This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves.

This book focuses on crisis management in software development which includes forecasting, responding and adaptive engineering models, methods, patterns and practices. It helps the stakeholders in understanding and identifying the key technology, business and human factors that may result in a software production crisis. These factors are particularly important for the enterprise-scale applications, typically considered very complex in managerial and technological aspects and therefore, specifically addressed by the discipline of software engineering. Therefore, this book throws light on the crisis responsive, resilient methodologies and practices; therewith, it also focuses on their evolutionary changes and the resulting benefits.

Proceedings of Machine Learning Research: Volume 119: International Conference on Machine Learning, 12-18 July 2020

Positive-Unlabeled (PU) learning is an analog to supervised binary classification for the case when only the positive sample is clean, while the negative sample is contaminated with latent instances of positive class and hence can be considered as an unlabeled mixture. The objectives are to classify the unlabeled sample and train an unbiased positive-negative classifier, which generally requires to identify the mixing proportions of positives and negatives first. Recently, unbiased risk estimation framework has achieved state-of-the-art performance in PU learning. This approach, however, exhibits two major bottlenecks. First, the mixing proportions are assumed to be identified, i.e. known in the domain or estimated with additional methods. Second, the approach relies on the classifier being a neural network. In this paper, we propose DEDPUL, a method that solves PU Learning without the aforementioned issues. The mechanism behind DEDPUL is to apply a computationally cheap post-processing procedure to the predictions of any classifier trained to distinguish positive and unlabeled data. Instead of assuming the proportions to be identified, DEDPUL estimates them alongside with classifying unlabeled sample. Experiments show that DEDPUL outperforms the current state-of-the-art in both proportion estimation and PU Classification and is flexible in the choice of the classifier.

Maps and diagrams have long been used by science and education. The results and achievements of geography, astronomy, biology, economics have always been presented in the form of maps. Modern methods and tools of network science allow to deeper understand collaboration because relations between agents of activity are represented as a map. For many collaborative educational systems maps of relations between agents and activity products are built automatically. However, these diagrams are not used in educational practice as tools for better learning. The paper provides examples of how the diagrams were used in educational practice in order to support a group reflection of collaborative activities.

The 24th European Conference on Advances in Databases and Information Systems (ADBIS 2020) was set to be held in Lyon, France, during August 25–28, 2020, in conjunction with the 24th International Conference on Theory and Practice of Digital Libraries (TPDL 2020) and the 16th EDA days on Business Intelligence & Big Data (EDA 2020). However, because of the worldwide COVID-19 crisis, ADBIS, TPDL, and EDA had to take place online during August 25–27, 2020. Yet, the three con- ferences joined their forces to propose common keynotes, workshops, and a Doctoral Consortium.  

The 24th European Conference on Advances in Databases and Information Systems (ADBIS 2020) was set to be held in Lyon, France, during August 25–28, 2020, in conjunction with the 24th International Conference on Theory and Practice of Digital Libraries (TPDL 2020) and the 16th EDA days on Business Intelligence & Big Data (EDA 2020). However, because of the worldwide COVID-19 crisis, ADBIS, TPDL, and EDA had to take place online during August 25–27, 2020. Yet, the three con- ferences joined their forces to propose common keynotes, workshops, and a Doctoral Consortium.

This CCIS volume published by Springer contains the post-proceedings of the XXI International Conference on Data Analytics and Management in Data Intensive Domains (DAMDID/RCDL 2019) that took place during October 15–18 at the Kazan Federal University, Russia.

DAMDID is held as a multidisciplinary forum of researchers and practitioners from various domains of science and research, promoting cooperation and exchange of ideas in the area of data analysis and management in domains driven by data-intensive research. Approaches to data analysis and management being developed in specific data-intensive domains (DID) of X-informatics (such as X = astro, bio, chemo, geo, med, neuro, physics, chemistry, material science, etc.), social sciences, as well as in various branches of informatics, industry, new technologies, finance, and business are expected to contribute to the conference content.

Proceedings of the SPIE PHOTONICS EUROPE Conference on Biophotonics in Point-of-Care, 6-10 April 2020, Online Only, France. Proc. SPIE volume 11361

This book studies complex systems with elements represented by random variables. Its main goal is to study and compare uncertainty of algorithms of network structure identification with applications to market network analysis. For this, a mathematical model of random variable network is introduced, uncertainty of identification procedure is defined through a risk function, random variables networks with different measures of similarity (dependence) are discussed, and general statistical properties of identification algorithms are studied. The volume also introduces a new class of identification algorithms based on a new measure of similarity and prove its robustness in a large class of distributions, and presents applications to social networks, power transmission grids, telecommunication networks, stock market networks, and brain networks through a theoretical analysis that identifies network structures. Both researchers and graduate students in computer science, mathematics, and optimization will find the applications and techniques presented useful.

