arXiv subjects

Arnab Roy

Publications and source records attributed to Arnab Roy.

At least 19 recordsLinked to original sources

arXiv2026

Guppy: Efficient Light Clients via Recursive Zero-Knowledge Proofs

Traditional light clients rely on validators committing to the entire blockchain state at every block via a state commitment such as a Merkle tree, allowing clients to verify facts using short proofs. However, maintaining large and ever-growing state trees imposes a significant burden on validators and lies on the critical path of block production. As a result, many modern high-throughput chains avoid this approach altogether. This work asks whether efficient inclusion proofs can be supported without requiring validators to maintain full state commitments. We present Guppy, a protocol that achieves this by having validators commit to just the state updates. An off-chain, untrusted service, secured by recursive Zero-Knowledge Proofs (ZKPs), then maintains a verifiable Merkle tree over the full state. This design keeps validator overhead negligible and does not increase the asymptotic complexity of block construction. Our design rests on two key technical ideas. First, a hash-chain commitment moves validator signature verification out of the ZK circuit, keeping the proving circuit efficient. Second, we design a parallel recursive proving pipeline that leverages cheap recursion in modern ZKPs to ensure latency grows only logarithmically with throughput. Our Plonky2-based implementation demonstrates that Guppy can maintain a Merkle tree of size 2^30 while processing thousands of updates per second, adding only 2-4 s of latency.

cs.CR↗

arXiv2026

A New Algebraic Algorithm for LWE

The Learning With Errors (LWE) problem, introduced by Regev in 2005, is central to modern cryptography and post-quantum security. The algorithms to solve the search version of the problem, Search-LWE, can be broadly categorised into algebraic, combinatorial and lattice-based. In this work we propose a new algebraic algorithm for the Search-LWE problem. At a high level, the algorithm combines linear-algebraic techniques with S-polynomial-based methods from Groebner basis computation. We provide a direct complexity analysis of our algorithm, avoiding semi-regularity assumptions and complexity bounds derived from the degree of regularity. Our algorithm achieves a polynomial improvement in complexity over prior results that use Groebner basis methods to solve Search-LWE.

cs.CR↗

arXiv2026

On smooth affine surfaces with the cohomology of a smooth projective curve

We prove that if a smooth affine complex surface has the same rational mixed Hodge structure as a smooth projective curve of positive genus, then it admits a smooth morphism to the curve with fibers isomorphic to affine line. In particular, every such surface is the total space of a torsor for a line bundle on the curve. The motivation comes from Jouanolou's trick, to which this result gives a kind of converse in dimension 2.

math.AG↗

arXiv2026

Steady Motion of a Self-Propelled Body in a Viscous Fluid: Dirichlet Boundary Conditions with Nonzero Flux

We study the steady self-propelled motion of a rigid body immersed in an incompressible viscous fluid occupying an exterior domain in $\mathbb{R}^3$. In a body-fixed reference frame, the problem is described by a coupled fluid-rigid body system posed in a fixed exterior domain, where the Navier--Stokes equations are coupled with the unknown translational and angular velocities of the rigid body. The self-propulsion is generated by prescribing a boundary velocity on the body surface. Our main result asserts the existence of weak solutions under the sole assumption that the prescribed boundary flux is sufficiently small. The crucial step is the construction of a divergence-free extension of the boundary data that does not rely on either the zero-flux condition or the smallness of the boundary data. As a result, we generalize the result of Galdi [Theorem 5.1 in On the steady self-propelled motion of a body in a viscous incompressible fluid. Arch. Rational Mech. Anal., 148 (1999), 53-88], where both assumptions were required.

math.AP↗

arXiv2026

On the impact of clusters of rigid balls on the motion of a viscous fluid

We develop a new approach to the problem of the motion of a large number of rigid bodies immersed in a viscous fluid. The leading idea is the concept of cluster - a collection of individual rigid objects that may be grouped or even connected in such a way that their collective impact on the bulk motion of the system is similar to that of a single body. The applications of the new approach include: 1. Improving the critical value of the number of balls of small radius such that their cloud has no impact on the limit system represented by the incompressible Navier--Stokes equations. 2. The balls follow the fluid flow in the asymptotic limit of vanishing radius and increasing number even if a gravitational force is imposed.

