Special Topics Available

Graph Theory

Eoghan McDowell

7 weeks, 4 hours per week (including lectures and exercise classes) starting June 19th to week beginning July 31st  see schedule.

Description
A graph is a collection of vertices joined by edges. The study of graphs is a rich area of discrete mathematics, and has applications in numerous other subjects where graphs can be used to model networks varying from electrical circuits to ecological relationships. In this course we will investigate graphs as abstract objects, but with no mathematical background required -- many interesting topics in this field are accessible to beginners, including famous problems such as the bridges of Königsberg, the three utilities problem, and colouring maps. Theorems we prove will include Halls' Theorem on the existence of a complete matching between two sets of vertices; Turan's Theorem on the existence of cliques in a graph; and Ramsey's Theorem on the existence of monochromatic cliques in an edge-coloured complete graph. The key skills of writing proofs and problem solving will be demonstrated in lectures and reinforced in homework problem sheets.

Student Learning Outcomes
Students successfully completing this course will be able to - determine various properties and statistics of a graph, such as whether it can be drawn in the plane, or how many colours are needed to colour it. - prove general statements about graphs, such as necessary and sufficient conditions for a matching, or bounds on Ramsey numbers.

Detailed Content
Sets and induction. (Mathematical notation. Methods of proof.)
Definitions and basic properties of graphs. (Order, size, degree, regularity, connectedness. Complete graphs. Cycles and paths.)
Trees. (Equivalent characterisations of trees. Existence of spanning trees.)
Bipartite graphs and matchings. (Equivalent characterisations of bipartite graphs. Hall's Theorem on the existence of matchings.)
Planarity. (Euler's formula. Size bounds on planar graphs. Statement of Kuratowski's Theorem. Graphs on general surfaces.)
Walks in graphs. (Eulerian walks and circuits. Hamiltonian paths. Paths in directed graphs and the Lindström--Gessel--Viennot lemma.)
Cliques. (Turan's theorem.)
Colourings. (Brooks' Theorem. Six, Five and Four Colour Theorems. Heawood's Theorem. The chromatic polynomial. Vizing's Theorem.)
Ramsey theory. (Ramsey's Theorem and variations.)
Random graphs. (Erdős's lower bound on Ramsey numbers. Graphs with large chromatic number and girth. Structure of a random graph.)

Assumed knowledge:
None.

Target Students
The course is intended for students of mathematics, physics, neuroscience (but may be of interest to any students)  

Textbook or required reading
No required reading. For those interested, Modern Graph Theory by Béla Bollobás is one possible source of further reading.

Assessment
Four homework problem sheets throughout the course.

Fibre Bundles and Spin Structure

David O’Connell

10 weeks, 2+1 hour per week,  see schedule.

Description
In this course we will introduce some of the differential geometry required to study various aspects of theoretical physics. We will start with the basics of smooth manifolds, and then move into the theory of vector bundles and principal G-bundles. We will then begin a study of characteristic classes. Roughly speaking, these are procedures for assigning cohomology classes to bundle information. It turns out that this is quite useful: it may allow us to see that particular geometric objects cannot be defined globally due to obstructions coming from topology. As an application of this idea, we will use some of these characteristic classes to determine the number of ways in which we can define spinors on a given manifold.

Student Learning Outcomes
Students successfully completing this course will be able to compute the number of inequivalent spin structures on the circle, the torus, and the 2-sphere.

Detailed Content
There will be lecture notes released at the end of each week. These will cover:
1) Preliminaries
2) Smooth Manifolds
3) Differential Forms
4) Lie Groups
5) Vector Bundles
6) Principal G-Bundles
7) Connections
8) Curvature
9) Characteristic Classes
10) Spin Structures

Assumed knowledge:
A firm grasp of Calculus and Linear Algebra are essential. Some knowledge of Topology and Group theory is also preferred.

Target Students
The course is intended for mathematicians/physicists looking for a second course on Differential Geometry.  

Textbook or required reading
There will be lecture notes released at the end of each week.

Assessment
There will be four homeworks, all revolving around the basic geometry of spheres. These will cover four key areas of the course, namely:
1) Spheres as manifolds and groups.
2) Bundles over spheres.
3) Connections on spheres.
4) Spin structures on the circle, the torus, and the 2-sphere.