 

This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,…,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry. 

The main target of the IEEE East-West Design & Test Symposium (EWDTS) is to exchange experiences between scientists and technologies from Eastern and Western Europe, as well as North America and other parts of the world, in the field of design, design automation and test of electronic circuits and systems. The symposium is typically held in countries around East Europe, the Black Sea, the Balkans and Central Asia region. We cordially invite you to participate and submit your contributions to EWDTS 2020 which covers (but is not limited to) the following topics. • Analog, Mixed-Signal and RF Test • ATPG and High-Level TPG • Automotive Reliability & Test • Built-In Self Test • Debug and Diagnosis • Defect/Fault Tolerance and Reliability • Design Verification and Validation • EDA Tools for Design and Test • Embedded Software • Failure Analysis & Fault Modeling • Functional Safely • High-level Synthesis • High-Performance Networks and Systems on a Chip • Internet of Things Design & Test • Low-power Design • Memory and Processor Test • Modeling & Fault Simulation • Network-on-Chip Design & Test • Flexible and Printed Electronics • Applied Electronics Automotive/Mechatronics • Algorithms • Object-Oriented System Specification and Design • On-Line Testing • Power Issues in Design & Test • Real Time Embedded Systems • Reliability of Digital Systems • Scan-Based Techniques • Self-Repair and Reconfigurable Architectures • Signal and Information Processing in Radio and Communication Engineering • System Level Modeling, Simulation & Test Generation • System-in-Package and 3D Design & Test • Using UML for Embedded System Specification • Optical signals in communication and Information Processing • CAD and EDA Tools, Methods and Algorithms • Hardware Security and Design for Security • Logic, Schematic and System Synthesis • Place and Route • Thermal and Electrostatic Analysis of SoCs • Wireless and RFID Systems Synthesis • Sensors and Transducers • Medical Electronics • Design of Integrated Passive Components

This book constitutes the proceedings of the 19th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2020, held in Novosibirsk, Russia, in July 2020. The 31 full papers presented in this volume were carefully reviewed and selected from 102 submissions. The papers are grouped in these topical sections: discrete optimization; mathematical programming; game theory; scheduling problem; heuristics and metaheuristics; and operational research applications.

The Arctic Council is well-positioned to play a leadership role in better understanding the impact of Covid-19 in the Arctic and spearheading activities to respond to the pandemic in the short-, medium- and longer-term. This briefing document was prepared to inform initial discussions regarding the coronavirus pandemic in the Arctic at the Senior Arctic Officials’ executive meeting (SAOX) on 24-25 June 2020. It draws together available information – to date (June 2020) – about the impact of Covid-19 in the Arctic: Briefing Document for SAOs June 2020 For public release Page 10 of 83 Covid-19 and the actions taken to respond in the Arctic region. The document draws from a wide spectrum of sources, reflecting the complex and intricate nature of how Covid-19 affects Arctic peoples and communities, including national and subnational statistical databases and tools, peer-reviewed articles, policy statements, technical guidelines, field surveys, and local observations from Arctic communities.

This book presents recent non-asymptotic results for approximations in multivariate statistical analysis. The book is unique in its focus on results with the correct error structure for all the parameters involved. Firstly, it discusses the computable error bounds on correlation coefficients, MANOVA tests and discriminant functions studied in recent papers. It then introduces new areas of research in high-dimensional approximations for bootstrap procedures, Cornish–Fisher expansions, power-divergence statistics and approximations of statistics based on observations with random sample size. Lastly, it proposes a general approach for the construction of non-asymptotic bounds, providing relevant examples for several complicated statistics. It is a valuable resource for researchers with a basic understanding of multivariate statistics.

The materials of The International Scientific – Practical Conference is presented below. The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies. It is interesting for a wide range of researchers, teachers, graduate students and professionals in the field of innovation and information technologies.

Forest ecosystems, their products and services play an important role in achieving ambitious climate change mitigation objectives at the same time requiring profound adaptation to climate change. Forest management schemes to support climate action have to be developed within their regional context but also have to be aligned with national or EU-level climate, forest and sustainability policies. The conference on “Managing forests in the 21st century” is the final conference of the FORMASAM, REFORCE and FOREXCLIM research projects. The conference bringstogether scientific experts on forest management from all over Europe facing very specific management challenges. The aim isto discuss and improve the understanding the role of forests and forest management in the context of climate change. The conference addresses climate change impacts, as well as needs for mitigation and adaptation especially with regard to the following scientific questions: 1. What are the impacts of climate extremes and disturbances? 2. What are the management challenges (and options) for resilient forests? 3. What can we do to increase the contribution of forest management to climate change mitigation?

