Ratios of characteristic polynomials in complex matrix models

We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as their Cauchy transforms, generalizing previous expressions for real eigenvalues. We restrict ourselves to ratios of characteristic polynomials over their complex conjugate

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD). The key idea consists in computing a bisimulation by exploring reachable pairs symbolically, so as to avoid redundancies. This idea can be combined with already existing optimisations, and we show in particular a nice integration with the disjoint sets forest data-structure from Hopcroft and Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an algebraic theory that can be used for verification in various domains ranging from compiler optimisation to network programming analysis. This theory is decidable by reduction to language equivalence of automata on guarded strings, a particular kind of automata that have exponentially large alphabets. We propose several methods allowing to construct symbolic automata out of KAT expressions, based either on Brzozowski's derivatives or standard automata constructions. All in all, this results in efficient algorithms for deciding equivalence of KAT expressions

Overview of adverse events related to invasive procedures in the intensive care unit

BackgroundThis study was conducted to determine the frequency, predictors, and clinical impact of adverse events (AEs) related to invasive procedures in the intensive care unit (ICU). Methods This was a prospective observational study of ICUs in a university hospital. Results A total of 893 patients requiring invasive procedures were admitted over a 1-year period. Among these, 310 patients (34.7%) experienced a total of 505 AEs. The mean number of AEs per patient was 1.6 ± 1.1 (range, 1-7). Infectious AEs were significantly more frequent than mechanical AEs (60.4% vs 39.6%; P = .01). Factors independently associated with AE occurrence were isolation of multidrug-resistant bacteria at ICU admission, >5 invasive procedures, and ICU length of stay >8 days. Thirty-three AEs (6.5%) resulted in severe clinical impact, including 24 deaths. Ventilator-associated pneumonia (VAP) accounted for 62.5% of the deaths related to AEs. Conclusions One-third of critically ill patients experienced AEs related to invasive procedures. Severe AEs were associated with 11% of all ICU deaths. VAP was the most frequent AE related to death. An improved assessment of the risk–benefit balance before each invasive procedure and increased efforts to decrease VAP prevalence are needed to reduce AE-related mortality

A certifying frontend for (sub)polyhedral abstract domains

Convex polyhedra provide a relational abstraction of numerical properties for static analysis of programs by abstract interpretation. We describe a lightweight certification of polyhedral abstract domains using the Coq proof assistant. Our approach consists in delegating most computations to an untrusted backend and in checking its outputs with a certified frontend. The backend is free to implement relaxations of domain operators in order to trade some precision for more efficiency, but must produce hints about the soundness of its results. Experiments with a full-precision backend show that the certification overhead is small and that the certified abstract domain has comparable performance to non-certifying state-of-the-art implementations

Nominal Logic Programming

Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates logic programming based on nominal logic. We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as of July 23, 200

