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Title: The maximum likelihood degree of Fermat hypersurfaces
Creator: Agostini, Daniele, Alberelli, Davide, Grande, Francesco, Lella, Paolo
Date: 2015, 2015-11-09
Description: We study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in...
Show moreWe study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in statistical optimization: maximum likelihood estimation. The number of critical points over a projective variety is a topological invariant of the variety and is called maximum likelihood degree. We provide closed formulas for the maximum likelihood degree of any Fermat curve in the projective plane and of Fermat hypersurfaces of degree 2 in any projective space. Algorithmic methods to compute the ML degree of a generic Fermat hypersurface are developed throughout the paper. Such algorithms heavily exploit the symmetries of the varieties we are considering. A computational comparison of the different methods and a list of the maximum likelihood degrees of several Fermat hypersurfaces are available in the last section.
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Collection: Journal of Algebraic Statistics

Title: Moment Varieties of Gaussian Mixtures, AS2015 Special Issue articles: This issue includes a series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics Conference held in Genoa, Italy, in June 2015. Special issue guest editors: Piotr Zwiernik and Fabio Rapallo.
Creator: Améndola, Carlos, Faugère, Jean-Charles, Sturmfels, Bernd
Date: 2016, 2016-07-12
Description: The points of a moment variety are the vectors of all moments up to some order, for a given family of probability distributions. We study the...
Show moreThe points of a moment variety are the vectors of all moments up to some order, for a given family of probability distributions. We study the moment varieties for mixtures of multivariate Gaussians. Following up on Pearson’s classical work from 1894, we apply current tools from computational algebra to recover the parameters from the moments. Our moment varieties extend objects familiar to algebraic geometers. For instance, the secant varieties of Veronese varieties are the loci obtained by setting all covariance matrices to zero. We compute the ideals of the 5-dimensional moment varieties representing mixtures of two univariate Gaussians, and we offer a comparison to the maximum likelihood approach.
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Collection: Journal of Algebraic Statistics

Title: On multivariable cumulant polynomial sequences with applications, AS2015 Special Issue articles: This issue includes a series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics Conference held in Genoa, Italy, in June 2015. Special issue guest editors: Piotr Zwiernik and Fabio Rapallo.
Creator: Di Nardo, Elvira
Date: 2016, 2016-07-12
Description: A new family of polynomials, called cumulant polynomial sequence, and its extension to the multivariate case is introduced relying on a purely...
Show moreA new family of polynomials, called cumulant polynomial sequence, and its extension to the multivariate case is introduced relying on a purely symbolic combinatorial method. The coefficients are cumulants, but depending on what is plugged in the indeterminates, moment sequences can be recovered as well. The main tool is a formal generalization of random sums, when a not necessarily integer-valued multivariate random index is considered. Applications are given within parameter estimations, L ?evy processes and random matrices and, more generally, problems involving multivariate functions. The connection between exponential models and multivariable Sheffer polynomial sequences offers a different viewpoint in employing the method. Some open problems end the paper.
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Collection: Journal of Algebraic Statistics

Title: Algebraic geometry of Poisson regression, AS2015 Special Issue articles: This issue includes a series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics Conference held in Genoa, Italy, in June 2015. Special issue guest editors: Piotr Zwiernik and Fabio Rapallo.
Creator: Kahle, Thomas, Oelbermann, Kai-Friederike, Schwabe, Rainer
Date: 2016, 2016-07-12
Description: Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. Here we investigate...
Show moreDesigning experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. Here we investigate local optimality. We propose to study for a given design its region of optimality in parameter space. Often these regions are semi-algebraic and feature interesting symmetries. We demonstrate this with the Rasch Poisson counts model. For any given interaction order between the explanatory variables we give a characterization of the regions of optimality of a special saturated design. This extends known results from the case of no interaction. We also give an algebraic and geometric perspective on optimality of experimental designs for the Rasch Poisson counts model using polyhedral and spectrahedral geometry.
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Collection: Journal of Algebraic Statistics

