Algorithms for Approximate Subtropical Matrix Factorization

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for finding patterns from the data. Rather than using the standard algebra -- and the summation of the rank-1 components to build the approximation of the original matrix -- we use the subtropical algebra, which is an algebra over the nonnegative real values with the summation replaced by the maximum operator. Subtropical matrix factorizations allow "winner-takes-it-all" interpretations of the rank-1 components, revealing different structure than the normal (nonnegative) factorizations. We study the complexity and sparsity of the factorizations, and present a framework for finding low-rank subtropical factorizations. We present two specific algorithms, called Capricorn and Cancer, that are part of our framework. They can be used with data that has been corrupted with different types of noise, and with different error metrics, including the sum-of-absolute differences, Frobenius norm, and Jensen--Shannon divergence. Our experiments show that the algorithms perform well on data that has subtropical structure, and that they can find factorizations that are both sparse and easy to interpret.Comment: 40 pages, 9 figures. For the associated source code, see http://people.mpi-inf.mpg.de/~pmiettin/tropical

Thinking Fragments: Adisciplinary Reflections on Feminisms and Environmental Justic

Feminisms and environmental justice are some of the names of struggles to understand nature-culture linkages and conceptualize just worlds for non-humans and their human kin. In this paper, I revisit my journey of doing environmental justice research, i.e. of my feminist scientific practice in Asia and Latin America. In this retrospective telling I highlight how gender, political economy, and race were and remain fundamental in producing the subjects and objects of my research and analysis. I discuss how an implicit feminism helped me grapply with the complex nature-culture linkages I observed in the field. Postcolonial and marxist insights supplement and complement feminisms in the questions I pose as we attempt to imagine new nature-cultures

Human brain evolution and the "Neuroevolutionary Time-depth Principle:" Implications for the Reclassification of fear-circuitry-related traits in DSM-V and for studying resilience to warzone-related posttraumatic stress disorder.

The DSM-III, DSM-IV, DSM-IV-TR and ICD-10 have judiciously minimized discussion of etiologies to distance clinical psychiatry from Freudian psychoanalysis. With this goal mostly achieved, discussion of etiological factors should be reintroduced into the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-V). A research agenda for the DSM-V advocated the "development of a pathophysiologically based classification system". The author critically reviews the neuroevolutionary literature on stress-induced and fear circuitry disorders and related amygdala-driven, species-atypical fear behaviors of clinical severity in adult humans. Over 30 empirically testable/falsifiable predictions are presented. It is noted that in DSM-IV-TR and ICD-10, the classification of stress and fear circuitry disorders is neither mode-of-acquisition-based nor brain-evolution-based. For example, snake phobia (innate) and dog phobia (overconsolidational) are clustered together. Similarly, research on blood-injection-injury-type-specific phobia clusters two fears different in their innateness: 1) an arguably ontogenetic memory-trace-overconsolidation-based fear (hospital phobia) and 2) a hardwired (innate) fear of the sight of one's blood or a sharp object penetrating one's skin. Genetic architecture-charting of fear-circuitry-related traits has been challenging. Various, non-phenotype-based architectures can serve as targets for research. In this article, the author will propose one such alternative genetic architecture. This article was inspired by the following: A) Nesse's "Smoke-Detector Principle", B) the increasing suspicion that the "smooth" rather than "lumpy" distribution of complex psychiatric phenotypes (including fear-circuitry disorders) may in some cases be accounted for by oligogenic (and not necessarily polygenic) transmission, and C) insights from the initial sequence of the chimpanzee genome and comparison with the human genome by the Chimpanzee Sequencing and Analysis Consortium published in late 2005. Neuroevolutionary insights relevant to fear circuitry symptoms that primarily emerge overconsolidationally (especially Combat related Posttraumatic Stress Disorder) are presented. Also introduced is a human-evolution-based principle for clustering innate fear traits. The "Neuroevolutionary Time-depth Principle" of innate fears proposed in this article may be useful in the development of a neuroevolution-based taxonomic re-clustering of stress-triggered and fear-circuitry disorders in DSM-V. Four broad clusters of evolved fear circuits are proposed based on their time-depths: 1) Mesozoic (mammalian-wide) circuits hardwired by wild-type alleles driven to fixation by Mesozoic selective sweeps; 2) Cenozoic (simian-wide) circuits relevant to many specific phobias; 3) mid Paleolithic and upper Paleolithic (Homo sapiens-specific) circuits (arguably resulting mostly from mate-choice-driven stabilizing selection); 4) Neolithic circuits (arguably mostly related to stabilizing selection driven by gene-culture co-evolution). More importantly, the author presents evolutionary perspectives on warzone-related PTSD, Combat-Stress Reaction, Combat-related Stress, Operational-Stress, and other deployment-stress-induced symptoms. The Neuroevolutionary Time-depth Principle presented in this article may help explain the dissimilar stress-resilience levels following different types of acute threat to survival of oneself or one's progency (aka DSM-III and DSM-V PTSD Criterion-A events). PTSD rates following exposure to lethal inter-group violence (combat, warzone exposure or intentionally caused disasters such as terrorism) are usually 5-10 times higher than rates following large-scale natural disasters such as forest fires, floods, hurricanes, volcanic eruptions, and earthquakes. The author predicts that both intentionally-caused large-scale bioevent-disasters, as well as natural bioevents such as SARS and avian flu pandemics will be an exception and are likely to be followed by PTSD rates approaching those that follow warzone exposure. During bioevents, Amygdala-driven and locus-coeruleus-driven epidemic pseudosomatic symptoms may be an order of magnitude more common than infection-caused cytokine-driven symptoms. Implications for the red cross and FEMA are discussed. It is also argued that hospital phobia as well as dog phobia, bird phobia and bat phobia require re-taxonomization in DSM-V in a new "overconsolidational disorders" category anchored around PTSD. The overconsolidational spectrum category may be conceptualized as straddling the fear circuitry spectrum disorders and the affective spectrum disorders categories, and may be a category for which Pitman's secondary prevention propranolol regimen may be specifically indicated as a "morning after pill" intervention. Predictions are presented regarding obsessive-compulsive disorder (OCD) (e.g., female-pattern hoarding vs. male-pattern hoarding) and "culture-bound" acute anxiety symptoms (taijin-kyofusho, koro, shuk yang, shook yong, suo yang, rok-joo, jinjinia-bemar, karoshi, gwarosa, Voodoo death). Also discussed are insights relevant to pseudoneurological symptoms and to the forthcoming Dissociative-Conversive disorders category in DSM-V, including what the author terms fright-triggered acute pseudo-localized symptoms (i.e., pseudoparalysis, pseudocerebellar imbalance, psychogenic blindness, pseudoseizures, and epidemic sociogenic illness). Speculations based on studies of the human abnormal-spindle-like, microcephaly-associated (ASPM) gene, the microcephaly primary autosomal recessive (MCPH) gene, and the forkhead box p2 (FOXP2) gene are made and incorporated into what is termed "The pre-FOXP2 Hypothesis of Blood-Injection-Injury Phobia." Finally, the author argues for a non-reductionistic fusion of "distal (evolutionary) neurobiology" with clinical "proximal neurobiology," utilizing neurological heuristics. It is noted that the value of re-clustering fear traits based on behavioral ethology, human-phylogenomics-derived endophenotypes and on ontogenomics (gene-environment interactions) can be confirmed or disconfirmed using epidemiological or twin studies and psychiatric genomics

