How to use ‘a small’ in a sentence

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… algor’ithm. Our results show that by allowing a small error in the solution of a problem, it is often possible to gain a significant reduction in the running time of an algorithm for that problem. In Chapte…

… which all categories become linearly separable. While, reaching this form is not possible, we will argue how by replacing a small fraction of these components, it is possible to obtain a descriptor which is, on average, closer to this ideal…

… of a small to moderate length sequence provided that the context present in a sequence of length M from the same source is memorized. We quantify the achievable performance improvement in the universal compression of the small to moderate…

… fundamental community structure. We also explore the structure of ([alpha], [beta]) -communities in various social networks. ([alpha], [beta]) -communities are well clustered into a small number of disjoint groups, and there are no isolated…

… interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a…

… surfaces with multiple wetting states, including some not previously tested or known to exist. Multiscale surfaces have structure on a small and a large scale. We evaluate the effect of changes in the large scale features on drag properties. We…

… effects model and found little shrinkage of the center effects towards the overall mean. This approach is thus particularly valuable when some centers have a small number of registered patients since the convergence of this estimation strategy…

… not be satisfied with traditional spoken dialogue systems, in which focal information is not described until a small number of the records comprising the domain are identified through a constraint-elicitation process. Specifically, we…

… more routes to add from the original set of routes. In selective column generation, we first generate a small set of feasible aircraft routes. Starting with this set of routes, we iteratively generate more routes by solving a relaxed version…

… to changes in all but approximately twenty parameters. This justifies our goal of developing a small, simple model that captures approximately the same behaviour among signals of interest. The simplicity of our model not only makes it…

… cancer. We also develop an automatic lesion detection method based on motion corrected images. A small lung lesion is only 2 or 3 voxels in diameter and of marginal contrast. It could easily be missed by human observers. Our method aims to…

… based on a small coupling assumption, they are nevertheless non-perturbative, since the kink backgrounds around which the semiclassical expansion is performed are non-perturbative too…

… image-search is performed over images and links to their source web pages in a database that indexes only a small fraction of the web. Then, relevant keywords on these web pages are automatically identified and submitted to an existing text-based…

In this thesis, we describe a statistical method for 3 D object detection. In this method, we decompose the 3 D geometry of each object into a small number of viewpoints. For each viewpoint, we construct a decision rule that determines if…

… theory. Start from the basic Maxwell equation, we derive the SHG efficiency that the excited power translates into the SHG signal. According to the SHG efficiency equation, a small radius and a long length will help to result in a high SHG…

In this thesis, we consider wireless ad hoc and sensor networks where energy matters. Indeed, sensor nodes are characterized by a small size, a low cost, an advanced communication technology, but also a limited amount of energy. This…

… for which f_t has an a. c. i. m. has positive Lebesgue measure. Most of the known results about the existence and the measure of parameter values with a. c. i. m. concern a small neighborhood of the Chebyshev parameter value t= 4.

… the cluster. One problem in computing zeros of polynomials using eigenvalue method is that a small pertubation in the elements of a companion matrix may produce significant changes in the eigenvalues of the companion matrix calculated by…

… function. We obtain a variational formula for the complex eigenvalue under a small perturbation added to the vocal tract shape. We then propose a shape design problem to form the vocal tract shape changing the position of complex eigenvalues…

… as a fractal structure of magnetic minibands known as Hofstadter’s butterfly. The second material is multilayer graphene, which consists of a small number of graphene layers stacked on top of one another. We determine the effect on the…

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