94 research outputs found
The Sivashinsky equation for corrugated flames in the large-wrinkle limit
Sivashinsky's (1977) nonlinear integro-differential equation for the shape of
corrugated 1-dimensional flames is ultimately reducible to a 2N-body problem,
involving the 2N complex poles of the flame slope. Thual, Frisch & Henon (1985)
derived singular linear integral equations for the pole density in the limit of
large steady wrinkles , which they solved exactly for monocoalesced
periodic fronts of highest amplitude of wrinkling and approximately otherwise.
Here we solve those analytically for isolated crests, next for monocoalesced
then bicoalesced periodic flame patterns, whatever the (large-) amplitudes
involved. We compare the analytically predicted pole densities and flame shapes
to numerical results deduced from the pole-decomposition approach. Good
agreement is obtained, even for moderately large Ns. The results are extended
to give hints as to the dynamics of supplementary poles. Open problems are
evoked
Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane
We consider flame front propagation in channel geometries. The steady state
solution in this problem is space dependent, and therefore the linear stability
analysis is described by a partial integro-differential equation with a space
dependent coefficient. Accordingly it involves complicated eigenfunctions. We
show that the analysis can be performed to required detail using a finite order
dynamical system in terms of the dynamics of singularities in the complex
plane, yielding detailed understanding of the physics of the eigenfunctions and
eigenvalues.Comment: 17 pages 7 figure
Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II
The current paper is a corrected version of our previous paper
arXiv:adap-org/9608001. Similarly to previous version we investigate the
problem of flame propagation. This problem is studied as an example of unstable
fronts that wrinkle on many scales. The analytic tool of pole expansion in the
complex plane is employed to address the interaction of the unstable growth
process with random initial conditions and perturbations. We argue that the
effect of random noise is immense and that it can never be neglected in
sufficiently large systems. We present simulations that lead to scaling laws
for the velocity and acceleration of the front as a function of the system size
and the level of noise, and analytic arguments that explain these results in
terms of the noisy pole dynamics.This version corrects some very critical
errors made in arXiv:adap-org/9608001 and makes more detailed description of
excess number of poles in system, number of poles that appear in the system in
unit of time, life time of pole. It allows us to understand more correctly
dependence of the system parameters on noise than in arXiv:adap-org/9608001Comment: 23 pages, 4 figures,revised, version accepted for publication in
journal "Combustion, Explosion and Shock Waves". arXiv admin note:
substantial text overlap with arXiv:nlin/0302021, arXiv:adap-org/9608001,
arXiv:nlin/030201
Sivashinsky equation in a rectangular domain
The (Michelson) Sivashinsky equation of premixed flames is studied in a
rectangular domain in two dimensions. A huge number of 2D stationary solutions
are trivially obtained by addition of two 1D solutions. With Neumann boundary
conditions, it is shown numerically that adding two stable 1D solutions leads
to a 2D stable solution. This type of solution is shown to play an important
role in the dynamics of the equation with additive noise
Image Co-localization by Mimicking a Good Detector's Confidence Score Distribution
Given a set of images containing objects from the same category, the task of
image co-localization is to identify and localize each instance. This paper
shows that this problem can be solved by a simple but intriguing idea, that is,
a common object detector can be learnt by making its detection confidence
scores distributed like those of a strongly supervised detector. More
specifically, we observe that given a set of object proposals extracted from an
image that contains the object of interest, an accurate strongly supervised
object detector should give high scores to only a small minority of proposals,
and low scores to most of them. Thus, we devise an entropy-based objective
function to enforce the above property when learning the common object
detector. Once the detector is learnt, we resort to a segmentation approach to
refine the localization. We show that despite its simplicity, our approach
outperforms state-of-the-art methods.Comment: Accepted to Proc. European Conf. Computer Vision 201
Flame front propagation I: The Geometry of Developing Flame Fronts: Analysis with Pole Decomposition
The roughening of expanding flame fronts by the accretion of cusp-like
singularities is a fascinating example of the interplay between instability,
noise and nonlinear dynamics that is reminiscent of self-fractalization in
Laplacian growth patterns. The nonlinear integro-differential equation that
describes the dynamics of expanding flame fronts is amenable to analytic
investigations using pole decomposition. This powerful technique allows the
development of a satisfactory understanding of the qualitative and some
quantitative aspects of the complex geometry that develops in expanding flame
fronts.Comment: 4 pages, 2 figure
Dynamic Key-Value Memory Networks for Knowledge Tracing
Knowledge Tracing (KT) is a task of tracing evolving knowledge state of
students with respect to one or more concepts as they engage in a sequence of
learning activities. One important purpose of KT is to personalize the practice
sequence to help students learn knowledge concepts efficiently. However,
existing methods such as Bayesian Knowledge Tracing and Deep Knowledge Tracing
either model knowledge state for each predefined concept separately or fail to
pinpoint exactly which concepts a student is good at or unfamiliar with. To
solve these problems, this work introduces a new model called Dynamic Key-Value
Memory Networks (DKVMN) that can exploit the relationships between underlying
concepts and directly output a student's mastery level of each concept. Unlike
standard memory-augmented neural networks that facilitate a single memory
matrix or two static memory matrices, our model has one static matrix called
key, which stores the knowledge concepts and the other dynamic matrix called
value, which stores and updates the mastery levels of corresponding concepts.
