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Title: Geometry of Higher-Order Markov Chains, AS2012 Special Volume, part 1: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Date: 2012, 2012
Description: We determine an explicit Gr ?obner basis, consisting of linear forms and determinantal quadrics, for the prime ideal of Raftery’s mixture...
Show moreWe determine an explicit Gr ?obner basis, consisting of linear forms and determinantal quadrics, for the prime ideal of Raftery’s mixture transition distribution model for Markov chains. When the states are binary, the corresponding projective variety is a linear space, the model itself consists of two simplices in a cross-polytope, and the likelihood function typically has two local maxima. In the general non-binary case, the model corresponds to a cone over a Segre variety.
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Collection: Journal of Algebraic Statistics

Title: Phylogenetic invariants for group-based models, AS2012 Special Volume, part 1: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Date: 2012, 2012
Description: In this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We propose a method of generating...
Show moreIn this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We propose a method of generating many phylogenetic invariants. We prove that we obtain all invariants for any tree for the two-state Jukes-Cantor model. We conjecture that for a large class of models our method can give all phylogenetic invariants for any tree. We show that for 3-Kimura our conjecture is equivalent to the conjecture of Sturmfels and Sullivant [22, Conjecture 2]. This, combined with the results in [22], would make it possible to determine all phylogenetic invariants for any tree for 3-Kimura model, and also other phylogenetic models. Next we give the (first) examples of non-normal varieties associated to general group-based model for an abelian group. Following Kubjas [17] we prove that for many group-based models varieties associated to trees with the same number of leaves do not have to be deformation equivalent.
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Collection: Journal of Algebraic Statistics

Title: Properties of semi-elementary imsets as sums of elementary imsets
Date: 2011, 2011
Description: We study properties of semi-elementary imsets and elementary imsets introduced by Studeny [10]. The rules of the semi-graphoid axiom ...
Show moreWe study properties of semi-elementary imsets and elementary imsets introduced by Studeny [10]. The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary imset and prove that all representations are connected by relations among four elementary imsets.
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Collection: Journal of Algebraic Statistics

Title: Connectivity for 3 x 3 x K contingency tables
Description: We consider an exact sequential conditional test for three-way conditional test of no interaction. At each time τ, the test uses as the...
Show moreWe consider an exact sequential conditional test for three-way conditional test of no interaction. At each time τ, the test uses as the conditional inference frame the set F(Hτ) of all tables with the same three two-way marginal tables as the obtained table Hτ . For 3 × 3 × K tables, we propose a method to construct F(Hτ) from F(Hτ−1). This enables us to perform efficiently the sequential exact conditional test. The subset Sτ of F (Hτ ) consisting of s + Hτ − Hτ −1 for s ∈ F(Hτ−1) contains Hτ , where the operations + and − are defined elementwise. Our argument is based on the minimal Markov basis for 3 × 3 × K contingency tables and we give a minimal subset M of some Markov basis which has the property that F (Hτ ) = {s − m | s ∈ Sτ , m ∈ M}.
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Collection: Journal of Algebraic Statistics

Title: FAST AUTOMATIC BAYESIAN CUBATURE USING MATCHING KERNELS AND DESIGNS
Date: 2019, 2019-12-20
Publisher: Chicago
Description: Automatic cubatures approximate multidimensional integrals to user-specified...
Show moreAutomatic cubatures approximate multidimensional integrals to user-specified error tolerances. In many real-world integration problems, the analytical solution is either unavailable or difficult to compute. To overcome this, one can use numerical algorithms that approximately estimate the value of the integral. For high dimensional integrals, quasi-Monte Carlo (QMC) methods are very popular. QMC methods are equal-weight quadrature rules where the quadrature points are chosen deterministically, unlike Monte Carlo (MC) methods where the points are chosen randomly. The families of integration lattice nodes and digital nets are the most popular quadrature points used. These methods consider the integrand to be a deterministic function. An alternate approach, called Bayesian cubature, postulates the integrand to be an instance of a Gaussian stochastic process.
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Title: Environmental Monitoring of University Archives and Special Collections
Date: 2020,
Description: This is the final report and analysis of activities conducted as part of Environmental Monitoring of University Archives and Special...
Show moreThis is the final report and analysis of activities conducted as part of Environmental Monitoring of University Archives and Special Collections, a project funded by a Preservation Assistance Grant from the National Endowment of the Humanities (PG-263471-19). This grant was awarded to support the first evercsystematic environmental monitoring of the UASC spaces. This report includes a summary of the collected data, analysis of the data, and potential future activities to be undertaken as a result of the grant activities and the data collected.
Sponsorship: National Endowment For The Humanities, Preservation Assistance Grants for Smaller Institutions
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Title: The Waste of Parts Capstone Examples
Date: 2020,
Description: The Waste of Parts is a prototype board game finished for my Digital Humanities Capstone Elective

