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We scrutinize the many known forms of BRST symmetries, as well as some new ones, realized within a prototypical first-class system. Similarities and differences among ordinary BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetries are highlighted and discussed. We identify a precise $\mathbb{Z}_4\times\mathbb{Z}_2$ discrete group of symmetries of the ghost sector, responsible for connecting the various forms of BRST transformations. Considering a Hamiltonian approach, those symmetries can be interrelated by canonical transformations among ghost variables. However, the distinguished characteristic role of the dual BRST symmetries can be fully appreciated within a gauge-fixed Lagrangian viewpoint. New forms of BRST symmetries are given, a set generalizing particular ones previously reported in the literature as well as a brand new unprecedented set. The featured gauge invariant prototypical first-class system encompasses an extensive class of physical models and sheds light on previous controversies in the current quantum field theory literature., Comment: 12 pages, No Figs, Latex

Federated learning has allowed the training of statistical models over remote devices without the transfer of raw client data. In practice, training in heterogeneous and large networks introduce novel challenges in various aspects like network load, quality of client data, security and privacy. Recent works in FL have worked on improving communication efficiency and addressing uneven client data distribution independently, but none have provided a unified solution for both challenges. We introduce a new family of Federated Learning algorithms called CatFedAvg which not only improves the communication efficiency but improves the quality of learning using a category coverage maximization strategy. We use the FedAvg framework and introduce a simple and efficient step every epoch to collect meta-data about the client's training data structure which the central server uses to request a subset of weight updates. We explore two distinct variations which allow us to further explore the tradeoffs between communication efficiency and model accuracy. Our experiments based on a vision classification task have shown that an increase of 10% absolute points in accuracy using the MNIST dataset with 70% absolute points lower network transfer over FedAvg. We also run similar experiments with Fashion MNIST, KMNIST-10, KMNIST-49 and EMNIST-47. Further, under extreme data imbalance experiments for both globally and individual clients, we see the model performing better than FedAvg. The ablation study further explores its behaviour under varying data and client parameter conditions showcasing the robustness of the proposed approach., Comment: Supplementary material included

The Federated Learning setting has a central server coordinating the training of a model on a network of devices. One of the challenges is variable training performance when the dataset has a class imbalance. In this paper, we address this by introducing a new loss function called Fed-Focal Loss. We propose to address the class imbalance by reshaping cross-entropy loss such that it down-weights the loss assigned to well-classified examples along the lines of focal loss. Additionally, by leveraging a tunable sampling framework, we take into account selective client model contributions on the central server to further focus the detector during training and hence improve its robustness. Using a detailed experimental analysis with the VIRTUAL (Variational Federated Multi-Task Learning) approach, we demonstrate consistently superior performance in both the balanced and unbalanced scenarios for MNIST, FEMNIST, VSN and HAR benchmarks. We obtain a more than 9% (absolute percentage) improvement in the unbalanced MNIST benchmark. We further show that our technique can be adopted across multiple Federated Learning algorithms to get improvements., Comment: Accepted for the Workshop on Federated Learning for Data Privacy and Confidentiality in Conjunction with IJCAI 2020 (FL-IJCAI'20)

We have studied (2+1) dimensional Dirac oscillator (DO) in an external magnetic field in the framework of generalized uncertainty principle (GUP). We have calculated the perturbative corrections for first few energy levels. We show that the infinite degeneracy of lowest Landau level is partially lifted due to GUP correction and obtained a critical value of the magnetic field for which there is no GUP correction and the DO stops oscillating., Comment: Latex, 11 pages, No Figs, Version to appear in Europhysics Letter

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformtaions in the sector of Lagrange multiplier and its corresponding momenta., Comment: 14 pages, No Figs

We show that (2+1) dimensional noncommutative Dirac oscillator in an external magnetic field is mapped onto the same but with reduced angular frequency in absence of magnetic field. We construct the relativistic Landau levels by solving corresponding Dirac equation in (2+1) dimensional noncommutative phase space. We observe that lowest Landau levels are exactly same as in commutative space and independent of non-commutative parameter. All the Landau levels become independent of noncommutative parameter for a critical value of the magnetic field. Several other interesting features along with the relevance of such models in the study of atomic transitions in a radiation field have been discussed., Comment: 10 pages, Np figs, communicated to journal. arXiv admin note: text overlap with arXiv:0907.4544

We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories, in the context of generalized BRST transformations with finite field dependent parameter. In the usual Faddeev-Popov formulation of gauge theories such finite field dependent BRST (FFBRST) transformations do not leave the generating functionals invariant as the path integral measure changes in a non-trivial way for a finite transformations. Here we show that FFBRST transformation, with appropriate choice of finite field-dependent parameter, is symmetry of the generating functionals in the Batalin-Vilkovisky formalism. The finite parameter is chosen in such a way that the contribution from the Jacobian of the path integral measure is adjusted with gauge fixed fermions which do not change the generating functionals. Several examples for such a finite parameters are constructed., Comment: 11 pages, To appear in EuroPhysics Letters(Fast track)

We derive the various forms of BRST symmetry using Batalin-Fradkin-Vilkovisky approach in the case of Abelian 2-form gauge theory. We show that the so-called dual BRST symmetry is not an independent symmetry but the generalization of BRST symmetry obtained from the canonical transformation in the bosonic and ghost sector. We further obtain the new forms of both BRST and dual-BRST symmetry by making a general transformation in the Lagrange multipliers of the bosonic and ghost sector of the theory., Comment: 14 pages, No figures, revtex

We develop the off-shell nilpotent finite field dependent BRST transformations and show that for different choices of the finite field dependent parameter these connect the generating functionals corresponding to different effective theories. We also construct both on-shell and off-shell finite field dependent anti-BRST tranformations for Yang Mills theories and show that these transformations play the similar role in connecting different generating functionals of different effective theories. Analogous to the finite field dependent BRST transformations, the non-trivial Jacobians of the path integral measure which arise due to the finite field dependent anti-BRST transformations are responsible for the new results. We consider several explicit examples in each case to demonstrate the results., Comment: 29 Pages, No figs., revtex

We derive the different forms of BRST symmetry by using the Batalin-Fradkin-Vilkovisky formalism in a rigid rotor. The so called "dual-BRST" symmetry is obtained from usual BRST symmetry by making a canonical transformation in the ghost sector. On the other hand, a canonical transformation in the sector involving Lagrange multiplier and its corresponding momentum leads to a new form of BRST as well as dual-BRST symmetry., Comment: 10 Pages, revtex, No Figs

We study the field/antifield formulation of pure Yang Mills theory in the framework of finite field dependent BRST transformation. We show that the generating functionals corresponding to different solutions of quantum master equation are connected through the finite field dependent BRST transformations. We establish this result with the help of several explicit examples., Comment: Revtex4, 18 pages, No figs, Accepted in Eur. Phys. J C