arXiv subjects

Soham Ghosh

Publications and source records attributed to Soham Ghosh.

At least 19 recordsLinked to original sources

arXiv2026

Fault tolerance of quantum circuits with tensor networks and symplectic geometry

We develop an operator-algebraic framework for analyzing fault tolerance in quantum circuits and establish necessary and sufficient conditions for exact recovery of the ideal computation under a prescribed noise model. For prescribed circuit families and noise models, we derive a semidefinite program (SDP) based test whose infeasibility certifies that there does not exist any recovery map restoring its intended operation. For non-adaptive stabilizer circuits, analyzing the stabilizer symmetries of its components with symplectic geometry, we obtain closed-form detection and logical-effect matrices that characterize circuit distance algebraically. Applied to a finite Hastings--Haah honeycomb Floquet-code circuit, these matrices certify the dynamical encoding of two logical qubits and distance four under Pauli noise including measurement errors. Using these matrices, we then derive MacWilliams identities for circuit weight enumerators and obtain linear-programming (LP) upper bounds on circuit distance. Output-code constraints give additional Singleton-like bounds. Under independent and identically distributed (i.i.d.) depolarizing noise, the weight enumerators determine decoder failure probabilities and yield upper bounds on circuit pseudothresholds. Finally, we derive LP distance bounds for families of flag syndrome-extraction circuits specified by their CNOT orderings, by incorporating the $t$-flag criterion as additional linear constraints to the distance-bounding LP. An analytical CSS Hamming-code benchmark yields a tight distance-three bound attained by the Chao--Reichardt one-flag construction.

quant-ph↗

arXiv2026

A dimension bound towards the Casas-Alvero Conjecture

The Casas-Alvero conjecture predicts that every univariate polynomial over an algebraically closed field of characteristic zero sharing a common factor with each of its Hasse-Schmidt derivatives is a power of a linear polynomial. The conjecture for polynomials of a fixed degree $n$ is equivalent to the projective variety of such polynomials being one-dimensional. In this paper, we produce dimension bounds for this variety (in degree $n$) over any algebraically closed field of characteristic zero using an arithmetic invariant $B(n)$ of $n$. Consequently for infintely many degrees $n$, we show that the associated arithmetic Casas-Alvero scheme has finitely many rational points over any characteristic zero field. Along the way, we prove several rigidity results towards the conjecture and study arithmetic properties of $B(n)$.

math.AG↗

arXiv2026

Torelli theorem for the moduli spaces of twisted vector bundles on smooth projective curves

We prove Torelli theorems for moduli space of twisted vector bundles on smooth projective curves over an arbitrary field of characteristic $\neq 2$. A twisted Hitchin construction recovers the curve in higher rank and degree, with partial recovery of the twisting class. For rank two with trivial determinant, we recover the curve and the Brauer class from the moduli stack through an ordered Kummer cover and its polarized Jacobian torsor. For odd determinant on hyperelliptic curves, residual gerbes give a relative Desale--Ramanan construction without an actual determinant line bundle over the ground field. An intrinsic polarized Fano torsor recovers the curve and the class, and a corrected polarization obstruction recovers the determinant gerbe. We also give a twisted Newstead construction in genus two, with an explicit descent condition for its converse, and period--index applications. This is the second part in a series of two papers.

math.AG↗

arXiv2026

Torelli Theorem for moduli stacks of vector bundles on tame Deligne Mumford curves

We prove a Torelli theorem for full moduli stacks of vector bundles of rank at least three with fixed determinant on a smooth, proper, geometrically connected, tame Deligne--Mumford curve of coarse genus at least two over an arbitrary field $k$. We also prove a Torelli theorem for the full moduli stack of vector bundles of rank at least three of fixed-degree under an explicit compatibility hypothesis. The method is intrinsic to the stack: faithful special-linear linearizations recover Picard stacks, and determinants of tangent complexes recover the canonical principal polarization. This is the first part in a series of two papers.

math.AG↗

arXiv2026

Spatial Dependencies in Item Response Theory: Gaussian Process Priors for Ecological and Cognitive Measurement

Measurement validity in Item Response Theory depends on appropriately modeling dependencies between items when these reflect meaningful theoretical structures rather than random measurement error. In ecological assessment, citizen scientists identifying species across geographic regions exhibit systematic spatial patterns in task difficulty due to environmental factors. Similarly, in Author Recognition Tests, literary knowledge organizes by genre, where familiarity with science fiction authors systematically predicts recognition of other science fiction authors. Current spatial Item Response Theory methods, represented by the 1PLUS, 2PLUS, and 3PLUS model family, address these dependencies but remain limited by (1) binary response restrictions, and (2) conditional autoregressive priors that impose rigid local correlation assumptions, preventing effective modeling of complex spatial relationships. Our proposed method, Spatial Gaussian Process Item Response Theory (SGP-IRT), addresses these limitations by replacing conditional autoregressive priors with flexible Gaussian process priors that adapt to complex dependency structures while maintaining principled uncertainty quantification. SGP-IRT accommodates polytomous responses and models spatial dependencies in both geographic and abstract cognitive spaces, where items cluster by theoretical constructs rather than physical proximity. Simulation studies demonstrate improved parameter recovery, particularly for item difficulty estimation. Empirical applications show enhanced recovery of meaningful difficulty surfaces and improved measurement precision across psychological, educational, and ecological research applications.

