Data-Discriminants of Likelihood Equations

Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to solve a very structured parameterized polynomial system called likelihood equations. For general choices of data, the number of complex solutions to the likelihood equations is finite and called the ML-degree of the model. The only solutions to the likelihood equations that are statistically meaningful are the real/positive solutions. However, the number of real/positive solutions is not characterized by the ML-degree. We use discriminants to classify data according to the number of real/positive solutions of the likelihood equations. We call these discriminants data-discriminants (DD). We develop a probabilistic algorithm for computing DDs. Experimental results show that, for the benchmarks we have tried, the probabilistic algorithm is more efficient than the standard elimination algorithm. Based on the computational results, we discuss the real root classification problem for the 3 by 3 symmetric matrix~model.Comment: 2 table

Rubidium "whiskers" in a vapor cell

Crystals of metallic rubidium are observed ``growing'' from paraffin coating of buffer-gas-free glass vapor cells. The crystals have uniform square cross-section, $\approx 30 \mu$m on the side, and reach several mm in length.Comment: 2 pages, 1 figur

Holographic three-point functions of giant gravitons

Working within the AdS/CFT correspondence we calculate the three-point function of two giant gravitons and one pointlike graviton using methods of semiclassical string theory and considering both the case where the giant gravitons wrap an S^3 in S^5 and the case where the giant gravitons wrap an S^3 in AdS_5. We likewise calculate the correlation function in N=4 SYM using two Schur polynomials and a single trace chiral primary. We find that the gauge and string theory results have structural similarities but do not match perfectly, and interpret this in terms of the Schur polynomials' inability to interpolate between dual giant and pointlike gravitons.Comment: 21 page

Holographic Correlation Functions for Open Strings and Branes

In this paper, we compute holographically the two-point and three-point functions of giant gravitons with open strings. We consider the maximal giant graviton in $S^5$ and the string configurations corresponding to the ground states of Z=0 and Y=0 open spin chain, and the spinning string in AdS$_5$ corresponding to the derivative type impurities in Y=0 or Z=0 open spin chain as well. We treat the D-brane and open string contribution separately and find the corresponding D3-brane and string configurations in bulk which connect the composite operators at the AdS$_5$ boundary. We apply a new prescription to treat the string state contribution and find agreements for the two-point functions. For the three-point functions of two giant gravitons with open strings and one certain half-BPS chiral primary operator, we find that the D-brane contributions to structure constant are always vanishing and the open string contribution for the Y=0 ground state is in perfect match with the prediction in the free field limit.Comment: 25 page

Correlation functions of three heavy operators - the AdS contribution

We consider operators in N=4 SYM theory which are dual, at strong coupling, to classical strings rotating in S^5. Three point correlation functions of such operators factorize into a universal contribution coming from the AdS part of the string sigma model and a state-dependent S^5 contribution. Consequently a similar factorization arises for the OPE coefficients. In this paper we evaluate the AdS universal factor of the OPE coefficients which is explicitly expressed just in terms of the anomalous dimensions of the three operators.Comment: 49 pages, 3 figures; v.2 references corrected; v3: corrected discussion in section 5, results unchange

Correlation function of null polygonal Wilson loops with local operators

We consider the correlator of a light-like polygonal Wilson loop with n cusps with a local operator (like the dilaton or the chiral primary scalar) in planar N =4 super Yang-Mills theory. As a consequence of conformal symmetry, the main part of such correlator is a function F of 3n-11 conformal ratios. The first non-trivial case is n=4 when F depends on just one conformal ratio \zeta. This makes the corresponding correlator one of the simplest non-trivial observables that one would like to compute for generic values of the `t Hooft coupling \lambda. We compute F(\zeta,\lambda) at leading order in both the strong coupling regime (using semiclassical AdS5 x S5 string theory) and the weak coupling regime (using perturbative gauge theory). Some results are also obtained for polygonal Wilson loops with more than four edges. Furthermore, we also discuss a connection to the relation between a correlator of local operators at null-separated positions and cusped Wilson loop suggested in arXiv:1007.3243.Comment: 36 pages, 2 figure

