Univalent Foundations and the UniMath Library

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander

Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds

We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient conditions for existence of Green currents in codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and Theorem 5.3 are adde

Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

A Retrospective Case Series Analysis of the Relationship Between Phenylalanine: Tyrosine Ratio and Cerebral Glucose Metabolism in Classical Phenylketonuria and Hyperphenylalaninemia.

We retrospectively examined the relationship between blood biomarkers, in particular the historical mean phenylalanine to tyrosine (Phe:Tyr) ratio, and cerebral glucose metabolism. We hypothesized that the historical mean Phe:Tyr ratio would be more predictive of cerebral glucose metabolism than the phenylalanine (Phe) level alone. We performed a retrospective case series analysis involving 11 adult classical phenylketonuria/hyperphenylalaninemia patients under the care of an Inherited Metabolic & Neuropsychiatry Clinic who had complained of memory problems, collating casenote data from blood biochemistry, and clinical [18F]fluorodeoxyglucose positron emission tomography ([18F]FDG PET). The Phe:Tyr ratio was calculated for individual blood samples and summarized as historical mean Phe:Tyr ratio (Phe:Tyr) and historical standard deviation in Phe:Tyr ratio (SD-Phe:Tyr), for each patient. Visual analyses of [18F]FDG PET revealed heterogeneous patterns of glucose hypometabolism for eight patients. [18F]FDG PET standardized uptake was negatively correlated with Phe in a large cluster with peak localized to right superior parietal gyrus. Even larger clusters of negative correlation that encompassed most of the brain, with frontal peaks, were observed with Phe:Tyr, and SD-Phe:Tyr. Our case series analysis provides further evidence for the association between blood biomarkers, and cerebral glucose hypometabolism. Mean historical blood Phe:Tyr ratio, and its standard deviation over time, appear to be more indicative of global cerebral glucose metabolism in patients with memory problems than Phe

Front Behav Neurosci

Cognitive impairment in Down syndrome (DS) has been linked to increased synaptic inhibition. The underlying mechanisms remain unknown, but memory deficits are rescued in DS mouse models by drugs targeting GABA receptors. Similarly, administration of epigallocatechin gallate (EGCG)-containing extracts rescues cognitive phenotypes in Ts65Dn mice, potentially through GABA pathway. Some developmental and cognitive alterations have been traced to increased expression of the serine-threonine kinase DYRK1A on Hsa21. To better understand excitation/inhibition balance in DS, we investigated the consequences of long-term (1-month) treatment with EGCG-containing extracts in adult mBACtgDyrk1a mice that overexpress Dyrk1a. Administration of POL60 rescued components of GABAergic and glutamatergic pathways in cortex and hippocampus but not cerebellum. An intermediate dose (60 mg/kg) of decaffeinated green tea extract (MGTE) acted on components of both GABAergic and glutamatergic pathways and rescued behavioral deficits as demonstrated on the alternating paradigm, but did not rescue protein level of GABA-synthesizing GAD67. These results indicate that excessive synaptic inhibition in people with DS may be attributable, in large part, to increased DYRK1A dosage. Thus, controlling the level of active DYRK1A is a clear issue for DS therapy. This study also defines a panel of synaptic markers for further characterization of DS treatments in murine models

Evaluation of factors influencing ¹⁸F-FET uptake in the brain.

PET using the amino-acid O-(2- <sup>18</sup> F-fluoroethyl)-l-tyrosine ( <sup>18</sup> F-FET) is gaining increasing interest for brain tumour management. Semi-quantitative analysis of tracer uptake in brain tumours is based on the standardized uptake value (SUV) and the tumour-to-brain ratio (TBR). The aim of this study was to explore physiological factors that might influence the relationship of SUV of <sup>18</sup> F-FET uptake in various brain areas, and thus affect quantification of <sup>18</sup> F-FET uptake in brain tumours. Negative <sup>18</sup> F-FET PET scans of 107 subjects, showing an inconspicuous brain distribution of <sup>18</sup> F-FET, were evaluated retrospectively. Whole-brain quantitative analysis with Statistical Parametric Mapping (SPM) using parametric SUV PET images, and volumes of interest (VOIs) analysis with fronto-parietal, temporal, occipital, and cerebellar SUV background areas were performed to study the effect of age, gender, height, weight, injected activity, body mass index (BMI), and body surface area (BSA). After multivariate analysis, female gender and high BMI were found to be two independent factors associated with increased SUV of <sup>18</sup> F-FET uptake in the brain. In women, SUV <sub>mean</sub> of <sup>18</sup> F-FET uptake in the brain was 23% higher than in men (p < 0.01). SUV <sub>mean</sub> of <sup>18</sup> F-FET uptake in the brain was positively correlated with BMI (r = 0.29; p < 0.01). The influence of these factors on SUV of <sup>18</sup> F-FET was similar in all brain areas. In conclusion, SUV of <sup>18</sup> F-FET in the normal brain is influenced by gender and weakly by BMI, but changes are similar in all brain areas

Crises and collective socio-economic phenomena: simple models and challenges

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important problems in economic theory. In this paper, we review recent efforts to include heterogeneities and interactions in models of decision. We argue that the Random Field Ising model (RFIM) indeed provides a unifying framework to account for many collective socio-economic phenomena that lead to sudden ruptures and crises. We discuss different models that can capture potentially destabilising self-referential feedback loops, induced either by herding, i.e. reference to peers, or trending, i.e. reference to the past, and account for some of the phenomenology missing in the standard models. We discuss some empirically testable predictions of these models, for example robust signatures of RFIM-like herding effects, or the logarithmic decay of spatial correlations of voting patterns. One of the most striking result, inspired by statistical physics methods, is that Adam Smith's invisible hand can badly fail at solving simple coordination problems. We also insist on the issue of time-scales, that can be extremely long in some cases, and prevent socially optimal equilibria to be reached. As a theoretical challenge, the study of so-called "detailed-balance" violating decision rules is needed to decide whether conclusions based on current models (that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several minor improvements along reviewers' comment

Evidence of the contribution of the X chromosome to systemic sclerosis susceptibility: Association with the functional IRAK1 196Phe/532Ser haplotype

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Clinically Relevant Characterization of Lung Adenocarcinoma Subtypes Based on Cellular Pathways: An International Validation Study

Lung adenocarcinoma (AD) represents a predominant type of lung cancer demonstrating significant morphologic and molecular heterogeneity. We sought to understand this heterogeneity by utilizing gene expression analyses of 432 AD samples and examining associations between 27 known cancer-related pathways and the AD subtype, clinical characteristics and patient survival. Unsupervised clustering of AD and gene expression enrichment analysis reveals that cell proliferation is the most important pathway separating tumors into subgroups. Further, AD with increased cell proliferation demonstrate significantly poorer outcome and an increased solid AD subtype component. Additionally, we find that tumors with any solid component have decreased survival as compared to tumors without a solid component. These results lead to the potential to use a relatively simple pathological examination of a tumor in order to determine its aggressiveness and the patient's prognosis. Additional results suggest the ability to use a similar approach to determine a patient's sensitivity to targeted treatment. We then demonstrated the consistency of these findings using two independent AD cohorts from Asia (N = 87) and Europe (N = 89) using the identical analytic procedures