Physical Sciences and Mathematics Commons^™

Four Functions Of Statistical Significance Tests, Xinshu Zhao

Professor Xinshu ZHAO

Nike Considered: Getting Traction On Sustainability, Christopher Lyddy, Rebecca Henderson, Richard M. Locke, Cate Reavis

Christopher J. Lyddy

No abstract provided.

Mixed-Initiative Personal Assistants, Joshua W. Buck, Saverio Perugini

Saverio Perugini

Specification and implementation of flexible human-computer dialogs is challenging because of the complexity involved in rendering the dialog responsive to a vast number of varied paths through which users might desire to complete the dialog. To address this problem, we developed a toolkit for modeling and implementing task-based, mixed-initiative dialogs based on metaphors from lambda calculus. Our toolkit can automatically operationalize a dialog that involves multiple prompts and/or sub-dialogs, given a high-level dialog specification of it. Our current research entails incorporating the use of natural language to make the flexibility in communicating user utterances commensurate with that in dialog completion …

Realising Step Functions As Harmonic Measure Distributions Of Planar Domains, Marie Snipes, Lesley A. Ward

Marie A. Snipes

No abstract provided.

Sequias En El Sur De La Peninsula De Yucatan: Analisis De La Variabilidad Anual Y Estacional De La Precipitacion (Droughts In The Southern Yucatan Peninsula: Analysis Of The Annual And Seasonal Precipitation Variability), Sofia Mardero, Elsa Nickl, Birgit Schmook, Laura Schneider, John Rogan, Zachary Christman, Deborah Lawrence

Zachary Christman

Paper is in Spanish. English abstract: This study analyzes the spatial and temporal variability of precipitation across the Southern Yucatán Peninsula in Mexico, addressing the anomalies and trends of annual and seasonal precipitation as well as the occurrence of meteorological droughts, using rainfall data from nine weather stations during the period 1953-2007. Linear regression in the annual and seasonal rainfall were used to analyze the increase or decrease in precipitation trends over this period. Precipitation anomalies enabled the evaluation of the stability, deficit, or surplus of precipitation for each year or season, and a quintile method was used to …

Persistent Organic Chemicals In The Environment. Volume 1244

Bommanna Loganathan

The Risk Of Public Data Availability On Critical Infrastructure Protection, Roba Abbas

Dr Roba Abbas

This paper examines the threat of freely available information on critical infrastructure protection (CIP) efforts. Critical infrastructure are the services required to maintain the stability and security of a country, and comprise both physical and cyber infrastructures. These interdependent entities must be protected from natural disasters, accidental errors, and deliberate attacks. The CIP process typically includes vulnerability assessment, risk assessment and risk management, and has been a global concern for many years; the concern now amplified in Australia due to a number of recent events such the 9/11 attacks, and the Bali bombings. The events have called into question the …

Grnsight: A Web Application And Service For Visualizing Models Of Small- To Medium-Scale Gene Regulatory Networks, Kam D. Dahlquist, John David N. Dionisio, Ben G. Fitzpatrick, Nicole A. Anguiano, Anindita Varshneya, Britain J. Southwick, Mihir Samdarshi

John David N. Dionisio

GRNsight is a web application and service for visualizing models of gene regulatory networks (GRNs). A gene regulatory network (GRN) consists of genes, transcription factors, and the regulatory connections between them which govern the level of expression of mRNA and protein from genes. The original motivation came from our efforts to perform parameter estimation and forward simulation of the dynamics of a differential equations model of a small GRN with 21 nodes and 31 edges. We wanted a quick and easy way to visualize the weight parameters from the model which represent the direction and magnitude of the influence of …

Hom Quandles, Alissa S. Crans, Sam Nelson

Alissa Crans

If A is an abelian quandle and Q is a quandle, the hom set Hom(Q,A) of quandle homomorphisms from Q to A has a natural quandle structure. We exploit this fact to enhance the quandle counting invariant, providing an example of links with the same counting invariant values but distinguished by the hom quandle structure. We generalize the result to the case of biquandles, collect observations and results about abelian quandles and the hom quandle, and show that the category of abelian quandles is symmetric monoidal closed.

Solving The Ko Labyrinth, Alissa S. Crans

Alissa Crans

No abstract provided.

