TY - JOUR
AB - Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Stromdnger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equal. This provides significant evidence in support of SYZ. Moreover, the examples are of great interest in their own right: they are spaces of flat SLr-connections on a smooth curve. The mirror is the corresponding space for the Langlands dual group PGLr. These examples therefore throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.
AU - Tamas Hausel
AU - Thaddeus, Michael
ID - 1457
IS - 1
JF - Inventiones Mathematicae
TI - Mirror symmetry, langlands duality, and the Hitchin system
VL - 153
ER -
TY - JOUR
AB - The moduli space of stable bundles of rank $2$ and degree $1$ on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the noncompact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance.
AU - Tamas Hausel
AU - Thaddeus, Michael
ID - 1458
IS - 2
JF - Journal of the American Mathematical Society
TI - Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles
VL - 16
ER -
TY - JOUR
AB - In this paper we explicitly calculate the analogue of the 't Hooft SU (2) Yang-Mills instantons on Gibbons-Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi-Hanson, or Ak ALE gravitational instantons and the multi-Taub-NUT spaces, or Ak ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU (2) magnetic monopole solutions of the Bogomolny equations on flat ℝ3.
AU - Etesi, Gábor
AU - Tamas Hausel
ID - 1459
IS - 2
JF - Communications in Mathematical Physics
TI - On Yang-Mills instantons over multi-centered gravitational instantons
VL - 235
ER -
TY - CONF
AB - Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D). We show how to build a grid graph and set its edge weights so that the cost of cuts is arbitrarily close to the length (area) of the corresponding contours (surfaces) for any anisotropic Riemannian metric. There are two interesting consequences of this technical result. First, graph cut algorithms can be used to find globally minimum geodesic contours (minimal surfaces in 3D) under arbitrary Riemannian metric for a given set of boundary conditions. Second, we show how to minimize metrication artifacts in existing graph-cut based methods in vision. Theoretically speaking, our work provides an interesting link between several branches of mathematics -differential geometry, integral geometry, and combinatorial optimization. The main technical problem is solved using Cauchy-Crofton formula from integral geometry.
AU - Boykov, Yuri
AU - Vladimir Kolmogorov
ID - 3170
TI - Computing geodesics and minimal surfaces via graph cuts
VL - 1
ER -
TY - CONF
AB - Reconstructing a 3-D scene from more than one camera is a classical problem in computer vision. One of the major sources of difficulty is the fact that not all scene elements are visible from all cameras. In the last few years, two promising approaches have been developed 11,12 that formulate the scene reconstruction problem in terms of energy minimization, and minimize the energy using graph cuts. These energy minimization approaches treat the input images symmetrically, handle visibility constraints correctly, and allow spatial smoothness to be enforced. However, these algorithm propose different problem formulations, and handle a limited class of smoothness terms. One algorithm 11 uses a problem formulation that is restricted to two-camera stereo, and imposes smoothness between a pair of cameras. The other algorithm 12 can handle an arbitrary number of cameras, but imposes smoothness only with respect to a single camera. In this paper we give a more general energy minimization formulation for the problem, which allows a larger class of spatial smoothness constraints. We show that our formulation includes both of the previous approaches as special cases, as well as permitting new energy functions. Experimental results on real data with ground truth are also included.
AU - Vladimir Kolmogorov
AU - Zabih, Ramin
AU - Gortler, Steven
ID - 3171
TI - Generalized multi camera scene reconstruction using graph cuts
VL - 2683
ER -
TY - CONF
AB - We address visual correspondence problems without assuming that scene points have similar intensities in different views. This situation is common, usually due to non-lambertian scenes or to differences between cameras. We use maximization of mutual information, a powerful technique for registering images that requires no a priori model of the relationship between scene intensities in different views. However, it has proven difficult to use mutual information to compute dense visual correspondence. Comparing fixed-size windows via mutual information suffers from the well-known problems of fixed windows, namely poor performance at discontinuities and in low-texture regions. In this paper, we show how to compute visual correspondence using mutual information without suffering from these problems. Using 'a simple approximation, mutual information can be incorporated into the standard energy minimization framework used in early vision. The energy can then be efficiently minimized using graph cuts, which preserve discontinuities and handle low-texture regions. The resulting algorithm combines the accurate disparity maps that come from graph cuts with the tolerance for intensity changes that comes from mutual information.
AU - Kim, Junhwan
AU - Vladimir Kolmogorov
AU - Zabih, Ramin
ID - 3174
TI - Visual correspondence using energy minimization and mutual information
VL - 2
ER -
TY - JOUR
AB - We show that the fixed alphabet shortest common supersequence (SCS) and the fixed alphabet longest common subsequence (LCS) problems parameterized in the number of strings are W[1]-hard. Unless W[1]=FPT, this rules out the existence of algorithms with time complexity of O(f(k)nα) for those problems. Here n is the size of the problem instance, α is constant, k is the number of strings and f is any function of k. The fixed alphabet version of the LCS problem is of particular interest considering the importance of sequence comparison (e.g. multiple sequence alignment) in the fixed length alphabet world of DNA and protein sequences.
AU - Krzysztof Pietrzak
ID - 3209
IS - 4
JF - Journal of Computer and System Sciences
TI - On the parameterized complexity of the fixed alphabet shortest common supersequence and longest common subsequence problems
VL - 67
ER -
TY - CONF
AB - Luby and Rackoff showed how to construct a (super-)pseudo-random permutation {0,1}2n→ {0,1}2n from some number r of pseudo-random functions {0,1}n → {0,1}n. Their construction, motivated by DES, consists of a cascade of r Feistel permutations. A Feistel permutation 1for a pseudo-random function f is defined as (L, R) → (R,L ⊕ f (R)), where L and R are the left and right part of the input and ⊕ denotes bitwise XOR or, in this paper, any other group operation on {0,1}n. The only non-trivial step of the security proof consists of proving that the cascade of r Feistel permutations with independent uniform random functions {0,1}n → {0,1}n, denoted Ψ2nr is indistinguishable from a uniform random permutation {0,1}2n → {0,1}2n by any computationally unbounded adaptive distinguisher making at most O(2cn) combined chosen plaintext/ciphertext queries for any c < α, where a is a security parameter. Luby and Rackoff proved α = 1/2 for r = 4. A natural problem, proposed by Pieprzyk is to improve on α for larger r. The best known result, α = 3/4 for r = 6, is due to Patarin. In this paper we prove a = 1 -O(1/r), i.e., the trivial upper bound α = 1 can be approached. The proof uses some new techniques that can be of independent interest.
AU - Maurer, Ueli M
AU - Krzysztof Pietrzak
ID - 3210
TI - The security of many round Luby Rackoff pseudo random permutations
VL - 2656
ER -
TY - CHAP
AU - Peter Jonas
AU - Unsicker, Klaus
ED - Schmidt, R. F.
ID - 3458
T2 - Lehrbuch Vorklinik
TI - Molekulare und zelluläre Grundlagen des Nervensystems.
VL - B
ER -
TY - JOUR
AB - Neurons can produce action potentials with high temporal precision(1). A fundamental issue is whether, and how, this capability is used in information processing. According to the `cell assembly' hypothesis, transient synchrony of anatomically distributed groups of neurons underlies processing of both external sensory input and internal cognitive mechanisms(2-4). Accordingly, neuron populations should be arranged into groups whose synchrony exceeds that predicted by common modulation by sensory input. Here we find that the spike times of hippocampal pyramidal cells can be predicted more accurately by using the spike times of simultaneously recorded neurons in addition to the animals location in space. This improvement remained when the spatial prediction was refined with a spatially dependent theta phase modulation(5-8). The time window in which spike times are best predicted from simultaneous peer activity is 10-30 ms, suggesting that cell assemblies are synchronized at this timescale. Because this temporal window matches the membrane time constant of pyramidal neurons(9), the period of the hippocampal gamma oscillation(10) and the time window for synaptic plasticity(11), we propose that cooperative activity at this timescale is optimal for information transmission and storage in cortical circuits.
AU - Harris, Kenneth D
AU - Jozsef Csicsvari
AU - Hirase, Hajima
AU - Dragoi, George
AU - Buzsáki, György
ID - 3526
IS - 6948
JF - Nature
TI - Organization of cell assemblies in the hippocampus
VL - 424
ER -