arXiv subjects

Sumit Roy

Publications and source records attributed to Sumit Roy.

At least 19 recordsLinked to original sources

arXiv2026

Quadratic one-forms on logarithmic Higgs moduli

Let $C$ be a compact Riemann surface of genus at least two, and let $G$ be a connected complex reductive group. We study quadratic one-forms associated to logarithmic $G$-Higgs bundles on a pointed curve $(C,D)$ with nilpotent residues. We use the elementary pole cancellation for invariant polynomials, where nilpotency of the residue removes the leading pole term. In degree two this places $B(\Phi,\Phi)$ in the cotangent space of pointed Teichmuller space, and hence gives a logarithmic quadratic one-form. We relate this one-form to the variation of the energy for tame nilpotent harmonic bundles. The energy formula is proved under a positive decay assumption near the punctures. We also write the corresponding compact formulae for classical groups and standard real forms.

math.DG↗

arXiv2026

Semiprojectivity and very stability in moduli of symplectic and orthogonal parabolic Higgs bundles

Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. We prove the semiprojectivity of the moduli space of semistable symplectic or orthogonal parabolic Higgs bundles over $X$. We show that a stable symplectic parabolic bundle $E$ on $X$ is strongly very stable, meaning $E$ does not have any nonzero strongly parabolic nilpotent Higgs field, if and only if the symplectic parabolic Hitchin morphism induced on the affine space $$H^0(X,\mathrm{SPEnd}_\mathrm{Sp}(E) \otimes K(D))$$ is a proper morphism, where $\mathrm{SPEnd}_\mathrm{Sp}(E)$ denotes the set of symplectic strongly parabolic endomorphisms of $E$. We remark that the same criterion for very stability applies to the orthogonal case.

math.AG↗

arXiv2025

A mathematical model to predict growth and treatment for UPS cancer

We propose a mathematical model for the growth and treatment of Undifferentiated Pleomorphic Sarcoma (UPS) using a system of nonlinear differential equations. The model combines Gompertz-type tumor growth with surface-dependent necrotic loss, surgical resection with residual disease, postoperative recovery, tumor--immune interaction, and radiation treatment scheduling. We study the mathematical properties of the model and obtain several results. The growth equation shows the existence of a threshold below which the tumor cannot survive and may disappear. The postoperative phase exhibits an early inflammatory stage followed by proliferative recovery. For the tumor-immune subsystem, equilibrium states and local stability conditions are identified. The radiation treatment problem is formulated as an optimal control problem, and the optimal strategy is shown to be of bang-bang type. The model suggests that tumor recurrence depends not only on tumor growth itself but also on residual disease, postoperative dynamics, immune response, and treatment timing.

math.OC↗

arXiv2025

LEO Downlink Channel Model Revisited: Scattering Geometry-Inspired Derivation

This paper presents a new derivation of LEO-to-ground receiver channel model to address a clear gap in the prior art: the lack of an appropriate geometry aware characterization of non LOS (NLOS) link model represented by the power spectral density (PSD). Specifically, the main contribution is a coherent derivation of the PSD from 1st principles that is able to reproduce results in prior art and explain the causal relationship of main PSD features to the propagation geometry parameters.

eess.SP↗

arXiv2024

Revisiting Multi-User Downlink in IEEE 802.11ax: A Designers Guide to MU-MIMO

Downlink (DL) Multi-User (MU) Multiple Input Multiple Output (MU-MIMO) is a key technology that allows multiple concurrent data transmissions from an Access Point (AP) to a selected sub-set of clients for higher network efficiency in IEEE 802.11ax. However, DL MU-MIMO feature is typically turned off as the default setting in AP vendors' products, that is, turning on the DL MU-MIMO may not help increase the network efficiency, which is counter-intuitive. In this article, we provide a sufficiently deep understanding of the interplay between the various underlying factors, i.e., CSI overhead and spatial correlation, which result in negative results when turning on the DL MU-MIMO. Furthermore, we provide a fundamental guideline as a function of operational scenarios to address the fundamental question "when the DL MU-MIMO should be turned on/off".

