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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 Materials on this site are not peer-reviewed by arXiv.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 Materials on this site are not peer-reviewed by arXiv.

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Research in the Mathematical Sciences

Research in the Mathematical Sciences is an international, peer-reviewed journal encompassing the full scope of theoretical and applied mathematics, as well as theoretical computer science.

• Encourages submission of longer articles for more complex and detailed analysis and proofing of theorems.
• Publishes shorter research communications (Letters) covering emerging areas of mathematical research.
• Actively seeks to publish seminal papers in emerging and interdisciplinary areas in all of the mathematical sciences.
• Editors play a pivotal role in soliciting high-quality research papers.
• Editorial decisions are made in a timely manner.

This is a transformative journal , you may have access to funding.

• Thomas Y. Hou,
• Lisa Jeffrey,
• Malabika Pramanik,
• Fadil Santosa,
• Yuri Tschinkel

Latest articles

Quantum q -series and mock theta functions.

• Amanda Folsom
• David Metacarpa

Some remarks about \( \rho \) -regularity for real analytic maps

• Maico Ribeiro
• Ivan Santamaria
• Thiago da Silva

Higher derivatives of functions with given critical points and values

Matroid products in tropical geometry.

• Nicholas Anderson

Closed orientable surfaces and fold Gauss maps

• C. Mendes de Jesus
• Pantaleón D. Romero
• E. Sanabria-Codesal

Journal updates

Transmission eigenvalues and related spectral problems in scattering theory (submission deadline: june 30, 2021).

This special issue will feature recent developments in the theory and applications of transmission eigenvalues and related spectral problems in direct and inverse scattering theory. The transmission eigenvalue problem is at the heart of inverse scattering theory for inhomogeneous media. It has a deceptively simple formulation but presents a perplexing mathematical structure; in particular it is a non-self-adjoint eigenvalue problem. This subject is rich, active and in the past decade has taken a multitude of directions, including developments in the spectral theory for various operators related to scattering, as well as many applications in inverse scattering problems and imaging. We solicit high quality original research papers targeting results on the theory, computations and applications of these topics.

Guest Editor : Fioralba Cakoni, Rutgers University and Houssem Haddar, CMAP Ecole Polytechnique

Submission Deadline : April 30, 2021

Download full details here:  Transmission eigenvalues and Related Spectral Problems in Scattering Theory (PDF, 19.17 kB)

Mathematical Theory of Machine Learning and Applications (Submission Deadline: 31st August, 2021)

In the past decade, deep learning as a branch of machine learning has influenced scientific computing in a fundamental way. This computational breakthrough presents tremendous opportunities and needs for new perspectives on computational mathematics and related emerging fields, such as approximation theory, operator estimation, numerical PDEs, inverse problems, data-driven modeling of dynamical systems, unsupervised and semi-supervised learnings. This special issue will feature high-quality original research, including (but not limited to) the theoretical and computational developments in these topics. Guest Editors:  John Harlim, Thomas Hou, Jinchao Xu Submission Deadline:  August 31, 2021 Download full details here:  Mathematical Theory of Machine Learning and Applications

PDE Methods for Machine Learning (Submission Deadline: 31st August 2021)

This special issue will feature recent developments in the application of partial differential equations (PDE) to problems in machine learning. We solicit high quality original research papers targeting the analysis and applications of PDEs to problems in machine learning and data science.

Guest Editors:  Jeff Calder (University of Minnesota), Xiuyuan Cheng (Duke University), Adam Oberman (McGill University), Lars Ruthotto (Rutgers University)

Submission Deadline:  31st August 2021

Download Full Details Here: 

PDE Methods for Machine Learning

Developments in Commutative Algebra: In honor of Jürgen Herzog on the occasion of his 80th Birthday

Jürgen Herzog is one of the most accomplished researchers in the modern developments of commutative algebra. He has produced more than 230 original research papers and is cited more than 6650 times by approximately 2150 authors. In honor of his great achievements, we look forward to publishing a special issue commemorating his 80th birthday and honoring his influence on the field of commutative algebra and mathematics in general.

Guest Editor:  Takayuki Hibi  Submission Deadline:  31st December 2021 Download Full Details Here:  Developments in Commutative Algebra

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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).

