Eigenvectors of the discrete Laplacian on regular graphs - a statistical approach

In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical observations, suggesting that the eigenvectors follow a Gaussian distribution. Following this assumption, we reconstruct some properties of the nodal structure which were observed in numerical simulations, but were not explained so far. We also show that some statistical properties of the nodal pattern cannot be described in terms of a percolation model, as opposed to the suggested correspondence for eigenvectors of 2 dimensional manifolds.Comment: 28 pages, 11 figure

A New Discrete Particle Swarm Algorithm Applied to Attribute Selection in a Bioinformatics Data Set

Many data mining applications involve the task of build- ing a model for predictive classification. The goal of such a model is to classify examples (records or data instances) into classes or categories of the same type. The use of variables (attributes) not related to the classes can reduce the accu- racy and reliability of a classification or prediction model. Superfluous variables can also increase the costs of build- ing a model - particularly on large data sets. We propose a discrete Particle Swarm Optimization (PSO) algorithm de- signed for attribute selection. The proposed algorithm deals with discrete variables, and its population of candidate solu- tions contains particles of different sizes. The performance of this algorithm is compared with the performance of a standard binary PSO algorithm on the task of selecting at- tributes in a bioinformatics data set. The criteria used for comparison are: (1) maximizing predictive accuracy; and (2) finding the smallest subset of attributes

Geometric characterization of nodal domains: the area-to-perimeter ratio

In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength $1/\sqrt{E}$. We show that the distribution function $P(\rho)$ can distinguish between domains in which the classical dynamics is regular or chaotic. For separable surfaces, we compute the limiting distribution, and show that it is supported by an interval, which is independent of the properties of the surface. In systems which are chaotic, or in random-waves, the area-to-perimeter distribution has substantially different features which we study numerically. We compare the features of the distribution for chaotic wave functions with the predictions of the percolation model to find agreement, but only for nodal domains which are big with respect to the wavelength scale. This work is also closely related to, and provides a new point of view on isoperimetric inequalities.Comment: 22 pages, 11 figure

Uniformity in the Wiener-Wintner theorem for nilsequences

We prove a uniform extension of the Wiener-Wintner theorem for nilsequences due to Host and Kra and a nilsequence extension of the topological Wiener-Wintner theorem due to Assani. Our argument is based on (vertical) Fourier analysis and a Sobolev embedding theorem.Comment: v3: 18 p., proof that the cube construction produces compact homogeneous spaces added, measurability issues in the proof of Theorem 1.5 addressed. We thank the anonymous referees for pointing out these gaps in v

Upregulated integrin α11 in the stroma of cutaneous squamous cell carcinoma promotes skin carcinogenesis

Integrin α11β1 is a collagen-binding integrin that is needed to induce and maintain the myofibroblast phenotype in fibrotic tissues and during wound healing. The expression of the α11 is upregulated in cancer-associated fibroblasts (CAFs) in various human neoplasms. We investigated α11 expression in human cutaneous squamous cell carcinoma (cSCC) and in benign and premalignant human skin lesions and monitored its effects on cSCC development by subjecting α11-knockout (Itga11−/−) mice to the DMBA/TPA skin carcinogenesis protocol. α11-deficient mice showed significantly decreased tumor cell proliferation, leading to delayed tumor development and reduced tumor burden. Integrin α11 expression was significantly upregulated in the desmoplastic tumor stroma of human and mouse cSCCs, and the highest α11 expression was detected in high-grade tumors. Our results point to a reduced ability of α11-deficient stromal cells to differentiate into matrix-producing and tumor-promoting CAFs and suggest that this is one causative mechanism underlying the observed decreased tumor growth. An unexpected finding in our study was that, despite reduced CAF activation, the α11-deficient skin tumors were characterized by the presence of thick and regularly aligned collagen bundles. This finding was attributed to a higher expression of TGFβ1 and collagen crosslinking lysyl oxidases in the Itga11-/- tumor stroma. In summary, our data suggest that α11β1 operates in a complex interactive tumor environment to regulate ECM synthesis and collagen organization and thus foster cSCC growth. Further studies with advanced experimental models are still needed to define the exact roles and molecular mechanisms of stromal α11β1 in skin tumorigenesis.publishedVersio

