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The course also rests on the approach that learning is promoted by feedback. The assessment design that participants in the course design will therefore be required to reflect significant and effective use of continuous formative assessment. Such formative assessment requires strategic learning activities and assignments, and the course therefore comes with an emphasis on communication-to-learn activities including peer learning.
Skoltech is an English medium instruction environment, and the course contains discussion topics to highlight ways of addressing the potential effects of language and culture barriers for high quality student learning.
All topics in the course are applied by participants on their own teaching and learning experiences and are meant to be used as they prepare and plan for their teaching assistantships or their supervisory activities to come. All participants will have a task to produce a reflection on their future actions to evolve as facilitators and meet the requirements of the scholarship of teaching and learning.
The course is addressed to undergraduates of the first year and contains applications of various mathematical methods for solving problems of mathematical physics. The course assumes familiarity with various sections of theoretical physics (classical mechanics, field theory, quantum mechanics, statistical physics, hydrodynamics, elasticity theory) on the example of solving specific problems. The main purpose of the course is to encourage undergraduates to independent research work. For this reason, the main element of the course is an independent solution to the problem, requiring the study of additional material.
The course starts with an overview of canonical machine learning (ML) applications and problems, learning scenarios, etc. and then introduces foundations of Bayesian approach to solve these problems. Bayesian approach allows one to take into account subject domain knowledge and/or user’s preferences through a prior distribution when constructing the model. Besides, it offers an efficient framework for model selection. We discuss which prior distributions types are usually used, limit properties of a posterior distribution, and provide some illustrations of the Bayesian approach.
The practical applicability of Bayesian methods in the last 20 years has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation, as well as posterior simulation methods based on the Markov chain Monte Carlo approach. As a result Bayesian methods have grown from a specialist niche to become mainstream. Therefore, we devoted a second part of the course to approximation tools, vitally important for Bayesian inference, and provide examples how to use Bayesian approaches to automatically select features, tune the regularization parameter in regression and classification, etc.
The last part of the course is devoted to advanced Bayesian methods, namely, Gaussian Processes and deep Bayesian neural networks, which have become widespread in the last 5-8 years. We discuss deep Bayesian framework and then illustrate its applications through construction of deep variational autoencoders, approaches to variational dropout, Wasserstein Generative Adversarial Networks, deep Kalman filter, etc. Home assignments include solution of applied problems, development of modifications of Bayesian ML algorithms, and some theoretical exercises.
Invited medical oncologists will give talks on the usolved questions in the field. A visit to a clinic or a laboratory is planned
1. General features of the soliton systems.
2. Algebraic-geometrical integration theory.
3. Hamiltonian theory of soliton equations.
4. Perturbation theory of soliton equations and its applications to Topological Quantum Field Theories and Sieberg-Witten solutions of N=2 Supersymmetric Gauge Theiories
Please see the seminar webpage at https://www.skoltech.ru/en/cms/
The second part of the course describes the physics of low-dimensional electron systems and nanostructures. Two-dimensional electron and electron-hole systems, low-dimensional disordered systems, quantum Hall effect, carbon nanostructures, photonic crystals and optical microcavities will be considered.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies.
Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies.
The Exam has two parts:
Part 1 – Pre-exam activities (Assignments 1, 2a, 2b) Part 2 – Activities on Examination day (Assignment 3): a ten-minute presentation based on the student's research, followed by a discussion.
The students will practice Academic vocabulary and grammar, as well as boost their reading, writing and speaking skills.
The blended format includes a weekly online workload plus an offline group tutorial providing a flexible and individualised learning trajectory.
Real-time feedback in online exercises will be complimented by tutor feedback for the writing and speaking assignments.
Matematical methods of modern theory of Hamiltonian systems are based on the concepts, arosen in different fields of mathematics: differential equations and dynamical systems, Lie groups and algebras, differential geometry on manifolds. Many modern directions in mathematics (e.g. symplectic geometry) got their origin from the problems of classical mechanics.This course is recommended to all students, interested in mathematical physics, and it does not imply any special preliminary education in physics.
