Then we prove an interpolation theorem for the pentablock with interpolating functions belonging to the corresponding Schur-Agler class. Also, we obtain an extension theorem for $\mathbb P$. Applying these results, we add a few new characterizations in the existing realization and interpolation theorems for the bidisc $\mathbb D^2$ and the symmetrized bidisc $\mathbb G_2$. Also, we give alternative proofs to the existing extension theorems for $\mathbb D^2, \, \mathbb G_2$.

math.CV↗

arXiv2026

A Toeplitz corona theorem for the pentablock and applications

We state and prove a Toeplitz corona theorem for the pentablock $\mathbb{P}$, a domain in $\mathbb{C}^3$ given by \[ \mathbb{P}=\{(a_{21}, \text{tr}(A), \det(A)) \in \mathbb C^3 : A=[a_{ij}] \in M_2(\mathbb C), \|A\|<1\}. \] By two different applications of this theorem, we obtain a few new characterizations in the Toeplitz corona theorems for the bidisc and the symmetrized bidisc.

math.CV↗

arXiv2026

Neutrino self-interactions in post-reionization era: Lyman-$\alpha$, 21-cm and cross-spectra

Neutrino self-interactions delay the onset of free-streaming in the early universe, leaving distinct, scale-dependent signatures on the matter power spectrum. We investigate these signatures in post-reionization 21-cm intensity mapping and the Lyman-$\alpha$ (Ly$\alpha$) forest at redshifts $z \sim 2$--$3.5$, and forecast the constraints achievable with upcoming surveys using Fisher matrix analysis. Modeling neutrino self-interactions through an effective four-fermion parameterization with coupling $G_{\rm eff}$, we compute modifications to the Ly$\alpha$ and 21-cm auto- and cross-power spectra for both strongly interacting (SI$_\nu$, $\log_{10}G_{\mathrm{eff}} = -1.77$) and moderately interacting (MI$_\nu$, $\log_{10}G_{\mathrm{eff}} = -5$) scenarios. We then combine these with forecasts for a representative next-generation cosmic microwave background (CMB) mission to evaluate the capabilities of SKA1-Mid and PUMA. We find that the Ly$\alpha$--21-cm cross-correlation provides a systematics-resilient probe of the interaction signal, and decisively breaks the degeneracy between the primordial scalar power spectrum amplitude ($A_s$) and $G_{\rm eff}$ that limits CMB only analysis, particularly for the SI$_\nu$ mode. Furthermore, the CMB+PUMA combination emerges as the optimal survey configuration for both regimes, reaching 1$\sigma$ constraints of $\mathcal{O}(10^{-3})$ on $\sigma(\log_{10}G_{\rm eff})$ for the SI$_\nu$ mode and $\mathcal{O}(10^{-2})$ for the MI$_\nu$ mode. Compared to the CMB-only baseline, this represents an improvement of approximately one order of magnitude for the SI$_\nu$ mode, and nearly two orders of magnitude for the MI$_\nu$ mode. We show that this conclusion holds uniformly over the full range of coupling strengths from $\log_{10}G_{\rm eff} = -6$ to $-1.77$.

astro-ph.CO↗

arXiv2026

Primordial magnetic fields in the light of upcoming post-EoR Lyman-$\alpha$ and 21-cm observations