Title: A linear-algebraic tool for conditional independence inference
Creator: Tanaka, Kentaro, Studeny, Milan, Takemura, Akimichi, Sei, Tomonari
Date: 2015, 2015-11-09
Description: In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is...
Show moreIn this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables.
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Collection: Journal of Algebraic Statistics

Title: Mode Poset Probability Polytopes, AS2015 Special Issue articles: This issue includes a series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics Conference held in Genoa, Italy, in June 2015. Special issue guest editors: Piotr Zwiernik and Fabio Rapallo.
Creator: Montúfar, Guido, Rauh, Johannes
Date: 2016, 2016-07-12
Description: A mode of a probability distribution is an elementary event that has more probability mass than each of its direct neighbors, with respect to...
Show moreA mode of a probability distribution is an elementary event that has more probability mass than each of its direct neighbors, with respect to some vicinity structure on the set of elementary events. The mode inequalities cut out a polytope from the simplex of probability distributions. Related to this is the concept of strong modes. A strong mode is an elementary event that has more probability mass than all its direct neighbors together. The set of probability distributions with a given set of strong modes is again a polytope. We study the vertices, the facets, and the volume of such polytopes depending on the sets of (strong) modes and the vicinity structures.
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Collection: Journal of Algebraic Statistics

Title: China's Unwritten Code of Engineering Ethics. English Final Data Set
Creator: Wei, Lina, Davis, Michael
Date: 2020, 2020
Publisher: Springer
Description: This dataset contains the final results of a survey completed by several hundred engineers in China about what they think about engineering...
Show moreThis dataset contains the final results of a survey completed by several hundred engineers in China about what they think about engineering ethics, their awareness of ethics in their work, and how Chinese engineers' view of engineering ethics is not very different from those of American Engineers.
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Title: L-cumulants, L-cumulant embeddings and algebraic statistics, 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.
Creator: Zwiernik, Piotr, AS2012 Special Volume, part 1: This issue includes a second series of papers from talks, posters and collaborations resulting from and
Description: Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization...
Show moreFocusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for independent blocks of random variables. These properties make L-cumulants useful for the algebraic analysis of statistical models. We illustrate this for general Markov models and hidden Markov processes in the case when the hidden process is binary. The main motivation of this work is to understand cumulant-like coordinates in alge- braic statistics and to give a more insightful explanation why tree cumulants give such an elegant description of binary hidden tree models. Moreover, we argue that L-cumulants can be used in the analysis of certain classical algebraic varieties.
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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
Creator: Richards, Donald, Uhler, Caroline
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
Creator: Bargagliotti, Anna E., Orrison, Michael
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: Connectivity for 3 x 3 x K contingency tables
Creator: Sumi, Toshio, 2012
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: Matrix Completion for the Independence Model
Creator: Kubjas, Kaie, Rosen, Zvi
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
Creator: Chiantini, Luca, Mella, Massimiliano, Ottaviani, Giorgio
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: Hilbert Polynomial of the Kimura 3-Parameter Model, 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.
Creator: Kubjas, Kaie, inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July
Description: In [2] Buczyn ́ska and Wi ́sniewski showed that the Hilbert polynomial of the algebraic variety associated to the Jukes-Cantor binary model on...
Show moreIn [2] Buczyn ́ska and Wi ́sniewski showed that the Hilbert polynomial of the algebraic variety associated to the Jukes-Cantor binary model on a trivalent tree depends only on the number of leaves of the tree and not on its shape. We ask if this can be generalized to other group-based models. The Jukes-Cantor binary model has Z2 as the underlying group. We consider the Kimura 3-parameter model with Z2 × Z2 as the underlying group. We show that the generalization of the statement about the Hilbert polynomials to the Kimura 3-parameter model is not possible as the Hilbert polynomial depends on the shape of a trivalent tree.
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Collection: Journal of Algebraic Statistics

