TY - JOUR AB - We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395). AU - Cipolloni, Giorgio AU - Erdös, László AU - Schröder, Dominik J ID - 15063 IS - 1 JF - Probability and Mathematical Physics KW - General Medicine SN - 2690-1005 TI - Optimal lower bound on the least singular value of the shifted Ginibre ensemble VL - 1 ER - TY - CONF AB - In this paper we present a room temperature radiometer that can eliminate the need of using cryostats in satellite payload reducing its weight and improving reliability. The proposed radiometer is based on an electro-optic upconverter that boosts up microwave photons energy by upconverting them into an optical domain what makes them immune to thermal noise even if operating at room temperature. The converter uses a high-quality factor whispering gallery mode (WGM) resonator providing naturally narrow bandwidth and therefore might be useful for applications like microwave hyperspectral sensing. The upconversion process is explained by providing essential information about photon conversion efficiency and sensitivity. To prove the concept, we describe an experiment which shows state-of-the-art photon conversion efficiency n=10-5 per mW of pump power at the frequency of 80 GHz. AU - Wasiak, Michal AU - Botello, Gabriel Santamaria AU - Abdalmalak, Kerlos Atia AU - Sedlmeir, Florian AU - Rueda Sanchez, Alfredo R AU - Segovia-Vargas, Daniel AU - Schwefel, Harald G. L. AU - Munoz, Luis Enrique Garcia ID - 15059 T2 - 14th European Conference on Antennas and Propagation TI - Compact millimeter and submillimeter-wave photonic radiometer for cubesats ER - TY - CONF AB - We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for the stable orientation problem, which is a special case of the more general locally optimal semi-matching problem. The prior work by Czygrinow et al. (DISC 2012) finds a locally optimal semi-matching in O(Δ⁵) rounds in graphs of maximum degree Δ, which directly implies an algorithm with the same runtime for stable orientations. We improve the runtime to O(Δ⁴) for stable orientations and prove a lower bound of Ω(Δ) rounds. AU - Brandt, Sebastian AU - Keller, Barbara AU - Rybicki, Joel AU - Suomela, Jukka AU - Uitto, Jara ID - 15074 T2 - 34th International Symposium on Distributed Computing TI - Brief announcement: Efficient load-balancing through distributed token dropping VL - 179 ER - TY - CONF AB - We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor. AU - Alistarh, Dan-Adrian AU - Nadiradze, Giorgi AU - Sabour, Amirmojtaba ID - 15077 T2 - 47th International Colloquium on Automata, Languages, and Programming TI - Dynamic averaging load balancing on cycles VL - 168 ER - TY - CONF AB - Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points two plane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which is disjoint compatible to both M1 and M2. We show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameter of this graph is either 4 or 5, independent of n. AU - Aichholzer, Oswin AU - Obmann, Julia AU - Patak, Pavel AU - Perz, Daniel AU - Tkadlec, Josef ID - 15082 T2 - 36th European Workshop on Computational Geometry TI - Disjoint tree-compatible plane perfect matchings ER - TY - JOUR AB - Fitting a function by using linear combinations of a large number N of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to kernel regression, to boosting. In general, the resulting risk minimization problem is non-convex and is solved by gradient descent or its variants. Unfortunately, little is known about global convergence properties of these approaches. Here we consider the problem of learning a concave function f on a compact convex domain Ω⊆ℝd, using linear combinations of `bump-like' components (neurons). The parameters to be fitted are the centers of N bumps, and the resulting empirical risk minimization problem is highly non-convex. We prove that, in the limit in which the number of neurons diverges, the evolution of gradient descent converges to a Wasserstein gradient flow in the space of probability distributions over Ω. Further, when the bump width δ tends to 0, this gradient flow has a limit which is a viscous porous medium equation. Remarkably, the cost function optimized by this gradient flow exhibits a special property known as displacement convexity, which implies exponential convergence rates for N→∞, δ→0. Surprisingly, this asymptotic theory appears to capture well the behavior for moderate values of δ,N. Explaining this phenomenon, and understanding the dependence on δ,N in a quantitative manner remains an outstanding challenge. AU - Javanmard, Adel AU - Mondelli, Marco AU - Montanari, Andrea ID - 6748 IS - 6 JF - Annals of Statistics SN - 1932-6157 TI - Analysis of a two-layer neural network via displacement convexity VL - 48 ER - TY - JOUR AB - This workshop focused on interactions between the various perspectives on the moduli space of Higgs bundles over a Riemann surface. This subject draws on algebraic geometry, geometric topology, geometric analysis and mathematical physics, and the goal was to promote interactions between these various branches of the subject. The main current directions of research were well represented