TY - CONF
AB - One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Random Fields (MRF's), the resulting energy minimization problems were widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the top-performing stereo methods. Unfortunately, most papers define their own energy function, which is minimized with a specific algorithm of their choice. As a result, the tradeoffs among different energy minimization algorithms are not well understood. In this paper we describe a set of energy minimization benchmarks, which we use to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods - graph cuts, LBP, and tree-reweighted message passing - as well as the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching and interactive segmentation. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods with minimal overhead. We expect that the availability of our benchmarks and interface will make it significantly easier for vision researchers to adopt the best method for their specific problems. Benchmarks, code, results and images are available at http://vision.middlebury.edu/MRF.
AU - Szeliski, Richard S
AU - Zabih, Ramin
AU - Scharstein, Daniel
AU - Veksler, Olga
AU - Vladimir Kolmogorov
AU - Agarwala, Aseem
AU - Tappen, Marshall F
AU - Rother, Carsten
ID - 3180
TI - A comparative study of energy minimization methods for Markov random fields
VL - 3952
ER -
TY - CONF
AB - Algorithms for discrete energy minimization play a fundamental role for low-level vision. Known techniques include graph cuts, belief propagation (BP) and recently introduced tree-reweighted message passing (TRW). So far, the standard benchmark for their comparison has been a 4-connected grid-graph arising in pixel-labelling stereo. This minimization problem, however, has been largely solved: recent work shows that for many scenes TRW finds the global optimum. Furthermore, it is known that a 4-connecled grid-graph is a poor stereo model since it does not take occlusions into account. We propose the problem of stereo with occlusions as a new test bed for minimization algorithms. This is a more challenging graph since it has much larger connectivity, and it also serves as a better stereo model. An attractive feature of this problem is that increased connectivity does not result in increased complexity of message passing algorithms. Indeed, one contribution of this paper is to show that sophisticated implementations of BP and TRW have the same time and memory complexity as that of 4-connecled grid-graph stereo. The main conclusion of our experimental study is that for our problem graph cut outperforms both TRW and BP considerably. TRW achieves consistently a lower energy than BP. However, as connectivity increases the speed of convergence of TRW becomes slower. Unlike 4-connected grids, the difference between the energy of the best optimization method and the lower bound of TRW appears significant. This shows the hardness of the problem and motivates future research.
AU - Vladimir Kolmogorov
AU - Rother, Carsten
ID - 3184
TI - Comparison of energy minimization algorithms for highly connected graphs
VL - 3952 LNCS
ER -
TY - JOUR
AB - This paper describes models and algorithms for the real-time segmentation of foreground from background layers in stereo video sequences. Automatic separation of layers from color/contrast or from stereo alone is known to be error-prone. Here, color, contrast, and stereo matching information are fused to infer layers accurately and efficiently. The first algorithm, Layered Dynamic Programming (LDP), solves stereo in an extended six-state space that represents both foreground/background layers and occluded regions. The stereo-match likelihood is then fused with a contrast-sensitive color model that is learned on-the-fly and stereo disparities are obtained by dynamic programming. The second algorithm, Layered Graph Cut (LGC), does not directly solve stereo. Instead, the stereo match likelihood is marginalized over disparities to evaluate foreground and background hypotheses and then fused with a contrast-sensitive color model like the one used in LDP. Segmentation is solved efficiently by ternary graph cut. Both algorithms are evaluated with respect to ground truth data and found to have similar performance, substantially better than either stereo or color/contrast alone. However, their characteristics with respect to computational efficiency are rather different. The algorithms are demonstrated in the application of background substitution and shown to give good quality composite video output.
AU - Vladimir Kolmogorov
AU - Criminisi, Antonio
AU - Blake, Andrew
AU - Cross, Geoffrey
AU - Rother, Carsten
ID - 3185
IS - 9
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Probabilistic fusion of stereo with color and contrast for bilayer segmentation
VL - 28
ER -
TY - CONF
AB - We introduce a new approach to modelling gradient flows of contours and surfaces. While standard variational methods (e.g. level sets) compute local interface motion in a differential fashion by estimating local contour velocity via energy derivatives, we propose to solve surface evolution PDEs by explicitly estimating integral motion of the whole surface. We formulate an optimization problem directly based on an integral characterization of gradient flow as an infinitesimal move of the (whole) surface giving the largest energy decrease among all moves of equal size. We show that this problem can be efficiently solved using recent advances in algorithms for global hypersurface optimization [4, 2, 11]. In particular, we employ the geo-cuts method [4] that uses ideas from integral geometry to represent continuous surfaces as cuts on discrete graphs. The resulting interface evolution algorithm is validated on some 2D and 3D examples similar to typical demonstrations of level-set methods. Our method can compute gradient flows of hypersurfaces with respect to a fairly general class of continuous functional and it is flexible with respect to distance metrics on the space of contours/surfaces. Preliminary tests for standard L2 distance metric demonstrate numerical stability, topological changes and an absence of any oscillatory motion.
AU - Boykov, Yuri
AU - Vladimir Kolmogorov
AU - Cremers, Daniel
AU - Delong, Andrew
ID - 3186
TI - An integral solution to surface evolution PDEs via geo cuts
VL - 3953
ER -
TY - CONF
AB - We introduce the term cosegmentation which denotes the task of segmenting simultaneously the common parts of an image pair. A generative model for cosegmentation is presented. Inference in the model leads to minimizing an energy with an MRF term encoding spatial coherency and a global constraint which attempts to match the appearance histograms of the common parts. This energy has not been proposed previously and its optimization is challenging and NP-hard. For this problem a novel optimization scheme which we call trust region graph cuts is presented. We demonstrate that this framework has the potential to improve a wide range of research: Object driven image retrieval, video tracking and segmentation, and interactive image editing. The power of the framework lies in its generality, the common part can be a rigid/non-rigid object (or scene), observed from different viewpoints or even similar objects of the same class.