.

We consider the problem of estimation of the drift parameter of an ergodic Ornstein– Uhlenbeck type process driven by a Lévy process with heavy tails. The process is observed continuously on a long time interval [0, T ], T →∞. We prove that the statistical model is locally asymptotic mixed normal and the maximum likelihood estimator is asymptotically efficient.

In this paper, we study network feature engineering for the problem of future co-author recommendation, also called collaborator recommender system. We present a system, which uses authors' research interests and existing collaboration information to predict missing and most probable in the future links in the co-authorship network. The recommender system is stated as a link prediction problem for the current network and for new edges that appear next year. From machine learning point of view, both problems are treated as binary classification. We evaluate our research on our University researchers co-authorship network, while also mentioning results on sub-network of publications indexed in Scopus. Our approach has high accuracy and provides scalable solution for any significantly large co-authorship network.

Autonomous driving highly depends on depth information for safe driving. Recently, major improvements have been taken towards improving both supervised and self-supervised methods for depth reconstruction. However, most of the current approaches focus on single frame depth estimation, where quality limit is hard to beat due to limitations of supervised learning of deep neural networks in general. One of the way to improve quality of existing methods is to utilize temporal information from frame sequences. In this paper, we study intelligent ways of integrating recurrent block in common supervised depth estimation pipeline. We propose a novel method, which takes advantage of the convolutional gated recurrent unit (convGRU) and convolutional long short-term memory (convLSTM). We compare use of convGRU and convLSTM blocks and determine the best model for real-time depth estimation task. We carefully study training strategy and provide new deep neural networks architectures for the task of depth estimation from monocular video using information from past frames based on attention mechanism. We demonstrate the efficiency of exploiting temporal information by comparing our best recurrent method with existing image-based and video-based solutions for monocular depth reconstruction.

We study the superconducting properties of the bulk states of a doped topological insulator. We obtain that hexagonal warping stabilizes the nematic spin-triplet superconducting phase with Eu pairing and the direction of the nematic order parameter which opens the full gap is the ground state. This order parameter exhibits non-BCS behavior. The ratio of the order parameter to the critical temperature of Δ(0)/Tc differs from the BCS ratio. It depends on the chemical potential and the value of the hexagonal warping. We discuss the relevance of the obtained results for the explanation of the experimental observations.

A few years ago we predicted theoretically that in systems with nesting of the Fermi surface the spin-valley half-metal has lower energy than the spin density wave state. In this paper we suggest a possible way to distinguish these phases experimentally. We calculate the dynamical spin susceptibility tensor for both states in the framework of the Kubo formalism. Discussed phases have different numbers of bands: four bands in the spin-valley half-metal and only two bands in the spin density wave. Therefore, their susceptibilities, as functions of frequency, have different numbers of peaks. Besides, the spin-valley half-metal does not have rotational symmetry, thus, in general the off-diagonal components of the susceptibility tensor are nonzero. The spin density wave obeys robust rotational symmetry and off-diagonal components of the susceptibility tensor are zero. These characteristic features can be observed in experiments with inelastic neutron scattering.

The Alexander polynomial in several variables is defined for links in three-dimensional homology spheres, in particular, in the Poincaré sphere: the intersection of the surface S={(z1,z2,z3)∈C3:(z1)5+(z2)3+(z3)2=0} with the 5-dimensional sphere Sε5={(z1,z2,z3)∈C3:|z1|2+|z2|2+|z3|2=ε2}. An algebraic link in the Poincaré sphere is the intersection of a germ of a complex analytic curve in (S, 0) with the sphere Sε5 of radius ε small enough. Here we discuss to which extent the Alexander polynomial in several variables of an algebraic link in the Poincaré sphere determines the topology of the link. We show that, if the strict transform of a curve in (S, 0) does not intersect the component of the exceptional divisor corresponding to the end of the longest tail in the corresponding E8-diagram, then its Alexander polynomial determines the combinatorial type of the minimal resolution of the curve and therefore the topology of the corresponding link. The Alexander polynomial of an algebraic link in the Poincaré sphere is determined by the Poincaré series of the filtration defined by the corresponding curve valuations. (They coincide with each other for a reducible curve singularity and differ by the factor (1−t) for an irreducible one.) We show that, under conditions similar to those for curves, the Poincaré series of a collection of divisorial valuations determines the combinatorial type of the minimal resolution of the collection.

