arXiv subjects

Arindam Mandal

Publications and source records attributed to Arindam Mandal.

At least 19 recordsLinked to original sources

arXiv2025

Approximation property in terms of Lipschitz maps via tensor product approach

This article explores the extension of the classical approximation property and its variants to the nonlinear framework of Lipschitz operator theory. Building on Grothendieck's tensor product methodology, we characterize the Lipschitz approximation property of Banach spaces using Lipschitz finite-rank operators and tensor products. Furthermore, inspired by the $p$-approximation property defined via $p$-compact sets, we introduce and examine the Lipschitz $p$-approximation property. We also establish a factorization theorem for dual Lipschitz $p$-compact operators, mirroring known linear results. This paper looks more closely at how the Lipschitz approximation property and the $p$-approximation property of a Banach space are related to those of its Lipschitz-free space.

math.FA↗

arXiv2025

Projection from space of \emph{two-Lipschitz} operators onto the space of Bilinear maps

In this article, we establish the existence of a norm-one projection from the space of all \emph{two-Lipschitz} operators onto the space of all bounded bilinear operators under certain conditions on the corresponding codomain spaces, using the method of invariant means. We also show that, when the codomain is an injective Banach space, the quotient of the \emph{two-Lipschitz} operator space by the bounded bilinear space is isometrically isomorphic to a specific operator space, via vector-valued duality. We conclude by proving a necessary and sufficient condition for a \emph{two-Lipschitz} operator to be a bilinear map. As an application of the theory developed here, we present an alternative proof that $\bigslant{L^{\infty}(\mathbb{R}\times \mathbb{R})}{span\{\textbf{1}\}}$ is a dual space.

math.FA↗

arXiv2025

A Proper Closed Subspace of the Lipschitz Dual Containing the Linear Dual

Motivated by classical results of Lindenstrauss and recent developments by Karn and Mandal, we investigate quotient spaces of the form $Lip_0(X)/\mathcal{A}$, where $\mathcal{A}$ is a finite-dimensional subspace, showing that these quotients are dual spaces with explicitly describable preduals. We then focus on $Lip_0^{ph}(X)$, the space of positively homogeneous real-valued Lipschitz functions. This space satisfies $ X^* \subsetneq Lip_0^{ph}(X) \subsetneq Lip_0(X), $ and is shown to be both a dual space and the preannihilator of a closed subspace of the Lipschitz-free space. Consequently it follows that $\bigslant{Lip_0(X)}{Lip_0^{ph}(X)}$ is also a dual space. Furthermore, with a suitable multiplication, $(Lip_0^{ph}(X), Lip(\cdot))$ forms a Banach algebra, exhibiting structural advantages over $Lip_0(X)$.

math.FA↗

arXiv2025

Techno economic feasibility study of solar ORC in India

Solar energy has enormous potential because there is a worldwide need to meet energy demands. Depleting non-renewable energy resources, increasing carbon emissions, and other environmental effects concern the scientific community to develop an alternative approach to electricity production. In this article, we present the study of a solar-powered Organic Rankine cycle considering Indian climatic conditions. Initially, we scrutinized seven working fluids and assessed their performance in the ORC at an evaporator pressure range of 9-30 bar and a mass flow rate range of 0.2 kg/s to 4.5 kg/s. For a fixed sink temperature of 298 K, we evaluate the system using four different power ratings of 2, 20, 50, and 100 kW based on four different source temperatures of 423 K, 403 K, 383 K, and 363 K. We estimate the system cost for each working fluid in each scenario separately. Our findings suggest that R 1233zd(E) is the optimum performing working fluid based on cost, cost-effectiveness, and environmental friendliness. We also notice that the estimated system scale cost is very competitive and could be a great alternative to the technologies already on the Indian market.

physics.soc-ph↗

arXiv2025

Position of $L(X, Y)$ in $Lip_0(X, Y)$

We prove that $L(X,Y)$ is complemented in $Lip_0(X, Y)$ (via a norm-one projection) provided that $Y$ is a dual space. Next, we introduce a vector-valued Lipschitz-free space $F_Y(X)$, a linear contraction $β_X^Y: F_Y(X) \to Y$ and prove that the quotient space ${Lip_{0}(X, Y)}/{L(X, Y) }$ is isometrically isomorphic to $L(\ker(β_X^Y), Y)$ whenever $Y$ is injective. We also consider a $Y$-valued duality pairing between $Lip_0(X, Y)$ and $F_Y(X)$ and obtain a necessary and sufficient condition for a Lipschitz map to be linear. As an application, we describe $\ker(β_{\mathbb{R}}^{\mathbb{R}})$ as the pre-dual of the quotient space $L^{\infty}(\mathbb{R})/\tilde{\mathbb{R}}$ where $\tilde{\mathbb{R}}$ is the set of all constant maps on $\mathbb{R}$.

