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Ledoit and Peche proved convergence of certain functions of a random covariance matrix's resolvent; we refer to this as the Ledoit-Peche law. One important application of their result is shrinkage covariance estimation with respect to so-called Minimum Variance (MV) loss, discussed in the work of Ledoit and Wolf. We provide an essentially optimal rate of convergence and hypothesize it to be the smallest possible rate of excess MV loss within the shrinkage class., 12 pages

Purpose The aim of this study was to assess the impact of pre-injury stimulant use (amphetamine, cocaine, methamphetamine and/or ecstasy) on outcomes after isolated severe traumatic brain injury (TBI). Methods Retrospective 2017 TQIP study, including adult trauma patients (≥16 years old) who underwent drug and alcohol screening on admission and sustained an isolated severe TBI (head AIS ≥3). Patients with significant extracranial trauma (AIS ≥3) were excluded. Epidemiological and clinical characteristics, procedures and outcome variables were collected. Patients with isolated stimulant use were matched 1:1 for age, gender, mechanism of injury, head AIS and overall comorbidities, with patients with negative toxicology and alcohol screen. Outcomes in the two groups were compared with univariable and multivariable regression analysis. Results 681 patients with isolated TBI and stimulant use were matched with 681 patients with negative toxicology and alcohol screen. The incidence of hypotension and CGS In multivariable regression analysis, stimulant use was not independently associated with mortality (OR 0.95, 95% CI 0.61–1.49). However, stimulant use was associated with longer hospital length of stay (HLOS) (RC 1.13, 95%CI 1.03–1.24). Conclusion Pre-injury stimulant use is common in patients admitted for severe TBI, but was not independently associated with mortality when compared to patients with negative toxicology. However, stimulant use was associated with a significant longer HLOS.

This essay proposes that Walter Benjamin’s writings on Schuld invite a rethinking of the Anthropocene. This in turn lends legibility to Benjamin’s century-old political writings, which show how a m...

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Benjamin Lewis Robinson, Introduction to the symposium Bad Taste?: Culture and Consumption in the Great Acceleration, ICI Berlin, 17 June 2022, video recording, mp4, 12:46

We report on the single-molecule electronic and thermoelectric properties of strategically chosen anthracene-based molecules with anchor groups capable of binding to noble metal substrates, such as gold and platinum. Specifically, we study the effect of different anchor groups, as well as quantum interference, on the electric conductance and the thermopower of gold/single-molecule/gold junctions and generally find good agreement between theory and experiment. All molecular junctions display transport characteristics consistent with coherent transport and a Fermi alignment approximately in the middle of the HOMO/LUMO gap. Single-molecule results are in agreement with previously reported thin-film data, further supporting the notion that molecular design considerations may be translated from the single- to the many-molecule devices. For combinations of anchor groups where one binds significantly more strongly to the electrodes than the other, the stronger anchor group appears to dominate the thermoelectric behaviour of the molecular junction. For other combinations, the choice of electrode material can determine the sign and magnitude of the thermopower. This finding has important implications for the design of thermoelectric generator devices, where both n- and p-type conductor are required for thermoelectric current generation.

We study a stochastic control problem for continuous multidimensional martingales with fixed quadratic variation. In a radially symmetric environment, we are able to find an explicit solution to the control problem and find an optimal strategy. We show that it is optimal to switch between two strategies, depending only on the radius of the controlled process. The optimal strategies correspond to purely radial and purely tangential motion. It is notable that the value function exhibits smooth fit even when switching to tangential motion, where the radius of the optimal process is deterministic. Under sufficient regularity on the cost function, we prove optimality via viscosity solutions of a Hamilton-Jacobi-Bellman equation. We extend the results to cost functions that may become infinite at the origin. Extra care is required to solve the control problem in this case, since it is not clear how to define the optimal strategy with deterministic radius at the origin. Our results generalise some problems recently considered in Stochastic Portfolio Theory and Martingale Optimal Transport., Comment: 41 pages, 6 figure. Additional motivating example added, definitions and problem formulations clarified and simplified

Supplemental material, sj-pdf-1-tak-10.1177_17539447211002687 for Epidemiology of infective endocarditis before versus after change of international guidelines: a systematic review by Michael L. Williams, Mathew P. Doyle, Nicholas McNamara, Daniel Tardo, Manish Mathew and Benjamin Robinson in Therapeutic Advances in Cardiovascular Disease

Supplemental material, sj-pdf-1-tak-10.1177_17539447211002687 for Epidemiology of infective endocarditis before versus after change of international guidelines: a systematic review by Michael L. Williams, Mathew P. Doyle, Nicholas McNamara, Daniel Tardo, Manish Mathew and Benjamin Robinson in Therapeutic Advances in Cardiovascular Disease

In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the purpose of computing measurement probabilities. Frames and their most common generalizations can be seen to give rise to POVMs, but does every reasonable POVM arise from a type of frame? In this paper we answer this question using a Radon-Nikodym-type result., Comment: 9 pages, submitted to the Rocky Mountain Math Journal

The Fisher-Rao geodesic distance on the statistical manifold consisting of zero-mean p-dimensional multivariate Gaussians appears without proof in several places (such as Steven Smith's "Covariance, Subspace, and Intrinsic Cramer-Rao Bounds"). In this paper, we give a proof using basic Riemannian geometry.