math.AP↗

arXiv2026

A Window onto New Invisible Particles via Semi-Visible Higgs Decays

Searches for new physics continue at the LHC in several forms, including new-particle searches, precision measurements of SM couplings, and searches for signals of new invisible particles. In this talk, we discuss the reach in parameter space of new invisible particles with the semi-visible Higgs decay modes $H\to \ell^+\ell^- + ~\rm E{\!\!\!/}_T$ and $H\to jj + ~\rm E{\!\!\!/}_T$. We first parametrise the new invisible particles and their interactions with the SM through an effective field theory at dimension six. We then study the respective signals and the corresponding background, finding small signals with large backgrounds. We find, however, that the kinematics of these processes are sufficiently rich to allow a signal extraction that we first quantify with a cut-based analysis and later with a multivariate BDT.

hep-ph↗

arXiv2026

Stochastically forced Navier-Stokes equations interacting with an elastic structure

We prove global-in-time strong pathwise well-posedness for a stochastic fluid-structure interaction problem coupling a two-dimensional incompressible Navier-Stokes fluid to a one-dimensional damped Kirchhoff plate. The coupling is imposed on a fixed interface through continuity of velocities and balance of normal stresses, and stochastic forcing, modeled by a cylindrical Wiener process, acts on both the fluid and structure equations. We split the problem into a linear stochastic part and a nonlinear deterministic remainder. The linear stochastic problem is treated by proving that the associated fluid-structure operator admits a bounded $\mathcal{H}^\infty$-calculus, yielding stochastic maximal regularity. This requires a decoupling procedure for the non-diagonal operator domain, and pressure estimates via suitable lifting constructions. The deterministic remainder is solved locally by quasilinear methods, and the resulting blow-up criterion is ruled out by higher-order a priori estimates. This is the first global-in-time strong pathwise well-posedness result for a stochastically forced Navier-Stokes system interacting with a deformable elastic structure.

math.AP↗

arXiv2026

Strong well-posedness of a fluid--poro-viscoelastic interaction problem: An approach by Spectral analysis

This article investigates a coupled viscoelastic Navier--Stokes--Biot system describing the interaction between an incompressible viscous fluid and a poro--viscoelastic medium in three spatial dimensions. The coupling between the fluid and the porous medium is realized through Beavers--Joseph--Saffman type interface conditions. Using spectral analysis, it is proved that the coupled system admits a unique, strong, global solution for small initial data. In addition, a Serrin--type blow-up criterion is established.

math.AP↗

arXiv2026

Local well-posedness for a moving rigid region in Surface Quasi-Geostrophic equations

We introduce and analyze a class of Surface Quasi-Geostrophic (SQG) equations in the presence of moving rigid obstacles. The model is motivated both by vortex-wave type asymptotics for singular structures in active scalar equations and by geophysical phenomena exhibiting rigid-like coherent regions, such as cyclone eyes or long-lived atmospheric dust clouds. We consider the critical SQG equation in a time-dependent exterior domain generated by a prescribed rigid motion and reconstruct the velocity through a nonlocal elliptic formulation adapted to impermeability constraints. The active scalar is assumed to remain constant inside the rigid region and in a neighborhood of its boundary, yielding a plateau structure compatible with the transport dynamics. For a single moving obstacle, we establish local well-posedness of classical solutions in Sobolev spaces $H^k$, $k\geq 4$ together with uniqueness, local stability, and a blow-up criterion. The analysis relies on a reformulation in adapted coordinates reducing the problem to a fixed domain, combined with integral representations for the fractional elliptic operator, regularization procedures, and a nonlinear fixed-point argument. A central difficulty comes from the critical singularity of the SQG Biot-Savart kernel in the case $s=\frac{1}{2}$, for which the velocity reconstruction near the moving boundary requires commutator estimates. We further prove propagation of the plateau property and derive a priori estimates controlling both the support of the scalar gradient and the Sobolev norm of the solution. This work provides, to our knowledge, the first well-posedness theory for SQG equations with moving rigid obstacles and constitutes a first step toward the rigorous derivation of point-vortex type dynamics from shrinking rigid bodies in SQG flows.

math.AP↗

arXiv2026

On Hamming-Lipschitz Type Stability of the Subdominant (Minmax) Ultrametric: Theory and Simple Proofs

