A geometric framework to predict structure from function in neural networks

Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context. Whether certain patterns of synaptic connectivity are required to generate specific network-level computations is largely unknown. Here we introduce a geometric framework for identifying synaptic connections required by steady-state responses in recurrent networks of threshold-linear neurons. Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate the solution space of all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs. A generalization accounting for noise further reveals that the solution space geometry can undergo topological transitions as the allowed error increases, which could provide insight into both neuroscience and machine learning. We ultimately use this geometric characterization to derive certainty conditions guaranteeing a non-zero synapse between neurons. Our theoretical framework could thus be applied to neural activity data to make rigorous anatomical predictions that follow generally from the model architecture.Comment: 45 pages, 12 figures, major revision, reorganized sections, altered notations, additional main text material, additional appendix materia

Discovery of an extended debris disk around the F2V star HD 15745

Using the Advanced Camera for Surveys aboard the Hubble Space Telescope, we have discovered dust-scattered light from the debris disk surrounding the F2V star HD 15745. The circumstellar disk is detected between 2.0" and 7.5" radius, corresponding to 128 - 480 AU radius. The circumstellar disk morphology is asymmetric about the star, resembling a fan, and consistent with forward scattering grains in an optically thin disk with an inclination of ~67 degrees to our line of sight. The spectral energy distribution and scattered light morphology can be approximated with a model disk composed of silicate grains between 60 and 450 AU radius, with a total dust mass of 10E-7 M_sun (0.03 M_earth) representing a narrow grain size distribution (1 - 10 micron). Galactic space motions are similar to the Castor Moving Group with an age of ~10E+8 yr, although future work is required to determine the age of HD 15745 using other indicators.Comment: 7 pages, 4 figures, ApJ Letters, in pres

Tensor formalism for predicting synaptic connections with ensemble modeling or optimization

Theoretical neuroscientists often try to understand how the structure of a neural network relates to its function by focusing on structural features that would either follow from optimization or occur consistently across possible implementations. Both optimization theories and ensemble modeling approaches have repeatedly proven their worth, and it would simplify theory building considerably if predictions from both theory types could be derived and tested simultaneously. Here we show how tensor formalism from theoretical physics can be used to unify and solve many optimization and ensemble modeling approaches to predicting synaptic connectivity from neuronal responses. We specifically focus on analyzing the solution space of synaptic weights that allow a threshold-linear neural network to respond in a prescribed way to a limited number of input conditions. For optimization purposes, we compute the synaptic weight vector that minimizes an arbitrary quadratic loss function. For ensemble modeling, we identify synaptic weight features that occur consistently across all solutions bounded by an arbitrary quadratic function. We derive a common solution to this suite of nonlinear problems by showing how each of them reduces to an equivalent linear problem that can be solved analytically. Although identifying the equivalent linear problem is nontrivial, our tensor formalism provides an elegant geometrical perspective that allows us to solve the problem numerically. The final algorithm is applicable to a wide range of interesting neuroscience problems, and the associated geometric insights may carry over to other scientific problems that require constrained optimization.Comment: 25 pages, 5 figure

Photon Shot Noise Limits on Optical Detection of Neuronal Spikes and Estimation of Spike Timing

AbstractOptical approaches for tracking neural dynamics are of widespread interest, but a theoretical framework quantifying the physical limits of these techniques has been lacking. We formulate such a framework by using signal detection and estimation theory to obtain physical bounds on the detection of neural spikes and the estimation of their occurrence times as set by photon counting statistics (shot noise). These bounds are succinctly expressed via a discriminability index that depends on the kinetics of the optical indicator and the relative fluxes of signal and background photons. This approach facilitates quantitative evaluations of different indicators, detector technologies, and data analyses. Our treatment also provides optimal filtering techniques for optical detection of spikes. We compare various types of Ca2+ indicators and show that background photons are a chief impediment to voltage sensing. Thus, voltage indicators that change color in response to membrane depolarization may offer a key advantage over those that change intensity. We also examine fluorescence resonance energy transfer indicators and identify the regimes in which the widely used ratiometric analysis of signals is substantially suboptimal. Overall, by showing how different optical factors interact to affect signal quality, our treatment offers a valuable guide to experimental design and provides measures of confidence to assess optically extracted traces of neural activity