Manual / Issue 10 / Polychrome

Manual, a journal about art and its making. Polychrome. In art, especially, polychrome invites us to the dialogue that colors are always having amongst themselves. A history of polychrome could be a series of poems exchanged among colors. The exchange might exhibit something like perpetual newness, again and again revealing differently bent hues and movingly novel blends. It would be a short-line poetry, excruciatingly sensitive to tone. Its speakers would have no names, so it would confuse the psychology of human orientation. In this connection, a warning against rendering polychrome as a pure positive seems in order: the parties to this dialogue talk at cross-purposes, always on the brink of divorcing. Polychrome can offend and destroy. It conscripts discrete colors in order to sacrifice them. Does polychrome offend by mocking our own failure to connect? In any case, polychrome has an advanced idiom for dealing with conflict. It’s at home with uncertainty. —Darby English, from the introduction to Issue 10: Polychrome. Softcover, 80 pages. Published 2018 by the RISD Museum. Manual 10 (Polychrome) contributors include David Batchelor, Gina Borromeo, Nicole Buchanan, Catherine Cooper, Darby English, Mara L. Hermano, Elon Cook Lee, Josephine Lee, Evelyn Lincoln, Dominic Molon, Maureen C. O\u27Brien, RISD Museum 2017 Summer Teen Intensive Students, and Elizabeth A. Williams.https://digitalcommons.risd.edu/risdmuseum_journals/1036/thumbnail.jp

Manual / Issue 12 / On Further Review

Manual, a journal about art and its making. On Further Review. This issue uncovers narratives once central to objects’ histories but that now have been systematically obscured, inadvertently overlooked, or otherwise lost. Softcover, 96 pages. Published 2019 by the RISD Museum.(On Further Review) contributors include Anita N. Bateman, Laurie Anne Brewer, Becci Davis, Jamie Gabbarelli, Bethany Johns, Elon Cook Lee, Kevin McBride, Walker Mettling, Jessica Rosner, Suzanne Scanlan, Nell Painter, Allison Pappas, Pamela A. Parmal, Shiyanthi Thavapalan, and Nick White.https://digitalcommons.risd.edu/risdmuseum_journals/1038/thumbnail.jp

EVEREST: automatic identification and classification of protein domains in all protein sequences

BACKGROUND: Proteins are comprised of one or several building blocks, known as domains. Such domains can be classified into families according to their evolutionary origin. Whereas sequencing technologies have advanced immensely in recent years, there are no matching computational methodologies for large-scale determination of protein domains and their boundaries. We provide and rigorously evaluate a novel set of domain families that is automatically generated from sequence data. Our domain family identification process, called EVEREST (EVolutionary Ensembles of REcurrent SegmenTs), begins by constructing a library of protein segments that emerge in an all vs. all pairwise sequence comparison. It then proceeds to cluster these segments into putative domain families. The selection of the best putative families is done using machine learning techniques. A statistical model is then created for each of the chosen families. This procedure is then iterated: the aforementioned statistical models are used to scan all protein sequences, to recreate a library of segments and to cluster them again. RESULTS: Processing the Swiss-Prot section of the UniProt Knoledgebase, release 7.2, EVEREST defines 20,230 domains, covering 85% of the amino acids of the Swiss-Prot database. EVEREST annotates 11,852 proteins (6% of the database) that are not annotated by Pfam A. In addition, in 43,086 proteins (20% of the database), EVEREST annotates a part of the protein that is not annotated by Pfam A. Performance tests show that EVEREST recovers 56% of Pfam A families and 63% of SCOP families with high accuracy, and suggests previously unknown domain families with at least 51% fidelity. EVEREST domains are often a combination of domains as defined by Pfam or SCOP and are frequently sub-domains of such domains. CONCLUSION: The EVEREST process and its output domain families provide an exhaustive and validated view of the protein domain world that is automatically generated from sequence data. The EVEREST library of domain families, accessible for browsing and download at [1], provides a complementary view to that provided by other existing libraries. Furthermore, since it is automatic, the EVEREST process is scalable and we will run it in the future on larger databases as well. The EVEREST source files are available for download from the EVEREST web site