The Fourier transform and its applications

Gunnar Wilken

10 weeks, 2+1 hour per week,  see schedule.

Description
The Fourier transform plays a central role in mathematics, science and engineering. This course motivates and carefully introduces the Fourier transform in both continuous and discrete form. Along the way striking applications in a variety of areas are discussed, some of which are computationally enabled by the FFT-algorithm (Fast Fourier Transform). A satisfactory understanding of the Fourier transform depends on generalizations of the notions of convergence and function, namely mean square convergence and the theory of distributions, which will be explained to a degree that enables a sufficiently broad basis of understanding. For practical applications, e.g. in signal processing, we derive the Sampling Theorem and discuss aliasing and filtering. After a short visit to the area of linear systems, higher-dimensional Fourier transforms are introduced and illustrated by applications in crystallography and tomography.

Student Learning Outcomes
Successful completion of this course as assessed by homework exercises and a final exam will enable students to recognize, understand, and explain methods and techniques in science and engineering in as far as the Fourier transform is involved. Students will become able to apply the Fourier transform and recognize possible, even new, use cases.

Detailed Content
Topic 1: Periodic phenomena and Fourier series, trigonometric polynomials, approximation and orthogonality.
Topic 2: The Fourier transform, its properties, inversion, and relationship with Fourier series.
Topic 3: Convolution and its central importance in applications of the Fourier transform.
Topic 4: Distributions (generalized functions) and their crucial role in Fourier analysis. Delta and Shah functions.
Topic 5: Sampling and Aliasing.
Topic 6: Linear Systems: Eigen-functions and -values, impulse response and transfer functions.
Topic 7: The Discrete Fourier Transform (DFT) and its implementation as Fast Fourier transform (FFT). Filtering.
Topic 8: Higher-dimensional Fourier transforms.
Topic 9: Applications in differential equations, probability, diffraction, crystallography, and tomography.

Assumed knowledge:
Students enrolled in this course are assumed to have sufficient proficiency at undergraduate level mathematics for scientists and engineers. This requirement ensures that we do not need to review basic results from calculus and linear algebra in class. A basic level of programming in any suitable language is assumed as well. Motivated students can of course review such prerequisites during the term.

Target Students
Students interested in Fourier techniques, e.g. in imaging.  

Textbook or required reading
Brad G. Osgood: Lectures on the Fourier Transform and its Applications,
The American Mathematical Society 2019.

Assessment
The assessment in terms of pass or fail of this course is by written homework and a final exam.

Ordinary Differential Equations

Antoni Kijowski

10 weeks, 2.0 hours per week, see schedule.

Description
Ordinary Differential Equations (ODEs) play a fundamental role in natural sciences. They enable a precise description of dynamics of quantities changing in time. Among many classical applications ODEs are used to study growth of a capital, describe predator and prey populations or dynamics of epidemic. During the course we focus on the classical theory of ODEs. We start with discussing first order scalar problems, then we pass to vector valued solutions, second order and higher order problems. We study existence and uniqueness of solution and its dependence on the initial value, in particular we prove Picard-Lindelöf and Peano theorems. Every step of the discussion is illustrated with many examples, emphasis of the geometry of the problem and visualization using graphic visualizations (e.g. Mathematica). Moreover, we learn how to model life observed phenomena and analyze it.

Student Learning Outcomes
After completing the course student will be able to:
- Name different types of ordinary differential equations and apply a proper solving method
- Give a geometric interpretation of the posed problem
- Construct and interpret an ODE model of real life phenomena

Detailed content
Topic 1: Definition of ODE, Cauchy problem, solutions, geometric notions
Topic 2: Separable equations, complete equations
Topic 3: Uniqueness and existence of solutions
Topic 4: Linear homogeneus and nonhomogeneous equations
Topic 5: Systems of linear equations
Topic 6: Second and higher order equations
Topic 7: Solution with series
Topic 8: Application in analysis of real life problems

Assumed knowledge:
Students enrolled in this course are assumed to have sufficient proficiency at basic calculus and linear algebra. We adjust discussed problems so that students can use the course as a geometric illustration of their knowledge and a way of developing a better understanding of undergraduate level mathematics.

