arXiv subjects

Amit Shah

Publications and source records attributed to Amit Shah.

At least 19 recordsLinked to original sources

arXiv2026

Quantum interference in a twisted high-Tc SQUID senses emergent interfacial order

Engineering artificial systems by twisting and stacking van der Waals materials has proven to be an excellent platform for exploring emergent quantum phenomena that can be significantly different from the constituents. Recent advances in the fabrication of high-quality twisted interfaces provide a unique opportunity to study the little-explored interfacial superconducting order in twisted cuprate superconductors. In our work, we fabricate superconducting quantum interference devices (SQUID) that utilize the twisted interface of $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$, a high-Tc cuprate superconductor. By measuring the magnetic field modulation of switching current and differential resistance, we find a $\mathrm{\pi}$ phase difference between the two Josephson junction arms of the SQUID reflecting chiral superconducting order -- a crucial aspect inaccessible to single Josephson junction devices of the past. Our observations also indicate co-tunneling of the Cooper pairs and a time-reversal symmetry-broken emergent superconducting order. Additionally, these SQUIDs are well suited for use as state-of-the-art flux sensors close to 77 K, achieving a flux noise sensitivity of $\sim$1.5 $\mathrm{\mu\Phi_0/\sqrt{Hz}}$. Stabilizing new superconducting orders using twisted interfaces and probing them using quantum interference opens new avenues to understanding the microscopic origin of unconventional superconductors. Our SQUID architecture is suitable for investigating the charge transport mechanisms and the symmetry of superconducting order at the interfaces of other systems, reflecting the broad applicability beyond cuprate superconductors.

cond-mat.supr-con↗

arXiv2025

Generalist vs Specialist Time Series Foundation Models: Investigating Potential Emergent Behaviors in Assessing Human Health Using PPG Signals

Foundation models are large-scale machine learning models that are pre-trained on massive amounts of data and can be adapted for various downstream tasks. They have been extensively applied to tasks in Natural Language Processing and Computer Vision with models such as GPT, BERT, and CLIP. They are now also increasingly gaining attention in time-series analysis, particularly for physiological sensing. However, most time series foundation models are specialist models - with data in pre-training and testing of the same type, such as Electrocardiogram, Electroencephalogram, and Photoplethysmogram (PPG). Recent works, such as MOMENT, train a generalist time series foundation model with data from multiple domains, such as weather, traffic, and electricity. This paper aims to conduct a comprehensive benchmarking study to compare the performance of generalist and specialist models, with a focus on PPG signals. Through an extensive suite of total 51 tasks covering cardiac state assessment, laboratory value estimation, and cross-modal inference, we comprehensively evaluate both models across seven dimensions, including win score, average performance, feature quality, tuning gain, performance variance, transferability, and scalability. These metrics jointly capture not only the models' capability but also their adaptability, robustness, and efficiency under different fine-tuning strategies, providing a holistic understanding of their strengths and limitations for diverse downstream scenarios. In a full-tuning scenario, we demonstrate that the specialist model achieves a 27% higher win score. Finally, we provide further analysis on generalization, fairness, attention visualizations, and the importance of training data choice.

cs.LG↗

arXiv2025

A Noise-Robust Model-Based Approach to T-Wave Amplitude Measurement and Alternans Detection

