arXiv subjects

Sudipta Ghosh

Publications and source records attributed to Sudipta Ghosh.

15 recordsLinked to original sources

arXiv2026

Cubical Type Theoretic Navya-Nyāya

We present a formalization of the technical language of Navya-Nyaya - the "New Logic" school of late-classical Indian philosophy - in CCHM De Morgan cubical type theory (CTT). Previous formalization attempts in first-order logic (Matilal), higher-order logic (Ganeri), and Martin-Lof type theory (Bhattacharyya) each lose load-bearing structure: dependent delimitation (avacchedaka), typed absence (abhava), non-extensional identity (tadatmya), or unbounded relational depth (parampara-sambandha). We argue that CTT closes this gap natively. We give CTT encodings for seven core constructs (sambandha, avacchedaka, abhava, vyapti, tadatmya, higher relations, paryapti) plus the qualifier-qualificand structure; develop a stratified-universe foundation for the padartha system; and prove four signature theorems internal to the encoding (involution of abhava, kevalanvayi irreducibility, coextension without identity, no h-set collapse) and six metatheoretic results (soundness, conservativity, faithfulness, distinction preservation, decidability, commentarial conservativity). We close with worked encodings of fifteen Tattvacintamani passages, comparison with prior formalizations, an implementation sketch in Cubical Agda, and five distinguishing predictions - including a novel argument from Navya-Nyaya's involutive-negation doctrine for the necessity of De Morgan over Cartesian cubical foundations.

cs.LO↗

arXiv2026

The Dunning-Kruger Effect in Large Language Models: An Empirical Study of Confidence Calibration

Large language models (LLMs) have demonstrated remarkable capabilities across diverse tasks, yet their ability to accurately assess their own confidence remains poorly understood. We present an empirical study investigating whether LLMs exhibit patterns reminiscent of the Dunning-Kruger effect -- a cognitive bias where individuals with limited competence tend to overestimate their abilities. We evaluate four state-of-the-art models (Claude Haiku 4.5, Gemini 2.5 Pro, Gemini 2.5 Flash, and Kimi K2) across four benchmark datasets totaling 24,000 experimental trials. Our results reveal striking calibration differences: Kimi K2 exhibits severe overconfidence with an Expected Calibration Error (ECE) of 0.726 despite only 23.3% accuracy, while Claude Haiku 4.5 achieves the best calibration (ECE = 0.122) with 75.4% accuracy. These findings demonstrate that poorly performing models display markedly higher overconfidence -- a pattern analogous to the Dunning-Kruger effect in human cognition. We discuss implications for safe deployment of LLMs in high-stakes applications.

cs.CL↗

arXiv2025

Framed instanton homology and Frøyshov's invariant

We determine the framed instanton homology with coefficients in $\mathbb F = \mathbb Z/2$ for Dehn surgeries on a knot in the $3$-sphere. The dimension of these groups is seen to have a close relationship with a homology cobordism invariant due to Froyshov. As an application, we show that $r$-surgery on a non-trivial knot cannot be nondegenerate $SU(2)$-abelian for any $|r| \le 4\lceil g(K)/2\rceil$, which is $2g(K)$ for $g$ even and $2g(K) + 2$ for $g$ odd.

math.GT↗

arXiv2025

Homology lens spaces and $\mathrm{SL}(2,\mathbb{C})$

We prove that if $Y$ is a closed, oriented 3-manifold with first homology $H_1(Y;\mathbb{Z})$ of order less than $5$, then there is an irreducible representation $π_1(Y) \to \mathrm{SL}(2,\mathbb{C})$ unless $Y$ is homeomorphic to $S^3$, a lens space, or $\mathbb{RP}^3 \# \mathbb{RP}^3$. By previous work it suffices to consider the case $H_1(Y;\mathbb{Z}) \cong \mathbb{Z}/4\mathbb{Z}$, which we accomplish using holonomy perturbation techniques in instanton Floer homology.

math.GT↗

arXiv2025

$SU(2)$-representations of Branched Covers

We study the existence of irreducible $SU(2)$-representations for cyclic branched covers of knots in $S^3$. Our main result establishes that if $K$ is a non-trivial prime knot and $d$ is an integer such that $d \geq 2$ and $Σ_d(K)$ is an integer homology sphere, then $π_1(Σ_d(K))$ admits an irreducible $SU(2)$-representation, whenever $K$ satisfies one of two conditions: either $K$ is $2$-periodic, or $K$ can be represented as the closure of a tangle adapted to a $d\times d$ SICUP matrix. The first condition leverages a commuting trick for covering spaces to realize higher-degree branched covers as 2-fold covers, allowing us to apply recent results of Kronheimer-Mrowka and others. The second condition uses equivariant surgery descriptions and the $ν^\sharp$ invariant from instanton Floer homology. As applications, we provide new infinite families of hyperbolic integer homology spheres admitting irreducible representations, including examples where previously known criteria fail.