Towards Lower Bounds on the Depth of ReLU Neural Networks

We contribute to a better understanding of the class of functions that is represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical geometry, we provide a mathematical counterbalance to the universal approximation theorems which suggest that a single hidden layer is sufficient for learning tasks. In particular, we investigate whether the class of exactly representable functions strictly increases by adding more layers (with no restrictions on size). This problem has potential impact on algorithmic and statistical aspects because of the insight it provides into the class of functions represented by neural hypothesis classes. However, to the best of our knowledge, this question has not been investigated in the neural network literature. We also present upper bounds on the sizes of neural networks required to represent functions in these neural hypothesis classes.Comment: Camera-ready version for NeurIPS 2021 conferenc

Millimeter waves study. Radio frequency system Quarterly report, 1 Sept. - 1 Dec. 1968

Millimeter wave studies on satellite-earth transmission channel, and construction of 2250 MHz television exciter uni

The 1984 ASEE-NASA summer faculty fellowship program (aeronautics and research)

The 1984 NASA-ASEE Faculty Fellowship Program (SFFP) is reported. The report includes: (1) a list of participants; (2) abstracts of research projects; (3) seminar schedule; (4) evaluation questionnaire; and (5) agenda of visitation by faculty programs committee. Topics discussed include: effects of multiple scattering on laser beam propagation; information management; computer techniques; guidelines for writing user documentation; 30 graphics software; high energy electron and antiproton cosmic rays; high resolution Fourier transform infrared spectrum; average monthly annual zonal and global albedos; laser backscattering from ocean surface; image processing systems; geomorphological mapping; low redshift quasars; application of artificial intelligence to command management systems

Accelerating large-eddy simulations of clouds with Tensor Processing Units

Clouds, especially low clouds, are crucial for regulating Earth's energy balance and mediating the response of the climate system to changes in greenhouse gas concentrations. Despite their importance for climate, they remain relatively poorly understood and are inaccurately represented in climate models. A principal reason is that the high computational expense of simulating them with large-eddy simulations (LES) has inhibited broad and systematic numerical experimentation and the generation of large datasets for training parametrization schemes for climate models. Here we demonstrate LES of low clouds on Tensor Processing Units (TPUs), application-specific integrated circuits that were originally developed for machine learning applications. We show that TPUs in conjunction with tailored software implementations can be used to simulate computationally challenging stratocumulus clouds in conditions observed during the Dynamics and Chemistry of Marine Stratocumulus (DYCOMS) field study. The TPU-based LES code successfully reproduces clouds during DYCOMS and opens up the large computational resources available on TPUs to cloud simulations. The code enables unprecedented weak and strong scaling of LES, making it possible, for example, to simulate stratocumulus with $10\times$ speedup over real-time evolution in domains with a $34.7~\mathrm{km} \times 53.8~\mathrm{km}$ horizontal cross section. The results open up new avenues for computational experiments and for substantially enlarging the sample of LES available to train parameterizations of low clouds