Title: Optimizing Cell-Free Protein Synthesis for Increased Yield and Activity of Colicins
Creator: Jin, Xing, Kightlinger, Weston, Hong, Seok Hoon
Date: 2019
Publisher: MDPI
Description: Colicins are antimicrobial proteins produced by Escherichia coli that hold great promise as viable complements or alternatives to antibiotics....
Show moreColicins are antimicrobial proteins produced by Escherichia coli that hold great promise as viable complements or alternatives to antibiotics. Cell-free protein synthesis (CFPS) is a useful production platform for toxic proteins because it eliminates the need to maintain cell viability, a common problem in cell-based production. Previously, we demonstrated that colicins produced by CFPS based on crude Escherichia coli lysates are e?ective in eradicating antibiotic-tolerant bacteria known as persisters. However, we also found that some colicins have poor solubility or low cell-killing activity. In this study, we improved the solubility of colicin M from 16% to nearly 100% by producing it in chaperone-enriched E. coli extracts, resulting in enhanced cell-killing activity. We also improved the cytotoxicity of colicin E3 by adding or co-expressing the E3 immunity protein during the CFPS reaction, suggesting that the E3 immunity protein enhances colicin E3 activity in addition to protecting the host strain. Finally, we con?rmed our previous ?nding that active colicins can be rapidly synthesized by observing colicin E1 production over time in CFPS. Within three hours of CFPS incubation, colicin E1 reached its maximum production yield and maintained high cytotoxicity during longer incubations up to 20 h. Taken together, our ?ndings indicate that colicin production can be easily optimized for improved solubility and activity using the CFPS platform.
Sponsorship: NIH R15AI130988
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Title: Controlling biofilms using synthetic biology approaches
Creator: Fang, Kuili, Park, Oh-Jin, Hong, Seok Hoon
Date: 2020
Description: Bacterial biofilms are formed by the complex but ordered regulation of intra- or inter-cellular communication, environmentally responsive gene...
Show moreBacterial biofilms are formed by the complex but ordered regulation of intra- or inter-cellular communication, environmentally responsive gene expression, and secretion of extracellular polymeric substances. Given the robust nature of bio?lms due to the non-growing nature of bio?lm bacteria and the physical barrier provided by the extracellular matrix, eradicating bio?lms is a very di?cult task to accomplish with conventional antibiotic or disinfectant treatments. Synthetic biology holds substantial promise for controlling bio?lms by improving and expanding existing biological tools, introducing novel functions to the system, and re-conceptualizing gene regulation. This review summarizes synthetic biology approaches used to eradicate bio?lms via protein engineering of bio?lm-related enzymes, utilization of synthetic genetic circuits, and the development of functional living agents. Synthetic biology also enables bene?cial applications of bio?lms through the production of biomaterials and patterning bio?lms with speci?c temporal and spatial structures. Advances in synthetic biology will add novel bio?lm functionalities for future therapeutic, biomanufacturing, and environmental applications.
Sponsorship: NIH-R15AI130988, NSF CBET-1917130
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Title: Engineering Escherichia coli to produce and secrete colicins for rapid and selective biofilm cell killing
Creator: Jin, Xing, An, Sungjun, Kightlinger, Weston, Zhou, Jiacheng, Hong, Seok Hoon
Date: 2021
Description: Bacterial biofilms are associated with chronic infectious diseases and are highly resistant to conventional antibiotics. Antimicrobial...
Show moreBacterial biofilms are associated with chronic infectious diseases and are highly resistant to conventional antibiotics. Antimicrobial bacteriocins are alternatives to conventional antibiotics and are characterized by unique cell-killing mechanisms, including pore formation on cell membranes, nuclease activity, and cell wall synthesis inhibition. Here, we used cell-free protein synthesis to rapidly evaluate the antibiofilm activities of colicins E1, E2, and E3. We found that E2 (with DNase activity) most effectively killed target biofilm cells (i.e., the K361 strain) while leaving nontargeted biofilms intact. We then engineered probiotic Escherichia coli microorganisms with genetic circuits to controllably synthesize and secrete colicin E2, which successfully inhibited biofilms and killed preformed indicator biofilms. Our findings suggest that colicins rapidly and selectively kill target biofilm cells in multispecies biofilms and demonstrate the potential of using microorganisms engineered to produce antimicrobial colicin proteins as live therapeutic strategies to treat biofilm-associated infections.
Sponsorship: NIH-R15AI130988
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Title: Editorial, "Cell-Free Synthetic Biology": Synthetic Biology Meets Cell-Free Protein Synthesis
Creator: Hong, Seok Hoon
Date: 2019
Publisher: MDPI
Description: Sponsorship: NIH R15AI130988

