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Manish Kumar

Publications and source records attributed to Manish Kumar.

At least 19 recordsLinked to original sources
arXiv2026

Quantitative linear approximation for controllability of quasi-linear parabolic equations

This paper studies the relationship between the controllability of a quasi-linear parabolic equation and that of its linear counterpart. Under suitable assumptions, we prove that for sufficiently small initial data both systems are null controllable, and that the differences between their corresponding controls and states satisfy a higher-order error estimate. Unlike standard controllability problems, the controls constructed here not only steer the system to a prescribed target at a given terminal time, but are also designed to ensure that the deviation between the nonlinear and linear dynamics obeys the aforementioned estimate. This method is applicable to general nonlinear partial differential equations, and the approximation order for controllability is optimal.

math.OC↗
arXiv2026

Monodromy of stratified vector bundles

We explore the interconnections between the monodromy group of stratified bundles on a smooth projective variety $X$ and the monodromy of the strongly semistable vector bundles $V$ on $X$ such that $c_1(V)$ and $c_2(V)$ are numerically trivial.

math.AG↗
arXiv2026

Anomalous metal and superconducting phases in rhombohedral graphene

Two-dimensional superconductivity is now well established in graphene-based systems, with many such realizations showing evidence for unconventional pairing. Yet in several of the gate-tuned phases that otherwise exhibit clear signatures of superconductivity, the resistance does not vanish as temperature is lowered, instead saturating at a finite value. Here we report a systematic study of this behavior in rhombohedral graphene on a WSe$_2$ substrate, finding regions of gate space with zero-resistance superconductivity alongside others with finite saturation resistance. At zero magnetic field, these regions appear as isolated pockets in gate space that otherwise exhibit strikingly similar phenomenology, including abrupt transitions to the normal state as temperature, perpendicular magnetic field, and current are raised above critical values. A small in-plane field expands and merges these pockets without qualitatively altering their behavior, producing a sharp boundary at millikelvin base temperature between states of zero or finite resistance. The finite-resistance state reproduces key phenomenology associated with the anomalous metal, a state that has been observed in thin-film superconductors for decades but lacks an accepted theoretical explanation. The tunability and reproducibility of ultra-clean rhombohedral graphene place strong constraints on extrinsic explanations and provide a new platform for understanding this behavior.

cond-mat.mes-hall↗
arXiv2026

Local B-site chemistry controls oxygen-vacancy energetics in Ca-Ce-Ti-Mn perovskites for thermochemical hydrogen production

Two-step thermochemical water splitting driven by concentrated solar heat is a scalable route to renewable hydrogen, but it requires oxides whose oxygen-vacancy formation energies balance facile reduction with favorable reoxidation. Perovskite solid solutions can tune this balance, but the relationship between bulk stoichiometry and local defect energetics remains poorly understood. Here we map oxygen-vacancy formation energetics across Ca-Ce-Ti-Mn (CCTM) perovskites by combining first-principles calculations with a coverage-constrained special quasirandom structure approach that realizes all fifteen symmetry-distinct oxygen nearest-neighbor environments, an interpretable crystal-feature model whose fitted coefficients directly encode the underlying Born-Haber thermochemistry, and a fine-tuned defect graph neural network. Local B-site chemistry dominates the oxygen-vacancy formation energy $E_\mathrm{v}$: varying the nearest-neighbor Mn fraction shifts $E_\mathrm{v}$ by 1.0-1.5 eV depending on local Ce content, whereas A-site Ce variation contributes a smaller, Mn-dependent shift of 0.2-0.6 eV. Short-range B-site cation order, if it can be established and kinetically retained through processing, is therefore a candidate means of tuning redox performance without changing bulk composition. Composition-space maps identify a Ce/Mn-balanced region ($X_\mathrm{Ce}$ = 0.29-0.33, $X_\mathrm{Mn}$ = 0.58-0.67) combining a high fraction of vacancy sites within the targeted $E_\mathrm{v}$ window with phase stability and solubility, whose predicted redox cycle capacity matches or exceeds the ceria benchmark at 1350 $^\circ$C rather than the roughly 1600 $^\circ$C ceria requires. Measurements on three CCTM compositions show cycle capacity increasing monotonically with Ce content under protocols close to the model conditions. The design rules are expected to transfer to related perovskite families.