Evidence of Long Term Benefit of Praziquantel Treatment Against Schistosoma mansoni in Kigungu Fishing Village of Entebbe, Uganda

Praziquantel (PZQ) is efficacious against all species of schistosome: Schistosoma mansoni; Schistosoma haematobium; Schistosoma japonicum and other parasites like the Taenia species. This cross-sectional cohorts study was carried out in Kigungu fishing village along Lake Victoria shore in Entebbe Uganda. Our analysis was based on examining microscopically three slides from a single stool specimen from each of base line cohorts 945.These included children and adults, participants from both sexes in Kigungu fishing village in Entebbe Uganda. Nine hundred and one (901) of the cohorts were re-examined after six months and 625 of the same cohorts who were examined at the baseline and after six months were re-examined 18 months later. The slides were prepared using modified Kato/Katz (Odongo-Aginya) method. The infection proportion with Schistosoma mansoni at baseline was 448 (47.5%) but this was reduced to 244 (25.8%) 18 months after treatment with a single oral dose of praziquantel at 40mg/kg. However 495 (52.5%) were negative at the baseline study. The cure proportion after six was significant {(P=0.00), (OR4.63) CI at 95% (3.53-6.06)}. Similarly the cure proportion after 18 months was significant {(P=0.00), (OR2.2) CI at 95% (1.87-3.34)}. The force of re-infection after six months was significant {(P=0.0001), (OR 0.47) CI at 95% (0.31-0.71)}. Nevertheless the force of re-infection was not significant after 18 months {(P=0.766), (OR 0.95) CI at 95% (0.68-1.34)} eggs excretion did not reach the level of the pre-treatment intensity. The egg reduction was 69.3%. This was associated with age and pre-treatment intensity < 400 eggs per gram (epg) of faeces and age groups ≥ 30 years. The egg reduction also resulted in marked decrease in clinical symptoms in the participants. Our study suggests evidence of long-term benefit of praziquantel in Kigungu and that the re-infection occurred more commonly in younger age group than in the older patients.Key words: Praziquantel; Schistosoma mansoni; Kigungu; Entebbe; Uganda

Risk scoring models for trade credit in small and medium enterprises

Trade credit refers to providing goods and services on a deferred payment basis. Commercial credit management is a matter of great importance for most small and medium enterprises (SMEs), since it represents a significant portion of their assets. Commercial lending involves assuming some credit risk due to exposure to default. Thus, the management of trade credit and payment delays is strongly related to the liquidation and bankruptcy of enterprises. In this paper we study the relationship between trade credit management and the level of risk in SMEs. Despite its relevance for most SMEs, this problem has not been sufficiently analyzed in the existing literature. After a brief review of existing literature, we use a large database of enterprises to analyze data and propose a multivariate decision-tree model which aims at explaining the level of risk as a function of several variables, both of financial and non-financial nature. Decision trees replace the equation in parametric regression models with a set of rules. This feature is an important aid for the decision process of risk experts, as it allows them to reduce time and then the economic cost of their decisions

More three-point correlators of giant magnons with finite size

In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to heavy string states, while the third vertex corresponds to a light state. This is done for the case when the heavy string states are finite-size giant magnons with one or two angular momenta, and for two different choices of the light state, corresponding to dilaton operator and primary scalar operator. The relevant operators in the dual gauge theory are Tr(F_{\mu\nu}^2 Z^j+...) and Tr(Z^j). We first consider the case of AdS_5 x S^5 and N = 4 super Yang-Mills. Then we extend the obtained results to the gamma-deformed AdS_5 x S^5_\gamma, dual to N = 1 super Yang-Mills theory, arising as an exactly marginal deformation of N = 4 super Yang-Mills.Comment: 14 pages, no figure