by the participants, and the talks included many from both senior and junior participants. AU - Anderson, Lara AU - Hausel, Tamás AU - Mazzeo, Rafe AU - Schaposnik, Laura ID - 15070 IS - 2 JF - Oberwolfach Reports KW - Organic Chemistry KW - Biochemistry SN - 1660-8933 TI - Geometry and physics of Higgs bundles VL - 16 ER - TY - JOUR AB - In ecology, climate and other fields, (sub)systems have been identified that can transition into a qualitatively different state when a critical threshold or tipping point in a driving process is crossed. An understanding of those tipping elements is of great interest given the increasing influence of humans on the biophysical Earth system. Complex interactions exist between tipping elements, e.g. physical mechanisms connect subsystems of the climate system. Based on earlier work on such coupled nonlinear systems, we systematically assessed the qualitative long-term behaviour of interacting tipping elements. We developed an understanding of the consequences of interactions on the tipping behaviour allowing for tipping cascades to emerge under certain conditions. The (narrative) application of these qualitative results to real-world examples of interacting tipping elements indicates that tipping cascades with profound consequences may occur: the interacting Greenland ice sheet and thermohaline ocean circulation might tip before the tipping points of the isolated subsystems are crossed. The eutrophication of the first lake in a lake chain might propagate through the following lakes without a crossing of their individual critical nutrient input levels. The possibility of emerging cascading tipping dynamics calls for the development of a unified theory of interacting tipping elements and the quantitative analysis of interacting real-world tipping elements. AU - Klose, Ann Kristin AU - Karle, Volker AU - Winkelmann, Ricarda AU - Donges, Jonathan F. ID - 8741 IS - 6 JF - Royal Society Open Science TI - Emergence of cascading dynamics in interacting tipping elements of ecology and climate: Cascading dynamics in tipping elements VL - 7 ER - TY - JOUR AB - A working group, which was established within the Network of Repository Managers (RepManNet), has dealt with common certifications for repositories. In addition, current requirements of the research funding agencies FWF and EU were also taken into account. The Core Trust Seal was examined in more detail. For this purpose, a questionnaire was sent to those organizations that are already certified with CTS in Austria. The answers were summarized and evaluated anonymously. It is recommended to go for a repository certification. Moreover, the development of a DINI certificate in Austria is strongly suggested. AU - Ernst, Doris AU - Novotny, Gertraud AU - Schönher, Eva Maria ID - 7687 IS - 1 JF - Mitteilungen der Vereinigung Österreichischer Bibliothekarinnen und Bibliothekare SN - 1022-2588 TI - (Core Trust) Seal your repository! VL - 73 ER - TY - JOUR AB - Large complex systems tend to develop universal patterns that often represent their essential characteristics. For example, the cumulative effects of independent or weakly dependent random variables often yield the Gaussian universality class via the central limit theorem. For non-commutative random variables, e.g. matrices, the Gaussian behavior is often replaced by another universality class, commonly called random matrix statistics. Nearby eigenvalues are strongly correlated, and, remarkably, their correlation structure is universal, depending only on the symmetry type of the matrix. Even more surprisingly, this feature is not restricted to matrices; in fact Eugene Wigner, the pioneer of the field, discovered in the 1950s that distributions of the gaps between energy levels of complicated quantum systems universally follow the same random matrix statistics. This claim has never been rigorously proved for any realistic physical system but experimental data and extensive numerics leave no doubt as to its correctness. Since then random matrices have proved to be extremely useful phenomenological models in a wide range of applications beyond quantum physics that include number theory, statistics, neuroscience, population dynamics, wireless communication and mathematical finance. The ubiquity of random matrices in natural sciences is still a mystery, but recent years have witnessed a breakthrough in the mathematical description of the statistical structure of their spectrum. Random matrices and closely related areas such as log-gases have become an extremely active research area in probability theory. This workshop brought together outstanding researchers from a variety of mathematical backgrounds whose areas of research are linked to random matrices. While there are strong links between their motivations, the techniques used by these researchers span a large swath of mathematics, ranging from purely algebraic techniques to stochastic analysis, classical probability theory, operator algebra, supersymmetry, orthogonal polynomials, etc. AU - Erdös, László AU - Götze, Friedrich AU - Guionnet, Alice ID - 15079 IS - 4 JF - Oberwolfach Reports SN - 1660-8933 TI - Random matrices VL - 16 ER -