stat.AP↗

arXiv2026

Characterizing Contractions and Weighted Blowdowns

This paper gives a partial answer to a question of Dan Abramovich: consider a proper morphism $f : \mathcal{X} \to \mathcal{Z}$ with connected fibers, between smooth separated Deligne--Mumford stacks, which defines an isomorphism away from a smooth effective Cartier divisor $\mathcal{E} \subseteq \mathcal{X}$. Then, is $f$ a weighted blowup? We confirm that $f$ is an ordinary smooth blowup when $\mathcal{X}$ and $\mathcal{Z}$ are smooth separated schemes of finite type over $\mathbb{C}$, and when $f :\mathcal{X} \to \mathcal{Z}$ is a representable morphism of smooth separated Deligne--Mumford stacks. Further, we show that $f$ is a weighted blowup when $\mathcal{X}$ and $\mathcal{Z}$ are smooth separated Deligne--Mumford surfaces, i.e., $\dim \mathcal{X} = \dim \mathcal{Z} = 2$. As an application we determine when a reduction morphism between Hassett moduli stacks of weighted stable curves is given by a blowup along a smooth center.

math.AG↗

arXiv2026

The Art of of Resilient Substation Design for 500 Year Storm Events Current State of the Art and Challenges for Floodplain Management and Infrastructure Hardening

This manuscript develops a unified, applications-oriented engineering framework for Substations of the Future that can withstand non-stationary 500-year flood events, addressing a critical gap in how erosion control, geotechnical stabilization, green infrastructure, and phased retrofit planning are currently treated in isolation. Electrical substations are among the most flood-exposed nodes in the bulk power system, with tens of thousands of U.S. assets located in 100 and 500-year FEMA floodplains, leading to cascading outages and large annualized economic losses under climate-amplified storms. In response, the paper consolidates several standalone engineering design essentials into a single multi-scalar resilience framework beginning with articulating concrete block (ACB) revetments for flexible, permeable erosion protection that support aquifer recharge and LEED-oriented heat-island mitigation. Lime, cement, and fly-ash-based soil stabilization is explored along with green infrastructure, including permeable hardscape, bioswales, and targeted floodplain preservation. A phased roadmap for resiliency upgrades for existing brownfield legacy substations through deployable barriers and pumps, perimeter ACB and drainage upgrades, yard re-grading and equipment elevation is also presented. Collectively, these elements operationalize resilience against 0.2 percent annual exceedance probability events while reducing life-cycle costs and delivering co-benefits in stormwater quality, habitat restoration, and long-term grid reliability.

eess.SY↗

arXiv2026

Pushing the Frontiers for Floating Solar Photovoltaics -- The Case for South America

Floating solar photovoltaic (FSPV) systems provide a land-efficient pathway to expand clean electricity access in energy-poor regions. South America has among the highest global FSPV potential (approx 38.26 TWh per million acres of water surface), yet deployment remains limited. This study presents a techno-socio-economic framework to assess FSPV for energy access, water security, and grid flexibility, with case studies in Nicaragua, Honduras, and Guyana. Estimated yields for 50 to 398 MW systems exceed 1,500 to 2,000 kWh per kW annually with capacity factors above 20 percent. At El Cajon, FSPV could significantly reduce emissions relative to fossil generation. Results show competitive costs with land-based PV when accounting for avoided land use, shared hydropower infrastructure, and water benefits. The framework also highlights co-location with hydropower and AI data centers, offering a scalable model for deployment in underserved regions.

eess.SY↗

arXiv2026

A Phased Development Framework Enabling Islanded Operation of Sustainable AI Data Centers With Onsite Grid-Following and Grid-Forming Energy Architectures

