applied mathematics research paper

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Applied mathematics articles within Nature

Article 19 June 2024 | Open Access

Multiscale topology classifies cells in subcellular spatial transcriptomics

 A method for topological automatic cell type classification across subcellular resolution spatial transcriptomic platforms is proposed, resolving cell type information and locating sparsely dispersed cells in human kidney and mouse kidney and brain.

• Katherine Benjamin
• , Aneesha Bhandari
•  &  Katherine R. Bull

Article 13 September 2023 | Open Access

Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel

Analysis of a large dataset of scanning transmission X-ray microscopy images of carbon-coated lithium iron phosphate nanoparticles shows that the heterogeneous reaction kinetics of battery materials can be learned from such videos pixel by pixel.

• Hongbo Zhao
• , Haitao Dean Deng
•  &  Martin Z. Bazant

Article | 09 August 2023

Solid-body trajectoids shaped to roll along desired pathways

An algorithm is developed to design a shape, a trajectoid, that can trace any given infinite periodic trajectory when rolling down a slope, finding unexpected implications for quantum and classical optics.

• Yaroslav I. Sobolev
• , Ruoyu Dong
•  &  Bartosz A. Grzybowski

Article | 26 July 2023

Heat-assisted detection and ranging

Heat-assisted detection and ranging is experimentally shown to see texture and depth through darkness as if it were day, and also perceives decluttered physical attributes beyond RGB or thermal vision.

• Fanglin Bao
• , Xueji Wang
•  &  Zubin Jacob

Article 05 October 2022 | Open Access

Discovering faster matrix multiplication algorithms with reinforcement learning

A reinforcement learning approach based on AlphaZero is used to discover efficient and provably correct algorithms for matrix multiplication, finding faster algorithms for a variety of matrix sizes.

• Alhussein Fawzi
• , Matej Balog
•  &  Pushmeet Kohli

Article | 24 August 2022

Mechanical integrated circuit materials

A mechanical integrated circuit material based on Boolean mathematics and reconfigurable electrical circuits is created to demonstrate scalable information processing in synthetic, engineered soft matter.

• Charles El Helou
• , Benjamin Grossmann
•  &  Ryan L. Harne

Perspective | 11 May 2022

Transitioning organizations to post-quantum cryptography

Standards and recommendations for transitioning organizations to quantum-secure cryptographic protocols are outlined, including a discussion of transition timelines and the leading strategies to protect systems against quantum attacks.

• David Joseph
• , Rafael Misoczki
•  &  Royal Hansen

Article | 09 February 2022

Outracing champion Gran Turismo drivers with deep reinforcement learning

Using the game Gran Turismo, an agent was trained with a combination of deep reinforcement learning algorithms and specialized training scenarios, demonstrating success against championship-level human racers.

• Peter R. Wurman
• , Samuel Barrett
•  &  Hiroaki Kitano

Article | 14 April 2021

Non-reciprocal phase transitions

A theoretical study of non-reciprocity in collective phenomena reveals the emergence of time-dependent phases heralded by exceptional points in contexts ranging from synchronization and flocking to pattern formation.

• Michel Fruchart
• , Ryo Hanai
•  &  Vincenzo Vitelli

Article | 18 March 2020

Loopy Lévy flights enhance tracer diffusion in active suspensions

A theoretical framework describing the hydrodynamic interactions between a passive particle and an active medium in out-of-equilibrium systems predicts long-range Lévy flights for the diffusing particle driven by the density of the active component.

• Kiyoshi Kanazawa
• , Tomohiko G. Sano
•  &  Adrian Baule

Letter | 04 September 2019

Information gerrymandering and undemocratic decisions

In a voter game, information gerrymandering can sway the outcome of the vote towards one party, even when both parties have equal sizes and each player has the same influence; and this effect can be exaggerated by strategically placed zealots or automated bots.

