Already in 1960s Alfred Yarbus pointed out that voluntary control of the eye movement system is very limited. He compared the act of looking to the act of walking: “when we have learned how to walk, we no longer think how we must move our legs, - we just walk; when we have learned how to see, we do not think in which order we must fixate- we just look”. Yarbus showed that even large amplitude eye movements, called saccades often occur involuntary and escape our awareness. I will describe recent studies that confirm these observations. Yarbus also acknowledged that saccades can also be controlled voluntarily. I will demonstrate that the eye movement system lives in a constant state of competition between goal-directed and involuntary oculomotor programs. On a basis of several experiments I will demonstrate that measuring competition for control of saccadic eye movements is a fruitful way to uncover the mechanisms of attentional selection, visual-spatial working memory and visual stability.

My talk will be devoted to the famous Stochastic Multi-Armed Bandit problem and its applications to web search. Bandit setting originates from a problem of a gambler facing a row of casino slot machines, also called ``one-armed bandits'' or just ``arms''. At each step, gambler chooses an arm, receives its reward, which is a sample from an unknown arm-associated distribution, and updates the stored information about observed rewards of the chosen arm. The goal is to maximize the expectation of cumulative reward over a fixed number of steps. An appropriate solution demands balancing between exploitation of arms whose previously received rewards are high and exploration of arms with little information about their possible rewards. The task of a commercial search engine can be formulated as a bandit problem in different ways. I will review the main existing approaches, some recent advances, and further challenges.

Information processing, or computation, can be performed by natural and man-made «devices». Man-made computers are made from silicon chips, whereas natural «computers», such as the brain, use cells and molecules. At the same time there is a growing understanding that a complex and intelligent information processing in living systems goes far beyond neurons, for example, in adaptive immune system, or in synthetically engineered bacterial cells. Even further, computation occurs on a subcellular level, that is regulatory and signaling pathways in individual cells. In fact, what we perceive as living processes originates from the remarkable ability of integrated biological «elementary» circuits to perform sophisticated computations. The next revolution is promised by synthetic biology that paves the way for rational design and engineering of biological computing systems. In the near future it can greatly enhance our ability to study and to control biological systems. More distant potential applications include tissue engineering and regeneration and medical treatments. In this lecture I will introduce key concepts and discuss recent progress that has been made in biomolecular computing. In conclusion I will present our recent result on a scheme of a synthetically engineered distributed genetic circuit capable of solving classification tasks for quite generic input vectors of chemical signals.

One often compares languages in their word stock, and one often compares individualvocabularies. However, to count “the total number of words” of any language is quite a difficult task. There are no generally accepted criteria that could unequivocally determine which lexical items are words and which are not, or how frequently a word must be used and how many speakers show know it in order to consider it a legitimate word. Counting estimates of individual vocabularies presupposes the existence of some clear criteria for what it means to "know" a word: so far, no such criteria are available. Finally, most words of any language have more than one senses, which are very differently distributed or popular among speakers. The lecture will cover the issues of determining lexical polysemy in texts and in different speakers’ minds and rendering it in dictionaries.

In this lecture we review technologies and techniques used in modern 4th communication systems, such as IEEE802.16m and 3GPP LTE-Advanced, and broadband wireless Internet access systems, such as Wi-Fi in the versions of IEEE802.11ac and IEEE802.11ad standards. We discuss the main directions of their further development during the next several years. For example, based on market research, various sources predict the 1000x increase in wireless traffic demand and corresponding increase of capacity of wireless communication systems in the nearest 10 years. However, capability analysis of 4G wireless technologies shows that evolutionary development thereof is not going to satisfy these new requirements, and there is a need in use of new millimeter- wave spectrum and signals with much wider frequency bandwidths. In the lecture we present the experimental results of propagation properties of millimeter-wave band radio signals together with estimates of main parameters of transceivers necessary to achieve the desired performance characteristics of communication systems. Then, the architecture, the building principles and key technologies of coming 5th 5G communication system will be a combination of large macro-cells powered by LTE technology and providing basic connectivity in the coverage area, and a number of millimeter-wave small cells working in the 57-63 GHz band and providing very high-speed access in the hotspots. We present the main performance characteristic estimates for such heterogeneous networks which were obtained via generation (5G) wireless systems are discussed. It is assumed that a typical numeric computer simulations.