The Lorentz force exerted by a primordial magnetic field (PMF) on the coupled baryon-dark matter system may enhance total matter power at small scales after recombination. In the post-reionization (post-EoR) era, a weakly scale-dependent PMF of sub-nG strength is thus expected to influence the Lyman-$\alpha$ (Ly$\alpha$) power spectrum, the 21 cm power spectrum, and the Ly$\alpha$-21 cm cross-spectrum at scales $k\gtrsim 1\:h/\textrm{Mpc}$. We investigate the prospects of constraining the PMF sector via these three cosmological observables, by employing SNR estimation and Fisher forecast on the PMF amplitude $B_0$ and spectral index $n_{\rm B}$, for a next-generation DESI-like spectroscopic survey and two upcoming 21 cm facilities, namely SKA1-Mid and PUMA. Our results indicate the possibility of constraining both PMF parameters with $\lesssim10\%$ relative errors through the uncontaminated 21 cm auto-spectrum as well as the Ly$\alpha$-21 cm cross-spectrum probed with the DESI-like+SKA1-Mid combination. Indicatively, the Ly$\alpha$-21 cm cross-correlation via DESI-like+SKA1-Mid is predicted to constrain a fiducial scenario $B_0=0.8$ nG and $n_{\rm B}=-2.9$ with $1\sigma$ errors $\Delta B_0\approx 0.07$ nG and $\Delta n_{\rm B}\approx0.02$. The DESI-like+PUMA setup is predicted to fare relatively worse due to its restriction to larger scales, resulting in comparatively one order of magnitude relaxed error bounds for similar fiducials. Since the Ly$\alpha$-21 cm cross-signal is expected to be largely insensitive to foreground contamination (unlike the 21 cm auto-spectrum), it may serve as an optimal foreground-immune post-EoR probe to constrain a weakly scale-dependent sub-nG PMF via future DESI-like+SKA1-Mid observations.

astro-ph.CO↗

arXiv2026

Rigidity of the structured singular value and applications

The structured singular value $\mu_E$ for a linear subspace $E$ of $M_n(\mathbb C)$ is defined by \[ \mu_E(A)=1 / \inf\{\|X\| \ : \ X \in E, \ \det(I_n-AX)=0 \} \quad (A \in M_n(\mathbb{C})), \] and $\mu_E(A)=0$ if there is no $X \in E$ with $\det(I_n-AX)=0$. It is well-known that $\mu_E(A)$ coincides with the spectral radius $r(A)$ when $E=\{cI_n: c \in \mathbb C \}$ and $\mu_E(A)=\|A\|$ when $E=M_n(\mathbb C)$, for all $A\in M_n(\mathbb C)$. Also, for any linear subspace $E$ satisfying $\{cI_n: c \in \mathbb C \} \subseteq E \subseteq M_n(\mathbb C)$, we have $r(A)\leq \mu_E(A) \leq \|A\|$. We prove that if $E=\{cI_n: c \in \mathbb C \}$ and $F$ is any linear subspace of $M_n(\mathbb C)$ containing $E$, then $\mu_E=\mu_F$ if and only if $E=F$. We prove the exact same rigidity theorem for the linear subspace consisting of the diagonal matrices of order $n$. On the contrary, when $E=M_n(\mathbb C)$, we show that there is a proper subspace $F$ of $M_n(\mathbb C)$, viz. the space of symmetric matrices such that $\mu_E=\mu_F=$ operator norm. Further, we characterize all linear subspaces $F\subseteq M_n(\mathbb C)$ such that $\mu_F$ coincides with the operator norm. Next, we show that in general there is no subspace $E$ of $M_n(\mathbb C)$ such that $\mu_E=$ the numerical radius, not even for $M_2(\mathbb C)$. We establish the rigidity of the structured singular value for each of the subspaces $E$ of $M_2(\mathbb C)$ such that the corresponding $\mu_E$-unit ball induces the domains -- symmetrized bidisc, tetrablock, pentablock, hexablock.

math.FA↗

arXiv2026

On a minimal And\^{o} dilation for a pair of strict contractions

The isometric dilation of a pair of commuting contractions due to And\^{o} is not minimal. We modify And\^{o}'s dilation and construct a minimal isometric dilation on $\mathcal H \oplus_2 \ell_2(\mathcal H \oplus_2 \mathcal H)$ for a commuting pair of strict contractions on a Hilbert space $\mathcal H$. In the same spirit, we construct under certain conditions a minimal And\^{o} dilation for a commuting pair of strict Banach space contractions. Further, we show that an And\^{o} dilation is possible even for a more general pair of commuting contractions $(T_1,T_2)$ on a normed space $\mathbb X$ provided that the function $A_{T_i}: \mathbb X \rightarrow \mathbb R$ given by $A_{T_i}(x)=(\|x\|^2-\|T_ix\|^2)^{\frac{1}{2}}$ defines a norm on $\mathbb X$ for $i=1,2$.

