Lower Bounds on Mutual Information

We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear correlations depend on the marginal (single variable) distributions. This is so in spite of the invariance of MI under reparametrizations, because linear correlations are not invariant under them. The simplest bounds are obtained for Gaussians, but the most interesting ones for practical purposes are obtained for uniform marginal distributions. The latter can be enforced in general by using the ranks of the individual variables instead of their actual values, in which case one obtains bounds on MI in terms of Spearman correlation coefficients. We show with gene expression data that these bounds are in general non-trivial, and the degree of their (non-)saturation yields valuable insight.Comment: 4 page

High-Fidelity Multi-Rotor Unmanned Aircraft System Simulation Development for Trajectory Prediction Under Off-Nominal Flight Dynamics

The NASA Unmanned Aircraft System (UAS) Traffic Management (UTM) project is conducting research to enable civilian low-altitude airspace and UAS operations. A goal of this project is to develop probabilistic methods to quantify risk during failures and off nominal flight conditions. An important part of this effort is the reliable prediction of feasible trajectories during off-nominal events such as control failure, atmospheric upsets, or navigation anomalies that can cause large deviations from the intended flight path or extreme vehicle upsets beyond the normal flight envelope. Few examples of high-fidelity modeling and prediction of off-nominal behavior for small UAS (sUAS) vehicles exist, and modeling requirements for accurately predicting flight dynamics for out-of-envelope or failure conditions are essentially undefined. In addition, the broad range of sUAS aircraft configurations already being fielded presents a significant modeling challenge, as these vehicles are often very different from one another and are likely to possess dramatically different flight dynamics and resultant trajectories and may require different modeling approaches to capture off-nominal behavior. NASA has undertaken an extensive research effort to define sUAS flight dynamics modeling requirements and develop preliminary high fidelity six degree-of-freedom (6-DOF) simulations capable of more closely predicting off-nominal flight dynamics and trajectories. This research has included a literature review of existing sUAS modeling and simulation work as well as development of experimental testing methods to measure and model key components of propulsion, airframe and control characteristics. The ultimate objective of these efforts is to develop tools to support UTM risk analyses and for the real-time prediction of off-nominal trajectories for use in the UTM Risk Assessment Framework (URAF). This paper focuses on modeling and simulation efforts for a generic quad-rotor configuration typical of many commercial vehicles in use today. An overview of relevant off-nominal multi-rotor behaviors will be presented to define modeling goals and to identify the prediction capability lacking in simplified models of multi-rotor performance. A description of recent NASA wind tunnel testing of multi-rotor propulsion and airframe components will be presented illustrating important experimental and data acquisition methods, and a description of preliminary propulsion and airframe models will be presented. Lastly, examples of predicted off-nominal flight dynamics and trajectories from the simulation will be presented

Punishment First: A Study of Juvenile Pretrial Detention

How society and the legal system should respond to youth crime is a volatile issue. Much research exists on this topic broadly. A largely overlooked subset exists regarding the rights of juveniles in the United States who face pretrial confinement, specifically how juveniles accused of delinquency are treated by the courts. Delinquency or a delinquent act, in the context of this study, is “an act that would be considered a crime if committed by an adult.”7. Adults and children are processed by the courts differently, each with their own rights and court mandated procedures to follow. This report analyzes juvenile detention with specific focus on the U.S. Supreme Court case Schall v. Martin (783) and how this case affects juveniles in the court system today.4

Link and subgraph likelihoods in random undirected networks with fixed and partially fixed degree sequence

The simplest null models for networks, used to distinguish significant features of a particular network from {\it a priori} expected features, are random ensembles with the degree sequence fixed by the specific network of interest. These "fixed degree sequence" (FDS) ensembles are, however, famously resistant to analytic attack. In this paper we introduce ensembles with partially-fixed degree sequences (PFDS) and compare analytic results obtained for them with Monte Carlo results for the FDS ensemble. These results include link likelihoods, subgraph likelihoods, and degree correlations. We find that local structural features in the FDS ensemble can be reasonably well estimated by simultaneously fixing only the degrees of few nodes, in addition to the total number of nodes and links. As test cases we use a food web, two protein interaction networks (\textit{E. coli, S. cerevisiae}), the internet on the autonomous system (AS) level, and the World Wide Web. Fixing just the degrees of two nodes gives the mean neighbor degree as a function of node degree, $_k$, in agreement with results explicitly obtained from rewiring. For power law degree distributions, we derive the disassortativity analytically. In the PFDS ensemble the partition function can be expanded diagrammatically. We obtain an explicit expression for the link likelihood to lowest order, which reduces in the limit of large, sparse undirected networks with $L$ links and with $k_{\rm max} \ll L$ to the simple formula $P(k,k') = kk'/(2L + kk')$. In a similar limit, the probability for three nodes to be linked into a triangle reduces to the factorized expression $P_{\Delta}(k_1,k_2,k_3) = P(k_1,k_2)P(k_1,k_3)P(k_2,k_3)$.Comment: 17 pages, includes 11 figures; first revision: shortened to 14 pages (7 figures), added discussion of subgraph counts, deleted discussion of directed network

