Mathematical Sciences Institute Research Articles

First person – Amruta Vasudevan and Reshma Maiya

ABSTRACT First Person is a series of interviews with the first authors of a selection of papers published in Journal of Cell Science, helping researchers promote themselves alongside their papers. Amruta Vasudevan and Reshma Maiya are two of the co-first authors on ‘Transport of synaptic vesicles is modulated by vesicular reversals and stationary cargo clusters’, published in JCS. Amruta is a PhD student in the lab of Dr Sandhya P. Koushika at the Tata Institute of Fundamental Research, Mumbai, India, investigating neuronal vesicular transport in the context of neuronal function and organismal behaviour. Reshma is a PhD student in the lab of Prof. Gautam I. Menon at The Institute of Mathematical Sciences, Chennai, India, modelling and performing theoretical studies of intracellular transport, specifically in neurons.

Practical Applications of Alternative Data in Investment Management: Usage, Challenges, and Valuation

In <ext-link><bold><italic>Alternative Data in Investment Management: Usage, Challenges, and Valuation</italic></bold></ext-link>, from the Fall 2021 issue of <bold><italic>The Journal of Financial Data Science</italic></bold>, <bold>Gene Ekster</bold> and <bold>Petter Kolm</bold>, both at <bold>New York University’s Courant Institute of Mathematical Sciences</bold>, provide insight into how to get the most out of this relatively new resource. Unlike traditional financial data used to analyze and manage investments, alternative data has unique technical challenges, an evolving industry of providers, and valuation challenges. Ekster and Kolm offer methods of dealing with these matters. They point out that it is crucial to understand the structure of the industry, particularly the difference between data originators and intermediaries. The authors also discuss entity mapping, tagging, and other ways of addressing technical issues with alternative data. Importantly, they provide investment professionals with methods of determining the likely value of an alternative dataset with a short history. They include a case study on predicting revenues of publicly traded companies, thus illustrating the design considerations for data processing pipelines and downstream analytics.

Руководитель Калининградской геометрической школы Владислав Степанович Малаховский

The article presents a very brief biography of a corresponding mem­ber of the Russian Academy of Natural Sciences, Honored Scientist of the Russian Federation, Honorary Doctor of Sciences of the I. Kant Baltic Federal University, professor-consultant of the Institute of Physical and Mathematical Sciences and Information Technologies of I. Kant BFU. The information about the scientific and pedagogical work of the scientist for 68 years is given. The article analyzes the active life position of Vladislav Stepanovich Malakhovsky during his years of study at school, at Tomsk University, as well as during his work at Tomsk University and the I. Kant Baltic Federal University up to December 14, 2022. Links are given to individual articles in which Vladislav Stepanovich's activities in all areas are described in more detail, including the content of recent pub­lications on number theory.

Corrigendum: Marangoni convection of nanofluid in a wavy trapezoidal enclosure

Simeon Oka, Editor-in-Chief Emeritus of the journal Thermal Science request that it is, due to request of the Corresponding author of this paper, necessary to correct Acknowledgement of the paper MARANGONI CONVECTION OF NANOFLUID IN A WAVY TRAPEZOIDAL ENCLOSURE written by Sharifah Nuriza Binti Syed Muhammad Naquib AL?AIDRUSa, Zailan Bin SIRIa*, and Mohd Nashrul Bin Mohd ZUBIRb a Institute of Mathematical Sciences, University Malaya, Kuala Lumpur, Malaysia b Department of Mechanical Engineering, University Malaya, Kuala Lumpur, Malaysia Original scientific paper https://doi.org/10.2298/TSCI21S2339A published in the journal Thermal Science, Vol. 25, Year 2021, Special issue 2, pp. S339-S345 since due to change regulations accepted by Government of Malaysia Condolement should have different and more detailed form. Instead of: ACKNOWLEDGEMENT This paper is part of a research project supported by the Malaysian Ministry of Higher Education Fundamental Research Grant no. FP068-2020. The authors would also like to express their thanks to the University of Malaya for supporting this research under grant no. IIRG006C19IISS. has to be written: Acknowledgment The work is supported financially by the Ministry of Higher Education Malaysia via Fundamental Research Grant Scheme (FRGS/1/2020/STG06/UM/02/4) and Impact Oriented Interdisciplinary Research Grant No. IIRG006C-19IISS. &lt;br&gt;&lt;br&gt;&lt;font color="red"&gt;&lt;b&gt; Link to the corrected article &lt;u&gt;&lt;a href="http://dx.doi.org/10.2298/TSCI21S2339A"&gt;10.2298/TSCI21S2339A&lt;/a&gt;&lt;/b&gt;&lt;/u&gt;