Target Students
Anyone who wants to learn classical theory of ODEs.

Textbook or required reading
The course is self-contained, but I refer interested students to M. Tenenbaum, H. Pollard: Ordinary differential equations, Dover Publications, New York 1985.

Assessment
60% final exam and 40% homeworks (problems based on the content of the lectures)

Cerebral Cortical Networks in Rodents and Primates

Dr Razvan Gamanut, Monash University, Australia (Sponsored by Prof Kenji Doya)

14 weeks, 1.5 hours per week,  see schedule.

Description
In neuroscience, there is a concerted effort underway to clarify the structure and function of the cerebral cortex, which is arguably the most important component of the mammalian brain. To this end, rodents and non-human primates currently receive a special focus. On the one hand an expanding suite of genetic tools are available for use in rodents, especially in mice and rats, and on the other hand non-human primates such as marmosets and macaques show some of the most complex neuroanatomical and neurophysiological features, close to those in humans. What has the research revealed so far in this quest? We will explore a select set of findings at cellular and regional level, primarily in the mentioned species, from which we will extract rules of neuroanatomical arrangement and of neurophysiological processing in the cerebral cortex of the two orders. The first sessions will be dedicated to topographical organisation and inter-regional connections. Then we will focus on the modular and hierarchical processing in the visual cortex. Finally, we will look at the default mode network and its involvement in introspection, together with the claustrum and its unique relations with the cerebral cortex.

Student Learning Outcomes
At the completion of this course, students will be able to
• Compare and contrast comparative neuroanatomical features in the cortex of rats and mice, and of marmosets and macaques.
• Discuss common rules of neuroanatomical arrangement and of neurophysiological processing in the cerebral cortex of the two orders, including the canonical microcircuit, the default mode network, and the interaction with the claustrum.
• Describe the application of modern genetic, optical, and electrophysiological techniques in network mapping and tracing connections.
• Describe hierarchical and non-hierarchical processing in the visual cortex.
This will be assessed by two written exams.

Detailed Content
01. Introduction to the course and to cerebral cortex
02. Theoretical constraints on connectivity with brain size
03. Connectivity, brain size and species
04. The role of weak projections
05. Components of the visual cortex
06. Exam 1
07. The canonical microcircuit
08. Modular processing in the visual cortex
09. Hierarchical processing in the visual cortex
10. Dorsal and ventral streams
11. Non-hierarchical processing in the visual cortex
12. Default mode network
13. Claustrum
14. Exam 2

Assumed knowledge:
No required prior knowledge as the course will introduce the necessary concepts and include discussions of the techniques.

Target Students
Primarily neuroscience students, but students in other life sciences, in physical sciences or engineering are also welcome.

Textbook or required reading
Students will receive up to five relevant scientific articles six days before each class, and are required to read their abstracts and the methods.

Assessment
Assessment will be in the form of two exams, one after the first 5 classes and worth 30% of the final grade, and the second at the end of the course, worth 70%. The exams will have questions from each class about the techniques discussed and the research findings. The questions will be based on the content of the lectures.

Advanced ICTS Lab

Prof. Mahesh Bandi

10 weeks, 1.5 hours per week.

Description
The course is comprised of four experiments drawn from condensed matter and statistical physics. Given the pandemic conditions in India (from where course is being taught) and in Okinawa alike, the first two experiments were designed such that students can perform them from their kitchen with homely components and perform data analysis under the instructor's guidance via zoom.

Student Learning Outcomes
Students will rotate amongst 4 experiments, devoting 2 weeks per experiment. Students are expected to devote 8 − 10 hours per week to each experiment. At the end of the allotted period for each experiment, students will give a short presentation to the instructors and the rest of the class. Students will submit a report detailing the theory for their experiment, the experimental procedure, their data and analysis as well as their conclusions regarding the challenges, what remains to be investigated and their advice to the next team. Experiments 1 and 2 will be performed individually but subsequent experiments will be performed in teams.