• Alexander J. Stewart
• , Mohsen Mosleh
•  &  Joshua B. Plotkin

Letter | 30 January 2019

Tissue curvature and apicobasal mechanical tension imbalance instruct cancer morphogenesis

Three-dimensional imaging of mouse pancreatic ducts before and after oncogenic transformation reveals that epithelial tumorigenesis is determined by the relationship between tissue curvature and apical–basal mechanical tension.

• Hendrik A. Messal
• , Silvanus Alt
•  &  Axel Behrens

Letter | 23 January 2019

Computational periscopy with an ordinary digital camera

A faint penumbra in a photograph of a diffuse surface enables recovery of the position of the object creating the penumbra and an image of the scene behind it.

• Charles Saunders
• , John Murray-Bruce
•  &  Vivek K Goyal

Letter | 17 October 2018

A separated vortex ring underlies the flight of the dandelion

The flight of dandelion seeds is enabled by an extraordinary vortex ring, which was revealed by the visualization of the flow around the seed.

• Cathal Cummins
• , Madeleine Seale
•  &  Naomi Nakayama

Letter | 23 May 2018

Addressing the minimum fleet problem in on-demand urban mobility

An optimal computationally efficient solution to the problem of finding the minimum taxi fleet size using a vehicle-sharing network is presented.

• M. M. Vazifeh
•  &  C. Ratti

Article 01 March 2018 | Open Access

Mapping local variation in educational attainment across Africa

Local-level analyses show that, despite marked progress in educational attainment from 2000 to 2015 across Africa, substantial differences persist between locations and sexes that have widened in many countries.

• Nicholas Graetz
• , Joseph Friedman
•  &  Simon I. Hay

Letter | 05 October 2017

Giga-voxel computational morphogenesis for structural design

Giga-voxel-resolution computational morphogenesis is used to optimize the internal structure of a full-scale aeroplane wing, yielding light-weight designs with more similarities to animal bone structures than to current aeroplane wing designs.

• , Erik Andreassen
•  &  Ole Sigmund

Article | 13 April 2017

A living mesoscopic cellular automaton made of skin scales

A mesoscopic cellular automaton arising from a microscopic reaction–diffusion system as a function of skin thickness is observed in ocellated lizards, showing that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

• Liana Manukyan
• , Sophie A. Montandon
•  &  Michel C. Milinkovitch

Letter | 29 March 2017

Evolutionary dynamics on any population structure

The authors derive a condition for how natural selection chooses between two competing strategies on any graph for weak selection, elucidating which population structures promote certain behaviours, such as cooperation.

• Benjamin Allen
• , Gabor Lippner
•  &  Martin A. Nowak

Letter | 27 April 2016

Dynamics from noisy data with extreme timing uncertainty

A data-analytical approach that can extract the history and dynamics of complex systems from noisy snapshots on timescales much shorter than the uncertainty with which the data were recorded is described; the approach is demonstrated by extracting the dynamics on the few-femtosecond timescale from experimental data recorded with 300-femtosecond timing uncertainty.

• , A. M. Hanna
•  &  A. Ourmazd

Letter | 21 October 2015

The rise of fully turbulent flow

Experiments, asymptotic theory and computer simulations of wall-bounded shear flow uncover a bifurcation scenario that explains the transition from localized turbulent patches to fully turbulent flow.

• Dwight Barkley
• , Baofang Song
•  &  Björn Hof

Letter | 26 August 2015

The disruption of multiplanet systems through resonance with a binary orbit

In a multiplanet system, when orbital precession is fast enough to resonate with the orbital motion of a distant binary companion, the results range from excitation of large planetary eccentricities and mutual inclinations to total disruption.

• Jihad R. Touma
•  &  S. Sridhar

Letter | 22 May 2013

Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence

A magnetohydrodynamic simulation of a magnetized plasma at high conductivity shows that, whereas the magnetic flux can be considered ‘frozen’ into the medium for laminar flow, in a turbulent medium the motion of the field lines can become indeterministic, leading to a breakdown in flux freezing.