Four Centuries of Change in Northeastern United States Forests

The northeastern United States is a predominately-forested region that, like most of the eastern U.S., has undergone a 400-year history of intense logging, land clearance for agriculture, and natural reforestation. This setting affords the opportunity to address a major ecological question: How similar are today's forests to those existing prior to European colonization? Working throughout a nine-state region spanning Maine to Pennsylvania, we assembled a comprehensive database of archival land-survey records describing the forests at the time of European colonization. We compared these records to modern forest inventory data and described: (1) the magnitude and attributes of forest compositional change, (2) the geography of change, and (3) the relationships between change and environmental factors and historical land use. We found that with few exceptions, notably the American chestnut, the same taxa that made up the pre-colonial forest still comprise the forest today, despite ample opportunities for species invasion and loss. Nonetheless, there have been dramatic shifts in the relative abundance of forest taxa. The magnitude of change is spatially clustered at local scales (<125 km) but exhibits little evidence of regional-scale gradients. Compositional change is most strongly associated with the historical extent of agricultural clearing. Throughout the region, there has been a broad ecological shift away from late successional taxa, such as beech and hemlock, in favor of early- and mid-successional taxa, such as red maple and poplar. Additionally, the modern forest composition is more homogeneous and less coupled to local climatic controls

"Development and Neutronic Validation of pelletized Cold and Very Cold Moderators for Pulsed Neutron Sources" Phase II Final report

Intense beams of cold neutrons are produced at several DOE facilities and are used by researchers to study the microscopic structure of materials. Energetic neutrons are produced by a high energy proton beam impacting a target. The fast neutrons are converted to the desired cold neutrons passing through a cryogenic moderator vessel, presently filled with dense cold hydrogen gas. Moderators made from solid methane have demonstrated superior performance to the hydrogen moderators but cannot be implemented on high power sources such as the SNS due to the difficulty of removing heat from the solid blocks of methane. Cryogenic Applications F, Inc has developed the methane pellet formation and transport technologies needed to produce a hydrogen cooled solid methane pellet moderator, potentially capable of being used in a high power spallation neutron facility. Such a methane pellet moderator could double the brightness of the neutron beam. Prior to this work a methane pellet moderator had not been produced or studied. The Indiana University LENS facility is a small pulsed neutron source used in part to study and develop cold neutron moderators. In this project cold neutrons were produced in a solid methane pellet moderator and analyzed with the LENS facility diagnostics. The results indicated that the neutron beam formed by the pellet moderator was similar to that of a solid methane block moderator

Equatorial paleomagnetic time-averaged field results from 0-5 Ma lavas from Kenya and the latitudinal variation of angular dispersion

Lavas of Pliocene-Pleistocene age were sampled in two regions in Kenya: Mount Kenya on the equator and the Loiyangalani region, east of Lake Turkana, at about 3°N. We sampled 100 sites distributed around the Mount Kenya Massif and to the northeast along the Nyambini Range. The equator bisects Mount Kenya, and all sites were sampled within 40′ of the equator. Thirty-two sites were sampled in the Loiyangalani area, making a total of 132 sites. Many sites from the Mount Kenya study were severely affected by lightning; however, after progressive AF demagnetization 69 sites yielded directions with α_95 equal to or less than 10°. Normal polarity sites dominate (N = 58 and a mean of declination (dec) = 1.2°, inclination (inc) = -0.7°, and α_95 = 3.6°) with only 11 reverse polarity sites (mean of dec = 182.3°, inc = 0.6°, and α_95 = 7.2°); no transitional directions were identified. Inverting the reverse sites yields a combined mean direction of dec = l.4°, inc = -0.7°, and α_95 = 3.2°. This result is not significantly different from what is expected from the geocentric axial dipole for the mean locality (dec = 0° and inc = 0°); a quadrupole component was not resolved. The samples from the Loiyangalani region were not seriously affected by lightning, and all 32 sites gave satisfactory data with α_95 less than 10° (17 reverse sites, dec = 183.4°, inc = 0.8°, and α_95 = 6.7°; 15 normal sites, dec = 358.6°, inc = -1.1°, and ° = 4.7°); after inverting the reverse sites the combined mean was dec = 1.1°, inc = -1.0°, and α_95 = 4.1°. Altogether, we had a total of 101 successful sites. A virtual geomagnetic pole (VGP) was calculated from each site mean; the VGP dispersion is low, with Sb = 10.9° for Mount Kenya and 9.8° for the Loiyangalani region. This dispersion agrees with updated Model G of McElhinny and McFadden (1997) and model TK03 of Tauxe and Kent (2004) that was tuned to the compilation of McElhinny and McFadden (1997) but disagrees with the higher dispersion near the equator and the smaller latitudinal gradient in dispersion estimated by Johnson et al. (2008). A new database is presented, and the included studies support a systematic decrease of dispersion from high to low latitudes

Phycomyces

This monographic review on a fungus is not addressed to mycologists. None of the authors has been trained or has otherwise acquired a general proficiency in mycology. They are motivated by a common interest in the performances of signal handling exhibited by the sense organs of all organisms and by the desire to attack these as yet totally obscure aspects of molecular biology by the study of a microorganism with certain desirable properties. The sporangiophore of the fungus Phycomyces is a gigantic, single-celled, erect, cylindrical, aerial hypha. It is sensitive to at least four distinct stimuli: light, gravity, stretch, and some unknown stimulus by which it avoids solid objects. These stimuli control a common output, the growth rate, producing either temporal changes in growth rate or tropic responses. We are interested in the output because it gives us information about the reception of the various signals. In the absence of external stimuli, the growth rate is controlled by internal signals keeping the network of biochemical processes in balance. The external stimuli interact with the internal signals. We wish to inquire into the early steps of this interaction. For light, for instance, the cell must have a receptor pigment as the first mediator. What kind of a molecule is this pigment? Which organelle contains it? What chemical reaction happens after a light quantum has been absorbed? And how is the information introduced by this primary photochemical event amplified in a controlled manner and processed in the next step? How do a few quanta or a few molecules trigger macroscopic responses? Will we find ourselves confronted with devices wholly distinct from anything now known in biology