On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections

We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Gr\"obner basis consisting of moves of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure

Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{ reg } I(G)$ and the asymptotic linear function $\text{ reg } I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$Comment: 31 pages, 15 figure

Blockade of T-cell activation by dithiocarbamates involves novel mechanisms of inhibition of nuclear factor of activated T cells.

Dithiocarbamates (DTCs) have recently been reported as powerful inhibitors of NF-kappaB activation in a number of cell types. Given the role of this transcription factor in the regulation of gene expression in the inflammatory response, NF-kappaB inhibitors have been suggested as potential therapeutic drugs for inflammatory diseases. We show here that DTCs inhibited both interleukin 2 (IL-2) synthesis and membrane expression of antigens which are induced during T-cell activation. This inhibition, which occurred with a parallel activation of c-Jun transactivating functions and expression, was reflected by transfection experiments at the IL-2 promoter level, and involved not only the inhibition of NF-kappaB-driven reporter activation but also that of nuclear factor of activated T cells (NFAT). Accordingly, electrophoretic mobility shift assays (EMSAs) indicated that pyrrolidine DTC (PDTC) prevented NF-kappaB, and NFAT DNA-binding activity in T cells stimulated with either phorbol myristate acetate plus ionophore or antibodies against the CD3-T-cell receptor complex and simultaneously activated the binding of AP-1. Furthermore, PDTC differentially targeted both NFATp and NFATc family members, inhibiting the transactivation functions of NFATp and mRNA induction of NFATc. Strikingly, Western blotting and immunocytochemical experiments indicated that PDTC promoted a transient and rapid shuttling of NFATp and NFATc, leading to their accelerated export from the nucleus of activated T cells. We propose that the activation of an NFAT kinase by PDTC could be responsible for the rapid shuttling of the NFAT, therefore transiently converting the sustained transactivation of this transcription factor that occurs during lymphocyte activation, and show that c-Jun NH2-terminal kinase (JNK) can act by directly phosphorylating NFATp. In addition, the combined inhibitory effects on NFAT and NF-KB support a potential use of DTCs as immunosuppressants

High-density information storage in an absolutely defined aperiodic sequence of monodisperse copolyester

Synthesis of a polymer composed of a large discrete number of chemically distinct monomers in an absolutely defined aperiodic sequence remains a challenge in polymer chemistry. The synthesis has largely been limited to oligomers having a limited number of repeating units due to the difficulties associated with the step-by-step addition of individual monomers to achieve high molecular weights. Here we report the copolymers of ??-hydroxy acids, poly(phenyllactic-co-lactic acid) (PcL) built via the cross-convergent method from four dyads of monomers as constituent units. Our proposed method allows scalable synthesis of sequence-defined PcL in a minimal number of coupling steps from reagents in stoichiometric amounts. Digital information can be stored in an aperiodic sequence of PcL, which can be fully retrieved as binary code by mass spectrometry sequencing. The information storage density (bit/Da) of PcL is 50% higher than DNA, and the storage capacity of PcL can also be increased by adjusting the molecular weight (~38???kDa)

On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

p63 is an alternative p53 repressor in melanoma that confers chemoresistance and a poor prognosis.

The role of apoptosis in melanoma pathogenesis and chemoresistance is poorly characterized. Mutations in TP53 occur infrequently, yet the TP53 apoptotic pathway is often abrogated. This may result from alterations in TP53 family members, including the TP53 homologue TP63. Here we demonstrate that TP63 has an antiapoptotic role in melanoma and is responsible for mediating chemoresistance. Although p63 was not expressed in primary melanocytes, up-regulation of p63 mRNA and protein was observed in melanoma cell lines and clinical samples, providing the first evidence of significant p63 expression in this lineage. Upon genotoxic stress, endogenous p63 isoforms were stabilized in both nuclear and mitochondrial subcellular compartments. Our data provide evidence of a physiological interaction between p63 with p53 whereby translocation of p63 to the mitochondria occurred through a codependent process with p53, whereas accumulation of p53 in the nucleus was prevented by p63. Using RNA interference technology, both isoforms of p63 (TA and ΔNp63) were demonstrated to confer chemoresistance, revealing a novel oncogenic role for p63 in melanoma cells. Furthermore, expression of p63 in both primary and metastatic melanoma clinical samples significantly correlated with melanoma-specific deaths in these patients. Ultimately, these observations provide a possible explanation for abrogation of the p53-mediated apoptotic pathway in melanoma, implicating novel approaches aimed at sensitizing melanoma to therapeutic agents