Detailed Content

Surfactant driven fracture of interfacial particle rafts: In this experiment, the surface of the water in a Petri dish is decorated with hydrophobic (water hating) particles. When a needle dipped in oil is introduced at the water surface at the center of the dish, the oil spreads across the surface to reduce surface tension. In doing so, the spreading oil pushes the hydrophobic particles radially outwards. When the particles come in contact, they can sustain stresses and form a quasi-2D solid. Further spreading of the oil fractures this solid in a pattern of periodic cracks. We will collect images of the experimental dynamics using your smartphones and convert them into a series of images. These images will be analyzed to study both the dynamics of this process as well as the structure of the resulting crack patterns. For extra credit, you will be asked to consider designing a setup to achieve the same dynamics but instead of introducing the surfactant at a point at the dish’s center, we introduce it simultaneously across the rim of the Petri dish. This sets up a convergent flow of the oil, and the ensuing dynamics fall under a class of problems in Applied Mathematics known as “Self-similar solutions of the second kind.” This extra credit is an open problem, if anyone solves it, you will be invited to write and publish a peer-reviewed paper with us.

Structure factor of disordered particle configurations: In this experiment, a mixture of small and large tapioca pearls (Sabudana used in food) is set in a container as a two-dimensional bed of spheres and the container is immersed in water. As the tapioca pearls puff up from soaking water, they come in contact and jam into a disordered solid. We will use the smartphones to collect Timelapse (every few minutes) images of the tapioca pearl configuration as they puff up and use them to extract measurable quantities such as the radial distribution function or structure factor, the most basic structural parameters used to parameterize any given solid or liquid.

Measurement of Seebeck and Peltier coefficients: In this experiment, we will use thermoelectric modules normally sandwiched between (passive) heat sinks and microprocessors to actively cool the microprocessor. Such modules are also routinely used in various electronics to improve the signal to noise characteristics. You will be provided with a thermoelectric module and asked to set up a simple circuit to drive it in the Peltier mode (application of voltage to cool one and heat the other side of the module) and measure its Peltier coefficient. In the second stage, you do the converse experiment (heat one side of the module and cool the other side) and measure the voltage difference across terminals and obtain the Seebeck coefficient. As extra credit, you will be asked whether it is possible to design a small fridge and/or air conditioner with these modules when run in the Peltier mode. If it is possible, you must show how and if it is not possible you must explain why. Similarly, you will be asked to design a simple setup to connect the terminals of the module being run in Seebeck mode to a voltage regulator with USB output to charge a smartphone.

Random Resistor Network: In this experiment, you will be given a bunch of plastic (non-conducting) and metallic (conducting) spheres in a case with electrodes along the case’s walls. You will apply a small voltage across the walls and as you place the spheres, a percolating conducting path emerges. Connecting the terminals to a LED with the case in between will allow you to know you have a percolating path when the bulb lights up. This is the real-world instance of a famous theoretical model that was employed to explain several phenomena in condensed matter physics, two of them being Elihu Abrahams et al’s Hopping Conduction and Sir Nevill Mott’s Variable Range Hopping Conduction mechanisms in amorphous semiconductors.

 

Assumed knowledge:
Basic Programming and unbounded curiosity for science.

Target Students
1st year students.

Textbook or required reading
Material will be provided by the instructors.

Assessment
i. (60%) Written report and presentation for each experiment ii. (20%) Participation in discussions iii. (10%) Ability to achieve open-ended goals of experiment iv. (10%) Final quiz: at the end of the final experiment each student will be individually quizzed on all experiments, for their understanding of the various concepts/ideas discussed throughout the term.

Covariant Physics and Black Hole Thermodynamics 

Drs. Josh Kirklin, Isha Kotecha, and Fabio Mele, Hoehn Unit (Sponsored by Prof Philipp Hoehn)

15 weeks, 1 hour per week, Friday 1300-1400 in Lab 4 F15

General covariance is one of the fundamental principles underlying gravity. It says that the laws of physics do not depend on our choice of coordinates. Geometrically speaking, this means that we can apply any diffeomorphism to a physical system without changing its properties. In other words, diffeomorphisms are a kind of gauge symmetry. In this course, we will explore an elegant modern perspective on general covariance, using an approach known as the covariant phase space formalism. This formalism tells you how to treat covariant theories using classical Hamiltonian mechanics. Quantum gravity must be a quantisation of this classical theory. This means that we can learn a lot about some aspects of the quantum theory using the covariant phase space approach. For example, the laws of black hole thermodynamics are a reflection of the fact that black holes are quantum objects. We will show how key fundamental thermodynamical properties of the black hole, such as its entropy, can be understood using the covariant phase space. We will also discuss more general properties of black hole thermodynamics. Finally, we will explore the connection between gauge symmetry and quantum entanglement, and how this relates to the thermodynamics of spacetime itself.

