The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Reputation, VC funding, and innovation: Evidence from the UK Micro and Nanotechnology sector

Startups’ contributions on economic growth have been widely realized. However, the funding gap is often a problem limiting startups’ development. To some extent, VC can be a means to solve this problem. VC is one of the optimal financial intermediaries for startups. Two streams of VC studies are focused in this dissertation: the criteria used by venture capitalists to evaluate startups and the effect of VC on innovation. First, although many criteria have been analyzed, the empirical assessment of the effect of startup reputation on VC funding has not been investigated. However, reputation is usually positively related with firm performance, which may affect VC funding. By analyzing reputation from the generalized visibility dimension and the generalized favorability dimension using a sample of 200 startups founded from 1995 operating in the UK MNT sector, we show that both the two dimensions of reputation have positive influence on the likelihood of receiving VC funding. We also find that management team heterogeneity positively influence the likelihood of receiving VC funding. Second, studies investigating the effect of venture capital on innovation have frequently resorted to patent data. However, innovation is a process leading from invention to successful commercialization, and while patents capture the upstream side of innovative performance, they poorly describe its downstream one. By reflecting the introduction of new products or services trademarks can complete the picture, but empirical studies on trademarking in startups are rare. Analyzing a sample of 192 startups founded from 1996 operating in the UK MNT sector, we find that VC funding has positive effect on the propensity to register trademarks, as well as on the number and breadth of trademarks.

Contribution to dynamic characteristics of the cutting temperature in the drilling process considering one dimension heat flow

The machining of hardened steels has always been a great challenge in metal cutting, particularly for drilling operations. Generally, drilling is the machining process that is most difficult to cool due to the tool`s geometry. The aim of this work is to determine the heat flux and the coefficient of convection in drilling using the inverse heat conduction method. Temperature was assessed during the drilling of hardened AISI H13 steel using the embedded thermocouple technique. Dry machining and two cooling/lubrication systems were used, and thermocouples were fixed at distances very close to the hole`s wall. Tests were replicated for each condition, and were carried out with new and worn drills. An analytical heat conduction model was used to calculate the temperature at tool-workpiece interface and to define the heat flux and the coefficient of convection. In all tests using new and worn out drills, the lowest temperatures and decrease of heat flux were observed using the flooded system, followed by the MQL, considering the dry condition as reference. The decrease of temperature was directly proportional to the amount of lubricant applied and was significant in the MQL system when compared to dry cutting. (C) 2011 Elsevier Ltd. All rights reserved.

Relationship between technological properties and slab surface roughness of siliceous dimension stones

Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)[06/52521-0]

Dimension stone for building facades: methodology for structural design

The importance of a careful selection of rocks used in building facade cladding is highlighted. A simple and viable methodology for the structural detailing of dimension stones and the verification of the global performance is presented based on a Strap software simulation. The results obtained proved the applicability of the proposed structural dimensioning methodology which represents an excellent simple tool for dimensioning rock slabs used for building facade cladding. The Strap software satisfactorily simulated the structural conditions of the stone slabs under the studied conditions, allowing the determination of alternative slab dimensions and the verification of the cladding strength at the support.

A hispanical dimension of the luso-american revolution (1820-1823)

The Independence of Brazil was proclaimed in September 1822 after two years during which constituent deputies elected on both sides of the Atlantic and gathered in Lisbon endeavoured to achieve unification with the former Portuguese metropoli. Due to the failure of these attempts a Constituent Assembly settled in independent Brazil in July 1823. Those two parlamentary experiences - the first to take place in the Portuguese dominions - were strongly influenced by the decisions adopted in Cadiz (1810-1814), and in Madrid (1820-1823), and by the independentist processes developed at the time in Spanish America. This work aims at observing that influence on the decisions adopted in Lisbon and Rio de Janeiro vis-a-vis the autonomical reivindications of several Brazilian provinces.

Brain structure and symptom dimension relationships in obsessive-compulsive disorder: A voxel-based morphometry study

Background: Obsessive-compulsive disorder (OCD) is a clinically heterogenous disorder characterized by temporally stable symptom dimensions. Past inconsistent results from structural neuroimaging studies of OCD may have resulted from the effects of these specific symptom dimensions as well as other socio-demographic and clinical variables upon gray matter (GM) volume. Methods: GM volume was measured in 25 adult OCD patients and 20 adult healthy controls using voxel-based morphometry (VBM), controlling for age and total brain GM volume. Univariate and multivariate regression analyses were carried out between regions of GM difference and age, age of onset, medication load, OCD severity, depression severity, and separate symptom dimension scores. Results: Significant GM volumetric differences in OCD patients relative to controls were found in dorsal cortical regions, including bilateral BA6, BA46, BA9 and right BA8 (controls > patients), and bilateral midbrain (patients > controls). Stepwise regression analyses revealed highly significant relationships between greater total OCD symptom severity and smaller GM volumes in dorsal cortical regions and larger GM volumes in bilateral midbrain. Greater age was independently associated with smaller GM volumes in right BA6, left BA9, left BA46 and larger GM volumes in right midbrain. Greater washing symptom severity was independently associated with smaller GM volume in right BA6, while there was a trend association between greater hoarding symptom severity and lower GM volume in left BA6. Limitations: The sample was relatively small to examine the relationship between symptom scores and GM volumes. Multiple patients were taking medication and had comorbid disorders. Conclusions: These analyses suggest dorsal prefrontal cortical and bilateral midbrain GM abnormalities in OCD that appear to be primarily driven by the effects of total OCD symptom severity. The results regarding the relationship between GM volumes and symptom dimension scores require examination in larger samples. (C) 2008 Elsevier B.V. All rights reserved.

Sludge population optimisation: a new dimension for the control of biological wastewater treatment systems

The activated sludge comprises a complex microbiological community. The structure (what types of microorganisms are present) and function (what can the organisms do and at what rates) of this community are determined by external physico -chemical features and by the influent to the sewage treatment plant. The external features we can manipulate but rarely the influent. Conventional control and operational strategies optimise activated sludge processes more as a chemical system than as a biological one. While optimising the process in a short time period, these strategies may deteriorate the long-term performance of the process due to their potentially adverse impact on the microbial properties. Through briefly reviewing the evidence available in the literature that plant design and operation affect both the structure and function of the microbial community in activated sludge, we propose to add sludge population optimisation as a new dimension to the control of biological wastewater treatment systems. We stress that optimising the microbial community structure and property should be an explicit aim for the design and operation of a treatment plant. The major limitations to sludge population optimisation revolve around inadequate microbiological data, specifically community structure, function and kinetic data. However, molecular microbiological methods that strive to provide that data are being developed rapidly. The combination of these methods with the conventional approaches for kinetic study is briefly discussed. The most pressing research questions pertaining to sludge population optimisation are outlined. (C) 2002 Elsevier Science Ltd. All rights reserved.