The preliminary program of the course includes: 1. Lagrangian formalism: minimal action principle, Euler-Lagrange equations, symmetries and integrals of motion, Noether theorem. 2. Simplest examples: dynamics for a single degree of freedom, Kepler's problem etc. 3. Basis of the Hamiltonian formalism: phase space, Legebdre transform, Hamilton equations, the Poisson and symplectic structures, Darboux theorem. 4. The Hamilton-Jacobi equation, canonical transform, Liouville theorem. 5. Integrable systems: separation of variables, Liouville integrability. Systems with Lax representation. 6. Examples of integrable systems: Toda and Calogero problems, integrable systems on Lie groups, geometry of spectral curves etc.
As final project students should select a research topic from one of the labs, write a short text about a possible project and discuss it. It will be the first step for future thesis research or just training.
The final schedule (what lecture reads which professor, and when) will be available by the end of the September.
Professors from the Center for Design, Manufacturing and Materials will provide overviews of their laboratories and research projects. This course will help students to select a specialization and a future research adviser. The information about the Center for Design, Manufacturing and Materials and its laboratories can be found at: https://https://crei.skoltech.ru/cdmm
As a final project students should select a research topic, write a short text about a possible project and discuss it.
As to the vicinity of the metal-insulator transition, I give a qualitative discussion of the mechanism behind the transition, as well as the most powerful tools for probing the properties of the system near the transition: analysis of inverse participation ratios and the concept of multifractality of the wave-functions.
In the metallic phase I discuss the weak localization corrections, including magnetoresistance, inelastic phase-breaking mechanisms and interaction-induced anomalies in the density of states near the Fermi surface.
At the end of the course I give a brief introduction to mesoscopics, including the Landauer formalism and quantization of the ballistic conductance.
Tentative plan: linear Lie groups and their Lie algebras; universal enveloping algebras; Haar measure on a linear Lie group; general facts about representations of compact groups and their characters; radial part of Haar measure; Weyl's formula for characters of the unitary groups; Weyl's unitary trick; classification and realization of representations; symmetric functions.
Students activities include: -listening to lectures -discussions/seminars -homework -tests
The course also offers a forum for TA and allows Skoltech TAs to collect and discuss resources and issues relevant for their TA experience. The forum provides a peer-to-peer feedback opportunity but also enables instructors to participate in the conversation when asked to.
The main bulk of the 81 hours of the course is spent in the actual courses in which the PhD-students do their TA-assignments. The assignments in the course itself require less than 10 hours of time.
The course teaches fundamentals of modern Materials Science (Part I of the course) and provides a survey of materials (Part II), covering all relevant Skoltech research areas and beyond, with brief explanation of structural, electronic, physical, chemical or other properties of materials relevant for their practical use, or from the point of view of utilizing their unique properties in applications. It is a core course in Materials Science educational track providing a reference knowledge base for the rest of material-specific courses as well for student research.
The student will perform the on-line measurements of number size distribution of aerosol synthesized nanoparticles by differential mobility analyzer (size range: 2-1000 nm). Students will become familiar with processes of the aerosol particle collection (filtration, electrostatic precipitation, thermophoretic precipitation). The produced samples of nanoparticles will be observed with means of transmission and scanning electron microscopies.
Totally 21 lecture hours and 12 exercise hours, 9 hours for seminar lessons, 6 presentation hours will be arranged. Students will write a short essay and give a presentation on one of the selected topics.
The design includes: concept development, conceptual design, systems engineering, 3D physical simulation (CFD and FEM), parametric and topology optimization, final solid design.
Educational process is focused on teamwork in this course. Siemens Teamcenter PLM platform is used as to provide interaction within students workgroup.
The course provides students with a theoretical and practical basis for implementing projects devoted to the design of complex technical systems, such as unmanned aerial vehicles.
The course assumes basic preliminary knowledge of quantum mechanics and statistical physics. Second-quantization formalism is introduced and used throughout the course.
Totally 21 lecture hours and 12 exercise hours and 3 hours for seminar lessons will be arranged.
General anatomy and histology of the heart and blood vessels. General anatomy and histology of the kidney. Morphogenesis of the heart and blood vessels. Morphogenesis of the kidney in mammals. Endorine mechanisms in regulation of heart function, blood pressure and electrolyte homeostasis.
The course also will include principles of regulation of blood pressure, Guton theory, Theory of vascular resistance. Genetic predisposition to hypertension. Genetic loci associated with essential hypertension and GWAS studies in humans. Mutagenesis screens for new genes involved in cardiovascular pathology. Atherosclerosis, myocardial infarction and heart failure. Stem cells and cellular therapies in cardiovascular disorders.
