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Goutam Das

Publications and source records attributed to Goutam Das.

At least 55 records · Page 3Linked to original sources

Automation of Beam and Jet functions at NNLO

We present a novel framework to streamline the calculation of jet and beam functions to next-to-next-to-leading order (NNLO) in perturbation theory. By exploiting the infrared behaviour of the collinear splitting functions, we factorise the singularities with suitable phase-space parametrisations and perform the observable-dependent integrations numerically. We have implemented our approach in the publicly available code {\tt pySecDec} and present first results for sample jet and beam functions.

hep-ph↗

Achieving QoS for Real-Time Bursty Applications over Passive Optical Networks

Emerging real-time applications such as those classified under ultra-reliable low latency (uRLLC) generate bursty traffic and have strict Quality of Service (QoS) requirements. Passive Optical Network (PON) is a popular access network technology, which is envisioned to handle such applications at the access segment of the network. However, the existing standards cannot handle strict QoS constraints. The available solutions rely on instantaneous heuristic decisions and maintain QoS constraints (mostly bandwidth) in an average sense. Existing works with optimal strategies are computationally complex and are not suitable for uRLLC applications. This paper presents a novel computationally-efficient, far-sighted bandwidth allocation policy design for facilitating bursty traffic in a PON framework while satisfying strict QoS (age of information/delay and bandwidth) requirements of modern applications. To this purpose, first we design a delay-tracking mechanism which allows us to model the resource allocation problem from a control-theoretic viewpoint as a Model Predictive Control (MPC). MPC helps in taking far-sighted decisions regarding resource allocations and captures the time-varying dynamics of the network. We provide computationally efficient polynomial-time solutions and show its implementation in the PON framework. Compared to existing approaches, MPC reduces delay violations by approximately 15% for a delay-constrained application of 1ms target. Our approach is also robust to varying traffic arrivals.

cs.NI↗

Centralized and Decentralized Non-Cooperative Load-Balancing Games among Federated Cloudlets

Edge computing servers like cloudlets from different service providers compensate scarce computational, memory, and energy resources of mobile devices, are distributed across access networks. However, depending on the mobility pattern and dynamically varying computational requirements of associated mobile devices, cloudlets at different parts of the network become either overloaded or under-loaded. Hence, load balancing among neighboring cloudlets appears to be an essential research problem. Nonetheless, the existing load balancing frameworks are unsuitable for low-latency applications. Thus, in this paper, we propose an economic and non-cooperative load balancing game for low-latency applications among federated neighboring cloudlets from the same as well as different service providers and heterogeneous classes of job requests. Firstly, we propose a centralized incentive mechanism to compute the pure strategy Nash equilibrium load balancing strategies of the cloudlets under the supervision of a neutral mediator. With this mechanism, we ensure that the truthful revelation of private information to the mediator is a weakly-dominant strategy for all the federated cloudlets. Secondly, we propose a continuous-action reinforcement learning automata-based algorithm, which allows each cloudlet to independently compute the Nash equilibrium in a completely distributed network setting. We critically study the convergence properties of the designed learning algorithm, scaffolding our understanding of the underlying load balancing game for faster convergence. Furthermore, through extensive simulations, we study the impacts of exploration and exploitation on learning accuracy. This is the first study to show the effectiveness of reinforcement learning algorithms for load balancing games among neighboring cloudlets.

cs.NI↗

Queuing Analysis of Opportunistic Cognitive Radio IoT Network with Imperfect Sensing

