New Approximability Results for the Robust k-Median Problem

We consider a robust variant of the classical $k$-median problem, introduced by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem}, we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i \subseteq V}_{i=1}^m$. The objective is to open a set $F \subseteq V$ of $k$ facilities such that the worst case connection cost over all client sets is minimized; in other words, minimize $\max_{i} \sum_{v \in S_i} d(F,v)$. Anthony et al.\ showed an $O(\log m)$ approximation algorithm for any metric and APX-hardness even in the case of uniform metric. In this paper, we show that their algorithm is nearly tight by providing $\Omega(\log m/ \log \log m)$ approximation hardness, unless ${\sf NP} \subseteq \bigcap_{\delta >0} {\sf DTIME}(2^{n^{\delta}})$. This hardness result holds even for uniform and line metrics. To our knowledge, this is one of the rare cases in which a problem on a line metric is hard to approximate to within logarithmic factor. We complement the hardness result by an experimental evaluation of different heuristics that shows that very simple heuristics achieve good approximations for realistic classes of instances.Comment: 19 page

On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP

Stimulation in vitro of galactocerebroside galactosidase by N‐decanoyl 2‐amino‐2‐methylpropanol

Amides resembling ceramide (fatty acyl sphingosine) were synthesized and tested in vitro for their effects on the rat brain β‐galactosidase which hydrolyzes galactosyl ceramide. The N‐decanoyl derivative of 2‐amino‐2‐methyl‐1‐propanol was most effective, giving a 34% stimulation at 0.15 mM concentration and a 60% stimulation at maximal levels. Addition of a hydroxyl group in the 3 position reduced the degree of stimulation, as did increasing or decreasing the length of the fatty acid portion. Omission of the branched methyl group resulted in inhibition instead of stimulation. Kinetic analysis indicates that the stimulator does not affect the binding of substrate to enzyme, but does speed the rate of hydrolytic action. Stimulation was also observed with the cerebrosidase in spleen and kidney. It is suggested that the stimulators act on an enzyme site other than the substrate‐active site.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141447/1/lipd0056.pd

GLYCOSYLTRANSFERASES OF RAT BRAIN THAT MAKE CEREBROSIDES: SUBSTRATE SPECIFICITY, INHIBITORS, AND ABNORMAL PRODUCTS 1

Brain homogenates from young rats were assayed for their ability to synthesize cerebrosides from radioactive UDP-galactose or UDP-glucose and ceramide. A comparison of galactose transfer with ceramides made from different 2-hydroxy acids showed that the shortest one tested (C 7 ) was by far the best acceptor, while the poorest contained 18 carbon atoms; longer fatty acids were better than CIS. Glucosyltransferase, on the other hand, showed rather little chain length specificity or discrimination against hydroxy acid ceramides. Synthetic compounds analogous in structure to ceramides were tested as inhibitors of the sugar transferases. Some were found to act as sugar acceptors themselves, particularly amides of DL-erythro-1- phenyl-2-amino-1,3-propanediol. Some amides were good inhibitors of glucosyltransferase, particularly decanoyl norephedrine, decanoyl threo-1-phenyl-2-amino-1,3-propanediol and decenoyl phenylalaninol. The secondary amine analogous to the first of these, N -decyl norephedrine, was also very effective. No strong inhibitors of galactosyl transferase were found, although octanoyl D-threo- p -nitrophenyla- minopropanediol showed promise (42% inhibition at 0.3 mM). Octanoyl phenylalaninol was nearly as good an inhibitor; the inhibition appeared only after a lag period. It is suggested that the glucosyltransferase inhibitors might he useful in therapy of Gaucher's disease, by reducing the degradative load normally falling on glucocerebrosidase.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65833/1/j.1471-4159.1976.tb06987.x.pd

Magic wavelengths for the np-ns transitions in alkali-metal atoms

Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest ns, np_1/2, np_3/2 states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states of alkali-metal atoms. We find magic wavelengths in alkali-metal atoms for which the ns and np_1/2 and np_3/2 atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.Comment: 12 pages, 8 figure

Targeting BRCA1-BER deficient breast cancer by ATM or DNA-PKcs blockade either alone or in combination with cisplatin for personalized therapy

BRCA1, a key factor in homologous recombination repair may also regulate base excision repair (BER). Targeting BRCA1-BER deficient cells by blockade of ATM and DNA-PKcs could be a promising strategy in breast cancer. We investigated BRCA1, XRCC1 and pol β protein expression in two cohorts (n=1602 sporadic and n=50 germ-line BRCA1 mutated) and mRNA expression in two cohorts (n=1952 and n=249). Artificial neural network analysis for BRCA1-DNA repair interacting genes was conducted in 249 tumours. Pre-clinically, BRCA1 proficient and deficient cells were DNA repair expression profiled and evaluated for synthetic lethality using ATM and DNA-PKcs inhibitors either alone or in combination with cisplatin. In human tumours, BRCA1 negativity was strongly associated with low XRCC1, and low pol β at mRNA and protein levels (p<0.0001). In patients with BRCA1 negative tumours, low XRCC1 or low pol β expression was significantly associated with poor survival in univariate and multivariate analysis compared to high XRCC1 or high pol β expressing BRCA1 negative tumours (ps<0.05). Pre-clinically, BRCA1 negative cancer cells exhibit low mRNA and low protein expression of XRCC1 and pol β. BRCA1-BER deficient cells were sensitive to ATM and DNA-PKcs inhibitor treatment either alone or in combination with cisplatin and synthetic lethality was evidenced by DNA double strand breaks accumulation, cell cycle arrest and apoptosis. We conclude that XRCC1 and pol β expression status in BRCA1 negative tumours may have prognostic significance. BRCA1-BER deficient cells could be targeted by ATM or DNA-PKcs inhibitors for personalized therapy

The application of mathematical and statistical methods in the study of value of patients' clinical and laboratory indicators before and after treatment

Multivariate data analysis has been actively developing and applying practically in all fields of study latly. An important task in medicine during the study of diseases, the treatment of the patient is search and selection of informative features for reliable diagnosis setting

State-insensitive trapping of Rb atoms: linearly versus circularly polarized lights

We study the cancellation of differential ac Stark shifts in the 5s and 5p states of rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single, double and important valence triple excitations approximation including all possible non-linear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. "Magic wavelengths" are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. Possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light are discussed. Using the optimized matrix elements, the lifetimes of the 4d and 6s states of this atom are ameliorated.Comment: 13 pages, 13 tables and 4 figure