The subdominant (minmax) ultrametric is a canonical tree-structured summary of a dissimilarity matrix, arising equivalently as the ultrametric induced by single-linkage clustering. While its classical stability theory is usually formulated in $\ell_\infty$ or Gromov--Hausdorff terms, such bounds are poorly suited to sparse perturbations that alter only a few pairwise distances. We develop an $\ell_0$-type stability theory for this operator. Our analysis shows that sparse edits propagate only through the minimum spanning tree (MST): a pairwise ultrametric value can change only if its tree path crosses an edited edge or a cut newly exposed by an edited off-tree edge. This yields a sharp per-edit exposed-cut score and a tree-only global envelope, leading to Hamming--Lipschitz bounds on the number of ultrametric entries that can change. We also prove sharpness results showing that this dependence on tree geometry is unavoidable: under strict cut separation the tree-edge bound is attained exactly, and for off-tree edits there are explicit families in which one edited distance changes $\Theta(n^2)$ ultrametric entries. In addition, we prove a conditional near-additivity principle for multiple edits under certified large per-edit changed regions and negligible aggregate overlap. Experiments on deep-embedding graphs show that the resulting structural scores provide useful vulnerability diagnostics for hierarchical representations.

cs.LG↗

arXiv2026

Existence of weak solutions for incompressible fluid-Koiter shell interactions with Navier slip boundary condition

We study a three-dimensional fluid-structure interaction problem describing the motion of an incompressible, viscous fluid coupled with a deformable elastic shell of Koiter type that forms part of the fluid boundary. The fluid motion is governed by the incompressible Navier--Stokes equations posed on a time-dependent domain, while the shell evolution is described by a nonlinear elastic model. At the fluid-structure interface, we impose Navier slip boundary conditions, allowing for tangential slip penalized by friction. Our main result establishes the global-in-time existence of weak solutions up to the first possible self-intersection of the shell, for arbitrarily large initial data with finite energy. The analysis is carried out in a fully three-dimensional setting and addresses the major mathematical challenges arising from the moving domain, the geometric nonlinearity of the shell, and the reduced regularization induced by the slip boundary condition. The proof relies on a careful construction of suitable approximation schemes, novel compactness arguments adapted to the slip framework, and a new extension operator for divergence-free test functions compatible with the fluid-shell coupling. As a further contribution, we provide a direct approach to the strong convergence of second-order spatial derivatives of the shell displacement, which allows us to treat nonlinear Koiter shell models within the same framework.

math.AP↗

arXiv2026

Operator learning for models of tear film breakup

Tear film (TF) breakup is a key driver of understanding dry eye disease, yet estimating TF thickness and osmolarity from fluorescence (FL) imaging typically requires solving computationally expensive inverse problems. We propose an operator learning framework that replaces traditional inverse solvers with neural operators trained on simulated TF dynamics. This approach offers a scalable path toward rapid, data-driven analysis of tear film dynamics.

math.NA↗

arXiv2025

Steady Self-Propelled Motion of a Rigid Body in a Viscous Fluid with Navier-Slip Boundary Conditions

We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the fluid occupies an exterior domain and the propulsion mechanism is modeled through nonhomogeneous Navier-slip boundary conditions at the fluid-body interface. Such conditions provide a realistic description of propulsion in microfluidic and rough-surface regimes, where partial slip effects are significant. Under suitable smallness assumptions on the boundary flux and on the normal component of the prescribed surface velocity, we establish the existence of weak steady solutions to the coupled fluid-structure system. A key analytical ingredient is the derivation of a Korn-type inequality adapted to exterior domains with rigid-body motion and Navier-slip interfaces, which yields uniform control of both the fluid velocity and the translational and rotational velocities of the body. Beyond existence, we provide a necessary and sufficient condition under which a prescribed slip velocity on the body surface induces nontrivial translational or rotational motion of the rigid body. This is achieved through the introduction of a finite-dimensional thrust space, defined via auxiliary exterior Stokes problems with Navier boundary conditions, which captures the effective contribution of boundary-driven flows to the rigid-body motion. Our results clarify how boundary effects generate propulsion and extend the classical Dirichlet-based theory to the Navier-slip setting.

