A Herding Model with Preferential Attachment and Fragmentation

We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either (i) with probability p an incoming agent joins an existing group, or (ii) with probability 1-p a group is fragmented into individual agents. The group size distribution is found to be power-law with an exponent that depends continuously on p. A number of variants of our basic model are discussed. Comparisons are made between these models and other models of herding and random growing networks

A model for the size distribution of customer groups and businesses

We present a generalization of the dynamical model of information transmission and herd behavior proposed by Eguiluz and Zimmermann. A characteristic size of group of agents s0 is introduced. The fragmentation and coagulation rates of groups of agents are assumed to depend on the size of the group. We present results of numerical simulations and mean field analysis. It is found that the size distribution of groups of agents ns exhibits two distinct scaling behavior depending on s ≤ s0 or s > s0. For s ≤ s0, ns ∼ s-(5/2 + δ), while for s > s0, ns ∼ s-(5/2 -δ), where δ is a model parameter representing the sensitivity of the fragmentation and coagulation rates to the size of the group. Our model thus gives a tunable exponent for the size distribution together with two scaling regimes separated by a characteristic size s0. Suitably interpreted, our model can be used to represent the formation of groups of customers for certain products produced by manufacturers. This, in turn, leads to a distribution in the size of businesses. The characteristic size s0, in this context, represents the size of a business for which the customer group becomes too large to be kept happy but too small for the business to become a brand name

Non-universal scaling and dynamical feedback in generalized models of financial markets

We study self-organized models for information transmission and herd behavior in financial markets. Existing models are generalized to take into account the effect of size-dependent fragmentation and coagulation probabilities of groups of agents and to include a demand process. Non-universal scaling with a tunable exponent for the group size distribution is found in the resulting system. We also show that the fragmentation and coagulation probabilities of groups of agents have a strong influence on the average investment rate of the system

Signals of Disoriented Chiral Condensate

If a disoriented chiral condensate is created over an extended space-time region following a rapid cooling in hadronic or nuclear collisions, the misalignment of the condensate with the electroweak symmetry breaking can generate observable effects in the processes which involve both strong and electromagnetic interactions. We point out the relevance of the dilepton decay of light vector mesons as a signal for formation of the disoriented condensate. We predict that the decay \rho^0 to dileptons will be suppressed and/or the \rho resonance peak widens, while the decay \omega to dileptons will not be affected by the condensate.Comment: 13 pages in LaTeX, UCB-PTH-94/05, LBL-3533

Cluster Structure of Disoriented Chiral Condensates in Rapidity Distribution

We study the creation of disoriented chiral condensates with some initial boundary conditions that may be expected in the relativistic heavy ion collisions. The equations of motion in the linear $\sigma$-model are solved numerically with and without a Lorentz-boost invariance. We suggest that a distinct cluster structure of coherent pion production in the rapidity distribution may emerge due to a quench and may be observed in experiments.Comment: 10 pages in LaTex, 2 uuencoded ps figures, LBL-3493

Spin squeezing and pairwise entanglement for symmetric multiqubit states

We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits greater than 1 or via the two-axis counter-twisting Hamiltonian for any even number of qubits, the numerical results suggest that such states are spin squeezed if and only if they are pairwise entangled.Comment: 6 pages. Version 3: Small corrections were mad

The vitamin D receptor is involved in the regulation of human breast cancer cell growth via a ligand-independent function in cytoplasm

Vitamin D has pleiotropic effects on multiple tissues, including malignant tumors. Vitamin D inhibits breast cancer growth through activation of the vitamin D receptor (VDR) and via classical nuclear signaling pathways. Here, we demonstrate that the VDR can also function in the absence of its ligand to control behaviour of human breast cancer cells both outside and within the bone microenvironment. Stable shRNA expression was used to knock down VDR expression in MCF-7 cells, generating two VDR knockdown clonal lines. In ligand-free culture, knockdown of VDR in MCF-7 cells significantly reduced proliferation and increased apoptosis, suggesting that the VDR plays a ligand-independent role in cancer cell growth. Implantation of these VDR knockdown cells into the mammary fat pad of nude mice resulted in reduced tumor growth in vivo compared with controls. In the intra-tibial xenograft model, VDR knockdown greatly reduced the ability of the cells to form tumors in the bone microenvironment. The in vitro growth of VDR knockdown cells was rescued by the expression of a mutant form of VDR which is unable to translocate to the nucleus and hence accumulates in the cytoplasm. Thus, our data indicate that in the absence of ligand, the VDR promotes breast cancer growth both in vitro and in vivo and that cytoplasmic accumulation of VDR is sufficient to produce this effect in vitro. This new mechanism of VDR action in breast cancer cells contrasts the known anti-proliferative nuclear actions of the VDR-vitamin D ligand complex

Multiplicity Studies and Effective Energy in ALICE at the LHC

In this work we explore the possibility to perform ``effective energy'' studies in very high energy collisions at the CERN Large Hadron Collider (LHC). In particular, we focus on the possibility to measure in $pp$ collisions the average charged multiplicity as a function of the effective energy with the ALICE experiment, using its capability to measure the energy of the leading baryons with the Zero Degree Calorimeters. Analyses of this kind have been done at lower centre--of--mass energies and have shown that, once the appropriate kinematic variables are chosen, particle production is characterized by universal properties: no matter the nature of the interacting particles, the final states have identical features. Assuming that this universality picture can be extended to {\it ion--ion} collisions, as suggested by recent results from RHIC experiments, a novel approach based on the scaling hypothesis for limiting fragmentation has been used to derive the expected charged event multiplicity in $AA$ interactions at LHC. This leads to scenarios where the multiplicity is significantly lower compared to most of the predictions from the models currently used to describe high energy $AA$ collisions. A mean charged multiplicity of about 1000-2000 per rapidity unit (at $\eta \sim 0$) is expected for the most central $Pb-Pb$ collisions at $\sqrt{s_{NN}} = 5.5 TeV$.Comment: 12 pages, 19 figures. In memory of A. Smirnitski

Isotropic-nematic phase equilibria in the Onsager theory of hard rods with length polydispersity

We analyse the effect of a continuous spread of particle lengths on the phase behavior of rodlike particles, using the Onsager theory of hard rods. Our aim is to establish whether ``unusual'' effects such as isotropic-nematic-nematic (I-N-N) phase separation can occur even for length distributions with a single peak. We focus on the onset of I-N coexistence. For a log-normal distribution we find that a finite upper cutoff on rod lengths is required to make this problem well-posed. The cloud curve, which tracks the density at the onset of I-N coexistence as a function of the width of the length distribution, exhibits a kink; this demonstrates that the phase diagram must contain a three-phase I-N-N region. Theoretical analysis shows that in the limit of large cutoff the cloud point density actually converges to zero, so that phase separation results at any nonzero density; this conclusion applies to all length distributions with fatter-than-exponentail tails. Finally we consider the case of a Schulz distribution, with its exponential tail. Surprisingly, even here the long rods (and hence the cutoff) can dominate the phase behaviour, and a kink in the cloud curve and I-N-N coexistence again result. Theory establishes that there is a nonzero threshold for the width of the length distribution above which these long rod effects occur, and shows that the cloud and shadow curves approach nonzero limits for large cutoff, both in good agreement with the numerical results.Comment: 20 pages, 13 figure