arXiv subjects

Rohan Sarkar

Publications and source records attributed to Rohan Sarkar.

At least 19 recordsLinked to original sources

arXiv2026

Heat content and spectrum for subordinated sub-Laplacians

We study heat content and spectral properties of subordinated sub-Laplacians on arbitrary Carnot groups. We consider restrictions of such operators to bounded open sets with zero Dirichlet boundary condition and study their spectral properties. In particular, for a large class of subordinators we give explicit eigenvalue estimates in terms of the subordinator and the eigenvalues of the sub-Laplacian. We also provide large-time asymptotics of the heat content for the subordinated sub-Laplacian in terms of its spectral gap. For fractional sub-Laplacians we prove short-time asymptotics for the corresponding heat content and relative heat content. Our approach combines semigroup methods, probabilistic techniques, geometric measure theory, and heat kernel estimates.

math.PR↗

arXiv2026

Operant Conditioning in Indian Free-Ranging Dogs: Effects of Positive and Threatening Cues on Sociability

Sociability toward humans is a key adaptive trait in free-ranging dogs, enabling them to access resources while navigating risks associated with human interactions. In this study, we investigated whether operant conditioning shapes sociability in Indian free-ranging dogs and whether learned responses generalize to unfamiliar individuals. We experimentally exposed 58 dog groups to either positive or a threatening cue over five consecutive days and assessed their behaviour using approach proportion, approach latency, and demeanor across repeated interactions with a familiar experimenter, followed by a test with an unfamiliar individual. Using Bayesian generalized linear mixed models, we found that cue type and repeated exposure significantly influenced sociability. Dogs exposed to a positive cue showed increased approach behaviour and reduced approach latency over time, along with increased affiliative demeanor. In contrast, dogs exposed to threatening cues exhibited reduced approach behaviour, increased approach latency, and a shift toward neutral and less affiliative responses across days. Importantly, positive cues partially generalized across individuals, as dogs showed increased approach toward an unfamiliar experimenter, although this was accompanied by hesitation to approach. In contrast, threatening cues did not generalize in the same way; dogs did not reduce their approach toward unfamiliar individuals but displayed increased approach latency, indicating heightened caution. Our findings demonstrate that operant conditioning plays a crucial role in shaping dog-human interactions, with asymmetric generalization of positive and threatening experiences.

q-bio.OT↗

arXiv2026

Fractional heat content asymptotics for Carnot groups

We propose a novel approach for studying small-time asymptotics of the fractional heat content of $C^2$ non-characteristic domains in Carnot groups. Denoting the sub-Laplacian operator by $\mathcal{L}$, the fractional heat content of a bounded domain $\Omega$ is defined as $Q^{(\alpha)}_\Omega(t)=\int_{\Omega}u_\alpha(x,t) dx$, where $u_\alpha$ is the solution to the heat equation corresponding to the fractional sub-Laplacian $\mathcal{L}_\alpha:=\mathcal{L}^{\alpha/2}$ with Dirichlet boundary condition on $\Omega$. We prove that for $1\le \alpha\le 2$, there exists explicit rate function $\mu_\alpha: (0,\infty)\to (0,\infty)$ such that \begin{align*} \lim_{t\to 0}\frac{|\Omega|-Q^{(\alpha)}_\Omega(t)}{\mu_\alpha(t)}=|\partial \Omega|_H, \end{align*} where $|\Omega|$, $|\partial \Omega|_H$ are the volume and horizontal perimeter of $\Omega$ respectively. Moreover, the rate function $\mu_\alpha$ coincides with the same for the Euclidean case.

math.AP↗

arXiv2025

Trick or Treat? Free-ranging dogs use human behavioural cues for foraging

Animals that display behavioural flexibility and adaptability thrive in urban environments, due to their ability to exploit novel anthropogenic resources. Since humans are an important component of such urban environments, animals that apply heterospecific learning in their decision-making are more likely to succeed as urban adapters. Free-ranging dogs, that have been living in human-dominated environments for centuries, are excellent urban adapters. In this study, we sought to understand the role and extent of human behavioural cues in decision-making during foraging by free-ranging dogs. We investigated whether these dogs were more attracted to items that humans appeared to be eating. When presented with a real and a fake biscuit, the dogs showed a clear preference for the food item. Between two identical biscuits, they chose the one that had been bitten by a human. However, when a fake biscuit was bitten and presented with a real one, the dogs failed to choose one over the other, suggesting a strong influence of the human-provided cue of biting over the natural cue of the smell of the food item. The dogs displayed left-bias during food choice across experimental conditions. These results demonstrate that dog foraging choices in urban environments are a mix of heterospecific learning and independent decision-making, highlighting an important facet behind their success in anthropogenic habitats. This also underscores the high level of dependence that free-ranging dogs have on humans in the urban habitat, not only as a source of food, but as an integral part of their ecological niche.

