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Mathematical Reviews ® /MathSciNet ®

Since 1940, Mathematical Reviews ® (MR) has served researchers and scholars in the mathematical sciences by providing timely information on peer-reviewed articles and books. MathSciNet ® , the electronic version of MR, presents a fully searchable database with many tools designed to help navigate the mathematical sciences literature, including:

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Applied mathematics articles from across Nature Portfolio

Applied mathematics is the application of mathematical techniques to describe real-world systems and solve technologically relevant problems. This can include the mechanics of a moving body, the statistics governing the atoms in a gas or developing more efficient algorithms for computational analysis. These ideas are closely linked with those of theoretical physics.

Latest Research and Reviews

Soliton solutions of nonlinear coupled Davey–Stewartson Fokas system using modified auxiliary equation method and extended \((G'/G^{2})\) -expansion method

• M. Atta Ullah Khan
• Maasoomah Sadaf
• Y. S. Hamed

Nonlinear flow modeling of electro hydrostatic pump unit based on Gauss Newton iterative method for high performance control

• Tiangui Zhang
• Guishan Yan

On complexity of colloid cellular automata

• Andrew Adamatzky
• Nic Roberts
• Alessandro Chiolerio

A plethora of novel solitary wave solutions related to van der Waals equation: a comparative study

• Asma Rashid Butt
• Adil Jhangeer
• Murad Khan Hassani

A drug mix and dose decision algorithm for individualized type 2 diabetes management

• Mila Nambiar
• Yong Mong Bee
• Pavitra Krishnaswamy

Sensitivity analysis and global stability of epidemic between Thais and tourists for Covid -19

• Rattiya Sungchasit
• I.-Ming Tang
• Puntani Pongsumpun

News and Comment

Computational design of art-inspired metamaterials

In recent years, there has been a surge of interest in the design of mechanical metamaterials for different science and engineering applications. In particular, various computational approaches have been developed to facilitate the systematic design of art-inspired metamaterials including origami and kirigami metamaterials. In this Comment, we highlight the recent advances and discuss the outlook for the computational design of art-inspired metamaterials.

• Gary P. T. Choi

50 years of Penrose tilings

50 years ago Roger Penrose described a set of aperiodic tilings, now named after him, that have fascinated artists, mathematicians and physicists ever since.

• Iulia Georgescu

The importance of spatial heterogeneity in disease transmission

Spatial heterogeneity in disease transmission rates and in mixing patterns between regions makes predicting epidemic trajectories hard. Quantifying the mixing rates within and between spatial regions can improve predictions.

• Emily Paige Harvey
• Dion R. J. O’Neale

Computational morphology and morphogenesis for empowering soft-matter engineering

Morphing soft matter, which is capable of changing its shape and function in response to stimuli, has wide-ranging applications in robotics, medicine and biology. Recently, computational models have accelerated its development. Here, we highlight advances and challenges in developing computational techniques, and explore the potential applications enabled by such models.

Long ties across networks accelerate the spread of social contagions

Long ties that bridge socially separate regions of networks are critical for the spread of contagions, such as innovations or adoptions of new norms. Contrary to previous thinking, long ties have now been found to accelerate social contagions, even for behaviours that involve the social reinforcement of adoption by network neighbours.

The curious case of the test set AUROC

The area under the receiver operating characteristic curve (AUROC) of the test set is used throughout machine learning (ML) for assessing a model’s performance. However, when concordance is not the only ambition, this gives only a partial insight into performance, masking distribution shifts of model outputs and model instability.

• Michael Roberts
• Carola-Bibiane Schönlieb

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arXiv is a free distribution service and an open-access archive for nearly 2.4 million scholarly articles in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics. Materials on this site are not peer-reviewed by arXiv.

arXiv is a free distribution service and an open-access archive for scholarly articles in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics. Materials on this site are not peer-reviewed by arXiv.

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Mathematics Preprints

Mathematics is the study of quantity, structure, pattern, and shape. It can be studied as abstract concepts independently of any direct application outside mathematics (i.e., pure mathematics), or applied to other disciplines such as physics, biology, and engineering (i.e., applied mathematics). The Mathematics Research Network on SSRN is an open access preprint server that provides a venue for authors to showcase their research papers in our digital library, speeding up the dissemination and providing the scholarly community access to groundbreaking working papers and early-stage research. SSRN provides the opportunity to share different outputs of research such as preprints, preliminary or exploratory investigations, book chapters, PhD dissertations, course and teaching materials, presentations, and posters among others. SSRN also helps mathematics scholars discover the latest research in their own and other fields of interest, while providing a platform for the early sharing of their own work, making it available for subsequent work to be built upon more quickly.

