Efficiency versus Convergence of Boolean Kernels for On-Line Learning Algorithms

The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses in this context is to expand the feature set to include conjunctions of basic features. This can be done explicitly or where possible by using a kernel function. Focusing on the well known Perceptron and Winnow algorithms, the paper demonstrates a tradeoff between the computational efficiency with which the algorithm can be run over the expanded feature space and the generalization ability of the corresponding learning algorithm. We first describe several kernel functions which capture either limited forms of conjunctions or all conjunctions. We show that these kernels can be used to efficiently run the Perceptron algorithm over a feature space of exponentially many conjunctions; however we also show that using such kernels, the Perceptron algorithm can provably make an exponential number of mistakes even when learning simple functions. We then consider the question of whether kernel functions can analogously be used to run the multiplicative-update Winnow algorithm over an expanded feature space of exponentially many conjunctions. Known upper bounds imply that the Winnow algorithm can learn Disjunctive Normal Form (DNF) formulae with a polynomial mistake bound in this setting. However, we prove that it is computationally hard to simulate Winnows behavior for learning DNF over such a feature set. This implies that the kernel functions which correspond to running Winnow for this problem are not efficiently computable, and that there is no general construction that can run Winnow with kernels

Electroweak Radiative Corrections to Off-Shell W-Pair Production

We briefly describe the RacoonWW approach to calculate radiative corrections to e+ e- -> W W -> 4 fermions and present numerical results for the total W-pair production cross section at LEP2.Comment: 3 pages, 2 figures, talk given at the DPF2000 meeting, Columbus, OH, August 9-12, 200

Probing anomalous quartic gauge-boson couplings via e+e- --> 4fermions+gamma

All lowest-order amplitudes for e+e- --> 4f+gamma are calculated including five anomalous quartic gauge-boson couplings that are allowed by electromagnetic gauge invariance and the custodial SU(2)_c symmetry. Three of these anomalous couplings correspond to the operators L_0, L_c, and L_n that have been constrained by the LEP collaborations in WWgamma production. The anomalous couplings are incorporated in the Monte Carlo generator RACOONWW. Moreover, for the processes e+e- --> 4f+gamma RACOONWW is improved upon including leading universal electroweak corrections such as initial-state radiation. The discussion of numerical results illustrates the size of the leading corrections as well as the impact of the anomalous quartic couplings for LEP2 energies and at 500GeV.Comment: 27 pages, latex, 42 postscript files, some misprints correcte

W-pair production at future e+e- colliders: precise predictions from RACOONWW

We present numerical results for total cross sections and various distributions for e+e- --> WW --> 4f(+gamma) at a future 500GeV linear collider, obtained from the Monte Carlo generator RACOONWW. This generator is the first one that includes O(alpha) electroweak radiative corrections in the double-pole approximation completely. Owing to their large size the corrections are of great phenomenological importance.Comment: 11 pages, latex, 10 postscript file

Bubble statistics and coarsening dynamics for quasi-two dimensional foams with increasing liquid content

We report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. The design of the sample cell permits control of the liquid content, through a constant pressure condition set by the height of the foam above a liquid reservoir. We find that in the scaling state, all bubble distributions are independent not only of time but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and with decreasing bubble size. We successfully model this behavior by explicitly incorporating the border blocking effect into the von Neumann argument. Two dimensionless bubble shape parameters naturally arise, one of which is primarily responsible for the violation of von Neumann's law for foams that are not perfectly dry

Monosynaptic connections between pairs of spiny stellate cells in layer 4 and pyramidal cells in layer 5A indicate that lemniscal and paralemniscal afferent pathways converge in the infragranular somatosensory cortex.

Monosynaptic interlaminar connections between spiny stellate cells in layer 4 (L4), the main cortical recipient layer for thalamic projections, and pyramidal cells in layer 5A (L5A), one of the main cortical output layers, were examined anatomically and functionally by paired recordings in acute brain slices. The somata of pairs forming interlaminar L4-to-L5A connections were located predominantly close to or directly under the barrel-septum wall in layer 4. Superposition of spiny stellate axon arbors and L5A pyramidal cell dendritic arbors suggested an innervation domain underneath an L4 barrel wall. Functionally, the L4-to-L5A connections were of high reliability and relatively low efficacy, with a unitary EPSP amplitude of 0.6 mV, and the connectivity was moderately high (one in seven pairs tested was connected). The EPSP amplitude was weakly depressing (paired-pulse ratio of approximately 0.8) during repetitive presynaptic action potentials at 10 Hz. The existence of Monosynaptic L4-to-L5A connections indicates that the specific 'lemniscal' thalamic input from the ventro-basal nucleus of the thalamus to the cortex and the more unspecific 'paralemniscal' afferent thalamic projections from the posterior medial nucleus of the thalamus merge already at an initial stage of cortical signal processing. These Monosynaptic connections establish a Monosynaptic coupling of the input to the cortex and its output, thereby effectively bypassing the supragranular layers