Modern methods in cardiac physiology, renal physiology, vascular biology. Students will learn most important techniques to study heart function, excretion and egulation of vascular resistance: ultrasound and MRI imaging, trelemetry, single nephron studies, wire myography and others.
The course provides an overview of modern atomistic computer simulations used to model, understand, and predict properties of realistic materials. The emphasis is on practical techniques, algorithms and programs to bridge theory and applications, from the discovery of materials to their use in real-world technologies. This introductory course is intended for both theoreticians and experimentalists in modern Materials Science at academic level ranging from MSc students to PhD students and postdocs.
Essential notions which are taught include: energy conversion; heat transfer; work; first and second principles; working fluids and thermoelastic coefficients; chemical reactions; thermodynamic cycles; motors and refrigerators: engines and heat pumps; sources of irreversibility; finite-time thermodynamics. Time permitting, notions of kinetic theory and statistical thermodynamics may be briefly introduced.
The course is organized around the learning of essential concepts and an awareness development of current energy technologies. It is based both on "teaching with lecture" and "teaching with discussions" methods. In addition to home assignments and project, students will solve problems during tutorials and discuss their solutions.
Lectures 1-3 are devoted to the Ancient Greek and Roman Science
Lectures 4-6 are devoted to Medieval and Renaissance Science
Lectures 7-9 are devoted to the Scientific Revolution of the XVII century
Lectures 10-12 are devoted to Science in the XVIII and XIX century
Lectures 13-15 are devoted to Science in the XX-XXI centuries
Lectures 16-18 are devoted to the Philosophy of Science
The solid mechanics part covers the elements of elasticity and fracture mechanics: plane strain elasticity, classical crack tip singularity, energy considerations in fracture, Linear Elastic Fracture Mechanics crack propagation criteria. This section also includes elasticity solution for a climb and edge dislocations, solution for a plane-strain traction-free singular and cohesive cracks. Problem formulation and physical reasoning for hydraulic fracture models are presented for: classic models PKN, KGD, radial. The near-tip behavior of hydraulic fractures, no leak-off. Toughness vs viscous dissipation are considered. Effect of the fluid lag. The near-tip behavior of hydraulic fractures with leak-off. Hierarchy of physical scales near the tip. Scaling for simple fracture geometries
The fluid mechanics part of the course includes the foundations for the muli-fluid model of particle transport in a hydraulic fracture, which includes the basics of the multi-continua approach, the derivation of the two-phase suspension flow model from first principles (mass and momentum conservation laws) within the two-fluid approach. Closure relations for suspension rheology and particle settling are discussed. Small scale phenomena during proppant transport are considered: particle migration, and bridging, transition to close packing. Fracture flowback and multiphase flow in well-frac system are discussed.
At the same time, through creativity lab students will be introduced to a variety of creative problem solving techniques and learn how to apply these techniques in the context of the development, evaluation and application of ideas and concepts with commercial potential; consider the evaluation of business ideas that translate existing business models into new national contexts.
The course is designed to help students develop the ability to find, evaluate, and develop technological ideas into commercially viable product and process concepts, and build those concepts into viable business propositions. The material covered is research and theory-based but the course is practice-oriented with much of the term spent on shaping technology-based opportunities. A central objective of this subject is to equip students with an understanding of the main issues involved in the commercialization of technological advances at both strategic and operational levels.
-) Introduction to cryptography, type of ciphers. Private and Public crypto systems -) Hash functions.Digital signatures and certificates. Public key infrastructure -) Secret sharing, esoteric protocols, mental poker -) Introduction to data base systems. Distributed data base systems -) Main concept of blockchain. Consensus and Impossibility of Distributed consensus with One Faulty Process -) Network and computational assumptions. Consensus properties -) Atomic broadcast. Tendermint. Exonum -) Cryptocurrency, Certification, Anchoring. Industrial examples
The course's concept is inspired by the international computer school "42" (https://www.42.us.org/) whose approach is based on peer-to-peer project-based learning. Inspite of its young age (the first 42 was opened in Paris in 2013), the approach used by the school has already demonstrated a remarkable efficiency: over the past years, "42" has opened branches in multiple locations worldwide. Inspired by the success of "42", Sberbank has recently adopted the method and implemented it in the corporate IT educational initiative (https://21-school.ru).
