Laser-capture microdissection (LCM) allows the visualization and isolation of morphologically distinct subpopulations of cells from heterogeneous tissue specimens. In combination with formalin-fixed and paraffin-embedded (FFPE) tissue it provides a powerful tool for retrospective and clinically relevant studies of tissue proteins in a healthy and diseased context. We first optimized the protocol for efficient LCM analysis of FFPE tissue specimens. The use of SDS containing extraction buffer in combination with the single-pot solid-phase-enhanced sample preparation (SP3) digest method gave the best results regarding protein yield and protein/peptide identifications. Microdissected FFPE human substantia nigra tissue samples (~3,000 cells) were then analyzed, using tandem mass tag (TMT) labeling and LC-MS/MS, resulting in the quantification of >5,600 protein groups. Nigral proteins were classified and analyzed by abundance, showing an enrichment of extracellular exosome and neuron-specific gene ontology (GO) terms among the higher abundance proteins. Comparison of microdissected samples with intact tissue sections, using a label-free shotgun approach, revealed an enrichment of neuronal cell type markers, such as tyrosine hydroxylase and alpha-synuclein, as well as proteins annotated with neuron-specific GO terms. Overall, this study provides a detailed protocol for laser-capture proteomics using FFPE tissue and demonstrates the efficiency of LCM analysis of distinct cell subpopulations for proteomic analysis using low sample amounts.

Mass spectrometry (MS)-based proteomics has great potential for overcoming the limitations of antibody-based immunoassays for antibody-independent, comprehensive, and quantitative proteomic analysis of single cells. Indeed, recent advances in nanoscale sample preparation have enabled effective processing of single cells. In particular, the concept of using boosting/carrier channels in isobaric labeling to increase the sensitivity in MS detection has also been increasingly used for quantitative proteomic analysis of small-sized samples including single cells. However, the full potential of such boosting/carrier approaches has not been significantly explored, nor has the resulting quantitation quality been carefully evaluated. Herein, we have further evaluated and optimized our recent boosting to amplify signal with isobaric labeling (BASIL) approach, originally developed for quantifying phosphorylation in small number of cells, for highly effective analysis of proteins in single cells. This improved BASIL (iBASIL) approach enables reliable quantitative single-cell proteomics analysis with greater proteome coverage by carefully controlling the boosting-to-sample ratio (e.g. in general <100x) and optimizing MS automatic gain control (AGC) and ion injection time settings in MS/MS analysis (e.g. 5E5 and 300 ms, respectively, which is significantly higher than that used in typical bulk analysis). By coupling with a nanodroplet-based single cell preparation (nanoPOTS) platform, iBASIL enabled identification of ~2500 proteins and precise quantification of ~1500 proteins in the analysis of 104 FACS-isolated single cells, with the resulting protein profiles robustly clustering the cells from three different acute myeloid leukemia cell lines. This study highlights the importance of carefully evaluating and optimizing the boosting ratios and MS data acquisition conditions for achieving robust, comprehensive proteomic analysis of single cells.

HNF4α is a nuclear receptor produced as 12 isoforms from two promoters by alternative splicing. To characterize the transcriptional capacities of all 12 HNF4α isoforms, stable lines expressing each isoform were generated. The entire transcriptome associated with each isoform was analyzed as well as their respective interacting proteome. Major differences were noted in the transcriptional function of these isoforms. The α1 and α2 isoforms were the strongest regulators of gene expression whereas the α3 isoform exhibited significantly reduced activity. The α4, α5, and α6 isoforms, which use an alternative first exon, were characterized for the first time, and showed a greatly reduced transcriptional potential with an inability to recognize the consensus response element of HNF4α. Several transcription factors and coregulators were identified as potential specific partners for certain HNF4α isoforms. An analysis integrating the vast amount of omics data enabled the identification of transcriptional regulatory mechanisms specific to certain HNF4α isoforms, hence demonstrating the importance of considering all isoforms given their seemingly diverse functions.

The respiratory epithelium comprises polarized cells at the interface between the environment and airway tissues. Polarized apical and basolateral protein secretions are a feature of airway epithelium homeostasis. Human respiratory syncytial virus (hRSV) is a major human pathogen that primarily targets the respiratory epithelium. However, the consequences of hRSV infection on epithelium secretome polarity and content remain poorly understood. To investigate the hRSV-associated apical and basolateral secretomes, a proteomics approach was combined with an ex vivo pediatric human airway epithelial (HAE) model of hRSV infection (data are available via ProteomeXchange and can be accessed at https://www.ebi.ac.uk/pride/ with identifier PXD013661). Following infection, a skewing of apical/basolateral abundance ratios was identified for several individual proteins. Novel modulators of neutrophil and lymphocyte activation (CXCL6, CSF3, SECTM1 or CXCL16), and antiviral proteins (BST2 or CEACAM1) were detected in infected, but not in uninfected cultures. Importantly, CXCL6, CXCL16, CSF3 were also detected in nasopharyngeal aspirates (NPA) from hRSV-infected infants but not healthy controls. Furthermore, the antiviral activity of CEACAM1 against RSV was confirmed in vitro using BEAS-2B cells. hRSV infection disrupted the polarity of the pediatric respiratory epithelial secretome and was associated with immune modulating proteins (CXCL6, CXCL16, CSF3) never linked with this virus before. In addition, the antiviral activity of CEACAM1 against hRSV had also never been previously characterized. This study, therefore, provides novel insights into RSV pathogenesis and endogenous antiviral responses in pediatric airway epithelium.

