62 research outputs found
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
The Fifteenth Marcel Grossmann Meeting
The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Testing, Learning, Sampling, Sketching
We study several problems about sublinear algorithms, presented in two parts.
Part I: Property testing and learning. There are two main goals of research in property testing and learning theory. The first is to understand the relationship between testing and learning, and the second is to develop efficient testing and learning algorithms.
We present results towards both goals.
- An oft-repeated motivation for property testing algorithms is to help with model selection in learning: to efficiently check whether the chosen hypothesis class (i.e. learning model) will successfully learn the target function. We present in this thesis a proof that, for many of the most useful and natural hypothesis classes (including halfspaces, polynomial threshold functions, intersections of halfspaces, etc.), the sample complexity of testing in the distribution-free model is nearly equal to that of learning. This shows that testing does not give a significant advantage in model selection in this setting.
- We present a simple and general technique for transforming testing and learning algorithms designed for the uniform distribution over {0, 1}^d or [n]^d into algorithms that work for arbitrary product distributions over R d . This leads to an improvement and simplification of state-of-the-art results for testing monotonicity, learning intersections of halfspaces, learning polynomial threshold functions, and others.
Part II. Adjacency and distance sketching for graphs. We initiate the thorough study of adjacency and distance sketching for classes of graphs. Two open problems in sublinear algorithms are: 1) to understand the power of randomization in communication; and 2) to characterize the sketchable distance metrics. We observe that constant-cost randomized communication is equivalent to adjacency sketching in a hereditary graph class, which in turn implies the existence of an efficient adjacency labeling scheme, the subject of a major open problem in structural graph theory. Therefore characterizing the adjacency sketchable graph classes (i.e. the constant-cost communication problems) is the probabilistic equivalent of this open problem, and an essential step towards understanding
the power of randomization in communication.
This thesis gives the first results towards a combined theory of these problems and uses this connection to obtain optimal adjacency labels for subgraphs of Cartesian products, resolving some questions from the literature. More generally, we begin to develop a theory of graph sketching for problems that generalize adjacency, including different notions of distance sketching. This connects the well-studied areas of distance sketching in sublinear algorithms, and distance labeling in structural graph theory
Radiation Effects in Materials
The study of radiation effects has developed as a major field of materials science from the beginning, approximately 70 years ago. Its rapid development has been driven by two strong influences. The properties of the crystal defects and the materials containing them may then be studied. The types of radiation that can alter structural materials consist of neutrons, ions, electrons, gamma rays or other electromagnetic waves with different wavelengths. All of these forms of radiation have the capability to displace atoms/molecules from their lattice sites, which is the fundamental process that drives the changes in all materials. The effect of irradiation on materials is fixed in the initial event in which an energetic projectile strikes a target. The book is distributed in four sections: Ionic Materials; Biomaterials; Polymeric Materials and Metallic Materials
Combinatorics
Combinatorics is a fundamental mathematical discipline that focuses on the study of discrete objects and their
properties. The present workshop featured research in such diverse areas as Extremal, Probabilistic
and Algebraic Combinatorics, Graph Theory, Discrete Geometry, Combinatorial Optimization,
Theory of Computation and Statistical Mechanics. It provided current accounts of exciting developments and challenges in these fields and a stimulating venue for a variety of fruitful interactions.
This is a report on the meeting, containing extended abstracts of the presentations and a summary of the problem session
Ramsey-goodness and otherwise
A celebrated result of Chvátal, Rödl, Szemerédi and Trotter states (in slightly weakened form) that, for every natural number ∆, there is a constant r ∆ such that, for any connected n-vertex graph G with maximum degree ∆, the Ramsey number R(G, G) is at most r ∆ n, provided n is sufficiently large. In 1987, Burr made a strong conjecture implying that one may take r ∆ = ∆. However, Graham, Rödl and Ruciński showed, by taking G to be a suitable expander graph, that necessarily r ∆ > 2 c∆ for some constant c > 0. We show that the use of expanders is essential: if we impose the additional restriction that the bandwidth of G be at most some function β(n) = o(n), then R(G, G) ≤ (2χ(G) + 4)n ≤ (2∆ + 6)n, i.e., r ∆ = 2∆ + 6 suffices. On the other hand, we show that Burr's conjecture itself fails even for P k n , the kth power of a path P n . Brandt showed that for any c, if ∆ is sufficiently large, there are connected nvertex graphs G with ∆(G) ≤ ∆ but R(G, K 3 ) > cn. We show that, given ∆ and H, there are β > 0 and n 0 such that, if G is a connected graph on n ≥ n 0 vertices with maximum degree at most ∆ and bandwidth at most βn, then we have R(G, H) = (χ(H) − 1)(n − 1) + σ(H), where σ(H) is the smallest size of any part in any χ(H)-partition of H. We also show that the same conclusion holds without any restriction on the maximum degree of G if the bandwidth of G is at most ε(H) log n/ log log n
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