q-bio.OT↗

arXiv2025

Small time asymptotics of spectral heat content of isotropic processes

The spectral heat content of a domain $\Omega\subset\mathbb{R}^d$ corresponding to a $d$-dimensional stochastic process $X=(X_t)_{t\ge 0}$ is defined as \[Q^{X}_\Omega(t)=\int_{\mathbb{R}^d} \mathbb{P}_x(\tau^X_\Omega>t)dx,\] where $\tau^X_\Omega$ is the first exit time of $X$ from $\Omega$. We provide a novel technique for proving small time asymptotic of spectral heat content for any translation invariant isotropic process satisfying negligible tail probability condition. As a consequence, we recover several existing results in the context of L\'evy processes and Gaussian processes, and provide spectral heat content asymptotics for a class of $\alpha$-stable L\'evy processes time-changed by right inverse of positive, increasing, self-similar Markov processes. The latter has connection to some Cauchy problems that are non-local in both time and space.

math.PR↗

arXiv2025

Exploring Scavenging Strategies and Cognitive Problem-Solving in Indian Free-Ranging Dogs

Animals employ strategic decision-making while carefully weighing nutritional benefits against the risks presented by aversive or harmful stimuli in their natural environment, to maximize foraging efficiency, In India, free-ranging dogs subsist predominantly on human-generated waste, where they often encounter food contaminated with unpalatable or noxious substances such as lemon juice while scavenging. The strategies these dogs use to navigate such challenges remain poorly understood, yet are critical for understanding their ecological adaptability and survival in human-dominated environments. A total of 156 randomly encountered free-ranging adult dogs were tested across 15 sites in Nadia district, West Bengal. Each individual was exposed to a single food source containing chicken placed in either lemon juice, diluted lemon solution, or water. All trials were video-recorded, and the behavioural sequences of the dogs, including sniffing, licking, eating, and food manipulation were coded and analysed to quantify strategic foraging responses under unpalatable conditions. They were found to use a flexible, multi-pronged strategy to manipulate the comparatively less palatable food option, and typically avoid the most unpalatable one, to maximize their acquiring options. Overall, this study revealed a hierarchically structured and context-dependent foraging strategy of free-ranging dogs, propelled by sensory evaluation, risk-reward balancing, and behavioural flexibility. These findings demonstrated how urban scavengers dynamically adapt to aversive conditions while scavenging, underscoring the cognitive mechanisms that support their survival in human-dominated environments.

q-bio.OT↗

arXiv2025

Sight, smell and more: What cues do free-ranging dogs use for decision-making while scavenging?

Finding food is a fundamental activity for survival of all living organisms. Free-ranging dogs have been known to use their olfaction to assess the quality and type of available food but their use of visual ability in foraging is not well-documented. In the current study, we seek to remedy that by testing free-ranging dogs in a food-based choice test. We tested whether the dogs implemented hierarchical or synergistic usage of cues while finding food. We found limited prioritization of olfactory cues over visual cues in dichromatic choice tests but in phases with similar perceptual elements, the sensory choice was not clear. Furthermore, free-ranging dogs display a dynamic decision-making in unpredictable urban environments adopting a good-enough strategy during foraging. They prefer speed over accuracy, settling for intermediate quality food if their preferred food item is not available. These dogs also displayed left-bias during food choice. In multi-sensorial, natural setting multiple modulators like environmental noise, risk, and internal perceptual elements apart from food cues seem to be affecting the decision-making in dogs.

q-bio.NC↗

arXiv2025

Spectral theory for L\'evy and L\'evy-Ornstein-Uhlenbeck semigroups on step 2 Carnot groups

