194 research outputs found
Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence
Spreading processes are conventionally monitored on a macroscopic level by
counting the number of incidences over time. The spreading process can then be
modeled either on the microscopic level, assuming an underlying interaction
network, or directly on the macroscopic level, assuming that microscopic
contributions are negligible. The macroscopic characteristics of both
descriptions are commonly assumed to be identical. In this work, we show that
these characteristics of microscopic and macroscopic descriptions can be
different due to coalescence, i.e., a node being activated at the same time by
multiple sources. In particular, we consider a (microscopic) branching network
(probabilistic cellular automaton) with annealed connectivity disorder, record
the macroscopic activity, and then approximate this activity by a (macroscopic)
branching process. In this framework, we analytically calculate the effect of
coalescence on the collective dynamics. We show that coalescence leads to a
universal non-linear scaling function for the conditional expectation value of
successive network activity. This allows us to quantify the difference between
the microscopic model parameter and established macroscopic estimates. To
overcome this difference, we propose a non-linear estimator that correctly
infers the model branching parameter for all system sizes.Comment: 13 page
Tailored ensembles of neural networks optimize sensitivity to stimulus statistics
The dynamic range of stimulus processing in living organisms is much larger
than a single neural network can explain. For a generic, tunable spiking
network we derive that while the dynamic range is maximal at criticality, the
interval of discriminable intensities is very similar for any network tuning
due to coalescence. Compensating coalescence enables adaptation of
discriminable intervals. Thus, we can tailor an ensemble of networks optimized
to the distribution of stimulus intensities, e.g., extending the dynamic range
arbitrarily. We discuss potential applications in machine learning.Comment: 6 pages plus supplemental materia
Tackling the subsampling problem to infer collective properties from limited data
Complex systems are fascinating because their rich macroscopic properties
emerge from the interaction of many simple parts. Understanding the building
principles of these emergent phenomena in nature requires assessing natural
complex systems experimentally. However, despite the development of large-scale
data-acquisition techniques, experimental observations are often limited to a
tiny fraction of the system. This spatial subsampling is particularly severe in
neuroscience, where only a tiny fraction of millions or even billions of
neurons can be individually recorded. Spatial subsampling may lead to
significant systematic biases when inferring the collective properties of the
entire system naively from a subsampled part. To overcome such biases, powerful
mathematical tools have been developed in the past. In this perspective, we
overview some issues arising from subsampling and review recently developed
approaches to tackle the subsampling problem. These approaches enable one to
assess, e.g., graph structures, collective dynamics of animals, neural network
activity, or the spread of disease correctly from observing only a tiny
fraction of the system. However, our current approaches are still far from
having solved the subsampling problem in general, and hence we conclude by
outlining what we believe are the main open challenges. Solving these
challenges alongside the development of large-scale recording techniques will
enable further fundamental insights into the working of complex and living
systems.Comment: 20 pages, 6 figures, review articl
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Cooperative Asymmetric Catalysis with Squaramide H-Bond Donors and Lewis Acids
A new mode of cooperative catalysis with chiral squaramide hydrogen-bond donors and trialkylsilyl trifluoromethanesulfonates (triflates) for asymmetric nucleophilic additions to oxocarbenium ions was explored. Evidence is provided for a dual role of the squaramide catalyst: rate acceleration through activation of the silicon Lewis acid and enantioinduction through triflate anion-binding. In the first chapter, we present examples of current methodologies used for activation of Brønsted and Lewis acids in organocatalysis. In the rest of this thesis, we explore the mechanism and applications of cooperative catalysis with chiral squaramide hydrogen-bond donors and trialkylsilyl triflates.
In Chapter 2, we show that in the presence of trialkylsilyl triflate, chiral squaramides can catalyze highly enantioselective (4+3) cycloaddition reactions of pyruvic aldehyde dimethyl acetal derivatives with furans. Detailed mechanistic studies reveal the formation of a resting state complex between the squaramide catalyst and the trialkylsilyl triflate, which leads to enhanced Lewis acidity of silicon. The chiral squaramide catalyst then controls the stereoselectivity of the subsequent nucleophilic addition to the oxocarbenium through binding of the triflate anion.