cond-mat.mtrl-sci↗
arXiv2026

Three-dimensional field of view of remote focusing microscopy system

Remote focusing (RF) microscopy is well known for its ability to sharply image a wide range of planes away from the working distance of the microscope objective. However, the exact nature of the three-dimensional (3D) field of view (FOV) is not known. In this letter we report an optical ray tracing based FOV study of a remote focusing microscopy system. We numerically simulate the Strehl ratio of two configurations of the remote focusing systems, and use this for the evaluation of the 3D FOV. The FOV tapers down as the sample plane moves away from the working distance. To cross-verify our simulation results, we experimentally measured the FOV at various offset planes. This rate of taper depends on the numerical aperture. We also discuss the advantages and limitations of remote focusing in microscopy.

physics.optics↗
arXiv2026

Nanoparticle Arrays for Efficient Organic Light-Emitting Diode Emission Management

OLEDs are increasingly applied in illumination and displays because they offer excellent color quality, are mechanically flexible, and are self-emissive. However, their usage is limited by low external quantum efficiency (EQE) and efficiency roll-off at high driving voltages. These limitations, together with demands for smaller pixels and device sizes in emerging technologies, motivate innovations that increase efficiency and allow replacing external optical elements with embedded solutions. Here, we demonstrate enhanced outcoupling as well as directional and polarization control of OLED emission, based on collective surface lattice resonances of plasmonic nanoparticle arrays that are embedded in the active layers of four different state-of-the-art OLED structures. Both square arrays and more complex lattices producing flat bands are demonstrated to guide the light to directions and polarizations determined by their optical modes. We show that by the design of the array geometry and the OLED structure, spectral and angular enhancement of the electroluminescence (EL), up to 30 %, can be achieved. Our results verify that surface lattice resonances of nanoparticle arrays offer a robust and versatile embedded solution for tailoring the OLED emission, as well as exciting prospects for efficiency increase if combined with narrow-spectrum emitters.

physics.optics↗
arXiv2026

The minimum genus of Galois covers of curves

Let $Y\longrightarrow X$ be a $G$-Galois connected cover of smooth projective curves over an algebraically closed field $k$ of positive characteristic $p$ with the branch locus contained in a finite subset of closed points $S_X$ in $X$, where $G$ is a finite cyclic $p$-group and $l$ is a prime number other than $p$. Let $\Gamma$ be an extension of an elementary abelian $l$-group $H$ by $G$. We find $G$-stable submodules of $l$-torsion of the Picard group of $Y$ and its generalisation. This is used to describe a method for finding the minimum genus of $\Gamma$-covers of $X$, \'etale over $X\setminus S_X$, dominating $Y$; and also the minimum of the genera of $\Gamma$-covers of $\mathbb{P}^1$ \'etale over $\mathbb{A}^1$.

math.AG↗
arXiv2026

Supervised Distributed Computing: Efficiency and Robustness under a Majority of Adversarial Workers

We consider a recently proposed \emph{supervised distributed computing} paradigm \cite{augustine2025supervised} that extends and refines the standard master-worker paradigm for parallel computations. In this paradigm, there is a supervisor, a source, a target, and a collection of workers. The distributed computation is given as an acyclic task graph that is known to the supervisor. The source initially stores the input and the target is supposed to store the output of the computation. The individual tasks of the computation are supposed to be executed by the workers under the guidance of the supervisor. The source, target and supervisor are assumed to be reliable, while a $\beta$-fraction of the workers might be adversarial, for some $\beta \in [0,1)$. This covers, for example, the case where a supervisor has to work with untrusted volunteers. In the standard master-worker approach, the master checks whether the workers correctly execute the assigned tasks, creating a severe bottleneck, whereas in the supervised approach, the supervisor outsources this checking to the workers. Prior to this work, only supervised solutions were known for the case that $\beta$ is a sufficiently small constant. We show that robust and efficient supervised solutions are possible for \emph{any} constant $\beta<1$ while the expected work for the honest workers is close to a \emph{single} execution per task, given that there is a lightweight verification mechanism that allows honest workers to check the correctness of task outputs, which is significantly better than all robust master-worker as well as peer-to-peer approaches known so far.