The course will be organized in the form of a continuous workshop in the computer class around individual students' projects. The first-term projects will be focused on acquiring the basic skills related to data manipulation and visualization, as well as linear algebra and numerical methods for solution of partial differential equations. The second-term projects will be addressing computer modeling of real-life problems, based on (adapted) topics from the actual research work in progress.
The workshop will run through the 2nd and 3rd terms. The credits for the workshop will be distributed 1,5 credits for each term.
Introduction to information (classical and quantum) Models of computation Reversible logic Quantum computing Tensor networks, gates and circuits Quantum protocols and open systems
Upon completion of this course the students will be able to master:
1.Classes of Materials
crystalline solids ionic, covalent, metallic, polymers 3-D structures, polymorphism, importance of defects, effect of nanoscale phase diagrams, transformations, glasses, composites
2. Property of Materials
Electrical Optical Magnetic
3. Materials Chemistry Analysis Methods
Surface Sensitivity and Specificity X-ray Photoelectron Spectroscopy Ultraviolet Photoelectron Spectroscopy
It includes considering strategies to choose the relevant variables, parameters and observables, model nature (e.g. discrete vs continuous), modeling technique (e.g. agent-based simulations vs. dynamical system approach), and visualization and interpretation of the results. The following classes of systems will be used as examples:
1. Population models 2. Evolution and speciation 3. Systems biology 4. Reaction-diffusion systems and pattern formation 5. Networks 6. Game-theoretical models
To pass, one would need to present a paper at least once during the module and actively take part in discussions of other papers. One absence is allowed no questions asked. Additional absences when unexplained will be a cause for no-pass grade. There will be a few home assignments. They must be submitted in time, typed–not written up–and done professionally (written in good language, be concise and free of spelling errors – consider them as part of academic writing exercises).
It is gonna be fun – students tend to like the seminar and its atmosphere
In this course I will show, how numerical linear algebra methods and algorithms are used to solve practical problems. Matrix decompositions play the key role in numerical linear algebra. We will study different matrix decompositions in details: what are they, how to compute them efficiently and robustly, and most importantly, how they are applied to the solution of linear systems, eigenvalue problems and data analysis applications. For large-scale problems iterative methods will be described. I will try to highlight recent developments when it is relevant to the current lecture.
This course should serve as a basis for other IT Skoltech courses. It will also serve as a first-time place where programming environment and infrastructure is introduced in a consistent manner.
Please see the seminar webpage at http://crei.skoltech.ru/cee/education/wednesday-scientific-seminar/
The course covers the entire spectrum of the lifecycle management of a system, encompassing conceptual design, design, implementation, assembly-Integration and test (AIT), operations and disposal of systems.
Being a foundational course for the Space and Engineering Systems students of Skoltech, the course discusses many applications of systems engineering including some parts of space systems engineering . The course also discusses systems architecture principles.
The Systems Engineering course follows the systems engineering V-model as an educational guideline. The course includes a design project that is conducted throughout the term.
The course lays the foundation to undertake a robust analysis and design of opportunities for technological innovation. It helps PhD students to develop the ability to recognize, evaluate, and develop technological ideas into commercially viable product and service concepts, and build those concepts into viable business propositions.
We introduce tools and frameworks to help isolate and control the factors shaping the identification, evaluation and development of commercial opportunities. During the course, students first gain practical experience in shaping technology-based opportunities (originating from problems found in engineering and scientific education) and in identifying market-based opportunities (from social, economic and environmental contexts). Students are then challenged to employ that same commercialization framework to reflect on and examine ideas and scientific results from their own doctoral research, link these with appropriate market-based opportunities, and identify one or more pathways to create practical impact from their ideas.
The material covered is research and theory-based but the course is practice-oriented with much of the term spent on shaping technology-based opportunities. A central objective of this subject is to equip students with an understanding of the main issues involved in the commercialization of technological advances at both strategic and operational levels.
The main goal of this course is to represent the latest developments in the field of additive manufacturing to the students. In this course a wide range of questions will be addressed, beginning from the process of designing the structures up to various printing technologies, as well as analysis of the final structures. Various kinds of applications of these materials from engineering to bio regenerative medicine will be considered. During laboratory class we will get acquainted with the additive technologies on various printing machines. Students will be able to create their own models, print them in metals, ceramics and polymers, and also analyze the properties of the final samples. During this course a complete cycle of production of samples using various 3D printing techniques will be explored both theoretically and practically.