Delivering the power of nanomedicine to patients today

The situation of the COVID-19 pandemic reminds us that we permanently need high-value flexible solutions to urgent clinical needs including simplified diagnostic technologies suitable for use in the field and for delivering targeted therapeutics. From our perspective nanotechnology is revealed as a vital resource for this, as a generic platform of technical solutions to tackle complex medical challenges. It is towards this perspective and focusing on nanomedicine that we take issue with Prof Park's recent editorial published in the Journal of Controlled Release. Prof. Park argued that in the last 15 years nanomedicine failed to deliver the promised innovative clinical solutions to the patients (Park, K. The beginning of the end of the nanomedicine hype. Journal of Controlled Release, 2019; 305, 221\u2013222 [1]. We, the ETPN (European Technology Platform on Nanomedicine) [2], respectfully disagree. In fact, the more than 50 formulations currently in the market, and the recent approval of 3 key nanomedicine products (e. g. Onpattro, Hensify and Vyxeos), have demonstrated that the nanomedicine field is concretely able to design products that overcome critical barriers in conventional medicine in a unique manner, but also to deliver within the cells new drug-free therapeutic effects by using pure physical modes of action, and therefore make a difference in patients lives. Furthermore, the >400 nanomedicine formulations currently in clinical trials are expecting to bring novel clinical solutions (e.g. platforms for nucleic acid delivery), alone or in combination with other key enabling technologies to the market, including biotechnologies, microfluidics, advanced materials, biomaterials, smart systems, photonics, robotics, textiles, Big Data and ICT (information & communication technologies) more generally. However, we agree with Prof. Park that \u201c it is time to examine the sources of difficulty in clinical translation of nanomedicine and move forward \u201c. But for reaching this goal, the investments to support clinical translation of promising nanomedicine formulations should increase, not decrease. As recently encouraged by EMA in its roadmap to 2025, we should create more unity through a common knowledge hub linking academia, industry, healthcare providers and hopefully policy makers to reduce the current fragmentation of the standardization and regulatory body landscape. We should also promote a strategy of cross-technology innovation, support nanomedicine development as a high value and low-cost solution to answer unmet medical needs and help the most promising innovative projects of the field to get better and faster to the clinic. This global vision is the one that the ETPN chose to encourage for the last fifteen years. All actions should be taken with a clear clinical view in mind, \u201c without any fanfare\u201d, to focus \u201con what matters in real life\u201d, which is the patient and his/her quality of life. This ETPN overview of achievements in nanomedicine serves to reinforce our drive towards further expanding and growing the maturity of nanomedicine for global healthcare, accelerating the pace of transformation of its great potential into tangible medical breakthroughs

Chirality Change in String Theory

It is known that string theory compactifications leading to low energy effective theories with different chiral matter content ({\it e.g.} different numbers of standard model generations) are connected through phase transitions, described by non-trivial quantum fixed point theories. We point out that such compactifications are also connected on a purely classical level, through transitions that can be described using standard effective field theory. We illustrate this with examples, including some in which the transition proceeds entirely through supersymmetric configurations.Comment: 50 pages, 2 figure

Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains

Exact analytic calculations in spin-1/2 XY chains, show the presence of long-time tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for $t\to \infty$, is given in the form of a power law $$(t/\tau_{Q}) ^{-\nu_{Q}}$$ where the relaxation time $\tau_{Q}$ and the exponent $\nu_{Q}$ depend on the wave vector $Q$, characterizing the spatial modulation of the initial excitation. We consider several variants of the XY model (dimerized, with staggered magnetic field, with bond alternation, and with isotropic and uniform interactions), that are grouped into two families, whether the energy spectrum has a gap or not. Once the initial condition is given, the non-equilibrium problem for the magnetization is solved in closed form, without any other assumption. The long-time behavior for $t\to \infty$ can be obtained systematically in a form of an asymptotic series through the stationary phase method. We found that gapped models show critical behavior with respect to $Q$, in the sense that there exist critical values $Q_{c}$, where the relaxation time $\tau_{Q}$ diverges and the exponent $\nu_{Q}$ changes discontinuously. At those points, a slowing down of the relaxation process is induced, similarly to phenomena occurring near phase transitions. Long-lived excitations are identified as incommensurate spin density waves that emerge in systems undergoing the Peierls transition. In contrast, gapless models do not present the above anomalies as a function of the wave vector $Q$.Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical Review

The use of indigenous knowledge in development: problems and challenges

The use of indigenous knowledge has been seen by many as an alternative way of promoting development in poor rural communities in many parts of the world. By reviewing much of the recent work on indigenous knowledge, the paper suggests that a number of problems and tensions has resulted in indigenous knowledge not being as useful as hoped for or supposed. These include problems emanating from a focus on the (arte)factual; binary tensions between western science and indigenous knowledge systems; the problem of differentiation and power relations; the romanticization of indigenous knowledge; and the all too frequent decontextualization of indigenous knowledge

HTS Dipole Insert Developments

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