Higher Dimensional Algebra Vi: Lie 2-Algebra, John C. Baez, Alissa S. Crans

Alissa Crans

The theory of Lie algebras can be categorified starting from a new notion of `2-vector space', which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector spaces as objects, `linear functors' as morphisms and `linear natural transformations' as 2-morphisms. We define a `semistrict Lie 2-algebra' to be a 2-vector space L equipped with a skew-symmetric bilinear functor [ . , . ] : L x L -> L satisfying the Jacobi identity up to a completely antisymmetric trilinear natural transformation called the `Jacobiator', which in turn must satisfy a certain law of its …

Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra

Alissa Crans

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber

Alissa Crans

We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism called the "Jacobiator". Similarly, a Lie 2-group is a categorified version of a Lie group. If G is a simply-connected compact simple Lie group, there is a 1-parameter family of Lie 2-algebras g_k each having Lie(G) as its Lie algebra of objects, but with a Jacobiator built from the canonical 3-form on G. There appears to be no Lie 2-group …

The Forbidden Number Of A Knot, Alissa S. Crans, Blake Mellor, Sandy Ganzell

Alissa Crans

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbid- den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

Torsion In One-Term Distributive Homology, Alissa S. Crans, Józef H. Przytycki, Krzysztof K. Putyra

Alissa Crans

The one-term distributive homology was introduced by J.H.Przytycki as an atomic replacement of rack and quandle homology, which was first introduced and developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and M.Saito. This homology was initially suspected to be torsion-free, but we show in this paper that the one-term homology of a finite spindle can have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their homology precisely. In addition, we show that any finite group can appear as the torsion subgroup of the first homology of some finite spindle. Finally, …

Polynomial Knot And Link Invariants From The Virtual Biquandle, Alissa S. Crans, Allison Henrich, Sam Nelson

Alissa Crans

The Alexander biquandle of a virtual knot or link is a module over a 2-variable Laurent polynomial ring which is an invariant of virtual knots and links. The elementary ideals of this module are then invariants of virtual isotopy which determine both the generalized Alexander polynomial (also known as the Sawollek polynomial) for virtual knots and the classical Alexander polynomial for classical knots. For a fixed monomial ordering <, the Gr\"obner bases for these ideals are computable, comparable invariants which fully determine the elementary ideals and which generalize and unify the classical and generalized Alexander polynomials. We provide examples to …

Exotic Statistics For Strings In 4d Bf Theory, John C. Baez, Derek K. Wise, Alissa S. Crans

Alissa Crans

After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point particles, but also a set of generators that switch two strings by passing one through the other. The first set generates a copy of the symmetric group, while the second generates a copy of the braid group. Thanks to recent work of Xiao-Song Lin, we can …

Cohomology Of The Adjoint Of Hopf Algebras, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Masahico Saito

Alissa Crans

A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of the super line. As applications, solutions to the YBE are given and quandle cocycles are constructed from groupoid cocycles.

Crossed Modules Of Racks, Alissa S. Crans, Friedrich Wagemann

Alissa Crans

We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the relation between crossed modules of groups and strict 2-groups. Then we explore topological applications. We show that by applying the rack-space functor, a crossed module of racks gives rise to a covering. Our main result shows how the fundamental racks associated to links upstairs and downstairs in a covering fit together to form a crossed module of racks.

Cohomology Of Categorical Self-Distributivity, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Masahico Saito

Alissa Crans

We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provide solutions of the Yang–Baxter equation, and, conversely, solutions of the Yang–Baxter equation can be used to construct self-distributive operations in certain categories. Moreover, we present a cohomology theory that encompasses both Lie algebra and quandle cohomologies, is analogous to Hochschild cohomology, and can be used to study deformations of these self-distributive structures. All …

Cohomology Of Frobenius Algebras And The Yang-Baxter Equation, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Enver Karadayi, Masahico Saito

Alissa Crans

A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions in analogy with Hochschild cohomology of bialgebras based on deformation theory. Concrete computations are provided for key examples. Skein theoretic constructions give rise to solutions to the Yang-Baxter equation using multiplications and comultiplications of Frobenius algebras, and 2-cocycles are used to obtain deformations of R-matrices thus obtained.