During the course, students should develop the technology for small unmanned aerial vehicle (UAV) prototype production. Educational process includes manufacturing technology development, prototype production, prototype testing, model validation. During the course, students learn how to use special software Simcenter 3D, LMS Test.Lab, LabView, 3D printers’ software, test machines
The course provides students with a theoretical and practical basis for advanced manufacturing of complex systems, such as UAV and forms the final understanding of the product lifecycle management.
Also, so called Hardware-in-the-Loop (HiL) testing is important part of the course. The idea of HiL is to upload the functional model of investigated system to real-time board and test it in combination with physical parts.
During the course students perform a number of tests with the system that was designed and prototyped during courses Advanced PLM I and Advanced PLM II. Finally the results are used for system model validation.
Course structure: lectures, seminars, exam.
Totally 32 hours of lectures, 12 hours of exercises and 4 hours of discussion work. During the courses each student is supposed to give a short presentation (15 min) on a selected topic, to write an essay on other selected topic and to prepare an exercise report.
Foundation of continuum mechanics consists of: 1) material continuum model in the form of a deformable (with mechanical stresses and other macroparameters) continuous medium, described via several piecewise continuous differentiable functions. Building such a model is carried out by averaging the parameters of real materials that have a discrete atomic and molecular structure; 2) differential, integral, tensor calculus and the theory of dimensions with the fundamental idea of invariance under transformation of coordinate systems and systems dimension; 3) The laws of conservation of mass, momentum, angular momentum and energy, the laws of thermodynamics, expressed in terms of macroscopic parameters of the material continuum; 4) mechanical (rheological), thermal and electrical experiments that allow us to find connections between macroparameters of different substances at different mechanical, thermal, electromagnetic and physical-chemical processes. These representations constitute, in particular, the mathematical theory of thermo-electro-magneto-mechanical field.
This course uses tensor representations in the Cartesian coordinate system of the observer. But it will one shown in detail how to to write the continuum mechanics equations in the arbitrary curvilinear coordinate system. This way the common link is not lost and the exposition becomes easier and clearer.
This course introduces students to the first principles and methods of the observation of Earth surface, monitoring of Earth atmosphere and detection of different kind of radiation coming from Space. The course will cover wide range of the satellites-, aircraft-, rockets- and balloon- based techniques designed for environmental monitoring, meteorology, map making etc. Goals of the course include: a comprehensive knowledge of the principles and approaches to the creation and operation of remote sensing systems; acquisition of analysis skills of modern ERS programs; practical application of acquired knowledge and skills for SWOT-analysis of complex information systems.
Course will also include a module on geomatics, i.e. platforms, sensors and methodologies related to the collection, processing, analysis and interpretation of (2D/3D) data related to Earth's surface. This includes platforms like satellite or drones, sensors like LiDAR or airborne cameras and techniques like photogrammetry, laser scanning, geodesy, topography, etc.
Major learning outcomes include operational principles and design of different sensors used in remote sensing of the Earth, practical skills to design an experiment in remote sensing with applications to a practical business need.
We start with several practical examples which demonstate the need for geomechanics in each of considered technological application with special application to hydraulic fracturing technology.
We then stop on continuum mechanics formulations for one phase models, suitable for one-point-view description of reservoir and well flow deformation processes. We also describe two-phase models, although intentionally do not go too deep in the topic. We also do not goal to make our formulations rigorous enough in mathematical sense. We do not thing that Master students need that at this stage. Instead, we put significant effort (and number of contact hours) to let Master students fell free in practical solutions of the governing equations they were just taught. To make the procedure more effective, the governing equations are divided into several (20) basic groups with their own specific modelling recipes which are taught to students at classes until they ensure that the procedures are simple. For doing that we developed 20 matlab codes. During their further project exercises, students will utilize these 20 "bricks" to construct solutions for real field and/or technological problems, presented in the first section of the course.
It has to be noticed, that the course is suitable for PhD students as well, although the project topics for them would be more complicated that that for the master students
The course is focused on the human immune system. The main medical aspects related to the functioning of the immune system will be considered, such as: autoimmune diseases, allergies, tumor-immune system interactions, immunotherapy, vaccinations and transplantation. Particular attention will be paid to the adaptive part of the immune system and immunogenomics: application of the new sequencing technologies and associated computational data analysis approaches to the studying of the antibody and T-cell receptor repertoires in health and disease.