AU - Rother, Carsten
AU - Vladimir Kolmogorov
AU - Minka, Thomas P
AU - Blake, Andrew
ID - 3188
TI - Cosegmentation of image pairs by histogram matching - Incorporating a global constraint into MRFs
ER -
TY - CONF
AB - This paper presents an algorithm capable of real-time separation of foreground from background in monocular video sequences. Automatic segmentation of layers from colour/contrast or from motion alone is known to be error-prone. Here motion, colour and contrast cues are probabilistically fused together with spatial and temporal priors to infer layers accurately and efficiently. Central to our algorithm is the fact that pixel velocities are not needed, thus removing the need for optical flow estimation, with its tendency to error and computational expense. Instead, an efficient motion vs non-motion classifier is trained to operate directly and jointly on intensity-change and contrast. Its output is then fused with colour information. The prior on segmentation is represented by a second order, temporal, Hidden Markov Model, together with a spatial MRF favouring coherence except where contrast is high. Finally, accurate layer segmentation and explicit occlusion detection are efficiently achieved by binary graph cut. The segmentation accuracy of the proposed algorithm is quantitatively evaluated with respect to existing ground-truth data and found to be comparable to the accuracy of a state of the art stereo segmentation algorithm. Fore-ground/background segmentation is demonstrated in the application of live background substitution and shown to generate convincingly good quality composite video.
AU - Criminisi, Antonio
AU - Cross, Geoffrey
AU - Blake, Andrew
AU - Vladimir Kolmogorov
ID - 3189
TI - Bilayer segmentation of live video
VL - 1
ER -
TY - JOUR
AB - Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper, we focus on the recent technique proposed by Wainwright et al. (Nov. 2005)- tree-reweighted max-product message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy. However, the algorithm is not guaranteed to increase this bound - it may actually go down. In addition, TRW does not always converge. We develop a modification of this algorithm which we call sequential tree-reweighted message passing. Its main property is that the bound is guaranteed not to decrease. We also give a weak tree agreement condition which characterizes local maxima of the bound with respect to TRW algorithms. We prove that our algorithm has a limit point that achieves weak tree agreement. Finally, we show that, our algorithm requires half as much memory as traditional message passing approaches. Experimental results demonstrate that on certain synthetic and real problems, our algorithm outperforms both the ordinary belief propagation and tree-reweighted algorithm in (M. J. Wainwright, et al., Nov. 2005). In addition, on stereo problems with Potts interactions, we obtain a lower energy than graph cuts.
AU - Vladimir Kolmogorov
ID - 3190
IS - 10
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Convergent tree reweighted message passing for energy minimization
VL - 28
ER -
TY - CONF
AB - The Feistel-network is a popular structure underlying many block-ciphers where the cipher is constructed from many simpler rounds, each defined by some function which is derived from the secret key.
Luby and Rackoff showed that the three-round Feistel-network – each round instantiated with a pseudorandom function secure against adaptive chosen plaintext attacks (CPA) – is a CPA secure pseudorandom permutation, thus giving some confidence in the soundness of using a Feistel-network to design block-ciphers.
But the round functions used in actual block-ciphers are – for efficiency reasons – far from being pseudorandom. We investigate the security of the Feistel-network against CPA distinguishers when the only security guarantee we have for the round functions is that they are secure against non-adaptive chosen plaintext attacks (nCPA). We show that in the information-theoretic setting, four rounds with nCPA secure round functions are sufficient (and necessary) to get a CPA secure permutation. Unfortunately, this result does not translate into the more interesting pseudorandom setting. In fact, under the so-called Inverse Decisional Diffie-Hellman assumption the Feistel-network with four rounds, each instantiated with a nCPA secure pseudorandom function, is in general not a CPA secure pseudorandom permutation.
AU - Maurer, Ueli M
AU - Oswald, Yvonne A
AU - Krzysztof Pietrzak
AU - Sjödin, Johan
ID - 3214
TI - Luby Rackoff ciphers from weak round functions
VL - 4004
ER -
TY - CONF
AB - Most cryptographic primitives such as encryption, authentication or secret sharing require randomness. Usually one assumes that perfect randomness is available, but those primitives might also be realized under weaker assumptions. In this work we continue the study of building secure cryptographic primitives from imperfect random sources initiated by Dodis and Spencer (FOCS’02). Their main result shows that there exists a (high-entropy) source of randomness allowing for perfect encryption of a bit, and yet from which one cannot extract even a single weakly random bit, separating encryption from extraction. Our main result separates encryption from 2-out-2 secret sharing (both in the information-theoretic and in the computational settings): any source which can be used to achieve one-bit encryption also can be used for 2-out-2 secret sharing of one bit, but the converse is false, even for high-entropy sources. Therefore, possibility of extraction strictly implies encryption, which in turn strictly implies 2-out-2 secret sharing.
AU - Dodis, Yevgeniy
AU - Krzysztof Pietrzak
AU - Przydatek, Bartosz
ID - 3215
TI - Separating sources for encryption and secret sharing
VL - 3876
ER -
TY - CONF
AB - We prove a new upper bound on the advantage of any adversary for distinguishing the encrypted CBC-MAC (EMAC) based on random permutations from a random function. Our proof uses techniques recently introduced in [BPR05], which again were inspired by [DGH + 04].
The bound we prove is tight — in the sense that it matches the advantage of known attacks up to a constant factor — for a wide range of the parameters: let n denote the block-size, q the number of queries the adversary is allowed to make and ℓ an upper bound on the length (i.e. number of blocks) of the messages, then for ℓ ≤ 2 n/8 and q≥ł2 the advantage is in the order of q 2/2 n (and in particular independent of ℓ). This improves on the previous bound of q 2ℓΘ(1/ln ln ℓ)/2 n from [BPR05] and matches the trivial attack (which thus is basically optimal) where one simply asks random queries until a collision is found.
AU - Krzysztof Pietrzak
ID - 3216
TI - A tight bound for EMAC
VL - 4052
ER -
TY - CONF
AB - To prove that a secure key-agreement protocol exists one must at least show P ≠NP. Moreover any proof that the sequential composition of two non-adaptively secure pseudorandom functions is secure against at least two adaptive queries must falsify the decisional Diffie-Hellman assumption, a standard assumption from public-key cryptography. Hence proving any of this two seemingly unrelated statements would require a significant breakthrough. We show that at least one of the two statements is true.
To our knowledge this gives the first positive cryptographic result (namely that composition implies some weak adaptive security) which holds in Minicrypt, but not in Cryptomania, i.e. under the assumption that one-way functions exist, but public-key cryptography does not.