Enhancements Of Rack Counting Invariants Via Dynamical Cocycles, Alissa S. Crans, Sam Nelson, Aparna Sarkar

Alissa Crans

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

Toy Blocks And Rotational Physics, Gabriele U. Varieschi, Isabel R. Jully

Gabriele Varieschi

Have you ever observed a child playing with toy blocks? A favorite game is to build towers and then make them topple like falling trees. To the eye of a trained physicist this should immediately look like an example of the physics of “falling chimneys,” when tall structures bend and break in mid-air while falling to the ground. The game played with toy blocks can actually reproduce well what is usually seen in photographs of falling towers, such as the one that appeared on the cover of the September 1976 issue of The Physics Teacher.1 In this paper we describe …

Kerr Metric, Geodesic Motion, And Flyby Anomaly In Fourth-Order Conformal Gravity, Gabriele U. Varieschi

Gabriele Varieschi

In this paper we analyze the Kerr geometry in the context of Conformal Gravity, an alternative theory of gravitation, which is a direct extension of General Relativity (GR). Following previous studies in the literature, we introduce an explicit expression of the Kerr metric in Conformal Gravity, which naturally reduces to the standard GR Kerr geometry in the absence of Conformal Gravity effects. As in the standard case, we show that the Hamilton–Jacobi equation governing geodesic motion in a space-time based on this geometry is indeed separable and that a fourth constant of motion—similar to Carter’s constant—can also be introduced in …

Intonation And Compensation Of Fretted String Instruments, Gabriele U. Varieschi, Christina M. Gower

Gabriele Varieschi

We discuss theoretical and physical models that are useful for analyzing the intonation of musical instruments such as guitars and mandolins and can be used to improve the tuning on these instruments. The placement of frets on the fingerboard is designed according to mathematical rules and the assumption of an ideal string. The analysis becomes more complicated when we include the effects of deformation of the string and inharmonicity due to other string characteristics. As a consequence, perfect intonation of all the notes on the instrument cannot be achieved, but complex compensation procedures can be introduced to minimize the problem. …

Simulating A Guitar With A Conventional Sonometer, Zily Burstein, Christina M. Gower, Gabriele U. Varieschi

Gabriele Varieschi

In this paper we present a simple way to convert a conventional sonometer into a simulated fretted instrument, such as a guitar or similar, by adding a fingerboard to the sonometer. In particular, we use this modified apparatus in relation to the problem of the instrument intonation, i.e., how to obtain correctly tuned notes on these string instruments. The experimental procedures presented in this study can become a more structured laboratory activity to be used in general physics courses or acoustics classes.

Astrophysical Tests Of Kinematical Conformal Cosmology In Fourth-Order Conformal Weyl Gravity, Gabriele U. Varieschi

Gabriele Varieschi

In this work we analyze kinematical conformal cosmology (KCC), an alternative cosmological model based on conformal Weyl gravity (CG), and test it against current type Ia supernova (SNIa) luminosity data and other astrophysical observations. Expanding upon previous work on the subject, we revise the analysis of SNIa data, confirming that KCC can explain the evidence for an accelerating expansion of the Universe without using dark energy or other exotic components. We obtain an independent evaluation of the Hubble constant, H0 = 67:53 kms-1 Mpc-1, very close to the current best estimates. The main KCC and CG parameters are re-evaluated and …

Toy Models For The Falling Chimney, Gabriele U. Varieschi, Kaoru Kamiya

Gabriele Varieschi

In this paper we review the theory of the ‘‘falling chimney,’’ which deals with the breaking in mid-air of tall structures when they fall to the ground. We show that these ruptures can be caused by either shear forces typically developing near the base, or by the bending of the structure which is caused primarily by the internal bending moment. In the latter case the breaking is more likely to occur between one-third and one-half of the height of the chimney. Small scale toy models are used to reproduce the dynamics of the falling chimney. By examining photos taken during …

Wormhole Geometries In Fourth-Order Conformal Weyl Gravity, Gabriele U. Varieschi, Kellie L. Ault

Gabriele Varieschi

We present an analysis of the classic wormhole geometries based on conformal Weyl gravity, rather than standard general relativity. The main characteristics of the resulting traversable wormholes remain the same as in the seminal study by Morris and Thorne, namely, that effective super-luminal motion is a viable consequence of the metric. Improving on previous work on the subject, we show that for particular choices of the shape and redshift functions the wormhole metric in the context of conformal gravity does not violate the main energy conditions at or near the wormhole throat. Some exotic matter might still be needed at …

Conformal Gravity And The Alcubierre Warp Drive Metric, Gabriele U. Varieschi, Zily Burstein

Gabriele Varieschi

We present an analysis of the classic Alcubierre metric based on conformal gravity, rather than standard general relativity. The main characteristics of the resulting warp drive remain the same as in the original study by Alcubierre, that is, effective superluminal motion is a viable outcome of the metric. We show that for particular choices of the shaping function, the Alcubierre metric in the context of conformal gravity does not violate the weak energy condition, as was the case of the original solution. In particular, the resulting warp drive does not require the use of exotic matter. Therefore, if conformal gravity …