Physical Sciences and Mathematics Commons^™

A Note On Solid Coloring Of Pure Simplicial Complexes, Joseph O'Rourke

Computer Science: Faculty Publications

We establish a simple generalization of a known result in the plane. The simplices in any pure simplicial complex in R^d may be colored with d+1 colors so that no two simplices that share a (d-1)-facet have the same color. In R² this says that any planar map all of whose faces are triangles may be 3-colored, and in R³ it says that tetrahedra in a collection may be "solid 4-colored" so that no two glued face-to-face receive the same color.

Superhydrophobic Thin Films Fabricated By Reactive Layer-By-Layer Assembly Of Azlactone-Functionalized Polymers, Maren E. Buck, Sarina C. Schwartz, David M. Lynn

Chemistry: Faculty Publications

We report an approach to the fabrication of superhydrophobic thin films that is based on the "reactive" layer-by-layer assembly of azlactone-containing polymer multilayers. We demonstrate that films fabricated from alternating layers of the azlactone functionalized polymer poly(2-vinyl- 4,4-dimethylazlactone) (PVDMA) and poly(ethyleneimine) (PEI) exhibit micro- and nanoscale surface features that result in water contact angles in excess of 150°. Our results reveal that the formation of these surface features is (i) dependent upon film thickness (i.e., the number of layers of PEI and PVDMA deposited) and (ii) that it is influenced strongly by the presence (or absence) of cyclic azlactone-functionalized oligomers …

Sweeping Minimum Perimeter Enclosing Parallelograms: Optimal Crumb Cleanup, Yonit Bousany, Mary Leah Karker, Joseph O'Rourke, Leona Sparaco

Computer Science: Faculty Publications

We examine the problem of pushing all the points of a planar region into one point using parallel sweeps of an infinite line, minimizing the sum of the lengths of the sweep vectors. We characterize the optimal 2-sweeps of triangles, and provide a linear-time algorithm for convex polygons.

Slider-Pinning Rigidity: A Maxwell-Laman-Type Theorem, Ileana Streinu, Louis Theran

Computer Science: Faculty Publications

We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley’s direction networks.

Testing Mechanisms Of Subduction Zone Segmentation And Seismogenesis With Slip Distributions From Recent Andean Earthquakes, John P. Loveless, M. E. Pritchard, K. Kukowski

Geosciences: Faculty Publications

A long-standing goal of subduction zone earthquake studies is to determine whether or not there are physical processes that control seismogenesis and the along-strike segmentation of the megathrust. Studies of individual earthquakes and global compilations of earthquakes find favorable comparison between coseismic interplate slip distributions and several different long-lived forearc characteristics, such as bathymetry, coastline morphology, crustal structure, and interplate frictional properties, but no single explanation seems to govern the location and slip distribution of all earthquakes. One possible reason for the lack of a unifying explanation is that the inferred earthquake parameters, most importantly the slip distribution, calculated in …

Interaction-Dependent Pcr: Identification Of Ligand-Target Pairs From Libraries Of Ligands And Libraries Of Targets In A Single Solution-Phase Experiment, Lynn M. Mcgregor, David J. Gorin, Christoph E. Dumelin, David R. Liu

Chemistry: Faculty Publications

Interaction-dependent PCR (IDPCR) is a solution-phase method to identify binding partners from combined libraries of small-molecule ligands and targets in a single experiment. Binding between DNA-linked targets and DNA-linked ligands induces formation of an extendable duplex. Extension links codes that identify the ligand and target into one selectively amplifiable DNA molecule. In a model selection, IDPCR resulted in the enrichment of DNA encoding all five known protein-ligand pairs out of 67 599 possible sequences.

Smoothness Of Lipschitz Minimal Intrinsic Graphs In Heisenberg Groups ℍN, N > 1, Luca Capogna, Giovanna Citti, Maria Manfredini

Mathematics Sciences: Faculty Publications

We prove that Lipschitz intrinsic graphs in the Heisenberg groups ℍn, with n > 1, which are vanishing viscosity solutions of the minimal surface equation, are smooth and satisfy the PDE in a strong sense.

Flat Zipper-Unfolding Pairs For Platonic Solids, Joseph O'Rourke

Computer Science: Faculty Publications

We show that four of the five Platonic solids' surfaces may be cut open with a Hamiltonian path along edges and unfolded to a polygonal net each of which can "zipper-refold" to a flat doubly covered parallelogram, forming a rather compact representation of the surface. Thus these regular polyhedra have particular flat "zipper pairs." No such zipper pair exists for a dodecahedron, whose Hamiltonian unfoldings are "zip-rigid." This report is primarily an inventory of the possibilities, and raises more questions than it answers.