Let C_d be the space of non-singular, univariate polynomials of degree d. The Viète map V sends a polynomial to its unordered set of roots. It is a classical fact that the induced map V_∗ at the level of fundamental groups realises an isomorphism between π_1(C_d) and the Artin braid group B_d. For fewnomials, or equivalently for the intersection C of C_d with a collection of coordinate hyperplanes, the image of the map V_∗:π_1(C)→B_d is not known in general. In the present paper, we show that the map V_∗ is surjective provided that the support of the corresponding polynomials spans Z as an affine lattice. If the support spans a strict sublattice of index b, we show that the image of V_∗ is the expected wreath product of Z/bZ with B_d/b. From these results, we derive an application to the computation of the braid monodromy for collections of univariate polynomials depending on a common set of parameters.

We offer a new approach to proving the Chen-Donaldson-Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a families of curves and its relation to the one-dimensional cycles in the moduli space of stable bundles on curves.  

Motivated by convex problems with linear constraints and, in particular, by entropy-regularized optimal transport, we consider the problem of finding ε-approximate stationary points, i.e. points with the norm of the objective gradient less than ε, of convex functions with Lipschitz p-th order derivatives. Lower complexity bounds for this problem were recently proposed in [Grapiglia and Nesterov, arXiv:1907.07053]. However, the methods presented in the same paper do not have optimal complexity bounds. We propose two optimal up to logarithmic factors methods with complexity bounds O~(ε−2(p+1)/(3p+1)) and O~(ε−2/(3p+1)) with respect to the initial objective residual and the distance between the starting point and solution respectively.

Ubiquitous in machine learning regularized empirical risk minimization problems are often composed of several blocks which can be treated using different types of oracles, e.g., full gradient, stochastic gradient or coordinate derivative. Optimal oracle complexity is known and achievable separately for the full gradient case, the stochastic gradient case, etc. We propose a generic framework to combine optimal algorithms for different types of oracles in order to achieve separate optimal oracle complexity for each block, i.e. for each block the corresponding oracle is called the optimal number of times for a given accuracy. As a particular example, we demonstrate that for a combination of a full gradient oracle and either a stochastic gradient oracle or a coordinate descent oracle our approach leads to the optimal number of oracle calls separately for the full gradient part and the stochastic/coordinate descent part.

Let $T\subset\mathbb{R}$ and $(X,\mathcal{U})$ be a uniform space with an at most countable gage of pseudometrics $\{d_p:p\in\mathcal{P}\}$ of the uniformity $\mathcal{U}$. Given $f\in X^T$ (=\,the family of all functions from $T$ into $X$), the {\em approximate variation\/} of $f$ is the two-parameter family $\{V_{\varepsilon,p}(f):\varepsilon>0,p\in\mathcal{P}\}$, where $V_{\varepsilon,p}(f)$ is the greatest lower bound of Jordan's variations $V_p(g)$ on $T$ with respect to $d_p$ of all functions $g\in X^T$ such that $d_p(f(t),g(t))\le\varepsilon$ for all $t\in T$. We establish the following pointwise selection principle: {\em If a pointwise relatively sequentially compact sequence of functions $\{f_j\}_{j=1}^\infty\subset X^T$ is such that $\limsup_{j\to\infty}V_{\varepsilon,p}(f_j)<\infty$ for all $\varepsilon>0$ and $p\in\mathcal{P}$, then it contains a subsequence which converges pointwise on $T$ to a bounded regulated function $f\in X^T$.} We illustrate this result by appropriate examples, and present a characterization of regulated functions $f\in X^T$ in terms of the approximate variation.  

We study the problem of fairly allocating indivisible goods and focus on the classic fairness notion of proportionality. The indivisibility of the goods is long known to pose highly non-trivial obstacles to achieving fairness, and a very vibrant line of research has aimed to circumvent them using appropriate notions of approximate fairness. Recent work has established that even approximate versions of proportionality (PROPx) may be impossible to achieve even for small instances, while the best known achievable approximations (PROP1) are much weaker. We introduce the notion of proportionality up to the maximin item (PROPm) and show how to reach an allocation satisfying this notion for any instance involving up to five agents with additive valuations. PROPm provides a well motivated middle-ground between PROP1 and PROPx, while also capturing some elements of the well-studied maximin share (MMS) benchmark: another relaxation of proportionality that has attracted a lot of attention.

