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"Complex Analysis"
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A crude look at the whole : the science of complex systems in business, life, and society
\"Imagine trying to understand a stained glass window by breaking it into pieces and examining it one shard at a time. While you could probably learn a lot about each piece, you would have no idea about what the entire picture looks like. This is reductionism--the idea that to understand the world we only need to study its pieces--and it is how most social scientists approach their work. In [this book], social scientist and economist John H. Miller shows why we need to start looking at whole pictures. For one thing, whether we are talking about stock markets, computer networks, or biological organisms, individual parts only make sense when we remember that they are part of larger wholes. And perhaps more importantly, those wholes can take on behaviors that are strikingly different from that of their pieces\"--Amazon.com.
The Mother Body Phase Transition in the Normal Matrix Model
by
Bleher, Pavel M.
,
Silva, Guilherme L. F.
in
Functions, Meromorphic
,
Integral transforms
,
Matrices
2020
The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to
several other topics as quadrature domains, inverse potential problems and the Laplacian growth.
In this present paper we
consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and
introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain
We also study in detail the mother body problem associated to
To construct the mother body measure, we define a quadratic differential
Following previous works of Bleher & Kuijlaars
and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou
nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials.
Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of
the associated
The dynamics of risk: changing technologies and collective action in seismic events
Earthquakes are a huge global threat. In thirty-six countries, severe seismic risks threaten populations and their increasingly interdependent systems of transportation, communication, energy, and finance. in this important book, the author provides an unprecedented examination of how twelve communities in nine countries responded to destructive earthquakes between 1999 and 2015. And many of the book's lessons can also be applied to other large-scale risks. This book sets the global problem of seismic risk in the framework of complex adaptive systems to explore how the consequences of such events ripple across jurisdictions, communities, and organizations in complex societies, triggering unexpected alliances but also exposing social, economic, and legal gaps. This book assesses how the networks of organizations involved in response and recovery adapted and acted collectively after the twelve earthquakes it examines. It describes how advances in information technology enabled some communities to anticipate seismic risk better and to manage response and recovery operations more effectively, decreasing losses. Finally, the book shows why investing substantively in global information infrastructure would create shared awareness of seismic risk and make postdisaster relief more effective and less expensive. The result is a landmark study of how to improve the way we prepare for and respond to earthquakes and other disasters in our ever-more-complex world.
Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory
by
Curto, Raúl E.
,
Lee, Woo Young
,
Hwang, In Sung
in
Functions of bounded variation
,
Interpolation
,
Operator theory
2019
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and
operator theory. We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the
Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. We propose a new notion of tensored-scalar singularity, and
then answer questions on Hankel operators with matrix-valued bounded type symbols. We also examine an interpolation problem related to a
certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér
Interpolation Problem for matrix rational functions. We then extend the
On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function
by
Lenells, Jonatan
,
Fokas, Athanassios S.
in
Asymptotic expansions
,
Functions of a complex variable -- Miscellaneous topics of analysis in the complex domain -- Asymptotic representations in the complex domain. msc
,
Functions, Zeta
2022
We present several formulae for the large
Conformal Graph Directed Markov Systems on Carnot Groups
by
Tyson, Jeremy
,
Chousionis, Vasilis
,
Urbański, Mariusz
in
Conformal mapping
,
Hausdorff measures
,
Markov processes
2020
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
Colonization by B. infantis EVC001 modulates enteric inflammation in exclusively breastfed infants
by
Henrick, Bethany M
,
Brown, Heather K
,
Smilowitz, Jennifer T
in
Baby foods
,
Breastfeeding & lactation
,
Cytokines
2019
BackgroundInfant gut dysbiosis, often associated with low abundance of bifidobacteria, is linked to impaired immune development and inflammation—a risk factor for increased incidence of several childhood diseases. We investigated the impact of B. infantis EVC001 colonization on enteric inflammation in a subset of exclusively breastfed term infants from a larger clinical study.MethodsStool samples (n = 120) were collected from infants randomly selected to receive either 1.8 × 1010 CFU B. infantis EVC001 daily for 21 days (EVC001) or breast milk alone (controls), starting at day 7 postnatal. The fecal microbiome was analyzed using 16S ribosomal RNA, proinflammatory cytokines using multiplexed immunoassay, and fecal calprotectin using ELISA at three time points: days 6 (Baseline), 40, and 60 postnatal.ResultsFecal calprotectin concentration negatively correlated with Bifidobacterium abundance (P < 0.0001; ρ = −0.72), and proinflammatory cytokines correlated with Clostridiaceae and Enterobacteriaceae, yet negatively correlated with Bifidobacteriaceae abundance. Proinflammatory cytokines were significantly lower in EVC001-fed infants on days 40 and 60 postnatally compared to baseline and compared to control infants.ConclusionOur findings indicate that gut dysbiosis (absence of B. infantis) is associated with increased intestinal inflammation. Early addition of EVC001 to diet represents a novel strategy to prevent enteric inflammation during a critical developmental phase.