AU - Krzysztof Pietrzak
ID - 3217
TI - Composition implies adaptive security in minicrypt
VL - 4004
ER -
TY - CHAP
AU - Harald Janovjak
AU - Sawhney, Ravi K
AU - Stark, Martin
AU - Mueller, Daniel J
ID - 3404
T2 - Techniques in Microscopy for Biomedical Applications
TI - Atomic force microscopy
VL - 2
ER -
TY - JOUR
AB - Despite their crucial importance for cellular function, little is known about the folding mechanisms of membrane proteins. Recently details of the folding energy landscape were elucidated by atomic force microscope (AFM)-based single molecule force spectroscopy. Upon unfolding and extraction of individual membrane proteins energy barriers in structural elements such as loops and helices were mapped and quantified with the precision of a few amino acids.
Here we report on the next logical step: controlled refolding of single proteins into the membrane. First individual bacteriorhodopsin monomers were partially unfolded and extracted from the purple membrane by pulling at the C-terminal end with an AFM tip. Then by gradually lowering the tip, the protein was allowed to refold into the membrane while the folding force was recorded.
We discovered that upon refolding certain helices are pulled into the membraneagainst a sizable externalforce of several tens of picoNewton. From the mechanical work, which the helix performs on the AFM cantilever, we derive an upper limit for the Gibbs free folding energy. Subsequent unfolding allowed us to analyze the pattern of unfolding barriers and corroborate that the protein had refolded into the native state.
AU - Kessler, Max
AU - Gottschalk, Kay E
AU - Harald Janovjak
AU - Mueller, Daniel J
AU - Gaub, Hermann
ID - 3413
IS - 2
JF - Journal of Molecular Biology
TI - Bacteriorhodopsin folds into the membrane against an external force
VL - 357
ER -
TY - JOUR
AB - Mechanisms of folding and misfolding of membrane proteins are of interest in cell biology. Recently, we have established single-molecule force spectroscopy to observe directly the stepwise folding of the Na+/H+antiporter NhaA from Escherichia coli in vitro. Here, we improved this approach significantly to track the folding intermediates of asingle NhaA polypeptide forming structural segments such as the Na+-binding site, transmembrane α-helices, and helical pairs. The folding rates of structural segments ranged from 0.31 s−1 to 47 s−1, providing detailed insight into a distinct folding hierarchy of an unfolded polypeptide into the native membrane protein structure. In some cases, however, the folding chain formed stable and kinetically trapped non-native structures, which could be assigned to misfolding events of the antiporter.
AU - Kedrov, Alexej
AU - Harald Janovjak
AU - Ziegler, Christine
AU - Kühlbrandt, Werner
AU - Mueller, Daniel J
ID - 3414
IS - 1
JF - Journal of Molecular Biology
TI - Observing folding pathways and kinetics of a single sodium-proton antiporter from Escherichia coli
VL - 355
ER -
TY - GEN
AU - Harald Janovjak
AU - Kedrov, Alexej
AU - Cisneros, David
AU - Sapra, Tanuj K
AU - Struckmeier, Jens
AU - Mueller, Daniel J
ID - 3415
T2 - Neurobiology of Aging
TI - Imaging and detecting molecular interactions of single membrane proteins
VL - 27
ER -
TY - GEN
AB - Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the retina, and show that pairwise interactions account for observed higher-order correlations. By first finding a representative ensemble for observed networks we can create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses.
AU - Gasper Tkacik
AU - Schneidman, E.
AU - Berry, M. J.
AU - Bialek, William S
ID - 3431
T2 - ArXiv
TI - Ising models for networks of real neurons
ER -
TY - JOUR
AB - The mutational landscape model is a theoretical model describing sequence evolution in natural populations. However, recent experimental work has begun to test its predictions in laboratory populations of microbes. Several of these studies have focused on testing the prediction that the effects of beneficial mutations should be roughly exponentially distributed. The prediction appears to be borne out by most of these studies, at least qualitatively. Another study showed that a modified version of the model was able to predict, with reasonable accuracy, which of a ranked set of beneficial alleles will be fixed next. Although it remains to be seen whether the mutational landscape model adequately describes adaptation in organisms other than microbes, together these studies suggest that adaptive evolution has surprisingly general properties that can be successfully captured by theoretical models.
AU - Betancourt, Andrea J
AU - Jonathan Bollback
ID - 3437
IS - 6
JF - Current Opinion in Genetics & Development
TI - Fitness effects of beneficial mutations: the mutational landscape model in experimental evolution
VL - 16
ER -
TY - CONF
AB - We argue that games are expressive enough to encompass (history-based) access control, (resource) usage control (e.g., dynamic adaptive access control of reputation systems), accountability based controls (e.g., insurance), controls derived from rationality assumptions on participants (e.g., network mechanisms), and their composition. Building on the extensive research into games, we demonstrate that this expressive power coexists with a formal analysis framework comparable to that available for access control.
AU - Krishnendu Chatterjee
AU - Jagadeesan, Rhada
AU - Pitcher, Corin
ID - 3449
TI - Games for controls
ER -
TY - GEN
AB - It is widely accepted that the hippocampus plays a major role in learning and memory. The mossy fiber synapse between granule cells in the dentate gyrus and pyramidal neurons in the CA3 region is a key component of the hippocampal trisynaptic circuit. Recent work, partially based on direct presynaptic patch-clamp recordings from hippocampal mossy fiber boutons, sheds light on the mechanisms of synaptic transmission and plasticity at mossy fiber synapses. A high Na(+) channel density in mossy fiber boutons leads to a large amplitude of the presynaptic action potential. Together with the fast gating of presynaptic Ca(2+) channels, this generates a large and brief presynaptic Ca(2+) influx, which can trigger transmitter release with high efficiency and temporal precision. The large number of release sites, the large size of the releasable pool of vesicles, and the huge extent of presynaptic plasticity confer unique strength to this synapse, suggesting a large impact onto the CA3 pyramidal cell network under specific behavioral conditions. The characteristic properties of the hippocampal mossy fiber synapse may be important for pattern separation and information storage in the dentate gyrus-CA3 cell network.