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Study Suggests Genetics as a Cause, Not Just a Risk, for Some Alzheimer’s

People with two copies of the gene variant APOE4 are almost certain to get Alzheimer’s, say researchers, who proposed a framework under which such patients could be diagnosed years before symptoms.

By Pam Belluck

Scientists are proposing a new way of understanding the genetics of Alzheimer’s that would mean that up to a fifth of patients would be considered to have a genetically caused form of the disease.

Currently, the vast majority of Alzheimer’s cases do not have a clearly identified cause. The new designation, proposed in a study published Monday, could broaden the scope of efforts to develop treatments, including gene therapy, and affect the design of clinical trials.

It could also mean that hundreds of thousands of people in the United States alone could, if they chose, receive a diagnosis of Alzheimer’s before developing any symptoms of cognitive decline, although there currently are no treatments for people at that stage.

The new classification would make this type of Alzheimer’s one of the most common genetic disorders in the world, medical experts said.

“This reconceptualization that we’re proposing affects not a small minority of people,” said Dr. Juan Fortea, an author of the study and the director of the Sant Pau Memory Unit in Barcelona, Spain. “Sometimes we say that we don’t know the cause of Alzheimer’s disease,” but, he said, this would mean that about 15 to 20 percent of cases “can be tracked back to a cause, and the cause is in the genes.”

The idea involves a gene variant called APOE4. Scientists have long known that inheriting one copy of the variant increases the risk of developing Alzheimer’s, and that people with two copies, inherited from each parent, have vastly increased risk.

The new study , published in the journal Nature Medicine, analyzed data from over 500 people with two copies of APOE4, a significantly larger pool than in previous studies. The researchers found that almost all of those patients developed the biological pathology of Alzheimer’s, and the authors say that two copies of APOE4 should now be considered a cause of Alzheimer’s — not simply a risk factor.

The patients also developed Alzheimer’s pathology relatively young, the study found. By age 55, over 95 percent had biological markers associated with the disease. By 65, almost all had abnormal levels of a protein called amyloid that forms plaques in the brain, a hallmark of Alzheimer’s. And many started developing symptoms of cognitive decline at age 65, younger than most people without the APOE4 variant.

“The critical thing is that these individuals are often symptomatic 10 years earlier than other forms of Alzheimer’s disease,” said Dr. Reisa Sperling, a neurologist at Mass General Brigham in Boston and an author of the study.

She added, “By the time they are picked up and clinically diagnosed, because they’re often younger, they have more pathology.”

People with two copies, known as APOE4 homozygotes, make up 2 to 3 percent of the general population, but are an estimated 15 to 20 percent of people with Alzheimer’s dementia, experts said. People with one copy make up about 15 to 25 percent of the general population, and about 50 percent of Alzheimer’s dementia patients.

The most common variant is called APOE3, which seems to have a neutral effect on Alzheimer’s risk. About 75 percent of the general population has one copy of APOE3, and more than half of the general population has two copies.

Alzheimer’s experts not involved in the study said classifying the two-copy condition as genetically determined Alzheimer’s could have significant implications, including encouraging drug development beyond the field’s recent major focus on treatments that target and reduce amyloid.

Dr. Samuel Gandy, an Alzheimer’s researcher at Mount Sinai in New York, who was not involved in the study, said that patients with two copies of APOE4 faced much higher safety risks from anti-amyloid drugs.

When the Food and Drug Administration approved the anti-amyloid drug Leqembi last year, it required a black-box warning on the label saying that the medication can cause “serious and life-threatening events” such as swelling and bleeding in the brain, especially for people with two copies of APOE4. Some treatment centers decided not to offer Leqembi, an intravenous infusion, to such patients.

Dr. Gandy and other experts said that classifying these patients as having a distinct genetic form of Alzheimer’s would galvanize interest in developing drugs that are safe and effective for them and add urgency to current efforts to prevent cognitive decline in people who do not yet have symptoms.

“Rather than say we have nothing for you, let’s look for a trial,” Dr. Gandy said, adding that such patients should be included in trials at younger ages, given how early their pathology starts.

Besides trying to develop drugs, some researchers are exploring gene editing to transform APOE4 into a variant called APOE2, which appears to protect against Alzheimer’s. Another gene-therapy approach being studied involves injecting APOE2 into patients’ brains.