The course is designed for students of different biomedical background. The necessary foundation will be given in the form of lectures. Independent work of students, mainly in the form of presentations aimed to dissect the particular immunological questions at the seminars, will be differentiated in compliance with individual background.
A workshop in applied bioinformatics is included within the course. In a few hours of guided and independent work it will cover the data analysis of immune receptor high-throughput sequencing.
Intellectual property affects not only technology commercialization strategy but also the direction of scientific research itself. University research groups increasingly compete with each other for scientific reputation and access to resources on the basis of their ability to obtain patent protection for the practical applications of their research; but also on the basis of their ability to plot research pathways to maneuver around the "proprietary territory" of other research groups. Skill in using IP data bases, and associated analytical tools, can empower university scientific teams to craft more powerful research strategies.
This course will survey basic concepts of intellectual property and provide an introduction to a variety of types of intellectual property and IP-related rights, such as patents, copyright, trade secrets, trademarks, design rights, database rights, domain names, and demarcations of origin. The classroom sessions will include lively discussions of case studies of the management of IP and the resolution of IP-related problems in the process of technology commercialization. Each student will conduct an analysis of intellectual property issues related to his or her own Ph.D. research topic. Use will be made of special IP data and IP analytics tools.
In this course the students will learn about • key concepts and methods of generating and testing customer-centric products and business ideas (e.g. Customer Development & Lean Startup, Design Thinking, User Research, Business Model Innovation, TRIZ, Design Sprints); • prospective markets and technologies enabling creation of new unique user experiences; • fundamentals for new products and innovations marketing; • modern tools and approaches fostering creativity & innovations, facilitating team-based and project-based work of a cross-disciplinary design teams.
In particular, students will learn how to get insights into customer needs, get hands-on knowledge on different approaches to market research and customer co-creation. As well the course reviews modern methods for generating market insights, turning them into promising concepts, validating and enhancing the concepts through rapid prototyping, experimentation and user tests.
Special focus is given to modern Digital Products and technologies in the areas of Internet of Things, Smart and Connected Devices, Industry 4.0.
Essential notions which are taught include: Onsager’s approach to linear nonequilibrium thermodynamics; coupled transport theory; Boltzmann equation; thermal conductivity; electrical conductivity; electrochemical potential in solid-state systems; force-flux formalism and its application to thermoelectric systems; device optimization modelling accounting for dissipative coupling to heat reservoirs; solar energy conversion.
The course is intended to provide the understanding and working knowledge of numerical methods required for modeling and simulation of complex phenomena. The course focuses on understanding fundamentals of numerical methods such as accuracy, stability, convergence, and consistency rather than learning how to use canned computer codes. The course involves a fair amount of first-hand experience with programing and solving real problems on computers. Although the solid knowledge of calculus, linear algebra, complex variables is essential, only basic understanding of the theory of ordinary and partial differential equations as governing equations for physical and engineering systems as well as basic programming skills are required. The following topics are discussed: interpolation, numerical differentiation, numerical integration, numerical solutions of ordinary differential equations, and numerical solution of partial differential equations. Students will have to complete four computer projects, mid-term and final exams.
Here is the list of topics which will be discussed in the course.
- Coordinate Bethe ansatz on the example of the Heisenberg model and one-dimensional Boe gas with point-like interaction between particles.
- Bethe ansatz in exactly solvable models of statistical mechanics on the lattice.
- Calculation of physical quantities in integrable models in thermodynamic limit, thermodynamic Bethe ansatz.
- Bethe equations and the Yang-Yang function, caclulation of norms of Bethe vectors.
- Quantum inverse scattering method and algebraic Bethe ansatz, quantum R-matrices, transfer matrices, Yang-Baxter equation.
- Functional Bethe ansatz and the method of Baxter's Q-operators, functional relations for transfer matrices, transfer matrices as classical tau-functions.
The knowledge of quantum mechanics and statistical physics for understanding of the course is highly desirable but not absolutely necessary. Out of the physical context ansatz Bethe in its finite-dimensional version is simply a method for diagonalization of big matrices of a special form. In this sense it does not require anything except the basic notions of linear algebra.