AU - Bischofberger, Joseph
AU - Engel, Dominique
AU - Frotscher, Michael
AU - Peter Jonas
ID - 3463
IS - 3
T2 - Pflugers Archiv : European Journal of Physiology
TI - Timing and efficacy of transmitter release at mossy fiber synapses in the hippocampal network. (Review)
VL - 453
ER -
TY - CONF
AB - We study infinite stochastic games played by n-players on a finite graph with goals specified by sets of infinite traces. The games are concurrent (each player simultaneously and independently chooses an action at each round), stochastic (the next state is determined by a probability distribution depending on the current state and the chosen actions), infinite (the game continues for an infinite number of rounds), nonzero-sum (the players’ goals are not necessarily conflicting), and undiscounted. We show that if each player has an upward-closed objective, then there exists an ε-Nash equilibrium in memoryless strategies, for every ε>0; and exact Nash equilibria need not exist. Upward-closure of an objective means that if a set Z of infinitely repeating states is winning, then all supersets of Z of infinitely repeating states are also winning. Memoryless strategies are strategies that are independent of history of plays and depend only on the current state. We also study the complexity of finding values (payoff profile) of an ε-Nash equilibrium. We show that the values of an ε-Nash equilibrium in nonzero-sum concurrent games with upward-closed objectives for all players can be computed by computing ε-Nash equilibrium values of nonzero-sum concurrent games with reachability objectives for all players and a polynomial procedure. As a consequence we establish that values of an ε-Nash equilibrium can be computed in TFNP (total functional NP), and hence in EXPTIME.
AU - Krishnendu Chatterjee
ID - 3499
TI - Nash equilibrium for upward-closed objectives
VL - 4207
ER -
TY - CONF
AB - The classical algorithm for solving Bu ̈chi games requires time O(n · m) for game graphs with n states and m edges. For game graphs with constant outdegree, the best known algorithm has running time O(n2/logn). We present two new algorithms for Bu ̈chi games. First, we give an algorithm that performs at most O(m) more work than the classical algorithm, but runs in time O(n) on infinitely many graphs of constant outdegree on which the classical algorithm requires time O(n2). Second, we give an algorithm with running time O(n · m · log δ(n)/ log n), where 1 ≤ δ(n) ≤ n is the outdegree of the game graph. Note that this algorithm performs asymptotically better than the classical algorithm if δ(n) = O(log n).
AU - Krishnendu Chatterjee
AU - Thomas Henzinger
AU - Piterman, Nir
ID - 3500
TI - Algorithms for Büchi Games
ER -
TY - GEN
AB - Embodiments automatically generate an accurate network of watertight NURBS patches from polygonal models of objects while automatically detecting and preserving character lines thereon. These embodiments generate from an initial triangulation of the surface, a hierarchy of progressively coarser triangulations of the surface by performing a sequence of edge contractions using a greedy algorithm that selects edge contractions by their numerical properties. Operations are also performed to connect the triangulations in the hierarchy using homeomorphisms that preserve the topology of the initial triangulation in the coarsest triangulation. A desired quadrangulation of the surface can then be generated by homeomorphically mapping edges of a coarsest triangulation in the hierarchy back to the initial triangulation. This quadrangulation is topologically consistent with the initial triangulation and is defined by a plurality of quadrangular patches. These quadrangular patches are linked together by a (U, V) mesh that is guaranteed to be continuous at patch boundaries. A grid is then preferably fit to each of the quadrangles in the resulting quadrangulation by decomposing each of the quadrangles into k.sup.2 smaller quadrangles. A watertight NURBS model may be generated from the resulting quadrangulation.
AU - Herbert Edelsbrunner
AU - Fu, Ping
AU - Nekhayev, Dmitry V
AU - Facello, Michael
AU - Williams, Steven P
ID - 3510
TI - Method, apparatus and computer program products for automatically generating NURBS models of triangulated surfaces using homeomorphism
ER -
TY - GEN
AB - Methods, apparatus and computer program products provide efficient techniques for designing and printing shells of hearing-aid devices with a high degree of quality assurance and reliability and with a reduced number of manual and time consuming production steps and operations. These techniques also preferably provide hearing-aid shells having internal volumes that can approach a maximum allowable ratio of internal volume relative to external volume. These high internal volumes facilitate the inclusion of hearing-aid electrical components having higher degrees of functionality and/or the use of smaller and less conspicuous hearing-aid shells. A preferred method includes operations to generate a watertight digital model of a hearing-aid shell by thickening a three-dimensional digital model of a shell surface in a manner that eliminates self-intersections and results in a thickened model having an internal volume that is a high percentage of an external volume of the model.
AU - Fu, Ping
AU - Nekhayev, Dmitry V
AU - Herbert Edelsbrunner
ID - 3511
TI - Manufacturing methods and systems for rapid production of hearing-aid shells
ER -
TY - GEN
AB - Methods, apparatus and computer program products provide efficient techniques for reconstructing surfaces from data point sets. These techniques include reconstructing surfaces from sets of scanned data points that have preferably undergone preprocessing operations to improve their quality by, for example, reducing noise and removing outliers. These techniques include reconstructing a dense and locally two-dimensionally distributed 3D point set (e.g., point cloud) by merging stars in two-dimensional weighted Delaunay triangulations within estimated tangent planes. The techniques include determining a plurality of stars from a plurality of points p.sub.i in a 3D point set S that at least partially describes the 3D surface, by projecting the plurality of points p.sub.i onto planes T.sub.i that are each estimated to be tangent about a respective one of the plurality of points p.sub.i. The plurality of stars are then merged into a digital model of the 3D surface.
AU - Fletcher, Yates G
AU - Gloth, Tobias
AU - Herbert Edelsbrunner
AU - Fu, Ping
ID - 3512
TI - Method, apparatus and computer products that reconstruct surfaces from data points
ER -
TY - JOUR
AB - We observed sharp wave/ripples (SWR) during exploration within brief (< 2.4 s) interruptions of or during theta oscillations. CA1 network responses of SWRs occurring during exploration (eSWR) and SWRs detected in waking immobility or sleep were similar. However, neuronal activity during eSWR was location dependent, and eSWR-related firing was stronger inside the place field than outside. The eSPW-related firing increase was stronger than the baseline increase inside compared to outside, suggesting a “supralinear” summation of eSWR and place-selective inputs. Pairs of cells with similar place fields and/or correlated firing during exploration showed stronger coactivation during eSWRs and subsequent sleep-SWRs. Sequential activation of place cells was not required for the reactivation of waking co-firing patterns; cell pairs with symmetrical cross-correlations still showed reactivated waking co-firing patterns during sleep-SWRs. We suggest that place-selective firing during eSWRs facilitates initial associations between cells with similar place fields that enable place-related ensemble patterns to recur during subsequent sleep-SWRs.