In this paper, we analyze a Cognitive Radio-based Internet-of-Things (CR-IoT) network comprising a Primary Network Provider (PNP) and an IoT operator. The PNP uses its licensed spectrum to serve its users. The IoT operator identifies the white-space in the licensed band at regular intervals and opportunistically exploits them to serve the IoT nodes under its coverage. IoT nodes are battery-operated devices that require periodical energy replenishment. We employ the Microwave Power Transfer (MPT) technique for its superior energy transfer efficiency over long-distance. The white-space detection process is not always perfect and the IoT operator may jeopardize the PNP's transmissions due to misdetection. To reduce the possibility of such interferences, some of the spectrum holes must remain unutilized, even when the IoT nodes have data to transmit. The IoT operator needs to decide what percentage of the white-space to keep unutilized and how to judiciously use the rest for data transmission and energy-replenishment to maintain an optimal balance between the average interference inflicted on PNP's users and the Quality-of-Service (QoS) experienced by IoT nodes. Due to the periodic nature of the spectrum-sensing process, Discrete Time Markov Chain (DTMC) method can realistically model this framework. In literature, activities of the PNP and IoT operator are assumed to be mutually exclusive, for ease of analysis. Our model incorporates possible overlaps between these activities, making the analysis more realistic. Using our model, the sustainability region of the CR-IoT network can be obtained. The accuracy of our analysis is demonstrated via extensive simulation.

cs.PF↗

GLRT based Adaptive-Thresholding for CFAR-Detection of Pareto-Target in Pareto-Distributed Clutter

After Pareto distribution has been validated for sea clutter returns in varied scenarios, some heuristics of adaptive-thresholding appeared in the literature for constant false alarm rate (CFAR) criteria. These schemes used the same adaptive-thresholding form that was originally derived for detecting Swerling-I (exponential) target in exponentially distributed clutter. Statistical procedures obtained under such idealistic assumptions would affect the detection performance when applied to newer target and clutter models, esp. heavy tail distributions like Pareto. Further, in addition to the sea clutter returns, it has also been reported that Generalized Pareto distribution fits best for the measured Radar-cross-section (RCS) data of a SAAB aircraft. Therefore, in Radar application scenarios like Airborne Warning and Control System (AWACS), when both the target and clutter are Pareto distributed, we pose the detection problem as a two-sample, Pareto vs. Pareto composite hypothesis testing problem. We address this problem by corroborating the binary hypothesis framework instead of the conventional way of tweaking the existing adaptive-thresholding CFAR detector. Whereby, for the composite case, considering no knowledge of both scale and shape parameters of Pareto distributed clutter, we derive the new adaptive-thresholding detector based on the generalized likelihood ratio test (GLRT) statistic. We further show that our proposed adaptive-thresholding detector has a CFAR property. We provide extensive simulation results to demonstrate the performance of the proposed detector.

stat.AP↗

Precision QCD phenomenology of exotic spin-2 search at the LHC

The complete next-to-next-to leading order (NNLO) QCD correction matched with next-to-next-to leading logarithm (NNLL) has been studied for Drell-Yan production through spin-2 particle at the Large hadron collider (LHC). We consider generic spin-2 particle which couples differently to the quarks and the gluons (non-universal scenario). The threshold enhanced analytical coefficient has been obtained up to third order exploiting the universality of the soft function as well as the process dependent form factors at the same order. We performed a detailed phenomenological analysis and give prediction for the 13 TeV LHC for the search of such BSM signature. We found that the matched correction at the second order gives sizeable corrections over wide range of invariant mass of the lepton pair. The scale variation also stabilizes at this order and reduces to 4%. As a by-product we also provide ingredients for third order soft-virtual (SV) prediction as well as resummation and study the impact on LHC searches.

hep-ph↗

Soft-virtual correction and threshold resummation for $n$-colorless particles to fourth order in QCD: Part I

We present the general form of a universal soft-collinear distribution operator to compute the soft-virtual cross-section to next-to-next-to-next-to-next-to-leading order (N$^4$LO) in QCD for a process with any number of final state colorless particles in hadron colliders. By acting this universal operator on the pure virtual corrections, which need to be computed explicitly for a process, the soft-virtual cross-section can be obtained. The operator is constructed by exploiting the factorization and renormalization group evolution of amplitudes in QCD, and the universality of soft gluon contributions. We also provide the hard coefficient to perform the threshold resummation to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. Furthermore, we present the approximate analytical results of the soft-virtual cross-sections at N$^4$LO and N$^3$LL for the Higgs boson production through gluon fusion and bottom quark annihilation, and also for the Drell-Yan production at the hadronic collider.

hep-ph↗

On Exact Distribution of Poisson-Voronoi Area in $K$-tier HetNets with Generalized Association Rule