In the past minute alone, your eyes made as many as 240 saccades. In your waking hours today, you will very likely make some 200,000 of them. Even when we think our eyes are completely still, in fact, we are still making eye motions, including tiny saccades called “microsaccades” — between 60 and 120 of them per minute. Just as we don’t notice most of our breathing, we are almost wholly unaware of this frenetic, nonstop ocular activity. But without it, we couldn’t see a thing. Every known visual system depends on movement: we see things either because they move or because our eyes do. What may be most surprising is that large and miniature eye motions help us see the world in similar ways — largely at the same time. In this presentation, I will discuss recent research from my lab and others suggesting that exploration and gaze-fixation are not all that different processes in the brain. Our eyes scan visual scenes with a same general strategy in all cases, whether the images are huge or tiny, or even when we try to fix our gaze. These findings indicate that exploration and fixation are not fundamentally different behaviors, but rather two ends of the same visual scanning continuum. They also imply that the same brain systems control our eye movements when we explore and when we fixate — an insight that may ultimately offer clues to understanding not only normal oculomotor function in the healthy brain, but also oculomotor dysfunction in neurological diseases, like Parkinson’s, that affect eye movements.

In recent years, data mining and optimization heuristics have been used to analyze many large (and massive) data-sets that can be represented as a network. In these networks, certain attributes are associated with vertices and edges. This analysis often provides useful information about the internal structure of the datasets they represent. We are going to discuss our work on several networks from telecommunications (call graph), financial networks (market graph), social networks, and neuroscience. In addition, we are going to present recent results on critical element selection. In network analysis, the problem of detecting subsets of elements important to the connectivity of a network (i.e., critical elements) has become a fundamental task over the last few years. Identifying the nodes, arcs, paths, clusters, cliques, etc., that are responsible for network cohesion can be crucial for studying many fundamental properties of a network.

I will give a survey of the last achievements in the field of constructing mathematical models of the Internet. I will also discuss applications of models to the solution of various problems encountered by search engines.

The number of people diagnosed with cancer is increasing year to year. It is clear that the earlier the disease is identified, the better are chances for clinical remission; however at present we lack reliable methods of early diagnosis, and successful screening tests are even more scarce. Effectiveness of the known biological cancer markers are low due to their insufficient specificity, and screening methods for early identification of all kinds of cancer are highly needed. It is true that mammography and screening of prostate-specific antigens have lead to a significant decrease in mortality due to breast and prostate cancer, but even for these kinds of cancer we could benefit from alternative methods that would be specific and sensitive at once. Other oncology diseases, such as lung cancer, are in even more acute need of early screening methods. Some substances are contained at different levels in normal and tumor cells. These substances can be measured to establish correlation with development of the disease. The more sophisticated methods of analysis become available, the more would-be biomarkers become known; their list includes compounds such as proteins, tumor antigens and anti-tumor antibodies, various metabolic products and so forth, but all these markers lack sensitivity, specificity, and/or repeatability sufficient to use them in full-scale early diagnostics and monitoring of cancer. An unexpected hope comes from the fact that some animals can distinguish cancer patients from healthy individuals: indeed, could relevant biomarkers be found among the metabolites excreted by the body? Monitoring of volatile markers is a very promising diagnostic tool, as the procedure is non-invasive and does not burden the patient. Modern analytic methods allow fast identification of volatile substances contained in breathe, blood, skin, or urine. However here too we do not see tests that would be widely used in clinical practice. Why? The possible reasons for these difficulties and prospective ways of circumventing them will be discussed in the lecture.

Alfred L. Yarbus was among the first to demonstrate that eye movements actively serve our perceptual and cognitive goals, a crucial recognition that is at the heart of today’s research on active vision. Indeed, we only begin to understand how tightly coupled oculomotor control is to functions as fundamental as visual attention and memory. I will present results from a series of studies showing how the preparation and execution of saccadic eye movements affect the selective allocation of visual attention and, therefore, what we see and what we remember. First, saccade preparation drives both objective visual performance and subjective experience of visual salience at the target of saccades. Second, visual attention supports perceptual continuity across saccades by facilitating perception predictively at those retinal locations that become relevant after the eye movement. Third, saccadic eye movements strongly affect the content of visual short-term memory, highlighting a crucial role in selecting which parts of a scene we remember (and which we forget). Together these findings support Yarbus’ idea that eye movements reflect visual and cognitive goals and further show that saccades actively shape visual perception and memory.