AU - Joseph O'Neill
AU - Senior,Timothy
AU - Jozsef Csicsvari
ID - 3522
IS - 1
JF - Neuron
TI - Place-selective firing of CA1 pyramidal cells during sharp wave/ripple network patterns in exploratory behavior
VL - 49
ER -
TY - JOUR
AB - The functional organization of the basal ganglia ( BG) is often defined according to one of two opposing schemes. The first proposes multiple, essentially independent channels of information processing. The second posits convergence and lateral integration of striatal channels at the level of the globus pallidus ( GP). We tested the hypothesis that these proposed aspects of functional connectivity within the striatopallidal axis are dynamic and related to brain state. Local field potentials ( LFPs) were simultaneously recorded from multiple sites in striatum and GP in anesthetized rats during slow-wave activity( SWA) and during global activation evoked by sensory stimulation. Functional connectivity was inferred from comparative analyses of the internuclear and intranuclear coherence between bipolar derivations of LFPs. During prominent SWA, as shown in the electrocorticogram and local field potentials in the basal ganglia, intranuclear coherence, and, thus, lateral functional connectivity within striatum or globus pallidus was relatively weak. Furthermore, the temporal coupling of LFPs recorded across these two nuclei involved functional convergence at the level of GP. Global activation, indicated by a loss of SWA, was accompanied by a rapid functional reorganization of the striatopallidal axis. Prominent lateral functional connectivity developed within GP and, to a significantly more constrained spatial extent, striatum. Additionally, functional convergence on GP was no longer apparent, despite increased internuclear coherence. These data demonstrate that functional connectivity within the BG is highly dynamic and suggest that the relative expression of organizational principles, such as parallel, independent processing channels, striatopallidal convergence, and lateral integration within BG nuclei, is dependent on brain state.
AU - Magill,Peter J
AU - Pogosyan,Alek
AU - Sharott,Andrew
AU - Jozsef Csicsvari
AU - Bolam, John Paul
AU - Brown,Peter
ID - 3545
IS - 23
JF - Journal of Neuroscience
TI - Changes in functional connectivity within the rat striatopallidal axis during global brain activation in vivo
VL - 26
ER -
TY - CONF
AB - Persistent homology is the mathematical core of recent work on shape, including reconstruction, recognition, and matching. Its per- tinent information is encapsulated by a pairing of the critical values of a function, visualized by points forming a diagram in the plane. The original algorithm in [10] computes the pairs from an ordering of the simplices in a triangulation and takes worst-case time cubic in the number of simplices. The main result of this paper is an algorithm that maintains the pairing in worst-case linear time per transposition in the ordering. A side-effect of the algorithm’s anal- ysis is an elementary proof of the stability of persistence diagrams [7] in the special case of piecewise-linear functions. We use the algorithm to compute 1-parameter families of diagrams which we apply to the study of protein folding trajectories.
AU - Cohen-Steiner, David
AU - Herbert Edelsbrunner
AU - Morozov, Dmitriy
ID - 3559
TI - Vines and vineyards by updating persistence in linear time
ER -
TY - CONF
AB - We continue the study of topological persistence [5] by investigat- ing the problem of simplifying a function f in a way that removes topological noise as determined by its persistence diagram [2]. To state our results, we call a function g an ε-simplification of another function f if ∥f − g∥∞ ≤ ε, and the persistence diagrams of g are the same as those of f except all points within L1-distance at most ε from the diagonal have been removed. We prove that for func- tions f on a 2-manifold such ε-simplification exists, and we give an algorithm to construct them in the piecewise linear case.
AU - Herbert Edelsbrunner
AU - Morozov, Dmitriy
AU - Pascucci, Valerio
ID - 3560
TI - Persistence-sensitive simplification of functions on 2-manifolds
ER -
TY - GEN
AU - Pemberton, Josephine M
AU - Swanson, Graeme M
AU - Nicholas Barton
AU - Livingstone, Suzanne R
AU - Senn, Helen V
ID - 3594
IS - 9
T2 - Deer
TI - Hybridisation between red and sika deer in Scotland
VL - 13
ER -
TY - JOUR
AB - We apply new analytical methods to understand the consequences of population bottlenecks for expected additive genetic variance. We analyze essentially all models for multilocus epistasis that have been numerically simulated to demonstrate increased additive variance. We conclude that for biologically plausible models, large increases in expected additive variance–attributable to epistasis rather than dominance–are unlikely. Naciri-Graven and Goudet (2003) found that as the number of epistatically interacting loci increases, additive variance tends to be inflated more after a bottleneck. We argue that this result reflects biologically unrealistic aspects of their models. Specifically, as the number of loci increases, higher-order epistatic interactions become increasingly important in these models, with an increasing fraction of the genetic variance becoming nonadditive, contrary to empirical observations. As shown by Barton and Turelli (2004), without dominance, conversion of nonadditive to additive variance depends only on the variance components and not on the number of loci per se. Numerical results indicating that more inbreeding is needed to produce maximal release of additive variance with more loci follow directly from our analytical results, which show that high levels of inbreeding (F > 0.5) are needed for significant conversion of higher-order components. We discuss alternative approaches to modeling multilocus epistasis and understanding its consequences.
AU - Turelli, Michael
AU - Nicholas Barton
ID - 3607
IS - 9
JF - Evolution; International Journal of Organic Evolution
TI - Will population bottlenecks and multilocus epistasis increase additive genetic variance?