This letter characterizes the exact distribution function of a typical Voronoi area in a $K$-tier Poisson network. The users obey a generalized association (GA) rule, which is a superset of nearest base station association and maximum received power based association (with arbitrary fading) rules that are commonly adopted in the literature. Combining the Robbins' theorem and the probability generating functional of a Poisson point process, we obtain the exact moments of a typical $k$-th tier Voronoi area, $k \in \{1,...,K\}$ under the GA rule. We apply this result in several special cases. For example, we prove that in multi-tier networks with the GA rule, the mean of $k$-th tier Voronoi area can exactly be expressed in a closed-form. We also obtain simplified expressions of its higher-order moments for both average and instantaneous received power based user association. In single-tier networks with exponential fading, the later association rule provides closed-form expression of the second-order moment of a typical Voronoi area. We numerically evaluate this exact expression and compare it with an approximated result.

cs.IT↗

Low Complexity Fair Scheduling in LTE/LTE-A Uplink Involving Multiple Traffic Classes

The bulk of the research on Long Term Evolution/Long Term Evolution-Advanced packet scheduling is concentrated in the downlink and the uplink is comparatively less explored. In up-link, channel aware scheduling with throughput maximization has been widely studied while considering an infinitely back-logged buffer model, which makes the investigations unrealistic. Therefore, we propose an optimal uplink packet scheduling pro-cedure with realistic traffic sources. Firstly, we advocate a joint channel and buffer aware algorithm, which maximizes the actual transmitted bit-count. Thereafter, we introduce delay constraints in our algorithm to support real-time traffic. We further enhance our algorithm by incorporating the varied delay and throughput requirements demanded by mixed traffic classes. Finally, we in-troduce priority flipping to minimize bandwidth starvation of lower priority traffic in presence of higher percentage of high priority traffic. We observe that a delay constraint may render the optimization-based proposals infeasible. Therefore, to avoid infeasibility, we replace the delay constraint with delay outage minimization (DOM). DOM aims at minimizing the packet drop due to delay violation. Moreover, DOM also helps in reducing the problems to a well-known assignment problem, which can be solved by applying the Hungarian algorithm. Hence, our approach delivers an optimal allocation with low computational complexity.

cs.NI↗

Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL

The complete next-to-next-to leading order (NNLO) QCD correction has been studied to the di-lepton invariant mass distribution within the Randall-Sundrum (RS) framework. In addition, the soft-virtual (SV) cross-section at next-to-next-to-next-to leading order (N$^3$LO) as well as threshold resummation to next-to-next-to leading logarithms (NNLL) level have been presented. The analytical coefficient for SV production has been obtained up to three loops very recently along with the process-dependent coefficients needed to perform resummation up to NNLL. These coefficients are universal for any universal spin-2 model where spin-2 particle couples to the Standard Model (SM) particles with equal strength. We use these coefficients in predicting N$^3$LO SV results as well as matched NNLO+NNLL results for invariant mass distribution for Drell-Yan (DY) production in RS model. We performed a detailed phenomenological analysis and present prediction for the 13 TeV centre-of-mass energy at the Large Hadron Collider (LHC) for the search of such RS Kaluza-Klein (KK) resonances. The NNLO cross-section adds about $21\%$ correction to the next-to-leading order (NLO) results. We found that the SV correction at the N$^3$LO order decreases the cross-section by $0.7\%$ near the first KK resonance ($M_1=1500$ GeV) whereas the resummed result shows an increment over NNLO by $7\%$ of LO. We performed a detailed analysis including scale variation and parton distribution function (PDF) variations. These new results provide an opportunity to stringently constrain the parameters of the model in particular in the search of heavy spin-2 resonances at the LHC.