Title: Detecting epistasis via Markov bases
Date: 2011, 2011
Description: Rapid research progress in genotyping techniques have allowed large genome-wide association studies. Existing methods often focus on...
Show moreRapid research progress in genotyping techniques have allowed large genome-wide association studies. Existing methods often focus on determining associations between single loci and a specific phenotype. However, a particular phenotype is usually the result of complex relationships between multiple loci and the environment. In this paper, we describe a two-stage method for detecting epistasis by combining the traditionally used single-locus search with a search for multiway interactions. Our method is based on an extended version of Fisher’s exact test. To perform this test, a Markov chain is constructed on the space of multidimensional contingency tables using the elements of a Markov basis as moves. We test our method on simulated data and compare it to a two-stage logistic regression method and to a fully Bayesian method, showing that we are able to detect the interacting loci when other methods fail to do so. Finally, we apply our method to a genome-wide data set consisting of 685 dogs and identify epistasis associated with canine hair length for four pairs of single nucleotide polymorphisms (SNPs).
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Collection: Journal of Algebraic Statistics

Title: Open Problems on Connectivity of Fibers with Positive Margins in Multi-dimensional Contingency Tables
Date: 2010, 2010
Description: Diaconis-Sturmfels developed an algorithm for sampling from conditional distributions for a statistical model of discrete exponential families...
Show moreDiaconis-Sturmfels developed an algorithm for sampling from conditional distributions for a statistical model of discrete exponential families, based on the algebraic theory of toric ideals. This algorithm is applied to categorical data analysis through the notion of Markov bases. Initiated with its application to Markov chain Monte Carlo approach for testing statistical fitting of the given model, many researchers have extensively studied the structure of Markov bases for models in computational algebraic statistics. In the Markov chain Monte Carlo approach for testing statistical fitting of the given model, a Markov basis is a set of moves connecting all contingency tables satisfying the given margins. Despite the computational advances, there are applied problems where one may never be able to compute a Markov basis. In general, the number of elements in a minimal Markov basis for a model can be exponentially many. Thus, it is important to compute a reduced number of moves which connect all tables instead of computing a Markov basis. In some cases, such as logistic regression, positive margins are shown to allow a set of Markov connecting moves that are much simpler than the full Markov basis. Such a set is called a Markov subbasis with assumption of positive margins. In this paper we summarize some computations of and open problems on Markov subbases for contingency tables with assumption of positive margins under specific models as well as develop algebraic methods for studying connectivity of Markov moves with margin positivity to develop Markov sampling methods for exact conditional inference in statistical models where the Markov basis is hard to compute.
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Collection: Journal of Algebraic Statistics

Title: Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables, Special Volume in honor of memory of S.E.Fienberg
Description: We consider the lattice, L, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and...
Show moreWe consider the lattice, L, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, n(·), on L. We derive from the supermodularity of n(·) some generalized Fr ́echet inequalities comple- menting and extending inequalities of Dobra and Fienberg. Further, we construct new monotonic and supermodular functions from n(·), and we remark on the connection between supermodularity and some correlation inequalities for probability distributions on lattices. We also apply an inequal- ity of Ky Fan to derive a new approach to Fr ́echet inequalities for multidimensional contingency tables.
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Collection: Journal of Algebraic Statistics

Title: Maximal Length Projections in Group Algebras with Applications to Linear Rank Tests of Uniformity
Description: Let G be a finite group, let CG be the complex group algebra of G, and let p ∈ CG. In this paper, we show how to construct submodules S of CG...
Show moreLet G be a finite group, let CG be the complex group algebra of G, and let p ∈ CG. In this paper, we show how to construct submodules S of CG of a fixed dimension with the property that the orthogonal projection of p onto S has maximal length. We then provide an example of how such submodules for the symmetric group Sn can be used to create new linear rank tests of uniformity in statistics for survey data that arises when respondents are asked to give a complete ranking of n items.
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Collection: Journal of Algebraic Statistics

Title: A Gröbner Basis Database
Date: 2022,

Title: Research in Architectural Education: Theory and Practice of Visual Training
Date: 2016, 12/12/2016
Collection: Enquiry

