Explains Cartan geometries for graduate students.
problem None explicitly stated, focuses on definition.
method Definition and explanation.
result Defines Cartan geometries for a specific audience.
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In a previous work arXiv:0903.4512, we have built an homotopical Turaev-Viro invariant and an HQFT from the universal graduation of a spherical category. In the present paper, we show that every graduation of a spherical category $\C$ defines an homotopical Turaev-Viro invariant $HTV_{\C}^{(G,p)}$ and an HQFT $…
Survival analysis of 832,941 Solana token launches shows a significant decline in graduation rate.
problem Analyzing the survival rate of Solana token launches and identifying factors affecting graduation.
method Survival analysis using Kaplan-Meier and Cox proportional-hazards models.
result The survival rate of Solana token launches has declined significantly, with a 3.18x decrease from previous rates.
Hyperbolic geometrymath.DG
An introductory course on hyperbolic geometry for advanced students.
problem None explicitly stated; focuses on teaching hyperbolic geometry.
method Textbook format, intended for advanced undergraduate and early graduate students.
result Teaches advanced students about hyperbolic geometry.
Study shows peers' graduation improves residents' success in TCs.
problem Identifying peer influence in therapeutic communities adjusting for latent homophily.
method Used data on affirmations and exit dates to form peer networks, modeled latent homophily, and proposed bias correction methods.
result Positive effect of peers' graduation on residents' graduation, varying by gender, race, and role model definition.
Introduces geometric control theory for students.
problem No specific problem addressed in the abstract.
method Expository presentation of geometric control theory.
result Suitable for advanced students with solid math background.
Hierarchical Count Echo State Network Models with Application to Graduate Student Enrollmentsstat.ME
The paper proposes count echo state networks for forecasting graduate student enrollments.
problem Forecasting graduate student enrollments from historical data.
method Developed hierarchical count echo state networks and compared them to Poisson autoregressions and negative binomial models.
result Hierarchical negative binomial based echo state network is the superior model.
AGGLIO optimizes non-convex functions with local convexity guarantees.
problem Optimizing non-convex functions with local convexity.
method Stage-wise, graduated optimization technique for locally convex functions.
result Global convergence to the global optimum for non-convex and locally convex objectives.
The paper covers the new model of wage distribution in typical group of people. The model provides the opportunity to reparameterize applicable income distribution model: Pareto, logarithmically normal, logarithmically logistic, Dagum etc. The model ensures the graduation of Gini index values by polynomial degree of wa…
Study predicts success of crypto-tokens on Pump.fun platform.
problem Identify factors affecting the success of new crypto-tokens.
method Build predictive models using bonding curve mechanism and structural/behavioral variables.
result Conditional variables significantly improve the predictive power of token success.
Lecture notes on mean curvature flow for beginners.
problem Existence and uniqueness of mean curvature flow solutions.
method Conditional existence and weak-strong uniqueness theory.
result Accessible introduction for graduate students.
With pressure to increase graduation rates and reduce time to degree in higher education, it is important to identify at-risk students early. Automated early warning systems are therefore highly desirable. In this paper, we use unsupervised clustering techniques to predict the graduation status of declared majors in fi…
Teaches deep learning to statisticians.
problem Statisticians lack expertise in deep learning.
method Developed a program and taught DL to statistics graduate students.
result Provided tips and resources for teaching DL.
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.
Lecture notes from the Concentrated Graduate Course preceding the Workshop on Hodge Theory in String Theory at the Fields Institute in Toronto, November 11--15, 2013.
Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available when the problem was discovered.
Lectures on Kähler Geometrymath.DG
These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different aspects of Kähler geometry.
These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March 2010 at the Chinese University of Hong Kong.
These are lecture notes on scale calculus and M-polyfolds written for a graduate course at UNICAMP March-June 2018 and an advanced mini-course given during the biannual meeting of Brazilian mathematicians, CBM-32, at IMPA in August 2019.
These notes are based on a lecture series given at the Park City Math Institute in the summer of 2013. The notes are intended as a leisurely introduction to the Kähler-Ricci flow on compact Kähler manifolds, aimed at graduate students with some background in differential geometry.
We collect together various facts about G_2 and Spin(7) geometry which are likely well known but which do not seem to have appeared explicitly in the literature before. These notes should be useful to graduate students and new researchers in G_2 and Spin(7) geometry.
The failure of landing a job for college students could cause serious social consequences such as drunkenness and suicide. In addition to academic performance, unconscious biases can become one key obstacle for hunting jobs for graduating students. Thus, it is necessary to understand these unconscious biases so that we…
This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced undergraduate and beginning graduate students. Applications include brief introductions to …
Preparation for Gauge Theorymath-ph
Class lecture notes at a beginning graduate level on the mathematical background needed to understand classical gauge theory. Covers group actions, fiber bundles, principal bundles, connections, gauge transformations, parallel transport, curvature, covariant derivatives, pseudo-riemannian manifolds, lagrangians, cliffo…
Motivated by the problem of tuning hyperparameters in machine learning, we present a new approach for gradually and adaptively optimizing an unknown function using estimated gradients. We validate the empirical performance of the proposed idea on both low and high dimensional problems. The experimental results demonstr…
We introduce a probabilistic model of labor markets for university graduates, in particular, in Japan. To make a model of the market efficiently, we take into account several hypotheses. Namely, each company fixes the (business year independent) number of opening positions for newcomers. The ability of gathering newcom…
Notes on Shapes of Polyhedramath.GT
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A number of people, both in and out of the class, found these notes very useful and so …
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from readers, I've decided to make a presentable half-finished version available here.…
We present a self-contained proof of the Gauss-Bonnet theorem for two-dimensional surfaces embedded in using just classical vector calculus. The exposition should be accessible to advanced undergraduate and non-expert graduate students. It may be viewed as an illustration and exercise in multivariate calculus and…
Notes on Khovanov homologymath.GT
Explains Khovanov homology and its applications.