Numerical linear algebra methods are widely considered as basis for computational mathematics and data analysis. Indeed, these methods formed the mainstream of research in the second half of the 20th century. By the advent of 21st century this domain has reached maturity, and the research community had to face the question, what topic is going to be the 21st century mainstream? We argue that it is the study of multi-dimensional matrices, or tensors. In the 20th century, tensors were studied and applied mostly in physics as a description tool. In theoretical physics, particular tensor constructions were used to describe quantum systems. In mathematics, study of tensors led to some famous results, such as Strassen's algorithm of matrix multiplication, which has complexity less than n^3 for matrices of order n. However, 20th century did not see effective tensor-based computational methods. It is only in 21st century that tensors became a computational tool. In multidimensional problems, even "simple" cases involve datasets whose cardinality is greater than that of the set of all atoms in the Universe. The key idea that makes these data manageable is to consider the specific structure of the data, data compression methods, and algorithms that exploit special parameterizations of the data. Various tensor decompositions of multi-dimensional matrices have long been known, but they are fundamentally insufficient to develop efficient methods of data analysis. We consider novel representations, in which a multi-dimensional matrix is replaced with an associated sequence of usual matrices. The main assumption is that these matrices either have low rank or can be approximated well by low-rank matrices. A compressed representation for a multi-dimensional matrices, or tensors, is constructed using the well-studied decompositions of these matrices. This allows to develop algorithms whose complexity is linear or polynomial in the dimension. Applications of these methods include interpolation of multivariate functions, multi-dimensional integration, solution of the Fokker-Planck and Smoluchowski equations, spin systems modeling, construction of wavelet filters, and many other problems. The most simple and practical are "tensor train" methods developed in the Institute of Computational Mathematics of RAS since 2009; principal publications are available at http://pub.inm.ras.ru. We recommend also the following works: [1] I. Oseledets, E. Tyrtyshnikov, Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comput., vol 31, no. 5 (2009), pp. 3744-3759. [2] I. Oseledets, E. Tyrtyshnikov, TT-cross approximation for multidimensional arrays, Linear Algebra Appl., 432 (2010), pp. 70-88. [3] V. A. Kazeev, B. N. Khoromskij, E. E. Tyrtyshnikov, Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity. SIAM J. Sci. Comput. 35 (2013), no. 3, A1511-A1536. [4] J. A. Roberts, D. V. Savostyanov D.V., E. E. Tyrtyshnikov, Superfast solution of linear convolutional Volterra equations using QTT approximation, Journal of Computational and Applied Mathematics, vol.260, pp. 434-448 (2014).

Alfred Yarbus introduced a new dimension of precision in recording how the eyes moved, either when attempts were made to keep them stationary or when scanning pictures. Eye movements had been remarked upon for millennia but recording how they move is a more recent preoccupation. Emphasis was initially placed on abnormalities of oculomotor function (like strabismus) before normal features were considered. Thus, for Aristotle the fundamental features of eye movements were binocular and he described the combined functions of the eyes. This was later given support using simple procedures like placing a finger over the eyelid of the closed eye and culminated in Hering’s law of equal innervation. The most venerable technique for examining ocular stability involved comparing the relative motion between an afterimage and a real image. In the late eighteenth century Wells compared afterimages generated before body rotation with real images observed following it when dizzy; he described both lateral and torsional nystagmus thereby demonstrating the directional discontinuities in eye velocities. At around the same time Erasmus Darwin used afterimages as a means of demonstrating ocular instability when attempting to fixate steadily. However, the overriding concern in the nineteenth century was with eye position rather than eye movements. Thus, the characteristics of nystagmus were recorded before those of saccades and fixations. Eye movements during reading were described by Hering and by Lamare (working in Javal’s laboratory) in 1879; both used similar techniques of listening (with tubes placed over the eye lids) to the sounds made during contractions of the extraocular muscles. Photographic records of eye movements during reading were made by Dodge early in the twentieth century and this stimulated research using a wider array of patterns. Eye movements over pictures were examined by Stratton and later by Buswell, who drew attention to the effects of instructions on the pattern of eye movements. In mid-century attention shifted back to the stability of the eyes during fixation, with the emphasis on involuntary movements. The contact lens methods developed by Yarbus were applied with some success to recording the perceptual effects of retinal image stabilization. It is an historical irony that the accuracy of image stabilization with contact lenses was assessed by comparison with the oldest method for examining eye movements – afterimages.

When taking your mobile phone to make a call, do you imagine, how many algorithms are serving you implicitly? The spread of wireless communications that we experience last three decades seems to hide the very cumbersome engineering and algorithms behind the trends like 4G and 5G. In this short talk I will present the general mathematical setup of Radio Resource Management and the main ideas of this science. I will try to address some open problems related to the forthcoming 5G revolution.

Russia is one of the top 10 countries in the world by Gross Domestic Expenditure on R&D Russia produces substantial amount of scientific knowledge, but lags in technology commercialization and innovation “Pros and cons” to be a part of Skolkovo echo-systems. Should your personal “Road map” includes “milestones” like the Skolkovo?