T-wave alternans (TWA) is a potential marker for sudden cardiac death, but its reliable analysis is often constrained to noise-free environments, limiting its utility in real-world settings. We explore model-based T-wave estimation to mitigate the impact of noise on TWA level. Detection was performed using a previous surrogate-based method as a benchmark and a new method based on a Markov model state transition matrix (STM). These were combined with a Modified Moving Average (MMA) method and polynomial T-wave modeling to enhance noise robustness. Methods were tested across a wide range of signal-to-noise ratios (SNRs), from -5 to 30 dB, and different noise types: baseline wander (BW), muscle artifacts (MA), electrode movement (EM), and respiratory modulation. Synthetic ECGs with known TWA levels were used: 0 uV for TWA-free and 30-72 uV for TWA-present signals. T-wave modeling improved estimation accuracy under noisy conditions. With EM noise at SNRs of -5 and 5 dB, mean absolute error (MAE) dropped from 62 to 49 uV and 27 to 25 uV, respectively (Mann-Whitney-U test, p < 0.05) with modeling applied. Similar improvements were seen with MA noise: MAE dropped from 100 to 70 uV and 26 to 23 uV. In detection, the STM method achieved an F1-score of 0.92, outperforming the surrogate-based method (F1 = 0.81), though both struggled under EM noise at -5 dB. Importantly, beyond SNR, detection performance depended on the number of beats analyzed. These findings show that combining model-based estimation with STM detection significantly improves TWA analysis under noise, supporting its application in ambulatory and wearable ECG monitoring.

physics.med-ph↗

arXiv2025

Tensor extriangulated categories

A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a notion of a biextriangulated functor $\mathcal{A} \times \mathcal{B} \to \mathcal{C}$, with compatibility conditions between the components. We have two versions of compatibility conditions, the stronger depending on the higher extensions of the extriangulated categories. We give many examples of tensor extriangulated categories. Finally, we generalise Balmer's classification of thick tensor ideals to tensor extriangulated categories.

math.CT↗

arXiv2024

Weak Waldhausen categories and a localization theorem

Waldhausen categories were introduced to extend algebraic $K$-theory beyond Quillen's exact categories. In this article, we modify Waldhausen's axioms so that it matches better with the theory of extriangulated categories, introducing a weak Waldhausen category and defining its Grothendieck group. Examples of weak Waldhausen categories include any extriangulated category, hence any exact or triangulated category, and any Waldhausen category. A key feature of this structure is that it allows for "one-sided" extriangulated localization theory, and thus enables us to extract right exact sequences of Grothendieck groups that we cannot obtain from the theory currently available. To demonstrate the utility of our Weak Waldhausen Localization Theorem, we give three applications. First, we give a new proof of the Extriangulated Localization Theorem proven by Enomoto--Saito, which is a generalization at the level of $K_0$ of Quillen's classical Localization Theorem for exact categories. Second, we give a new proof that the index with respect to an $n$-cluster tilting subcategory $\mathscr{X}$ of a triangulated category $\mathscr{C}$ induces an isomorphism between $K_0^{\mathsf{sp}}(\mathscr{X})$ and the Grothendieck group of an extriangulated substructure of $\mathscr{C}$. Last, we produce a weak Waldhausen $K_0$-generalization of a localization construction due to Sarazola that involves cotorsion pairs but allows for non-Serre localizations. We show that the right exact sequences of Grothendieck groups obtained from our Sarazola construction and the Extriangulated Localization Theorem agree under a common setup.

math.KT↗

arXiv2024

The index in $d$-exact categories

Starting from its original definition in module categories with respect to projective modules, the index has played an important role in various aspects of homological algebra, categorification of cluster algebras and $K$-theory. In the last few years, the notion of index has been generalised to several different contexts in (higher) homological algebra, typically with respect to a (higher) cluster-tilting subcategory $\mathcal{X}$ of the relevant ambient category $\mathcal{C}$. The recent tools of extriangulated and higher-exangulated categories have permitted some conditions on the subcategory $\mathcal{X}$ to be relaxed. In this paper, we introduce the index with respect to a generating, contravariantly finite subcategory of a $d$-exact category that has $d$-kernels. We show that our index has the important property of being additive on $d$-exact sequences up to an error term.

math.RT↗

arXiv2024

Pick-up and assembling of chemically sensitive van der Waals heterostructures using dry cryogenic exfoliation