Title: Incorporation of non-standard amino acids into proteins: challenges, recent achievements, and emerging applications
Creator: Jin, Xing, Park Oh-Jin, Hong, Seok Hoon
Date: 2019
Description: The natural genetic code only allows for 20 standard amino acids in protein translation, but genetic code reprogramming enables the...
Show moreThe natural genetic code only allows for 20 standard amino acids in protein translation, but genetic code reprogramming enables the incorporation of non-standard amino acids (NSAAs). Proteins containing NSAAs provide enhanced or novel properties and open diverse applications. With increased attention to the recent advancements in synthetic biology, various improved and novel methods have been developed to incorporate single and multiple distinct NSAAs into proteins. However, various challenges remain in regard to NSAA incorporation, such as low yield and misincorporation. In this review, we summarize the recent efforts to improve NSAA incorporation by utilizing orthogonal translational system optimization, cell-free protein synthesis, genomically recoded organisms, artificial codon boxes, quadruplet codons, and orthogonal ribosomes, before closing with a discussion of the emerging applications of NSAA incorporation.
Sponsorship: NIH R15AI130988
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Title: Undecanoic Acid, Lauric Acid, and N-Tridecanoic Acid Inhibit Escherichia coli Persistence and Biofilm Formation
Creator: Jin, Xing, Zhou, Jiacheng, Richey, Gabriella, Wang, Mengya, Hong, Sung Min Choi, Hong, Seok Hoon
Date: 2021
Description: Persister cell formation and biofilms of pathogens are extensively involved in the development of chronic infectious diseases. Eradicating...
Show morePersister cell formation and biofilms of pathogens are extensively involved in the development of chronic infectious diseases. Eradicating persister cells is challenging, owing to their tolerance to conventional antibiotics, which cannot kill cells in a metabolically dormant state. A high frequency of persisters in biofilms makes inactivating biofilm cells more difficult, because the biofilm matrix inhibits antibiotic penetration. Fatty acids may be promising candidates as antipersister or antibiofilm agents, because some fatty acids exhibit antimicrobial effects. We previously reported that fatty acid ethyl esters effectively inhibit Escherichia coli persister formation by regulating an antitoxin. In this study, we screened a fatty acid library consisting of 65 different fatty acid molecules for altered persister formation. We found that undecanoic acid, lauric acid, and N-tridecanoic acid inhibited E. coli BW25113 persister cell formation by 25-, 58-, and 44-fold, respectively. Similarly, these fatty acids repressed persisters of enterohemorrhagic E. coli EDL933. These fatty acids were all medium-chain saturated forms. Furthermore, the fatty acids repressed Enterohemorrhagic E. coli (EHEC) biofilm formation (for example, by 8-fold for lauric acid) without having antimicrobial activity. This study demonstrates that medium-chain saturated fatty acids can serve as antipersister and antibiofilm agents that may be applied to treat bacterial infections.
Sponsorship: NIH-R15AI130988; NSF REU-1757989
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