• Gregory Eyink
• , Ethan Vishniac
•  &  Alexander Szalay

Shear-driven dynamo waves at high magnetic Reynolds number

High-resolution simulations show that dynamos can generate organized fields at high conductivity in the form of propagating dynamo waves.

• S. M. Tobias
•  &  F. Cattaneo

Letter | 23 December 2012

Topological colloids

Topologically distinct colloidal particles introduced into a nematic liquid crystal align and generate topology-constrained three-dimensional director fields and defects in the liquid crystal fluid that can be manipulated with a variety of methods, opening up a new area of exploration in the field of soft matter.

• Bohdan Senyuk
• , Qingkun Liu
•  &  Ivan I. Smalyukh

News | 14 September 2012

The astronomical unit gets fixed

Earth–Sun distance changes from slippery equation to single number.

• Geoff Brumfiel

News | 10 September 2012

Proof claimed for deep connection between primes

If it is true, a solution to the abc conjecture about whole numbers would be an ‘astounding’ achievement.

• Philip Ball

Books & Arts | 05 September 2012

Q&A: Maths demystifier

Mathematician Glen Whitney left a job in finance to set up the Museum of Mathematics (MoMath), which is due to open in Manhattan, New York, on 15 December. He wants to spread the word that mathematics is a beautiful discipline and all around us, from the geometry of soap bubbles to the algorithms that control traffic lights.

• Jascha Hoffman

News | 06 January 2012

Mathematician claims breakthrough in Sudoku puzzle

Puzzles must have at least 17 clues to have a valid solution.

• Eugenie Samuel Reich

Books & Arts | 26 October 2011

Q&A: The mathemagician

Mathematician Persi Diaconis of Stanford University in California ran away from home in his teens to perform card tricks. As he publishes a book on the mathematics of magic, co-authored with juggler and fellow mathematician Ron Graham, he explains what makes a good trick.

Books & Arts | 24 August 2011

Mathematics: Life models

Biology is too complex to be unified by mathematics, finds Marc Feldman.

• Marc Feldman

Correspondence | 10 August 2011

Mathematics walks into history

News | 23 February 2011

Testing the expanding Universe

A model of the cosmological constant invokes alternate realities.

• Kate McAlpine

News & Views | 12 January 2011

Beyond Feynman's diagrams

Generations of physicists have spent much of their lives using Richard Feynman's famous diagrams to calculate how particles interact. New mathematical tools are simplifying the results and suggesting improved underlying principles.

Review Article | 15 December 2010

Emerging properties of animal gene regulatory networks

• Eric H. Davidson

Obituary | 17 November 2010

Benoît Mandelbrot (1924–2010)

Mathematician, and father of fractal geometry, who described the roughness of nature.

• Ralph Gomory

News Feature | 16 June 2010

Metrics: Do metrics matter?

Many researchers believe that quantitative metrics determine who gets hired and who gets promoted at their institutions. With an exclusive poll and interviews, Nature probes to what extent metrics are really used that way.

• Alison Abbott
• , David Cyranoski
•  &  Richard Van Noorden

Opinion | 16 June 2010

How to improve the use of metrics

Since the invention of the science citation index in the 1960s, quantitative measuring of the performance of researchers has become ever more prevalent, controversial and influential. Six commentators tell Nature what changes might ensure that individuals are assessed more fairly.

Metrics: A profusion of measures

Scientific performance indicators are proliferating — leading researchers to ask afresh what they are measuring and why. Richard Van Noorden surveys the rapidly evolving ecosystem.

• Richard Van Noorden

News & Views | 24 February 2010

The statistics of style

A mathematical method has been developed that distinguishes between the paintings of Pieter Bruegel the Elder and those of his imitators. But can the approach be used to spot imitations of works by any artist?

• Bruno A. Olshausen
•  &  Michael R. DeWeese

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Recent Master’s Research Papers - Applied Mathematics

Master's research papers 2022.