Title: Views on Ethical Issues in Research Labs: a University-Wide Survey
Date: 2021,
Description: Full survey used for "Views on Ethical Issues in Research Labs" published in the journal Accountability in Research: Policies and Quality...
Show moreFull survey used for "Views on Ethical Issues in Research Labs" published in the journal Accountability in Research: Policies and Quality Assurance in 2021. This survey was completed in 2017.
Sponsorship: National Science Foundation
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Collection: Accountability in Research: Policies and Quality Assurance

Title: Modeling enantiomeric separations as an interfacial process using amylose tris(3,5-dimethylphenyl carbamate) (ADMPC) polymers coated on amorphous silica
Date: 2020, 2020-01-20
Publisher: ACS Langmuir
Description: In the present study, we present a model to predict the chiral separation results for drug enantiomers by ADMPC chiral stationary phase in...
Show moreIn the present study, we present a model to predict the chiral separation results for drug enantiomers by ADMPC chiral stationary phase in high performance liquid chromatography (HPLC) wherein multiple ADMPC polymer strands are coated on an amorphous silica slab. Both reactive and classical MD are used to prepare the surface. Using various MD techniques, we successfully coat ADMPCs onto the surface without losing the structural character of the backbone in the presence of the solvent system. Not only is this model more representative of the polymer surface on a solid support that is encountered by the enantiomers, it also provides more opportunities for chiral molecules interacting with ADMPC, resulting in a better agreement compared with experiment when we use overall average quantities as the metric. In our previous studies, we had used a single polymer strand of amylose tris(3,5-dimethylphenyl carbamate) (ADMPC) in the solvent system. The new model provides the possibility for large drug molecules to interact with two polymer strands at the same instant, which was not possible to model with only a single polymer strand in the solvent. For a better understanding of why some metrics are better predictors than others, we use charts of the distribution of hydrogen bonding lifetimes in this work to display the hydrogen-bonding information for various donor-acceptor pairs that contribute to the interaction events determining the relative retention times for the enantiomers. We also examine the contribution of the ring-ring interactions to the molecular recognition process and ultimately to differential retention of S and R enantiomers. The results using the new model are more consistent than the previous models and resolves the problematic case of two drugs, thalidomide and valsartan.
Sponsorship: The National Science Foundation (CBET 1545560)
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Title: USING COMPUTATIONAL MOLECULAR MODELING TO STUDY TRANSPORT PROCESSES OF INTEREST IN SEPARATIONS
Date: 2020, 2020
Publisher: ProQuest
Description: Separation processes are widely used in chemical productions. The further development of membrane-based separation processes, compared with...
Show moreSeparation processes are widely used in chemical productions. The further development of membrane-based separation processes, compared with thermal separations, can lead to significant energy savings in chemical process industries. However, the main obstacle of experiments is that many separation processes are not well understood at the fundamental molecular level. In this dissertation, we use computational molecular modeling tools, mainly classical molecular dynamics (MD), to clarify molecular forces and provide detail at a molecular level, which can aid in the understanding of transport process and designing materials for a proposed application. In the first study, we investigated separation of water/alcohol vapor using zeolite membranes. Experimentally, the separation of water/isopropanol (IPA) mixtures shows a dramatic decrease in selectivity due to increase of IPA flux as the feed water concentration decrease when using the sodium A zeolite membrane. We used molecular dynamics simulations to help our experimental collaborators understand these puzzling results. The MD results reveal that the water molecules gather around the defect pores on the zeolite membrane, which stops the IPA from going through the membrane and has a positive effect on separation. Then, we studied the HPLC used to separate chiral drug mixtures. One popular chiral stationary phase, amylose tris(3,5-dimethylphenyl carbamate) (ADMPC), has been investigated using both experimental and computational methods; however, the dynamic nature of the interaction between enantiomers and ADMPC, as well as the solvent effects on the ADMPC-enantiomer interaction, are currently absent from the chiral recognition mechanism. We used MD simulations to model the ADMPC in different solvents to elucidate the chiral recognition mechanism from a new dynamic perspective. The ADMPC is found to hold the left-handed helical structure in both methanol and heptane/IPA (90/10); however, the ADMPC has a more extended average structure in heptane/IPA. We developed a model where the ADMPC atoms were restricted in the MD simulation. To better understand the molecular dynamic chiral recognition that provides the retention factor and the elution order in HPLC, we examined hydrogen bonding lifetimes, and mapped out ring-ring interactions between the drugs and the ADMPC. We discover several MD metrics related to hydrogen-bonding lifetimes and correlate them with HPLC results. One metric provides a prediction of the correct elution order 90%, and the ratios of these quantities for the enantiomers provide linear correlation (0.85 coefficient) with experimental retention factors. In the following study, we presented an improved model wherein multiple ADMPC polymer strands are coated on an amorphous silica slab. Using various MD techniques, we successfully coated ADMPCs onto the surface without losing the structural character of the backbone in the solvent. This model provides more opportunities for chiral molecules interacting with ADMPC, resulting in a better agreement compared with experiment when using the overall average metric. The new model also provides the possibility for drug molecules to interact with two polymer strands simultaneously, which is not possible in the previous single-strand model. For a better understanding of why some metrics are better predictors than others, we used charts of the distribution of hydrogen bonding lifetimes to display the information for various donor-acceptor pairs. The results are more consistent than the previous models and resolves the problematic cases of thalidomide and valsartan. Besides the membrane-based separations, immiscible liquid-liquid equilibrium states were also studied. We successfully predicted results based on MD simulations and showed comparable accuracy with experimental data. This method has applications in liquid-liquid extraction which is widely used in industrial separation process.
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Title: The City in the Landscape: Alfred Caldwell's Broader Perspective on Urban Design
Date: 2020, 2020
Publisher: Editorial Universitat Politècnica de València
Description: Alfred Caldwell was among the first full- time American professors Mies van der Rohe hired at the Illinois...
Show moreAlfred Caldwell was among the first full- time American professors Mies van der Rohe hired at the Illinois Institute of Technology (IIT). Many have admired Mies’s architecture since the 1920s, and know that his ideas were also transmitted as a professor, first at the Bauhaus in Europe and then as Director of the Department of Architecture at IIT. Caldwell, a practicing landscape architect and protégé of Jens Jensen, is perhaps less widely known, but was a major influence on IIT’s program especially in the areas of construction, landscape, and architectural history. Caldwell completed a Master of Science in City Planning with a thesis entitled The City in the Landscape: A Preface for Planning, which can be considered a manifesto of both his professional ideas and IIT’s planning pedagogy. In addition to his own works, Caldwell collaborated with Mies and architect Ludwig Hilberseimer, Director of City and Regional Planning at IIT and former Head of Building Theory at the Bauhaus, on the design of built works which left behind artifacts representing the ideal of “the city in the landscape.” This communication examines the broader perspective on urban design influenced by the symbiotic disciplines of architecture, city-regional planning and landscape as manifested in the individual and collaborative built work and pedagogy of Caldwell, Hilberseimer, and Mies.
Originally published as paper #1.01 in volume 1 of the conference proceedings of the EAAE-ARCC International Conference & 2nd Valencia International Biennial.
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Collection: EAAE-ARCC International Conference & 2nd Valencia International Biennial

