The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity

We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we extract the optimal couplings for subsets of size up to 200 neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with those found from Boltzmann learning. Two of these methods- inversion of the TAP equations and an approximation proposed by Sessak and Monasson- are remarkably accurate. Using these approximations for larger subsets of neurons, we find that extracting couplings using data from a subset smaller than the full network tends systematically to overestimate their magnitude. This effect is described qualitatively by infinite-range spin glass theory for the normal phase. We also show that a globally-correlated input to the neurons in the network lead to a small increase in the average coupling. However, the pair-to-pair variation of the couplings is much larger than this and reflects intrinsic properties of the network. Finally, we study the quality of these models by comparing their entropies with that of the data. We find that they perform well for small subsets of the neurons in the network, but the fit quality starts to deteriorate as the subset size grows, signalling the need to include higher order correlations to describe the statistics of large networks.Comment: 12 pages, 10 figure

Newly-Discovered Planets Orbiting HD~5319, HD~11506, HD~75784 and HD~10442 from the N2K Consortium

Initially designed to discover short-period planets, the N2K campaign has since evolved to discover new worlds at large separations from their host stars. Detecting such worlds will help determine the giant planet occurrence at semi-major axes beyond the ice line, where gas giants are thought to mostly form. Here we report four newly-discovered gas giant planets (with minimum masses ranging from 0.4 to 2.1 MJup) orbiting stars monitored as part of the N2K program. Two of these planets orbit stars already known to host planets: HD 5319 and HD 11506. The remaining discoveries reside in previously-unknown planetary systems: HD 10442 and HD 75784. The refined orbital period of the inner planet orbiting HD 5319 is 641 days. The newly-discovered outer planet orbits in 886 days. The large masses combined with the proximity to a 4:3 mean motion resonance make this system a challenge to explain with current formation and migration theories. HD 11506 has one confirmed planet, and here we confirm a second. The outer planet has an orbital period of 1627.5 days, and the newly-discovered inner planet orbits in 223.6 days. A planet has also been discovered orbiting HD 75784 with an orbital period of 341.7 days. There is evidence for a longer period signal; however, several more years of observations are needed to put tight constraints on the Keplerian parameters for the outer planet. Lastly, an additional planet has been detected orbiting HD 10442 with a period of 1043 days.Comment: Accepted for publication in Ap

Incompatibilism and the Fixity of the Past

A style of argument that calls into question our freedom (in the sense that involves freedom to do otherwise) has been around for millennia; it can be traced back to Origen. The argument-form makes use of the crucial idea that the past is over-and-done-with and thus fixed; we cannot now do anything about the distant past (or, for that matter, the recent past)—it is now too late. Peter van Inwagen has presented this argument (what he calls the Consequence Argument) in perhaps its clearest and most forceful way, but debate over the argument has arguably reached a stalemate. Recently, however, Wes Holliday has attempted to break this seeming stalemate by presenting a new argument for the Principle of the Fixity of the Past. Holliday’s argument is subtle and ingenious, and worthy of serious consideration, especially given the promise it holds for genuinely advancing this old debate. In what follows, however, we argue that despite its considerable ingenuity, Holliday’s argument fails to convince, and the stalemate appears to remain