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

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