The new study had some limitations, including a lack of diversity that might make the findings less generalizable. Most patients in the study had European ancestry. While two copies of APOE4 also greatly increase Alzheimer’s risk in other ethnicities, the risk levels differ, said Dr. Michael Greicius, a neurologist at Stanford University School of Medicine who was not involved in the research.

“One important argument against their interpretation is that the risk of Alzheimer’s disease in APOE4 homozygotes varies substantially across different genetic ancestries,” said Dr. Greicius, who cowrote a study that found that white people with two copies of APOE4 had 13 times the risk of white people with two copies of APOE3, while Black people with two copies of APOE4 had 6.5 times the risk of Black people with two copies of APOE3.

“This has critical implications when counseling patients about their ancestry-informed genetic risk for Alzheimer’s disease,” he said, “and it also speaks to some yet-to-be-discovered genetics and biology that presumably drive this massive difference in risk.”

Under the current genetic understanding of Alzheimer’s, less than 2 percent of cases are considered genetically caused. Some of those patients inherited a mutation in one of three genes and can develop symptoms as early as their 30s or 40s. Others are people with Down syndrome, who have three copies of a chromosome containing a protein that often leads to what is called Down syndrome-associated Alzheimer’s disease .

Dr. Sperling said the genetic alterations in those cases are believed to fuel buildup of amyloid, while APOE4 is believed to interfere with clearing amyloid buildup.

Under the researchers’ proposal, having one copy of APOE4 would continue to be considered a risk factor, not enough to cause Alzheimer’s, Dr. Fortea said. It is unusual for diseases to follow that genetic pattern, called “semidominance,” with two copies of a variant causing the disease, but one copy only increasing risk, experts said.

The new recommendation will prompt questions about whether people should get tested to determine if they have the APOE4 variant.

Dr. Greicius said that until there were treatments for people with two copies of APOE4 or trials of therapies to prevent them from developing dementia, “My recommendation is if you don’t have symptoms, you should definitely not figure out your APOE status.”

He added, “It will only cause grief at this point.”

Finding ways to help these patients cannot come soon enough, Dr. Sperling said, adding, “These individuals are desperate, they’ve seen it in both of their parents often and really need therapies.”

Pam Belluck is a health and science reporter, covering a range of subjects, including reproductive health, long Covid, brain science, neurological disorders, mental health and genetics. More about Pam Belluck

The Fight Against Alzheimer’s Disease

Alzheimer’s is the most common form of dementia, but much remains unknown about this daunting disease..

How is Alzheimer’s diagnosed? What causes Alzheimer’s? We answered some common questions .

A study suggests that genetics can be a cause of Alzheimer’s , not just a risk, raising the prospect of diagnosis years before symptoms appear.

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Alzheimer’s can make communicating difficult. We asked experts for tips on how to talk to someone with the disease .

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CSIR NET Syllabus 2024: Subject-wise Latest Syllabus PDF Download

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CSIR NET Syllabus 2024: The Council of Scientific and Industrial Research (CSIR) has published the CSIR NET subject-wise syllabus on its official website. The CSIR NET syllabus is categorized into three parts: Part A, Part B, and Part C. Part A syllabus primarily focuses on General Aptitude, while Part B & Part C vary depending on the subjects. The syllabus comprises five subjects: Earth, Atmospheric, Ocean, and Planetary Sciences, Chemical Sciences, Life Sciences, Mathematical Sciences, and Physical Sciences.

Candidates should thoroughly familiarize themselves with all the topics of the respective CSIR NET subjects for effective exam preparation. Alongside the subject-wise syllabus, aspirants should also review the exam pattern to grasp the exam requirements comprehensively.

Check the complete CSIR NET syllabus 2024, including the exam pattern, exam strategy, and recommendations for the best books to excel in the exam. Also, find the direct CSIR NET Syllabus 2024 PDF download link here.

Also, read:

• CSIR NET Eligibility
• CSIR NET Application Form
• CSIR NET Cut Off

CSIR NET Syllabus 2024

CSIR NET exam is held annually to determine the eligibility of Indian Nationals for Junior Research Fellowships and Assistant Professor positions in Indian universities and colleges. Aspirants should have the CSIR NET syllabus readily available before beginning their exam preparation. The syllabus is divided into three parts, all of which consist of objective-type multiple-choice questions. There will be no break between papers. Below, we have discussed the CSIR NET exam syllabus for all five subjects: Earth, Atmospheric, Ocean and Planetary Sciences, Chemical Sciences, Life Sciences, Mathematical Sciences, and Physical Sciences.

