Faster Family-wise Error Control for Neuroimaging with a Parametric Bootstrap

In neuroimaging, hundreds to hundreds of thousands of tests are performed across a set of brain regions or all locations in an image. Recent studies have shown that the most common family-wise error (FWE) controlling procedures in imaging, which rely on classical mathematical inequalities or Gaussian random field theory, yield FWE rates that are far from the nominal level. Depending on the approach used, the FWER can be exceedingly small or grossly inflated. Given the widespread use of neuroimaging as a tool for understanding neurological and psychiatric disorders, it is imperative that reliable multiple testing procedures are available. To our knowledge, only permutation joint testing procedures have been shown to reliably control the FWER at the nominal level. However, these procedures are computationally intensive due to the increasingly available large sample sizes and dimensionality of the images, and analyses can take days to complete. Here, we develop a parametric bootstrap joint testing procedure. The parametric bootstrap procedure works directly with the test statistics, which leads to much faster estimation of adjusted \emph{p}-values than resampling-based procedures while reliably controlling the FWER in sample sizes available in many neuroimaging studies. We demonstrate that the procedure controls the FWER in finite samples using simulations, and present region- and voxel-wise analyses to test for sex differences in developmental trajectories of cerebral blood flow

Striatal intrinsic reinforcement signals during recognition memory: relationship to response bias and dysregulation in schizophrenia

Ventral striatum (VS) is a critical brain region for reinforcement learning and motivation, and VS hypofunction is implicated in psychiatric disorders including schizophrenia. Providing rewards or performance feedback has been shown to activate VS. Intrinsically motivated subjects performing challenging cognitive tasks are likely to engage reinforcement circuitry even in the absence of external feedback or incentives. However, such intrinsic reinforcement responses have received little attention, have not been examined in relation to behavioral performance, and have not been evaluated for impairment in neuropsychiatric disorders such as schizophrenia. Here we used fMRI to examine a challenging “old” vs. “new” visual recognition task in healthy subjects and patients with schizophrenia. Targets were unique fractal stimuli previously presented as salient distractors in a visual oddball task, producing incidental memory encoding. Based on the prediction error theory of reinforcement learning, we hypothesized that correct target recognition would activate VS in controls, and that this activation would be greater in subjects with lower expectation of responding correctly as indexed by a more conservative response bias. We also predicted these effects would be reduced in patients with schizophrenia. Consistent with these predictions, controls activated VS and other reinforcement processing regions during correct recognition, with greater VS activation in those with a more conservative response bias. Patients did not show either effect, with significant group differences suggesting hyporesponsivity in patients to internally generated feedback. These findings highlight the importance of accounting for intrinsic motivation and reward when studying cognitive tasks, and add to growing evidence of reward circuit dysfunction in schizophrenia that may impact cognition and function

Memory-delineated subtypes of schizophrenia: Relationship to clinical, neuroanatomical, and neurophysiological measures.

Memory performance was examined in patients with schizophrenia to determine whether subgroups conforming to cortical and subcortical dementias could be identified and, if so, whether subgroups differed on clinical, neuroanatomical, and neurophysiological measures. A cluster analysis of California Verbal Learning Test performance classified patients into 3 subgroups. Two groups exhibited memory deficits consistent with the cortical–subcortical distinction, whereas 1 group was unimpaired. Cortical patients tended to be male, and they had earlier illness onset, reduced temporal lobe gray matter, and hypometabolism. Subcortical patients had ventricular enlargement and more negative symptoms. Unimpaired patients had fewer negative symptoms and dorsal medial prefrontal hypermetabolism. The authors con-clude that categorizing patients on the basis of memory deficits may yield neurobiologically meaningful disease subtypes. There is increasing consensus that Kraepelin’s conceptu-alization of schizophrenia as a disorder characterized by disturbed cognition rather than psychotic symptomatology was fundamentally correct (see Sharma & Harvey, 2000, fo