The realization of self-assembled molecular-electronic films, whose room-temperature transport properties are controlled by quantum interference (QI), is an essential step in the scale-up QI effects from single molecules to parallel arrays of molecules. Recently, the effect of destructive QI (DQI) on the electrical conductance of self-assembled monolayers (SAMs) has been investigated. Here, through a combined experimental and theoretical investigation, we demonstrate chemical control of different forms of constructive QI (CQI) in cross-plane transport through SAMs and assess its influence on cross-plane thermoelectricity in SAMs. It is known that the electrical conductance of single molecules can be controlled in a deterministic manner, by chemically varying their connectivity to external electrodes. Here, by employing synthetic methodologies to vary the connectivity of terminal anchor groups around aromatic anthracene cores, and by forming SAMs of the resulting molecules, we clearly demonstrate that this signature of CQI can be translated into SAM-on-gold molecular films. We show that the conductance of vertical molecular junctions formed from anthracene-based molecules with two different connectivities differ by a factor of approximately 16, in agreement with theoretical predictions for their conductance ratio based on constructive QI effects within the core. We also demonstrate that for molecules with thiol anchor groups, the Seebeck coefficient of such films is connectivity dependent and with an appropriate choice of connectivity can be boosted by ~50%. This demonstration of QI and its influence on thermoelectricity in SAMs represents a critical step towards functional ultra-thin-film devices for future thermoelectric and molecular-scale electronics applications.

Graph-theoretic methods have seen wide use throughout the literature on multi-agent control and optimization. When communications are intermittent and unpredictable, such networks have been modeled using random communication graphs. When graphs are time-varying, it is common to assume that their unions are connected over time, yet, to the best of our knowledge, there are not results that determine the number of finite-size random graphs needed to attain a connected union. Therefore, this paper bounds the probability that individual random graphs are connected and bounds the same probability for connectedness of unions of random graphs. The random graph model used is a generalization of the classic Erdos-Renyi model which allows some edges never to appear. Numerical results are presented to illustrate the analytical developments made., Comment: 16 pages, 5 figures. arXiv admin note: text overlap with arXiv:1703.07804

Benjamin Lewis Robinson, Introduction to the conference Post-Truth and Politics: Departing from the Thought of Hannah Arendt, ICI Berlin, 29 April 2017, video recording, mp4, 11:53

Extracellular matrix (ECM) remodelling is integral to numerous physiological and pathological processes in biology, such as embryogenesis, wound healing, fibrosis and cancer. Until recently, most cellular studies have been conducted on 2D environments where mechanical cues significantly differ from physiologically relevant 3D environments, impacting cellular behaviour and masking the interpretation of cellular function in health and disease. We present an integrated methodology where cell-ECM interactions can be investigated in 3D environments via ECM remodelling. Monitoring and quantification of collagen-I structure in remodelled matrices, through designated algorithms, show that 3D matrices can be used to correlate remodelling with increased ECM stiffness observed in fibrosis. Pancreatic stellate cells (PSCs) are the key effectors of the stromal fibrosis associated to pancreatic cancer. We use PSCs to implement our methodology and demonstrate that PSC matrix remodelling capabilities depend on their contractile machinery and β1 integrin-mediated cell-ECM attachment., Summary: A 3D platform to characterise biomechanical remodelling of ECM by myofibroblast-like cells, using SHG microscopy, atomic force microscopy and quantitative algorithms to reveal structural, topological and mechanical properties of 3D matrices.

Atomically thin layers of two-dimensional (2D) materials such as graphene, MoS2 and h-BN have immense potential as sensors and electronic devices thanks to their highly desirable electronic, mechanical, optical and heat transport properties. In particular their extreme stiffness, tensile strength and low density allows for high frequency electronic devices, resonators and ultra-sensitive detectors providing realistic avenues for down-scaling electronic devices and nanoelectromechanical systems (NEMS). Whilst nanoscale morphology and electronic properties of 2D materials can be studied using existing electron or scanning probe microscopy approaches, time-dependant phenomena on the ns and shorter time-scales cannot be readily explored. Here we use the heterodyne principle to reach into this ns time-scale and create a local nanoscale probe for electrostatically induced actuation of a graphene resonator, with amplitude sensitivity down to pm range and time sensitivity in the ns range. We experimentally observed response times of 20-120 ns for resonators with beam lengths of 180 nm to 2.5 um in line with the theoretical predictions for such NEMS devices.

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It is challenging for conventional top-down lithography to fabricate reproducible devices very close to atomic dimensions, whereas identical molecules and very similar nanoparticles can be made bottom-up in large quantities, and can be self-assembled on surfaces. The challenge is to fabricate electrical contacts to many such small objects at the same time, so that nanocrystals and molecules can be incorporated into conventional integrated circuits. Here, we report a scalable method for contacting a self-assembled monolayer of nanoparticles with a single layer of graphene. This produces single-electron effects, in the form of a Coulomb staircase, with a yield of 87 ± 13% in device areas ranging from < 800 nm2 to 16 μm2, containing up to 650,000 nanoparticles. Our technique offers scalable assembly of ultra-high densities of functional particles or molecules that could be used in electronic integrated circuits, as memories, switches, sensors or thermoelectric generators.

It is challenging for conventional top-down lithography to fabricate reproducible devices very close to atomic dimensions, whereas identical molecules and very similar nanoparticles can be made bottom-up in large quantities, and can be self-assembled on surfaces. The challenge is to fabricate electrical contacts to many such small objects at the same time, so that nanocrystals and molecules can be incorporated into conventional integrated circuits. Here, we report a scalable method for contacting a self-assembled monolayer of nanoparticles with a single layer of graphene. This produces single-electron effects, in the form of a Coulomb staircase, with a yield of 87 ± 13% in device areas ranging from, The integration of nano-molecules into microelectronic circuitry is challenging. Here, the authors provide a scalable method for contacting a self-assembled monolayer of nanoparticles with a single layer of graphene that produces single-electron effects, in the form of a Coulomb staircase, with a yield of at least 70%.