The Purpose and Value of Research

Human cognition and intellect have always strived for improvement of the human condition. Improvements are primarily based upon development of new knowledge and its application. This remains the prime purpose of all research and its value.There is often a spatiotemporal disconnect between the occurrence of research and realization of its value. Translation of new knowledge into socio economically valuable application takes time. An apt example is as follow:Alfred Haar, a Hungarian mathematician-scientist, introduced the idea of HAAR orthogonal system through his doctoral thesis at University of Gottingen, Germany in 1909. Ingrid Daubechics, a Belgian mathematicianphysicist, working at Courount Institute of Mathematical Sciences at New York University, USA, in 1980s developed compactly supported continuous wavelets finding useful application of wavelet theory in digital signal processing especially image compression. Stephen Hallet, originally from France, also helped develop wavelet theory applications in signal and image processing. It took at least seven decades before valuable applications were developed based on Haar's theoretical concepts. New knowledge thus created through research, in one part of the world, may lead to production of valuable applications in a different part of theworld, at a different time.The puritan idea of research as enumerated above, has been corrupted with time. A lot of Ivory tower's research today is taking place to fulfil criteria of job placement and promotions. The concept of impact factor supports this purpose by providing a mechanism, howsoever flawed, of providing a quantitative mechanism to judge research capabilities of individuals and institutions. This lends greater impetus to self-serving researchthan to society serving. This impact factor approach appears to have helped increase the quantity of research, but certainly not its quality in terms of socio economic value.Much greater interaction between the elements of quadruple helix (of academia, industry, society and government) is required to improve our understanding to develop means for enhancing the ratio of socioeconomically valuable research to self serving one.By directing our endeavors to yield better fruits for the society as a whole, serves a far higher purpose and generates much greater value.

Robo-Advisors Today and Tomorrow: Investment Advice Is Just an App Away

1. Adam Grealish 1. is head of investments at Altruist in Los Angeles, CA. (agrealish{at}gmail.com) 2. Petter N. Kolm 1. is a clinical full professor and director of the Mathematics in Finance Master’s Program at New York University’s Courant Institute of Mathematical Sciences in New York, NY. (petter.kolm{at}nyu.edu) <!-- --> 1. To order reprints of this article, please contact David Rowe at d.rowe{at}pageantmedia.com or 646-891-2157. Over the past decade robo-advisors have gone from offerings from a handful of start-ups to an established and fast-growing segment of the wealth management industry. Robo-advisors use technology to translate core retail investing principles—establishing an investment plan, seeking broad diversification, weighting cost and value, and accounting for taxes—into automated platforms with easy-to-use interfaces. Intuitive user experience backed by well-established investment processes allow individual investors to create and execute investment strategies with little or no interaction with a financial professional, resulting in large economies of scale for robo-advisors and low costs for clients. In this article, the authors discuss how robo-advisors assess client risk tolerance, build, and recommend portfolios, manage risk, and optimize taxes. They discuss the implementation of goal-based investing, socially responsible (ESG) investing, and smart beta strategies on robo-advisory platforms. Additionally, they examine robo-advisor performance during the market downturn in March 2020, the first significant market drawdown since their introduction, and find portfolio performance in agreement with broadly diversified stock and bond holdings. Consistent with expectations, robo-advisors also reported increased tax-loss harvesting activity during this downturn. Key Findings

Applications to $${\mathbb {A}}^1$$-enumerative geometry of the $${\mathbb {A}}^1$$-degree

These are lecture notes from the conference Arithmetic Topology at the Pacific Institute of Mathematical Sciences on applications of Morel's A1-degree to questions in enumerative geometry. Additionally, we give a new dynamic interpretation of the A1-Milnor number inspired by the first named author's enrichment of dynamic intersection numbers.

A Statistician Teaches Deep Learning

Deep learning (DL) has gained much attention and become increasingly popular in modern data science. Computer scientists led the way in developing deep learning techniques, so the ideas and perspectives can seem alien to statisticians. Nonetheless, it is important that statisticians become involved—many of our students need this expertise for their careers. In this paper, developed as part of a program on DL held at the Statistical and Applied Mathematical Sciences Institute, we address this culture gap and provide tips on how to teach deep learning to statistics graduate students. After some background, we list ways in which DL and statistical perspectives differ, provide a recommended syllabus that evolved from teaching two iterations of a DL graduate course, offer examples of suggested homework assignments, give an annotated list of teaching resources, and discuss DL in the context of two research areas.