A Ring of Warm Dust in the HD 32297 Debris Disk

We report the detection of a ring of warm dust in the edge-on disk surrounding HD 32297 with the Gemini-N/MICHELLE mid-infrared imager. Our N'-band image shows elongated structure consistent with the orientation of the scattered-light disk. The Fnu(11.2 um) = 49.9+/-2.1 mJy flux is significantly above the 28.2+/-0.6 mJy photosphere. Subtraction of the stellar point spread function reveals a bilobed structure with peaks 0.5"-0.6" from the star. An analysis of the stellar component of the SED suggests a spectral type later than A0, in contrast to commonly cited literature values. We fit three-dimensional, single-size grain models of an optically thin dust ring to our image and the SED using a Markov chain Monte Carlo algorithm in a Bayesian framework. The best-fit effective grain sizes are submicron, suggesting the same dust population is responsible for the bulk of the scattered light. The inner boundary of the warm dust is located 0.5"-0.7" (~65 AU) from the star, which is approximately cospatial with the outer boundary of the scattered-light asymmetry inward of 0.5". The addition of a separate component of larger, cooler grains that provide a portion of the 60 um flux improves both the fidelity of the model fit and consistency with the slopes of the scattered-light brightness profiles. Previous indirect estimates of the stellar age (~30 Myr) indicate the dust is composed of debris. The peak vertical optical depths in our models (~0.3-1 x 1e-2) imply that grain-grain collisions likely play a significant role in dust dynamics and evolution. Submicron grains can survive radiation pressure blow-out if they are icy and porous. Similarly, the inferred warm temperatures (130-200 K) suggest that ice sublimation may play a role in truncating the inner disk.Comment: ApJ accepted, 8 pages, 4 figure

First scattered light images of debris disks around HD 53143 and HD 139664

We present the first scattered light images of debris disks around a K star (HD 53143) and an F star (HD 139664) using the coronagraphic mode of the Advanced Camera for Surveys (ACS) aboard the Hubble Space Telescope (HST). With ages 0.3 - 1 Gyr, these are among the oldest optically detected debris disks. HD 53143, viewed ~45 degrees from edge-on, does not show radial variation in disk structure and has width >55 AU. HD 139664 is seen close to edge-on and has belt-like morphology with a dust peak 83 AU from the star and a distinct outer boundary at 109 AU. We discuss evidence for significant diversity in the radial architecture of debris disks that appears unconnected to stellar spectral type or age. HD 139664 and possibly the solar system belong in a category of narrow belts 20-30 AU wide. HD 53143 represents a class of wide disk architecture with characteristic width >50 AU.Comment: 7 pages, 3 figure

South Virgin-White Hills detachment fault system of SE Nevada and NW Arizona: Applying apatite fission track thermochronology to constrain the tectonic evolution of a major continental detachment fault