CSIR UGC NET Syllabus 2024 Overview

Before beginning with the preparation, the candidate must be aware of everything about CSIR NET Syllabus and we have provided all the details below.

CSIR NET Syllabus 2024 PDF

Candidates must download the subject-wise CSIR NET syllabus PDF to understand topics that need to be covered during the preparation. It will help them to learn about the topics and their sub-topics from the exam perspective. Get the direct link to download the CSIR NET syllabus PDF for all the subjects below.

CSIR NET Syllabus 2024 PDF Download (To be activated)

CSIR NET Exam Pattern 2024

Candidates should review the CSIR NET Subject Wise exam pattern 2024 to understand the exam format, language of the exam, number of sections, total number of questions, marking scheme, and more. This understanding will enable them to align their exam strategy with the specific requirements and maximize their scores in the exam. Below are the key highlights of the CSIR NET exam pattern 2024 for all subjects.

• It will be conducted in Computer Based Test (CBT) mode.
• The test comprises three parts. All the parts will consist of objective-type, multiple-choice questions.
• The medium of the paper will be bilingual i.e. Hindi and English.
• There shall be a negative marking of 25% for Parts A, B, and C.

CSIR NET Paper 1 Syllabus 2024

The CSIR NET syllabus for Part A is common for all five subjects. This part shall contain questions about General Aptitude with emphasis on logical reasoning, graphical analysis, analytical and numerical ability, quantitative comparison, series formation, puzzles etc. Here is the topic-wise CSIR NET syllabus paper 1 shared below for the reference of the candidates.

CSIR NET Syllabus 2024 Paper 2

The CSIR NET Part B and C syllabus varies depending on the subject. Part 'B' consists of subject-related conventional Multiple-Choice questions (MCQs), typically covering topics outlined in the syllabus. Part 'C' contains higher-order questions that may evaluate the candidate's understanding of scientific concepts and/or their ability to apply these concepts. The subject-wise syllabus is mentioned below.

CSIR NET Syllabus Life Science

Those who opted for Life Science Syllabus can check the detailed syllabus in the table below. It encompasses topics like Cellular Organization, Developmental Biology, Ecological Principles, Applied Biology etc.

CSIR NET Syllabus Mathematics

The CSIR NET Part B & C Syllabus for Mathematics is mentioned below. Through this, candidates’ understanding of the number and capabilities of solving numerical problems are tested.

• Linear Algebra
• Complex Analysis
• Ordinary Differential Equations (ODEs)
• Partial Differential Equations (PDEs)
• Numerical Analysis
• Calculus of Variations
• Linear Integral Equations
• Classical Mechanics
• Descriptive Statistics, Exploratory Data Analysis

CSIR NET Physical Science Syllabus 2024

• Mathematical Methods of Physics
• Electromagnetic Theory
• Quantum Mechanics
• Thermodynamic and Statistical Physics
• Electronics and Experimental Methods

CSIR NET Earth Science Syllabus 2024

The syllabus of CSIR NET Earth Science is divided into two parts: B and C. We have mentioned the topics outlined in the CSIR NET syllabus for Earth Science in the table below.

CSIR NET Syllabus 2024 Chemical Sciences

• Inorganic Chemistry
• Physical Chemistry
• Organic Chemistry
• Chemistry in nanoscience and technology
• Catalysis and Green Chemistry
• Medicinal Chemistry
• Supramolecular Chemistry
• Environmental Chemistry

Preparation Tips for CSIR NET Syllabus 2024

Once you are familiar with the syllabus and exam pattern, aspirants must follow the best tips and tricks to ace the exam in one attempt.

• Check the CSIR NET exam syllabus 2024 to know about the topics important for the exam and strategize accordingly.
• Incorporate the best books and resources to learn the fundamentals of basic topics and core chapters.
• Solve mock tests and CSIR NET previous year papers to boost their question-solving speed with accuracy and time-management skills.
• Regularly revise the important topics to maximise their scores on the test.

Best Books for CSIR NET Syllabus 2024

A plethora of books and study materials are available for comprehensive preparation for the exam. Candidates with the right set of books can address all aspects of the CSIR NET syllabus 2024. In the table below, we have mentioned the best books for all subjects.