Autoimmune thyroid diseases (AITD) are the most common group of autoimmune diseases, associated with lymphocyte infiltration and the production of thyroid autoantibodies, like thyroid peroxidase antibodies (TPOAb), in the thyroid gland. Immunoglobulins and cell-surface receptors are glycoproteins with distinctive glycosylation patterns that play a structural role in maintaining and modulating their functions. We investigated associations of total circulating IgG and peripheral blood mononuclear cells glycosylation with AITD and the influence of genetic background in a case-control study with several independent cohorts and over 3,000 individuals in total. The study revealed an inverse association of IgG core fucosylation with TPOAb and AITD, as well as decreased peripheral blood mononuclear cells antennary α1,2 fucosylation in AITD, but no shared genetic variance between AITD and glycosylation. These data suggest that the decreased level of IgG core fucosylation is a risk factor for AITD that promotes antibody-dependent cell-mediated cytotoxicity previously associated with TPOAb levels.

The study of protein subcellular distribution, their assembly into complexes and the set of proteins with which they interact with is essential to our understanding of fundamental biological processes. Complementary to traditional assays, proximity-dependent biotinylation (PDB) approaches coupled with mass spectrometry (such as BioID or APEX) have emerged as powerful techniques to study proximal protein interactions and the subcellular proteome in the context of living cells and organisms. Since their introduction in 2012, PDB approaches have been used in an increasing number of studies and the enzymes themselves have been subjected to intensive optimization. How these enzymes have been optimized and considerations for their use in proteomics experiments are important questions. Here, we review the structural diversity and mechanisms of the two main classes of PDB enzymes: the biotin protein ligases (BioID) and the peroxidases (APEX). We describe the engineering of these enzymes for PDB and review emerging applications, including the development of PDB for coincidence detection (split-PDB). Lastly, we briefly review enzyme selection and experimental design guidelines and reflect on the labeling chemistries and their implication for data interpretation.

Signaling networks process intra- and extracellular information to modulate the functions of a cell. Deregulation of signaling networks results in abnormal cellular physiological states and often drives diseases. Network responses to a stimulus or a drug treatment can be highly heterogeneous across cells in a tissue because of many sources of cellular genetic and non-genetic variance. Signaling network heterogeneity is the key to many biological processes, such as cell differentiation and drug resistance. Only recently, the emergence of multiplexed single-cell measurement technologies has made it possible to evaluate this heterogeneity. In this review, we categorize currently established single-cell signaling network profiling approaches by their methodology, coverage, and application, and we discuss the advantages and limitations of each type of technology. We also describe the available computational tools for network characterization using single-cell data and discuss potential confounding factors that need to be considered in single-cell signaling network analyses.

K. D. Cherednichenko, Yu. Yu. Ershova, A. V. Kiselev and S. N. Naboko
Trans. Moscow Math. Soc. 80 (2020), 251-294.
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A. M. Savchuk and I. V. Sadovnichaya
Trans. Moscow Math. Soc. 80 (2020), 235-250.
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I. V. Astashova, D. A. Lashin and A. V. Filinovskii
Trans. Moscow Math. Soc. 80 (2020), 221-234.
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A. A. Vladimirov
Trans. Moscow Math. Soc. 80 (2020), 211-219.
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I. A. Sheipak and T. A. Garmanova
Trans. Moscow Math. Soc. 80 (2020), 189-210.
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V. V. Vlasov and N. A. Rautian
Trans. Moscow Math. Soc. 80 (2020), 169-188.
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N. F. Valeev, Ya. T. Sultanaev and É. A. Nazirova
Trans. Moscow Math. Soc. 80 (2020), 153-167.
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K. A. Mirzoev and T. A. Safonova
Trans. Moscow Math. Soc. 80 (2020), 133-151.
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V. A. Sadovnichii, Ya. T. Sultanaev and A. M. Akhtyamov
Trans. Moscow Math. Soc. 80 (2020), 123-131.
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Trans. Moscow Math. Soc. 80 (2020), 113-122.
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A. G. Sergeev and Kh. A. Khachatryan
Trans. Moscow Math. Soc. 80 (2020), 95-111.
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V. V. Ryzhikov
Trans. Moscow Math. Soc. 80 (2020), 83-94.
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S. Yu. Orevkov
Trans. Moscow Math. Soc. 80 (2020), 73-81.
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S. A. Kashchenko
Trans. Moscow Math. Soc. 80 (2020), 53-71.
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S. A. Nazarov
Trans. Moscow Math. Soc. 80 (2020), 1-51.
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Many movie animation techniques are based on mathematics. Characters, background, and motion are all created using software that combines pixels into geometric shapes which are stored and manipulated using the mathematics of computer graphics. Software encodes features that are important to the eye, like position, motion, color, and texture, into each pixel. The software uses vectors, matrices, and polygonal approximations to curved surfaces to determine the shade of each pixel. Each frame in a computer-generated film has over two million pixels and can have over forty million polygons. The tremendous number of calculations involved makes computers necessary, but without mathematics the computers wouldn.t know what to calculate. Said one animator, ". . . it.s all controlled by math . . . all those little X,Y.s, and Z.s that you had in school - oh my gosh, suddenly they all apply." For More Information: Mathematics for Computer Graphics Applications, Michael E. Mortenson, 1999.

