Generalized Permutohedra from Probabilistic Graphical Models

A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. There is an analogous polytope for conditional independence relations coming from a regular Gaussian model, and it can be defined using multiinformation or relative entropy. For directed acyclic graphical models and also for mixed graphical models containing undirected, directed and bidirected edges, we give a construction of this polytope, up to equivalence of normal fans, as a Minkowski sum of matroid polytopes. Finally, we apply this geometric insight to construct a new ordering-based search algorithm for causal inference via directed acyclic graphical models.Comment: Appendix B is expanded. Final version to appear in SIAM J. Discrete Mat

Enhancement of cancer chemotherapy in vitro by intense ultrawideband electric field pulses

Experiments have been performed to enhance the Jurkat cell-killing effects of the cancer chemotherapy agent bleomycin using electric field pulses of 50–200 kV/cm50–200kV∕cm peak electric field strength, ∼ 150 ns∼150ns duration, and nanosecond rise time. Dramatic increases in cell killing (factors of ∼ 1000∼1000) were observed with a low dose of bleomycin after treatment with trains of ten or more pulses at all electric field strengths tested, compared to pulse-only or drug-only treatments. Cell death occurred within 24 h24h for treated cells, with some evidence of membrane phosphatidylserine externalization at 6 h6h postexposure but no significant increase in caspase activity, indicating that the primary mode of cell death was not caspase-mediated apoptosis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87477/2/094701_1.pd

Differentially Private Model Selection with Penalized and Constrained Likelihood

In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning, and statistics. It provides a rigorous and strong notion of protection for individuals' sensitive information. A fundamental question is how to incorporate differential privacy into traditional statistical inference procedures. In this paper we study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and propose two algorithms to do so. We show that our private procedures are consistent under essentially the same conditions as the corresponding non-private procedures. We also find that under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method using simulation studies and two real data examples

Phosphatidylinositol 3‐kinase and Akt effectors mediate insulin‐like growth factor‐I neuroprotection in dorsal root ganglia neurons

Insulin‐like growth factor‐I (IGF‐I) protects neurons of the peripheral nervous system from apoptosis, but the underlying signaling pathways are not well understood. We studied IGF‐I mediated signaling in embryonic dorsal root ganglia (DRG) neurons. DRG neurons express IGF‐I receptors (IGF‐IR), and IGF‐I activates the phosphatidylinositol 3‐kinase (PI3K)/Akt pathway. High glucose exposure induces apoptosis, which is inhibited by IGF‐I through the PI3K/Akt pathway. IGF‐I stimulation of the PI3K/Akt pathway phosphorylates three known Akt effectors: the survival transcription factor cyclic AMP response element binding protein (CREB) and the pro‐apoptotic effector proteins glycogen synthase kinase‐3β (GSK‐3β) and forkhead (FKHR). IGF‐I regulates survival at the nuclear level through accumulation of phospho‐Akt in DRG neuronal nuclei, increased CREB‐mediated transcription, and nuclear exclusion of FKHR. High glucose increases expression of the pro‐apoptotic Bcl protein Bim (a transcriptional target of FKHR). However, IGF‐I does not regulate Bim or anti‐apoptotic Bcl‐xL protein expression levels, which suggests that IGF‐I neuroprotection is not through regulation of their expression. High glucose also induces loss of the initiator caspase‐9 and increases caspase‐3 cleavage, effects blocked by IGF‐I. These data suggest that IGF‐I prevents apoptosis in DRG neurons by regulating PI3K/Akt pathway effectors, including GSK‐3β, CREB, and FKHR, and by blocking caspase activation.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154325/1/fsb2fj041581fje.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154325/2/fsb2fj041581fje-sup-0001.pd