RETRACTED: A proof of Nirenberg conjecture on expansive mappings in Hilbert spaces

This article has been retracted: please see Elsevier Policy on Article Withdrawal ( https://www.elsevier.com/about/our-business/policies/article-withdrawal ). This article has been retracted at the request of the Editors-in-Chief. A profound not fixable error has been found. The mistake is explained here below. Please note that this retraction notice has been updated in September 2021, as follows: The author claims to prove the following theorem that answers a challenging open problem from the book [L. Nirenberg, Topics in nonlinear functional analysis. Notes by R. A. Artino. New York: Courant Institute of Mathematical Sciences, New York University (1974; Zbl 0286.47037 )]: let X be a real Hilbert space, T : X → X be a continuous and α -expansive map such that T ( X ) has non-empty interior. Then T is surjective. Unfortunately, Step 1 of the proof essentially relies on the following erroneous “Bolzano-Weierstrass theorem for double sequences” (Theorem 6.5 from the paper [E. Habil, “Double sequences and double series”, IUG J. Nat. Stud. 14, 32 p. (2006)]): let ( p ( n , m ) ) n , m ∈ N be a bounded double sequence of reals, then there are n 1 < n 2 < … and m 1 < m 2 < … such that the double sequence ( p ( n k , m j ) ) k , j ∈ N converges. An easy counterexample to such a “Bolzano-Weierstrass theorem” appears if one takes p ( n , m ) = 0 for n < m and p ( n , m ) = 1 for n ⩾ m . ZB Math: https://zbmath.org/07265518

A Conversation about COVID-19 with Economists, Sociologists, Statisticians, and Operations Researchers

The COVID-19 pandemic is causing economic and social change. Moderated by David Banks, the Director of the Statistical and Applied Mathematical Sciences Institute (SAMSI), six eminent scientists who study different aspects of social change and public policy came together to discuss the impacts of the COVID-19 pandemic on the U.S. and the world. The discussion took a range of quantitative perspectives on how to respond to the crisis and to forecast what challenges lie ahead. Specific topics include the role of data science, strategies for beginning to reopen the economy, the international impact of the disease, and its effect upon universities.

A Conversation about COVID-19 with Biostatisticians and Epidemiologists

The COVID-19 pandemic is an almost unprecedented challenge. Moderated by David Banks, Director of the Statistical and Applied Mathematical Sciences Institute (SAMSI), five leading biostatisticians and epidemiologists discuss the probable scope and duration of the pandemic, the kinds of medical responses that we need, and some of the impacts they foresee on the U.S. and on the world. They also discuss the pandemic’s likely effect on higher education.

Corrigendum to "Incorporating structural prior information and sparsity into EIT using parallel level sets"

The copyright of the paper entitled Incorporating structural prior information and sparsity into EIT using parallel level sets [ 1 ] was originally owned by American Institute of Mathematical Sciences (AIMS, LLC) when it was published online in IPI Volume 13, Issue 2, April 2019 regular issue. The authors of this paper [ 1 ] paid the Open Access fee after the paper was published. The paper entitled Incorporating structural prior information and sparsity into EIT using parallel level sets [ 1 ] is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).

American Institute of Mathematical Sciences

This work aims to study the negative-order KdV equation in (3+1)-dimensions which is developed via using the recursion operator of the KdV equation by employing the three-wave methods. As a consequence, a variety of novel multiwave solutions with several arbitrary parameters to the considered equation are presented. Moreover, selecting particular values for the parameters, some graphs are plotted to show the spatial structures and dynamics of the resulting solutions. These results enrich the variety of the dynamics in the field of nonlinear waves.

A tutorial review of mathematical techniques for quantifying tumor heterogeneity.

Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.

A Compact Eulerian Representation of Axisymmetric Inviscid Vortex Sheet Dynamics

AbstractA classical problem in fluid mechanics is the motion of an axisymmetric vortex sheet evolving under the action of surface tension, surrounded by an inviscid fluid. Lagrangian descriptions of these dynamics are well‐known, involving complex nonlocal expressions for the radial and longitudinal velocities in terms of elliptic integrals. Here we use these prior results to arrive at a remarkably compact and exact Eulerian evolution equation for the sheet radius r(z, t) in an explicit flux form associated with the conservation of enclosed volume. The flux appears as an integral involving the pairwise mutual induction formula for vortex loop pairs first derived by Helmholtz and Maxwell. We show how the well‐known linear stability results for cylindrical vortex sheets in the presence of surface tension and streaming flows [A. M. Sterling and C. A. Sleicher, J. Fluid Mech. 68, 477 (1975)] can be obtained directly from this formulation. Furthermore, the inviscid limit of the empirical model of Eggers and Dupont [J. Fluid Mech. 262 205 (1994); SIAM J. Appl. Math. 60, 1997 (2000)], which has served as the basis for understanding singularity formation in droplet pinchoff, is derived within the present formalism as the leading‐order term in an asymptotic analysis for long slender axisymmetric vortex sheets and should provide the starting point for a rigorous analysis of singularity formation. © 2019 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.

Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations

AbstractWe study local regularity properties for solutions of linear, nonuniformly elliptic equations. Assuming certain integrability conditions on the coefficient field, we prove local boundedness and Harnack inequality. The assumed integrability assumptions are essentially sharp and improve upon classical results by Trudinger. We then apply the deterministic regularity results to the corrector equation in stochastic homogenization and establish sublinearity of the corrector. © 2019 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.

Inequalities in access to higher education in Africa: How large are they? Do they mirror the situation in the metropole 60 years ago?

There have been many studies of the socio-economic background of students in developed countries; but – apart from extensive commentary on the gender gap – far fewer in developing countries. In Africa, this is mostly because the University record systems do not record corresponding data; and because the international standard household surveys such as DHS only ask about educational attainment of household members which of course mainly excludes current students. This paper uses the record systems of the African Institute of Mathematical Sciences (AIMS) and specifically the Pre-Assessment form completed by all students on entry with information about their parental background.The combination of parents not having more than primary education, renting and not owning land identified only between 1 and 3 students a year. Taking the opposite extreme, the percentage of entrants reporting that their parents had a post-Secondary qualification is considerably higher (around 57% on average) than the norm at the time the parents would have been studying (around 7%). These students were certainly not poor, they are upper middle class. Further analysis identifies differences in the patterns for those at Anglophone or Francophone centres; and trends over the last four years.The paper then reviews the trends in inequality in access to higher education in the ‘mother’ countries – UK and France – from about sixty years ago until recently, to ask whether the social inequalities observed among AIMS students can be seen as ‘derived’ from those in the mother countries, with a nuanced positive conclusion.

Highlights of the Inaugural Data Science Leadership Summit

On March 26, 2018, the Data Science Institute at Columbia University <https://datascience.columbia.edu/> hosted the inaugural Data Science Leadership Summit. It drew together a cross-section of academic researchers and administrators to discuss how university practices could best adapt to the emerging field of data science. The summit was co-funded by the National Science Foundation, the Gordon and Betty Moore Foundation, and the Alfred P. Sloan Foundation. This interview with Jeannette Wing, the Avanessians Director of the Data Science Institute at Columbia University and the author of The Data Life Cycle <https://hdsr.mitpress.mit.edu/pub/577rq08d> , discusses the motivation of the summit and summarizes its key findings. The interview was conducted by another experienced leader in data science, David Banks, the Director of the Statistical and Applied Mathematical Sciences Institute (SAMSI). <https://www.samsi.info/people/staff/> Keywords: data science institute, education units, inter-disciplinary, multi-disciplinary, university administration

Endocrine disruptors database selects by evidence

A new database identifies 686 potential endocrine-disrupting chemicals (EDCs) on the basis of published data from rodent and human studies. Endocrine-disrupting chemicals interfere with the body’s regulatory system. Such chemicals can cause adverse developmental, immune, metabolic, neurological, and reproductive effects. To create the Database of Endocrine Disrupting Chemicals and their Toxicity Profiles (DEDuCT), a team from India’s Institute of Mathematical Sciences (IMSc) computationally mined more than 16,000 published research articles to identify those with information on EDCs. The compounds included in DEDuCT are those that had in vivo rodent, in vitro human, or in vivo human experimental evidence for endocrine disruption (Sci. Total Environ. 2019, DOI: 10.1016/j.scitotenv.2019.07.225). DEDuCT classifies the chemicals based on the type of experimental evidence, exposure sources, chemical structures, and physiological systems they affect. The database also includes the compounds’ known and predicted...

Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times

AbstractWe consider the Fröhlich model of the polaron, whose path integral formulation leads to the transformed path measureurn:x-wiley:15347710:media:cpa21858:cpa21858-math-0001with respect to ℙ that governs the law of the increments of the three‐dimensional Brownian motion on a finite interval [−T, T], and Zα, T is the partition function or the normalizing constant and α &gt; 0 is a constant, or the coupling parameter. The polaron measure reflects a self‐attractive interaction. According to a conjecture of Pekar that was proved in [9], urn:x-wiley:15347710:media:cpa21858:cpa21858-math-0002 exists and has a variational formula. In this article we show that when α &gt; 0 is either sufficiently small or sufficiently large, the limit exists, which is also identified explicitly. As a corollary, we deduce the central limit theorem for urn:x-wiley:15347710:media:cpa21858:cpa21858-math-0003 under and obtain an expression for the limiting variance. © 2019 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, LLC.