1,267 research outputs found
Probability of local bifurcation type from a fixed point: A random matrix perspective
Results regarding probable bifurcations from fixed points are presented in
the context of general dynamical systems (real, random matrices), time-delay
dynamical systems (companion matrices), and a set of mappings known for their
properties as universal approximators (neural networks). The eigenvalue spectra
is considered both numerically and analytically using previous work of Edelman
et. al. Based upon the numerical evidence, various conjectures are presented.
The conclusion is that in many circumstances, most bifurcations from fixed
points of large dynamical systems will be due to complex eigenvalues.
Nevertheless, surprising situations are presented for which the aforementioned
conclusion is not general, e.g. real random matrices with Gaussian elements
with a large positive mean and finite variance.Comment: 21 pages, 19 figure
Antimullerian hormone and obesity: insights in oral contraceptive users
The study was conducted to examine the impact of oral contraceptives (OCs) on serum antimullerian hormone (AMH) levels by obesity status in reproductive-age women
Smooth analysis of the condition number and the least singular value
Let \a be a complex random variable with mean zero and bounded variance.
Let be the random matrix of size whose entries are iid copies of
\a and be a fixed matrix of the same size. The goal of this paper is to
give a general estimate for the condition number and least singular value of
the matrix , generalizing an earlier result of Spielman and Teng for
the case when \a is gaussian.
Our investigation reveals an interesting fact that the "core" matrix does
play a role on tail bounds for the least singular value of . This
does not occur in Spielman-Teng studies when \a is gaussian.
Consequently, our general estimate involves the norm .
In the special case when is relatively small, this estimate is nearly
optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde
Sparse Exploratory Factor Analysis
Sparse principal component analysis is a very active research area in the last decade. It produces component loadings with many zero entries which facilitates their interpretation and helps avoid redundant variables. The classic factor analysis is another popular dimension reduction technique which shares similar interpretation problems and could greatly benefit from sparse solutions. Unfortunately, there are very few works considering sparse versions of the classic factor analysis. Our goal is to contribute further in this direction. We revisit the most popular procedures for exploratory factor analysis, maximum likelihood and least squares. Sparse factor loadings are obtained for them by, first, adopting a special reparameterization and, second, by introducing additional [Formula: see text]-norm penalties into the standard factor analysis problems. As a result, we propose sparse versions of the major factor analysis procedures. We illustrate the developed algorithms on well-known psychometric problems. Our sparse solutions are critically compared to ones obtained by other existing methods
Constraining Unmodeled Physics with Compact Binary Mergers from GWTC-1
We present a flexible model to describe the effects of generic deviations of observed gravitational wave signals from modeled waveforms in the LIGO and Virgo gravitational wave detectors. With the detection of 11 gravitational wave events from the GWTC-1 catalog, we are able to constrain possible deviations from our modeled waveforms. In this paper we present our coherent spline model that describes the deviations, then choose to validate our model on an example phenomenological and astrophysically motivated departure in waveforms based on extreme spontaneous scalarization. We find that the model is capable of recovering the simulated deviations. By performing model comparisons we observe that the spline model effectively describes the simulated departures better than a normal compact binary coalescence (CBC) model. We analyze the entire GWTC-1 catalog of events with our model and compare it to a normal CBC model, finding that there are no significant departures from the modeled template gravitational waveforms used
Phase diagram of bismuth in the extreme quantum limit
Elemental bismuth provides a rare opportunity to explore the fate of a
three-dimensional gas of highly mobile electrons confined to their lowest
Landau level. Coulomb interaction, neglected in the band picture, is expected
to become significant in this extreme quantum limit with poorly understood
consequences. Here, we present a study of the angular-dependent Nernst effect
in bismuth, which establishes the existence of ultraquantum field scales on top
of its complex single-particle spectrum. Each time a Landau level crosses the
Fermi level, the Nernst response sharply peaks. All such peaks are resolved by
the experiment and their complex angular-dependence is in very good agreement
with the theory. Beyond the quantum limit, we resolve additional Nernst peaks
signaling a cascade of additional Landau sub-levels caused by electron
interaction
Network analysis of England's single parent household COVID-19 control policy impact: a proof-of-concept study
Lockdowns have been a core infection control measure in many countries during the COVID-19 pandemic. In England s first lockdown, children of single parent households (SPHs) were permitted to move between parental homes. By the second lockdown, SPH support bubbles between households were also permitted, enabling larger within-household networks. We investigated the combined impact of these approaches on household transmission dynamics, to inform policymaking for control and support mechanisms in a respiratory pandemic context. This network modelling study applied percolation theory to a base model of SPHs constructed using population survey estimates of SPH family size. To explore putative impact, varying estimates were applied regarding extent of bubbling and proportion of Different-parentage SPHs (DSPHs) (in which children do not share both the same parents). Results indicate that the formation of giant components (in which Covid-19 household transmission accelerates) are more contingent on DSPHs than on formation of bubbles between SPHs, and that bubbling with another SPH will accelerate giant component formation where one or both are DSPHs. Public health guidance should include supportive measures that mitigate the increased transmission risk afforded by support bubbling among DSPHs. Future network, mathematical and epidemiological studies should examine both independent and combined impact of policies
GSP with General Independent Click-Through-Rates
The popular generalized second price (GSP) auction for sponsored search is
built upon a separable model of click-through-rates that decomposes the
likelihood of a click into the product of a "slot effect" and an "advertiser
effect" --- if the first slot is twice as good as the second for some bidder,
then it is twice as good for everyone. Though appealing in its simplicity, this
model is quite suspect in practice. A wide variety of factors including
externalities and budgets have been studied that can and do cause it to be
violated. In this paper we adopt a view of GSP as an iterated second price
auction (see, e.g., Milgrom 2010) and study how the most basic violation of
separability --- position dependent, arbitrary public click-through-rates that
do not decompose --- affects results from the foundational analysis of GSP
(Varian 2007, Edelman et al. 2007). For the two-slot setting we prove that for
arbitrary click-through-rates, for arbitrary bidder values, an efficient
pure-strategy equilibrium always exists; however, without separability there
always exist values such that the VCG outcome and payments cannot be realized
by any bids, in equilibrium or otherwise. The separability assumption is
therefore necessary in the two-slot case to match the payments of VCG but not
for efficiency. We moreover show that without separability, generic existence
of efficient equilibria is sensitive to the choice of tie-breaking rule, and
when there are more than two slots, no (bid-independent) tie-breaking rule
yields the positive result. In light of this we suggest alternative mechanisms
that trade the simplicity of GSP for better equilibrium properties when there
are three or more slots
The fundamental cycle of concept construction underlying various theoretical frameworks
In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning
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