The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex

A Demonstration Study of Drainage Water Management in Eastern South Dakota

Subsurface drainage is a common water management practice for improving crop production in poorly drained soils; however, the practice is associated with several environmental concerns such as nutrient losses to downstream surface waters. These environmental concerns from subsurface drainage have prompted interest in drainage water management strategies such as controlled drainage. This study assessed the agronomic and environmental impacts of drainage water management in eastern South Dakota by using two demonstration plots for controlled and conventional drainage. Drain flow, nitrate and dissolved phosphorous concentration in drain water, shallow groundwater, crop yield, residual soil nitrate, soil moisture and temperature, soil penetration resistance, bulk density, soil pH, and leaf area index (LAI) were measured from 2014 to 2016 from the two adjacent drainage plots. Soybean, oats, and corn were planted in 2014, 2015, and 2016, respectively with urea fertilizer applied during the corn year. Results showed that controlled drainage reduced drain flow by 58% compared to conventional drainage. Nitrate concentration in drain water increased and exceeded maximum contaminant level (10 mg/L) for drinking water in both controlled and conventional drainage plots during the second project year. Annual nitrate load was reduced by 55% with controlled drainage compared to conventional drainage. Nitrate concentration in shallow groundwater was slightly higher in the conventional drainage plot than in the controlled drainage plot, and generally higher than 10 mg/L for both plots. Dissolved phosphorous concentration in drain water and shallow groundwater exceeded the critical level of 0.03 mg/L for freshwater eutrophication. The dissolved phosphorous concentration in drain water was higher in controlled drainage compared to conventional drainage; but significantly higher in conventional drainage compared to controlled drainage in shallow groundwater samples (p \u3c 0.05). Unlike nitrate load, controlled drainage increased dissolved phosphorous load by 35% compared to conventional drainage. Shallow groundwater table was significantly higher in the controlled drainage plot than in the conventional drainage plot. The soil moisture content near the outlet and middle of plots was higher in the conventional drainage plot than in the controlled drainage plot at all depths, except for 20 cm depth in the middle of controlled drainage plot and 105 cm depth near the plot outlet in the conventional drainage plot. Soil temperature and penetration resistance showed no statistical difference in mean between the controlled and conventional drainage plots. However, the controlled drainage plot had slightly higher soil temperature than the conventional drainage plot, and slightly higher soil penetration resistance was measured in the conventional drainage plot. Mean residual soil nitrate content in the controlled drainage plot was significantly higher than in the conventional drainage plot. Controlled drainage showed 8% less yield for soybean, and 9% less yield for corn, while 5% increase in yield for oats was observed in controlled drainage compared to conventional drainage. Comparison of LAI between the controlled and conventional drainage plots was statistically not significant. However, the controlled drainage plot had slightly higher LAI than the conventional drainage plot

Reshaping Third-Party Funding

Third-party funding is a controversial business arrangement whereby an outside entity—called a third-party funder—finances the legal representation of a party involved in litigation or arbitration or finances a law firm’s portfolio of cases in return for a profit. Attorney ethics regulations and other laws permit nonlawyers to become partial owners of law firms in the District of Columbia, England and Wales, Scotland, Australia, two provinces in Canada, Germany, the Netherlands, New Zealand, and other jurisdictions around the world. Recently, a U.S.-based third-party funder that is publicly traded in England started its own law firm in England. In addition, some U.S. law firms are actively seeking advice (including from this Author) regarding partnering with third-party funders or starting their own internal third- party funders to fund their own cases, both of which are controversial practices. This Article analyzes the benefits and drawbacks of third-party funders becoming internal partners of U.S. law firms, rather than remaining as external investors. To that end, this Article diagrams the existing structure of the third-party funding transaction and suggests new possible structures. This Article then explores how those new structures may affect procedure, evidentiary, and ethics rules and reshape both the third-party funding industry and the legal services industry. This Article concludes that careful, limited experimentation would reveal whether such a practice is a viable, desirable addition to the menu of third-party funding transactions or whether the existing third-party funding transaction paradigm remains the best option. Ultimately, this Article aims to start a conversation about rethinking the structure of third-party funding transactions