cs.DC↗
arXiv2026

Comparative Study of Weighted and Coupled Second- and Fourth-Order PDEs for Image Despeckling in Grayscale, Color, SAR, and Ultrasound

Partial Differential Equation (PDE)-based approaches have gained significant attention in image despeckling due to their strong capability to preserve structural details while suppressing noise. However, conventional second-order PDE models tend to generate blocky artifacts, whereas higher-order models often introduce speckle patterns. To resolve it, this paper proposes and comparatively analyzes two advanced PDE-based frameworks designed for speckle noise suppression while preserving the fine edges. The first model introduces a novel weighted formulation that combines second and fourth-order PDEs through a weighting parameter. The second-order diffusion coefficient employs grayscale and gradient-based indicators, while the fourth-order term is guided solely by a Laplacian-based indicator. The second model constructs a coupled PDE framework, where independent fourth and second-order components are explicitly solved in an iterative manner. In this coupled structure, each diffusion coefficient is defined separately to enhance adaptability in varying image regions. Both models are implemented using the explicit finite difference method. The proposed techniques are extensively evaluated on a variety of datasets, including standard grayscale, color, Synthetic Aperture Radar (SAR), and ultrasound images. Comparative experiments with the existing Telegraph Diffusion Model (TDM) and Fourth-Order Telegraph Diffusion Model (TDFM) demonstrate the superiority of the proposed approaches in reducing speckle noise while effectively preserving fine image structures and edges. Quantitative evaluations using PSNR, SSIM and Speckle Index metrics confirm that the proposed models produce higher image quality and enhanced visual perception. Overall, the presented PDE-based formulations provide a reliable and efficient framework for image despeckling in both natural and medical imaging.

cs.CV↗
arXiv2026

Single Image Defogging Using a Fourth-Order Telegraph PDE Guided by Physical Haze Modeling

In real-world scenarios, image defogging is an inverse problem due to unknown scene depth, atmospheric scattering, and the common absence of ground truth . To resolve the issue, we propose a hybrid defogging model that integrates a fourth-order nonlinear PDE with a physical haze formation model. We used Dark Channel Prior to estimate atmospheric parameters and to generate a guidance image, while the final restoration is performed via a fourth-order PDE-based evolution. A fourth-order PDE of the type telegraph is then evolved, incorporating an edge-adaptive diffusion coefficient and a fidelity term weighted by the transmission map. Fourth-order diffusion effectively suppresses haze while preserving structural details, and the hyperbolic formulation improves numerical stability and convergence behavior. We use relative error norm criteria for the convergence of our PDE. The proposed method is compared with Dark Channel prior, modified Dark Channel prior, and variational-based single-image defogging techniques. When we have ground truth available, we use MSE and SSIM for quantitative evaluation, whereas no-reference metrics, including FADE, Contrast Restoration Index, Average Gradient, and Entropy, are applied to real-world foggy images. Experimental results demonstrate that the proposed hybrid PDE-based method provides comparable visual quality and maintains structural details.

cs.CV↗
arXiv2026

A Coupled Fourth Order Telegraph Diffusion Framework Using Grayscale Indicators for Image Despeckling