Experiments show that our model consistently outperforms the state-of-the-art
model in a range of KT datasets. Moreover, the DKVMN model can automatically
discover underlying concepts of exercises typically performed by human
annotations and depict the changing knowledge state of a student.Comment: To appear in 26th International Conference on World Wide Web (WWW),
201
Resolvent methods for steady premixed flame shapes governed by the Zhdanov-Trubnikov equation
Using pole decompositions as starting points, the one parameter (-1 =< c < 1)
nonlocal and nonlinear Zhdanov-Trubnikov (ZT) equation for the steady shapes of
premixed gaseous flames is studied in the large-wrinkle limit. The singular
integral equations for pole densities are closely related to those satisfied by
the spectral density in the O(n) matrix model, with n = -2(1 + c)/(1 - c). They
can be solved via the introduction of complex resolvents and the use of complex
analysis. We retrieve results obtained recently for -1 =< c =< 0, and we
explain and cure their pathologies when they are continued naively to 0 < c <
1. Moreover, for any -1 =< c < 1, we derive closed-form expressions for the
shapes of steady isolated flame crests, and then bicoalesced periodic fronts.
These theoretical results fully agree with numerical resolutions. Open problems
are evoked.Comment: v2: 29 pages, 6 figures, some typos correcte
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
Interferon and B-cell Signatures Inform Precision Medicine in Lupus Nephritis
Introduction: Current therapeutic management of lupus nephritis (LN) fails to induce long-term remission in over 50% of patients, highlighting the urgent need for additional options. Methods: We analyzed differentially expressed genes (DEGs) in peripheral blood from patients with active LN (n = 41) and active nonrenal lupus (n = 62) versus healthy controls (HCs) (n = 497) from the European PRECISESADS project (NTC02890121), and dysregulated gene modules in a discovery (n = 26) and a replication (n = 15) set of active LN cases. Results: Replicated gene modules qualified for correlation analyses with serologic markers, and regulatory network and druggability analysis. Unsupervised coexpression network analysis revealed 20 dysregulated gene modules and stratified the active LN population into 3 distinct subgroups. These subgroups were characterized by low, intermediate, and high interferon (IFN) signatures, with differential dysregulation of the “B cell” and “plasma cells/Ig” modules. Drugs annotated to the IFN network included CC-motif chemokine receptor 1 (CCR1) inhibitors, programmed death-ligand 1 (PD-L1) inhibitors, and irinotecan; whereas the anti-CD38 daratumumab and proteasome inhibitor bortezomib showed potential for counteracting the “plasma cells/Ig” signature. In silico analysis demonstrated the low-IFN subgroup to benefit from calcineurin inhibition and the intermediate-IFN subgroup from B-cell targeted therapies. High-IFN patients exhibited greater anticipated response to anifrolumab whereas daratumumab appeared beneficial to the intermediate-IFN and high-IFN subgroups. Conclusion: IFN upregulation and B and plasma cell gene dysregulation patterns revealed 3 subgroups of LN, which may not necessarily represent distinct disease phenotypes but rather phases of the inflammatory processes during a renal flare, providing a conceptual framework for precision medicine in LN. © 2024 International Society of Nephrolog
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