Detection and treatment of cancer have progressed, but neither is as precise as doctors would like. For example, tumors can change shape or location between pre-operative diagnosis and treatment so that radiation is aimed at a target which may have moved. Geometry, partial differential equations, and integer linear programming are three areas of mathematics used to process data in real-time, which allows doctors to inflict maximum damage to the tumor, with minimum damage to healthy tissue. One promising area of investigation is virotherapy: using viruses to destroy cancerous cells. Researchers are using mathematical models to discover how to use the viruses most beneficially.The models provide numerical outcomes for each of the many possibilities, thereby eliminating unsuccessful approaches and identifying candidates for further experimentation.Testing by simulation, which led to the development of anti-HIV cocktails, means good medicine is developed faster and cheaper than it can be by lab experiments and clinical trials alone. For More Information: Treatment Planning for Brachytherapy, Eva Lee, et al, Physics in Medicine and Biology, 1999.

Storm surge is often the most devastating part of a hurricane. Mathematical models used to predict surge must incorporate the effects of winds, atmospheric pressure, tides, waves and river flows, as well as the geometry and topography of the coastal ocean and the adjacent floodplain. Equations from fluid dynamics describe the movement of water, but most often such huge systems of equations need to be solved by numerical analysis in order to better forecast where potential flooding will occur. Much of the detailed geometry and topography on or near a coast require very fine precision to model, while other regions such as large open expanses of deep water can typically be solved with much coarser resolution. So using one scale throughout either has too much data to be feasible or is not very predictive in the area of greatest concern, the coastal floodplain. Researchers solve this problem by using an unstructured grid size that adapts to the relevant regions and allows for coupling of the information from the ocean to the coast and inland. The model was very accurate in tests of historical storms in southern Louisiana and is being used to design better and safer levees in the region and to evaluate the safety of all coastal regions. For More Information: A New Generation Hurricane Storm Surge Model for Southern Louisiana, by Joannes Westerink et al.

Mathematics is not just numbers and brute force calculation there is considerable art and elegance to the subject. So it is natural that mathematics is now being used to analyze artists. styles and to help determine the identities of the creators of disputed works. Attempts at measuring style began with literature based on statistics of word use and have successfully identified disputed works such as some of The Federalist Papers. But drawings and paintings resisted quantification until very recently. In the case of Jackson Pollock, his paintings have a demonstrated complexity to them (corresponding to a fractal dimension between 1 and 2) that distinguishes them from simple random drips. A team examining digital photos of drawings used modern mathematical transforms known as wavelets to quantify attributes of a collection of 16th century master.s drawings. The analysis revealed measurable differences between authentic drawings and imitations, clustering the former away from the latter. This is an impressive feat for the non-experts and their model, yet the team agrees that its work, like mathematics itself, is not designed to replace humans, but to assist them. For More Information: The Style of Numbers Behind a Number of Styles, Dan Rockmore, The Chronicle of Higher Education, June 9, 2006.

Mathematics and music have long been closely associated. Now a recent mathematical breakthrough uses topology (a generalization of geometry) to represent musical chords as points in a space called an orbifold, which twists and folds back on itself much like a Mobius strip does. This representation makes sense musically in that sounds that are far apart in one sense yet similar in another, such as two notes that are an octave apart, are identified in the space.This latest insight provides a way to analyze any type of music. In the case of Western music, pleasing chords lie near the center of the orbifolds and pleasing melodies are paths that link nearby chords. Yet despite the new connection between music and coordinate geometry, music is still more than a connect-the-dots exercise, just as mathematics is more than addition and multiplication. For More Information: The Geometry of Musical Chords, Dmitri Tymoczko, Science, July 7, 2006.