The topics covered include:
Penalty functions and embedding problems into the ground state of Ising spins Quantum vs stochastic models of computation Hamiltonian simulation and variational algorithms Quantum enhanced machine learning
It turns out that all these problems have a general mathematical structure, which can be encoded in the term "integrability". This structure is behind a lot of beautiful exact mathematical results. Moreover, these results have remarkable universality property, which play the same role as the law of large numbers and the central limit theorem in the probability theory. Looking at our random systems from afar, we find that they posess completely nonrandom limiting forms. Random fluctuations around these forms are described by a small number of universal probability distributions that are completely independent of the details of original system. The course attendees are going to get acquainted with the range of issues described and to learn about the latest achievements in the field.
This course will cover the fundamentals of signal and image processing. We will provide a mathematical framework to describe and analyze images as two- or three-dimensional signals in the spatial and frequency domains. The students will become familiar with the theory behind fundamental processing tasks including image enhancement, recovery and reconstruction. They will also learn how to perform these key processing tasks in practice using current state-of-the-art techniques and computational tools. A wide variety of such tools will be introduced including large-scale optimization algorithms and statistical methods. Emphasis will also be given on sparsity, which plays a central role in modern image processing systems
This class will focus on concept preparation in the V-diagram logic. Further results can be explored either in the Space Sector course, where commercial aspects of the mission can be considered, as well as in the PLM course, where technical details can be worked out in a systematic fashion.
The goal of this course is to give a broad review of modern photonic and spectroscopic studies of quantum materials. The course requires basic knowledge of quantum mechanics, optics and solid state physics. In the introductory part of the course, the basic theory of electromagnetic response of quantum systems, centered around linear response functions and their spectral properties, is outlined. The rest of the course describes such quantum materials as graphene and graphene-based structures, topological insulators, topological Dirac and Weyl semimetals, high-temperature superconductors, exotic magnetics, transition metal dichalcogenides, oxide interfaces, and novel electromagnetically-engineered quantum materials. The students will be introduced to basic models and to both conventional and ultrafast pump-probe spectroscopy studies of these materials.
Independent student work on discipline includes preparation for lectures, seminars, labs and other learning activities, as well as the implementation of individual tasks / independent works / projects and others. Educational and methodical support of Independent student work presented by topics of all kinds of tasks and guidelines for their implementation.
The course will include practical data analysis work conducted by the student in front of a computer, but also introductory lectures into principles of data analysis and basic elements of statistical analysis of large-scale biological data.
At the end of the course, students would be expected to accomplish an independent data analysis project on a model dataset including several heterogeneous types of biological “omics” data.
Students will learn what forms the backbone of biomedical imaging, drawing from the mathematical, physical, chemical and biological sciences, including the subjects of: • Light microscopy (live cell imaging, deconvolution and superresolution microscopy, 3D microscopy, Optical Coherence Tomography); • Medical imaging (X-ray, Magnetic Resonance Imaging, Computed Tomography, Ultrasound, Positron Emission Topography); • Image analytics (filtering and signal processing, machine learning and artificial neural networks, computer vision, image-based biological and physiological modeling).
There will be one mid-term take-home exam devoted to image formation and a related biomedical application. And a final computer vision project on a dataset from an imaging modality of a student’s choice.
• Introduction: What is a composite? Classification. Metals vs composites, advantages and disadvantages. Applications in industry. • Matrices. Micromechanics. • Mesomechanics: Stresses and strains. Ply. Laminate theories. Hygrothermal strains and stresses. Edge effect. • Manufacturing: Unidirectional vs. textile. Thermoplastic vs. thermoset. Prepreg vs. infusion. • Experimental characterisation: Tension, bending, compression, shear, impact, fatigue. • Damage and failure. Fracture toughness. • Finite element analysis. Abaqus.
Participants will learn fundamentals of these areas through active participation in teamwork. The course will provide practical knowledge on applications of composite materials in aerospace and mechanical engineering. The course includes practical experience of composite manufacturing and mechanical tests. During the last part of the course the participants will be presented a 'challenge' project in design and structural analysis, which they may attack experimentally, analytically or by means of finite-element package Abaqus. Participants are expected to demonstrate their collective knowledge while at the same time solving individually a real problem.
The prerequisites are: undergraduate math, chemistry, and physics.