Student Learning Outcomes 
At the completion of this course, students will be able to use the covariant phase space formalism to analyse a covariant field theory, and apply it to the study of black hole thermodynamics. They will also understand some broader properties of black hole and spacetime thermodynamics. This will be assessed by a short essay on a topic TBD.

Detailed content (arranged by class session, or arranged in topics, with description) 
1. Geometry of phase space, the symplectic form.
2. Hamiltonian mechanics.
3. Gauge symmetry and constraints in mechanics.
4. Covariant field theories.
5. Geometry of field space.
6. Gauge symmetry and constraints in field theory.
7. Global symmetries and large gauge symmetries.
8. Conserved charges in general relativity.
9. Black hole spacetimes and symmetries.
10. Energy, angular momentum and electric charge.
11. Black hole entropy as a Noether charge.
12. The laws of black hole thermodynamics.
13. Entanglement and gauge symmetry.
14. The first law of entanglement entropy.
15. Spacetime thermodynamics and the Einstein equations.

 

Target Students Theoretical physicists / mathematicians with some familiarity with quantum mechanics, thermodynamics, field theory and general relativity.

Recommended reading:
Introductory Lectures on Black Hole Thermodynamics, T. Jacobson.
Black Hole Entropy is Noether Charge, Robert M. Wald.
Advanced Lectures on General Relativity, Geoffrey Compère

Supersymmetric Quantum Mechanics and Morse Theory

Dr. Slava Lysov, Neiman Unit (sponsored by Yasha Neiman)

13 weeks, 2 x 1 hour per week, Tuesday and Thursday 1400-1500 in L4E01 except the four dates:

May  20, Thursday - L4E45
May  25, Tuesday  - L4E48
June 17, Thursday - L4E48
July  15, Thursday - L4E48    

Companion Course to Supersymmetric Field Theories and Superstrings (below)

Modern theoretical physics has a deep connection with modern mathematics. The foundations of this connection were established by Edward Witten in his works around the 1980s. We will use Witten's paper "Supersymmetry and Morse theory" as prime reference for the course. It is a scientific paper, so it assumes some background knowledge of both supersymmetry and Morse theory, which we will cover in the rest of the course. The second part of the course will be focused on two different approach to the Morse theory: the standard mathematical one, based on differential geometry and topology, and the physical one using supersymmetric quantum mechanics.

1.  Introduction to topological invariants and cohomology.

2.  Differential forms and de Rham cohomology.

3.  Quantum mechanics of a particle on Riemann manifold.

4.  Grassmann variables.

5.  Introduction to supersymmetric quantum mechanics.

6.  Superspace formalism.

7.  Supersymmetric sigma model as a de Rham theory.

8.  Superpotential as a Morse function.

9.  Morse theory.

10. Morse complex for de Rham cohomology.

11. Tunneling in quantum mechanics.

12. Instantons in supersymmetric sigma model.

13.  Vacuum degeneracy lift by instantons as a Morse complex for de Rham cohomology.

 

Students should have some knowledge of quantum mechanics and differential geometry.

There will be biweekly home assignments.
 

E. Witten, "Supersymmetry and Morse theory," J. Diff. Geom. 17 (1982) no.4, 661-692.

Hori, K., Thomas, R., Katz, S., Vafa, C., Pandharipande, R., Klemm, A., Vakil, R. and Zaslow, E., 2003. Mirror Symmetry (Vol. 1). American Mathematical Soc.

