Learning polyhedral classifiers using logistic function

In this paper we propose a new algorithm for learning polyhedral classifiers. In contrast to existing methods for learning polyhedral classifier which solve a constrained optimization problem, our method solves an unconstrained optimization problem. Our method is based on a logistic function based model for the posterior probability function. We propose an alternating optimization algorithm, namely, SPLA1 (Single Polyhedral Learning Algorithm1) which maximizes the loglikelihood of the training data to learn the parameters. We also extend our method to make it independent of any user specified parameter (e.g., number of hyperplanes required to form a polyhedral set) in SPLA2. We show the effectiveness of our approach with experiments on various synthetic and real world datasets and compare our approach with a standard decision tree method (OC1) and a constrained optimization based method for learning polyhedral sets.

Reliable Means of Diagnosis and Serovar Determination of Blood-Borne Salmonella Strains: Quick PCR Amplification of Unique Genomic Loci by Novel Primer Sets

Typhoid fever is becoming an ever increasing threat in the developing countries. We have improved considerably upon the existing PCR-based diagnosis method by designing primers against a region that is unique to Salmonella enterica subsp. enterica serovar Typhi and Salmonella enterica subsp. enterica serovar Paratyphi A, corresponding to the STY0312 gene in S. Typhi and its homolog SPA2476 in S. Paratyphi A. An additional set of primers amplify another region in S. Typhi CT18 and S. Typhi Ty2 corresponding to the region between genes STY0313 to STY0316 but which is absent in S. Paratyphi A. The possibility of a false-negative result arising due to mutation in hypervariable genes has been reduced by targeting a gene unique to typhoidal Salmonella serovars as a diagnostic marker. The amplified region has been tested for genomic stability by amplifying the region from clinical isolates of patients from various geographical locations in India, thereby showing that this region is potentially stable. These set of primers can also differentiate between S. Typhi CT18, S. Typhi Ty2, and S. Paratyphi A, which have stable deletions in this specific locus. The PCR assay designed in this study has a sensitivity of 95% compared to the Widal test which has a sensitivity of only 63%. As observed, in certain cases, the PCR assay was more sensitive than the blood culture test was, as the PCR-based detection could also detect dead bacteria.

Coding for Two-User Gaussian MAC with PSK and PAM Signal Sets

Constellation Constrained (CC) capacity regions of a two-user Gaussian Multiple Access Channel(GMAC) have been recently reported. For such a channel, code pairs based on trellis coded modulation are proposed in this paper with MPSK and M-PAM alphabet pairs, for arbitrary values of M,toachieve sum rates close to the CC sum capacity of the GMAC. In particular, the structure of the sum alphabets of M-PSK and M-PAMmalphabet pairs are exploited to prove that, for certain angles of rotation between the alphabets, Ungerboeck labelling on the trellis of each user maximizes the guaranteed squared Euclidean distance of the sum trellis. Hence, such a labelling scheme can be used systematically,to construct trellis code pairs to achieve sum rates close to the CC sum capacity. More importantly, it is shown for the first time that ML decoding complexity at the destination is significantly reduced when M-PAM alphabet pairs are employed with almost no loss in the sum capacity.

Comparative measurements of HV impulses to evaluate different sets of response parameters

Results are reported of comparative measurements made in 14 HV (high-voltage) laboratories in ten different countries. The theory of the proposed methods of characterizing the dynamic behavior is given, and the parameters to be used are discussed. Comparative measurements made using 95 systems based on 53 dividers are analyzed. This analysis shows that many of the system now in use, even though they fulfil the basic response requirements of the standards, do not meet the accuracy requirements. Because no transfer measurements were made between laboratories, there is no way to detect similar errors in both the system under test and the reference system. Hence, the situation may be worse than reported. This has led to the recommendation that comparative measurements should be the main route for quantifying industrial impulse measuring systems

Minimal sets of generators for the relation ideals of certain monomial curves

Let O be a monomial curve in the affine algebraic e-space over a field K and P be the relation ideal of O. If O is defined by a sequence of e positive integers some e - 1 of which form an arithmetic sequence then we construct a minimal set of generators for P and write an explicit formula for mu(P).

Tree structure for efficient data mining using rough sets

In data mining, an important goal is to generate an abstraction of the data. Such an abstraction helps in reducing the space and search time requirements of the overall decision making process. Further, it is important that the abstraction is generated from the data with a small number of disk scans. We propose a novel data structure, pattern count tree (PC-tree), that can be built by scanning the database only once. PC-tree is a minimal size complete representation of the data and it can be used to represent dynamic databases with the help of knowledge that is either static or changing. We show that further compactness can be achieved by constructing the PC-tree on segmented patterns. We exploit the flexibility offered by rough sets to realize a rough PC-tree and use it for efficient and effective rough classification. To be consistent with the sizes of the branches of the PC-tree, we use upper and lower approximations of feature sets in a manner different from the conventional rough set theory. We conducted experiments using the proposed classification scheme on a large-scale hand-written digit data set. We use the experimental results to establish the efficacy of the proposed approach. (C) 2002 Elsevier Science B.V. All rights reserved.

