How to Choose a Champion

League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest number of wins is declared to be the champion. The total number of games needed for the best team to win the championship with high certainty, T, grows as the cube of the number of teams, N, i.e., T ~ N^3. This number can be substantially reduced using preliminary rounds where teams play a small number of games and subsequently, only the top teams advance to the next round. When there are k rounds, the total number of games needed for the best team to emerge as champion, T_k, scales as follows, T_k ~N^(\gamma_k) with gamma_k=1/[1-(2/3)^(k+1)]. For example, gamma_k=9/5,27/19,81/65 for k=1,2,3. These results suggest an algorithm for how to infer the best team using a schedule that is linear in N. We conclude that league format is an ineffective method of determining the best team, and that sequential elimination from the bottom up is fair and efficient.Comment: 6 pages, 3 figure

Alternating Spin and Orbital Dimerization in Strong-coupling Two-band Models

We study a one-dimensional Hamiltonian consisting of coupled SU(2) spin and orbital degrees of freedom. Using the density matrix renormalization group, we calculate the phase-diagram and the ground state correlation functions for this model. We find that, in addition to the ferromagnetic and power-law antiferromagnetic phases for spin and orbital degrees of freedom, this model has a gapless line extending from the ferromagnetic phase to the Bethe ansatz solvable SU(4) critical point, and a gapped phase with doubly degenerate ground states which form alternating spin and orbital singlets. The spin-gap and the order parameters are evaluated and the relevance to several recently discovered spin-gap materials is discussed.Comment: 4 pages REVTEX and 4 Postscript figure

Spinons in a Crossed-Chains Model of a 2D Spin Liquid

Using Random Phase Approximation, we show that a crossed-chains model of a spin-1/2 Heisenberg spins, with frustrated interchain couplings, has a non-dimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a `sliding Luttinger liquid'. In an external field, the system develops an incommensurate field-induced long range order with a finite transition temperature.Comment: 4 pages, 3 figures; added references; scaling analysis, preserving spin rotational invariance, is extended to finite temperatur

Comparative analysis of miRNAs and their targets across four plant species

BACKGROUND: MicroRNA (miRNA) mediated regulation of gene expression has been recognized as a major posttranscriptional regulatory mechanism also in plants. We performed a comparative analysis of miRNAs and their respective gene targets across four plant species: Arabidopsis thaliana (Ath), Medicago truncatula(Mtr), Brassica napus (Bna), and Chlamydomonas reinhardtii (Cre). RESULTS: miRNAs were obtained from mirBase with 218 miRNAs for Ath, 375 for Mtr, 46 for Bna, and 73 for Cre, annotated for each species respectively. miRNA targets were obtained from available database annotations, bioinformatic predictions using RNAhybrid as well as predicted from an analysis of mRNA degradation products (degradome sequencing) aimed at identifying miRNA cleavage products. On average, and considering both experimental and bioinformatic predictions together, every miRNA was associated with about 46 unique gene transcripts with considerably variation across species. We observed a positive and linear correlation between the number miRNAs and the total number of transcripts across different plant species suggesting that the repertoire of miRNAs correlates with the size of the transcriptome of an organism. Conserved miRNA-target pairs were found to be associated with developmental processes and transcriptional regulation, while species-specific (in particular, Ath) pairs are involved in signal transduction and response to stress processes. Conserved miRNAs have more targets and higher expression values than non-conserved miRNAs. We found evidence for a conservation of not only the sequence of miRNAs, but their expression levels as well. CONCLUSIONS: Our results support the notion of a high birth and death rate of miRNAs and that miRNAs serve many species specific functions, while conserved miRNA are related mainly to developmental processes and transcriptional regulation with conservation operating at both the sequence and expression level

Field dependent thermodynamics and Quantum Critical Phenomena in the dimerized spin system Cu2(C5H12N2)2Cl4