hep-ph↗

Soft corrections to inclusive deep-inelastic scattering at four loops and beyond

We study the threshold corrections for inclusive deep-inelastic scattering (DIS) and their all-order resummation. Using recent results for the QCD form factor, related anomalous dimensions and Mellin moments of DIS structure functions at four loops we derive the complete soft and collinear contributions to the DIS Wilson coefficients at four loops. For a general $SU(n_c)$ gauge group the results are exact in the large-$n_c$ approximation and for QCD with $n_c=3$ we present precise approximations. We extend the threshold resummation exponent $G^N$ in Mellin-$N$ space to the fifth logarithmic (N$^4$LL) order collecting the terms $α_{\rm s}^{\,3} (α_{\rm s} \ln N)^n$ to all orders in the strong coupling constant $α_{\rm s}$. We study the numerical effect of the N$^4$LL corrections using both the fully exponentiated form and the expansion of the coefficient function in towers of logarithms. As a byproduct, we derive a numerical result for the complete pole structure of the QCD form factor in the parameter of dimensional regularization $\varepsilon$ at four loops.

hep-ph↗

Resummed Drell-Yan cross-section at N$^3$LL

We present the resummed predictions for inclusive cross-section for Drell-Yan (DY) production as well as onshell $Z,W^\pm$ productions at next-to-next-to-next-to leading logarithmic (N$^{3}$LL) accuracy. Using the standard techniques, we derive the $N$-dependent coefficients in the Mellin-$N$ space as well as the $N$-independent constants and match the resummed result through the minimal prescription matching procedure with that of existing next-to next-to leading order (NNLO). In addition to the standard $\ln N$ exponentiation, we study the numerical impacts of exponentiating $N$-independent part of the soft function and the complete $\bar{g}_0$ that appears in the resummed predictions in $N$ space. All the analytical pieces needed in these different approaches are extracted from the soft-virtual part of the inclusive cross section known to next-to-next-to-next-to leading order (N$^3$LO). We perform a detailed analysis on the scale and parton distribution function (PDF) variations and present predictions for the 13 TeV LHC for the neutral Drell-Yan process as well as onshell charged and neutral vector boson productions.

hep-ph↗

Resummed inclusive cross-section in ADD model at N$^3$LL+NNLO

We present three loop soft-plus-virtual (SV) corrections to the spin-2 production at the Large Hadron Collider (LHC). For this calculation, we make use of the recently computed quark and gluon three loop form factors for the spin-2 production, the universal soft-collinear coefficients as well as the mass factorization kernels. The SV coefficients are presented up to next-to-next-to-next-to leading order (N$^3$LO). We also use these coefficients at three loops to compute the resummed prediction for inclusive cross-section to next-to-next-to-next-to leading logarithmic accuracy (N$^3$LL) matched to next-to-next-to leading order (NNLO). We use the standard technique to derive the Mellin N-dependent coefficients and also the N-independent coefficients to achieve the resummation using the minimal prescription matching procedure. Considering the spin-2 propagator in the large extra dimensional (ADD) model, we also study the numerical impact of these three-loop SV corrections as well as the resummed predictions on the di-lepton invariant mass distribution at the 13 TeV LHC. We find that the conventional scale uncertainties in the NNLO+N$^3$LL resummed results substantially get reduced to as low as 2\% in the high invariant mass region. We also estimate the PDF uncertainties in our predictions that will be useful in the experimental searches for large extra dimensions.

hep-ph↗

Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N$^3$LL

We present an accurate theoretical prediction for the production of Higgs boson through bottom quark annihilation at the LHC up to next-to-next-to-next-to leading order (N$^3$LO) plus next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. We determine the third order perturbative Quantum Chromodynamics (QCD) correction to the process dependent constant in the resummed expression using the three loop bottom quark form factor and third order quark soft distribution function. Thanks to the recent computation of N$^3$LO corrections to this production cross-section from all the partonic channels, an accurate matching can be obtained for a consistent predictions at N$^3$LO+N$^3$LL accuracy in QCD. We have studied in detail the impact of resummed threshold contributions to inclusive cross-sections at various centre-of-mass energies and also discussed their sensitivity to renormalization and factorization scales at next-to-next-to leading order (NNLO) matched with next-to-next-to leading logarithm (NNLL). At N$^3$LO+N$^3$LL, we predict the cross-section for different centre-of-mass energies using the recently available results in \cite{Duhr:2019kwi} as well as study the renormalization scale dependence at the same order.

hep-ph↗

Protocol design for energy efficient OLT transmitter in TWDM-PON guaranteeing SLA of up-stream and down-stream traffic