cs.NI↗

arXiv2024

On some topological equivalences for moduli spaces of $G$-bundles

Let $X$ be a smooth projective curve of genus $g \geq 3$, and let $G$ be a nontrivial connected reductive affine algebraic group over $\mathbb{C}$. Examining the moduli spaces of regularly stable $G$-Higgs bundles and holomorphic $G$-connections with a fixed topological type $d\in \pi_1(G)$ over $X$, we establish that the $k$-th homotopy groups of these two moduli spaces are isomorphic for $k \leq 2g-4$. We also prove that the mixed Hodge structures on the rational cohomology groups of these two moduli spaces are pure and isomorphic. Lastly, we explicitly describe the homotopy groups of the moduli space of $\mathrm{SL}(n,\mathbb{C})$-connections over $X$.

math.AG↗

arXiv2023

IEEE 802.11be Network Throughput Optimization with Multi-Link Operation and AP Coordination

IEEE 802.11be (Wi-Fi 7) introduces a new concept called multi-link operation (MLO), which allows multiple Wi-Fi interfaces in different bands (2.4, 5, and 6 GHz) to work together to increase network throughput, reduce latency, and improve spectrum reuse efficiency in dense overlapping networks. To make the most of MLO, this paper proposes a new data-driven resource allocation algorithm for the 11be network with the aid of an access point (AP) controller. To maximize network throughput, a network topology optimization problem is formulated for 11be network, which is solved by exploiting the totally unimodular property of the bipartite graph formed by the connection between AP and station (STA) in Wi-Fi networks. Subsequently, a proportional fairness algorithm is applied for radio link allocation, network throughput optimization considering the channel condition, and the fairness of the multi-link device (MLD) data rate. The performance of the proposed algorithm on two main MLO implementations - multi-link multi-radio (MLMR) with simultaneous transmission and reception (STR), and the interplay between multiple nodes employing them are evaluated through cross-layer (PHY-MAC) data rate simulation with PHY abstraction.

cs.NI↗

arXiv2023

Topology of moduli of parabolic connections with fixed determinant

Let $X$ be a compact Riemann surface of genus $g \geq 2$ and $D\subset X$ be a fixed finite subset. Let $\xi$ be a line bundle of degree $d$ over $X$. Let $\mathcal{M}(\alpha, r, \xi)$ (respectively, $\mathcal{M}_{\mathrm{conn}}(\alpha, r, \xi)$) denote the moduli space of stable parabolic bundles (respectively, parabolic connections) of rank $r$ $(\geq 2)$, determinant $\xi$ and full flag generic parabolic weight type $\alpha$. We show that $ \pi_k(\mathcal{M}_{\mathrm{conn}}(\alpha, r, \xi)) \cong \pi_k(\mathcal{M}(\alpha, r, \xi)) $ for $k \leq2(r-1)(g-1)-1$. As a consequence, we deduce that the moduli space $\mathcal{M}_{\mathrm{conn}}(\alpha, r, \xi)$ is simply connected. We also show that the Hodge structures on the torsion-free parts of both the cohomologies $H^k(\mathcal{M}_{\mathrm{conn}}(\alpha, r, \xi),\mathbb{Z})$ and $H^k(\mathcal{M}(\alpha, r, \xi),\mathbb{Z})$ are isomorphic for all $k\leq 2(r-1)(g-1)+1$.

math.AG↗

arXiv2023

Semiprojectivity of the moduli of principal $G$-bundles with $\lambda$-connections

Let $X$ be a compact connected Riemann surface of genus $g \geq 2$ and $G$ a connected reductive affine algebraic group over $\mathbb{C}$. We prove the semiprojectivity of the moduli spaces of semistable $G$-Higgs bundles and $G$-bundles with $\lambda$-connections of fixed topological type $d\in \pi_1(G)$. As an application, in the smooth case we describe the resulting Bialynicki - Birula decomposition and derive cohomological and motivic consequences.

