Modular Kernel Research Articles

On the Virasoro fusion and modular kernels at any irrational central charge

We propose a series representation for the Virasoro fusion and modular kernels at any irrational central charge. Two distinct, yet closely related formulas are needed for the cases c∈ \mathbb{C} \backslash (-∞,1]c∈ℂ∖(−∞,1] and c <1c<1. Our proposal for c <1c<1 agrees numerically with the fusion transformation of the four-point spherical conformal blocks, whereas our proposal for c∈ \mathbb{C} \backslash (-∞,1]c∈ℂ∖(−∞,1] agrees numerically with Ponsot and Teschner’s integral formula for the fusion kernel. The case of the modular kernel is studied as a special case of the fusion kernel.

Large-scale pinball twin support vector machines

Twin support vector machines (TWSVMs) have been shown to be effective classifiers for a range of pattern classification tasks. However, the TWSVM formulation suffers from a range of shortcomings: (i) TWSVM uses hinge loss function which renders it sensitive to dataset outliers (noise sensitivity). (ii) It requires a matrix inversion calculation in the Wolfe-dual formulation which is intractable for datasets with large numbers of features/samples. (iii) TWSVM minimizes the empirical risk instead of the structural risk in its formulation with the consequent risk of overfitting. This paper proposes a novel large scale pinball twin support vector machines (LPTWSVM) to address these shortcomings. The proposed LPTWSVM model firstly utilizes the pinball loss function to achieve a high level of noise insensitivity, especially in relation to data with substantial feature noise. Secondly, and most significantly, the proposed LPTWSVM formulation eliminates the need to calculate inverse matrices in the dual problem (which apart from being very computationally demanding may not be possible due to matrix singularity). Further, LPTWSVM does not employ kernel-generated surfaces for the non-linear case, instead using the kernel trick directly; this ensures that the proposed LPTWSVM is a fully modular kernel approach in contrast to the original TWSVM. Lastly, structural risk is explicitly minimized in LPTWSVM with consequent improvement in classification accuracy (we explicitly analyze the properties of classification accuracy and noise insensitivity of the proposed LPTWSVM). Experiments on benchmark datasets show that the proposed LPTWSVM model may be effectively deployed on large datasets and that it exhibits similar or better performance on most datasets in comparison to relevant baseline methods.

On modular transformations of toric conformal blocks

We derive and solve the difference equations on the toric modular kernel following from the consistency relations in the fusion algebra. The result is explicit and simple series expansion for the toric modular kernel of non-degenerate Virasoro conformal blocks. We show that this expansion is equivalent to the celebrated integral representation due to B. Ponsot and J. Teschner. We also interpret obtained series representation as a non-perturbative expansion and note that this raises further questions.

S-duality and modular transformation as a non-perturbative deformation of the ordinary pq-duality

A recent claim that the S-duality between 4d SUSY gauge theories, which is AGT related to the modular transformations of 2d conformal blocks, is no more than an ordinary Fourier transform at the perturbative level, is further traced down to the commutation relation [P,Q]=-i\hbar between the check-operator monodromies of the exponential resolvent operator in the underlying Dotsenko-Fateev matrix models and beta-ensembles. To this end, we treat the conformal blocks as eigenfunctions of the monodromy check operators, what is especially simple in the case of one-point toric block. The kernel of the modular transformation is then defined as the intertwiner of the two monodromies, and can be obtained straightforwardly, even when the eigenfunction interpretation of the blocks themselves is technically tedious. In this way, we provide an elementary derivation of the old expression for the modular kernel for the one-point toric conformal block.

Characterization of modular frobenius groups of special type

In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G' is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G' as a modular Frobenius kernel has no more than four conjugacy classes in G.

