On the Optimality of a Class of LP-based Algorithms

In this paper we will be concerned with a class of packing and covering problems which includes Vertex Cover and Independent Set. Typically, one can write an LP relaxation and then round the solution. In this paper, we explain why the simple LP-based rounding algorithm for the \\VC problem is optimal assuming the UGC. Complementing Raghavendra's result, our result generalizes to a class of strict, covering/packing type CSPs

Developing multilingual pedagogies and research through language study and reflection

Globalization and increased transnational migration underscore the need for educational responses to multilingualism and multilingual discourses. One way to heighten awareness of multilingual pedagogies (while simultaneously providing data for multilingual research) is the use of reflective language study and journaling by language educators/researchers. The purpose of this collaborative autoethnography, which focuses on the United States, is to demonstrate how this can be accomplished in language teacher education courses to help raise awareness and interest of how to capitalize on students’ linguistic and cultural resources. Data for this study included three participant/researcher journals and observational notes from collaborative discussions among researcher/participants about the lived experiences of multilingual language educators as they studied a new language and wrote about their experiences. Findings reveal possibilities for future research in cross-linguistic transfer as well as the teaching of multilingual pedagogies and issues of social justice as it relates to multilingual education

Analyzing a higher order q(t)q(t) model and its implications in the late evolution of the Universe using recent observational datasets

In this research paper, we explore a well-motivated parametrization of the time-dependent deceleration parameter, characterized by a cubic form, within the context of late time cosmic acceleration. The current analysis is based on the $f(Q,T)$ gravity theory, by considering the background metric as the homogeneous and isotropic Friedmann Lema\^itre Robertson Walker (FLRW) metric. Investigating the model reveals intriguing features of the late universe. To constrain the model, we use the recent observational datasets, including cosmic chronometer (CC), Supernovae (SNIa), Baryon Acoustic Oscillation (BAO), Cosmic Microwave Background Radiation (CMB), Gamma Ray Burst (GRB), and Quasar (Q) datasets. The joint analysis of these datasets results in tighter constraints for the model parameters, enabling us to discuss both the physical and geometrical aspects of the model. Moreover, we determine the present values of the deceleration parameter ($q_0$), the Hubble parameter ($H_0$), and the transition redshift ($z_t$) from deceleration to acceleration ensuring consistency with some recent results of Planck 2018. Our statistical analysis yields highly improved results, surpassing those obtained in previous investigations. Overall, this study presents valuable insights into the higher order $q(t)$ model and its implications for late-time cosmic acceleration, shedding light on the nature of the late universe

On the Feasibility of Linear Discrete-Time Systems of the Green Scheduling Problem

Peak power consumption of buildings in large facilities like hospitals and universities becomes a big issue because peak prices are much higher than normal rates. During a power demand surge an automated power controller of a building may need to schedule ON and OFF different environment actuators such as heaters and air quality control while maintaining the state variables such as temperature or air quality of any room within comfortable ranges. The green scheduling problem asks whether a scheduling policy is possible for a system and what is the necessary and sufficient condition for systems to be feasible. In this paper we study the feasibility of the green scheduling problem for HVAC(Heating, Ventilating, and Air Conditioning) systems which are approximated by a discrete-time model with constant increasing and decreasing rates of the state variables. We first investigate the systems consisting of two tasks and find the analytical form of the necessary and sufficient conditions for such systems to be feasible under certain assumptions. Then we present our algorithmic solution for general systems of more than 2 tasks. Given the increasing and decreasing rates of the tasks, our algorithm returns a subset of the state space such that the system is feasible if and only if the initial state is in this subset. With the knowledge of that subset, a scheduling policy can be computed on the fly as the system runs, with the flexibility to add power-saving, priority-based or fair sub-policies