The South Virgin-White Hills detachment (SVWHD) in the central Basin and Range province with an along-strike extent of similar to 60 km is a major continental detachment fault system. Displacement on the SVWHD decreases north to south from similar to 17 to <6 km. This is accompanied by a change in fault and footwall rock type from mylonite overprinted by cataclasite to chlorite cataclasite and then fault breccia reflecting decreasing fault displacement and footwall exhumation. Apatite fission track (AFT) thermochronology was applied both along-strike and across-strike to assess this displacement gradient. The overall thermal history reflects Laramide cooling (similar to 75 Ma) and then rapid cooling beginning in the late early Miocene. Age patterns reflect some complexity but extension along the SVWHD appears synchronous with rapid cooling initiated at similar to 17 Ma due to tectonic exhumation. Slip rate is more rapid (similar to 8.6 km/Ma) in the north compared to similar to 1 km/Ma in the south. The displacement gradient results from penecontemporaneous along-strike motion and formation of the SVWHD by linkage of originally separate fault segments that have differential displacements and hence differential slip rates. East west transverse structures likely play a role in linkage of different fault segments. The preextension paleogeothermal gradient is well constrained in the Gold Butte block as 18-20 degrees C/km. We present a new thermochronologic approach to constrain fault dip during slip, treating the vertical exhumation rate and the slip as vectors, with the angle between them used to constrain fault dip during slip through the closure temperature of a particular thermochronometer. AFT data from the western rim of the Colorado Plateau. Citation: Fitzgerald, P. G., E. M. Duebendorfer, J. E. Faulds, and P. O'Sullivan (2009), South Virgin-White Hills detachment fault system of SE Nevada and NW Arizona: Applying apatite fission track thermochronology to constrain the tectonic evolution of a major continental detachment fault, Tectonics, 28, TC2001, doi:10.1029/2007TC002194

Medication adherence in patients with myotonic dystrophy and facioscapulohumeral muscular dystrophy

Myotonic dystrophy (DM) and facioscapulohumeral muscular dystrophy (FSHD) are the two most common adult muscular dystrophies and have progressive and often disabling manifestations. Higher levels of medication adherence lead to better health outcomes, especially important to patients with DM and FSHD because of their multisystem manifestations and complexity of care. However, medication adherence has not previously been studied in a large cohort of DM type 1 (DM1), DM type 2 (DM2), and FSHD patients. The purpose of our study was to survey medication adherence and disease manifestations in patients enrolled in the NIH-supported National DM and FSHD Registry. The study was completed by 110 DM1, 49 DM2, and 193 FSHD patients. Notable comorbidities were hypertension in FSHD (44 %) and DM2 (37 %), gastroesophageal reflux disease in DM1 (24 %) and DM2 (31 %) and arrhythmias (29 %) and thyroid disease (20 %) in DM1. Each group reported high levels of adherence based on regimen complexity, medication costs, health literacy, side effect profile, and their beliefs about treatment. Only dysphagia in DM1 was reported to significantly impact medication adherence. Approximately 35 % of study patients reported polypharmacy (taking 6 or more medications). Of the patients with polypharmacy, the DM1 cohort was significantly younger (mean 55.0 years) compared to DM2 (59.0 years) and FSHD (63.2 years), and had shorter disease duration (mean 26 years) compared to FSHD (26.8 years) and DM2 (34.8 years). Future research is needed to assess techniques to ease pill swallowing in DM1 and to monitor polypharmacy and potential drug interactions in DM and FSHD

Organizing memories for generalization in complementary learning systems

Memorization and generalization are complementary cognitive processes that jointly promote adaptive behavior. For example, animals should memorize safe routes to specific water sources and generalize from these memories to discover environmental features that predict new ones. These functions depend on systems consolidation mechanisms that construct neocortical memory traces from hippocampal precursors, but why systems consolidation only applies to a subset of hippocampal memories is unclear. Here we introduce a new neural network formalization of systems consolidation that reveals an overlooked tension—unregulated neocortical memory transfer can cause overfitting and harm generalization in an unpredictable world. We resolve this tension by postulating that memories only consolidate when it aids generalization. This framework accounts for partial hippocampal–cortical memory transfer and provides a normative principle for reconceptualizing numerous observations in the field. Generalization-optimized systems consolidation thus provides new insight into how adaptive behavior benefits from complementary learning systems specialized for memorization and generalization

Recent Decisions

Comments on recent decisions by Robert E. Veverka, John W. Dell, James A. Wysocki, Theodore A. Fitzgerald, Robert W. Cox, Philip B. Byrne, Thomas R. Joyce, and Cornelius Collins