An Introduction to Supersymmetric Field Theories and (Super)Strings

Dr. Mirian Tsulaia, Neiman Unit (sponsored by Yasha Neiman)

13 weeks, 1.5 hours per week Monday afternoons 1300-1430 in B714a

The course consists of three parts: Bosonic strings, Supersymmetric Field Theories and Superstrings. We start with a description of Open and Closed bosonic strings: we describe their classical actions, a quantization and the corresponding spectrum.
We explain how to compute the partition function of the closed bosonic string on torus. Further we consider interacting bosonic strings and derive the Veneziano amplitude. Then we discuss a compactification on a circle and finally introduce non perturbative objects, so called D-branes. As a preparation to the superstrings, we cover some topics from N=1 supersymmetric field theories and supergravities. We describe N=1 superspace, superfields in general and chiral and vector superfields in particular. Then we give a brief introduction to four-dimensional N=1 supergravity and to higher dimensional supergravities. We tentatively plan to cover some selected topics in supersymmetric field theories such as elements of Minimal Supersymmetric Standard Model and nonperturbative superpotentials. In the final part of the course, we explain how to generalize the topics that we covered for bosonic strings to the case of superstrings.

Weekly Content:
1. Introduction, dual models
2. Bosonic string action, equations of motion
3. Quantization. States and operators
4. Partition function on torus
5. Compactification on a circle, T duality
6. D branes
7. Veneziano amplitude
8. N=1 SUSY algebra and its representations
9. Superspace, superfields
10. Supersymmetric Lagrangians
11. Perturbation theory
12. Spontaneous SUSY breaking, Supergravities
13. Selected topics: MSSM, Nonperturbative Superpotentials, Superstrings

Students should have some familiarity with quantum field theory and general relativity.

Textbooks:
M.B. Green, J.H. Schwarz, E. Witten 'Superstring Theory'
J. Wess, J. Bagger "Supersymmetry and Supergravity"
Reviews:
C. Angelantonj, A. Sagnotti ''Open Strings'' Physics Reports 371 (2002), 1; hep-th/0204089
R. J. Szabo, ''BUSSTEPP lectures on string theory: An Introduction to string theory and D-brane dynamics,'', hep-th/0207142
J. D. Lykken "Introduction to Supersymmetry" hep-th/9612114

Introduction to Modern Astrophysics

Dr Alessandro Trani, University of Tokyo (Visiting Scholar, sponsored by Yasha Neiman)

13 weeks, 1.5 hours per week on Thursday mornings 10:00 - 11:30 in B711

A gentle introduction to the topics of modern astrophysics. We will start from the most fundamental topics, such as stellar structure and evolution, and gradually venture towards the 'hot topics' of contemporary astrophysics, namely exoplanets and gravitational waves. The aim is to provide the students with the essential knowledge to navigate the current landscape of astrophysical research, and put them into contact with the latest breakthroughs in the field. The emphasis will be put on our theoretical understanding of the Universe, rather than on observational techniques. If time allows, some notions of computational astrophysics will be discussed.

Class 1: Why study astrophysics? Telescopes and the electromagnetic spectrum

Class 2: The celestial sphere, parallax, dopplershift

Class 3: What is a star? Stellar structure and equilibria

Class 4: The lives of stars. From protostars to giants. The Hertzsprung–Russell diagram.

Class 5: The death of stars. Black holes, white dwarfs and neutron stars

Class 6: Binary stars. The gravitational two-body problem

Class 7: Interacting binaries. Tides, Roche lobe overflow, common envelope evolution

Class 8: Keplerian orbital elements. The solar system

Class 9: Planetary dynamics and origin of the solar system

Class 10: Exoplanets and how to find them

Class 11: Stellar clusters. Evolution and dynamics

Class 12: Gravitational waves I. Discovery and astrophysical conundrums

Class 13: Gravitational waves II. Formation pathways & pitfalls

Assumed knowledge: The students should have an undergraduate-level background in mathematics, physics or statistics.  Specifically, a few classes will require some degree of familiarity with differential equations, Newtonian mechanics and thermodynamics.

Reference textbooks
Karttunen H., Kroger P., et al. - Fundamental Astronomy (5th ed.)
Kippenhanh R., et al. - Stellar Structure and Evolution (2nd ed.)
Carroll B.W., Ostlie D.A. - An Introduction to Modern Astrophysics (2nd ed.)
Binney J., Tremaine S. - Galactic Dynamics (2nd ed.)