Actually, they weren.t caught together at all their images were put together with software. The shadows cast by the stars. faces give it away: The sun is coming from two different directions on the same beach! More elaborate digital doctoring is detected with mathematics. Calculus, linear algebra, and statistics are especially useful in determining when a portion of one image has been copied to another or when part of an image has been replaced. Tampering with an image leaves statistical traces in the file. For example, if a person is removed from an image and replaced with part of the background, then two different parts of the resulting file will be identical. The difficulty with exposing this type of alteration is that both the location of the replacement and its size are unknown beforehand. One successful algorithm finds these repetitions by first sorting small regions according to their digital color similarity, and then moving to larger regions that contain similar small ones. The algorithm.s designer, a leading digital forensics expert, admits that image alterers generally stay a step ahead of detectors, but observes that forensic advances have made it much harder for them to escape notice. He adds that to catch fakers, At the end of the day you need math.(1) For More Information: Can Digital Photos be Trusted?, Steve Casimiro, Popular Science, October 2005. _______ 1 It May Look Authentic; Here.s How to Tell It Isn't, Nicholas Wade, The New York Times, January 24, 2006.

Origami paper-folding may not seem like a subject for mathematical investigation or one with sophisticated applications, yet anyone who has tried to fold a road map or wrap a present knows that origami is no trivial matter. Mathematicians, computer scientists, and engineers have recently discovered that this centuries-old subject can be used to solve many modern problems.The methods of origami are now used to fold objects such as automobile air bags and huge space telescopes efficiently, and may be related to how proteins fold. Manufacturers often want to make a product out of a single piece of material. The manufacturing problem then becomes one of deciding whether a shape can be folded and if so, is there an efficient way to find a good fold? Thus, many origami research problems have to do with algorithm complexity and optimization theory. A testament to the diversity of origami, as well as the power of mathematics, is its applicability to problems at the molecular level, in manufacturing, and in outer space. For More Information: http://db.uwaterloo.ca/~eddemain/papers/MapFolding/

The outcome of elections that offer more than two alternatives but with no preference by a majority, is determined more by the voting procedure used than by the votes themselves. Mathematicians have shown that in such elections, illogical results are more likely than not. For example, the majority of this group want to go to a warm place, but the South Pole is the group.s plurality winner. So if these people choose their group.s vacation destination in the same way most elections are conducted, they will all go to the South Pole and six people will be disappointed, if not frostbitten. Elections in which only the top preference of each voter is counted are equivalent to a school choosing its best student based only on the number of A.s earned. The inequity of such a situation has led to the development of other voting methods. In one method, points are assigned to choices, just as they are to grades. Using this procedure, these people will vacation in a warm place a more desirable conclusion for the group. Mathematicians study voting methods in hopes of finding equitable procedures, so that no one is unfairly left out in the cold. For more information: Chaotic Elections: A Mathematician Looks at Voting, Donald Saari

Votes are cast by the full membership in each house of Congress, but much of the important maneuvering occurs in committees. Graph theory and linear algebra are two mathematics subjects that have revealed a level of organization in Congress groups of committees above the known levels of subcommittees and committees. The result is based on strong connections between certain committees that can be detected by examining their memberships, but which were virtually unknown until uncovered by mathematical analysis. Mathematics has also been applied to individual congressional voting records. Each legislator.s record is represented in a matrix whose larger dimension is the number of votes cast (which in a House term is approximately 1000). Using eigenvalues and eigenvectors, researchers have shown that the entire collection of votes for a particular Congress can be approximated very well by a two-dimensional space. Thus, for example, in almost all cases the success or failure of a bill can be predicted from information derived from two coordinates. Consequently it turns out that some of the values important in Washington are, in fact, eigenvalues. For More Information: Porter, Mason A; Mucha, Peter J.; Newman, M. E. J.; and Warmbrand, Casey M., A Network Analysis of Committees in the United States House of Representatives, Proceedings of the National Academy of Sciences, Vol. 102 [2005], No. 20, pp. 7057-7062.

Invisibility is no longer confined to fiction. In a recent experiment, microwaves were bent around a cylinder and returned to their original trajectories, rendering the cylinder almost invisible at those wavelengths. This doesn't mean that we're ready for invisible humans (or spaceships), but by using Maxwell's equations, which are partial differential equations fundamental to electromagnetics, mathematicians have demonstrated that in some simple cases not seeing is believing, too. Part of this successful demonstration of invisibility is due to metamaterials electromagnetic materials that can be made to have highly unusual properties. Another ingredient is a mathematical transformation that stretches a point into a ball, "cloaking" whatever is inside. This transformation was discovered while researchers were pondering how a tumor could escape detection. Their attempts to improve visibility eventually led to the development of equations for invisibility. A more recent transformation creates an optical "wormhole," which tricks electromagnetic waves into behaving as if the topology of space has changed. We'll finish with this: For More Information: Metamaterial Electromagnetic Cloak at Microwave Frequencies, D. Schurig et al, Science, November 10, 2006.