We consider non-local perturbations $\Delta^\psi_G$ of sub-Laplacians on a step $2$ Carnot group $G$. The perturbations are by translation-invariant non-local operators acting along the vertical directions in $G$. We use harmonic analysis on $G$ to obtain intertwining relationship between the semigroups generated by $\Delta^\psi_G$ and some strongly continuous contraction semigroups on Euclidean spaces with purely continuous spectrum, and as a result we identify the spectrum of $\Delta^\psi_G$. Further we introduce the L\'evy-Ornstein-Uhlenbeck (OU) semigroup corresponding to $\Delta^\psi_G$. We prove that these Markov semigroups are ergodic, though they are not normal operators on $L^2$ space with respect to the invariant distribution $\mathsf{p}_\psi$. The intertwining relationships allow us to show that all L\'evy-OU generators on $G$ are isospectral, that is, they have the same eigenvalues with the same multiplicities. As a byproduct, we obtain a precise description of the eigenspaces, and also derive explicit formula for the co-eigenfunctions corresponding to some eigenvalues.

math.PR↗

arXiv2025

Spectral theory of non-local Ornstein-Uhlenbeck operators

We consider non-local Ornstein-Uhlenbeck (OU) operators that correspond to Ornstein-Uhlenbeck processes driven by L\'evy processes. These are ergodic Markov processes and the OU operator is in general non-normal in the $L^2$ space weighted with the invariant distribution. Under some mild assumptions on the L\'evy process, we carry out in-depth analysis of the spectrum, spectral multilicities, eigenfunctions and co-eigenfunctions (eigenfunctions of the adjoint), and the existence of spectral expansion of the semigroups. When the drift matrix $B$ is diagonalizable, we derive explicit formulas for eigenfunctions and co-eigenfunctions which are also biorthogonal, and such results continue to hold when the L\'evy process is a pure jump process. A key ingredient in our approach is \emph{intertwining relationship}: we prove that every L\'evy-OU semigroup is intertwined with a diffusion OU semigroup. Additionally, we study the compactness properties of these semigroups and provide some necessary and sufficient conditions for compactness.

math.PR↗

arXiv2024

When Life Gives You Lemons, Squeeze Your Way Through: Understanding Citrus Avoidance Behaviour by Free-Ranging Dogs in India

Palatability of food is driven by multiple factors like taste, smell, texture, freshness, etc. and can be very variable across species. There are classic examples of local adaptations leading to speciation, driven by food availability. Urbanization across the world is causing rapid decline of biodiversity, while also driving local adaptations in some species. Free-ranging dogs are an interesting example of adaptation to a human-dominated environment across varied habitats. They have co-existed with humans for centuries and are a perfect model system for studying local adaptations. We attempted to understand a specific aspect of their scavenging behaviour in India: citrus aversion. Pet dogs are known to avoid citrus fruits and food contaminated by them. In India, lemons are used widely in the cuisine, and discarded in the garbage. Hence, free-ranging dogs, that typically are scavengers of human leftovers, are likely to encounter lemons and lemon-contaminated food on a regular basis. We carried out a population level experiment to test response of free-ranging dogs to chicken contaminated with various parts of lemon. The dogs avoided chicken contaminated with lemon juice the most. Further, when provided with chicken dipped in three different concentrations of lemon juice, the lowest concentration was most preferred. A survey confirmed that the local people use lemon in their diet extensively and also discard these with the leftovers. People avoided giving citrus contaminated food to their pets but did not follow the same caution for free-ranging dogs. This study revealed that free-ranging dogs in West Bengal, India, are well adapted to scavenging among citrus-contaminated garbage and have their own strategies to avoid the contamination as far as possible, while maximizing their preferred food intake.

q-bio.OT↗

arXiv2024

The mouth speaks as much as the eyes: Free-ranging dogs depend on inner facial features for human recognition

The human face is a multi-signal system continuously transmitting information of identity and emotion. In shared human-animal environments, the face becomes a reliable tool of heterospecific recognition. Because humans display mixed behaviour and pose differential risk to animals, adaptable decision-making based on recognition and classification of humans confer a fitness benefit. The human-dog dyad is an ideal model to study heterospecific recognition due to their shared history, niche overlap, and cognitive co-evolution. Multiple studies on pet dogs have examined their human facial information processing. However, no study has examined these perceptual abilities in free-living populations in their natural habitat where the human-dog relationship is more complex and impacts survival. Comprehensive behavioural analysis of 416 free-ranging dogs in an approach-based task with differential facial occlusion of a human, demonstrated that these dogs recognize and discriminate between familiar and unfamiliar people. Negative behaviours like aggression and avoidance were unlikely to be displayed. Inner facial components like eyes, nose and mouth were more important than outer components like hair in human recognition. Unlike in pet dogs, the occlusion of even a single inner component of the face prevented recognition by facial cue alone. Personality and habitat conditions influenced the behavioural strategy adopted by the dogs too. Considering the ambiguous nature of human interactions, recognition and response in free-ranging dogs relied on dual assessment of identity and intent of a human based, in part, on their ontogeny. Such a cue-processing system highlights the selection pressures inherent in the unpredictable environment of free-living populations.

