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Fraudulent activities are an expensive problem for many financial institutions, costing billions of dollars to corporations annually. More commonly occurring activities in this regard are credit card frauds. In this context, the credit card fraud detection concept has been developed over the lines of incorporating the uncertainty in our prediction system to ensure better judgment in such a crucial task. We propose to use a sparse Gaussian classification method to work with the large data-set and use the concept of pseudo or inducing inputs. We perform the same with different sets of kernels and the different number of inducing data points to show the best accuracy was obtained with the selection of RBF kernel with a higher number of inducing points. Our approach was able to work over large financial data given the stochastic nature of our method employed and also good test accuracy with low variance over the prediction suggesting confidence and robustness in our model. Using the methodologies of Bayesian learning techniques with the incorporated inducing points phenomenon, are successfully able to obtain a healthy accuracy and a high confidence score.

We propose a unique framework to study the topological properties of an optical bound state in the continuum(BIC). We employ the interactions between proximity resonances undergoing avoided resonance crossing in a specialty optical microcavity. We utilize a continuous system parameter tuning to induce destructive interference between the resonances with cancelling leakage losses. Similar to the physical insight of Friedrich-Wingten type-BIC, we demonstrate the evolution of an ultra-high quality mode. We report the formation of a special-BIC line in the system parameter space connecting locations of multiple quasi-BICs. Aiming to develop a novel scheme to enhance the performance of optical sensing in microcavity, we study the sensitivity of transmission coefficients and quality factor to sense even ultra-small perturbations in the system configuration., Comment: 5 pages, 3 figures

The physics of topological singularities, namely exceptional points (EPs), has been a key to wide range of intriguing and unique physical effects in non-Hermitian systems. In this context, the mutual interactions among four coupled states around fourth-order EPs (EP4s) are yet to be explored. Here we report a four-level parameter-dependent perturbed non-Hermitian Hamiltonian, mimicking quantum or wave-based systems, to explore the physical aspects of an EP4 analytically as well as numerically. The proposed Hamiltonian exhibit different orders of interaction schemes with the simultaneous presence of different higher-order EPs. Here an EP4 has been realized by mutual interaction between four coupled states with proper parameter manipulation. We comprehensively investigate the dynamics of corresponding coupled eigenvalues with stroboscopic parametric variation in the vicinity of the embedded EP4 to establish a new successive state-switching phenomenon among them; which proves to be robust even in the presence of different order of EPs. Implementing the relation of the perturbation parameters with the coupling control parameters, we exclusively report a region to host multiple EP4 in a specific system. The chiral behaviour of successive state-exchange has also been established near EP4. Proposed scheme enriched with physical aspects of EP4s should provide a new light manipulation tool in any anisotropic multi-state integrated system., Comment: 10 pages, 6 figures

We exploit the interaction between supported proximity resonances in an open non-uniformly pumped optical microcavity to host a Bound State in Continuum (BIC). Using the modeling of the S-matrix, we study the coupling between the interacting states forming a BIC. We report the divergence of Quality Factor (Q-factor) of one of the interacting states, numerically demonstrated with the appropriate tuning of the spatial variation of unequal gain-loss within the system whose stability has been discussed in terms of the Petermann factor at the point of BIC. Such high lifetime has been marked as a signature of BIC., Comment: 4 pages, 7 figures

Dynamical encirclement of an Exceptional Point (EP) and corresponding time-asymmetric mode evolution properties due to breakdown in adiabatic theorem have been a key to range of exotic physical effects in various open atomic, molecular and optical systems. Here, exploiting a gain-loss assisted dual-mode optical waveguide that hosts a dynamical EP-encirclement scheme, we have explored enhanced nonreciprocal effect in the dynamics of light with onset of saturable nonlinearity in the optical medium. We propose a prototype waveguide-based isolation scheme with judicious tuning of nonlinearity level where one can pass only a chosen mode in any of the desired directions as per device requirement. The deliberate presence of EP enormously enhances the nonreciprocal transmission contrast even up to 40 dB over the proposed device length with a scope of further scalability. This exclusive topologically robust mode selective all-optical isolation scheme will certainly offer opportunities in integrated photonic circuits for efficient coupling operation from external sources and improve device performances., Comment: 5 pages, 6 figures

We investigate the astonishing physical aspects of Exceptional Points (EPs) in a 1D planar few-mode optical waveguide. The waveguide hosts four quasi-guided modes. Here interactions between the selected pair of modes are modulated by a spatial distribution of inhomogeneous gain-loss profile. Both the coupled pairs approach two different second-order EPs in parameter plane. Considering a proper parametric loop to encircle the identified EPs simultaneously, we establish a specific topological feature where one round encirclement in parameter space yields the switching between the propagation constants ({\beta}) of the corresponding pairs of couple modes in complex {\beta}-plane. Choosing two different patterns of the parametric loop, we establish the immutable topology in {\beta}- switching phenomena. This robust mode conversion scheme shall provide a platform to realize selective mode switching devices or optical-mode converters., Comment: 6 pages, 4 figures

We report an asymmetric behavior of optical pulses during their propagation through a time-varying linear optical medium. The refractive index of the medium is considered to be varying with time and complex such that a sufficient amount of gain and loss is present to realize their effect on pulse propagation. We have exploited the universal formula for optical fields in time-varying media. Numerically simulated results reveal that pulses undergo opposite temporal shifts around their initial center position during their bi-directional propagation through the medium along with corresponding spectral shifts. Moreover, the peak power and accumulated chirp (time derivative of accumulated phase) of the output pulse in both propagation directions are also opposite in nature irrespective of their initial state. Numerically simulated behavior of the pulses agrees well with the analytical solutions. Possibilities have been explored in context of pulse shaping and unconventional optical devices., Comment: 5 pages, 5 figures