The colored "strings" you see represent air flow around the soccer ball, with the dark blue streams behind the ball signifying a low-pressure wake. Computational fluid dynamics and wind tunnel experiments have shown that there is a transition point between smooth and turbulent flow at around 30 mph, which can dramatically change the path of a kick approaching the net as its speed decreases through the transition point. Players taking free-kicks need not be mathematicians to score, but knowing the results obtained from mathematical facts can help players devise better strategies. The behavior of a ball depends on its surface design as well as on how it.s kicked. Topology, algebra, and geometry are all important to determine suitable shapes, and modeling helps determine desirable ones. The researchers studying soccer ball trajectories incorporate into their mathematical models not only the pattern of a new ball, but also details right down to the seams. Recently there was a radical change from the long-used pentagon-hexagon pattern to the adidas +TeamgeistTM. Yet the overall framework for the design process remains the same: to approximate a sphere, within less than two percent, using two-dimensional panels.

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea ice present and to the microscopic communities that sustain polar ecosystems. By taking samples, doing on-site experiments, and then incorporating the data into models of porous materials, mathematicians are working to understand sea ice and help refine climate predictions. Using probability, numerical analysis, and partial differential equations, researchers have recently shown that the permeability of sea ice is similar to that of some sedimentary rocks in the earth.s crust, even though the substances are otherwise dissimilar. One major difference between the two is the drastic changes in permeability of sea ice, from total blockage to clear passage, that occur over a range of just a few degrees. This difference can have a major effect on measurements by satellite, which provide information on the extent and thickness of sea ice. Results about sea ice will not only make satellite measurements more reliable, but they can also be applied to descriptions of lung and bone porosity, and to understanding ice on other planets. Image: Pancake ice in Antarctica, courtesy of Ken Golden. For More Information: "Thermal evolution of permeability and microstructure in sea ice," K. M. Golden, et al., Geophysical Research Letters, August 28, 2007.

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea ice present and to the microscopic communities that sustain polar ecosystems. By taking samples, doing on-site experiments, and then incorporating the data into models of porous materials, mathematicians are working to understand sea ice and help refine climate predictions. Using probability, numerical analysis, and partial differential equations, researchers have recently shown that the permeability of sea ice is similar to that of some sedimentary rocks in the earth.s crust, even though the substances are otherwise dissimilar. One major difference between the two is the drastic changes in permeability of sea ice, from total blockage to clear passage, that occur over a range of just a few degrees. This difference can have a major effect on measurements by satellite, which provide information on the extent and thickness of sea ice. Results about sea ice will not only make satellite measurements more reliable, but they can also be applied to descriptions of lung and bone porosity, and to understanding ice on other planets. Image: Pancake ice in Antarctica, courtesy of Ken Golden. For More Information: "Thermal evolution of permeability and microstructure in sea ice," K. M. Golden, et al., Geophysical Research Letters, August 28, 2007.

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea ice present and to the microscopic communities that sustain polar ecosystems. By taking samples, doing on-site experiments, and then incorporating the data into models of porous materials, mathematicians are working to understand sea ice and help refine climate predictions. Using probability, numerical analysis, and partial differential equations, researchers have recently shown that the permeability of sea ice is similar to that of some sedimentary rocks in the earth.s crust, even though the substances are otherwise dissimilar. One major difference between the two is the drastic changes in permeability of sea ice, from total blockage to clear passage, that occur over a range of just a few degrees. This difference can have a major effect on measurements by satellite, which provide information on the extent and thickness of sea ice. Results about sea ice will not only make satellite measurements more reliable, but they can also be applied to descriptions of lung and bone porosity, and to understanding ice on other planets. Image: Pancake ice in Antarctica, courtesy of Ken Golden. For More Information: "Thermal evolution of permeability and microstructure in sea ice," K. M. Golden, et al., Geophysical Research Letters, August 28, 2007.

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea ice present and to the microscopic communities that sustain polar ecosystems. By taking samples, doing on-site experiments, and then incorporating the data into models of porous materials, mathematicians are working to understand sea ice and help refine climate predictions. Using probability, numerical analysis, and partial differential equations, researchers have recently shown that the permeability of sea ice is similar to that of some sedimentary rocks in the earth.s crust, even though the substances are otherwise dissimilar. One major difference between the two is the drastic changes in permeability of sea ice, from total blockage to clear passage, that occur over a range of just a few degrees. This difference can have a major effect on measurements by satellite, which provide information on the extent and thickness of sea ice. Results about sea ice will not only make satellite measurements more reliable, but they can also be applied to descriptions of lung and bone porosity, and to understanding ice on other planets. Image: Pancake ice in Antarctica, courtesy of Ken Golden. For More Information: "Thermal evolution of permeability and microstructure in sea ice," K. M. Golden, et al., Geophysical Research Letters, August 28, 2007.

