A theory of the infinite horizon LQ-problem for composite systems of PDEs with boundary control

We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential Equations (PDE) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall `predominant' hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic components of the dynamics has been introduced by the authors in 2005, and a full theory of the LQ-problem on a finite time horizon has been developed. The present paper provides the infinite time horizon theory, culminating in well-posedness of the corresponding (algebraic) Riccati equations. New technical challenges are encountered and new tools are needed, especially in order to pinpoint the differentiability of the optimal solution. The theory is illustrated by means of a boundary control problem arising in thermoelasticity.Comment: 50 pages, submitte

An Assessment of the Impact of Climate Change on Human Health in New Hampshire

Climate change threatens human health in many ways. The negative impacts of climate change on human health are likely to increase in both magnitude and frequency as the climate continues to change in response to ever increasing global emissions of heat-trapping gases released from a variety of human activities.The Centers for Disease Control and Prevention (CDC) Building Resilience Against Climate Effects (BRACE) framework provides guidance to states and cities to develop strategies and programs to confront the health implications of climate change. This report serves to address Steps 1 and 2 of the BRACE framework via an assessment of past and future climate change across New Hampshire combined with an assessment of the impact of climate change on human health. A key component of the BRACE framework is building resilience. In public health, resilience is a measure of a community’s ability to utilize available resources to respond to, withstand, and recover from adverse situations. More generally, people think of resilience as the ability to recover, persist, or thrive amid change. The New Hampshire Climate and Health Workgroup has tentatively developed the following definition: Resilience is the ability and capacity to anticipate, prepare for, respond to, and recover from significant threats with minimum damage to human health and well-being, the economy, and the environment. The importance of the way we plan our built environment—including land use, transportation, and water management decisions, as well as how we interact with our natural environment and preserve its life-supporting functions—must be emphasized as pivotal points of intersection as we develop climate adaptation strategies. Notably, a resilience-based approach to climate change adaptation should align with New Hampshire’s transformative State Health Improvement Plan. That plan underscores the importance of cross-sector collaboration and coordinated strategies to address the social and environmental determinants of health. These strategies not only support healthy communities for all New Hampshire residents, but they are also critically important for reducing health care costs and reducing the burden of disease

Image Analysis Workflow for 2-D Electrophoresis Gels Based on ImageJ

A number of commercial software packages are currently available to perform digital two-dimensional electrophoresis (2D-GE) gel analysis. However, both the high cost of the commercial packages and the unavailability of a standard data analysis workflow, have prompted several groups to develop freeware systems to perform certain steps of gel analysis. Unfortunately, to the best of our knowledge none of them offer a package that performs all the steps envisaged in a 2D-GE gel analysis. Here we describe an ImageJ-based procedure, able to manage all the steps of a 2D-GE gel analysis. ImageJ is a free available image processing and analysis application developed by National Institutes of Health (NIH) and widely used in different life sciences fields as medical imaging, microscopy, western blotting and PAGE. Nevertheless no one has yet developed a procedure enabled to compare spots on 2D-GE gels. We collected all used ImageJ tools in a plug-in that allows us to perform the whole 2D-GE analysis. To test it, we performed a set of 2D-GE experiments on plasma samples from 9 patients victims of acute myocardial infarction and 8 controls, and we compared the results obtained by our procedure to those obtained using a widely diffuse commercial package, finding similar performance

Measles in Italy: Viral strains and crossing borders.

In 2017, Italy experienced one of the largest outbreaks of measles in recent years, with 5404 notified cases and 4347 confirmed cases. A further 2029 cases were notified during the first 6 months of 2018, and 1516 of them were laboratory-confirmed. The B3 and D8 genotypes were identified as those responsible for the outbreak. Possible transmission routes can be established by monitoring the circulating measles virus strains in support of the national health authorities to warn people and travellers

Palindromic Length of Words with Many Periodic Palindromes

The palindromic length $\text{PL}(v)$ of a finite word $v$ is the minimal number of palindromes whose concatenation is equal to $v$. In 2013, Frid, Puzynina, and Zamboni conjectured that: If $w$ is an infinite word and $k$ is an integer such that $\text{PL}(u)\leq k$ for every factor $u$ of $w$ then $w$ is ultimately periodic. Suppose that $w$ is an infinite word and $k$ is an integer such $\text{PL}(u)\leq k$ for every factor $u$ of $w$. Let $\Omega(w,k)$ be the set of all factors $u$ of $w$ that have more than $\sqrt[k]{k^{-1}\vert u\vert}$ palindromic prefixes. We show that $\Omega(w,k)$ is an infinite set and we show that for each positive integer $j$ there are palindromes $a,b$ and a word $u\in \Omega(w,k)$ such that $(ab)^j$ is a factor of $u$ and $b$ is nonempty. Note that $(ab)^j$ is a periodic word and $(ab)^ia$ is a palindrome for each $i\leq j$. These results justify the following question: What is the palindromic length of a concatenation of a suffix of $b$ and a periodic word $(ab)^j$ with "many" periodic palindromes? It is known that $\lvert\text{PL}(uv)-\text{PL}(u)\rvert\leq \text{PL}(v)$, where $u$ and $v$ are nonempty words. The main result of our article shows that if $a,b$ are palindromes, $b$ is nonempty, $u$ is a nonempty suffix of $b$, $\vert ab\vert$ is the minimal period of $aba$, and $j$ is a positive integer with $j\geq3\text{PL}(u)$ then $\text{PL}(u(ab)^j)-\text{PL}(u)\geq 0$

Retrosplenial Cortex and Long-Term Memory: Molecules to Behavior

The retrosplenial cortex (RSC) is reciprocally connected with the hippocampus and various parahippocampal cortical regions, suggesting that RSC is well-positioned to contribute to hippocampal-dependent memory. Consistent with this, substantial behavioral evidence indicates that RSC is essential for consolidating and/or retrieving contextual and spatial memories. In addition, there is growing evidence that RSC neurons undergo activity-dependent plastic changes during memory formation and retrieval. In this paper we review both the behavioral and cellular/molecular data and posit that the RSC has a particularly important role in the storage and retrieval of spatial and contextual memories perhaps due its involvement in binding together multiple cues in the environment. We identify remaining questions and avenues for future research that take advantage of emerging methods to selectively manipulate RSC neurons both spatially and temporally and to image the RSC in awake, behaving animals

Complete elimination of 1K Pot vibrations in dilution refrigerators

Cryogenic vibrations generated by continuously filled 1K Pots are a well known source of noise in all cryogenic experiments using dilution refrigerators. Starting from recent developments we realized a non invasive modification to the cryostat that completely eliminated vibrations, thermalizing the helium coming from the main bath at the pot temperature. We describe the new experimental setup and complete study of the phenomena

Comparing unconstrained parametrization methods for return covariance matrix prediction

Forecasting covariance matrices is a difficult task in many research fields since the predicted matrices should be at least positive semidefinite. This problem can be overcome by including constraints in the predictive model or through a parametrization of the matrices to be predicted. In this paper, we focus on the latter approach in a financial application and analyse four parametrizations of the covariance matrices of asset returns. The aim of the manuscript is to understand if the parametrizations of the covariance matrices exhibit differences in terms of predictive accuracy. To this end, we critically analyse their predictive performance through both a Monte Carlo simulation and an empirical application with daily and weekly realized covariance matrices of stock assets. Our findings highlight that the Cholesky decomposition and the parametrization recently introduced by Archakov and Hansen are the overall best-performing methods in terms of forecasting accuracy