Ziyuan Sun:  An Introduction to the Optimal Trajectory Tracking Problem with Feedback Control Designs

Nathaniel Stemen: Quantum Circuit Compilation From The Ground Up

Master's Research Papers 2018

Jian Liang:  Design of an Automatic Facial Expression Detector

Master's Research Papers 2017

Riley Brooks:  Convergence Analysis of Deterministic and Stochastic Methods

Alexander Vukadinovic:  Using Machine Learning Algorithms to Better Bound the Uncertainty Ranges of Parameters in GCMs

Master's Research Papers 2016

Zhanlue Liang:  System and Network Synchronization

Master's Research Papers 2015

In-Ting Ho:  Improvements on circle packing algorithms in two-dimensional cross-sectional areas

Kenneth Webster:  Image Inpainting: A Review of Early Work and Introduction of a Multilevel Approach

Master's Research Papers 2014

Amir Issaei:  Estimation of Infinite-Dimensional Systems

Trefethen's list of 13 classic papers in applied mathematics

• J.W. Cooley and J.W. Tukey, " An algorithm for the machine calculation of complex Fourier series ," Math. Comp. , 19 (1965), pp. 297–301.
• R. Courant, K. Friedrichs, and H. Lewy, " On the partial difference equations of mathematical physics ," IBM J. Res. Develop. , 11 (1967), pp. 215–234.
• A.S. Householder, " Unitary triangularization of a nonsymmetric matrix ," J. Assoc. Comput. Mach. , 5 (1958), pp. 339–342.
• C.F. Curtiss and J.O. Hirschfelder, " Integration of stiff equations ," Proc. Nat. Acad. Sci. U.S.A. , 38 (1952), pp. 235–243.
• C. de Boor, " On calculating with B -splines ," J. Approximation Theory , 6 (1972), pp. 50–62.
• R. Courant, " Variational methods for the solution of problems of equilibrium and vibrations ," Bull. Amer. Math. Soc. , 49 (1943), pp. 1–23.
• G. Golub and W. Kahan, " Calculating the singular values and pseudo-inverse of a matrix ," J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. , 2 (1965), pp. 205–224.
• A. Brandt, " Multi-level adaptive solutions to boundary-value problems ," Math. Comp. , 31 (1977), no. 138, pp. 333–390.
• M.R. Hestenes and E. Stiefel, " Methods of conjugate gradients for solving linear systems ," J. Research Nat. Bur. Standards , 49 (1952), pp. 409–436.
• R. Fletcher and M.J.D. Powell, "A rapidly convergent descent method for minimization," Comput. J. , 6 (1963/1964), pp. 163–168.
• G. Wanner, E. Hairer, and S.P. Nørsett, " Order stars and stability theorems ," BIT , 18 (1978), no. 4, pp. 475–489.
• N. Karmarkar, "A new polynomial-time algorithm for linear programming," Combinatorica , 4 (1984), no. 4, pp. 373–395.
• L. Greengard and V. Rokhlin, " A fast algorithm for particle simulations ," J. Comput. Phys. , 73 (1987), no. 2, pp. 325–348.

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Indian Journal of Pure and Applied Mathematics

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Mathematics > Numerical Analysis

Title: iterative refinement with low-precision posits.

Abstract: This research investigates using a mixed-precision iterative refinement method using posit numbers instead of the standard IEEE floating-point format. The method is applied to solve a general linear system represented by the equation $Ax = b$, where $A$ is a large sparse matrix. Various scaling techniques, such as row and column equilibration, map the matrix entries to higher-density regions of machine numbers before performing the $O(n^3)$ factorization operation. Low-precision LU factorization followed by forward/backward substitution provides an initial estimate. The results demonstrate that a 16-bit posit configuration combined with equilibration produces accuracy comparable to IEEE half-precision (fp16), indicating a potential for achieving a balance between efficiency and accuracy.

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