As hyperscale and colocation AI data centers continue to expand, the electric grid is increasingly required to support large, concentrated loads, with individual facilities ranging from 500 MW to 2 GW. Current projections estimate that approximately 50 GW of AI data center capacity will require grid connectivity in the United States by 2030. While prior research has extensively examined the environmental and operational impacts of AI data centers, as well as their potential role as grid-interactive assets, limited attention has been given to the challenges associated with their scalable deployment through engineering, procurement, and construction (EPC) processes. This manuscript addresses this gap by proposing a phased development framework for AI data center expansion. The approach is designed to enable developers to meet aggressive time-to-market objectives while navigating multi-year constraints associated with interconnection approvals and lead times associated with the procurement of component equipment. A modular construction architecture is presented, along with a detailed analysis of integrated energy systems and the role of hybrid on-site generation in supporting incremental capacity growth. Electromagnetic transient simulations (EMT) are used to evaluate system performance, demonstrating that a combination of on-site natural gas generation and grid-forming energy storage can reliably support data center operations during early and intermediate deployment phases. The study further examines the transition to full grid interconnection, including the capability of the data center to operate in islanded mode during grid disturbances. Finally, the manuscript compares grid-forming control strategies for system reconnection and restoration under varying conditions.

eess.SY↗

arXiv2026

Multivariate Varying-Coefficient BART with Graphical Horseshoe Priors

Modern multivariate regression problems involve several related outcomes whose regression effects are not only nonlinear, heterogeneous, and outcome-specific, but also where the residual dependence among outcomes is scientifically meaningful. Existing multivariate Bayesian tree-based methods typically address only part of this problem: some impose substantial sharing of tree architecture across outcomes, which is overly restrictive when responses depend on distinct predictors or effect modifiers, while others accommodate residual dependence but retain simpler mean structures. This paper develops multiVCBART, a multivariate varying-coefficient Bayesian additive regression tree framework that jointly models flexible outcome-specific coefficient surfaces and a sparse residual precision matrix. Each entry of the coefficient matrix $B(x)$ is represented by an independent BART ensemble, allowing predictor effects to vary nonlinearly with modifiers $x$ across outcomes, while a Graphical Horseshoe prior on the precision matrix $Ω$ captures parsimonious residual conditional dependence. To permit efficient computation, we introduce a sampler that reduces the multivariate Gaussian likelihood to a sequence of scalar pseudo-response updates, decoupling the tree backfitting from the Graphical Horseshoe step. Theoretically, we establish the first posterior contraction rates for a multivariate BART model with jointly estimated residual dependence, proving near-minimax adaptation to underlying smoothness and structural sparsity. Empirically, multiVCBART outperforms existing multivariate tree models and Bayesian SUR competitors on sparse, high-dimensional datasets. Finally, in a re-analysis of the Genomics of Drug Sensitivity in Cancer dataset, our method identifies distinct biomarker signals and recovers a coherent residual pharmacologic network.

stat.ME↗

arXiv2026

Voxtral Realtime

We introduce Voxtral Realtime, a natively streaming automatic speech recognition model that matches offline transcription quality at sub-second latency. Unlike approaches that adapt offline models through chunking or sliding windows, Voxtral Realtime is trained end-to-end for streaming, with explicit alignment between audio and text streams. Our architecture builds on the Delayed Streams Modeling framework, introducing a new causal audio encoder and Ada RMS-Norm for improved delay conditioning. We scale pretraining to a large-scale dataset spanning 13 languages. At a delay of 480ms, Voxtral Realtime achieves performance on par with Whisper, the most widely deployed offline transcription system. We release the model weights under the Apache 2.0 license.

cs.AI↗

arXiv2026

Voxtral TTS

We introduce Voxtral TTS, an expressive multilingual text-to-speech model that generates natural speech from as little as 3 seconds of reference audio. Voxtral TTS adopts a hybrid architecture that combines auto-regressive generation of semantic speech tokens with flow-matching for acoustic tokens. These tokens are encoded and decoded with Voxtral Codec, a speech tokenizer trained from scratch with a hybrid VQ-FSQ quantization scheme. In human evaluations conducted by native speakers, Voxtral TTS is preferred for multilingual voice cloning due to its naturalness and expressivity, achieving a 68.4\% win rate over ElevenLabs Flash v2.5. We release the model weights under a CC BY-NC license.

cs.AI↗

arXiv2026

Distributed Snitch Digital Twin-Based Anomaly Detection for Smart Voltage Source Converter-Enabled Wind Power Systems

Existing cyberattack detection methods for smart grids such as Artificial Neural Networks (ANNs) and Deep Reinforcement Learning (DRL) often suffer from limited adaptability, delayed response, and inadequate coordination in distributed energy systems. These techniques may struggle to detect stealthy or coordinated attacks, especially under communication delays or system uncertainties. This paper proposes a novel Snitch Digital Twin (Snitch-DT) architecture for cyber-physical anomaly detection in grid-connected wind farms using Smart Voltage Source Converters (VSCs). Each wind generator is equipped with a local Snitch-DT that compares real-time operational data with high-fidelity digital models and generates trust scores for measured signals. These trust scores are coordinated across nodes to detect distributed or stealthy cyberattacks. The performance of the Snitch-DT system is benchmarked against previously published Artificial Neural Network (ANN) and Deep Reinforcement Learning (DRL)-based detection frameworks. Simulation results using an IEEE 39-bus wind-integrated test system demonstrate improved attack detection accuracy, faster response time, and higher robustness under various cyberattack scenarios.