VL - 60
ER -
TY - JOUR
AB - We study the evolution of inversions that capture locally adapted alleles when two populations are exchanging migrants or hybridizing. By suppressing recombination between the loci, a new inversion can spread. Neither drift nor coadaptation between the alleles (epistasis) is needed, so this local adaptation mechanism may apply to a broader range of genetic and demographic situations than alternative hypotheses that have been widely discussed. The mechanism can explain many features observed in inversion systems. It will drive an inversion to high frequency if there is no countervailing force, which could explain fixed differences observed between populations and species. An inversion can be stabilized at an intermediate frequency if it also happens to capture one or more deleterious recessive mutations, which could explain polymorphisms that are common in some species. This polymorphism can cycle in frequency with the changing selective advantage of the locally favored alleles. The mechanism can establish underdominant inversions that decrease heterokaryotype fitness by several percent if the cause of fitness loss is structural, while if the cause is genic there is no limit to the strength of underdominance that can result. The mechanism is expected to cause loci responsible for adaptive species-specific differences to map to inversions, as seen in recent QTL studies. We discuss data that support the hypothesis, review other mechanisms for inversion evolution, and suggest possible tests.
AU - Kirkpatrick, Mark
AU - Nicholas Barton
ID - 3608
IS - 1
JF - Genetics
TI - Chromosome inversions, local adaptation, and speciation
VL - 173
ER -
TY - JOUR
AB - Bombina bombina and B. variegata are two anciently diverged toad taxa that have adapted to different breeding habitats yet hybridize freely in zones of overlap where their parapatric distributions meet. Here, we report on a joint genetic and ecological analysis of a hybrid zone in the vicinity of Stryi in western Ukraine. We used five unlinked allozyme loci, two nuclear single nucleotide polymorphisms and a mitochondrial DNA haplotype as genetic markers. Parallel allele frequency clines with a sharp central step occur across a sharp ecotone, where transitions in aquatic habitat, elevation, and terrestrial vegetation coincide. The width of the hybrid zone, estimated as the inverse of the maximum gradient in allele frequency, is 2.3 km. This is the smallest of four estimates derived from different clinal transects across Europe. We argue that the narrow cline near Stryi is mainly due to a combination of habitat distribution and habitat preference. Adult toads show a preference for either ponds (B. bombina) or puddles (B. variegata), which is known to affect the distribution of genotypes within the hybrid zones. At Stryi, it should cause a reduction of the dispersal rate across the ecotone and thus narrow the cline. A detailed comparison of all five intensively studied Bombina transects lends support to the hypothesis that habitat distribution plus habitat preference can jointly affect the structure of hybrid zones and, ultimately, the resulting barriers to gene flow between differentiated gene pools. This study also represents a resampling of an area that was last studied more than 70 years ago. Our allele-frequency clines largely coincide with those that were described then on the basis of morphological variation. However, we found asymmetrical introgression of B. variegata genes into B. bombina territory along the bank of a river.
AU - Yanchukov, Alexey
AU - Hofman, Sebastian
AU - Szymura, Jacek M
AU - Mezhzherin, Sergey V
AU - Morozov-Leonov, Sviatoslav
AU - Nicholas Barton
AU - Nürnberger, Beate
ID - 3609
IS - 3
JF - Evolution; International Journal of Organic Evolution
TI - Hybridization of Bombina bombina and B. variegata (Anura, Discoglossidae) at a sharp ecotone in western Ukraine: comparisons across transects and over time
VL - 60
ER -
TY - JOUR
AB - For a model of diallelic loci with arbitrary epistasis, Barton and Turelli [2004. Effects of genetic drift on variance components under a general model of epistasis. Evolution 58, 2111–2132] gave results for variances among and within replicate lines obtained by inbreeding without selection. Here, we discuss the relation between their population genetic methods and classical quantitative genetic arguments. In particular, we consider the case of no dominance using classical identity by descent arguments, which generalizes their results from two alleles to multiple alleles. To clarify the connections between the alternative methods, we obtain the same results using an intermediate method, which explicitly identifies the statistical effects of sets of loci. We also discuss the effects of population bottlenecks on covariances among relatives.
AU - Hill, William G
AU - Nicholas Barton
AU - Turelli, Michael
ID - 3610
IS - 1
JF - Theoretical Population Biology
TI - Prediction of effects of genetic drift on variance components under a general model of epistasis
VL - 70
ER -
TY - CONF
AB - We propose a video retrieval framework based on a novel combination of spatiograms and the Jensen-Shannon divergence, and validate its performance in two quantitative experiments on TRECVID BBC Rushes data. In the first experiment, color-based methods are tested by grouping redundant shots in an unsupervised clustering. Results of the second experiment show that motion-based spatiograms make a promising fast, compressed-domain descriptor for the detection of interview scenes.
AU - Ulges, Adrian
AU - Christoph Lampert
AU - Keysers,Daniel
ID - 3677
TI - Spatiogram-based shot distances for video retrieval
ER -
TY - CONF
AB - This paper describes a new system for "Finding Satellite Tracks” in astronomical images based on the modern geometric approach. There is an increasing need of using methods with solid mathematical and statistical foundation in astronomical image processing. Where the computational methods are serving in all disciplines of science, they are becoming popular in the field of astronomy as well. Currently different computational systems are required to be numerically optimized before to get applied on astronomical images. So at present there is no single system which solves the problems of astronomers using computational methods based on modern approaches. The system "Finding Satellite Tracks” is based on geometric matching method "Recognition by Adaptive Subdivision of Transformation Space (RAST)".
AU - Ali,Haider
AU - Christoph Lampert
AU - Breuel,Thomas M
ID - 3679
TI - Satellite tracks removal in astronomical images
VL - 4225
ER -
TY - CONF
AB - The detection of counterfeit in printed documents is currently based mainly on built-in security features or on human expertise. We propose a classification system that supports non-expert users to distinguish original documents from PC-made forgeries by analyzing the printing technique used. Each letter in a document is classified using a support vector machine that has been trained to distinguish laser from inkjet printouts. A color-coded visualization helps the user to interpret the per-letter classification results
AU - Christoph Lampert
AU - Mei,Lin
AU - Breuel,Thomas M
ID - 3680
TI - Printing technique classification for document counterfeit detection
VL - 1
ER -
TY - CONF
AB - Many algorithms to remove distortion from document images have be proposed in recent years, but so far there is no reliable method for comparing their performance. In this paper we propose a collection of methods to measure the quality of such restoration algorithms for document image which show a non-linear distortion due to perspective or page curl. For the result from these measurement to be meaningful, a common data set of ground truth is required. We therefore started with the buildup of a document image database that is meant to serve as a common data basis for all kinds of restoration from images of 3D-shaped document. The long term goal would be to establish this database and following extensions in the area of document image dewarping as an as fruitful and indispensable tool as e.g. the NIST database is for OCR, or the Caltech database is for object and face recognition.