q-bio.NC↗

arXiv2024

A Dataset and Framework for Learning State-invariant Object Representations

We add one more invariance - the state invariance - to the more commonly used other invariances for learning object representations for recognition and retrieval. By state invariance, we mean robust with respect to changes in the structural form of the objects, such as when an umbrella is folded, or when an item of clothing is tossed on the floor. In this work, we present a novel dataset, ObjectsWithStateChange, which captures state and pose variations in the object images recorded from arbitrary viewpoints. We believe that this dataset will facilitate research in fine-grained object recognition and retrieval of 3D objects that are capable of state changes. The goal of such research would be to train models capable of learning discriminative object embeddings that remain invariant to state changes while also staying invariant to transformations induced by changes in viewpoint, pose, illumination, etc. A major challenge in this regard is that instances of different objects (both within and across different categories) under various state changes may share similar visual characteristics and therefore may be close to one another in the learned embedding space, which would make it more difficult to discriminate between them. To address this, we propose a curriculum learning strategy that progressively selects object pairs with smaller inter-object distances in the learned embedding space during the training phase. This approach gradually samples harder-to-distinguish examples of visually similar objects, both within and across different categories. Our ablation related to the role played by curriculum learning indicates an improvement in object recognition accuracy of 7.9% and retrieval mAP of 9.2% over the state-of-the-art on our new dataset, as well as three other challenging multi-view datasets such as ModelNet40, ObjectPI, and FG3D.

cs.CV↗

arXiv2024

Dimension-independent functional inequalities by tensorization and projection arguments

We study stability under tensorization and projection-type operations of gradient-type estimates and other functional inequalities for Markov semigroups on metric spaces. Using transportation-type inequalities obtained by F. Baudoin and N. Eldredge in 2021, we prove that constants in the gradient estimates can be chosen to be independent of the dimension. Our results are applicable to hypoelliptic diffusions on sub-Riemannian manifolds and some hypocoercive diffusions. As a byproduct, we obtain dimension-independent reverse Poincar\'{e}, reverse logarithmic Sobolev, and gradient bounds for Lie groups with a transverse symmetry and for non-isotropic Heisenberg groups.

math.PR↗

arXiv2024

Dual Pose-invariant Embeddings: Learning Category and Object-specific Discriminative Representations for Recognition and Retrieval

In the context of pose-invariant object recognition and retrieval, we demonstrate that it is possible to achieve significant improvements in performance if both the category-based and the object-identity-based embeddings are learned simultaneously during training. In hindsight, that sounds intuitive because learning about the categories is more fundamental than learning about the individual objects that correspond to those categories. However, to the best of what we know, no prior work in pose-invariant learning has demonstrated this effect. This paper presents an attention-based dual-encoder architecture with specially designed loss functions that optimize the inter- and intra-class distances simultaneously in two different embedding spaces, one for the category embeddings and the other for the object-level embeddings. The loss functions we have proposed are pose-invariant ranking losses that are designed to minimize the intra-class distances and maximize the inter-class distances in the dual representation spaces. We demonstrate the power of our approach with three challenging multi-view datasets, ModelNet-40, ObjectPI, and FG3D. With our dual approach, for single-view object recognition, we outperform the previous best by 20.0% on ModelNet40, 2.0% on ObjectPI, and 46.5% on FG3D. On the other hand, for single-view object retrieval, we outperform the previous best by 33.7% on ModelNet40, 18.8% on ObjectPI, and 56.9% on FG3D.