Speckle noise severely limits the quality of images acquired from coherent imaging systems such as Synthetic Aperture Radar (SAR) and medical ultrasound. Traditional second-order PDE-based despeckling approaches, although popular, often introduce staircase artifacts and blur fine details. To overcome these limitations, we present a nonlinear, fourth-order coupled hyperbolic-parabolic PDE model that effectively reduces noise while preserving the structure. The framework consists of two evolution equations: one governing fourth-order diffusion for effective speckle reduction and smooth intensity transitions, and another refining an edge indicator to protect textures and structural features. The diffusion coefficient is adaptively constructed using both the image intensity variable u and a grayscale-based indicator function, ensuring structure-aware denoising while avoiding blocky artifacts and preserving fine details. We also prove the existence of a weak solution to the proposed model by applying Schauder fixed-point theorem. A finite-difference scheme with Gauss Seidel iteration is employed for efficient implementation. We compare the proposed model with the existing coupled second-order PDE model (HPCPDE) and the fourth-order telegraph diffusion model (TDFM). The results show that our model consistently outperforms these approaches. Experiments on standard grayscale images, real SAR and ultrasound data, as well as speckle-corrupted color images, demonstrate that the proposed method achieves superior performance over conventional PDE-based techniques in terms of PSNR, MSSIM, and Speckle Index.

eess.IV↗
arXiv2026

Floquet mobility edges and transport in a periodically driven generalized Aubry-Andr\'e model

We investigate the effect of a periodic electric field drive on the generalized Aubry-Andr\'e model, also known as the Ganeshan-Pixley-Das Sarma (GPD) model, which is well known as a host of mobility edges. Our study of the Floquet spectrum of the driven GPD model uncovers the emergence of two distinct Floquet mobility edges, a delocalized--localized (DL) edge in the bounded regime, and a multifractal--localized (ML) edge in the unbounded regime. Using analytical results derived from Avila's global theory applied to the high frequency effective Hamiltonian, together with numerical diagnostics such as the fractal dimension and inverse participation ratio, we demonstrate that these mobility edges can be effectively controlled by the amplitude and frequency of the electric field drive. We also identify drive-induced localization at specific values of the driving parameters, corresponding to dynamical localization points in the absence of quasiperiodic potential. Furthermore, the dynamical study of the periodically driven GPD model demonstrates superdiffusive to almost ballistic transport in the bounded regime corresponding to the DL edges, whereas subdiffusive transport is observed in the unbounded regime associated with the ML edges. We also analyze deviations from the high-frequency effective description by explicitly examining the low-frequency driving regime, where significant and counterintuitive deviations in both spectral properties and transport behavior are observed. Our study highlights the interplay of a quasiperiodic potential and a periodically varying electric field drive as a powerful mechanism to engineer mobility edges and control transport in systems with rich spectral features.

cond-mat.dis-nn↗
arXiv2026

From Uniform to Learned Knots: A Study of Spline-Based Numerical Encodings for Tabular Deep Learning

Numerical preprocessing remains a critical component of tabular deep learning, as the representation of continuous features can strongly affect downstream performance. We systematically study spline-based numerical encodings, including B-splines, M-splines, and integrated splines (I-splines), under uniform, quantile-based, target-aware, and learnable-knot placement. For the learnable variants, we adopt a differentiable knot parameterization that enables stable end-to-end optimization of knot locations jointly with the backbone. We evaluate these encodings on a diverse collection of public regression and classification datasets using MLP, ResNet, and FT-Transformer backbones, and compare them against common numerical preprocessing baselines. Our results show that the effectiveness of numerical encoding depends strongly on the task, encoding size, and backbone. For classification, piecewise-linear encoding (PLE) is the most robust choice overall, while spline-based encodings remain competitive. For regression, no single encoding dominates, with performance depending on the spline family and knot-placement strategy, and larger gains generally observed for MLP and ResNet than for FT-Transformer. Learnable-knot variants can be optimized stably but may substantially increase training cost. Overall, numerical encodings should therefore be assessed jointly in terms of predictive performance and computational overhead. The implementation is publicly available at https://github.com/mkumar73/tdl-numerical-encodings/.

cs.LG↗
arXiv2026

Cotunneling theory and multiplet excitations: emergence of asymmetric line shape in inelastic scanning tunneling spectroscopy of correlated molecules on surfaces