math.AG↗

arXiv2023

On motives of parabolic Higgs bundles and parabolic connections

Let $X$ be a compact Riemann surface of genus $g \geq 2$ and let $D\subset X$ be a fixed finite subset. We considered the moduli spaces of parabolic Higgs bundles and of parabolic connections over $X$ with the parabolic structure over $D$. For generic weights, we showed that these two moduli spaces have equal Grothendieck motivic classes and their $E$-polynomials are the same. We also show that the Voevodsky and Chow motives of these two moduli spaces are also equal. We showed that the Grothendieck motivic classes and the $E$-polynomials of parabolic Higgs moduli and of parabolic Hodge moduli are closely related. Finally, we considered the moduli spaces with fixed determinants and showed that the above results also hold for the fixed determinant case.

math.AG↗

arXiv2023

Static Background Removal in Vehicular Radar: Filtering in Azimuth-Elevation-Doppler Domain

Anti-collision assistance, integral to the current drive towards increased vehicular autonomy, relies heavily on precise detection and localization of moving targets in the vehicle's vicinity. A crucial step towards achieving this is the removal of static objects from the scene, thereby enhancing the detection and localization of dynamic targets - a pivotal aspect in augmenting overall system performance. In this paper, we propose a static background removal algorithm tailored for automotive scenarios, designed for common frequency-modulated continuous wave (FMCW) radars. This algorithm effectively eliminates reflections corresponding to static backgrounds from radar images through a two-step process: 4-dimensional (4D) radar imaging and filtering in the azimuth-elevation-Doppler domain. Our proposed approach is underpinned by a model customized for FMCW radar signals, incorporating a time-division multiplexing-based multiple-input multiple-output scheme on the non-uniform radar array. Furthermore, our filtering process requires knowledge of the 3-dimensional (3D) radar ego-motion velocity, typically obtained from an external sensor. To address scenarios where such sensors are unavailable, we introduce a self-contained 3D ego-motion estimation approach. Finally, we evaluate the performance of our algorithm using both simulated and real-world data, analyzing its sensitivity and time complexity in comparison to established baselines.

eess.SP↗

arXiv2023

On torsion-freeness of K\"{a}hler differential sheaves

Let $X$ be a normal algebraic variety over an algebraically closed field $k$ of characteristic zero. We prove that the K\"{a}hler differential sheaf of $X$ is torsion-free if and only if any regular section of the ideal sheaf of the first order deformation of $X$ inside $X\times_k X$, defined outside the singular locus of $X \times_k X$, extends regularly to the singular locus.

math.AG↗

arXiv2023

Mutual Interference Mitigation for MIMO-FMCW Automotive Radar

This paper considers mutual interference mitigation among automotive radars using frequency-modulated continuous wave (FMCW) signal and multiple-input multiple-output (MIMO) virtual arrays. For the first time, we derive a general interference signal model that fully accounts for not only the time-frequency incoherence, e.g., different FMCW configuration parameters and time offsets, but also the slow-time code MIMO incoherence and array configuration differences between the victim and interfering radars. Along with a standard MIMO-FMCW object signal model, we turn the interference mitigation into a spatial-domain object detection under incoherent MIMO-FMCW interference described by the explicit interference signal model, and propose a constant false alarm rate (CFAR) detector. More specifically, the proposed detector exploits the structural property of the derived interference model at both \emph{transmit} and \emph{receive} steering vector space. We also derive analytical closed-form expressions for probabilities of detection and false alarm. Performance evaluation using both synthetic-level and phased array system-level simulation confirms the effectiveness of our proposed detector over selected baseline methods.

eess.SP↗

arXiv2022

Optimal Beam Training for mmWave Massive MIMO using 802.11ay

Beam training of 802.11 ad is a technology that helps accelerate the analog weighting vector (AWV) selection process under the constraint of the existing code-book for AWV. However, 5G milli-meter wave (mmWave) multiple-input-multiple-output (MIMO) system brings challenges to this new technology due to the higher order of complexity of antennae. Hence, the existing codebook of 11ad is unlikely to even include the near-optimal AWV and the data rate will degrade severely. To cope with this situation, this paper proposed a new beam training protocol combined with the state-of-the-art compressed sensing channel estimation in order to find the AWV to maximize the optimal data-rate. Simulation is implemented to show the data-rate of AWV achieved by 11 ad is worse than the proposed protocol.