Assessment: 100% final presentation

Introduction to Machine Learning

Dr. Mirian Tsulaia, Neiman Unit (sponsored by Yasha Neiman)

13 weeks, 1.5 hours per week Wednesday afternoons 1300-1430 in L4F01 (first class only is B250)

A good follow-on for students who take Prof Fukai's course B32 Statistical Modelling.

In order to familiarize students with the basic skills used in Machine Learning and Data Science, we shall cover some relevant topics from Statistical Learning and provide examples of practical applications of the theory. We shall briefly cover some basic concepts from Python programming language. Further, we give an introduction to libraries such as Numpy and Pandas which are commonly used in data science. Then we shall cover various regression and classification methods. For each of these methods we shall first give a theoretical description. After that, we shall demonstrate how this approach can be implemented for a specific problem in science or in business by building a corresponding model using Python.

Finally, we shall give an introduction to more advanced topics such as Deep Learning. In particular, we shall explain the theoretical foundations of Artificial Neural Networks, Convolutional Neural Networks, Recurrent Neural Networks, and Boltzmann Machines. Finally, we shall explain to which kind of problems these algorithms can be applied.

Topic 1: Python crash course
Topic 2: NumPy
Topic 3: Pandas
Topic 4: Linear regression
Topic 5: Multiple Linear regression
Topic 6: Logistic Regression
Topic 7: K Nearest Neighbors
Topic 8: Decision Trees
Topic 9: Support Vector Machines
Topic 10: K-Means Clustering
Topic 11: Principal Component analysis
Topic 12: Artificial Neural Networks, Convolutional Neural Networks
Topic 13: Recurrent Neural Networks, Boltzmann Machine
 

"An Introduction to Statistical Learning"
by James, Witten, Hastie and Tibshirani

"A High-Bias, Low-Variance Introduction to Machine Learning for Physicists" . arXiv 1803.08823
by Mehta, Wang, Day, Richardson, Bukov, Fisher, and Schwab

Bring your laptops with Python installed! (Preferably the Jupyter Notebook or Spyder.)

You will find the notes from the course here.

Biological Networks. Bioinformatics and modelling. 

Professor Igor Goryanin (OIST adjunct professor)
Professor Anatoly Sorokin (Moscow Physical Technical Institute)

18 hours 
2019 October 21 onwards
 

PART I

Day 1: Oct 21 (Mon), 3 – 5pm
Theory: introduction, Enzymes kinetics (Goryanin)

Day 2: Oct 23 (Wed), 3 – 5 pm
Theory: Metabolic Pathways, Graph analysis of Biological networks.  Standards in Systems Biology (Goryanin)

Day 3: Oct 24 (Thurs), 3 – 5 pm
Theory: Stoichiometric matrix and its properties.  Flux Balance Analysis.  Extreme pathways (Goryanin)

Day 4: Oct 25 (Fri), 3 – 5 pm
Theory: Metabolic Engineering and synthetic biology (Goryanin)

Part II

Day 5: Oct 28 (Mon), 3 – 5pm
Theory: Applications in Systems Biology (Goryanin)

Day 5: Oct 29 (Tue), 3 – 5pm
Theory: Introduction, installing software (Goryanin/Sorokin)

Day 6: Oct 30 (Wed),  3 – 5pm
Theory: Cytoscape, SBGN.  Analysis and reconstruction of metabolic networks (Goryanin/Sorokin)

Day 7: Oct 31 (Thurs), 3 – 5pm
Theory: Flux Balance Analysis.  Stoichiometric matrix and its properties.  Extreme pathways.  Practical. FBA with pyCOBRA/Sybi.  Modeling of mutations and environment changes (Goryanin/Sorokin)

Day 8: Nov 1 (Fri), 3 – 5pm
Theory and Practical: Metagenomes analysis (Goryanin/Boerner)

Efficient Scientific Computing with Julia

Taught by Valentin Churavy, PhD student at MIT
Under the approval of Prof Ulf Skoglund, Dean of the Graduate  School

Scientific computing is a cornerstone of research, many scientific projects now involve coding in some form — may it be modeling, simulations or data analysis — and doing so in a performant and reproducible manner is a requirement to contribute effectively. This course uses Julia to teach the fundamentals of best practices for reproducible code, performance analysis, and contributing to open-source. It furthermore focuses on aspects of HPC computing necessary to analysis and study large problems — in particular GPU computing.