Title: Matrix Completion for the Independence Model
Description: We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex ∆mn−1. The motivation for studying this...
Show moreWe investigate the problem of completing partial matrices to rank-one matrices in the standard simplex ∆mn−1. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for partial observations to come from the independence model. For each pattern of specified entries, we give equations and inequalities which are satisfied if and only if an eligible completion exists. We also describe the set of valid completions, and we optimize over this set.
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Collection: Journal of Algebraic Statistics

Title: One example of general unidentifiable tensors
Description: Abstract. Theidentifiabilityofparametersinaprobabilisticmodelisacrucialnotioninstatistical inference. We prove that a general tensor of rank 8...
Show moreAbstract. Theidentifiabilityofparametersinaprobabilisticmodelisacrucialnotioninstatistical inference. We prove that a general tensor of rank 8 in C3 ⊗ C6 ⊗ C6 has at least 6 decompositions as sum of simple tensors, so it is not 8-identifiable. This is the highest known example of balanced tensors of dimension 3, which are not k-identifiable, when k is smaller than the generic rank.
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Collection: Journal of Algebraic Statistics

Title: Understanding Requirement & the necessary tools
Date: 2021,
Description: Effective use of the Requirement gathering is our greatest and most critical role. We need to communicate with stakeholders to make the best...
Show moreEffective use of the Requirement gathering is our greatest and most critical role. We need to communicate with stakeholders to make the best of it. The techniques mentioned here are mixed and for each project, the mix shall be different. This technique for gathering requirements is perhaps the most common way to obtain requirements from all the required techniques. This article also looks at how to run a Delphi session, Creating Affinity Diagram & Mind maps.
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