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Chandan Biswas

Publications and source records attributed to Chandan Biswas.

10 recordsLinked to original sources

Freezing of Gait Prediction Under Spatial Occlusion: An IMU-Supervised Cross-Modal Distillation Approach

Parkinson's disease is a progressive neurodegenerative disorder characterised by gradual deterioration of movement control. Automated freezing-of-gait (FOG) detection supports the objective assessment of gait-related motor impairment. Two common approaches are used for FOG prediction: (i) analysing video recordings of the patient's movements and (ii) analysing data collected using inertial measurement unit (IMU) wearable sensors attached to the patient's lower limbs. Video-based approaches may suffer detection errors during continuous turning-in-place tasks because the lower limbs undergo substantial geometric self-occlusion, degrading pose-estimation accuracy. IMU-based approaches are generally less affected by visual occlusion; however, they are difficult to deploy outside clinical or laboratory settings, as the sensors must be attached securely and remain in place throughout the assessment. Motivated by this, we propose a cross-modal subspace distillation framework to mitigate the limitations of unimodal FOG detection by combining IMU accuracy with video-based practicality. We extract invariant latent topologies from a pre-trained kinematic oracle to structurally supervise a non-encoded visual architecture during training. To resolve periods of severe spatial occlusion, a dual-stream visual model probabilistically fuses skeletal graph nodes and continuous spatial pixels, dynamically shifting reliance to uninterrupted pixel boundaries as joint tracking confidence drops. Evaluated against a public, multi-modal sequence dataset of Parkinson's individuals executing continuous $360^\circ$ turns, empirical results demonstrate that applying sensory boundary topologies strictly mitigates tracking evaluation entropy. Our constrained optimisation confirms that highly precise FOG prediction bounds can be achieved over zero-wearable inference environments.

cs.CV

Supervised Cross-Modal Feature Alignment for Zero-Wearable Freezing of Gait Detection in Parkinsonism

Objective assessment of Freezing of Gait (FoG) in Parkinson's disease (PD) relies predominantly on wearable Inertial Measurement Units (IMUs). While IMUs provide optimal kinematic precision, mandatory sensor attachment restricts continuous clinical deployment. Conversely, unobtrusive vision-based alternatives suffer substantial classification errors during turning-in-place tasks, where geometric self-occlusion degrades deterministic skeletal coordinates and obscures the high-frequency precursors required for FoG detection. To resolve these physical observation limits, we propose a supervised cross-modal subspace distillation framework. During optimisation, pre-trained kinematic data from IMU sensors and contextual clinical metadata act as oracles to guide a deployable visual architecture. By incorporating joint velocity and acceleration derivatives, utilising a confidence-based gating mechanism, the visual model mitigates some of the tracking errors during occlusion events. Empirical evaluations confirm this latent alignment transfers the predictive fidelity of hardware sensors directly into the visual representation, yielding $85.5\%$ accuracy, and $82.4\%$ balanced accuracy. All the while maintaining a vision only model at inference.

cs.CV

Sharp endpoint extension inequalities for the moment curve on finite fields

We investigate the sharp endpoint extension inequality for the moment curve in finite fields. We determine the optimal constant and characterize the maximizers in two complementary regimes: (i) low dimensions $d\leq 20$; (ii) large field cardinality $q\geq \frac{d(d-1)}{2 \log 6} + \frac{(2d-1)}{3}$. Our proof strategy relies on an intriguing interplay between analysis, algebra and combinatorics.

math.CA

Sharp Fourier restriction to monomial curves

We establish lower bounds for the operator norms of the Fourier restriction/extension operators associated to monomial curves with affine arclength measure. Furthermore, we prove that the set of all extremizing sequences of such an operator is precompact modulo the operator's symmetry group if and only if the operator norm is strictly larger than this threshold. For the proof, we introduce a number of new ingredients, some of which may be applicable to analogous questions on more general manifolds.

math.CA

Approximate Nearest Neighbour Search on Privacy-aware Encoding of User Locations to Identify Susceptible Infections in Simulated Epidemics

Amidst an increasing number of infected cases during the Covid-19 pandemic, it is essential to trace, as early as possible, the susceptible people who might have been infected by the disease due to their close proximity with people who were tested positive for the virus. This early contact tracing is likely to limit the rate of spread of the infection within a locality. In this paper, we investigate how effectively and efficiently can such a list of susceptible people be found given a list of infected persons and their locations. To address this problem from an information retrieval (search) perspective, we represent the location of each person at each time instant as a point in a vector space. By using the locations of the given list of infected persons as queries, we investigate the feasibility of applying approximate nearest neighbour (ANN) based indexing and retrieval approaches to obtain a list of top-k suspected users in real-time. Since leveraging information from true user location data can lead to security and privacy concerns, we also investigate what effects does distance-preserving encoding methods have on the effectiveness of the ANN methods. Experiments conducted on real and synthetic datasets demonstrate that the top-k retrieved lists of susceptible users retrieved with existing ANN approaches (KD-tree and HNSW) yield satisfactory precision and recall values, thus indicating that ANN approaches can potentially be applied in practice to facilitate real-time contact tracing even under the presence of imposed privacy constraints.

cs.IR

Compactness of a restricted X-ray transform

We show that the X-ray transform with directions restricted along the moment curve possesses extremizers and that $L^p$-normalized extremizing sequences are precompact modulo symmetry. Our approach advances the Lorentz space method of Christ to a mixed norm Lebesgue space setting.

math.CA

Existence of extremizers for a model convolution operator

The operator $T$, defined by convolution with the affine arc length measure on the moment curve parametrized by $h(t)=(t,t^{2},...,t^{d})$ is a bounded operator from $L^{p}$ to $L^{q}$ if $(\frac{1}{p}, \frac{1}{q})$ lies on a line segment. In this article we prove that at non-end points there exist functions which extremize the associated inequality and any extremizing sequence is pre compact modulo the action of the symmetry of $T$. We also establish a relation between extremizers for $T$ at the end points and the extremizers of an X-ray transform restricted to directions along the moment curve. Our proof is based on the ideas of Michael Christ on convolution with the surface measure on the paraboloid.

math.CA

$\ell^2$ Decoupling in $\mathbb R^2$ for curves with Vanishing Curvature

We expand the class of curves $(φ_1(t),φ_2(t)),\ t\in[0,1]$ for which the $\ell^2$ decoupling conjecture holds for $2\leq p\leq 6$. Our class of curves includes all real-analytic regular curves with isolated points of vanishing curvature and all curves of the form $(t,t^{1+ν})$ for $ν\in (0,\infty)$.

math.CA

A Simple Kontinuitätssatz

We are interested in several informal statements referred as "Kontinuitätssatz" in the recent literature on analytic continuation. The basic (unstated) principle that seems to be in use in these works appears to be a folk theorem. We provide a precise statement of this folk Kontinuitätssatz and give a proof of it.

math.CV