Near Optimal Subdivision Algorithms for Real Root Isolation

We describe a subroutine that improves the running time of any subdivision algorithm for real root isolation. The subroutine first detects clusters of roots using a result of Ostrowski, and then uses Newton iteration to converge to them. Near a cluster, we switch to subdivision, and proceed recursively. The subroutine has the advantage that it is independent of the predicates used to terminate the subdivision. This gives us an alternative and simpler approach to recent developments of Sagraloff (2012) and Sagraloff-Mehlhorn (2013), assuming exact arithmetic. The subdivision tree size of our algorithm using predicates based on Descartes's rule of signs is bounded by $O(n\log n)$, which is better by $O(n\log L)$ compared to known results. Our analysis differs in two key aspects. First, we use the general technique of continuous amortization from Burr-Krahmer-Yap (2009), and second, we use the geometry of clusters of roots instead of the Davenport-Mahler bound. The analysis naturally extends to other predicates.Comment: 19 pages, 3 figure

Unlocking the Potential of Machine Learning in the Derivation of Low-Energy Models for Metallic Magnets

Condensed matter physics often grapples with complex many-particle problems lacking definitive closed-form solutions, necessitating approximation strategies to investigate low-energy sectors of the Hilbert space. Perturbation theory, though widely used for this purpose, is limited when expansion terms diverge. This work introduces a machine learning (ML) assisted protocol to extract effective low-energy models for lattice models of fermions interacting with classical fields, specifically focusing on the Kondo Lattice Model (KLM). Skyrmions, featuring whirling spin texture and topological protection, are promising candidates for future spintronic devices. Materials featuring conduction electrons coupled to localized $f$-electrons\u27 net moment are ideal for realizing skyrmions and can be modeled using the KLM. The RKKY model approximates the KLM in the weak-coupling regime. Away from this regime, significant four-spin interactions that are non-analytic functions of the coupling constant emerge, rendering perturbative treatment inapplicable. We employ our supervised ML-assisted protocol to extract effective two- and four-spin interactions by integrating out the KLM’s conduction electrons. Utilizing the resultant low-energy effective Hamiltonian, both in real and momentum space, we explore multiple-${\bm Q}$ magnetic orderings on a triangular KLM. We demonstrate the existence of the skyrmion phase even in the absence of spin anisotropy, unattainable within the pure RKKY model. The effective spin models reproduce the original KLM’s phase diagram, revealing the effective four-spin interactions stabilizing field-induced skyrmion crystal phases. The ML-derived minimal spin models enable efficient computation of static and dynamical properties at a significantly reduced numerical cost. A comparison of the dynamical spin structure factor in the fully polarized phase computed with the effective models and the original KLM reveals good agreement for the magnon dispersion, even though this information was not incorporated during training. Our ML-assisted protocol identifies patterns from limited data sets, generating effective models that save substantial computational time while reproducing the original model\u27s low-energy physics. Free from human bias, this approach unveils unconventional skyrmion stabilization mechanisms and debunks prior incorrect assumptions. It efficiently aids the search for new magnetic skyrmion hosts, accelerating simulations and paving the way for efficient exploration a more expansive class of materials

ICT in Universities of the Western Himalayan Region in India: Status, Performance- An Assessment

The present paper describes a live project study carried out for the universities located in the western Himalayan region of India in the year 2009. The objective of this study is to undertake the task of assessment regarding initiative, utilization of ICT resources, its performance and impact in these higher educational institutions/universities. In order to answer these, initially basic four- tier framework was prepared. Followed by a questionnaire containing different ICT components 18 different groups like vision, planning, implementation, ICT infrastructure and related activities exhibiting performance. Primary data in the form of feedback on the five point scale, of the questionnaire, was gathered from six universities of the region. A simple statistical analysis was undertaken using weighted mean, to assess the ICT initiative, status and performance of various universities. In the process, a question related to Performance Indicator was identified from each group, whose Coefficient of Correlation was calculated. This study suggests that a progressive vision, planning and initiative regarding academic syllabi, ICT infrastructure, used in training the skilled human resource, is going to have a favourable impact through actual placement, research and play a dominant role at the National and International level.Comment: International Journal of Computer Science Issues, IJCSI Volume 6, Issue 2, pp44-52, November 200

Role of Brassinosteroids in plants responses to salinity stress: A review

Brassinosteroid emerges as an essential phytohormone that helps the plant to maintain plant growth and development. It also helps the plants grow well under adverse conditions along with normal conditions. In this review article, we have discussed the functional role of brassinosteroid (BRS) in plants under salinity stress conditions. Salinity stress is one of the most devastating abiotic stresses which adversely affect plant growth by disturbing their metabolic pathway. This article also comprises the occurrence, structure and signalling pathway of the brassinosteroid. Application of brassinosteroid improves the plant status under salinity by enhancing the antioxidant enzyme activity in plants. Moreover, we also reported the different growth parameters enhanced by brassinosteroid application in plants under salinity. BRSs also maintain plant growth through the regulation of expression of various genes whose products are involved in various biochemical and physiological processes. This review is based on the various aspects in much detail which are required to understand the proper mechanism of BRS, such as i) the role of BRS signaling pathways in providing tolerance to the plants, ii) changes due to the presence or absence of BRS in plants under stress conditions, iii) BRSs application on the regulation of different genes and transcriptional factor, iv) regulation in ion homeostasis, v) reduction of oxidative stress via different mechanisms under salinity stress. However, a lot of knowledge is required to understand the role of BRS in alleviating salinity stress and needs future research work on BRS with its different derivatives in the alleviation of salt stress.       

Revisiting Punjab’s Transformative Journey: 1947 to 1966

Punjab, the “Land of five rivers”, has played a major role in the history of India and had left a deep imprint on the course of Indian History. This imprint on Indian History is due to the people of Punjab, who through their courage and patriotism have carved out an important place for themselves. To understand the nature and dynamics of Punjab history in its true perspective, it is important to study the people of Punjab; their historical, cultural and religious background and their political heritage. In 1947, India got Independence from the British rule and at the same time it was partitioned on the on the basis of two nation theory. In this partition Punjab had to pay a heavy price both in term of human and territorial loss. The joy and achievement of independence for Punjab was marred by the holocaust of partition. After partition Punjab presented a very gloomy and downright dismal picture. Migration of refugees significantly altered the communal composition of Indian Punjab.  It also shook the administrative, economic and political machinery of the province to its foundation and brought in its wake a host complicated problems. The division of Punjab on communal lines spread a sense of indignation and frustration among the Sikhs because the hopes of creating a Sikh State in Independent India rose by the Sikh leaders and supported by the congress and Hindu leaders had not been fulfilled. The Sikhs felt that they had been given a raw deal in the distribution of territory between the Hindus and the Muslims giving the expression to this feeling hence the demand for a Punjabi Suba was made and in its struggle for the achievement of Punjabi Suba, the Akali Dal employed a variety of strategies, due to which on 21st March 1966 reorganization of the Punjab took place and Punjab was further trifurcated