Detailed Structural Characterization of Sphingolipids via 193 nm Ultraviolet Photodissociation and Ultra High Resolution Tandem Mass Spectrometry

Sphingolipids serve not only as components of cellular membranes but also as bioactive mediators of numerous cellular functions. As the biological activities of these lipids are dependent on their structures, and due to the limitations of conventional ion activation methods employed during tandem mass spectrometry (MS/MS), there is a recognized need for the development of improved structure-specific methods for their comprehensive identification and characterization. Here, positive-ionization mode 193 nm ultraviolet photodissociation (UVPD)-MS/MS has been implemented for the detailed structural characterization of lipid species from a range of sphingolipid classes introduced to the mass spectrometer via electrospray ionization as their lithiated or protonated adducts. These include sphingosine d18:1(4E), dihydrosphingosine (sphinganine) d18:0, sphingadiene d18:2(4E,11Z), the isomeric sphingolipids ceramide d18:1(4E)/18:0 and dihydroceramide d18:0/18:1(9Z), ceramide-1-phosphate d18:1(4Z)/16:0, sphingomyelin d18:1(4E)/18:1(9Z) the glycosphingolipids galactosyl ceramide d18:1(4E)/24:1(15Z) and lactosyl ceramide d18:1(4E)/24:0, and several endogenous lipids present within a porcine brain total lipid extract. In addition to the product ions formed by higher energy collision dissociation (HCD), UVPD is shown to yield a series of novel structurally diagnostic product ions resulting from cleavage of both sphingosine carbon–carbon and acyl chain carbon–carbon double bonds for direct localization of site(s) of unsaturation, as well as via diagnostic cleavages of the sphingosine backbone and N–C amide bond linkages. With activation timescales and dissociation efficiencies similar to those found in conventional MS/MS strategies, this approach is therefore a promising new tool in the arsenal of ion activation techniques toward providing complete structural elucidation in automated, high-throughput lipid analysis workflows.

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Determination of selected elements in bone samples by neutron activation and γ-spectrometry

A non-destructive method for the quantification of eleven elements in bone samples is described. The analytical scheme is based on short (30 s) irradiation with thermal neutrons followed immediately (decay time 10 s) by counting fluorine-20 for 30 s and, after a total waiting time of 150 s, by 10-min γ-spectrometry counting, which give data for Ca, Cl, Mg, Mn, Na, and V. Use of a boron carbide shield for a second set of irradiations with epithermal neutrons permits the additional determination of bromine and strontium and calculation of the contribution of aluminium and phosphorus to the total activity of ₂₈Al.     

Raman study of SO2 at high pressure: aggregation,phase transformations,and photochemistry

We report Raman measurements made on SO₂ in a diamond cell up to 75 kbar showing two new phases, solid II and solid III, which differ from known, zero-pressure solid I. Spectra indicate that SO₂ molecules aggregate in solid III to possibly form a cyclical trimer; solid III is shown to be photochemically active to blue radiation.     

Bunny hops: using multiplicities of zeroes in calculus for graphing

Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students’ pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities.     

Generators and normal forms of Richard Thompson’s group F and the four-color theorem

We use a result of Kauffman to explore the connection between Richard Thompson’s Group F and the four-color theorem.     

A Characterization of Graphs Where the Independence Number Equals the Radius

In a classical 1986 paper by Erdös, Saks and Saós every graph of radius r has an induced path of order at least 2r ? 1. This result implies that the independence number of such graphs is at least r. In this paper, we use a result of S. Fajtlowicz about radius-critical graphs to characterize graphs where the independence number is equal to the radius, for all possible values of the radius except 2, 3, and 4. We briefly discuss these remaining cases as well.     

New inequalities for subspace arrangements

For each positive integer n?4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n=4 we recover Ingleton's inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also presented.     

Nonuniqueness of infinity ground states

In this paper, we construct a dumbbell domain for which the associated principal ∞-eigenvalue is not simple. This gives a negative answer to the outstanding problem posed in Juutinen et al. (Arch Ration Mech Anal 148(2):89–105, 1999; The infinity Laplacian: examples and observations, 2001). It remains a challenge to determine whether simplicity holds for convex domains.     

Ramsey numbers of odd cycles versus larger even wheels

The generalized Ramsey number $R(G_1,G_2)$ is the smallest positive integer $N$ such that any red–blue coloring of the edges of the complete graph $K_N$ either contains a red copy of $G_1$ or a blue copy of $G_2$. Let $C_m$ denote a cycle of length $m$ and $W_n$ denote a wheel with $n+1$ vertices. In 2014, Zhang, Zhang and Chen determined many of the Ramsey numbers $R(C_{2k+1},W_n)$ of odd cycles versus larger wheels, leaving open the particular case where $n=2j$ is even and $k<j<3k∕2$. They conjectured that for these values of $j$ and $k$, $R(C_{2k+1},W_{2j})=4j+1$. In 2015, Sanhueza-Matamala confirmed this conjecture asymptotically, showing that $R(C_{2k+1},W_{2j})\le 4j+334$. In this paper, we prove the conjecture of Zhang, Zhang and Chen for almost all of the remaining cases. In particular, we prove that $R(C_{2k+1},W_{2j})=4j+1$ if $j?k\ge 251$, $k<j<3k∕2$, and $j\ge 212299$.     

Optimal Decisions in a Time Priority Queue

We show how the position of a limit order (LO) in the queue influences the decision of whether to cancel the order or let it rest. Using ultra-high-frequency data from the Nasdaq exchange, we perform empirical analysis on various LO book events and propose novel ways for modelling some of these events, including cancellation of LOs in various positions and size of market orders. Based on our empirical findings, we develop a queuing model that captures stylized facts on the data. This model includes a distinct feature which allows for a potentially random effect due to the agent’s impulse control. We apply the queuing model in an algorithmic trading setting by considering an agent maximizing her expected utility through placing and cancelling of LOs. The agent’s optimal strategy is presented after calibrating the model to real data. A simulation study shows that for the same level of standard deviation of terminal wealth, the optimal strategy has a 2.5% higher mean compared to a strategy which ignores the effect of position, or an 8.8% lower standard deviation for the same level of mean. This extra gain stems from posting an LO during adverse conditions and obtaining a good queue position before conditions become favourable.