The purpose of this section is to provide an example of a particularly natural scaffold (with precision c=∞) in the setting of purely inseparable extensions, and since the results of §3 are therefore applicable, submit the topic of generalized Galoi…

Let $L/K$ be a finite, totally ramified $p$-extension of complete local fields with residue fields of characteristic $p > 0$, and let $A$ be a $K$-al…

The National Science Foundation supported this research through Grants DEB-0918392 and DEB-0918413. We thank J. Newman, G. Robinson, I.-N. Wang and A.C. Gorski for comments. D. Yoakam kept us energized.

Certain invasive plants may rely on interference mechanisms (allelopathy, e.g.) to gain competitive superiority over native species. But expending re…

Patient notes contain a wealth of information of potentially great interest to medical investigators. However, to protect patients' privacy, Protecte…

The matching distance is a pseudometric on multi-parameter persistence modules, defined in terms of the weighted bottleneck distance on the restricti…

In this paper we establish the stability and its trade-off with optimization error of SGD algorithms for pairwise learning. Stability results of SGD hold true for both convex and non-convex cases. The trade-off results are established by deriving th…

In this paper we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learn…

Subjective Logic (SL) is one of well-known belief models that can explicitly deal with uncertain opinions and infer unknown opinions based on a rich …

According to our understanding of the everyday physical world, observable phenomena are underpinned by persistent objects that can be reidentified (o…

Drones, or general UAVs, equipped with cameras have been fast deployed with a wide range of applications, including agriculture, aerial photography, …

Phase contrast microscopy (PCM) has been widely used in biomedicine research, which allows users to observe objectives without staining or killing th…

In this paper, a framework of learning through empirical gain maximization was developed to deal with robust regression problems. The development of such a framework was inspired by several well-established but yet not fully-understood regression sc…

We develop in this paper a framework of empirical gain maximization (EGM) to address the robust regression problem where heavy-tailed noise or outlie…

Numerous networks in the real world change over time, in the sense that nodes and edges enter and leave the networks. Various dynamic random graph mo…

Using a design derivation, we showed that the TC is the functional designed to rank the global amount of correlations in a system between all of its variables. We relied heavily on the PCC, which while quite simple, is restrictive enough to isolate …

Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respe…

All data are digitized, and hence are essentially integers rather than true real numbers. Ordinarily this causes no difficulties since the truncation…

5G network is envisioned to deploy a massive Internet-of-Things (IoTs) with requirements of low-latency, low control overhead and low power. Current …

Spectrally and energy efficient orthogonal frequency division multiplexing (SEE-OFDM) is an optical OFDM technique based on combining multiple asymme…

In this paper, we propose a new model to segment cells in phase contrast microscopy images. Cell images collected from the similar scenario share a s…

This work is part of a project on weight bases for the irreducible representations of semisimple Lie algebras with respect to which the representatio…

In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diag…

For node level graph encoding, a recent important state-of-art method is the graph convolutional networks (GCN), which nicely integrate local vertex …

In this paper, we propose Object-driven Attentive Generative Adversarial Newtorks (Obj-GANs) that allow object-centered text-to-image synthesis for c…

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