A Model for Lysogenic and Lytic Cycle For Bacteria-Bacteriophage Interaction

Bacteriophage is a kind of virus that infects the bacteria by often following two life cycles. The one which is very common is the lytic path cycle and the other less common is the lysogenic cycle. In this article, a mathematical model consisting of two path cycles for bacteria-bacteriophage interaction has been proposed and studied. The underlying mathematical model is analyzed for local stability that helps to derive the local behaviour. A simple Hopf bifurcation analysis is carried out for the existence of possible small amplitude periodic solutions. Numerical investigations have been performed to check the validity of the conditions and derive the long-term dynamics of the model equations. These studies facilitate us to draw the possible consequences of bacterial infection.Saroj Kumar Sahani, A Model for Lysogenic and Lytic Cycle For Bacteria-Bacteriophage Interaction, J. Innovation Sciences and Sustainable Technologies, 3(3)(2023), 111 - 138. https://doie.org/10.0904/JISST.2023363133, Email:[email protected]

Convolutional higher order matching pursuit

We introduce a greedy generalised convolutional algorithm to efficiently locate an unknown number of sources in a series of (possibly multidimensional) images, where each source contributes a localised and low-dimensional but otherwise variable signal to its immediate spatial neighbourhood. Our approach extends convolutional matching pursuit in two ways: first, it takes the signal generated by each source to be a variable linear combination of aligned dictionary elements; and second, it executes the pursuit in the domain of high-order multivariate cumulant statistics. The resulting algorithm adapts to varying signal and noise distributions to flexibly recover source signals in a variety of settings

Adsorption and Diffusion of Gases in Nano-Porous Materials

In this work, a systematic computational study directed toward developing a molecular-level understanding of gas adsorption and diffusion characteristics in nano-porous materials is presented. Two different types of porous adsorbents were studied, one crystalline and the other amorphous. Physisorption and diffusion of hydrogen in ten iso-reticular metal-organic frameworks (IRMOFs) were investigated. A set of nine adsorbents taken from a class of novel, amorphous nano-porous materials composed of spherosilicate building blocks and isolated metal sites was also studied, with attention paid to the adsorptive and diffusive behavior of hydrogen, methane, carbon dioxide and their binary mixtures. Both classes of materials were modeled to correspond to experimentally synthesized materials. While much research has targeted adsorption in IRMOFs, very little has appeared for these amorphous silicates, which contain cubic silicate building blocks: Si8O20 [spherosilicate units], cross-linked by SiCl2O2 [silicon chloride] bridges and decorated with either -OTiCl3 [titanium chloride] or -OSiMe3 [trimethylsilyl] groups. Based only on physisorption, the amorphous silicates show competitive adsorptive capacities and selectivities with other commercial gas adsorbents. The tools employed in this dissertation were computational in nature. Adsorptive properties, such as adsorption isotherms, binding energies and selectivities, were generated from Grand Canonical Monte Carlo molecular (GCMC) simulations. Self-diffusivities and activation energies for diffusion were generated using Molecular Dynamics simulations. Adsorption isotherms are reported at temperatures of 77 K [Kelvin] and 300 K for pressures ranging up to 100 bar. The most favorable adsorption sites for all gases studied in the amorphous silicates are located in front of the faces of the spherosilicate cubes. Regardless of material, the hydrogen adsorption process is governed by entropic considerations at 300 K. At 77 K energetic considerations control hydrogen adsorption at low pressures and entropic effects dominate at high pressure. For methane and carbon dioxide at 300 K, the adsorption process is governed by energetic considerations at low pressure and by entropic (packing) constraints at high pressure. The amorphous silicates showed very high selectivity for carbon dioxide over hydrogen. The presence of titanium sitesdid not enhance physisorptive capacity or selectivity