math.FA↗

arXiv2026

A domain in $\mathbb C^4$ and its connection with $\mu$-synthesis problem

We explore a domain $\mathbb F$ in $\mathbb C^4$ that has structural similarities with the hexablock $\mathbb{H} \subset \mathbb C^4$. It leads to the question if these two domains are biholomorphic. In this paper, we answer this question in negative. We provide alternative characterizations of the domain $\mathbb{F}$ and find its connection with the domains associated with $\mu$-synthesis problem such as the symmetrized bidisc, the tetrablock, the pentablock and the hexablock. We also address the following question: does $\mathbb{F}$ (which is biholomorphic with $\mathbb L_4$) arise from a $\mu$-synthesis problem in the same manner as $\mathbb{G}_2$ and $\mathbb{E}$ ?

math.CV↗

arXiv2026

Stationary densities in a weakly nonconserving asymmetric exclusion processes with finite resources

Asymmetric exclusion process (TASEP) along a one-dimensional (1D) open channel sets the paradigm for 1D driven models and nonequilibrium phase transitions in open 1D models. Inspired by the phenomenologies of an open TASEP with Langmuir kinetics (Lk) and with finite resources, we study the stationary densities and phase transitions in a TASEP with Lk connected to a particle reservoir at its both ends. We calculate the stationary density profiles and the phase transitions. The resulting phase diagrams in the plane of the control parameters are significantly different from their counterparts in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model that is closely related to a TASEP coupled with Lk on a ring with a point defect, admits more phases than the latter. Phenomenological implications of our results are discussed.

cond-mat.stat-mech↗

arXiv2026

Redshift-space 21-cm bispectrum multipoles as an SKA-era gravity test in the post-reionization Universe

The redshifted 21-cm line from neutral hydrogen ($\textrm{H}\textsc{i}$) enables volumetric intensity mapping of large-scale structure in the post-reionization Universe. In anticipation of \texttt{SKA-MID}'s wide redshift coverage and high signal-to-noise clustering measurements, we study the redshift-space 21-cm bispectrum and its spherical-harmonic multipoles as probes of anisotropic non-linear structure formation and departures from General Relativity. Using a tree-level perturbative description for the 21-cm brightness-temperature field in redshift space, and adopting the Hu--Sawicki $f(R)$ model as a representative modified-gravity scenario, we forecast the detectability of configuration-dependent signatures with an \texttt{SKA-MID}--like survey. We derive the bispectrum-multipole covariance including sample variance and thermal noise and evaluate the expected signal-to-noise of deviations relative to $\Lambda$CDM. We find that the observable information is dominated by the lowest multipoles, while higher-order modes are strongly suppressed. This concentration in the lowest multipoles is well matched to \texttt{SKA-MID} sensitivity and to the quasi-linear modes that are expected to remain accessible in practice. The strongest modified-gravity sensitivity arises from squeezed and stretched triangle configurations on quasi-linear scales, where scale-dependent growth enhances the bispectrum relative to the total variance. Our results position 21-cm bispectrum multipoles as a practical, SKA-ready observable for testing gravity beyond $\Lambda$CDM in the post-reionization epoch.

astro-ph.CO↗

arXiv2026

Spectral constants for the quantum annulus

We find several new estimates for the spectral constants $K(\mathbb A_r)$ for which a closed annulus $\overline{\mathbb A}_r$ or closed polyannulus $\overline{\mathbb A}^n_r$ is a $K$-spectral set for operators in the quantum annulus $\mathbb Q \mathbb A_r$. We give two alternative proofs to an existing estimate of spectral constant. The first proof capitalizes a dilation theorem due to McCullough and Pascoe, while the second proof involves a certain variety in the Euclidean biball. For commuting and doubly commuting operators in $\mathbb Q \mathbb A_r$, we find upper and lower bounds for the smallest spectral constants.

