Plenary Speakers: Downstream Migration of Fish in Regulated Rivers: Patterns and Mechanisms

Dmitrii Pavlov graduated from the Moscow State University, Dept. of Ichthyology, in 1960 where currently he is a Head of the Department. His main study area covers fish behavior and ecology, and the behavior of fishes including orientation, locomotion, and migrations in the water flow. He has been studying patterns and mechanisms of downstream migrations in the field and in laboratory experiments since 1962. His field studies, with the main focus on down-stream migration through dams have been carried out in many rivers of Europe, Asia, Africa, and South America. Field programs were complemented with experimental studies on behavior, morphology, physiology, and biochemical traits of migrants. Dmitrii Pavlov has written several books and many papers on down-stream migration of young fish, control of their behavior in the water flow, and the protection of migrating fish in regulated rivers. Dmitrii Pavlov is a member of the Russian Academy of Sciences, and the Lithuanian Academy of Sciences. Drs. Victor Mikheev and Vasilii Kostin, co-authors of the plenary talk for FP2015, have been working together with Dmitrii Pavlov in the field of fish behavior and ecology since 1981. Dr Mikheev presented on Prof Pavlov’s behalf

On real and observable realizations of input-output equations

Given a single algebraic input-output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand sides. It has been shown that in the case where the input-output equation is of order one, rational realizations can be computed, if they exist. In this work, we focus first on the existence and actual computation of the so-called observable rational realizations, and secondly on rational realizations with real coefficients. The study of observable realizations allows to find every rational realization of a given first order input-output equation, and the necessary field extensions in this process. We show that for first order input-output equations the existence of a rational realization is equivalent to the existence of an observable rational realization. Moreover, we give a criterion to decide the existence of real rational realizations. The computation of observable and real realizations of first order input-output equations is fully algorithmic. We also present partial results for the case of higher order input-output equations

Algebraic Geometry of Quantum Graphical Models

Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical models are families of quantum states satisfying certain locality or correlation conditions encoded by a graph. We lay out several ways to associate an algebraic variety to a quantum graphical model. The classical graphical models can be recovered from most of these varieties by restricting to quantum states represented by diagonal matrices. We study fundamental properties of these varieties and provide algorithms to compute their defining equations. Moreover, we study quantum information projections to quantum exponential families defined by graphs and prove a quantum analogue of Birch's Theorem.Comment: 20 pages, comments welcome

Session E5: What Should We Know About Behavior of Sturgeons to Provide Their Efficient Passage?

Abstract: To provide passage of migrating sturgeons through dams, we have, first of all, to monitor and control their behavior in the water flow. To achieve this, we have to know following behavioral and ecological traits such as: rheoreaction, threshold and critical swimming velocity, swimming endurance, behavior in the flow velocity gradient, diel and seasonal patterns of spawning migrations, and vertical and horizontal distribution of migrating sturgeons. Such information is needed to determine optimum flow velocities attracting fish to the entrance of a fish pass (FP), FP operation regime, duration of attraction of migrants, location of the entrance to FP downstream the dam, and conditions at the fish release site upstream the dam. Since 1955 to 2005, 16 FP, to enhance fish spawning migration, were built at 11 large dams in the basins of rivers Volga, Don, and Kuban. One of the main functions of the FP was to facilitate spawning migration of sturgeons - Huso huso, Acipenser gueldenstaedti, A. stellatus, and A. ruthenus. Several types of FP were built: hydraulic (1 FP) and mechanic (2) fish lifts; fish locks (10), natural (spawning) bypass channels (2), and experimental floating FP (1). Most of them were efficient. Efficiency of some FP was as high as 67% (of the number of approached fish; river Don – Kochetovskii powerplant). The number of sturgeons that passed through the Volgogradskaya dam (river Volga) reached 60000 ind. per year (1967); 2050 ind. (Kochetovskaya dam, 1975); 2130 ind. through the Fedorovskaya dam (river Kuban, 1987). In the 1990s, the number of sturgeons in the Russian rivers decreased dramatically, mainly due to heavy poaching. This resulted in an abrupt decrease of the number of passed fish. In consequence, operation of some FP was suspende

Gibbs Manifolds

Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum~physics, where they extend the ubiquitous role of toric geometry. The Gibbs variety is the zero locus of all polynomials that vanish on the Gibbs manifold. We compute these polynomials and show that the Gibbs variety is low-dimensional. Our theory is applied to a wide range of scenarios, including matrix pencils and quantum optimal transport.Comment: 22 page

From algebra to analysis: new proofs of theorems by Ritt and Seidenberg

Ritt's theorem of zeroes and Seidenberg's embedding theorem are classical results in differential algebra allowing to connect algebraic and model-theoretic results on nonlinear PDEs to the realm of analysis. However, the existing proofs of these results use sophisticated tools from constructive algebra (characteristic set theory) and analysis (Riquier's existence theorem). In this paper, we give new short proofs for both theorems relying only on basic facts from differential algebra and the classical Cauchy-Kovalevskaya theorem for PDEs.Comment: 13 page