Curvedland: An Applet For Illustrating Curved Geometry Without Embedding, Gary Felder, Stephanie Erickson

Physics: Faculty Publications

We have written a Java applet to illustrate the meaning of curved geometry. The applet provides a mapping interface similar to MapQuest or Google Maps; features include the ability to navigate through a space and place permanent point objects and/or shapes at arbitrary positions. The underlying two-dimensional space has a constant, positive curvature, which causes the apparent paths and shapes of the objects in the map to appear distorted in ways that change as you view them from different relative angles and distances.

Flattening Single-Vertex Origami: The Non-Expansive Case, Gaiane Panina, Ileana Streinu

Computer Science: Faculty Publications

A single-vertex origami is a piece of paper with straight-line rays called creases emanating from a fold vertex placed in its interior or on its boundary. The Single-Vertex Origami Flattening problem asks whether it is always possible to reconfigure the creased paper from any configuration compatible with the metric, to a flat, non-overlapping position, in such a way that the paper is not torn, stretched and, for rigid origami, not bent anywhere except along the given creases. Streinu and Whiteley showed how to reduce the problem to the carpenter's rule problem for spherical polygons. Using spherical expansive motions, they solved …

Nano-Imprinted Thin Films Of Reactive, Azlactone-Containing Polymers: Combining Methods For The Topographic Patterning Of Cell Substrates With Opportunities For Facile Post-Fabrication Chemical Functionalization, Nathaniel J. Fredin, Ryan M. Flessner, Christopher M. Jewell, Shane L. Bechler, Maren E. Buck, David M. Lynn

Chemistry: Faculty Publications

Laser scanning confocal microscopy (LSCM) and atomic force microscopy (AFM) were used to characterize changes in nanoscale structure that occur when ultrathin polyelectrolyte multilayers (PEMs) are incubated in aqueous media. The PEMs investigated here were fabricated by the deposition of alternating layers of plasmid DNA and a hydrolytically degradable polyamine onto a precursor film composed of alternating layers of linear poly(ethylene imine) (LPEI) and sodium poly(styrene sulfonate) (SPS). Past studies of these materials in the context of gene delivery revealed transformations from a morphology that is smooth and uniform to one characterized by the formation of nanometer-scale particulate structures. We …

Grouped Variable Model Selection For Heterogeneous Medical Signals, Jamie Macbeth, Majid Sarrafzadeh

Computer Science: Faculty Publications

We explore statistical regression techniques for use in medical monitoring and telehealth applications. Medical embedded systems of the present and future are recording vast sets of data related to medical conditions and physiology. In this paper, distributed time-lag linear models are proposed as a means to help explain relationships between two or more medical and physiological measurements. The issues associated with performing multiple regression with heterogeneous medical data are treated as problems in model selection. An automatic method of model selection is proposed to construct models for high sample rate data by grouping sets of predictor variables.

The grouped predictor …

Wanda B.: Weight And Activity With Blood Pressure Monitoring System For Heart Failure Patients, Myung Kyung Suh, Lorraine S. Evangelista, Victor Chen, Wen Sao Hong, Jamie Macbeth, Ani Nahapetian, Florence Joy Figueras, Majid Sarrafzadeh

Computer Science: Faculty Publications

Heart failure is a leading cause of death in the United States, with around 5 million Americans currently suffering from congestive heart failure. The WANDA B. wireless health technology leverages sensor technology and wireless communication to monitor heart failure patient activity and to provide tailored guidance. Patients who have cardiovascular system disorders can measure their weight, blood pressure, activity levels, and other vital signs in a real-time automated fashion. The system was developed in conjunction with the UCLA Nursing School and the UCLA Wireless Health Institute for use on actual patients. It is currently in use with real patients in …

Convexity And Horizontal Second Fundamental Forms For Hypersurfaces In Carnot Groups, Luca Capogna, Scott D. Pauls, Jeremy T. Tyson

Mathematics Sciences: Faculty Publications

We use a Riemannian approximation scheme to give a characterization for smooth convex functions on a Carnot group (in the sense of Danielli-Garofalo- Nhieu or Lu-Manfredi-Stroffolini) in terms of the positive semidefiniteness of the horizontal second fundamental form of their graph.