Recent advances in on-surface chemistry, combined with scanning probe microscopy, have enabled the synthesis of correlated molecules on surfaces and the characterization of their chemical and electronic properties with unprecedented spatial resolution. Low-energy magnetic excitations of individual molecules are frequently investigated by scanning tunneling spectroscopy (STS) and often appear as symmetric step-like features in the differential conductance as a function of bias voltage. The interpretation of such steps is well established within cotunneling theory and effective model Hamiltonians (e.g., Hubbard- and spin-based models). Here, we extend the cotunneling formalism to general multireference systems. We show that multireference character, together with orbital-dependent and strongly asymmetric tip/substrate couplings, can produce pronounced asymmetric line shapes in inelastic STS. These results provide an alternative microscopic mechanism for the asymmetric peaks and dips near the Fermi level frequently observed in STS experiments.

cond-mat.mes-hall↗
arXiv2026

Strongly entangled Quantum Spin Rings driven by H\"uckel rule

Quantum spin rings represent an intriguing platform for studying unconventional magnetic order and exotic quantum phases, and they are also promising materials for emerging quantum technologies. Conventional spin systems consist of a set of weakly interacting localized spins that are well described by the Heisenberg spin models. Here, we demonstrate that strong interactions between radical centers in macrocycles of different sizes lead to fluctuations in the total number of unpaired electrons and to non-trivial antiferromagnetic order that extends beyond the Heisenberg picture. We demonstrate that the electronic structure of these spin rings is governed by the concept of 4n/4n+2 H\"uckel (anti)aromaticity for even-membered rings, whereas odd-membered rings possess a highly degenerate frustrated magnetic ground state. The strongly coupled spin rings are experimentally realized through the on-surface synthesis of {\pi}-magnetic carbon-based macrocycles, which consist of [2]triangulene units. The close correlation between the electronic structure and the H\"uckel aromaticity rule is revealed by scanning tunneling spectroscopy and multireference calculations. This work establishes a novel design principle employing the concept of H\"uckel aromaticity for quantum spin macrocycles.

cond-mat.mes-hall↗
arXiv2026

Inapplicability of Avila's theory in the diamond chain with quasiperiodic disorder

The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic frequencies on the mobility edge formation. We focus on the example of the addition of a constant offset to the quasiperiodic potential of the one-dimensional all-bands-flat diamond chain. We show that this additional offset can transform the anomalous mobility edges (AMEs), i.e. the energies, separating localized and multifractal states, into conventional mobility edges, separating localized from delocalized states. Also this appears to be the first example which shows the inability of Avila's global theory to analytically predict the ME location. We observe this both quantitatively, through the ME location mismatch, and qualitatively, via the formation of multiple MEs, not predicted by the theory.

cond-mat.str-el↗
arXiv2026

Sublinear-Time Reconfiguration of Programmable Matter with Joint Movements

We study centralized reconfiguration problems for geometric amoebot structures. A set of $n$ amoebots occupy nodes on the triangular grid and can reconfigure via expansion and contraction operations. We focus on the joint movement extension, where amoebots may expand and contract in parallel, enabling coordinated motion of larger substructures. Prior work introduced this extension and analyzed reconfiguration under additional assumptions such as metamodules. In contrast, we investigate the intrinsic dynamics of reconfiguration without such assumptions by restricting attention to centralized algorithms, leaving distributed solutions for future work. We study the reconfiguration problem between two classes of amoebot structures $A$ and $B$: For every structure $S\in A$, the goal is to compute a schedule that reconfigures $S$ into some structure $S'\in B$. Our focus is on sublinear-time algorithms. We affirmatively answer the open problem by Padalkin et al. (Auton. Robots, 2025) whether a within-the-model sublinear-time universal reconfiguration algorithm is possible, by proving that any structure can be reconfigured into a canonical line-segment structure in $O(\sqrt{n}\log n)$ rounds. Additionally, we give a constant-time algorithm for reconfiguring any spiral structure into a line segment. These results are enabled by new constant-time primitives that facilitate efficient parallel movement. Our findings demonstrate that the joint movement model supports sublinear reconfiguration without auxiliary assumptions. A central open question is whether universal reconfiguration within this model can be achieved in polylogarithmic or even constant time.

cs.DS↗