Adaptive introgression - the flow of adaptive genetic variation between species or populations - has attracted significant interest in recent years and it has been implicated in a number of cases of adaptation, from pesticide resistance and immunity, to local adaptation. Despite this, methods for identification of adaptive introgression from population genomic data are lacking. Here, we present Ancestry_HMM-S, a Hidden Markov Model based method for identifying genes undergoing adaptive introgression and quantifying the strength of selection acting on them. Through extensive validation, we show that this method performs well on moderately sized datasets for realistic population and selection parameters. We apply Ancestry_HMM-S to a dataset of an admixed Drosophila melanogaster population from South Africa and we identify 18 loci which show signatures of adaptive introgression, four of which have previously been shown to confer resistance to insecticides. Ancestry_HMM-S provides a powerful method for inferring adaptive introgression in datasets that are typically collected when studying admixed populations. This method will enable powerful insights into the genetic consequences of admixture across diverse populations. Ancestry_HMM-S can be downloaded from https://github.com/jesvedberg/Ancestry_HMM-S/.

We introduce a family of linear relations between cell-zeta values that have a form similar to product map relations and jointly with them imply stuffle relations between multiple zeta values.

We apply Weyl n-algebras to prove formality theorems for higher Hochschild cohomology. We present two approaches: via propagators and via the factorization complex. It is shown that the second approach is equivalent to the first one taken with a new family of propagators we introduce.

We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs duality and the star-triangle transformation at the critical point n=2. We deduce the Matiyasevich theorem and its inverse from the Biggs duality, apply the duality argument to construct the recursion on the parameter n. We provide two different proofs of the Zamolodchikov tetrahderon equation satisfied by the star-triangle transformation in the case of n=2 multivariate Tutte polynomial, extend the latter to the case of valency 2 points and show that the Biggs duality and the star-triangle transformation commute.

We derive a new explicit formula in terms of sums over graphs for the n-point correlation functions of general formal weighted double Hurwitz numbers coming from the Orlov-Scherbin partition functions. Notably, we use the change of variables suggested by the associated spectral curve, and our formula turns out to be a polynomial expression in a certain small set of formal functions defined on the spectral curve.

Schubert polynomials for the classical groups were defined by S.Billey and M.Haiman in 1995; they are polynomial representatives of Schubert classes in a full flag variety of a classical group. We provide a combinatorial description for these polynomials, as well as their double versions, by introducing analogues of pipe dreams, or RC-graphs, for the Weyl groups of the classical types.

A brief description of the relations between the factorization method in quantum mechanics, self-similar potentials, integrable systems and the theory of special functions is given. New coherent states of the harmonic oscillator related to the Fourier transformation are constructed.

Moulin (1981) has argued in favour of electing an alternative by giving each coalition the ability to veto a number of alternatives roughly proportional to the size of the coalition and considering the core of the resulting cooperative game. This core is guaranteed to be non-empty, and offers a large measure of protection for minorities (Kondratev and Nesterov, 2020). However, as is the norm for cooperative game theory the formulation of the concept involves considering all possible coalitions of voters, so the naive algorithm would run in exponential time, limiting the application of the rule to trivial cases only. In this work we present a polynomial time algorithm to compute the proportional veto core.

Recently, many matching systems around the world have been reformed. These reforms responded to objections that the matching mechanisms in use were unfair and manipulable. Surprisingly, the mechanisms remained unfair even after there forms: the new mechanisms may induce an out come with a blocking student who desires and deserves a school which she did not receive. However,as we show in this paper, the reforms introduced matching mechanisms which are more fair compared to the counterfactuals. First, most of there forms introduced mechanisms that are more fair by stability: when ever the old mechanism does not have a blocking student, the new mechanism does not have a blocking student either. Second,some reforms introduced mechanisms that are more fair by counting: the old mechanism always has at least as many blocking students as the new mechanism. These findings give a novel rationale to there forms and complement there cent literature showing that the same reforms have introduced less manipulable matching mechanisms.We furthers how that the fairness and manipulability of the mechanisms are strongly logically related.

Given the final ranking of a competition, how should the total prize endowment be allocated among the competitors? We study consistent prize allocation rules satisfying elementary solidarity and fairness principles. In particular, we axiomatically characterize two families of rules satisfying anonymity, order preservation, and endowment monotonicity, which all fall between the Equal Division rule and the Winner-Takes-All rule. Specific characterizations of rules and subfamilies are directly obtained.

We prove that a quasi-smooth Fano threefold hypersurface is birationally rigid if and only if it has Fano index one.

We study toric G-solid Fano threefolds that have at most terminal singularities, where G is an algebraic subgroup of the normalizer of a maximal torus in their automorphism groups.

We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety X equals the dimension of the anticanonical system of X. We verify this conjecture for log Calabi--Yau compactifications of toric Landau--Ginzburg models for smooth Fano threefolds, complete intersections, and some toric varieties.