1. When is it true? (5 points for each correct answer, -3 point for each wrong answer, 0 point for each blank) Fill in each blank with “always,” “sometimes,” or “never.” For example, • A nonsingular matrix is always invertible. • A square matrix is sometimes full-rank. • A strictly tall matrix is never onto. Here the matrix dimensions are such that each expression makes sense, but they are othe...

1. When is it true? (5 points for each correct answer, -3 point for each wrong answer, 0 point for each blank) Fill in each blank with “always,” “sometimes,” or “never.” For example, • A nonsingular matrix is always invertible. • A square matrix is sometimes full-rank. • A strictly tall matrix is never onto. Here the matrix dimensions are such that each expression makes sense, but they are othe...

MRI quantification of cranial nerves such as anterior visual pathway (AVP) in MRI is challenging due to their thin small size, structural variation along its path, and adjacent anatomic structures. Segmentation of pathologically abnormal optic nerve (e.g. optic nerve glioma) poses additional challenges due to changes in its shape at unpredictable locations. In this work, we propose a partitione...

The known bijections on Dyck paths are either involutions or have notoriously intractable cycle structure. Here we present a size-preserving bijection on Dyck paths whose cycle structure is amenable to complete analysis. In particular, each cycle has length a power of 2. A new manifestation of the Catalan numbers as labeled forests crops up enroute as does the Pascal matrix mod 2. We use the bi...

In this article we shall give a survey of Hasse’s problem for integral power bases of algebraic number fields during the last half of century. Specifically, we developed this problem for the abelian number fields and we shall show several substantial examples for our main theorem [7] [9], which will indicate the actual method to generalize for the forthcoming theme on Hasse’s problem [15].

Implementation of floating point algorithms in FPGA (Field Programmable Gate Arrays) creates an open problem. One of possible solutions is the representation of floating point numbers as an integer (fixed point) logarithm (32 bit) [1]. Basic arithmetical operations can be performed in the logarithm numbering system which is suitable for FPGA and ASIC implementation. Simulator of such system has...

Let q be a power of a prime p. Matrices over Fq in which every subset of basis size of the columns are independent, are of interest in coding theory, matroid theory, and projective geometry. For any positive integer m ≤ p and bijection σ : N≤q−1 ∪ {0} → Fq, we show that the m× (q + 1) matrix Hq,m, with {Uq}i,j = 

In general, we shall start with one 1 in the first row and three l's in the second row. The recurrence then determines the subsequent rows. The first few rows of the rhombus are given in Figure 2. We assume all blank positions are zero. So, for example, when calculating the second entry in the third row the two zeros are assumed to be up two places and up one and to the left. We call this array...

In the exemplar SVM (E-SVM) approach of Malisiewicz et al., ICCV 2011, an ensemble of SVMs is learnt, with each SVM trained independently using only a single positive sample and all negative samples for the class. In this paper we develop a multi-sample learning (MSL) model which enables joint regularization of the E-SVMs without any additional cost over the original ensemble learning. The adva...

This paper describes a neural compiler. The input of the compiler is a PASCAL Program. The compiler produces a neural network that computes what is speciied by the PASCAL program. The compiler generates an intermediate code called cellular code.