The spools of wire below contain the only known live recording of the legendary folk singer Woody Guthrie. A mathematician, Kevin Short, was part of a team that used signal processing techniques associated with chaotic music compression to recapture the live performance, which was often completely unintelligible. The modern techniques employed, instead of resulting in a cold, digital output, actually retained the original concert.s warmth and depth. As a result, Short and the team received a Grammy Award for their remarkable restoration of the recording. To begin the restoration the wire had to be manually pulled through a playback device and converted to a digital format. Since the pulling speed wasn.t constant there was distortion in the sound, frequently quite considerable. Algorithms corrected for the speed variations and reconfigured the sound waves to their original shape by using a background noise with a known frequency as a "clock." This clever correction also relied on sampling the sound selectively, and reconstructing and resampling the music between samples. Mathematics did more than help recreate a performance lost for almost 60 years: These methods are used to digitize treasured tapes of audiophiles everywhere. For More Information: "The Grammy in Mathematics," Julie J. Rehmeyer, Science News Online, February 9, 2008.

The racing team is just as important to a car.s finish as the driver is. With little to separate competitors over hundreds of laps, teams search for any technological edge that will propel them to Victory Lane. Of special use today is computational fluid dynamics, which is used to predict airflow over a car, both alone and in relation to other cars (for example, when drafting). Engineers also rely on more basic subjects, such as calculus and geometry, to improve their cars. In fact, one racing team engineer said of his calculus and physics teachers, the classes they taught to this day were the most important classes I.ve ever taken.(1) Mathematics helps the performance and efficiency of non-NASCAR vehicles, as well. To improve engine performance, data must be collected and processed very rapidly so that control devices can make adjustments to significant quantities such as air/fuel ratios. Innovative sampling techniques make this real-time data collection and processing possible. This makes for lower emissions and improved fuel economy goals worthy of a checkered flag. For More Information: The Physics of NASCAR, Diandra Leslie-Pelecky, 2008.

Stents are expandable tubes that are inserted into blocked or damaged blood vessels. They offer a practical way to treat coronary artery disease, repairing vessels and keeping them open so that blood can flow freely. When stents work, they are a great alternative to radical surgery, but they can deteriorate or become dislodged. Mathematical models of blood vessels and stents are helping to determine better shapes and materials for the tubes. These models are so accurate that the FDA is considering requiring mathematical modeling in the design of stents before any further testing is done, to reduce the need for expensive experimentation. Precise modeling of the entire human vascular system is far beyond the reach of current computational power, so researchers focus their detailed models on small subsections, which are coupled with simpler models of the rest of the system. The Navier-Stokes equations are used to represent the flow of blood and its interaction with vessel walls. A mathematical proof was the central part of recent research that led to the abandonment of one type of stent and the design of better ones. The goal now is to create better computational fluid-vessel models and stent models to improve the treatment and prediction of coronary artery disease the major cause of heart attacks. For More Information: Design of Optimal Endoprostheses Using Mathematical Modeling, Canic, Krajcer, and Lapin, Endovascular Today, May 2006.

Stents are expandable tubes that are inserted into blocked or damaged blood vessels. They offer a practical way to treat coronary artery disease, repairing vessels and keeping them open so that blood can flow freely. When stents work, they are a great alternative to radical surgery, but they can deteriorate or become dislodged. Mathematical models of blood vessels and stents are helping to determine better shapes and materials for the tubes. These models are so accurate that the FDA is considering requiring mathematical modeling in the design of stents before any further testing is done, to reduce the need for expensive experimentation. Precise modeling of the entire human vascular system is far beyond the reach of current computational power, so researchers focus their detailed models on small subsections, which are coupled with simpler models of the rest of the system. The Navier-Stokes equations are used to represent the flow of blood and its interaction with vessel walls. A mathematical proof was the central part of recent research that led to the abandonment of one type of stent and the design of better ones. The goal now is to create better computational fluid-vessel models and stent models to improve the treatment and prediction of coronary artery disease the major cause of heart attacks. For More Information: Design of Optimal Endoprostheses Using Mathematical Modeling, Canic, Krajcer, and Lapin, Endovascular Today, May 2006.

Archimedes was one of the most brilliant people ever, on a par with Einstein and Newton. Yet very little of what he wrote still exists because of the passage of time, and because many copies of his works were erased and the cleaned pages were used again. One of those written-over works (called a palimpsest) has resurfaced, and advanced digital imaging techniques using statistics and linear algebra have revealed his previously unknown discoveries in combinatorics and calculus. This leads to a question that would stump even Archimedes: How much further would mathematics and science have progressed had these discoveries not been erased? One of the most dramatic revelations of Archimedes. work was done using X-ray fluorescence. A painting, forged in the 1940s by one of the book.s former owners, obscured the original text, but X-rays penetrated the painting and highlighted the iron in the ancient ink, revealing a page of Archimedes. treatise The Method of Mechanical Theorems. The entire process of uncovering this and his other ideas is made possible by modern mathematics and physics, which are built on his discoveries and techniques. This completion of a circle of progress is entirely appropriate since one of Archimedes. accomplishments that wasn.t lost is his approximation of pi. For More Information: The Archimedes Codex, Reviel Netz and William Noel, 2007.