Lecture 1: Introduction to silicon based devices for logic electronics Lecture 2: MOSFET device operation Lecture 3: Band structure of materials, tight binding approach Lecture 4: Carrier scattering by phonons and Coulomb interaction Lecture 5: Boltzmann Transport Equation (BTE) low bias Lecture 6: BTE at high bias, numerical approaches Lecture 7: P-N junctions and diodes Lecture 8: Photovoltaic devices Lecture 9: Contact resistance: diffusive limit Lecture 10: Contact resistance: ballistic limit Lecture 11: 2D materials: graphene and beyond Lecture 12: Current status of the semiconducting industry
Many machine learning problems are fundamentally geometric in nature. The general goal of machine learning is to extract previously unknown information from data, which is reflected in the structure (underlying geometry) of the data. Thus, understanding the shape of the data plays an important role in modern learning theory and data analytics. Real-world data obtained from natural sources are usually non- uniform and concentrate along lower dimensional structures, and geometrical methods allow discovering the shape of these structures from given data.
Originally being part of dimensionality reduction research, geometrical methods in machine learning has now become the central methodology for uncovering the semantics of information from the data.
The aim of the course is to explain basic ideas and results in using the modern geometrical methods for solving main machine learning problems such as classification, regression, dimensionality reduction, representation learning, clustering, etc.
A large part of the course addresses to most popular geometrical model of high-dimensional data called manifold model and introduces modern manifold learning methods. Necessary short information on differential geometry and topology will be given in the course.
The course lets students to be involved in meaningful real-life machine learning projects, such as mobile robot navigation, neuroimaging, to cope with challenging problems.
Topics also include clearing agents and techniques, optical imaging of brain activity in vivo using genetically encoded probes, immediate early gene mapping, intravital imaging, applications for functional analyses of neuronal circuits.
The course aims to teach students to understand basic principles of the current imaging techniques, microscope design, and image formation. The course will also offer a practice in image analysis with open source software. Students will learn how to choose the most appropriate imaging method for their own research project.
Choosing the appropriate computational method for a photonics modeling problem requires a clear understanding of the pros and cons of the available numerical methods. Numerical Methods in Photonics presents six of the most frequently used methods: FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green’s function, and FEM.
The Course outlines the basics of Maxwell’s equations and includes self-contained information focusing on each of the methods. Each method is accompanied by a review of the mathematical principles in which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATLAB® is used throughout the text.
This course provides a solid basis to practice writing your own codes. The theoretical formulation is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools.
On the other hand the emerging 21st Century power system is characterized by bidirectional flows between a very large number of uncontrollable and stochastic generators (usually, but not always, renewable ones such as wind or solar) and stochastic and often poorly-predictable demand. Demand ceases to be predictable as it consists of consumers equipped with smart meters and wind/solar generators hence possibly becoming net generators – so-called prosumers. Increased penetration of energy storage, both stationary and mobile due to a take-up of electric vehicles, offers buffering possibilities in dispatch (generation does not have to be equal to demand at any time). Controlling such a power system is the main research challenge in power systems and it is made possible by latest advances in ICT (Information and Control Technology), communication networks, Internet, GPS, sensors, etc. However it requires new tools and methodologies, the Smartgrid course will give the basis of this new grid scenario.
Every topic is covered by a top expert from the field. The topics of lectures are: New space – a Russian view; System thinking; Economics of a firm; Critical thinking; Earth Observation; How a firm competes; Space Sector Agencies, Organizations and Plans: Russia; Launch Systems; Technology assessment; Capabilities of human spaceflight; Value chain analysis; Space navigation services; Space science payloads and missions Exomars; International competition in the space sector; Space Data systems; Space communications; Space Sector Agencies, Organizations and Plans: Europe; Satellite manufacturing and operations, including sensors and payloads; Space Policy.
Students are expected to utilize the course to (i) design; (ii) conduct and (iii) present research.
The course roadmap (and your project team journey) is built around: – Assessing the status of your project (team, technology, market, etc.) – Planning your “project progress sprints” – practical actions bringing your project to the next level – Supporting your sprints with Customer Development and Lean Product Development classes, working sessions, mentors meetings, etc. – Final Demo Day to showcase your projects
Course benefits: – Learn and develop the advanced and practical skills in the area of Technology Entrepreneurship & Innovations – Connect to top-notch mentors, investors and fellow entrepreneurs – Receive coaching from successful entrepreneurs and industry experts as well as Skoltech Faculty and Researchers – Propel your projects (IW-based or new ones) up to viable products, biz concepts, realizing funding opportunities, etc.
The course will be useful to all students willing to improve their understanding of natural (e.g. mineral oil) and man-made colloids, such as suspensions, emulsions and foams, as well as natural and synthetic porous materials.