Participants should posses some programming experience in either Julia, Python, MATLAB or C/C++. As part of the course students will design a small project, that can lead to an open-source contribution, an implementation of scientific program, or the performance improvement thereof. While the course uses Julia the knowledge should be transferable to other languages.

More information and signup here.

Computational Biology: Artificial Intelligence for Bioinformatics 

Professor Hiroaki Kitano (OIST adjunct professor)
with other presenters

7/22 (Mon) 09:00-13:00: Kitano & Asai (Intro /Hands-on I Physiological Modeling)

7/23 (Tue) 09:00-13:00: Kitano (Signal Transaction/Cell Cycle)

7/24 (Wed) 09:00-13:00: Funahashi (Hands-on Ⅱ CellDesigner Modeling)

7/25 (Thu) 09:00-13:00: Kitano (AI for Life Science/Wrap-up)

Class times, room, and syllabus TBD

Non-equilibrium Nanophysics

Dr Juan David Vasquez Jaramillo (Pauly Unit)

Statistical mechanics, a beautiful approach to equilibrium, is well known in physics for its broad range of applicability to describe the state of systems with a macroscopic number of particles. When the context changes, and the length scale is reduced as far as the Nanoscale, defining thermodynamics becomes cumbersome and new approaches must be introduced.

In the present course, we will develop the theory of quantum mechanical non-equilibrium processes from the Brownian harmonic oscilator, deriving Keldysh field theory, and putting it into context in models describing tunneling probes such as scanning tunneling microscopy (STM) or inelastic electron tunneling spectroscopy (IETS). Computer exercises will be developed to illustrate these examples and the students will be expected to be able to reproduce a scientific paper in their field of interest in relation to advanced statistical mechanics, non-equilibrium nanophysics or molecular electronics, as well they will be able to write a review on their topic of interest of maximum 25 pages and a minimum of 75 references.

20 hours (4 hours per week for 5 weeks) in Term 3
Class times and location TBD

States and Properties of Matter
Professor Mahesh Bandi 

Offered as a series of four special topics courses presented over two terms (two courses per term). It treats the standard (gases, liquids and solids) and few exotic (polymers and colloids) classical states of matter, and explains how these states and their bulk properties emerge from the few interatomic and intermolecular forces at play. The emphasis is on developing strong physical intuition for microscopic mechanics using the simplest models that illuminate the concept. In doing so, we explain both the strengths and shortcomings of these simple models, and in particular, analyse the limiting conditions where they fail. Therefore, rather than theoretical rigour, the focus of the treatment is on performing quick order-of-magnitude calculations. As a result, although the mathematics is unsophisticated, Calculus is a pre-requisite. Wherever possible, scientific facts will be connected with the seminal experiments that established them.

Term 2, Classes Wednesday 2-4 and Thursday 3-5, Room B714a (modules 3 & 4 in term 3 at time and location TBD)

Quantum Models for Black Holes: Sachdev-Ye-Kitaev and generalizations
Professor Frank Ferrari (Université Libre de Bruxelles), Visitor in Toriumi Unit

Holography predicts that black holes can be described quantum mechanically by large N matrix models at strong coupling. We shall describe very recent ideas that have allowed to build exactly solvable models of this kind, providing an explicit quantum mechanical description of string-size black holes. These ideas are at the confluence of several different fields: condensed matter theory (disordered systems); quantum chaos; string theory and holography; matrix and tensor models (graph theory), etc. Many properties associated with black holes are found in the quantum mechanical description and will be discussed in the course, in particular the loss of unitarity at large N (and unitarity restoration at finite N), the quasi-normal behaviour, an emergent reparameterization invariance and maximal chaos.

Lectures 12 hours between 22 March to 10 April, and attendance at parts of workshop
“Workshop on recent developments in AdS/CFT” on 2 & 3 April 2019