math.FA↗

arXiv2025

The Amazon Nova Family of Models: Technical Report and Model Card

We present Amazon Nova, a new generation of state-of-the-art foundation models that deliver frontier intelligence and industry-leading price performance. Amazon Nova Pro is a highly-capable multimodal model with the best combination of accuracy, speed, and cost for a wide range of tasks. Amazon Nova Lite is a low-cost multimodal model that is lightning fast for processing images, video, documents and text. Amazon Nova Micro is a text-only model that delivers our lowest-latency responses at very low cost. Amazon Nova Canvas is an image generation model that creates professional grade images with rich customization controls. Amazon Nova Reel is a video generation model offering high-quality outputs, customization, and motion control. Our models were built responsibly and with a commitment to customer trust, security, and reliability. We report benchmarking results for core capabilities, agentic performance, long context, functional adaptation, runtime performance, and human evaluation.

cs.AI↗

arXiv2025

A generalization of Lipschitz mappings

Using the notion of modulus of continuity at a point of a mapping between metric spaces, we introduce the notion of extensively bounded mappings generalizing that of Lipschitz mappings. We also introduce a metric on it which becomes a norm if the codomain is a normed linear space. We study its basic properties. We also discuss a linearization of an extensively bounded mapping into a bounded linear mapping. As an application, we introduce the notion of extensively bounded operator ideals. We also discuss extensively bounded finite rank and extensively bounded compact mappings and their corresponding operator ideals.

math.FA↗

arXiv2024

Genuine lepton-flavor-universality-violating observables in the $τ-μ$ sector of $B \to (K,\,K^*) \ell \ell $ decays

It was previously shown that unlike the ratios $R_K^{μe} \equiv R_K \equiv Γ(B \to K μ^+ μ^-)/Γ(B \to K e^+ e^-)$ and $R_{K^*}^{μe} \equiv R_{K^*} \equiv Γ(B \to K^* μ^+ μ^-)/Γ(B \to K^* e^+ e^-)$, the ratios $R_K^{τμ}$ and $R_{K^*}^{τμ}$ can deviate from their Standard Model (SM) predictions even with universal new physics couplings. This observation highlights the critical need to identify and establish genuine lepton flavor universality violating (LFUV) observables in the $τ-μ$ sector. This work embarks on establishing genuine LFUV ratio observables in $B \to K \ell \ell$ and $B \to K^* \ell \ell$ decays through comprehensive analysis of their angular distributions. We find that like $R_{K^*}^{τμ}$, the ratios $R_{A_{FB}}^{τμ}$ and $R_{f_L}^{τμ}$ do not qualify as genuine LFUV observables, whereas the ratios of all optimized observables in $B \to K^* \ell \ell$ decays within the $τ-μ$ sector definitively do. In the case of $B \to K \ell \ell$ decays, similar to $R_K^{τμ}$, the ratio $R_{F_H}$ is influenced by mass effects and therefore cannot be considered a genuine LFUV observable in the $τ-μ$ sector. However, the ratio $Γ_τ(1-F_{H}^τ)/Γ_μ(1-F_{H}^μ)$ stands as the sole genuine LFUV observable in $B \to K \ell \ell$ decays. Furthermore, by making use of new physics Lorentz structures which provide a better fit to the current $b \to s \ell \ell$ data as compared to the SM, we demonstrate how the non-genuine LFUV ratios $R_{A_{FB}}^{τμ}$ and $R_{f_L}^{τμ}$ can be employed to distinguish between framework with solely universal lepton couplings and those with both universal and non-universal couplings.

hep-ph↗

arXiv2024

Majorana CP-violating phases and NSI effects in Neutrino Decay

In this work, we investigate the impact of neutrino decay in the presence of Non-Standard Interactions (NSI) along with the effects of the Majorana phase on neutrino decay in matter in the context of two-flavor neutrino oscillations. These effects are studied on neutrino oscillation probabilities $P_{αβ} \equiv P(ν_α \to ν_β)$, and the difference $ΔP_{αβ} \equiv P(ν_α \to ν_β) - P(\bar ν_α \to \barν_β)$ for several accelerator and reactor neutrino experiments. We find that for $P_{αβ}$, the influence of the Majorana phase on decay in matter can be replicated by the simultaneous presence of both decay and NSI. However, precise measurements of the $P_{αβ}$ and $ΔP_{αβ}$ observables have the potential to unequivocally identify the presence of the Majorana phase by discerning its effects from the concurrent presence of both decay and NSI.