cs.IT↗

arXiv2022

Spectral data for parabolic projective symplectic/orthogonal Higgs bundles

Hitchin in [Duke Math. J. 54 (1), 91-114 (1987)] introduced a proper morphism from the moduli space of stable $G$-Higgs bundles ($G=\mathrm{GL}(n,\mathbb{C}),\mathrm{Sp}(2m,\mathbb{C})$ and $\mathrm{SO}(n,\mathbb{C})$) over a curve to a vector space of invariant polynomials and he described the generic fibers of that morphism. In this paper, we first describe the generic Hitchin fibers for the moduli space of stable parabolic projective symplectic/orthogonal Higgs bundles without fixing the determinant. We also describe the generic fibers when the determinant is trivial.

math.AG↗

arXiv2022

Picard group of moduli of parabolic Higgs bundles

Let $X$ be a compact Riemann surface of genus $g\geq 3$ and let $\mathcal{M}_{\mathrm{par}}$ be the moduli space of semistable parabolic bundles over $X$. Let $\mathcal{M}_{\mathrm{parH}}$ denote the moduli space of semistable parabolic Higgs bundles over $X$. In this article, we study the Picard group of $\mathcal{M}_{\mathrm{par}}$ and $\mathcal{M}_{\mathrm{parH}}$.

math.AG↗

arXiv2022

Architecture-Algorithmic Trade-offs in Multi-path Channel Estimation for mmWAVE Systems

5G mmWave massive MIMO systems are likely to be deployed in dense urban scenarios, where increasing network capacity is the primary objective. A key component in mmWave transceiver design is channel estimation which is challenging due to the very large signal bandwidths (order of GHz) implying significant resolved spatial multipath, coupled with large # of Tx/Rx antennas for large-scale MIMO. This results in significantly increased training overhead that in turn leads to unacceptably high computational complexity and power cost. Our work thus highlights the interplay of transceiver architecture and receiver signal processing algorithm choices that fundamentally address (mobile) handset power consumption, with minimal degradation in performance. We investigate trade-offs enabled by conjunction of hybrid beamforming mmWave receiver and channel estimation algorithms that exploit available sparsity in such wideband scenarios. A compressive sensing (CS) framework for sparse channel estimation -- Binary Iterative Hard Thresholding (BIHT) \cite{jacques2013robust} followed by linear reconstruction method with varying quantization (ADC) levels -- is explored to compare the trade-offs between bit-depth and sampling rate for a given ADC power budget. Performance analysis of the BIHT+ linear reconstruction method is conducted via simulation studies for 5G specified multi-path channel models and compared to oracle-assisted bounds for validation.

cs.IT↗

arXiv2022

Multi-Access Point Coordination for Next-Gen Wi-Fi Networks Aided by Deep Reinforcement Learning

Wi-Fi in the enterprise - characterized by overlapping Wi-Fi cells - constitutes the design challenge for next-generation networks. Standardization for recently started IEEE 802.11be (Wi-Fi 7) Working Groups has focused on significant medium access control layer changes that emphasize the role of the access point (AP) in radio resource management (RRM) for coordinating channel access due to the high collision probability with the distributed coordination function (DCF), especially in dense overlapping Wi-Fi networks. This paper proposes a novel multi-AP coordination system architecture aided by a centralized AP controller (APC). Meanwhile, a deep reinforcement learning channel access (DLCA) protocol is developed to replace the binary exponential backoff mechanism in DCF to enhance the network throughput by enabling the coordination of APs. First-Order Model-Agnostic Meta-Learning further enhances the network throughput. Subsequently, we also put forward a new greedy algorithm to maintain proportional fairness (PF) among multiple APs. Via the simulation, the performance of DLCA protocol in dense overlapping Wi-Fi networks is verified to have strong stability and outperform baselines such as Shared Transmission Opportunity (SH-TXOP) and Request-to-Send/Clear-to-Send (RTS/CTS) in terms of the network throughput by 10% and 3% as well as the network utility considering proportional fairness by 28.3% and 13.8%, respectively.

eess.SY↗