AU - Christoph Lampert
AU - Breuel,Thomas M
ID - 3683
TI - Objective quality measurement for geometric document image restoration
ER -
TY - CONF
AB - Video compression currently is dominated by engineering and fine-tuned heuristic methods. In this paper, we propose to instead apply the well-developed machinery of machine learning in order to support the optimization of existing video encoders and the creation of new ones. Exemplarily, we show how by machine learning we can improve one encoding step that is crucial for the performance of all current video standards: macroblock mode decision. By formulating the problem in a Bayesian setup, we show that macroblock mode decision can be reduced to a classification problem with a cost function for misclassification that is sample dependent. We demonstrate how to apply different machine learning techniques to obtain suitable classifiers and we show in detailed experiments that all of these perform better than the state-of-the-art heuristic method
AU - Christoph Lampert
ID - 3685
TI - Machine learning for video compression: Macroblock mode decision
ER -
TY - CONF
AU - Keysers,Daniel
AU - Christoph Lampert
AU - Breuel,Thomas M
ID - 3692
TI - Color image dequantization by constrained diffusion
VL - 6058
ER -
TY - CONF
AB - Gaussian filtering in one, two or three dimensions is among the most commonly needed tasks in signal and image processing. Finite impulse response filters in the time domain with Gaussian masks are easy to implement in either floating or fixed point arithmetic, because Gaussian kernels are strictly positive and bounded. But these implementations are slow for large images or kernels. With the recursive IIR-filters and FFT-based methods, there are at least two alternative methods to perform Gaussian filtering in a faster way, but so far they are only applicable when floating-point hardware is available. In this paper, a fixed-point implementation of recursive Gaussian filtering is discussed and applied to isotropic and anisotropic image filtering by making use of a non-orthogonal separation scheme of the Gaussian filter.
AU - Christoph Lampert
AU - Wirjadi,Oliver
ID - 3693
TI - Anisotropic Gaussian filtering using fixed point arithmetic
ER -
TY - JOUR
AB - We give an analytical and geometrical treatment of what it means to separate a Gaussian kernel along arbitrary axes in Ropfn, and we present a separation scheme that allows us to efficiently implement anisotropic Gaussian convolution filters for data of arbitrary dimensionality. Based on our previous analysis we show that this scheme is optimal with regard to the number of memory accesses and interpolation operations needed. The proposed method relies on nonorthogonal convolution axes and works completely in image space. Thus, it avoids the need for a fast Fourier transform (FFT)-subroutine. Depending on the accuracy and speed requirements, different interpolation schemes and methods to implement the one-dimensional Gaussian (finite impulse response and infinite impulse response) can be integrated. Special emphasis is put on analyzing the performance and accuracy of the new method. In particular, we show that without any special optimization of the source code, it can perform anisotropic Gaussian filtering faster than methods relying on the FFT.
AU - Christoph Lampert
AU - Wirjadi,Oliver
ID - 3695
IS - 11
JF - IEEE Transactions on Image Processing (TIP)
TI - An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter
VL - 15
ER -
TY - JOUR
AB - Cytosine methylation, a common form of DNA modification that antagonizes transcription, is found at transposons and repeats in vertebrates, plants and fungi. Here we have mapped DNA methylation in the entire Arabidopsis thaliana genome at high resolution. DNA methylation covers transposons and is present within a large fraction of A. thaliana genes. Methylation within genes is conspicuously biased away from gene ends, suggesting a dependence on RNA polymerase transit. Genic methylation is strongly influenced by transcription: moderately transcribed genes are most likely to be methylated, whereas genes at either extreme are least likely. In turn, transcription is influenced by methylation: short methylated genes are poorly expressed, and loss of methylation in the body of a gene leads to enhanced transcription. Our results indicate that genic transcription and DNA methylation are closely interwoven processes.
AU - ZILBERMAN, Daniel
AU - Gehring, Mary
AU - Tran, Robert K.
AU - Ballinger, Tracy
AU - Henikoff, Steven
ID - 9505
IS - 1
JF - Nature Genetics
SN - 1061-4036
TI - Genome-wide analysis of Arabidopsis thaliana DNA methylation uncovers an interdependence between methylation and transcription
VL - 39
ER -
TY - JOUR
AB - The human norepinephrine (NE) transporter (hNET) attenuates neuronal signaling by rapid NE clearance from the synaptic cleft, and NET is a target for cocaine and amphetamines as well as therapeutics for depression, obsessive-compulsive disorder, and post-traumatic stress disorder. In spite of its central importance in the nervous system, little is known about how NET substrates, such as NE, 1-methyl-4-tetrahydropyridinium (MPP+), or amphetamine, interact with NET at the molecular level. Nor do we understand the mechanisms behind the transport rate. Previously we introduced a fluorescent substrate similar to MPP+, which allowed separate and simultaneous binding and transport measurement (Schwartz, J. W., Blakely, R. D., and DeFelice, L. J. (2003) J. Biol. Chem. 278, 9768-9777). Here we use this substrate, 4-(4-(dimethylamino)styrl)-N-methyl-pyridinium (ASP+), in combination with green fluorescent protein-tagged hNETs to measure substrate-transporter stoichiometry and substrate binding kinetics. Calibrated confocal microscopy and fluorescence correlation spectroscopy reveal that hNETs, which are homo-multimers, bind one substrate molecule per transporter subunit. Substrate residence at the transporter, obtained from rapid on-off kinetics revealed in fluorescence correlation spectroscopy, is 526 μs. Substrate residence obtained by infinite dilution is 1000 times slower. This novel examination of substrate-transporter kinetics indicates that a single ASP + molecule binds and unbinds thousands of times before being transported or ultimately dissociated from hNET. Calibrated fluorescent images combined with mass spectroscopy give a transport rate of 0.06 ASP +/hNET-protein/s, thus 36,000 on-off binding events (and 36 actual departures) occur for one transport event. Therefore binding has a low probability of resulting in transport. We interpret these data to mean that inefficient binding could contribute to slow transport rates.