Environmental and economic concerns promote research on designing energy-efficient Time and Wavelength Division Multiplexed Ethernet Passive Optical Network (TWDM-EPON), which is the future extension to TDM-EPON. In TDM-EPON, a plethora of research is already present to achieve energy savings at Optical Network Units (ONUs) which can easily be applied for TWDM-EPON ONUs. However, TWDM-EPON provides an additional opportunity for saving energy at the Optical Line Terminal (OLT). All existing protocols have primarily been designed for saving energy at the OLT receivers. The protocols to save energy at the OLT receives depends only on the Up-Stream(US) traffic scheduling while its transmitter counterpart depends on both US and Down-Stream (DS) scheduling since the OLT transmits GATE message along with DS traffic. The US and DS scheduling have a basic difference. The MAC protocol doesn't allow scheduling of US traffic of an ONU after its REPORT arrival at multiple disjoint time slots. However, this restriction is absent for DS traffic and hence, the grant-size of an ONU can be partitioned and every part can be scheduled at different times. In this paper, we propose a method for saving energy at the OLT transmitters in TWDM-EPON while satisfying the SLAs. This includes a heuristic algorithm to partition the DS grant and schedule them. Through extensive simulations, we demonstrate that the proposed method provides a significant improvement in energy efficiency as compared to existing protocols (up to 45%).

cs.NI↗

Soft corrections to inclusive DIS at four loops and beyond

We study the threshold corrections to the structure functions in deep-inelastic scattering (DIS) at the fifth logarithmic (N$^4$LL) order of the soft-gluon exponentiation in massless perturbative QCD. Using recent results for the splitting functions and the quark form factor, we derive the fourth-order contribution to the coefficient $f^{\rm q}$ of the form factor and from it the N$^4$LL part of the exponentiation coefficient $B^{\rm DIS}$ in the limit of a large number of colours. An approximation scheme is shown that leads to sufficiently accurate N$^4$LL results for full QCD. The N$^4$LL corrections are small and lead to a further stabilization of the perturbative expansion for the soft-gluon exponent.

hep-ph↗

Buffer-aided Resource Allocation for a Price Based Opportunistic Cognitive Radio Network

In this paper, a resource allocation problem for an opportunistic cooperative cognitive radio network is considered, where cognitive radio nodes send their hard decisions to the fusion center. The fusion center plays dual role, i.e., takes the global decision (i.e., decision about the primary user's activity) as well as allocates transmission time durations among cognitive radio nodes. Revenue based utility functions are considered at the fusion center and cognitive radio nodes. An optimization problem is formulated to maximize the fusion center's revenue while satisfying some well defined constraints. User selection among cognitive radio nodes is performed in order to make the optimization problem feasible.

cs.IT↗

A 1-approximation algorithm for energy-efficient TDM-PON guaranteeing SLA of up-stream and down-stream traffic

Economical and environmental concerns necessitate research on designing energy-efficient optical access network especially Ethernet Passive Optical Network (EPON) which is one of the most widely accepted and deployed last-mile access network. In this paper, our primary focus is on designing a protocol for saving energy at Optical Network Units (ONUs) while satisfying the Service Label Agreement (SLA). The SLA of both Up-Stream (US) and Down-Stream (DS) traffic can be satisfied only if the EPON network can react to their instantaneous load change during sleep periods of ONUs and to the best of our knowledge, there doesn't exist any such proposal. Towards this target, we propose a mechanism that allows the Optical Line Terminal (OLT) to force ONUs to wake-up from sleep mode. Here, we demonstrate that if the OLT can distribute the active ONUs (transceivers are active) fairly among cycles then it provides a significant improvement in energy-efficiency. To achieve this, we formulate an ILP for fairly distributing active ONUs among cycles while satisfying the SLA of both US and DS traffic at the same time. A polynomial time $1$-approximation algorithm is proposed for solving this ILP. The convergence and the complexity analysis of the algorithm are also performed. Extensive simulations depict that fair distribution of ONUs reduces the power consumption and average delay figure at the same time and the reduction increases with an increment of the number of ONUs and round-trip time.

cs.NI↗