Pionic Deuterium

The strong interaction shift and broadening in pionic deuterium have been remeasured with high statistics by means of the (3p-1s) X-ray transition using the cyclotron trap and a high-resolution crystal spectrometer. Preliminary results are (-2325+/-31) meV (repulsive) for the shift and (1171+23/-49} meV for the width, which yields precise values for the pion-deuteron scattering length and the threshold parameter for pion production.Comment: Conf. Proc. Few Body 19 (FB19), August 31 - September 5, 2009, Bonn, Germany 9 pages, 13 figure

Incorporating spatial dependence into a multicellular tumor spheroid growth model

Recent models for organism and tumor growth yield simple scaling laws based on conservation of energy. Here, we extend such a model to include spatial dependence to model necrotic core formation. We adopt the allometric equation for tumor volume with a reaction-diffusion equation for nutrient concentration. In addition, we assume that the total metabolic energy and average cellular metabolic rate depend on nutrient concentration in a Michaelis-Menten-like manner. From experimental results, we relate the necrotic volume to nutrient consumption and estimate both the time and nutrient concentration at necrotic core formation. Based on experimental results, we demand that the necrotic core radius varies linearly with tumor radius after core formation and extend the equations for tumor volume and nutrient concentration to the postnecrotic core regime. In particular, we obtain excellent agreement with experimental data and the final steady-state viable rim thickness.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87333/2/124701_1.pd

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities

The dynamical behavior of a harmonic chain in a spatially periodic potential (Frenkel-Kontorova model, discrete sine-Gordon equation) under the influence of an external force and a velocity proportional damping is investigated. We do this at zero temperature for long chains in a regime where inertia and damping as well as the nearest-neighbor interaction and the potential are of the same order. There are two types of regular sliding states: Uniform sliding states, which are periodic solutions where all particles perform the same motion shifted in time, and nonuniform sliding states, which are quasi-periodic solutions where the system forms patterns of domains of different uniform sliding states. We discuss the properties of this kind of pattern formation and derive equations of motion for the slowly varying average particle density and velocity. To observe these dynamical domains we suggest experiments with a discrete ring of at least fifty Josephson junctions.Comment: Written in RevTeX, 9 figures in PostScrip

Floating oil-covered debris from Deepwater Horizon : identification and application

Author Posting. © IOP Publishing, 2012. This article is posted here by permission of IOP Publishing. Re-use is limited to non-commercial purposes. The definitive version was published in Environmental Research Letters 7 (2012): 015301, doi:10.1088/1748-9326/7/1/015301.The discovery of oiled and non-oiled honeycomb material in the Gulf of Mexico surface waters and along coastal beaches shortly after the explosion of Deepwater Horizon sparked debate about its origin and the oil covering it. We show that the unknown pieces of oiled and non-oiled honeycomb material collected in the Gulf of Mexico were pieces of the riser pipe buoyancy module of Deepwater Horizon. Biomarker ratios confirmed that the oil had originated from the Macondo oil well and had undergone significant weathering. Using the National Oceanic and Atmospheric Administration's records of the oil spill trajectory at the sea surface, we show that the honeycomb material preceded the front edge of the uncertainty of the oil slick trajectory by several kilometers. We conclude that the observation of debris fields deriving from damaged marine materials may be incorporated into emergency response efforts and forecasting of coastal impacts during future offshore oil spills, and ground truthing predicative models.This research was supported by NSF grant OCE-1043976 to CR

Making connections: technological interventions to support students in using, and tutors in creating, assessment feedback

This paper explores the potential of technology to enhance the assessment and feedback process for both staff and students. The ‘Making Connections’ project aimed to better understand the connections that students make between the feedback that they receive and future assignments, and explored whether technology can help them in this activity. The project interviewed 10 tutors and 20 students, using a semi-structured approach. Data were analysed using a thematic approach, and the findings have identified a number of areas in which improvements could be made to the assessment and feedback process through the use of technology. The findings of the study cover each stage of the assessment process from the perspective of both staff and students. The findings are discussed in the context of current literature, and special attention is given to projects from the UK higher education sector intended to address the same issues. Keywords: feed-forward; assessment; practices; technology; technology-enhanced learnin