hep-ph↗

arXiv2024

Spin-Flavor Oscillations of Relic Neutrinos in Primordial Magnetic Field

The neutrino magnetic moment operator clasps a tiny but non-zero value within the standard model (SM) of particle physics and rather enhanced values in various new physics models. This generation of the magnetic moment ($μ_ν$) is through quantum loop corrections which can exhibit spin-flavor oscillations in the presence of an external magnetic field. Also, several studies predict the existence of a primordial magnetic field (PMF) in the early universe, extending back to the era of Big Bang Nucleosynthesis (BBN) and before. The recent NANOGrav measurement can be considered as a strong indication of the presence of these PMFs. In this work, we consider the effect of the PMF on the flux of relic neutrinos. For Dirac neutrinos, we show that half of the active relic neutrinos can become sterile due to spin-flavor oscillations well before becoming non-relativistic owing to the expansion of the Universe and also before the timeline of the formation of galaxies and hence intergalactic fields, subject to the constraints on the combined value of $μ_ν$ and the cosmic magnetic field at the time of neutrino decoupling. For the upper limit of PMF allowed by the BBN, this can be true even if the experimental bounds on $μ_ν$ approaches a few times its SM value.

hep-ph↗

arXiv2024

Correlating neutrino millicharge and muon $(g-2)$ in an abelian $L_μ-L_τ$ model

The inclusion of an additional $U(1)$ gauge symmetry is a common feature in many extensions of the Standard Model, revealing the intricate connections between particle physics and cosmology. The $L_μ - L_τ$ model stands as a prominent member of this distinguished family, characterized by its anomaly-free nature and resilience in the face of collider constraints. This framework provides a unique vantage point for investigating both the intriguing mystery of the muon $(g-2)$ anomaly and the puzzling issue of the Hubble tension. However, due to the presence of kinetic mixing between the photon and $Z'$ in this model, the neutrinos have the potential to acquire minuscule electric charges, often referred to as millicharges ($q_ν$) which is directly related to the strength of the new gauge couplings. A crucial question emerges: how does the model's inclusion of millicharges, while adhering to the stringent constraints imposed by experimental observations, influence its inherent ability to address the muon $(g-2)$ anomaly and the Hubble tension? We find the current upper bounds on $q_ν$ derived from experiments such as the beam dump, XENONnT and LUX-ZEPLIN experiments can impose strong constraints on the $U(1)_{L_μ - L_τ}$ coupling. Consequently, these constraints may limit the ability of the model to fully accommodate the current measurement of $(g-2)_μ$ while having a relatively minor impact on the resolution of the Hubble tension.

hep-ph↗

arXiv2023

Investigating the potential of $R_{K^{(*)}}^{τμ}$ to probe lepton flavor universality violation

In this work we study the potential of the lepton flavor ratios $R_{K}^{τμ} \equiv Γ(B \to K τ^+ τ^-)/ Γ(B \to K μ^+ μ^-)$ and $ R_{K^{*}}^{τμ} \equiv Γ(B \to K^* τ^+ τ^-)/ Γ(B \to K^* μ^+ μ^-)$ to probe lepton flavor universality (LFU) violation in $τ-μ$ sector. We show that these ratios can deviate from their SM values even if the new physics couplings are universal in nature, i.e., having equal couplings to $e$, $μ$ and $τ$ leptons. Therefore in order to utilize these observables to probe LFU violation, we need to compare the allowed range of $R_{K^{(*)}}^{τμ}$ for class of solutions with only universal couplings to leptons and solutions having both universal and non-universal components. For the current $b \to s \ell \ell$ ($\ell=e,\,μ$) data, we find that these two class of solutions can be discriminated provided the measured value of $ R_{K^{*}}^{τμ} $ is greater than the SM prediction.

hep-ph↗

arXiv2023

Alexa, play with robot: Introducing the First Alexa Prize SimBot Challenge on Embodied AI

The Alexa Prize program has empowered numerous university students to explore, experiment, and showcase their talents in building conversational agents through challenges like the SocialBot Grand Challenge and the TaskBot Challenge. As conversational agents increasingly appear in multimodal and embodied contexts, it is important to explore the affordances of conversational interaction augmented with computer vision and physical embodiment. This paper describes the SimBot Challenge, a new challenge in which university teams compete to build robot assistants that complete tasks in a simulated physical environment. This paper provides an overview of the SimBot Challenge, which included both online and offline challenge phases. We describe the infrastructure and support provided to the teams including Alexa Arena, the simulated environment, and the ML toolkit provided to teams to accelerate their building of vision and language models. We summarize the approaches the participating teams took to overcome research challenges and extract key lessons learned. Finally, we provide analysis of the performance of the competing SimBots during the competition.