Assembling atomic layers of van der Waals materials (vdW) combines the physics of two materials, offering opportunities for novel functional devices. Realization of this has been possible because of advancements in nanofabrication processes which often involve chemical processing of the materials under study; this can be detrimental to device performance. To address this issue, we have developed a modified micro-manipulator setup for cryogenic exfoliation, pick up, and transfer of vdW materials to assemble heterostructures. We use the glass transition of a polymer PDMS to cleave a flake into two, followed by its pick-up and drop to form pristine twisted junctions. To demonstrate the potential of the technique, we fabricated twisted heterostructure of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (BSCCO), a van der Waals high-temperature cuprate superconductor. We also employed this method to re-exfoliate NbSe$_2$ and make twisted heterostructure. Transport measurements of the fabricated devices indicate the high quality of the artificial twisted interface. In addition, we extend this cryogenic exfoliation method for other vdW materials, offering an effective way of assembling heterostructures and twisted junctions with pristine interfaces.

cond-mat.mes-hall↗

arXiv2024

The index with respect to a contravariantly finite subcategory

Cluster algebras are categorified by cluster categories, and $g$-vectors are categorified by the classic index with respect to cluster tilting subcategories. However, the recently introduced completed discrete cluster categories of Dynkin type $\mathbb{A}$ have a very limited supply of cluster tilting subcategories, so we define the index with respect to additive, contravariantly finite subcategories of which there are many more. This permits us to extend several strong results from the classic theory to completed discrete cluster categories of Dynkin type $\mathbb{A}$. Notably, the index with respect to the subcategory generated by a fan triangulation distinguishes between rigid objects. We also prove that our index is additive on triangles up to an error term. This extends the key property which permits the classic index to be used in the categorification of cluster algebras.

math.RT↗

arXiv2023

A resolution theorem for extriangulated categories with applications to the index

Quillen's Resolution Theorem in algebraic $K$-theory provides a powerful computational tool for calculating $K$-groups of exact categories. At the level of $K_0$, this result goes back to Grothendieck. In this article, we first establish an extriangulated version of Grothendieck's Resolution Theorem. Second, we use this Extriangulated Resolution Theorem to gain new insight into the index theory of triangulated categories. Indeed, we propose an index with respect to an extension-closed subcategory $\mathscr{N}$ of a triangulated category $\mathscr{C}$ and we prove an additivity formula with error term. Our index recovers the index with respect to a contravariantly finite, rigid subcategory $\mathscr{X}$ defined by J{\o}rgensen and the second author, as well as an isomorphism between $K_0^{\mathsf{sp}}(\mathscr{X})$ and the Grothendieck group of a relative extriangulated structure $\mathscr{C}_{R}^{\mathscr{X}}$ on $\mathscr{C}$ when $\mathscr{X}$ is $n$-cluster tilting. In addition, we generalize and enhance some results of Fedele. Our perspective allows us to remove certain restrictions and simplify some arguments. Third, as another application of our Extriangulated Resolution Theorem, we show that if $\mathscr{X}$ is $n$-cluster tilting in an abelian category, then the index introduced by Reid gives an isomorphism $K_0(\mathscr{C}_R^{\mathscr{X}}) \cong K_0^{\mathsf{sp}}(\mathscr{X})$.

math.KT↗

arXiv2023

SiamAF: Learning Shared Information from ECG and PPG Signals for Robust Atrial Fibrillation Detection

Atrial fibrillation (AF) is the most common type of cardiac arrhythmia. It is associated with an increased risk of stroke, heart failure, and other cardiovascular complications, but can be clinically silent. Passive AF monitoring with wearables may help reduce adverse clinical outcomes related to AF. Detecting AF in noisy wearable data poses a significant challenge, leading to the emergence of various deep learning techniques. Previous deep learning models learn from a single modality, either electrocardiogram (ECG) or photoplethysmography (PPG) signals. However, deep learning models often struggle to learn generalizable features and rely on features that are more susceptible to corruption from noise, leading to sub-optimal performances in certain scenarios, especially with low-quality signals. Given the increasing availability of ECG and PPG signal pairs from wearables and bedside monitors, we propose a new approach, SiamAF, leveraging a novel Siamese network architecture and joint learning loss function to learn shared information from both ECG and PPG signals. At inference time, the proposed model is able to predict AF from either PPG or ECG and outperforms baseline methods on three external test sets. It learns medically relevant features as a result of our novel architecture design. The proposed model also achieves comparable performance to traditional learning regimes while requiring much fewer training labels, providing a potential approach to reduce future reliance on manual labeling.

cs.LG↗

arXiv2023

The category of extensions and idempotent completion

Building on previous work, we study the splitting of idempotents in the category of extensions $\mathbb{E}\operatorname{-Ext}(\mathcal{C})$ associated to a pair $(\mathcal{C},\mathbb{E})$ of an additive category and a biadditive functor to the category of abelian groups. In particular, we show that idempotents split in $\mathbb{E}\operatorname{-Ext}(\mathcal{C})$ whenever they do so in $\mathcal{C}$, allowing us to prove that idempotent completions and extension categories are compatible constructions in a $2$-category-theoretic sense. Furthermore, we show that the exact category obtained by first taking the idempotent completion of an $n$-exangulated category $(\mathcal{C},\mathbb{E},\mathfrak{s})$, in the sense of Klapproth-Msapato-Shah, and then considering its category of extensions is equivalent to the exact category obtained by first passing to the extension category and then taking the idempotent completion. These two different approaches yield a pair of $2$-functors each taking small $n$-exangulated categories to small idempotent complete exact categories. The collection of equivalences that we provide constitutes a $2$-natural transformation between these $2$-functors. Similar results with no smallness assumptions and regarding weak idempotent completions are also proved.

math.CT↗

arXiv2022

Learning From Alarms: A Robust Learning Approach for Accurate Photoplethysmography-Based Atrial Fibrillation Detection using Eight Million Samples Labeled with Imprecise Arrhythmia Alarms

Atrial fibrillation (AF) is a common cardiac arrhythmia with serious health consequences if not detected and treated early. Detecting AF using wearable devices with photoplethysmography (PPG) sensors and deep neural networks has demonstrated some success using proprietary algorithms in commercial solutions. However, further advancement of this paradigm of continuous AF detection in ambulatory settings, towards a population-wide screening use case, still faces several challenges, one of which is the lack of large-scale labeled training data. To address this challenge, in this study, we propose to leverage AF alarms from bedside patient monitors to label concurrent PPG signals, resulting in the largest PPG-AF dataset so far (8.5M 30-second records from 24100 patients) and demonstrating a practical approach to build large labeled PPG datasets. Furthermore, we recognize that the AF labels thus obtained contain errors because of false AF alarms generated from imperfect built-in algorithms from bedside monitors. Dealing with label noise with unknown distribution characteristics in this case requires advanced algorithms. We, therefore, introduce and open source a novel loss design, the cluster membership consistency (CMC) loss, to mitigate label errors. By comparing CMC with state-of-the-art methods selected from a noisy label competition, we demonstrate its superiority in multiple aspects including handling label noise in PPG data, resilience to poor-quality signals, and computational efficiency.

eess.SP↗

arXiv2022

Krull-Remak-Schmidt decompositions in Hom-finite additive categories

An additive category in which each object has a Krull-Remak-Schmidt decomposition -- that is, a finite direct sum decomposition consisting of objects with local endomorphism rings -- is known as a Krull-Schmidt category. A Hom-finite category is an additive category $\mathcal{A}$ for which there is a commutative unital ring $k$, such that each Hom-set in $\mathcal{A}$ is a finite length $k$-module. The aim of this note is to provide a proof that a Hom-finite category is Krull-Schmidt, if and only if it has split idempotents, if and only if each indecomposable object has a local endomorphism ring.