Experimental data for the uniform susceptibility, magnetization and specific heat for the material Cu2(C5H12N2)2Cl4 (abbreviated CuHpCl) as a function of temperature and external field are compared with those of three different dimerized spin models: alternating spin-chains, spin-ladders and the bilayer Heisenberg model. It is shown that because this material consists of weakly coupled spin-dimers, much of the data is insensitive to how the dimers are coupled together and what the effective dimensionality of the system is. When such a system is tuned to the quantum critical point by application of a field, the dimensionality shows up in the power-law dependences of thermodynamic quantities on temperature. We discuss the temperature window for such a quantum critical behavior in CuHpCl.Comment: Revtex, 5 pages, 4 figures (postscript

Effect of Hund coupling in the one-dimensional SU(4) Hubbard model

The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of {\it coherent} spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become {\it incoherent}. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.Comment: 10 pages, 1 figur

Effects of a magnetic field on the one-dimensional spin-orbital model

We study the effects of a uniform magnetic field on the one-dimensional spin-orbital model in terms of effective field theories. Two regions are examined: one around the SU(4) point (J=K/4) and the other with K<<J. We found that when $J\leq K/4$, the spin and orbital correlation functions exhibit power-law decay with nonuniversal exponents. In the region with J>K/4, the excitation spectrum has a gap. When the magnetic field is beyond some critical value, a quantum phase transition occurs. However, the correlation functions around the SU(4) point and the region with K<<J exhibit distinct behavior. This results from different structures of excitation spectra in both regime.Comment: 22 pages, no figure

Fractal Profit Landscape of the Stock Market

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q. Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.Comment: 12 pages, 4 figure

Functional Specialization of the Plant miR396 Regulatory Network through Distinct MicroRNA–Target Interactions

MicroRNAs (miRNAs) are ∼21 nt small RNAs that regulate gene expression in animals and plants. They can be grouped into families comprising different genes encoding similar or identical mature miRNAs. Several miRNA families are deeply conserved in plant lineages and regulate key aspects of plant development, hormone signaling, and stress response. The ancient miRNA miR396 regulates conserved targets belonging to the GROWTH-REGULATING FACTOR (GRF) family of transcription factors, which are known to control cell proliferation in Arabidopsis leaves. In this work, we characterized the regulation of an additional target for miR396, the transcription factor bHLH74, that is necessary for Arabidopsis normal development. bHLH74 homologs with a miR396 target site could only be detected in the sister families Brassicaceae and Cleomaceae. Still, bHLH74 repression by miR396 is required for margin and vein pattern formation of Arabidopsis leaves. MiR396 contributes to the spatio-temporal regulation of GRF and bHLH74 expression during leaf development. Furthermore, a survey of miR396 sequences in different species showed variations in the 5′ portion of the miRNA, a region known to be important for miRNA activity. Analysis of different miR396 variants in Arabidopsis thaliana revealed that they have an enhanced activity toward GRF transcription factors. The interaction between the GRF target site and miR396 has a bulge between positions 7 and 8 of the miRNA. Our data indicate that such bulge modulates the strength of the miR396-mediated repression and that this modulation is essential to shape the precise spatio-temporal pattern of GRF2 expression. The results show that ancient miRNAs can regulate conserved targets with varied efficiency in different species, and we further propose that they could acquire new targets whose control might also be biologically relevant

Spatial interactions in agent-based modeling

Agent Based Modeling (ABM) has become a widespread approach to model complex interactions. In this chapter after briefly summarizing some features of ABM the different approaches in modeling spatial interactions are discussed. It is stressed that agents can interact either indirectly through a shared environment and/or directly with each other. In such an approach, higher-order variables such as commodity prices, population dynamics or even institutions, are not exogenously specified but instead are seen as the results of interactions. It is highlighted in the chapter that the understanding of patterns emerging from such spatial interaction between agents is a key problem as much as their description through analytical or simulation means. The chapter reviews different approaches for modeling agents' behavior, taking into account either explicit spatial (lattice based) structures or networks. Some emphasis is placed on recent ABM as applied to the description of the dynamics of the geographical distribution of economic activities, - out of equilibrium. The Eurace@Unibi Model, an agent-based macroeconomic model with spatial structure, is used to illustrate the potential of such an approach for spatial policy analysis.Comment: 26 pages, 5 figures, 105 references; a chapter prepared for the book "Complexity and Geographical Economics - Topics and Tools", P. Commendatore, S.S. Kayam and I. Kubin, Eds. (Springer, in press, 2014