Journal Article
Cell type‐specific nuclear pores: a case in point for context‐dependent stoichiometry of molecular machines
by
Ori, Alessandro
,
Solis‐Mezarino, Victor
,
Andrés‐Pons, Amparo
in
Architecture
,
Calibration
,
Cell cycle
2013
To understand the structure and function of large molecular machines, accurate knowledge of their stoichiometry is essential. In this study, we developed an integrated targeted proteomics and super‐resolution microscopy approach to determine the absolute stoichiometry of the human nuclear pore complex (NPC), possibly the largest eukaryotic protein complex. We show that the human NPC has a previously unanticipated stoichiometry that varies across cancer cell types, tissues and in disease. Using large‐scale proteomics, we provide evidence that more than one third of the known, well‐defined nuclear protein complexes display a similar cell type‐specific variation of their subunit stoichiometry. Our data point to compositional rearrangement as a widespread mechanism for adapting the functions of molecular machines toward cell type‐specific constraints and context‐dependent needs, and highlight the need of deeper investigation of such structural variants.
The stoichiometry of the human nuclear pore complex is revealed by targeted mass spectrometry and super‐resolution microscopy. The analysis reveals that the composition of the nuclear pore and other nuclear protein complexes is remodeled as a function of the cell type.
Synopsis
The stoichiometry of the human nuclear pore complex is revealed by targeted mass spectrometry and super‐resolution microscopy. The analysis reveals that the composition of the nuclear pore and other nuclear protein complexes is remodeled as a function of the cell type.
The human NPC has a previously unanticipated stoichiometry that varies across cell types.
Primarily functional Nups are dynamic, while the NPC scaffold is static.
Stoichiometries of many complexes are fine‐tuned toward cell type‐specific needs.
Journal Article
The Effect of Etrasimod on Fecal Calprotectin and High-sensitivity C-reactive Protein: Results From the ELEVATE UC Clinical Program
2025
Abstract
Background
Biomarkers offer potential alternatives to endoscopies in monitoring ulcerative colitis (UC) progression and therapeutic response. This post hoc analysis of the ELEVATE UC clinical program assessed potential predictive values of fecal calprotectin (fCAL) and high-sensitivity C-reactive protein (hsCRP) as biomarkers and associated responses to etrasimod, an oral, once-daily, selective sphingosine 1-phosphate (S1P)1,4,5 receptor modulator for the treatment of moderately to severely active UC, in 2 phase 3 clinical trials.
Methods
In ELEVATE UC 52 and ELEVATE UC 12, patients were randomized 2:1 to 2 mg of etrasimod once daily or placebo for 52 or 12 weeks, respectively. Fecal calprotectin/hsCRP differences between responders and nonresponders for efficacy end points (clinical remission, clinical response, endoscopic improvement-histologic remission [EIHR]) were assessed by Wilcoxon P-values. Sensitivity and specificity were presented as receiver operating characteristics (ROC) curves with area under the curve (AUC).
Results
In ELEVATE UC 52 and ELEVATE UC 12, 289 and 238 patients received etrasimod and 144 and 116 received placebo, respectively. Baseline fCAL/hsCRP concentrations were generally balanced. Both trials had lower week-12 median fCAL levels in week-12 responders vs nonresponders receiving etrasimod for clinical remission, clinical response, and EIHR (all P < .001), with similar trends for hsCRP levels (all P < .01). For etrasimod, AUCs for fCAL/hsCRP and EIHR were 0.85/0.74 (week 12; ELEVATE UC 52), 0.83/0.69 (week 52; ELEVATE UC 52), and 0.80/0.65 (week 12; ELEVATE UC 12).
Conclusions
Fecal calprotectin/hsCRP levels decreased with etrasimod treatment; ROC analyses indicated a prognostic correlation between fCAL changes during induction and short-/long-term treatment response.
Lay Summary
We show associations between fecal calprotectin (fCAL) and high-sensitivity C-reactive protein (hsCRP) levels with efficacy outcomes among patients receiving 2 mg of etrasimod once daily, and that fCAL levels may be an early indicator of the achievement of long-term efficacy end point achievement.
Journal Article
A pilot randomized controlled trial investigating the effects of an anti-inflammatory dietary pattern on disease activity, symptoms and microbiota profile in adults with inflammatory bowel disease
2024
Background/ObjectivesThere is a lack of certainty in dietary prescription for individuals with inflammatory bowel disease (IBD) due to heterogeneity in studies to date. The aim of this study was to investigate the efficacy on disease activity of a modified anti-inflammatory dietary pattern purposely designed to reduce intake of food additives (IBD-MAID), compared to standard care, in adults with IBD.Subject/MethodsAdults with IBD were randomised to IBD-MAID (meals provided) [n = 29] or general healthy eating (GHE) [n = 29] for 8 weeks. Disease activity, faecal calprotectin (FC), C-reactive protein (CRP), symptoms, and quality of life (S&QOL) were assessed using validated tools.ResultsThe IBD-MAID was well tolerated and adhered to (92% adherence). At week 8, there was no statistically significant difference in change from baseline in outcome measures between groups. However, baseline to week 8 analysis indicated: (1) statistically significant improvements in S (p = 0.001) & QOL (p = 0.004), FC (p = 0.007), and Crohn’s disease activity (p = 0.03) but not ulcerative colitis, in individuals following the IBD-MAID and (2) statistically significant improvement in QOL in individuals receiving GHE (p = 0.015). Correlation analysis on change from baseline to week 8 revealed a greater decrease in food additives intake was associated with statistically significant improvements in FC, S & QOL and alignment of anti-inflammatory dietary principles with improvements in QOL.ConclusionThe IBD-MAID was well tolerated. The most novel finding pertains to the correlation between reduced food additives intake and improvements in inflammatory markers, S&QOL. Further research is needed to explore the effects of food additives exposure on IBD course.Trial registration12619001500145
Journal Article