Mathematics serves as a fundamental tool for our scientific understanding of the world. Since the beginning of recorded history, mathematical discovery has been at the forefront of every civilized society and, with its continuous contribution to other disciplines, has facilitated a more profound understanding of other scientific areas. SSRN fosters this interdisciplinary connection by enabling scholars to find related research in all research areas, including natural science, engineering, physics, medicine, architecture, computer science, and the social sciences.

Mathematics Papers

On the zeros of partition functions with multi-spin interactions

Computing the theta function, a quick estimate for the volume of a polyhedron (with m. rudelson), when a system of real quadratic equations has a solution (with m. rudelson), smoothed counting of 0-1 points in polyhedra, testing systems of real quadratic equations for approximate solutions, more on zeros and approximation of the ising partition function (with n. barvinok), a remark on approximating permanents of positive definite matrices, integrating products of quadratic forms, testing for dense subsets in a graph via the partition function (with a. della pella), approximating real-rooted and stable polynomials, with combinatorial applications, stability and complexity of mixed discriminants, computing permanents of complex diagonally dominant matrices and tensors, weighted counting of solutions to sparse systems of equations (with g. regts), approximating permanents and hafnians, concentration of the mixed discriminant of well-conditioned matrices, computing the partition function of a polynomial on the boolean cube, computing the partition function for graph homomorphisms with multiplicities (with p. soberon), computing the partition function for graph homomorphisms (with p. soberon), computing the partition function for cliques in a graph, computing the permanent of (some) complex matrices, on testing hamiltonicity of graphs, convexity of the image of a quadratic map via the relative entropy distance, thrifty approximations of convex bodies by polytopes, approximations of convex bodies by polytopes and by projections of spectrahedra, explicit constructions of centrally symmetric k -neighborly polytopes and large strictly antipodal sets (with s.j. lee and i. novik), a bound for the number of vertices of a polytope with applications, centrally symmetric polytopes with many faces (with s.j. lee and i. novik), neighborliness of the symmetric moment curve (with s.j. lee and i. novik), matrices with prescribed row and column sums, computing the partition function for perfect matchings in a hypergraph (with a. samorodnitsky), the number of graphs and a random graph with a given degree sequence (with j.a. hartigan), an asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums (with j.a. hartigan), maximum entropy gaussian approximation for the number of integer points and volumes of polytopes (with j.a. hartigan), what does a random contingency table look like, on the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries, an approximation algorithm for counting contingency tables (with z. luria, a. samorodnitsky and a. yong), asymptotic estimates for the number of contingency tables, integer flows, and volumes of transportation polytopes, a centrally symmetric version of the cyclic polytope (with i. novik), the computational complexity of convex bodies (with e. veomett), brunn-minkowski inequalities for contingency tables and integer flows, the complexity of generating functions for integer points in polyhedra and beyond, enumerating contingency tables via random permanents, approximating orthogonal matrices by permutation matrices, computing the ehrhart quasi-polynomial of a rational simplex, integration and optimization of multivariate polynomials by restriction onto a random subspace, lattice points, polyhedra, and complexity, convex geometry of orbits (with g. blekherman), c++ codes for estimating permanents, hafnians and the number of forests in a graph, random weighting, asymptotic counting, and inverse isoperimetry (with a. samorodnitsky), short rational generating functions for lattice point problems (with k. woods), estimating l- infinity norms by l 2k norms for functions on orbits, approximating a norm by a polynomial, the distribution of values in the quadratic assignment problem (with t. stephen), the maximum traveling salesman problem (with e.kh. gimadi and a.i. serdyukov), new permanent estimators via non-commutative determinants, a c++ code to compute bounds for the permanent of a 0-1 matrix by the ``average distance'' approach, the distance approach to approximate combinatorial counting (with a. samorodnitsky), a remark on the rank of positive semidefinite matrices subject to affine constraints, polynomial time algorithms to approximate permanents and mixed discriminants within a simply exponential factor, finding maximum length tours under polyhedral norms (with d. johnson, g. woeginger, and r. woodroofe), an algorithmic theory of lattice points in polyhedra (with j. pommersheim).

Mathematics at MIT is administratively divided into two categories: Pure Mathematics and Applied Mathematics. They comprise the following research areas:

Pure Mathematics

• Algebra & Algebraic Geometry
• Algebraic Topology
• Analysis & PDEs
• Mathematical Logic & Foundations
• Number Theory
• Probability & Statistics
• Representation Theory

Applied Mathematics

In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications.

• Combinatorics
• Computational Biology
• Physical Applied Mathematics
• Computational Science & Numerical Analysis
• Theoretical Computer Science
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Natural Sciences Tripos Mathematics Papers 2024

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