problem Understanding Khovanov homology and its applications.
method Expository lecture notes covering Jones polynomial, Khovanov homology, cobordism category, spectral sequences, and skein lasagna modules.
result Explains the Jones polynomial, Khovanov homology, and their applications.
The materials accompany a lecture short course presented at the 2011 Park City Mathematics Institute, Graduate Summer School on Moduli Spaces of Riemann Surfaces. The lectures were part of/coordinated with an overall program, including lectures by Ursula Hamenstadt on Teichmueller Theory, Andy Putman on Mapping Class a…
Statistical tests for fairness in admissions data reveal hidden patterns.
problem Simpson's paradox in admissions data hides true gender bias.
method Introduces a new statistical test based on Pearl's instrumental-variable inequalities.
result Statistical tests for fairness coincide with causal notions for the Berkeley admissions case.
These lecture notes, which were designed for the Summer School "Heegaard-Floer Homology and Khovanov Homology" in Marseilles, 29th May - 2nd June, 2006, provide an elementary introduction to Khovanov homology. The intended audience is graduate students with some minimal background in low-dimensional and algebraic topol…
Lecture Notes in Lie Groupsmath.DG
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engi…
Mostow Rigidity Made Easiermath.GT
Simplified proof of a famous geometry result for students.
problem Mostow Rigidity in geometry and topology
method Self-contained, accessible proof for grad students
result Clean and analytically light proof accessible to students
Unified framework improves robust causal inference, overcoming Gaussian barriers and optimization issues.
problem Improving robust causal inference in non-Gaussian settings.
method Combines gamma-Divergence, GNC, and Gatekeeper mechanism.
result Enhanced robustness and global optimization in causal effect estimation.
This are the notes of a course, given by the first author for the Graduiertenkollegs (=graduate students) at the Ruhr-University Bochum, in December 1997. These lectures pursued two main tasks: FIRST - to give a systematic and self-contained introduction to the Gromov theory of pseudoholomorphic curves. This is done in…
This article intends to provide an introduction to the construction of small exotic 4-manifolds. Some of the necessary background is covered. An exposition is given of J. Park's construction in arXiv:math.GT/0311395 of an exotic CP^2#7(-CP^2). This article does not intend to present any new results. It was originally a…
We introduce a toy probabilistic model to analyze job-matching processes in recent Japanese labor markets for university graduates by means of statistical physics. We show that the aggregation probability of each company is rewritten by means of non-linear map under several conditions. Mathematical treatment of the map…
In this paper we propose two new algorithms based on biclustering analysis, which can be used at the basis of a recommender system for educational orientation of Russian School graduates. The first algorithm was designed to help students make a choice between different university faculties when some of their preference…
Explains how knots relate to 4D shapes.
problem Understanding 4D shapes through knot theory.
method Combines knot theory with 4D manifold topology.
result Connects 4D shapes to knot theory and other geometries.
We expand Topological Field Theory on some special CW-complexes (brane complexes). This Brane Topological Field Theory one-to-one corresponds to infinite dimensional Frobenius Algebras, graduated by CW-complexes of lesser dimension. We define general and regular Hurwitz numbers of brane complexes and prove that they ge…
These are the lecture notes for my course at the 2011 Park City Mathematics Graduate Summer School. The first two lectures covered the basics of the Torelli group and the Johnson homomorphism, and the third and fourth lectures discussed the second cohomology group of the level p congruence subgroup of the mapping class…
We offer a simplified proof for Expected Shortfall's dual representation.
problem The dual representation of Expected Shortfall.
method Basic properties of quantile functions.
result New proof of Expected Shortfall's subadditivity.
Geometric group theory explores groups through their geometric properties.
problem Understanding groups via geometric properties.
method Cayley and Schreier graphs, ping-pong lemma, quasi-isometries, growth of groups, hyperbolicity.
result Gromov's theorem on groups of polynomial growth and amenability.
These notes grew out of a lecture series given at RIMS in the summer of 2001. The lecture series was aimed at a broad audience that included many graduate students. Its purpose lay in familiarizing the audience with the basics of 3-manifold theory and introducing some topics of current research. The first portion of th…
Book introduces principles of LCK geometry for complex manifold students.
problem Understanding locally conformally Kahler manifolds.
method Explains the concept and properties of LCK manifolds.
result Provides insights into the structure and behavior of LCK manifolds.