math.AP↗

arXiv2025

Muonphilic asymmetric dark matter at a future muon collider

We explore phenomenological constraints on, and future muon collider sensitivities to, the parameter spaces of various muonphilic portals to fermionic asymmetric dark matter (ADM). Both WEFT-level dimension-6 effective operators and two UV models based on gauged $L_\mu - L_\tau$ are considered. One of the latter features a vector coupling to the dark matter and the other an axial vector coupling. The ADM criterion that at least $99\%$ of the dark matter relic density is asymmetric is also imposed. We identify which of these scenarios are currently allowed by direct detection and collider constraints, and then determine how much more of the parameter space could be probed by 3 and 10 TeV muon colliders with 1 ab$^{-1}$ of data. For the UV models, the constraints from $g-2$ of the muon are included. The future sensitivity curves due to neutron star heating considerations are also depicted. We present results for both the few-GeV dark matter mass regime motivated by ADM approaches to the $\Omega_b \simeq \Omega_\text{DM}/5$ coincidence problem, and for larger masses in the context of more general ADM.

hep-ph↗

arXiv2025

Semi-visible higgs decay as a probe for new invisible particles

We discuss the HL-LHC sensitivity to probe new invisible particles including scalars and fermions using semi-visible Higgs decays in the $pp\to ZH, Z\to jj\, (\ell^+\ell^-), ~H\to \ell^+\ell^- (jj) + ~\rm E{\!\!\!/}_T$ production mode. The kinematics of these decays allow new particle masses below $m\lesssim 50$ GeV. We carry out our analysis using both a cut-based approach and a multivariate method based on a boosted decision tree. We work within the dark-SMEFT framework with operators up to dimension six and a discrete $\mathbb{Z}_2$ symmetry under which the new particles are odd and the SM particles are even. We compare our results to those obtained from considering the invisible $Z$-width, as well as perturbative unitarity arguments. Finally, we outline kinematic strategies at the LHC to distinguish different operator structures of the postulated invisible particles.

hep-ph↗

arXiv2025

Monojet and direct detection constraints on real scalar dark matter: EFT and a simple UV completion

We consider constraints that can be placed on certain invisible scalar particles through monojet studies at the LHC and compare them with those from direct detection experiments when interpreted as dark matter. Whereas direct detection constraints are typically more restrictive, we identify regions of parameter space where monojet studies provide important complementary bounds. We carry out our analysis using both a $\phi$SMEFT for real scalar particle pairs coupled to standard-model fields through operators of up to dimension six, and a simple UV completion with vector-like quarks, with both the scalars and the vector-like quarks being odd under a $\mathbb{Z}_2$ symmetry, while the SM particles are even. The vector-like quarks can only decay into a jet and an invisible scalar, and we recast the current ATLAS monojet data to constrain their parameter space. Comparison of the two descriptions yields some insight into interpreting dark matter constraints obtained with EFTs.

hep-ph↗

arXiv2025

Strong time-periodic solutions for a multilayered fluid-structure interaction system with nonlinear coupling

We investigate a time-periodic fully three-dimensional fluid-structure interaction system in which the Navier-Stokes equations for an incompressible viscous fluid are coupled with a multilayered elastic structure composed of a damped thin linear plate and a thick viscoelastic layer. The coupling is nonlinear, meaning that it is on a moving interface that is not known a priori, rendering the problem a moving-domain problem. We prove the existence of strong time-periodic solutions. The proof relies on a fixed point argument, combining sharp nonlinear estimates with a detailed analysis of the linearized system. The linearized problem is analyzed by employing the Arendt-Bu theorem on maximal periodic $\mathrm{L}^p$-regularity, which requires several new analytical ingredients including a refined lifting procedure, a decoupling strategy establishing $\mathcal{R}$-sectoriality of the coupled operator, a careful treatment of the thick structural layer, and a spectral analysis adapted to the multilayered setting. This provides the first strong time-periodic existence result for multilayered fluid-structure interaction systems, and the methods are expended to extend more broadly to nonlinear coupled PDEs on moving domains with periodic forcing.

math.AP↗

arXiv2025

On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid

We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in $R^3$. We introduce a new concept of dissipative weak solution of the problem based on a combination of the approach proposed by Judakov with a suitable form of energy inequality. We show that global--in--time dissipative solutions always exist as long as the rigid bodies are connected compact sets. In addition, in the absence of external driving forces, the system always tends to a static equilibrium as time goes to infinity. The results hold independently of possible collisions of rigid bodies and for any finite energy initial data.

math.AP↗