On spectral hypergraph theory of the adjacency tensor

We study both $H$ and $E/Z$-eigenvalues of the adjacency tensor of a uniform multi-hypergraph and give conditions for which the largest positive $H$ or $Z$-eigenvalue corresponds to a strictly positive eigenvector. We also investigate when the $E$-spectrum of the adjacency tensor is symmetric

Toward a Theory of Marginally Efficient Markets

Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it favorable games}, in the sense that there is a small probabilistic edge that smart speculators can exploit. We propose to identify this probability using conditional entropy concept. A perfect random walk has this entropy maximized, and departure from the maximal value represents a price history's predictability. We propose that market participants should be divided into two categories: producers and speculators. The former provides the negative entropy into the price, upon which the latter feed. We show that the residual negative entropy can never be arbitraged away: infinite arbitrage capital is needed to make the price a perfect random walk.Comment: 9 pages, 3 ps figure

Thermal Spin-Transfer Torques in Magnetoelectronic Devices

We predict that the magnetization direction of a ferromagnet can be reversed by the spin-transfer torque accompanying spin-polarized thermoelectric heat currents. We illustrate the concept by applying a finite-element theory of thermoelectric transport in disordered magnetoelectronic circuits and devices to metallic spin valves. When thermalization is not complete, a spin heat accumulation vector is found in the normal metal spacer, i.e., a directional imbalance in the temperature of majority and minority spins.Comment: Accepted for publication by Physical Review Letter

Dark Matter and Neutrino Mass from the Smallest Non-Abelian Chiral Dark Sector

All pieces of concrete evidence for phenomena outside the standard model (SM) - neutrino masses and dark matter - are consistent with the existence of new degrees of freedom that interact very weakly, if at all, with those in the SM. We propose that these new degrees of freedom organize themselves into a simple dark sector, a chiral SU(3) x SU(2) gauge theory with the smallest nontrivial fermion content. Similar to the SM, the dark SU(2) is spontaneously broken while the dark SU(3) confines at low energies. At the renormalizable level, the dark sector contains massless fermions - dark leptons - and stable massive particles - dark protons. We find that dark protons with masses between 10-100 TeV satisfy all current cosmological and astrophysical observations concerning dark matter even if dark protons are a symmetric thermal relic. The dark leptons play the role of right-handed neutrinos and allow simple realizations of the seesaw mechanism or the possibility that neutrinos are Dirac fermions. In the latter case, neutrino masses are also parametrically different from charged-fermion masses and the lightest neutrino is predicted to be massless. Since the new "neutrino" and "dark matter" degrees of freedom interact with one another, these two new-physics phenomena are intertwined. Dark leptons play a nontrivial role in early universe cosmology while indirect searches for dark matter involve, decisively, dark matter annihilations into dark leptons. These, in turn, may lead to observable signatures at high-energy neutrino and gamma-ray observatories, especially once one accounts for the potential Sommerfeld enhancement of the annihilation cross-section, derived from the low-energy dark-sector effective theory, a possibility we explore quantitatively in some detail.Comment: 35 pages, 7 figures. Matches published versio