An Improved Interactive Streaming Algorithm for the Distinct Elements Problem

The exact computation of the number of distinct elements (frequency moment $F_0$) is a fundamental problem in the study of data streaming algorithms. We denote the length of the stream by $n$ where each symbol is drawn from a universe of size $m$. While it is well known that the moments $F_0,F_1,F_2$ can be approximated by efficient streaming algorithms, it is easy to see that exact computation of $F_0,F_2$ requires space $\Omega(m)$. In previous work, Cormode et al. therefore considered a model where the data stream is also processed by a powerful helper, who provides an interactive proof of the result. They gave such protocols with a polylogarithmic number of rounds of communication between helper and verifier for all functions in NC. This number of rounds $\left(O(\log^2 m) \;\text{in the case of} \;F_0 \right)$ can quickly make such protocols impractical. Cormode et al. also gave a protocol with $\log m +1$ rounds for the exact computation of $F_0$ where the space complexity is $O\left(\log m \log n+\log^2 m\right)$ but the total communication $O\left(\sqrt{n}\log m\left(\log n+ \log m \right)\right)$. They managed to give $\log m$ round protocols with $\operatorname{polylog}(m,n)$ complexity for many other interesting problems including $F_2$, Inner product, and Range-sum, but computing $F_0$ exactly with polylogarithmic space and communication and $O(\log m)$ rounds remained open. In this work, we give a streaming interactive protocol with $\log m$ rounds for exact computation of $F_0$ using $O\left(\log m \left(\,\log n + \log m \log\log m\,\right)\right)$ bits of space and the communication is $O\left( \log m \left(\,\log n +\log^3 m (\log\log m)^2 \,\right)\right)$. The update time of the verifier per symbol received is $O(\log^2 m)$.Comment: Submitted to ICALP 201

On the power of relaxed Local Decoding Algorithms

A locally decodable code (LDC) C from {0,1} to the k to {0,1} to the n is an error correcting code wherein individual bits of the message can be recovered by only querying a few bits of a noisy codeword. LDCs found a myriad of applications both in theory and in practice, ranging from probabilistically checkable proofs to distributed storage. However, despite nearly two decades of extensive study, the best known constructions of O(1)-query LDCs have super-polynomial block length. The notion of relaxed LDCs is a natural relaxation of LDCs, which aims to bypass the foregoing barrier by requiring local decoding of nearly all individual message bits, yet allowing decoding failure (but not error) on the rest. State of the art constructions of O(1)-query relaxed LDCs achieve blocklength n is order of k to the power of 1 plus gamma for an arbitrarily small constant. We prove a lower bound which shows that O(1)-query relaxed LDCs cannot achieve blocklength n = k to the power of 1 + o(1). This resolves an open problem raised by Goldreich in 2004

Resolving the emission transition dipole moments of single doubly-excited seeded nanorods via heralded defocused imaging

Semiconductor nanocrystal emission polarization is a crucial probe of nanocrystal physics and an essential factor for nanocrystal-based technologies. While the transition dipole moment of the lowest excited state to ground state transition is well characterized, the dipole moment of higher multiexcitonic transitions is inaccessible via most spectroscopy techniques. Here, we realize direct characterization of the doubly-excited state relaxation transition dipole by heralded defocused imaging. Defocused imaging maps the dipole emission pattern onto a fast single-photon avalanche diode detector array, allowing the post-selection of photon pairs emitted from the biexciton-exciton emission cascade and resolving the differences in transition dipole moments. Type-I1/2 seeded nanorods exhibit higher anisotropy of the biexciton-to-exciton transition compared to the exciton-to-ground state transition. In contrast, type-II seeded nanorods display a reduction of biexciton emission anisotropy. These findings are rationalized in terms of an interplay between transient dynamics of the refractive index and the excitonic fine structure

Renormalization group approach to vibrational energy transfer in protein

Renormalization group method is applied to the study of vibrational energy transfer in protein molecule. An effective Lagrangian and associated equations of motion to describe the resonant energy transfer are analyzed in terms of the first-order perturbative renormalization group theory that has been developed as a unified tool for global asymptotic analysis. After the elimination of singular terms associated with the Fermi resonance, amplitude equations to describe the slow dynamics of vibrational energy transfer are derived, which recover the result obtained by a technique developed in nonlinear optics [S.J. Lade, Y.S. Kivshar, Phys. Lett. A 372 (2008) 1077].Comment: 11 page

Double- to Single-Strand Transition Induces Forces and Motion in DNA Origami Nanostructures

The design of dynamic, reconfigurable devices is crucial for the bottom-up construction of artificial biological systems. DNA can be used as an engineering material for the de-novo design of such dynamic devices. A self-assembled DNA origami switch is presented that uses the transition from double- to single-stranded DNA and vice versa to create and annihilate an entropic force that drives a reversible conformational change inside the switch. It is distinctively demonstrated that a DNA single-strand that is extended with 0.34 nm per nucleotide - the extension this very strand has in the double-stranded configuration - exerts a contractive force on its ends leading to large-scale motion. The operation of this type of switch is demonstrated via transmission electron microscopy, DNA-PAINT super-resolution microscopy and darkfield microscopy. The work illustrates the intricate and sometimes counter-intuitive forces that act in nanoscale physical systems that operate in fluids