AU - Schwartz, Joel W
AU - Gaia Novarino
AU - Piston, David W
AU - DeFelice, Louis J
ID - 2307
IS - 19
JF - Journal of Biological Chemistry
TI - Substrate binding stoichiometry and kinetics of the norepinephrine transporter
VL - 280
ER -
TY - BOOK
AB - This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ID - 2335
T2 - The mathematics of the Bose gas and its condensation
TI - The mathematics of the Bose gas and its condensation
VL - 34
ER -
TY - CHAP
AB -
Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, ρ, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4–5 decades ago, and to explore new regimes not treated before. For systems with repulsive (i.e. positive) interaction potentials the experimental low temperature state and the ground state are effectively synonymous — and this fact is used in all modeling. In such cases, the leading term in the energy/particle is 2πħ2 aρ/m where a is the scattering length of the two-body potential. Owing to the delicate and peculiar nature of bosonic correlations (such as the strange N 7/5 law for charged bosons), four decades of research failed to establish this plausible formula rigorously. The only previous lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct asymptotic formula has been obtained by us and this work will be presented. The reason behind the mathematical difficulties will be emphasized. A different formula, postulated as late as 1971 by Schick, holds in two dimensions and this, too, will be shown to be correct. With the aid of the methodology developed to prove the lower bound for the homogeneous gas, several other problems have been successfully addressed. One is the proof by us that the Gross-Pitaevskii equation correctly describes the ground state in the ‘traps’ actually used in the experiments. For this system it is also possible to prove complete Bose condensation and superfluidity as we have shown. On the frontier of experimental developments is the possibility that a dilute gas in an elongated trap will behave like a one-dimensional system; we have proved this mathematically. Another topic is a proof that Foldy’s 1961 theory of a high density Bose gas of charged particles correctly describes its ground state energy; using this we can also prove the N 7/5 formula for the ground state energy of the two-component charged Bose gas proposed by Dyson in 1967. All of this is quite recent work and it is hoped that the mathematical methodology might be useful, ultimately, to solve more complex problems connected with these interesting systems.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ED - Benedicks, Michael
ED - Jones, Peter W
ED - Smirnov, Stanislav
ED - Winckler, Björn
ID - 2336
T2 - Perspectives in Analysis
TI - The quantum-mechanical many-body problem: The Bose gas
VL - 27
ER -
TY - JOUR
AB - The validity of substituting a c-number z for the k = 0 mode operator a0 is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities such as the pressure or ground state energy, but also the value of |z|2 that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry-breaking term. This point had previously been elusive.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2359
IS - 8
JF - Physical Review Letters
TI - Justification of c-number substitutions in bosonic hamiltonians
VL - 94
ER -
TY - JOUR
AB - The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(Ï±lnÏ±) of a density matrix Ï±123 on the product of three Hilbert spaces satisfies S[Ï±123]- S[Ï±12]≤S[Ï±23]-S[Ï±2]. We strengthen this to S[Ï±123]-S[Ï±12] ≤αnα(S[Ï±23α]-S[Ï±2α]), where the nα are weights and the Ï±23α are partitions of Ï±23. Correspondingly, there is a strengthening of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2361
IS - 6
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Stronger subadditivity of entropy
VL - 71
ER -
TY - JOUR
AB - Recent developments in the physics of low-density trapped gases make it worthwhile to verify old, well-known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the ground-state energy of a dilute gas of N fermions interacting with a short-range, positive potential of scattering length a. For spin-12 fermions, this is E∼E0+(22m)2πNa, where E0 is the energy of the noninteracting system and is the density. A similar formula holds in two dimensions (2D), with a replaced by ln(a2). Obviously this 2D energy is not the expectation value of a density-independent pseudopotential.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2362
IS - 5
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Ground state energy of the low density Fermi gas
VL - 71
ER -
TY - JOUR
AB - Intersection graphs of disks and of line segments, respectively, have been well studied, because of both practical applications and theoretically interesting properties of these graphs. Despite partial results, the complexity status of the Clique problem for these two graph classes is still open. Here, we consider the Clique problem for intersection graphs of ellipses, which, in a sense, interpolate between disks and line segments, and show that the problem is APX-hard in that case. Moreover, this holds even if for all ellipses, the ratio of the larger over the smaller radius is some prescribed number. Furthermore, the reduction immediately carries over to intersection graphs of triangles. To our knowledge, this is the first hardness result for the Clique problem in intersection graphs of convex objects with finite description complexity. We also describe a simple approximation algorithm for the case of ellipses for which the ratio of radii is bounded.
AU - Ambühl, Christoph
AU - Uli Wagner
ID - 2427
IS - 3
JF - Theory of Computing Systems
TI - The Clique problem in intersection graphs of ellipses and triangles
VL - 38
ER -
TY - CONF
AB - We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I. We present several deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of inserted points. We first show that a natural and simple (deterministic) approach may perform rather poorly, requiring Ω(√n) colors in the worst case. We then modify this approach, to obtain an efficient deterministic algorithm that uses a maximum of Θ(log 2 n) colors. Next, we present two randomized solutions. The first algorithm requires an expected number of at most O(log 2 n) colors, and produces a coloring which is valid with high probability, and the second one, which is a variant of our efficient deterministic algorithm, requires an expected number of at most O(log n log log n) colors but always produces a valid coloring. We also analyze the performance of the simplest proposed algorithm when the points are inserted in a random order, and present an incomplete analysis that indicates that, with high probability, it uses only O(log n) colors. Finally, we show that in the extension of this problem to two dimensions, where the relevant ranges are disks, n colors may be required in the worst case. The average-case behavior for disks, and cases involving other planar ranges, are still open.
AU - Fiat, Amos
AU - Levy, Meital B
AU - Matoušek, Jiří
AU - Pach, Elchanan M
AU - Sharir, Micha
AU - Smorodinsky, Shakhar
AU - Uli Wagner
AU - Welzl, Emo
ID - 2428
TI - Online conflict-free coloring for intervals
ER -