math.FA↗

arXiv2025

Constrained dilation and $\Gamma$-contractions

A commuting pair of Hilbert space operators having the closed symmetrized bidisc \[ \Gamma=\{(z_1+z_2, z_1z_2) \in \mathbb C^2 \ : \ |z_1| \leq 1, |z_2| \leq 1\} \] as a spectral set is called a \textit{$\Gamma$-contraction}. A $\Gamma$-contraction $(S,P)$ is called \textit{$\Gamma$-distinguished} if $(S,P)$ is annihilated by a polynomial $q \in \mathbb C[z_1,z_2]$ whose zero set $Z(q)$ defines a distinguished variety in the symmetrized bidisc $\mathbb G$. There is Schaffer-type minimal $\Gamma$-isometric dilation of a $\Gamma$-contraction $(S,P)$ in the literature. In this article, we study when such a minimal $\Gamma$-isometric dilation is $\Gamma$-distinguished provided that $(S,P)$ is a $\Gamma$-distinguished $\Gamma$-contraction. We show that a pure $\Gamma$-isometry $(T,V)$ with defect space $\dim \mathcal D_{V^*}< \infty$, is $\Gamma$-distinguished if and only if the fundamental operator of $(T^*,V^*)$ has numerical radius less than $1$. Further, it is proved that a $\Gamma$-contraction acting on a finite-dimensional Hilbert space dilates to a $\Gamma$-distinguished $\Gamma$-isometry if its fundamental operator has numerical radius less than $1$. We also provide sufficient conditions for a pure $\Gamma$-contraction to be $\Gamma$-distinguished. Wold decomposition splits an isometry into two orthogonal parts of which one is a unitary and the other is a completely non-unitary contraction. In this direction, we find a few decomposition results for the $\Gamma$-distinguished $\Gamma$-unitaries and $\Gamma$-distinguished pure $\Gamma$-isometries.

math.FA↗

arXiv2025

Exploring the Co-SIMP dark matter model using the 21-cm signal from the dark ages

The redshifted 21-cm signal from the dark ages offers a powerful probe of cosmological models and the underlying dark matter (DM) microphysics. We investigate deviations from the standard $\Lambda$CDM prediction, an absorption trough of approximately $-40.6\,\mathrm{mK}$ at redshift $z\simeq85.6$, in the context of co-SIMP (strongly interacting massive particle) DM. The co-SIMP interaction strength is encoded by the parameter $C_{\rm int}$, incorporating the masses of DM and standard model (SM) particles, the interaction cross-section, and the amount of heat exchange between the two sectors. Increasing $C_{\rm int}$ deepens the absorption feature and shifts the trough to higher redshifts in the global signal. For $C_{\rm int}=1.0$, the minimum brightness temperature reaches $-50.6,\mathrm{mK}$ at $z\simeq86.2$. The 21-cm power spectrum increases with $C_{\rm int}$ in addition to the global signal. We assess the detectability of these signatures using signal-to-noise ratio (SNR) and Fisher forecasts. The maximum SNR reaches $\sim 15.7$ for $C_{\rm int}=1.0$ for the global signal. Fisher forecasts for $1,000$ hours of integration time show that this model can be distinguished from a null-signal at $4.3\sigma$ and a mild 1.6$\sigma$ from $\Lambda$CDM, improving by an order of magnitude for 100,000 hours. For the 21-cm power spectrum, a $5,\mathrm{km}^2$ array with 1,000 hours yields a $4.63\sigma$ detection and mildly separated from the standard scenario at $1.78\sigma$. These findings highlight the potential of the 21-cm cosmology to probe the properties of DM and demonstrate that upcoming dark ages experiments, particularly space-based and lunar observations, can offer a promising avenue to test co-SIMP models.

astro-ph.CO↗

arXiv2025

NLP threshold corrections to W+jet production

We perform a detailed computation of the helicity-dependent next-to-leading power leading logarithms in W+jet production, originating from next-to-soft gluon radiation and soft (anti-)quark emissions. These contributions are systematically captured via helicity-sensitive spinor shifts and soft quark operators. The resulting expressions exhibit full agreement with a recently proposed universal structure of NLP corrections for processes involving the production of an arbitrary massive colourless final state in association with a jet.

hep-ph↗