A general construction of space-time trellis codes for PSK signal sets

The diversity order and coding gain are crucial for the performance of a multiple antenna communication system. It is known that space-time trellis codes (STTC) can be used to achieve these objectives. In particular, we can use STTCs to obtain large coding gains. Many attempts have been made to construct STTCs which achieve full-diversity and good coding gains, though a general method of construction does not exist. Delay diversity code (rate-1) is known to achieve full-diversity, for any number of transmit antennas and any signal set, but does not give a good coding gain. A product distance code based delay diversity scheme (Tarokh, V. et al., IEEE Trans. Inform. Theory, vol.44, p.744-65, 1998) enables one to improve the coding gain and construct STTCs for any given number of states using coding in conjunction with delay diversity; it was stated as an open problem. We achieve such a construction. We assume a shift register based model to construct an STTC for any state complexity. We derive a sufficient condition for this STTC to achieve full-diversity, based on the delay diversity scheme. This condition provides a framework to do coding in conjunction with delay diversity for any signal constellation. Using this condition, we provide a formal rate-1 STTC construction scheme for PSK signal sets, for any number of transmit antennas and any given number of states, which achieves full-diversity and gives a good coding gain.

Gas-phase synthesis of size-classified polyhedral In(2)O(3) nanoparticles

Monodisperse polyhedral In(2)O(3) nanoparticles were synthesized by differential mobility classification of a polydisperse aerosol formed by evaporation of indium at atmospheric pressure. When free molten indium particles oxidize, oxygen is absorbed preferentially on certain planes leading to the formation of polyhedral In(2)O(3) nanoparticles. It is shown that the position of oxygen addition, its concentration, the annealing temperature and the type of carrier gas are crucial for the resulting particle shape and crystalline quality. Semiconducting nanopolyhedrals, especially nanocubes used for sensors, are expected to offer enhanced sensitivity and improved response time due to the higher surface area as compared to spherical particles.

Minimal unsatisfiable sets: Classification and bounds

Proving the unsatisfiability of propositional Boolean formulas has applications in a wide range of fields. Minimal Unsatisfiable Sets (MUS) are signatures of the property of unsatisfiability in formulas and our understanding of these signatures can be very helpful in answering various algorithmic and structural questions relating to unsatisfiability. In this paper, we explore some combinatorial properties of MUS and use them to devise a classification scheme for MUS. We also derive bounds on the sizes of MUS in Horn, 2-SAT and 3-SAT formulas.

Badly approximable numbers and vectors in Cantor-like sets

We show that a large class of Cantor-like sets of R-d, d >= 1, contains uncountably many badly approximable numbers, respectively badly approximable vectors, when d >= 2. An analogous result is also proved for subsets of R-d arising in the study of geodesic flows corresponding to (d+1)-dimensional manifolds of constant negative curvature and finite volume, generalizing the set of badly approximable numbers in R. Furthermore, we describe a condition on sets, which is fulfilled by a large class, ensuring a large intersection with these Cantor-like sets.

Rainbow connection number and connected dominating sets

The rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this article we show that for every connected graph on n vertices with minimum degree delta, the rainbow connection number is upper bounded by 3n/(delta + 1) + 3. This solves an open problem from Schiermeyer (Combinatorial Algorithms, Springer, Berlin/Hiedelberg, 2009, pp. 432437), improving the previously best known bound of 20n/delta (J Graph Theory 63 (2010), 185191). This bound is tight up to additive factors by a construction mentioned in Caro et al. (Electr J Combin 15(R57) (2008), 1). As an intermediate step we obtain an upper bound of 3n/(delta + 1) - 2 on the size of a connected two-step dominating set in a connected graph of order n and minimum degree d. This bound is tight up to an additive constant of 2. This result may be of independent interest. We also show that for every connected graph G with minimum degree at least 2, the rainbow connection number, rc(G), is upper bounded by Gc(G) + 2, where Gc(G) is the connected domination number of G. Bounds of the form diameter(G)?rc(G)?diameter(G) + c, 1?c?4, for many special graph classes follow as easy corollaries from this result. This includes interval graphs, asteroidal triple-free graphs, circular arc graphs, threshold graphs, and chain graphs all with minimum degree delta at least 2 and connected. We also show that every bridge-less chordal graph G has rc(G)?3.radius(G). In most of these cases, we also demonstrate the tightness of the bounds.

Maximum weight independent sets in hole- and dart-free graphs

The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. The complexity of the MWIS problem for hole-free graphs is unknown. In this paper, we first prove that the MWIS problem for (hole, dart, gem)-free graphs can be solved in O(n(3))-time. By using this result, we prove that the MWIS problem for (hole, dart)-free graphs can be solved in O(n(4))-time. Though the MWIS problem for (hole, dart, gem)-free graphs is used as a subroutine, we also give the best known time bound for the solvability of the MWIS problem in (hole, dart, gem)-free graphs. (C) 2012 Elsevier B.V. All rights reserved.

A numerical approach to determine the sufficiency of given boundary data sets for uniquely estimating interior elastic properties

We consider an inverse elasticity problem in which forces and displacements are known on the boundary and the material property distribution inside the body is to be found. In other words, we need to estimate the distribution of constitutive properties using the finite boundary data sets. Uniqueness of the solution to this problem is proved in the literature only under certain assumptions for a given complete Dirichlet-to-Neumann map. Another complication in the numerical solution of this problem is that the number of boundary data sets needed to establish uniqueness is not known even under the restricted cases where uniqueness is proved theoretically. In this paper, we present a numerical technique that can assess the sufficiency of given boundary data sets by computing the rank of a sensitivity matrix that arises in the Gauss-Newton method used to solve the problem. Numerical experiments are presented to illustrate the method.

Polyceptron a polyhedral learning algorithm

In this paper we propose a new algorithm for learning polyhedral classifiers which we call as Polyceptron. It is a Perception like algorithm which updates the parameters only when the current classifier misclassifies any training data. We give both batch and online version of Polyceptron algorithm. Finally we give experimental results to show the effectiveness of our approach.