TY - JOUR
AB - Electron microscopy (EM) allows for the simultaneous visualization of all tissue components at high resolution. However, the extent to which conventional aldehyde fixation and ethanol dehydration of the tissue alter the fine structure of cells and organelles, thereby preventing detection of subtle structural changes induced by an experiment, has remained an issue. Attempts have been made to rapidly freeze tissue to preserve native ultrastructure. Shock-freezing of living tissue under high pressure (high-pressure freezing, HPF) followed by cryosubstitution of the tissue water avoids aldehyde fixation and dehydration in ethanol; the tissue water is immobilized in â ̂1/450 ms, and a close-to-native fine structure of cells, organelles and molecules is preserved. Here we describe a protocol for HPF that is useful to monitor ultrastructural changes associated with functional changes at synapses in the brain but can be applied to many other tissues as well. The procedure requires a high-pressure freezer and takes a minimum of 7 d but can be paused at several points.
AU - Studer, Daniel
AU - Zhao, Shanting
AU - Chai, Xuejun
AU - Jonas, Peter M
AU - Graber, Werner
AU - Nestel, Sigrun
AU - Frotscher, Michael
ID - 2176
IS - 6
JF - Nature Protocols
TI - Capture of activity-induced ultrastructural changes at synapses by high-pressure freezing of brain tissue
VL - 9
ER -
TY - CONF
AB - We give evidence for the difficulty of computing Betti numbers of simplicial complexes over a finite field. We do this by reducing the rank computation for sparse matrices with to non-zero entries to computing Betti numbers of simplicial complexes consisting of at most a constant times to simplices. Together with the known reduction in the other direction, this implies that the two problems have the same computational complexity.
AU - Edelsbrunner, Herbert
AU - Parsa, Salman
ID - 2177
T2 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
TI - On the computational complexity of betti numbers reductions from matrix rank
ER -
TY - JOUR
AB - We consider the three-state toric homogeneous Markov chain model (THMC) without loops and initial parameters. At time T, the size of the design matrix is 6 × 3 · 2T-1 and the convex hull of its columns is the model polytope. We study the behavior of this polytope for T ≥ 3 and we show that it is defined by 24 facets for all T ≥ 5. Moreover, we give a complete description of these facets. From this, we deduce that the toric ideal associated with the design matrix is generated by binomials of degree at most 6. Our proof is based on a result due to Sturmfels, who gave a bound on the degree of the generators of a toric ideal, provided the normality of the corresponding toric variety. In our setting, we established the normality of the toric variety associated to the THMC model by studying the geometric properties of the model polytope.
AU - Haws, David
AU - Martin Del Campo Sanchez, Abraham
AU - Takemura, Akimichi
AU - Yoshida, Ruriko
ID - 2178
IS - 1
JF - Beitrage zur Algebra und Geometrie
TI - Markov degree of the three-state toric homogeneous Markov chain model
VL - 55
ER -
TY - JOUR
AB - We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 to the case when the matrix of variances has an eigenvalue -1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X*X, where the variances of the entries of X may vary.
AU - Ajanki, Oskari H
AU - Erdös, László
AU - Krüger, Torben H
ID - 2179
JF - Electronic Communications in Probability
TI - Local semicircle law with imprimitive variance matrix
VL - 19
ER -
TY - JOUR
AB - Weighted majority votes allow one to combine the output of several classifiers or voters. MinCq is a recent algorithm for optimizing the weight of each voter based on the minimization of a theoretical bound over the risk of the vote with elegant PAC-Bayesian generalization guarantees. However, while it has demonstrated good performance when combining weak classifiers, MinCq cannot make use of the useful a priori knowledge that one may have when using a mixture of weak and strong voters. In this paper, we propose P-MinCq, an extension of MinCq that can incorporate such knowledge in the form of a constraint over the distribution of the weights, along with general proofs of convergence that stand in the sample compression setting for data-dependent voters. The approach is applied to a vote of k-NN classifiers with a specific modeling of the voters' performance. P-MinCq significantly outperforms the classic k-NN classifier, a symmetric NN and MinCq using the same voters. We show that it is also competitive with LMNN, a popular metric learning algorithm, and that combining both approaches further reduces the error.
AU - Bellet, Aurélien
AU - Habrard, Amaury
AU - Morvant, Emilie
AU - Sebban, Marc
ID - 2180
IS - 1-2
JF - Machine Learning
TI - Learning a priori constrained weighted majority votes
VL - 97
ER -
TY - JOUR
AB - We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be nontrivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: Nodes can be divided in differently synchronized classes but, contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behavior can evolve from undifferentiated nodes.
AU - Botella Soler, Vicente
AU - Glendinning, Paul
ID - 2183
IS - 6
JF - Physical Review E Statistical Nonlinear and Soft Matter Physics
TI - Hierarchy and polysynchrony in an adaptive network
VL - 89
ER -
TY - JOUR
AB - Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X→ Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools from effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X,Y] is known to be uncomputable for general X,Y, since for X = S1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, and extended to other problems, such as the extension problem, where we are given a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or computing the Z2-index-everything in the stable range. Outside the stable range, the extension problem is undecidable.