eess.SY↗

arXiv2026

Proof of the Casas-Alvero conjecture

The Casas-Alvero conjecture states that if $f(X)$ is a monic univariate polynomial of degree $d$ over a characteristic $0$ field $\mathbb{K}$ such that $\gcd(f, f_{i})$ is non-trivial for each $i=1, \dots, d-1$, then $f(X)=(X-α)^d$ for some $α\in \mathbb{K}$. In this paper, we prove the Casas-Alvero conjecture for polynomials of any degree $d\geq 3$ over any characteristic $0$ field, by using Koszul homology. Along the way we show existence of various "almost counterexamples" over $\mathbb{C}$, satisfying mildly weaker hypotheses, using Brouwer degree techniques.

math.AC↗

arXiv2026

Agentic AI Systems in Electrical Power Systems Engineering: Current State-of-the-Art and Challenges

Agentic AI systems have recently emerged as a critical and transformative approach in artificial intelligence, offering capabilities that extend far beyond traditional AI agents and contemporary generative AI models. This rapid evolution necessitates a clear conceptual and taxonomical understanding to differentiate this new paradigm. Our paper addresses this gap by providing a comprehensive review that establishes a precise definition and taxonomy for "agentic AI," with the aim of distinguishing it from previous AI paradigms. The concepts are gradually introduced, starting with a highlight of its diverse applications across the broader field of engineering. The paper then presents four detailed, state-of-the-art use case applications specifically within electrical engineering. These case studies demonstrate practical impact, ranging from an advanced agentic framework for streamlining complex power system studies and benchmarking to a novel system developed for survival analysis of dynamic pricing strategies in battery swapping stations. Finally, to ensure robust deployment, the paper provides detailed failure mode investigations. From these findings, we derive actionable recommendations for the design and implementation of safe, reliable, and accountable agentic AI systems, offering a critical resource for researchers and practitioners.

eess.SY↗

arXiv2026

Kovács' conjecture on characterization of projective space and hyperquadrics

We prove Kovács' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective space or the $p$-dimensional quadric hypersurface. We also prove a similar characterization involving symmetric powers instead of exterior powers. This provides a common generalization of Mori, Wahl, Cho-Sato, Andreatta-Wiśniewski, Kobayashi-Ochiai, and Araujo-Druel-Kovács type characterizations of such varieties.

math.AG↗

arXiv2026

Ministral 3

We introduce the Ministral 3 series, a family of parameter-efficient dense language models designed for compute and memory constrained applications, available in three model sizes: 3B, 8B, and 14B parameters. For each model size, we release three variants: a pretrained base model for general-purpose use, an instruction finetuned, and a reasoning model for complex problem-solving. In addition, we present our recipe to derive the Ministral 3 models through Cascade Distillation, an iterative pruning and continued training with distillation technique. Each model comes with image understanding capabilities, all under the Apache 2.0 license.

cs.CL↗

arXiv2025

Enhancing Grid Resilience for Giga-Watt Scale Data Centers Using High Voltage Circuit Breaker Operated Braking Resistors

As hyperscale and co-located data centers scale, the electric grid sees an increase in large, voltage-sensitive IT loads with these data center plant size ranging between 500 MW to 2 GW. A sudden loss of these loads as they switch to onsite UPS during grid voltage excursion events causes a grid frequency rise from generation and load imbalance, and a voltage rise because less power is flowing through the network. This paper proposes and theoretically demonstrates the use of high voltage circuit breaker operated braking resistors at data center transmission substations as an effective strategy in enhancing grid resilience under such large load loss scenarios. We developed a test bed to illustrate the dynamic behavior of the system with resistive braking on a gigawatt scale data center load cluster connected to a 345 kV network. The braking resistor(s), which in the case of inverter rich system comes in a multi-stage configuration, are connected or disconnected via high-speed circuit breaker(s). Results show that insertion for 0.25 to 0.85 seconds sufficiently reduce rate of change of frequency and provides time for primary governor response and capacitor switching to restore steady state. Sensitivity across different synchronous machines and inverter-based resource mix are tested and confirms robustness. We conclude circuit breaker controlled resistive braking is a practical means to enhance Bulk Electric System (BES) resilience for gigawatt scale data centers. The approach integrates with protection, needs no generator changes, and can be scaled with cluster size or growth of the data center facility load.

eess.SY↗