Archimedes was one of the most brilliant people ever, on a par with Einstein and Newton. Yet very little of what he wrote still exists because of the passage of time, and because many copies of his works were erased and the cleaned pages were used again. One of those written-over works (called a palimpsest) has resurfaced, and advanced digital imaging techniques using statistics and linear algebra have revealed his previously unknown discoveries in combinatorics and calculus. This leads to a question that would stump even Archimedes: How much further would mathematics and science have progressed had these discoveries not been erased? One of the most dramatic revelations of Archimedes. work was done using X-ray fluorescence. A painting, forged in the 1940s by one of the book.s former owners, obscured the original text, but X-rays penetrated the painting and highlighted the iron in the ancient ink, revealing a page of Archimedes. treatise The Method of Mechanical Theorems. The entire process of uncovering this and his other ideas is made possible by modern mathematics and physics, which are built on his discoveries and techniques. This completion of a circle of progress is entirely appropriate since one of Archimedes. accomplishments that wasn.t lost is his approximation of pi. For More Information: The Archimedes Codex, Reviel Netz and William Noel, 2007.

The collective motion of many groups of animals can be stunning. Flocks of birds and schools of fish are able to remain cohesive, find food, and avoid predators without leaders and without awareness of all but a few other members in their groups. Research using vector analysis and statistics has led to the discovery of simple principles, such as members maintaining a minimum distance between neighbors while still aligning with them, which help explain shapes such as the one below. Although collective motion by groups of animals is often beautiful, it can be costly as well: Destructive locusts affect ten percent of the world.s population. Many other animals exhibit group dynamics; some organisms involved are small while their groups are huge, so researchers. models have to account for distances on vastly different scales. The resulting equations then must be solved numerically, because of the incredible number of animals represented. Conclusions from this research will help manage destructive insects, such as locusts, as well as help speed the movement of people.ants rarely get stuck in traffic. Photo by Jose Luis Gomez de Francisco. For More Information: Swarm Theory, Peter Miller. National Geographic, July 2007.

The music of most hit songs is pretty well known, but sometimes there are mysteries. One question that remained unanswered for over forty years is: What instrumentation and notes make up the opening chord of the Beatles. "A Hard Day.s Night"? Mathematician Jason Brown - a big Beatles fan - recently solved the puzzle using his musical knowledge and discrete Fourier transforms, mathematical transformations that help decompose signals into their basic parts. These transformations simplify applications ranging from signal processing to multiplying large numbers, so that a researcher doesn.t have to be "working like a dog" to get an answer. Brown is also using mathematics, specifically graph theory, to discover who wrote "In My Life," which both Lennon and McCartney claimed to have written. In his graphs, chords are represented by points that are connected when one chord immediately follows another. When all songs with known authorship are diagrammed, Brown will see which collection of graphs - McCartney.s or Lennon.s - is a better fit for "In My Life." Although it may seem a bit counterintuitive to use mathematics to learn more about a revolutionary band, these analytical methods identify and uncover compositional principles inherent in some of the best Beatles. music. Thus it.s completely natural and rewarding to apply mathematics to the Fab 4 For More Information: Professor Uses Mathematics to Decode Beatles Tunes, "The Wall Street Journal", January 30, 2009..

With 468 stops served by 26 lines, the New York subway system can make visitors feel lucky when they successfully negotiate one planned trip in a day. Yet these two New Yorkers, Chris Solarz and Matt Ferrisi, took on the task of breaking a world record by visiting every stop in the system in less than 24 hours. They used mathematics, especially graph theory, to narrow down the possible routes to a manageable number and subdivided the problem to find the best routes in smaller groups of stations. Then they paired their mathematical work with practice runs and crucial observations (the next-to-last car stops closest to the stairs) to shatter the world record by more than two hours!

Although Chris and Matt.s success may not have huge ramifications in other fields, their work does have a lot in common with how people do modern mathematics research

* They worked together, frequently using computers and often asking experts for advice;
* They devoted considerable time and effort to meet their goal; and
* They continually refined their algorithm until arriving at a solution that was nearly optimal.
Finally, they also experienced the same feeling that researchers do that despite all the hours and intense preparation, the project .felt more like fun than work.
For More Information: Math whizzes shoot to set record for traversing subway system,. Sergey Kadinsky and Rich Schapiro, New York Daily News, January 22, 2009.
Photo by Elizabeth Ferrisi.
Map New York Metropolitan Transit Authority.
The Mathematical Moments program promotes appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture.