AU - Čadek, Martin
AU - Krcál, Marek
AU - Matoušek, Jiří
AU - Sergeraert, Francis
AU - Vokřínek, Lukáš
AU - Wagner, Uli
ID - 2184
IS - 3
JF - Journal of the ACM
TI - Computing all maps into a sphere
VL - 61
ER -
TY - CONF
AB - We revisit the classical problem of converting an imperfect source of randomness into a usable cryptographic key. Assume that we have some cryptographic application P that expects a uniformly random m-bit key R and ensures that the best attack (in some complexity class) against P(R) has success probability at most δ. Our goal is to design a key-derivation function (KDF) h that converts any random source X of min-entropy k into a sufficiently "good" key h(X), guaranteeing that P(h(X)) has comparable security δ′ which is 'close' to δ. Seeded randomness extractors provide a generic way to solve this problem for all applications P, with resulting security δ′ = O(δ), provided that we start with entropy k ≥ m + 2 log (1/δ) - O(1). By a result of Radhakrishnan and Ta-Shma, this bound on k (called the "RT-bound") is also known to be tight in general. Unfortunately, in many situations the loss of 2 log (1/δ) bits of entropy is unacceptable. This motivates the study KDFs with less entropy waste by placing some restrictions on the source X or the application P. In this work we obtain the following new positive and negative results in this regard: - Efficient samplability of the source X does not help beat the RT-bound for general applications. This resolves the SRT (samplable RT) conjecture of Dachman-Soled et al. [DGKM12] in the affirmative, and also shows that the existence of computationally-secure extractors beating the RT-bound implies the existence of one-way functions. - We continue in the line of work initiated by Barak et al. [BDK+11] and construct new information-theoretic KDFs which beat the RT-bound for large but restricted classes of applications. Specifically, we design efficient KDFs that work for all unpredictability applications P (e.g., signatures, MACs, one-way functions, etc.) and can either: (1) extract all of the entropy k = m with a very modest security loss δ′ = O(δ·log (1/δ)), or alternatively, (2) achieve essentially optimal security δ′ = O(δ) with a very modest entropy loss k ≥ m + loglog (1/δ). In comparison, the best prior results from [BDK+11] for this class of applications would only guarantee δ′ = O(√δ) when k = m, and would need k ≥ m + log (1/δ) to get δ′ = O(δ). - The weaker bounds of [BDK+11] hold for a larger class of so-called "square- friendly" applications (which includes all unpredictability, but also some important indistinguishability, applications). Unfortunately, we show that these weaker bounds are tight for the larger class of applications. - We abstract out a clean, information-theoretic notion of (k,δ,δ′)- unpredictability extractors, which guarantee "induced" security δ′ for any δ-secure unpredictability application P, and characterize the parameters achievable for such unpredictability extractors. Of independent interest, we also relate this notion to the previously-known notion of (min-entropy) condensers, and improve the state-of-the-art parameters for such condensers.
AU - Dodis, Yevgeniy
AU - Pietrzak, Krzysztof Z
AU - Wichs, Daniel
ED - Nguyen, Phong
ED - Oswald, Elisabeth
ID - 2185
TI - Key derivation without entropy waste
VL - 8441
ER -
TY - JOUR
AB - We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in ℝ3. Moreover, we show that an exponential energy growth condition commonly used in the well-posedness theory of the GP hierarchy is, in a specific sense, necessary. In fact, we prove that without the latter, there exist initial data for the focusing cubic GP hierarchy for which instantaneous blowup occurs.
AU - Chen, Thomas
AU - Hainzl, Christian
AU - Pavlović, Nataša
AU - Seiringer, Robert
ID - 2186
IS - 7
JF - Letters in Mathematical Physics
TI - On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti
VL - 104
ER -
TY - JOUR
AB - Systems should not only be correct but also robust in the sense that they behave reasonably in unexpected situations. This article addresses synthesis of robust reactive systems from temporal specifications. Existing methods allow arbitrary behavior if assumptions in the specification are violated. To overcome this, we define two robustness notions, combine them, and show how to enforce them in synthesis. The first notion applies to safety properties: If safety assumptions are violated temporarily, we require that the system recovers to normal operation with as few errors as possible. The second notion requires that, if liveness assumptions are violated, as many guarantees as possible should be fulfilled nevertheless. We present a synthesis procedure achieving this for the important class of GR(1) specifications, and establish complexity bounds. We also present an implementation of a special case of robustness, and show experimental results.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Greimel, Karin
AU - Henzinger, Thomas A
AU - Hofferek, Georg
AU - Jobstmann, Barbara
AU - Könighofer, Bettina
AU - Könighofer, Robert
ID - 2187
IS - 3-4
JF - Acta Informatica
TI - Synthesizing robust systems
VL - 51
ER -