cs.CV↗

arXiv2023

Shape of You: Precise 3D shape estimations for diverse body types

This paper presents Shape of You (SoY), an approach to improve the accuracy of 3D body shape estimation for vision-based clothing recommendation systems. While existing methods have successfully estimated 3D poses, there remains a lack of work in precise shape estimation, particularly for diverse human bodies. To address this gap, we propose two loss functions that can be readily integrated into parametric 3D human reconstruction pipelines. Additionally, we propose a test-time optimization routine that further improves quality. Our method improves over the recent SHAPY method by 17.7% on the challenging SSP-3D dataset. We consider our work to be a step towards a more accurate 3D shape estimation system that works reliably on diverse body types and holds promise for practical applications in the fashion industry.

cs.CV↗

arXiv2023

Weak Similarity Orbit of (log)-Self-Similar Markov Semigroups on the Euclidean Space

We start by identifying a class of pseudo-differential operators, generated by the set of continuous negative definite functions, that are in the weak similarity (WS) orbit of the self-adjoint log-Bessel operator on the Euclidean space. These WS relations turn out to be useful to first characterize a core for each operator in this class, which enables us to show that they generate a class, denoted by $\mathscr{P}$, of non-self-adjoint $\mathcal{C}_0$-contraction positive semigroups. Up to a homeomorphism, $\mathscr{P}$ includes, as fundamental objects in probability theory, the family of self-similar Markov semigroups on $\mathbb{R}_+^d$. Relying on the WS orbit, we characterize the nature of the spectrum of each element in $\mathscr{P}$ that is used in their spectral representation which depends on analytical properties of the Bernstein-gamma functions defined from the associated negative definite functions, and, it is either the point, residual, approximate or continuous spectrum. We proceed by providing a spectral representation of each element in $\ccP$ which is expressed in terms of Fourier multiplier operators and valid, at least, on a dense domain of a natural weighted $L^2$-space. Surprisingly, the domain is the full Hilbert space when the spectrum is the residual one, something which seems to be noticed for the first time in the literature. We end up the paper by presenting a series of examples for which all spectral components are computed explicitly in terms of special functions or recently introduced power series.

math.PR↗

arXiv2022

Eating Smart: Free-ranging dogs follow an optimal foraging strategy while scavenging in groups

Foraging and acquiring of food is a delicate balance between managing the costs, both energy and social, and individual preferences. Previous research on the solitary foraging of free ranging dogs showed that they prioritized the nutritionally highest valued food patch first but do not ignore other less valuable food either, displaying typical scavenger behaviour. The current experiment was carried out on groups of dogs with the same set up to see the change in foraging strategies, if any, under the influence of social cost like intra-group competition. We found multiple differences between the strategies of dogs foraging alone versus in groups with competition playing an implicit role in the decision making of dogs when foraging in groups. Dogs were able to continually assess and evaluate the available resources in a patch and adjust their behaviour accordingly. Foraging in groups also provided benefits of reduced individual vigilance. The various decisions and choices made seemed to have a basis in the optimal foraging theory wherein the dogs harvested the nutritionally richest patch possible with the least risk and cost involved but was willing to compromise if that was not possible. This underscores the cognitive, quick decision-making abilities and adaptable behaviour of these dogs.

q-bio.PE↗

arXiv2022

OutfitTransformer: Learning Outfit Representations for Fashion Recommendation

Learning an effective outfit-level representation is critical for predicting the compatibility of items in an outfit, and retrieving complementary items for a partial outfit. We present a framework, OutfitTransformer, that uses the proposed task-specific tokens and leverages the self-attention mechanism to learn effective outfit-level representations encoding the compatibility relationships between all items in the entire outfit for addressing both compatibility prediction and complementary item retrieval tasks. For compatibility prediction, we design an outfit token to capture a global outfit representation and train the framework using a classification loss. For complementary item retrieval, we design a target item token that additionally takes the target item specification (in the form of a category or text description) into consideration. We train our framework using a proposed set-wise outfit ranking loss to generate a target item embedding given an outfit, and a target item specification as inputs. The generated target item embedding is then used to retrieve compatible items that match the rest of the outfit. Additionally, we adopt a pre-training approach and a curriculum learning strategy to improve retrieval performance. Since our framework learns at an outfit-level, it allows us to learn a single embedding capturing higher-order relations among multiple items in the outfit more effectively than pairwise methods. Experiments demonstrate that our approach outperforms state-of-the-art methods on compatibility prediction, fill-in-the-blank, and complementary item retrieval tasks. We further validate the quality of our retrieval results with a user study.

cs.CV↗