Autonomic and brain morphological predictors of stress resilience

Stressful life events are an important cause of psychopathology. Humans exposed to aversive or stressful experiences show considerable inter-individual heterogeneity in their responses. However, the majority does not develop stress-related psychiatric disorders. The dynamic processes encompassing positive and functional adaptation in the face of significant adversity have been broadly defined as resilience. Traditionally, the assessment of resilience has been confined to self-report measures, both within the general community and putative high-risk populations. Although this approach has value, it is highly susceptible to subjective bias and may not capture the dynamic nature of resilience, as underlying construct. Recognizing the obvious benefits of more objective measures of resilience, research in the field has just started investigating the predictive value of several potential biological markers. This review provides an overview of theoretical views and empirical evidence suggesting that individual differences in heart rate variability (HRV), a surrogate index of resting cardiac vagal outflow, may underlie different levels of resilience toward the development of stress-related psychiatric disorders. Following this line of thought, recent studies describing associations between regional brain morphometric characteristics and resting state vagally-mediated HRV are summarized. Existing studies suggest that the structural morphology of the anterior cingulated cortex (ACC), particularly its cortical thickness, is implicated in the expression of individual differences in HRV. These findings are discussed in light of emerging structural neuroimaging research, linking morphological characteristics of the ACC to psychological traits ascribed to a high-resilient profile and abnormal structural integrity of the ACC to the psychophysiological expression of stress-related mental health consequences. We conclude that a multidisciplinary approach integrating brain structural imaging with HRV monitoring could offer novel perspectives about brain-body pathways in resilience and adaptation to psychological stres

One example of general unidentifiable tensors

The identifiability of parameters in a probabilistic model is a crucial notion in statistical inference. We prove that a general tensor of rank 8 in C^3\otimes C^6\otimes C^6 has at least 6 decompositions as sum of simple tensors, so it is not 8-identifiable. This is the highest known example of balanced tensors of dimension 3, which are not k-identifiable, when k is smaller than the generic rank.Comment: 7 pages, one Macaulay2 script as ancillary file, two references adde

Extreme Ultraviolet (EUV) Sources for Lithography based on Synchrotron Radiation

The study presented here was initiated by a discussion to investigate the possibility of using synchrotron radiation as a source for the Next Generation Lithography (NGL) based on the EUV-concept (Extreme Ultra-Violet; here 13.5 nm or 11.3 nm radiation, respectively). The requirements are: 50 W, 2% bandwidth and minimal power outside this bandwidth. Three options were investigated. The first two deal with radiation from bending magnets and undulators. The results confirm the earlier work by Oxfords Instrument and others that these light-sources lack in-band power while emitting excessive out-of-band radiation. The third approach is a FEL (Free Electron Laser) driven by a 500 MeV linear accelerator with a superconducting mini-undulator as radiation emitting device. Such a device would produce in-band EUV-power in excess of 50 W with negligible out-of-band power.Comment: Submitted to Nuclear Instruments and Methods

Effective criteria for specific identifiability of tensors and forms

In applications where the tensor rank decomposition arises, one often relies on its identifiability properties for interpreting the individual rank-$1$ terms appearing in the decomposition. Several criteria for identifiability have been proposed in the literature, however few results exist on how frequently they are satisfied. We propose to call a criterion effective if it is satisfied on a dense, open subset of the smallest semi-algebraic set enclosing the set of rank-$r$ tensors. We analyze the effectiveness of Kruskal's criterion when it is combined with reshaping. It is proved that this criterion is effective for both real and complex tensors in its entire range of applicability, which is usually much smaller than the smallest typical rank. Our proof explains when reshaping-based algorithms for computing tensor rank decompositions may be expected to recover the decomposition. Specializing the analysis to symmetric tensors or forms reveals that the reshaped Kruskal criterion may even be effective up to the smallest typical rank for some third, fourth and sixth order symmetric tensors of small dimension as well as for binary forms of degree at least three. We extended this result to $4 \times 4 \times 4 \times 4$ symmetric tensors by analyzing the Hilbert function, resulting in a criterion for symmetric identifiability that is effective up to symmetric rank $8$, which is optimal.Comment: 31 pages, 2 Macaulay2 code

Refined methods for the identifiability of tensors

We prove that the general tensor of size 2^n and rank k has a unique decomposition as the sum of decomposable tensors if k<= 0.9997 (2^n)/(n+1) (the constant 1 being the optimal value). Similarly, the general tensor of size 3^n and rank k has a unique decomposition as the sum of decomposable tensors if k<= 0.998 (3^n)/(2n+1) (the constant 1 being the optimal value). Some results of this flavor are obtained for tensors of any size, but the explicit bounds obtained are weaker.Comment: 12 pages, three Macaulay2 scripts as ancillary files. v3: final version to appear in Annali di Matematica Pura e Applicat

Adapting Methods and Tools for Participatory Heritage-Based Tourism Planning to Embrace the Four Pillars of Sustainability

Sustainable cultural tourism, understood as heritage-based tourism, can support inclusive and sustainable development, especially in remote or peripheral areas. While participatory processes are mandatory, they are not sufficient to ensure sustainable cultural tourism planning. For the latter, cultural tourism must embrace the four pillars of sustainable development: focusing on economic, cultural, environmental, and social sustainability. Nevertheless, a comprehensive methodology that addresses all the aspects of sustainable planning at each stage of the process through inclusive and diverse participation of local communities is still missing. The paper introduces a specific participatory methodology for cultural tourism developed and tested in eight case studies across Europe and beyond and analyzes how the devised participatory process and tools guarantee proper incorporation of the different pillars for sustainable development at each stage. The methodology and tools presented are based on three replicable steps that aim to enhance cultural tourism in a sustainable, diverse, inclusive, and innovative way. The paper specifically focuses on three activities designed for the participatory workshops: the co-mapping exercise, the Action Co-creation, and an adapted Business Model Canvas, providing an analysis of how those contribute to an innovative participatory process, constantly considering the four pillars of sustainable development