A person needing a kidney transplant may have a friend or relative who volunteers to be a living donor, but whose kidney is incompatible, forcing the person to wait for a transplant from a deceased donor. In the U.S. alone, thousands of people die each year without ever finding a suitable kidney. A new technique applies graph theory to groups of incompatible patient-donor pairs to create the largest possible number of paired-donation exchanges. These exchanges, in which a donor paired with Patient A gives a kidney to Patient B while a donor paired with Patient B gives to Patient A, will dramatically increase transplants from living donors. Since transplantation is less expensive than dialysis, this mathematical algorithm, in addition to saving lives, will also save hundreds of millions of dollars annually. Naturally there can be more transplants if matches along longer patient-donor cycles are considered (e.g., A.s donor to B, B.s donor to C, and C.s donor to A). The problem is that the possible number of longer cycles grows so fast hundreds of millions of A >B>C>A matches in just 5000 donor-patient pairs that to search through all the possibilities is impossible. An ingenious use of random walks and integer programming now makes searching through all three-way matches feasible, even in a database large enough to include all incompatible patient-donor pairs. For More Information: Matchmaking for Kidneys, Dana Mackenzie, SIAM News, December 2008. Image of suboptimal two-way matching (in purple) and an optimal matching (in green), courtesy of Sommer Gentry.

What.s in store for our climate and us? It.s an extraordinarily complex question whose answer requires physics, chemistry, earth science, and mathematics (among other subjects) along with massive computing power. Mathematicians use partial differential equations to model the movement of the atmosphere; dynamical systems to describe the feedback between land, ocean, air, and ice; and statistics to quantify the uncertainty of current projections. Although there is some discrepancy among different climate forecasts, researchers all agree on the tremendous need for people to join this effort and create new approaches to help understand our climate. It.s impossible to predict the weather even two weeks in advance, because almost identical sets of temperature, pressure, etc. can in just a few days result in drastically different weather. So how can anyone make a prediction about long-term climate? The answer is that climate is an average of weather conditions. In the same way that good predictions about the average height of 100 people can be made without knowing the height of any one person, forecasts of climate years into the future are feasible without being able to predict the conditions on a particular day. The challenge now is to gather more data and use subjects such as fluid dynamics and numerical methods to extend today.s 20-year projections forward to the next 100 years. For More Information: Mathematics of Climate Change: A New Discipline for an Uncertain Century, Dana Mackenzie, 2007.

What.s in store for our climate and us? It.s an extraordinarily complex question whose answer requires physics, chemistry, earth science, and mathematics (among other subjects) along with massive computing power. Mathematicians use partial differential equations to model the movement of the atmosphere; dynamical systems to describe the feedback between land, ocean, air, and ice; and statistics to quantify the uncertainty of current projections. Although there is some discrepancy among different climate forecasts, researchers all agree on the tremendous need for people to join this effort and create new approaches to help understand our climate. It.s impossible to predict the weather even two weeks in advance, because almost identical sets of temperature, pressure, etc. can in just a few days result in drastically different weather. So how can anyone make a prediction about long-term climate? The answer is that climate is an average of weather conditions. In the same way that good predictions about the average height of 100 people can be made without knowing the height of any one person, forecasts of climate years into the future are feasible without being able to predict the conditions on a particular day. The challenge now is to gather more data and use subjects such as fluid dynamics and numerical methods to extend today.s 20-year projections forward to the next 100 years. For More Information: Mathematics of Climate Change: A New Discipline for an Uncertain Century, Dana Mackenzie, 2007.

One of the most useful tools in analyzing the spread of disease is a system of evolutionary equations that reflects the dynamics among three distinct categories of a population: those susceptible (S) to a disease, those infected (I) with it, and those recovered (R) from it. This SIR model is applicable to a range of diseases, from smallpox to the flu. To predict the impact of a particular disease it is crucial to determine certain parameters associated with it, such as the average number of people that a typical infected person will infect. Researchers estimate these parameters by applying statistical methods to gathered data, which aren.t complete because, for example, some cases aren.t reported. Armed with reliable models, mathematicians help public health officials battle the complex, rapidly changing world of modern disease. Today.s models are more sophisticated than those of even a few years ago. They incorporate information such as contact periods that vary with age (young people have contact with one another for a longer period of time than do adults from different households), instead of assuming equal contact periods for everyone. The capacity to treat variability makes it possible to predict the effectiveness of targeted vaccination strategies to combat the flu, for instance. Some models now use graph theory and matrices to represent networks of social interactions, which are important in understanding how far and how fast a given disease will spread. For More Information: Mathematical Models in Population Biology and Epidemiology, Fred Brauer and Carlos Castillo-Chavez.