cs.HC↗

arXiv2023

Alexa Arena: A User-Centric Interactive Platform for Embodied AI

We introduce Alexa Arena, a user-centric simulation platform for Embodied AI (EAI) research. Alexa Arena provides a variety of multi-room layouts and interactable objects, for the creation of human-robot interaction (HRI) missions. With user-friendly graphics and control mechanisms, Alexa Arena supports the development of gamified robotic tasks readily accessible to general human users, thus opening a new venue for high-efficiency HRI data collection and EAI system evaluation. Along with the platform, we introduce a dialog-enabled instruction-following benchmark and provide baseline results for it. We make Alexa Arena publicly available to facilitate research in building generalizable and assistive embodied agents.

cs.HC↗

arXiv2023

Imprints of flavor anomalies on neutrino oscillations through dark matter halo

In this work we study the impact of new physics, stimulated by flavor anomalies, on neutrino oscillations through dense dark matter halo. Inspired by a model where a Majorana dark matter fermion and two new scalar fields contribute to $b \to s μ^+ μ^-$ transition at the one loop level, we study the impact of neutrino-dark matter interaction on the oscillation patterns of ultra-high energy cosmic neutrinos passing through this muonphilic halo located near the center of Milky Way. We find that due to this interaction, the flavor ratios of neutrinos reaching earth would be different from that of vacuum oscillations. We also consider a $Z'$ model driven by $L_μ-L_τ$ symmetry and containing a vector-like fermion as a dark matter candidate. It was previously shown that for such a model, the three flavors of neutrinos decouple from each other. This will render a flavor ratio similar to that of vacuum oscillations. Therefore, the interaction of neutrinos with dense dark matter halo can serve as an important tool to discriminate between flavor models with a dark connection.

hep-ph↗

arXiv2023

Aerodynamic performance of a tandem wing configuration inspired from dragonfly gliding flight for MAV application

The design of micro air vehicles (MAVs) introduces aerodynamic performance challenges due to the small size and, consequently, the low Reynolds number 10000-100000. Natural fliers are naturally optimized and are comparable in size to MAVs, making them a potent candidate to mimic for the design of MAVs. The dragonfly frequently uses a gliding mode of flight relative to the other small fliers and operates at a range of 100-10000. The literature suggests that the corrugated profile improves the aerodynamic efficiency around Re at 104. It allows us to investigate the aerodynamic advantages of tandem corrugated airfoil inspired by the dragonfly wing. In this paper, we perform direct numerical simulations of flow past bio-inspired corrugated wing to understand the impact of the tandem wing configuration. The horizontal distance between the wings is fixed, and the vertical distance varies. The results reveal that the forewing/hindwing interaction increases the lift of the forewing relative to the isolated wing for all the case studies. The combined drag coefficient drops by approximately 7%, and overall efficiency drops by approximately 13% relative to an isolated wing for a case study with zero vertical spacing between forewing and hindwing at 3 degree angle of attack, fixed for both wings. With no vertical gap, the aerodynamic efficiency matches close to the isolated wing with the decrease in tandem wing combined drag coefficient compared to an isolated wing.

physics.flu-dyn↗

arXiv2023

Cosmic neutrino flux and spin flavor oscillations in intergalactic medium

The ultra high energy (UHE) cosmic neutrinos are expected to play a pivotal role in the disquisition of physics beyond the standard model of particle physics as well as serve as an ideal cosmic messengers. This epitomizes the selling point of several currently running or planned neutrino telescopes. The UHE cosmic neutrinos usually perambulate gargantuan scales in the extragalactic universe having a magnetic field. If neutrinos have a finite magnetic moment ($μ_ν$) owing to quantum loop corrections, this may result in spin-flavor oscillations, which can affect the cosmic neutrino flux. Using the current limit and assuming neutrinos to be Dirac particles, we show that the flux of cosmic neutrinos will reduce by half if they traverse few Mpcs through the intergalactic magnetic field, in the range of $\rm μG$ to $nG$. Moreover, one can safely neglect the effect of $μ_ν$ if the current upper bound is improved by a few orders of magnitude even if the neutrinos travel through the size of the visible universe.

hep-ph↗

arXiv2023

The Demailly systems with the Vortex ansatz

For an arbitrary-rank vector bundle over a projective manifold, J.-P. Demailly proposed several systems of equations of Hermitian-Yang-Mills type for the curvature tensor to settle a conjecture of Griffiths on the equivalence of Hartshorne ampleness and Griffiths positivity. In this article, we have studied two proposed systems and proved that these equations have smooth solutions for the Vortex bundle using the continuity method.

math.DG↗