Facial Recognition Using Multisensor Images Based on Localized Kernel Eigen Spaces

A feature selection technique along with an information fusion procedure for improving the recognition accuracy of a visual and thermal image-based facial recognition system is presented in this paper. A novel modular kernel eigenspaces approach is developed and implemented on the phase congruency feature maps extracted from the visual and thermal images individually. Smaller sub-regions from a predefined neighborhood within the phase congruency images of the training samples are merged to obtain a large set of features. These features are then projected into higher dimensional spaces using kernel methods. The proposed localized nonlinear feature selection procedure helps to overcome the bottlenecks of illumination variations, partial occlusions, expression variations and variations due to temperature changes that affect the visual and thermal face recognition techniques. AR and Equinox databases are used for experimentation and evaluation of the proposed technique. The proposed feature selection procedure has greatly improved the recognition accuracy for both the visual and thermal images when compared to conventional techniques. Also, a decision level fusion methodology is presented which along with the feature selection procedure has outperformed various other face recognition techniques in terms of recognition accuracy.

A modular kernel approach for integrative analysis of protein domain boundaries

BackgroundIn this paper, we introduce a novel inter-range interaction integrated approach for protein domain boundary prediction. It involves (1) the design of modular kernel algorithm, which is able to effectively exploit the information of non-local interactions in amino acids, and (2) the development of a novel profile that can provide suitable information to the algorithm. One of the key features of this profiling technique is the use of multiple structural alignments of remote homologues to create an extended sequence profile and combines the structural information with suitable chemical information that plays an important role in protein stability. This profile can capture the sequence characteristics of an entire structural superfamily and extend a range of profiles generated from sequence similarity alone.ResultsOur novel profile that combines homology information with hydrophobicity from SARAH1 scale was successful in providing more structural and chemical information. In addition, the modular approach adopted in our algorithm proved to be effective in capturing information from non-local interactions. Our approach achieved 82.1%, 50.9% and 31.5% accuracies for one-domain, two-domain, and three- and more domain proteins respectively.ConclusionThe experimental results in this study are encouraging, however, more work is need to extend it to a broader range of applications. We are currently developing a novel interactive (human in the loop) profiling that can provide information from more distantly related homology. This approach will further enhance the current study.

ROSS: A high-performance, low-memory, modular Time Warp system

In this paper, we introduce a new Time Warp system called ROSS: Rensselaer’ s optimistic simulation system. ROSS is an extremely modular kernel that is capable of achieving event rates as high as 1,250,000 events per second when simulating a wireless telephone network model (PCS) on a quad processor PC server. In a head-to-head comparison, we observe that ROSS out performs the Georgia Tech Time Warp (GTW) system by up to 180% on a quad processor PC server and up to 200% on the SGI Origin 2000. ROSS only requires a small constant amount of memory buffers greater than the amount needed by the sequential simulation for a constant number of processors. ROSS demonstrates for the first time that stable, highly efficient execution using little memory above what the sequential model would require is possible for low-event granularity simulation models. The driving force behind these high-performance and low-memory utilization results is the coupling of an efficient pointer-based implementation framework, Fujimoto's fast GVT algorithm for shared memory multiprocessors, reverse computation and the introduction of kernel processes ( KPs). KPs lower fossil collection overheads by aggregating processed event lists. This aspect allows fossil collection to be done with greater frequency, thus lowering the overall memory necessary to sustain stable, efficient parallel execution. These characteristics make ROSS an ideal system for use in large-scale networking simulation models. The principle conclusion drawn from this study is that the performance of an optimistic simulator is largely determined by its memory usage.

RT/OS — realtime programming and application environment for the COSY control system

This paper presents the highlights and constraints of RT/OS and how it can be used at other places. The support of approximately 1000 VME and VXI CPUs in network-based multiprocessor systems needs a special set of programming tools and application environment which are bundled as the RT/OS Real-Time-Operating-System. Supporting the Motorola 680χ0 processors and micro-controller with a development system on UNIX and MS-DOS platforms, the tool set gives the opportunity of bringing small embedded controllers as well as VME multiprocessor systems into operation. The tool set includes a cross compiler and a special version of a remote debugger, as well as application support such as downloading and configuration management. The main feature is a modular kernel with message-based task switching, using the rendezvous principle to allow easy extension. Special features of this kernel for a distributed system are networking with the Berkeley socket library supporting TCP/IP, XNS and Novell Netware, a multiprocessor system on VMEbus with the interprocessor Communication Module (IPC), a device driver library for almost every G64 I/O card using a FieldBus Interface called PDV and a X11R4 port.