On Folding A Polygon To A Polyhedron, Joseph O'Rourke

Computer Science: Faculty Publications

We show that the open problem presented in "Geometric Folding Algorithms: Linkages, Origami, Polyhedra" [DO07] is solved by a theorem of Burago and Zalgaller [BZ96] from more than a decade earlier.

Poset Pinball, Gkm-Compatible Subspaces, And Hessenberg Varieties, Megumi Harada, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

This paper has three main goals. First, we set up a general framework to address the problem of constructing module bases for the equivariant cohomology of certain subspaces of GKM spaces. To this end we introduce the notion of a GKM-compatible subspace of an ambient GKM space. We also discuss poset-upper-triangularity, a key combinatorial notion in both GKM theory and more generally in localization theory in equivariant cohomology. With a view toward other applications, we present parts of our setup in a general algebraic and combinatorial framework. Second, motivated by our central problem of building module bases, we introduce a …

On Flat Polyhedra Deriving From Alexandrov's Theorem, Joseph O'Rourke

Computer Science: Faculty Publications

We show that there is a straightforward algorithm to determine if the polyhedron guaranteed to exist by Alexandrov's gluing theorem is a degenerate flat polyhedron, and to reconstruct it from the gluing instructions. The algorithm runs in O(n³) time for polygons whose gluings are specified by n labels.

Shrinking Symbolic Regression Over Medical And Physiological Signals, Jamie Macbeth, Majid Sarrafzadeh

Computer Science: Faculty Publications

Medical embedded systems of the present and future are recording vast sets of data related to medical conditions and physiology. Linear modeling techniques are proposed as a means to help explain relationships between two or more medical or physiological signal measurements from the same human subject. In this paper a statistical regression algorithm is explored for use in medical monitoring, telehealth, and medical research applications.

An essential element in applying linear modeling to physiological data is determining functional forms for the predictor signals. In this paper we demonstrate an efficient method for symbolic regression and model selection among possible transformation …

Health Econometrics: Respiration- Oxygenation Correlation Through Spectral Models, Jamie Macbeth, Majid Sarrafzadeh

Computer Science: Faculty Publications

Medical embedded systems are capable of recording vast data sets for physiological and medical research. Linear modeling techniques are proposed as a means to explore relationships between two or more medical or physiological signal measurements where a causal relationship is believed to be present. Multiple regression is explored for use in medical monitoring, telehealth, and clinical applications.

Spectral regression methods for high-bandwidth medical and physiological signals are demonstrated. The twostage method consists of performing an FFT over a timelagged window of the predictor signal, and constructing a model based on the FFT coefficients. The output of the regression is used …

Star Unfolding Convex Polyhedra Via Quasigeodesic Loops, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu

Computer Science: Faculty Publications

We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron ℘ to a simple (nonoverlapping) planar polygon: cut along one shortest path from each vertex of ℘ toQ, and cut all but one segment of Q.

Immobilization Of Polymer-Decorated Liquid Crystal Droplets On Chemically Tailored Surfaces, Michael I. Kinsinger, Maren E. Buck, Nicholas L. Abbott, David M. Lynn

Chemistry: Faculty Publications

We demonstrate that the assembly of an amphiphilic polyamine on the interfaces of micrometer-sized droplets of a thermotropic liquid crystal (LC) dispersed in aqueous solutions can be used to facilitate the immobilization of LC droplets on chemically functionalized surfaces. Polymer 1 was designed to contain both hydrophobic (alkylfunctionalized) and hydrophilic (primary and tertiary amine-functionalized) side chain functionality. The assembly of this polymer at the interfaces of aqueous dispersions of LC droplets was achieved by the spontaneous adsorption of polymer from aqueous solution. Polymer adsorption triggered transitions in the orientational ordering of the LCs, as observed by polarized light and bright-field …

Climatic Cycles Recorded In The Middle Eocene Hemipelagites From A Dinaric Foreland Basin Of Istria (Croatia), Borna Lužar-Oberiter, Peter A. Hochuli, Ljubomir Babić, Bosiljka Glumac, Darko Tibljas

Geosciences: Faculty Publications

Middle Eocene hemipelagic marls from the Pazin-Trieste Basin, a foreland basin of the Croatian Dinarides, display repetitive alternations of two types of marls with different resistance to weathering. This study focuses on the chemical composition, stable isotopes, and palynomorph content of these marls in order to better understand the nature of their cyclic deposition and to identify possible paleoenvironmental drivers responsible for their formation. The less resistant marls (LRM) have consistently lower carbonate content, lower δ18O and δ13C values, and more abundant dinoflagellate cysts than the more resistant marls (MRM). We interpret these differences between the two marl types to …

The Yao Graph Y6 Is A Spanner, Joseph O'Rourke

Computer Science: Faculty Publications

We prove that Y₆ is a spanner. Y₆ is the Yao graph on a set of planar points, which has an edge from each point x to a closest point y within each of the six angular cones of 60^◦ surrounding x .

