4,837 research outputs found
A complete characterization of plateaued Boolean functions in terms of their Cayley graphs
In this paper we find a complete characterization of plateaued Boolean
functions in terms of the associated Cayley graphs. Precisely, we show that a
Boolean function is -plateaued (of weight ) if and only
if the associated Cayley graph is a complete bipartite graph between the
support of and its complement (hence the graph is strongly regular of
parameters ). Moreover, a Boolean function is
-plateaued (of weight ) if and only if the associated
Cayley graph is strongly -walk-regular (and also strongly
-walk-regular, for all odd ) with some explicitly given
parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201
On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit
We study the Nekrasov-Shatashvili limit of the N=2 supersymmetric gauge
theory and topological string theory on certain local toric Calabi-Yau
manifolds. In this limit one of the two deformation parameters \epsilon_{1,2}
of the Omega background is set to zero and we study the perturbative expansion
of the topological amplitudes around the remaining parameter. We derive
differential equations from Seiberg-Witten curves and mirror geometries, which
determine the higher genus topological amplitudes up to a constant. We show
that the higher genus formulae previously obtained from holomorphic anomaly
equations and boundary conditions satisfy these differential equations. We also
provide a derivation of the holomorphic anomaly equations in the
Nekrasov-Shatashvili limit from these differential equations.Comment: 41 pages, no figure. v2: references adde
Extension and approximation of -subharmonic functions
Let be a bounded domain, and let be a
real-valued function defined on the whole topological boundary . The aim of this paper is to find a characterization of the functions
which can be extended to the inside to a -subharmonic function under
suitable assumptions on . We shall do so by using a function algebraic
approach with focus on -subharmonic functions defined on compact sets. We
end this note with some remarks on approximation of -subharmonic functions
A potential risk of overestimating apparent diffusion coefficient in parotid glands
Objectives: To investigate transient signal loss on diffusion weighted images (DWI) and overestimation of apparent diffusion coefficient (ADC) in parotid glands using single shot echoplanar DWI (EPDWI). Materials and Methods: This study enrolled 6 healthy subjects and 7 patients receiving radiotherapy. All participants received dynamic EPDWI with a total of 8 repetitions. Imaging quality of DWI was evaluated. Probability of severe overestimation of ADC (soADC), defined by an ADC ratio more than 1.2, was calculated. Error on T2WI, DWI, and ADC was computed. Statistical analysis included paired Student t testing and Mann-Whitney U test. A P value less than 0.05 was considered statistically significant. Results: Transient signal loss was visually detected on some excitations of DWI but not on T2WI or mean DWI. soADC occurred randomly among 8 excitations and 3 directions of diffusion encoding gradients. Probability of soADC was significantly higher in radiotherapy group (42.86%) than in healthy group (24.39%). The mean error percentage decreased as the number of excitations increased on all images, and, it was smallest on T2WI, followed by DWI and ADC in an increasing order. Conclusions: Transient signal loss on DWI was successfully detected by dynamic EPDWI. The signal loss on DWI and overestimation of ADC could be partially remedied by increasing the number of excitations. © 2015 Liu et al.published_or_final_versio
Bioinformatics advances in saliva diagnostics
There is a need recognized by the National Institute of Dental & Craniofacial Research and the National Cancer Institute to advance
basic, translational and clinical saliva research. The goal of the Salivaomics Knowledge Base (SKB) is to create a data management system and web resource constructed to support human salivaomics research. To maximize the utility of the SKB for retrieval,
integration and analysis of data, we have developed the Saliva Ontology and SDxMart. This article reviews the informatics advances in saliva diagnostics made possible by the Saliva Ontology and SDxMart
On the Equivalence between Neural Network and Support Vector Machine
Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) [27]. Under the squared loss, the infinite-width NN trained by gradient descent with an infinitely small learning rate is equivalent to kernel regression with NTK [4]. However, the equivalence is only known for ridge regression currently [6], while the equivalence between NN and other kernel machines (KMs), e.g. support vector machine (SVM), remains unknown. Therefore, in this work, we propose to establish the equivalence between NN and SVM, and specifically, the infinitely wide NN trained by soft margin loss and the standard soft margin SVM with NTK trained by subgradient descent. Our main theoretical results include establishing the equivalence between NN and a broad family of `2 regularized KMs with finite-width bounds, which cannot be handled by prior work, and showing that every finite-width NN trained by such regularized loss functions is approximately a KM. Furthermore, we demonstrate our theory can enable three practical applications, including (i) non-vacuous generalization bound of NN via the corresponding KM; (ii) nontrivial robustness certificate for the infinite-width NN (while existing robustness verification methods would provide vacuous bounds); (iii) intrinsically more robust infinite-width NNs than those from previous kernel regression
Solving the Topological String on K3 Fibrations
We present solutions of the holomorphic anomaly equations for compact
two-parameter Calabi-Yau manifolds which are hypersurfaces in weighted
projective space. In particular we focus on K3-fibrations where due to
heterotic type II duality the topological invariants in the fibre direction are
encoded in certain modular forms. The formalism employed provides holomorphic
expansions of topological string amplitudes everywhere in moduli space.Comment: 60 pages, 1 figure, With an appendix by Sheldon Kat
Response to arXiv:0811.3876 "Comment on a recent conjectured solution of the three dimensional Ising model" by Wu et al
This is a Response to a recent Comment [F.Y. Wu et al., Phil. Mag. 88, 3093
(2008), arXiv:0811.3876] on the conjectured solution of the three-dimensional
(3D) Ising model [Z.D. Zhang, Phil. Mag. 87, 5309 (2007), arXiv:0705.1045].
Several points are made: 1) Conjecture 1, regarding the additional rotation, is
understood as performing a transformation for smoothing all the crossings of
the knots; 2) The weight factors in Conjecture 2 are interpreted as a novel
topologic phase; 3) The conjectured solution and its low- and high-temperature
expansions are supported by the mathematical theorems for the analytical
behavior of the Ising model. The physics behind the extra dimension is also
discussed briefly.Comment: 11 pages, 0 figure
Global Properties of Topological String Amplitudes and Orbifold Invariants
We derive topological string amplitudes on local Calabi-Yau manifolds in
terms of polynomials in finitely many generators of special functions. These
objects are defined globally in the moduli space and lead to a description of
mirror symmetry at any point in the moduli space. Holomorphic ambiguities of
the anomaly equations are fixed by global information obtained from boundary
conditions at few special divisors in the moduli space. As an illustration we
compute higher genus orbifold Gromov-Witten invariants for C^3/Z_3 and C^3/Z_4.Comment: 34 pages, 3 figure
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