Linear Relations Among Poincare Series via Harmonic Weak Maass Forms

We discuss the problem of the vanishing of Poincar\'e series. This problem is known to be related to the existence of weakly holomorphic forms with prescribed principal part. The obstruction to the existence is related to the pseudomodularity of Ramanujan's mock theta functions. We embed the space of weakly holomorphic modular forms into the larger space of harmonic weak Maass forms. From this perspective we discuss the linear relations between Poincar\'e series and the connection to Ramanujan's mock theta functions

Optimal linear Glauber model

Contrary to the actual nonlinear Glauber model (NLGM), the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate ($w_j$) in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear $w_j$ are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau (TDGL) equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.Comment: 25 pages; final version; appeared in Journal of Statistical Physic

An Alternate Approach to LC-Circuits

ABSTRACT When an Inductor of self inductance L and a fully charged capacitor o

Garcinol loaded vitamin E TPGS emulsified PLGA nanoparticles: preparation, physicochemical characterization, in vitro and in vivo studies

Garcinol (GAR) is a naturally occurring polyisoprenylated phenolic compound. It has been recently investigated for its biological activities such as antioxidant, anti-inflammatory, anti ulcer, and antiproliferative effect on a wide range of human cancer cell lines. Though the outcomes are very promising, its extreme insolubility in water remains the main obstacle for its clinical application. Herein we report the formulation of GAR entrapped PLGA nanoparticles by nanoprecipitation method using vitamin E TPGS as an emulsifier. The nanoparticles were characterized for size, surface morphology, surface charge, encapsulation efficiency and in vitro drug release kinetics. The MTT assay depicted a high amount of cytotoxicity of GAR-NPs in B16F10, HepG2 and KB cells. A considerable amount of cell apoptosis was observed in B16f10 and KB cell lines. In vivo cellular uptake of fluorescent NPs on B16F10 cells was also investigated. Finally the GAR loaded NPs were radiolabeled with technetium-99m with >95% labeling efficiency and administered to B16F10 melanoma tumor bearing mice to investigate the in vivo deposition at the tumor site by biodistribution and scintigraphic imaging study. In vitro cellular uptake studies and biological evaluation confirm the efficacy of the formulation for cancer treatmen

What You Like: Generating Explainable Topical Recommendations for Twitter Using Social Annotations

With over 500 million tweets posted per day, in Twitter, it is difficult for Twitter users to discover interesting content from the deluge of uninteresting posts. In this work, we present a novel, explainable, topical recommendation system, that utilizes social annotations, to help Twitter users discover tweets, on topics of their interest. A major challenge in using traditional rating dependent recommendation systems, like collaborative filtering and content based systems, in high volume social networks is that, due to attention scarcity most items do not get any ratings. Additionally, the fact that most Twitter users are passive consumers, with 44% users never tweeting, makes it very difficult to use user ratings for generating recommendations. Further, a key challenge in developing recommendation systems is that in many cases users reject relevant recommendations if they are totally unfamiliar with the recommended item. Providing a suitable explanation, for why the item is recommended, significantly improves the acceptability of recommendation. By virtue of being a topical recommendation system our method is able to present simple topical explanations for the generated recommendations. Comparisons with state-of-the-art matrix factorization based collaborative filtering, content based and social recommendations demonstrate the efficacy of the proposed approach

Financial Numeric Extreme Labelling: A Dataset and Benchmarking for XBRL Tagging

The U.S. Securities and Exchange Commission (SEC) mandates all public companies to file periodic financial statements that should contain numerals annotated with a particular label from a taxonomy. In this paper, we formulate the task of automating the assignment of a label to a particular numeral span in a sentence from an extremely large label set. Towards this task, we release a dataset, Financial Numeric Extreme Labelling (FNXL), annotated with 2,794 labels. We benchmark the performance of the FNXL dataset by formulating the task as (a) a sequence labelling problem and (b) a pipeline with span extraction followed by Extreme Classification. Although the two approaches perform comparably, the pipeline solution provides a slight edge for the least frequent labels.Comment: Accepted to ACL'23 Findings Pape

FinRED: A Dataset for Relation Extraction in Financial Domain

Relation extraction models trained on a source domain cannot be applied on a different target domain due to the mismatch between relation sets. In the current literature, there is no extensive open-source relation extraction dataset specific to the finance domain. In this paper, we release FinRED, a relation extraction dataset curated from financial news and earning call transcripts containing relations from the finance domain. FinRED has been created by mapping Wikidata triplets using distance supervision method. We manually annotate the test data to ensure proper evaluation. We also experiment with various state-of-the-art relation extraction models on this dataset to create the benchmark. We see a significant drop in their performance on FinRED compared to the general relation extraction datasets which tells that we need better models for financial relation extraction.Comment: Accepted at FinWeb at WWW'2