math.GT↗

arXiv2025

Degree-1 maps and rank inequalities in Heegaard Floer homology

Ghosh-Sivek-Zentner constructed degree-1 maps from certain rational homology solid tori to the twisted $I$-bundle over the Klein bottle. We show that these maps yield rank inequalities for Heegaard Floer homology. To do so, we use Hanselman-Rasmussen-Watson's immersed curve interpretation of bordered Floer homology, extending their proof of a similar rank inequality corresponding to degree-1 maps to the solid torus. Our result provides further evidence for Kronheimer-Mowka's conjectured relationship between Heegaard Floer homology and instanton Floer homology.

math.GT↗

arXiv2024

Connected sums and directed systems in knot Floer homologies

We prove a number of fundamental properties about instanton knot Floer homology. Our arguments rely on general properties of sutured Floer theories and apply also in the Heegaard Floer and monopole Floer settings, where many of our results were already known. Our main result is the connected sum formula for instanton knot Floer homology. An extension of this result proves the oriented skein exact triangle for the minus version of instanton knot Floer homology. Finally, we derive a new model of the minus version of instanton knot Floer homology, which takes the form of a free, finitely generated chain complex over a polynomial ring, as opposed to a direct limit. This construction is new to all of the Floer theories. We explore these results also in the context of Heegaard Floer theory as well.

math.GT↗

arXiv2023

Knot cobordism, torsion order and framed instanton homology

We construct cobordism maps for the \textit{minus} version of instanton knot homology associated to a \textit{specially decorated} knot cobordisms of arbitrary genus between two null-homologous knots in closed oriented $3$-manifolds. As an application of our construction, we recover an inequality between the torsion order of knots in instanton theory, which was originally established in Heegaard Floer theory by work of Juhász, Miller, and Zemke. We further use this inequality to compute the framed instanton Floer homology of any non-zero Dehn surgeries along an alternating knot of bridge index at most $3$.

math.GT↗

arXiv2023

Rational homology 3-spheres and SL(2,$\mathbb{C}$) representations

We use instanton gauge theory to prove that if $Y$ is a closed, orientable $3$-manifold such that $H_1(Y;\mathbb{Z})$ is nontrivial and either $2$-torsion or $3$-torsion, and if $Y$ is neither $\#^r \mathbb{RP}^3$ for some $r\geq 1$ nor $\pm L(3,1)$, then there is an irreducible representation $π_1(Y) \to \mathrm{SL}(2,\mathbb{C})$. We apply this to show that the Kauffman bracket skein module of a non-prime 3-manifold has nontrivial torsion whenever two of the prime summands are different from $\mathbb{RP}^3$, answering a conjecture of Przytycki (Kirby problem 1.92(F)) unless every summand but one is $\mathbb{RP}^3$. As part of the proof in the $2$-torsion case, we also show that if $M$ is a compact, orientable $3$-manifold with torus boundary whose rational longitude has order 2 in $H_1(M)$, then $M$ admits a degree-1 map onto the twisted $I$-bundle over the Klein bottle.

math.GT↗

arXiv2021

On the tau invariants in instanton and monopole Floer theories

We unify two existing approaches to the tau invariants in instanton and monopole Floer theories, by identifying $τ_{\mathrm{G}}$, defined by the second author via the minus flavors $\underline{\operatorname{KHI}}^-$ and $\underline{\operatorname{KHM}}^-$ of the knot homologies, with $τ_{\mathrm{G}}^{\sharp}$, defined by Baldwin and Sivek via cobordism maps of the $3$-manifold homologies induced by knot surgeries. We exhibit several consequences, including a relationship with Heegaard Floer theory, and use our result to compute $\underline{\operatorname{KHI}}^-$ and $\underline{\operatorname{KHM}}^-$ for twist knots.

math.GT↗

arXiv2021

Decomposing sutured monopole and Instanton Floer homologies

In this paper, we generalize the work of the second author and prove a grading shifting property, in sutured monopole and instanton Floer theories, for general balanced sutured manifolds. This result has a few consequences. First, we offer an algorithm that computes the Floer homologies of a family of sutured handle-bodies. Second, we obtain a canonical decomposition of sutured monopole and instanton Floer homologies and build polytopes for these two theories, which was initially achieved by Juhász for sutured (Heegaard) Floer homology. Third, we establish a Thurston-norm detection result for monopole and instanton knot Floer homologies, which were introduced by Kronheimer and Mrowka. The same result was originally proved by Ozsváth and Szabó for link Floer homology. Last, we generalize the construction of minus versions of monopole and instanton knot Floer homology, which was initially done for knots by the second author, to the case of links. Along with the construction of polytopes, we also proved that, for a balanced sutured manifold with vanishing second homology, the rank of the sutured monopole or instanton Floer homology bounds the depth of the balanced sutured manifold. As a corollary, we obtain an independent proof that monopole and instanton knot Floer homologies, as mentioned above, both detect fibred knots in $S^3$. This result was originally achieved by Kronheimer and Mrowka.