Functionalization Of Fibers Using Azlactone-Containing Polymers: Layer-By-Layer Fabrication Of Reactive Thin Films On The Surfaces Of Hair And Cellulose-Based Materials, Maren E. Buck, David M. Lynn

Chemistry: Faculty Publications

We report an approach to the functionalization of fibers and fiber-based materials that is based on the deposition of reactive azlactone-functionalized polymers and the "reactive" layer-by-layer assembly of azlactone-containing thin films. We demonstrate (i) that the azlactone-functionalized polymer poly(2-vinyl-4,4-dimethylazlactone) (PVDMA) can be used to modify the surfaces of a model protein-based fiber (horsehair) and cellulose-based materials (e.g., cotton and paper), and (ii) that fibers functionalized in this manner can be used to support the fabrication of covalently cross-linked and reactive polymer multilayers assembled using PVDMA and poly(ethyleneimine) (PEI). The growth, chemical reactivity, and uniformity of films deposited on these substrates …

Schubert Polynomials And Classes Of Hessenberg Varieties, Dave Anderson, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Regular semisimple Hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory, numerical analysis, representation theory, algebraic geometry, and combinatorics. We give a " Giambelli formula" expressing the classes of regular semisimple Hessenberg varieties in terms of Chern classes. In fact, we show that the cohomology class of each regular semisimple Hessenberg variety is the specialization of a certain double Schubert polynomial, giving a natural geometric interpretation to such specializations. We also decompose such classes in terms of the Schubert basis for the cohomology ring of the flag variety. The coefficients obtained are nonnegative, …

Realistic Reconfiguration Of Crystalline (And Telecube) Robots, Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D. Demaine, Dania El-Khechen, Robin Flatland, Stefan Langerman, Joseph O'Rourke, Val Pinciu, Suneeta Ramaswami, Vera Sacristán, Stefanie Wuhrer

Computer Science: Faculty Publications

In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2×2×2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target configuration. Our algorithms involve a total of …

Normal And Reverse Faulting Driven By The Subduction Zone Earthquake Cycle In The Northern Chilean Forearc, John P. Loveless, Richard W. Allmendinger, Matthew E. Pritchard, Gabriel González

Geosciences: Faculty Publications

Despite its location in a convergent tectonic setting, the Coastal Cordillera of northern Chile between 21°S and 25°S is dominated by structures demonstrating extension in the direction of plate convergence. In some locations, however, normal faults have been reactivated as reverse faults, complicating the interpretation of long-term strain. In order to place these new observations in a tectonic context, we model stress changes induced on these faults by the subduction earthquake cycle. Our simulations predict that interseismic locking on the plate boundary encourages normal slip on fore-arc faults, which may result from elastic rebound due to interplate earthquakes or from …

Reactive Layer-By-Layer Assembly Of Suspended Thin Films And Semipermeable Membranes At Interfaces Created Between Aqueous And Organic Phases, Maren E. Buck, David M. Lynn

Chemistry: Faculty Publications

Thin films of polymer suspended across the openings of pores, channels, and microcavities are of interest in a broad range of fundamental and applied contexts. A "reactive" layer-by-layer approach Is demonstrated for the fabrication of suspended thin films and semipermeable membranes that makes use of liquid/ liquid interfaces created between immiscible aqueous and organic phases as templates for film fabrication (see image). (Figure Presented).

A Sharp Diameter Bound For Unipotent Groups Of Classical Type Overℤ /Pℤ, Jordan S. Ellenberg, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

The unipotent subgroup of a finite group of Lie type over a prime field Fp comes equipped with a natural set of generators; the properties of the Cayley graph associated to this set of generators have been much studied. In the present paper, we show that the diameter of this Cayley graph is bounded above and below by constant multiples of np + n2 log p, where n is the rank of the associated Lie group. This generalizes the result of Ellenberg, A sharp diameter bound for an upper triangular matrix group, Harvard University, 1993, which treated the case of …

Lie Algebroid Structures On Double Vector Bundles And Representation Theory Of Lie Algebroids, Alfonso Gracia-Saz, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB-algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids.