Search for: All records

Abstract In this paper, an invariant is introduced for negative definite plumbed 3-manifolds equipped with a spin c {{}^{c}} -structure. It unifies and extends two theories with rather different origins and structures. One theory is lattice cohomology, motivated by the study of normal surface singularities, known to be isomorphic to the Heegaard Floer homology for certain classes of plumbed 3-manifolds. Another specialization gives BPS q -series which satisfy some remarkable modularity properties and recover SU ⁢ ( 2 ) {{\rm SU}(2)} quantum invariants of 3-manifolds at roots of unity.In particular, our work gives rise to a 2-variable refinement of the Z ^ {\widehat{Z}} -invariant. 

Abstract Viruses are the most numerically abundant biological entities on Earth. As ubiquitous replicators of molecular information and agents of community change, viruses have potent effects on the life on Earth, and may play a critical role in human spaceflight, for life-detection missions to other planetary bodies and planetary protection. However, major knowledge gaps constrain our understanding of the Earth's virosphere: (1) the role viruses play in biogeochemical cycles, (2) the origin(s) of viruses and (3) the involvement of viruses in the evolution, distribution and persistence of life. As viruses are the only replicators that span all known types of nucleic acids, an expanded experimental and theoretical toolbox built for Earth's viruses will be pivotal for detecting and understanding life on Earth and beyond. Only by filling in these knowledge and technical gaps we will obtain an inclusive assessment of how to distinguish and detect life on other planetary surfaces. Meanwhile, space exploration requires life-support systems for the needs of humans, plants and their microbial inhabitants. Viral effects on microbes and plants are essential for Earth's biosphere and human health, but virus–host interactions in spaceflight are poorly understood. Viral relationships with their hosts respond to environmental changes in complex ways which are difficult to predict by extrapolating from Earth-based proxies. These relationships should be studied in space to fully understand how spaceflight will modulate viral impacts on human health and life-support systems, including microbiomes. In this review, we address key questions that must be examined to incorporate viruses into Earth system models, life-support systems and life detection. Tackling these questions will benefit our efforts to develop planetary protection protocols and further our understanding of viruses in astrobiology. 

In this work, we utilize progressive growth-based Generative Adversarial Networks (GANs) to develop the Clarkson Fingerprint Generator (CFG). We demonstrate that the CFG is capable of generating realistic, high fidelity, 512×512 pixels, full, plain impression fingerprints. Our results suggest that the fingerprints generated by the CFG are unique, diverse, and resemble the training dataset in terms of minutiae configuration and quality, while not revealing the underlying identities of the training data. We make the pre-trained CFG model and the synthetically generated dataset publicly available at https://github.com/keivanB/Clarkson_Finger_Gen 

Abstract For positive integers n and d > 0, let $$G(\mathbb {Q}^n,\; d)$$ denote the graph whose vertices are the set of rational points $$\mathbb {Q}^n$$ , with $$u,v \in \mathbb {Q}^n$$ being adjacent if and only if the Euclidean distance between u and v is equal to d . Such a graph is deemed “non-trivial” if d is actually realized as a distance between points of $$\mathbb {Q}^n$$ . In this paper, we show that a space $$\mathbb {Q}^n$$ has the property that all pairs of non-trivial distance graphs $$G(\mathbb {Q}^n,\; d_1)$$ and $$G(\mathbb {Q}^n,\; d_2)$$ are isomorphic if and only if n is equal to 1, 2, or a multiple of 4. Along the way, we make a number of observations concerning the clique number of $$G(\mathbb {Q}^n,\; d)$$ .