145 research outputs found
Markov chains and optimality of the Hamiltonian cycle
We consider the Hamiltonian cycle problem (HCP) embedded in a controlled Markov decision process. In this setting, HCP reduces to an optimization problem on a set of Markov chains corresponding to a given graph. We prove that Hamiltonian cycles are minimizers for the trace of the fundamental matrix on a set of all stochastic transition matrices. In case of doubly stochastic matrices with symmetric linear perturbation, we show that Hamiltonian cycles minimize a diagonal element of a fundamental matrix for all admissible values of the perturbation parameter. In contrast to the previous work on this topic, our arguments are primarily based on probabilistic rather than algebraic methods
The Impact of Litigation on Venture Capitalist Reputation
Venture capital contracts give VCs enormous power over entrepreneurs and early equity investors of portfolio companies. A large literature examines how these contractual terms protect VCs against misbehavior by entrepreneurs. But what constrains misbehavior by VCs? We provide the first systematic analysis of legal and non-legal mechanisms that penalize VC misbehavior, even when such misbehavior is formally permitted by contract. We hand-collect a sample of over 177 lawsuits involving venture capitalists. The three most common types of VC-related litigation are: 1) lawsuits filed by entrepreneurs, which most often allege freezeout and transfer of control away from founders; 2) lawsuits filed by early equity investors in startup companies; and 3) lawsuits filed by VCs. Our empirical analysis of the lawsuit data proceeds in two steps. We first estimate an empirical model of the propensity of VCs to get involved in litigation as a function of VC characteristics. We match each venture firm that was involved in litigation to otherwise similar venture firm that was not involved in litigation and find that less reputable VCs are more likely to participate in litigation, as are VCs focusing on early-stage investments, and VCs with larger deal flow. Second, we analyze the relationship between different types of lawsuits and VC fundraising and deal flow. Although plaintiffs lose most VC-related lawsuits, litigation does not go unnoticed: in subsequent years, the involved VCs raise significantly less capital than their peers and invest in fewer deals. The biggest losers are VCs who were defendants in a lawsuit, and especially VCs who were alleged to have expropriated founders.
Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling
Identifying a coupled dynamical system out of many plausible candidates, each
of which could serve as the underlying generator of some observed measurements,
is a profoundly ill posed problem that commonly arises when modelling real
world phenomena. In this review, we detail a set of statistical procedures for
inferring the structure of nonlinear coupled dynamical systems (structure
learning), which has proved useful in neuroscience research. A key focus here
is the comparison of competing models of (ie, hypotheses about) network
architectures and implicit coupling functions in terms of their Bayesian model
evidence. These methods are collectively referred to as dynamical casual
modelling (DCM). We focus on a relatively new approach that is proving
remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid
evaluation and comparison of models that differ in their network architecture.
We illustrate the usefulness of these techniques through modelling
neurovascular coupling (cellular pathways linking neuronal and vascular
systems), whose function is an active focus of research in neurobiology and the
imaging of coupled neuronal systems
Investigating cortico-striatal beta oscillations in Parkinson's disease cognitive decline
This scientific commentary refers to ‘Corticostriatal beta oscillation changes associated with cognitive function in Parkinson’s disease’ by Paulo et al. (https://doi.org/10.1093/brain/awad206)
A tutorial on group effective connectivity analysis, part 2: second level analysis with PEB
This tutorial provides a worked example of using Dynamic Causal Modelling
(DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject
variability in neural circuitry (effective connectivity). This involves
specifying a hierarchical model with two or more levels. At the first level,
state space models (DCMs) are used to infer the effective connectivity that
best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG).
Subject-specific connectivity parameters are then taken to the group level,
where they are modelled using a General Linear Model (GLM) that partitions
between-subject variability into designed effects and additive random effects.
The ensuing (Bayesian) hierarchical model conveys both the estimated connection
strengths and their uncertainty (i.e., posterior covariance) from the subject
to the group level; enabling hypotheses to be tested about the commonalities
and differences across subjects. This approach can also finesse parameter
estimation at the subject level, by using the group-level parameters as
empirical priors. We walk through this approach in detail, using data from a
published fMRI experiment that characterised individual differences in
hemispheric lateralization in a semantic processing task. The preliminary
subject specific DCM analysis is covered in detail in a companion paper. This
tutorial is accompanied by the example dataset and step-by-step instructions to
reproduce the analyses
Neurovascular coupling: insights from multi-modal dynamic causal modelling of fMRI and MEG
This technical note presents a framework for investigating the underlying
mechanisms of neurovascular coupling in the human brain using multi-modal
magnetoencephalography (MEG) and functional magnetic resonance (fMRI)
neuroimaging data. This amounts to estimating the evidence for several
biologically informed models of neurovascular coupling using variational
Bayesian methods and selecting the most plausible explanation using Bayesian
model comparison. First, fMRI data is used to localise active neuronal sources.
The coordinates of neuronal sources are then used as priors in the
specification of a DCM for MEG, in order to estimate the underlying generators
of the electrophysiological responses. The ensuing estimates of neuronal
parameters are used to generate neuronal drive functions, which model the pre
or post synaptic responses to each experimental condition in the fMRI paradigm.
These functions form the input to a model of neurovascular coupling, the
parameters of which are estimated from the fMRI data. This establishes a
Bayesian fusion technique that characterises the BOLD response - asking, for
example, whether instantaneous or delayed pre or post synaptic signals mediate
haemodynamic responses. Bayesian model comparison is used to identify the most
plausible hypotheses about the causes of the multimodal data. We illustrate
this procedure by comparing a set of models of a single-subject auditory fMRI
and MEG dataset. Our exemplar analysis suggests that the origin of the BOLD
signal is mediated instantaneously by intrinsic neuronal dynamics and that
neurovascular coupling mechanisms are region-specific. The code and example
dataset associated with this technical note are available through the
statistical parametric mapping (SPM) software package
Breaking the Circularity in Circular Analyses: Simulations and Formal Treatment of the Flattened Average Approach
There has been considerable debate and concern as to whether there is a replication crisis in the scientific literature. A likely cause of poor replication is the multiple comparisons problem. An important way in which this problem can manifest in the M/EEG context is through post hoc tailoring of analysis windows (a.k.a. regions-of-interest, ROIs) to landmarks in the collected data. Post hoc tailoring of ROIs is used because it allows researchers to adapt to inter-experiment variability and discover novel differences that fall outside of windows defined by prior precedent, thereby reducing Type II errors. However, this approach can dramatically inflate Type I error rates. One way to avoid this problem is to tailor windows according to a contrast that is orthogonal (strictly parametrically orthogonal) to the contrast being tested. A key approach of this kind is to identify windows on a fully flattened average. On the basis of simulations, this approach has been argued to be safe for post hoc tailoring of analysis windows under many conditions. Here, we present further simulations and mathematical proofs to show exactly why the Fully Flattened Average approach is unbiased, providing a formal grounding to the approach, clarifying the limits of its applicability and resolving published misconceptions about the method. We also provide a statistical power analysis, which shows that, in specific contexts, the fully flattened average approach provides higher statistical power than Fieldtrip cluster inference. This suggests that the Fully Flattened Average approach will enable researchers to identify more effects from their data without incurring an inflation of the false positive rate
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