On data analysis and variable selection: the minimum entropy analysis

In this work, we present a minimum entropy analysis scheme for variable selection and preliminary data analysis. The variable selection can be achieved by the increasing preference of variables. We show such a preference to has a unqiue form, which is given by the entropy of models associated with variables. Evaluating the entropy provides a complete ranking scheme of variables. This scheme not only indicates preferred variables but also may reveal the system's nature and properties. We illustrate the proposed scheme to analyze a set of geological data for three carbonate rock units in Texas and Oklahoma, and compare to the discriminant function analysis. The result suggests this scheme to provide a quick and robust analysis, and the use in data analysis is promising.Comment: 9 pages and 2 table

Generalized Affine Programming & Duality Gap with non-Division Rings

Classical primal-dual affine programming takes place over finite dimensional real vector spaces. This results in beautiful duality theory, connecting the optimal solu- tions of the primal maximization problem and the dual minimization problems. These results include the Existence Duality Theorem, which guarantees optimal solutions to any feasible bounded program; and the Strong Duality Theorem, which implies that optimal solutions for primal and dual programs must have the same objective value. In a common extension of classical affine programming, we see that the Strong Duality does not hold when ring of scalars is the integers. Extension of classical affine programming results to ordered division rings are explored in. In this paper, we describe the generalized setting of affine programming using ordered ring (not necessarily division), and classify the rings for which the Existence Duality Theorem or the Strong Duality Theorem fail

Electron localization in linear chains of identical loop scatterers

We show that electron localization is generic in a linear chain of identical simple quantum wire loops with equal arm lengths in the presence of either a perpendicular magnetic field or the spin-orbit interaction, and has less to do with the shapes of the loops. We calculate the transfer matrices for a general simple loop scatterer in the presence of these effects. Based on the knowledge of the transfer matrices, we thus provide a criterion for the occurrence of the localization and present a simple formalism to integrate the transmission probability over the injection wave vector of electron.Comment: 16 pages, 8 figure

Classical random walks over complex networks and network complexity

In this paper we view the steady states of classical random walks over complex networks with an arbitrary degree distribution as states in thermal equilibrium. By identifying the distribution of states as a canonical ensemble, we are able to define the temperature and the Hamiltonian for the random walk systems. We then calculate the Helmholtz free energy, the average energy, and the entropy for the thermal equilibrium states. The results shows equipartition of energy for the average energy. The entropy is found to consist of two parts. The first part decreases as the number of walkers increases. The second part of the entropy depends solely on the topology of the network, and will increase when more edges or nodes are added to the network. We compare the topological part of entropy with some of the network descriptors and find that the topological entropy could be used as a measure of network complexity. In addition, we discuss the scenario that a walker has a prior probability of resting on the same node at the next time step, and find that the effect of the prior resting probabilities is equivalent to increasing the degree for every node in the network.Comment: 18 pages, 6 figure

MULTI-CHANNEL SEARCH FOR SUPERGRAVITY AT THE LARGE HADRON COLLIDER

The potential of seeing supersymmetry (SUSY) at the CERN Large Hadron Collider (LHC) was studied by looking at 3 types of signals: dilepton events from slepton pair productions, trilepton events from chargino/neutralino productions and missing energy plus multi-jet events from gluino/squark productions. I described my results by mapping out reachable areas in the supergravity parameter space. Areas explorable at LEP II were also mapped out for comparison.Comment: proceedings for 'BEYOND THE STANDARD MODEL IV' conference; 3 pages; an unencoded postscript figure was appende

Non-Empty Quantum Dot as a Spin-Entangler

We consider a three-port single-level quantum dot system with one input and two output leads. Instead of considering an empty dot, we study the situations that two input electrons co-tunnel through the quantum dot occupied by one or two dot electrons. We show that electron entanglement can be generated via the co-tunneling processes when the dot is occupied by two electrons, yielding non-local spin-singlet states at the output leads. When the dot is occupied by a single electron, net spin-singlet final states could be generated by injecting polarized electrons to the dot system. When the input electrons are unpolarized, we show that by carefully arranging model parameters non-local spin-triplet electrons can also be obtained at the output leads if the dot-electron spin remains unchanged in the final state.Comment: 10 pages, 4 figures;monir changes on abstract and content, typos correcte

The MHV lagrangian vertices and the Parke-Taylor formula

We explicitly calculate the vertices of the MHV-rules lagrangian in 4-dimensions. This proves that the vertices in the lagrangian obtained by a canonical transformation from light-cone Yang-Mills theory coincide to all order with the Parke-Taylor formula, filling the gap originally left in the lagrangian derivation of the CSW rules.Comment: 12 pages, 3 figures, JHEP3 styl

Nickel Bubble Expansion in Type Ia Supernovae: Adiabatic Solutions

This paper presents hydrodynamical and radiation-hydrodynamical simulations of the nickel bubble effect in Type Ia supernovae, comparison of results to self-similar solutions, and application to observations of Type Ia supernova remnants, with a particular emphasis on Tycho's SNR.Comment: ApJ, 2008, accepted, 36 page

On rr-Equitable Coloring of Complete Multipartite Graphs

Let $r \geqslant 0$ and $k \geqslant 1$ be integers. We say that a graph $G$ has an $r$-equitable $k$-coloring if there exists a proper $k$-coloring of $G$ such that the sizes of any two color classes differ by at most $r$. The least $k$ such that a graph $G$ has an $r$-equitable $k$-coloring is denoted by $\chi_{r=} (G)$, and the least $n$ such that a graph $G$ has an $r$-equitable $k$-coloring for all $k \geqslant n$ is denoted by $\chi^*_{r=} (G)$. In this paper, we propose a necessary and sufficient condition for a complete multipartite graph $G$ to have an $r$-equitable $k$-coloring, and also give exact values of $\chi_{r=} (G)$ and $\chi^*_{r=} (G)$.Comment: 8 pages, 1 figur

Code Annealing and the Suppressing Effect of the Cyclically Lifted LDPC Code Ensemble

Code annealing, a new method of designing good codes of short block length, is proposed, which is then concatenated with cyclic lifting to create finite codes of low frame error rate (FER) error floors without performance outliers. The stopping set analysis is performed on the cyclically lifted code ensemble assuming uniformly random lifting sequences, and the suppressing effect/weight of the cyclic lifting is identified for the first time, based on which the ensemble FER error floor can be analytically determined and a scaling law is derived. Both the first-order and high-order suppressing effects are discussed and quantified by different methods including the explicit expression, an algorithmic upper bound, and an algebraic lower bound. The mismatch between the suppressing weight and the stopping distances explains the dramatic performance discrepancy among different cyclically lifted codes when the underlying base codes have degree 2 variable nodes or not. For the former case, a degree augmentation method is further introduced to mitigate this metric mismatch, and a systematic method of constructing irregular codes of low FER error floors is presented. Both regular and irregular codes of very low FER error floors are reported, for which the improvement factor ranges from 10^6-10^4 when compared to the classic graph-based code ensembles.Comment: To appear in the Proc. 2006 IEEE Information Theory Workshop, Chengdu, Chin