ROSE: a Package for Binary Imbalanced Learning

The ROSE package provides functions to deal with binary classification problems in the presence of imbalanced classes. Artificial balanced samples are generated according to a smoothed bootstrap approach and allow for aiding both the phases of estimation and accuracy evaluation of a binary classifier in the presence of a rare class. Functions that implement more traditional remedies for the class imbalance and different metrics to evaluate accuracy are also provided. These are estimated by holdout, bootstrap or cross-validation methods

Automorphism groups and new constructions of maximum additive rank metric codes with restrictions

Let $d, n \in \mathbb{Z}^+$ such that $1\leq d \leq n$. A $d$-code $\mathcal{C} \subset \mathbb{F}_q^{n \times n}$ is a subset of order $n$ square matrices with the property that for all pairs of distinct elements in $\mathcal{C}$, the rank of their difference is greater than or equal to $d$. A $d$-code with as many as possible elements is called a maximum $d$-code. The integer $d$ is also called the minimum distance of the code. When $d<n$, a classical example of such an object is the so-called generalized Gabidulin code. There exist several classes of maximum $d$-codes made up respectively of symmetric, alternating and hermitian matrices. In this article we focus on such examples. Precisely, we determine their automorphism groups and solve the equivalence issue for them. Finally, we exhibit a maximum symmetric $2$-code which is not equivalent to the one with same parameters known so far

Preface

This is the preface of the special volume of Discrete Mathematics dedicated to Combinatorics 2008 we curated as guest editors

Laboratory Tests of Low Density Astrophysical Equations of State

Clustering in low density nuclear matter has been investigated using the NIMROD multi-detector at Texas A&M University. Thermal coalescence modes were employed to extract densities, $\rho$, and temperatures, $T$, for evolving systems formed in collisions of 47 $A$ MeV $^{40}$Ar + $^{112}$Sn,$^{124}$Sn and $^{64}$Zn + $^{112}$Sn, $^{124}$Sn. The yields of $d$, $t$, $^{3}$He, and $^{4}$He have been determined at $\rho$ = 0.002 to 0.032 nucleons/fm$^{3}$ and $T$= 5 to 10 MeV. The experimentally derived equilibrium constants for $\alpha$ particle production are compared with those predicted by a number of astrophysical equations of state. The data provide important new constraints on the model calculations.Comment: 5 pages, 3 figure

Experimental Determination of In-Medium Cluster Binding Energies and Mott Points in Nuclear Matter

In medium binding energies and Mott points for $d$, $t$, $^3$He and $\alpha$ clusters in low density nuclear matter have been determined at specific combinations of temperature and density in low density nuclear matter produced in collisions of 47$A$ MeV $^{40}$Ar and $^{64}$Zn projectiles with $^{112}$Sn and $^{124}$Sn target nuclei. The experimentally derived values of the in medium modified binding energies are in good agreement with recent theoretical predictions based upon the implementation of Pauli blocking effects in a quantum statistical approach.Comment: 5 pages, 3 figure

Families of twisted tensor product codes

Using geometric properties of the variety \cV_{r,t}, the image under the Grassmannian map of a Desarguesian $(t-1)$-spread of \PG(rt-1,q), we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We exactly determine the parameters of these codes and characterise the words of minimum weight.Comment: Keywords: Segre Product, Veronesean, Grassmannian, Desarguesian spread, Subgeometry, Twisted Product, Constacyclic error correcting code, Minimum weigh

Critical Behavior in Light Nuclear Systems: Experimental Aspects

An extensive experimental survey of the features of the disassembly of a small quasi-projectile system with $A \sim$ 36, produced in the reactions of 47 MeV/nucleon $^{40}$Ar + $^{27}$Al, $^{48}$Ti and $^{58}$Ni, has been carried out. Nuclei in the excitation energy range of 1-9 MeV/u have been investigated employing a new method to reconstruct the quasi-projectile source. At an excitation energy $\sim$ 5.6 MeV/nucleon many observables indicate the presence of maximal fluctuations in the de-excitation processes. The fragment topological structure shows that the rank sorted fragments obey Zipf's law at the point of largest fluctuations providing another indication of a liquid gas phase transition. The caloric curve for this system shows a monotonic increase of temperature with excitation energy and no apparent plateau. The temperature at the point of maximal fluctuations is $8.3 \pm 0.5$ MeV. Taking this temperature as the critical temperature and employing the caloric curve information we have extracted the critical exponents $\beta$, $\gamma$ and $\sigma$ from the data. Their values are also consistent with the values of the universality class of the liquid gas phase transition. Taken together, this body of evidence strongly suggests a phase change in an equilibrated mesoscopic system at, or extremely close to, the critical point.Comment: Physical Review C, in press; some discussions about the validity of excitation energy in peripheral collisions have been added; 24 pages and 32 figures; longer abstract in the preprin

Evidence of Critical Behavior in the Disassembly of Nuclei with A ~ 36

A wide variety of observables indicate that maximal fluctuations in the disassembly of hot nuclei with A ~ 36 occur at an excitation energy of 5.6 +- 0.5 MeV/u and temperature of 8.3 +- 0.5 MeV. Associated with this point of maximal fluctuations are a number of quantitative indicators of apparent critical behavior. The associated caloric curve does not appear to show a flattening such as that seen for heavier systems. This suggests that, in contrast to similar signals seen for liquid-gas transitions in heavier nuclei, the observed behavior in these very light nuclei is associated with a transition much closer to the critical point.Comment: v2: Major changes, new model calculations, new figure

Towards the critical behavior for the light nuclei by NIMROD detector

The critical behavior for the light nuclei with A$\sim 36$ has been investigated experimentally by the NIMROD multi-detectors. The wide variety of observables indicate the critical point has been reached in the disassembly of hot nuclei at an excitation energy of 5.6$\pm$0.5 MeV/u.Comment: 4 pages, 2 figures; Proceeding of 18th Nuclear Physics Division Conference of the Euro. Phys. Society (NPDC18) "Phase transitions in strongly interacting matter", Prague, 23.8.-29.8. 2004. To be published in Nuclear Physics