Chapter 3 describes the development of an asymmetric squaramide and trialkylsilyl triflate co-catalyzed nucleophilic substitution of acetals. High enantioselectivities are achieved in this transformation with a range of nucleophiles spanning five orders of magnitude in nucleophilicity parameter, from methallyltrimethylsilane to silyl ketene acetal. In Chapter 4, we expand this new reactivity concept to aldehyde substrates. A synthetically practical chiral squaramide is shown to catalyze an asymmetric Mukaiyama aldol reaction with moderate enantioselectivities.Chemistry and Chemical Biolog
A Mild, Palladium-Catalyzed Method for the Dehydrohalogenation of Alkyl Bromides: Synthetic and Mechanistic Studies
We have exploited a typically undesired elementary step in cross-coupling reactions, β-hydride elimination, to accomplish palladium-catalyzed dehydrohalogenations of alkyl bromides to form terminal olefins. We have applied this method, which proceeds in excellent yield at room temperature in the presence of a variety of functional groups, to a formal total synthesis of (R)-mevalonolactone. Our mechanistic studies have established that the rate-determining step can vary with the structure of the alkyl bromide and, most significantly, that L_2PdHBr (L = phosphine), an intermediate that is often invoked in palladium-catalyzed processes such as the Heck reaction, is not an intermediate in the active catalytic cycle
Recent Jewish immigrants\u27 communication in Postville, Iowa: A case study
For this paper the author researched Iowa\u27s immigration history and modern day Postville, a small town that represents a tossed salad of cultural, religious, and linguistic diversities. The author analyzed the current effect of immigration as well as the process of integration and assimilation into the small town through the eyes of its immigrants. The major emphasis is placed on Postville located in northeast Iowa. For 150 years Postville was an all-white, all-Christian farming community of 1,000 souls, most of European ancestry. Today the population of Postville has doubled and of the 2,000 people who reside in Postville almost one quarter are Jewish, and Hispanics, Russians, and other ethnicities make up another 300 people. Within the last decade this small town has undergone considerable social and cultural changes.
With this research project the author explored how communication between different cultures in small Iowa town has affected the life of the immigrants; the researcher wanted to learn the pros and cons that people see in being an immigrant, what struggles they face living in another culture, and how they maintain their home traditions, culture, and native language
When to be critical? Performance and evolvability in different regimes of neural Ising agents
It has long been hypothesized that operating close to the critical state is
beneficial for natural, artificial and their evolutionary systems. We put this
hypothesis to test in a system of evolving foraging agents controlled by neural
networks that can adapt agents' dynamical regime throughout evolution.
Surprisingly, we find that all populations that discover solutions, evolve to
be subcritical. By a resilience analysis, we find that there are still benefits
of starting the evolution in the critical regime. Namely, initially critical
agents maintain their fitness level under environmental changes (for example,
in the lifespan) and degrade gracefully when their genome is perturbed. At the
same time, initially subcritical agents, even when evolved to the same fitness,
are often inadequate to withstand the changes in the lifespan and degrade
catastrophically with genetic perturbations. Furthermore, we find the optimal
distance to criticality depends on the task complexity. To test it we introduce
a hard and simple task: for the hard task, agents evolve closer to criticality
whereas more subcritical solutions are found for the simple task. We verify
that our results are independent of the selected evolutionary mechanisms by
testing them on two principally different approaches: a genetic algorithm and
an evolutionary strategy. In summary, our study suggests that although optimal
behaviour in the simple task is obtained in a subcritical regime, initializing
near criticality is important to be efficient at finding optimal solutions for
new tasks of unknown complexity.Comment: arXiv admin note: substantial text overlap with arXiv:2103.1218
Estimations by stable motions and applications
We propose a nonparametric parameter estimation of confidence intervals when
the underlying has large or infinite variance. We explain the method by a
simple numerical example and provide an application to estimate the coupling
strength in neuronal networks
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