math.RT↗

arXiv2022

Stratifying systems and Jordan-H\"{o}lder extriangulated categories

Stratifying systems, which have been defined for module, triangulated and exact categories previously, were developed to produce examples of standardly stratified algebras. A stratifying system $\Phi$ is a finite set of objects satisfying some orthogonality conditions. One very interesting property is that the subcategory $\mathcal{F}(\Phi)$ of objects admitting a composition series-like filtration with factors in $\Phi$ has the Jordan-H\"{o}lder property on these filtrations. This article has two main aims. First, we introduce notions of subobjects, simple objects and composition series for an extriangulated category, in order to define a Jordan-H\"{o}lder extriangulated category. Moreover, we characterise Jordan-H\"{o}lder, length, weakly idempotent complete extriangulated categories in terms of the associated Grothendieck monoid and Grothendieck group. Second, we develop a theory of stratifying systems in extriangulated categories. We define projective stratifying systems and show that every stratifying system $\Phi$ in an extriangulated category is part of a minimal projective one $(\Phi,Q)$. We prove that $\mathcal{F}(\Phi)$ is a length, Jordan-H\"{o}lder extriangulated category when $(\Phi,Q)$ satisfies a left exactness condition. We give several examples and answer a recent question of Enomoto--Saito in the negative.

math.RT↗

arXiv2022

Idempotent completions of $n$-exangulated categories

Suppose $(\mathcal{C},\mathbb{E},\mathfrak{s})$ is an $n$-exangulated category. We show that the idempotent completion and the weak idempotent completion of $\mathcal{C}$ are again $n$-exangulated categories. Furthermore, we also show that the canonical inclusion functor of $\mathcal{C}$ into its (resp. weak) idempotent completion is $n$-exangulated and $2$-universal among $n$-exangulated functors from $(\mathcal{C},\mathbb{E},\mathfrak{s})$ to (resp. weakly) idempotent complete $n$-exangulated categories. Furthermore, we prove that if $(\mathcal{C},\mathbb{E},\mathfrak{s})$ is $n$-exact, then so too is its (resp. weak) idempotent completion. We note that our methods of proof differ substantially from the extriangulated and $(n+2)$-angulated cases. However, our constructions recover the known structures in the established cases up to $n$-exangulated isomorphism of $n$-exangulated categories.

math.CT↗

arXiv2022

The category of extensions and a characterisation of $n$-exangulated functors

Additive categories play a fundamental role in mathematics and related disciplines. Given an additive category equipped with a biadditive functor, one can construct its category of extensions, which encodes important structural information. We study how functors between categories of extensions relate to those at the level of the original categories. When the additive categories in question are $n$-exangulated, this leads to a characterisation of $n$-exangulated functors. Our approach enables us to study $n$-exangulated categories from a $2$-categorical perspective. We introduce $n$-exangulated natural transformations and characterise them using categories of extensions. Our characterisations allow us to establish a $2$-functor between the $2$-categories of small $n$-exangulated categories and small exact categories. A similar result with no smallness assumption is also proved. We employ our theory to produce various examples of $n$-exangulated functors and natural transformations. Although the motivation for this article stems from representation theory and the study of $n$-exangulated categories, our results are widely applicable: several require only an additive category equipped with a biadditive functor with no extra assumptions; others can be applied by endowing an additive category with its split $n$-exangulated structure.