math.GT↗

arXiv2020

Detection and localization of Coronary Arterial Lesion with the Aid of Impedance Cardiography

In recent years, coronary artery disease is escalating and is likely to assume an epidemic proportion by 2030. Currently the reliable methods for detection of coronary arterial lesions are either conventional coronary angiogram (CAG) or MDCT (Multiple Detector Computed Tomography) coronary angiogram. Conventional CAG is an invasive procedure. Conventional CAG and CT (Computed Tomography) angiogram, both require expert supervision of either an interventional cardiologist or a radiologist. In this work, we have proposed a novel design and method for non-invasive detection and localization of coronary arterial lesion using Impedance Cardiography (ICG). The ICG signal recorded by the proposed device is used to extract feature points and compute augmentation index, amplitude and other time related parameters. The extracted features are used as input to a trained artificial neural network, for detection and prediction of coronary arterial lesions. The trained network generates specialized models, to be used for diagnosis of arterial lesions. The proposed methodology detects lesion in Left main coronary artery (LMCA), Left anterior descending artery (LAD), Diagonal branch, Left circumflex artery (LCX), and Right coronary artery (RCA) with an accuracy of 92%, 82%, 76%, 76%, 84% respectively. The proposed device could be also used by a common individual for detection of arterial lesion without any expert supervision, unassisted. The proposed algorithm eliminates the need of CAG for diagnosis of coronary arterial lesions (stenosis), and provides an insight into a new method for non-invasive monitoring of cardiovascular haemodynamics, detection and localization of coronary arterial lesion.

physics.med-ph↗

arXiv2019

Sensorless Real-Time Reduced Order Model Based Adaptive Maximum Power Tracking Pitch Controller for Grid Connected Wind Turbines

This paper presents a sensor-less maximum power tracking (MPT) pitch controller for grid connected Wind Turbine (WT). The main advantage of the proposed architecture is that the approach ensures smooth operation and thus minimizes the mechanical stress and damage on the WT during high wind speed and grid transient conditions. Simultaneously, it also: a) reduces transients in Point of Common Coupling (PCC) bus voltage, b) reduces rotor speed oscillations, and c) controls the output power of the wind turbine without exceeding its thermal limits. The approach can work without wind speed measurements. In order to consider the effect of grid variations at the PCC, the affected area in the grid is modeled as a study area (area of interest), and remaining area (external area) is modeled as frequency dependent reduced order model (FDROM). The reduced order model (ROM) is then used to estimate the reference speed. The proposed controller is designed using the error between actual speed of the generator and the reference speed, to ensure smooth operation and limit the speed and aerodynamic power at the rated values. The architecture is evaluated using wind farm integrated Kundur's two-area and IEEE-39 bus test systems using real-time digital simulator (RTDS).

eess.SY↗

arXiv2019

Real-time frequency based reduced order modeling of large power grid

Large power systems are complex and real-time modeling of the grid for electromagnetic simulation (EMT) studies is impractical. In general, there are methods that reduce large power system into an equivalent network that requires less computational resource, while preserving electromechanical (low frequency) and high frequency behavior of the original system. This can be achieved by modeling the area not of interest (external area) as a combination of Transient Stability Analysis (TSA) type phasor model equivalent and Frequency Dependent Network Equivalent (FDNE). TSA retains electromechanical behavior, whereas FDNE retains high frequency behavior of the original power system. To this effect, this paper introduces a method of developing FDNE based on an online recursive least squares (RLS) identification algorithm in z-domain, and modeling of reduced power systems as FDNE and as a combination of TSA and FDNE using real-time digital simulators.

eess.SP↗

arXiv2019

Development and Applicability of Online Passivity Enforced Wide-Band Multi-Port Equivalents For Hybrid Transient Simulation

This paper presents a method for developing single and multi-port frequency dependent network equivalent (FDNE) based on a passivity enforced online recursive least squares identification algorithm, which identifies the input admittance matrix in z-domain. Furthermore, with the proposed architecture, a real-time hybrid model of the reduced power system is developed that integrate transient stability analysis and FDNE. Main advantages of the proposed architecture are, it identifies the FDNE even with unknown network parameters in the frequency range of interest, and yet can be implemented directly due to discrete formulation while maintaining desired accuracy, stability, and passivity conditions. The accuracy and characteristics of the proposed method are verified by implementing on two-area, IEEE 39 and 68 bus power system models.

eess.SP↗