On the dimension of $H^{*}((\mathbb Z_2)^{\times t}, \mathbb Z_2)$ as a module over Steenrod ring

We write $\mathbb P$ for the polynomial algebra in one variable over the finite field $\mathbb Z_2$ and $\mathbb P^{\otimes t} = \mathbb Z_2[x_1, \ldots, x_t]$ for its $t$-fold tensor product with itself. We grade $\mathbb P^{\otimes t}$ by assigning degree $1$ to each generator. We are interested in determining a minimal set of generators for the ring of invariants $(\mathbb P^{\otimes t})^{G_t}$ as a module over Steenrod ring, $\mathscr A_2.$ Here $G_t$ is a subgroup of the general linear group $GL(t, \mathbb Z_2).$ An equivalent problem is to find a monomial basis of the space of "unhit" elements, $\mathbb Z_2\otimes_{\mathscr A_2} (\mathbb P^{\otimes t})^{G_t}$ in each $t$ and degree $n\geq 0.$ The structure of this tensor product is proved surprisingly difficult and has been not yet known for $t\geq 5,$ even for the trivial subgroup $G_t = \{e\}.$ In the present paper, we consider the subgroup $G_t = \{e\}$ for $t \in \{5, 6\},$ and obtain some new results on $\mathscr A_2$-generators of $(\mathbb P^{\otimes t})^{G_t}$ in some degrees. At the same time, some of their applications have been proposed. We also provide an algorithm in MAGMA for verifying the results. This study can be understood as a continuation of our recent works in [23, 25].

Problem with data on the characteristics for a loaded system of hyperbolic equations

We consider a problem with data on the characteristics for a loaded system of hyperbolic equations of the second order on a rectangular domain. The questions of the existence and uniqueness of the classical solution of the considered problem, as well as the continuity dependence of the solution on the initial data, are investigated. We propose a new approach to solving the problem with data on the characteristics for the loaded system of hyperbolic equations second order based on the introduction new functions. By introducing new unknown functions the problem is reduced to an equivalent family of Cauchy problems for a loaded system of differential with a parameters and integral relations. An algorithm for finding an approximate solution to the equivalent problem is proposed and its convergence is proved. Conditions for the unique solvability of the problem with data on the characteristics for the loaded system of hyperbolic equations of the second order are established in the terms of coefficient's system.

Homogenization of a 2D Tidal Dynamics Equation

This work deals with the homogenization of two dimensions’ tidal equations. We study the asymptotic behavior of the sequence of the solutions using the sigma-convergence method. We establish the convergence of the sequence of solutions towards the solution of an equivalent problem of the same type.

Joint optimisation of privacy and cost of in-app mobile user profiling and targeted ads

Online mobile advertising ecosystems provide advertising and analytics services that collect, aggregate, process and trade rich amount of consumer's personal data and carries out interests-based ads targeting, which raised serious privacy risks and growing trends of users feeling uncomfortable while using internet services. In this paper, we address user's privacy concerns by developing an optimal dynamic optimisation cost-effective framework for preserving user privacy for profiling, ads-based inferencing, temporal apps usage behavioral patterns and interest-based ads targeting. A major challenge in solving this dynamic model is the lack of knowledge of time-varying updates during profiling process. We formulate a mixed-integer optimisation problem and develop an equivalent problem to show that proposed algorithm does not require knowledge of time-varying updates in user behavior. Following, we develop an online control algorithm to solve equivalent problem using Lyapunov optimisation and to overcome difficulty of solving nonlinear programming by decomposing it into various cases and achieve trade-off between user privacy, cost and targeted ads. We carry out extensive experimentations and demonstrate proposed framework's applicability by implementing its critical components using POC `System App'. We compare proposed framework with other privacy protecting approaches and investigate that it achieves better privacy and functionality for various performance parameters.<br>

Joint optimisation of privacy and cost of in-app mobile user profiling and targeted ads

Online mobile advertising ecosystems provide advertising and analytics services that collect, aggregate, process and trade rich amount of consumer's personal data and carries out interests-based ads targeting, which raised serious privacy risks and growing trends of users feeling uncomfortable while using internet services. In this paper, we address user's privacy concerns by developing an optimal dynamic optimisation cost-effective framework for preserving user privacy for profiling, ads-based inferencing, temporal apps usage behavioral patterns and interest-based ads targeting. A major challenge in solving this dynamic model is the lack of knowledge of time-varying updates during profiling process. We formulate a mixed-integer optimisation problem and develop an equivalent problem to show that proposed algorithm does not require knowledge of time-varying updates in user behavior. Following, we develop an online control algorithm to solve equivalent problem using Lyapunov optimisation and to overcome difficulty of solving nonlinear programming by decomposing it into various cases and achieve trade-off between user privacy, cost and targeted ads. We carry out extensive experimentations and demonstrate proposed framework's applicability by implementing its critical components using POC `System App'. We compare proposed framework with other privacy protecting approaches and investigate that it achieves better privacy and functionality for various performance parameters.<br>

A Stochastic Programming Model for Service Scheduling with Uncertain Demand: An Application in Open-Access Clinic Scheduling

This paper addresses a scheduling problem which handles urgent tasks along withexisting schedules. The uncertainty in this problem comes from random situations ofexisting schedules and arrival of upcoming urgent tasks. To deal with the uncertainty,this paper proposes a stochastic integer programming (SIP) based aggregated onlinescheduling method. The method is illustrated through a study case from the outpatientclinic block-wise scheduling system which is under a hybrid scheduling policycombining regular far-in-advance policy and the open-access policy. The COVID-19pandemic brings more challenges for the healthcare system including the fluctuationsof serving time, and increasing urgent requests which this paper is designed for. TheSIP model designed in the method can easily accommodate uncertainties of theproblems, such as: no-shows, cancellations and punctuality of previously scheduledpatients as well as random arrival and preference of new patients. To solve the SIPmodel, the deterministic equivalent problem formulations are solved using theproposed bound-based sampling method.

Understanding Generalization in Neural Networks for Robustness against Adversarial Vulnerabilities

Neural networks have contributed to tremendous progress in the domains of computer vision, speech processing, and other real-world applications. However, recent studies have shown that these state-of-the-art models can be easily compromised by adding small imperceptible perturbations. My thesis summary frames the problem of adversarial robustness as an equivalent problem of learning suitable features that leads to good generalization in neural networks. This is motivated from learning in humans which is not trivially fooled by such perturbations due to robust feature learning which shows good out-of-sample generalization.

Heat transfer from convecting-radiating fin through optimized Chebyshev polynomials with interior point algorithm

In this paper, the problem of determining heat transfer from convecting-radiating fin of triangular and concave parabolic shapes is investigated.We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. A novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Additionally, heat transfer rate and the fin efficiency are reported.

Generalization of Parameter Recovery in Binocular Vision for a Planar Scene

In this paper, we consider a mobile platform with two cameras directed towards the floor. In earlier work, this specific problem geometry has been considered under the assumption that the cameras have been mounted at the same height. This paper extends the previous work by removing the height constraint, as it is hard to realize in real-life applications. We develop a method based on an equivalent problem geometry, and show that much of previous work can be reused with small modification to account for the height difference. A fast solver for the resulting nonconvex optimization problem is devised. Furthermore, we propose a second method for estimating the height difference by constraining the mobile platform to pure translations. This is intended to simulate a calibration sequence, which is not uncommon to impose. Experiments are conducted using synthetic data, and the results demonstrate a robust method for determining the relative parameters comparable to previous work.