math.CT↗

arXiv2022

The index with respect to a rigid subcategory of a triangulated category

Palu defined the index with respect to a cluster tilting object in a suitable triangulated category, in order to better understand the Caldero-Chapoton map that exhibits the connection between cluster algebras and representation theory. We push this further by proposing an index with respect to a contravariantly finite, rigid subcategory, and we show this index behaves similarly to the classical index. Let $\mathcal{C}$ be a skeletally small triangulated category with split idempotents, which is thus an extriangulated category $(\mathcal{C},\mathbb{E},\mathfrak{s})$. Suppose $\mathcal{X}$ is a contravariantly finite, rigid subcategory in $\mathcal{C}$. We define the index $\mathrm{ind}_{\mathcal{X}}(C)$ of an object $C\in\mathcal{C}$ with respect to $\mathcal{X}$ as the $K_{0}$-class $[C]_{\mathcal{X}}$ in Grothendieck group $K_{0}(\mathcal{C},\mathbb{E}_{\mathcal{X}},\mathfrak{s}_{\mathcal{X}})$ of the relative extriangulated category $(\mathcal{C},\mathbb{E}_{\mathcal{X}},\mathfrak{s}_{\mathcal{X}})$. By analogy to the classical case, we give an additivity formula with error term for $\mathrm{ind}_{\mathcal{X}}$ on triangles in $\mathcal{C}$. In case $\mathcal{X}$ is contained in another suitable subcategory $\mathcal{T}$ of $\mathcal{C}$, there is a surjection $Q\colon K_{0}(\mathcal{C},\mathbb{E}_{\mathcal{T}},\mathfrak{s}_{\mathcal{T}}) \twoheadrightarrow K_{0}(\mathcal{C},\mathbb{E}_{\mathcal{X}},\mathfrak{s}_{\mathcal{X}})$. Thus, in order to describe $K_{0}(\mathcal{C},\mathbb{E}_{\mathcal{X}},\mathfrak{s}_{\mathcal{X}})$, it suffices to determine $K_{0}(\mathcal{C},\mathbb{E}_{\mathcal{T}},\mathfrak{s}_{\mathcal{T}})$ and $\operatorname{Ker} Q$. We do this under certain assumptions.

math.RT↗

arXiv2021

Grothendieck groups of $d$-exangulated categories and a modified Caldero-Chapoton map

A strong connection between cluster algebras and representation theory was established by the cluster category. Cluster characters, like the original Caldero-Chapoton (CC) map, are maps from certain triangulated categories to cluster algebras and they have generated much interest. Holm and J{\o}rgensen constructed a modified CC map from a sufficiently nice triangulated category to a commutative ring, which is a generalised frieze under some conditions. In their construction, a quotient $K_{0}^{sp}(\mathcal{T})/M$ of a Grothendieck group of a cluster tilting subcategory $\mathcal{T}$ is used. In this article, we show that this quotient is the Grothendieck group of a certain extriangulated category, thereby exposing the significance of it and the relevance of extriangulated structures. We use this to define another modified CC map that recovers the one of Holm--J{\o}rgensen. We prove our results in a higher homological context. Suppose $\mathcal{S}$ is a $(d+2)$-angulated category with subcategories $\mathcal{X}\subseteq\mathcal{T}\subseteq\mathcal{S}$, where $\mathcal{X}$ is functorially finite and $\mathcal{T}$ is $2d$-cluster tilting, satisfying some mild conditions. We show there is an isomorphism between the Grothendieck group $K_{0}(\mathcal{S},\mathbb{E}_{\mathcal{X}},\mathfrak{s}_{\mathcal{X}})$ of the category $\mathcal{S}$, equipped with the $d$-exangulated structure induced by $\mathcal{X}$, and the quotient $K_{0}^{sp}(\mathcal{T})/N$, where $N$ is the higher analogue of $M$ above. When $\mathcal{X}=\mathcal{T}$ the isomorphism is induced by the higher index with respect to $\mathcal{T}$ introduced recently by J{\o}rgensen. Thus, in the general case, we can understand the map taking an object in $\mathcal{S}$ to its $K_{0}$-class in $K_{0}(\mathcal{S},\mathbb{E}_{\mathcal{X}},\mathfrak{s}_{\mathcal{X}})$ as a higher index with respect to the rigid subcategory $\mathcal{X}$.

math.RT↗