FPTAS for Weighted Fibonacci Gates and Its Applications

Fibonacci gate problems have severed as computation primitives to solve other problems by holographic algorithm and play an important role in the dichotomy of exact counting for Holant and CSP frameworks. We generalize them to weighted cases and allow each vertex function to have different parameters, which is a much boarder family and #P-hard for exactly counting. We design a fully polynomial-time approximation scheme (FPTAS) for this generalization by correlation decay technique. This is the first deterministic FPTAS for approximate counting in the general Holant framework without a degree bound. We also formally introduce holographic reduction in the study of approximate counting and these weighted Fibonacci gate problems serve as computation primitives for approximate counting. Under holographic reduction, we obtain FPTAS for other Holant problems and spin problems. One important application is developing an FPTAS for a large range of ferromagnetic two-state spin systems. This is the first deterministic FPTAS in the ferromagnetic range for two-state spin systems without a degree bound. Besides these algorithms, we also develop several new tools and techniques to establish the correlation decay property, which are applicable in other problems

Bonding mechanism in the nitrides Ti2AlN and TiN: an experimental and theoretical investigation

The electronic structure of nanolaminate Ti2AlN and TiN thin films has been investigated by bulk-sensitive soft x-ray emission spectroscopy. The measured Ti L, N K, Al L1 and Al L2,3 emission spectra are compared with calculated spectra using ab initio density-functional theory including dipole transition matrix elements. Three different types of bond regions are identified; a relatively weak Ti 3d - Al 3p bonding between -1 and -2 eV below the Fermi level, and Ti 3d - N 2p and Ti 3d - N 2s bonding which are deeper in energy observed at -4.8 eV and -15 eV below the Fermi level, respectively. A strongly modified spectral shape of 3s states of Al L2,3 emission from Ti2AlN in comparison to pure Al metal is found, which reflects the Ti 3d - Al 3p hybridization observed in the Al L1 emission. The differences between the electronic and crystal structures of Ti2AlN and TiN are discussed in relation to the intercalated Al layers of the former compound and the change of the materials properties in comparison to the isostructural carbides.Comment: 18 pages, 7 figures; http://link.aps.org/doi/10.1103/PhysRevB.76.19512

Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants

We continue the discussion of the fermion models on graphs that started in the first paper of the series. Here we introduce a Graphical Gauge Model (GGM) and show that : (a) it can be stated as an average/sum of a determinant defined on the graph over $\mathbb{Z}_{2}$ (binary) gauge field; (b) it is equivalent to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the model allows an explicit expression in terms of a series over disjoint directed cycles, where each term is a product of local contributions along the cycle and the determinant of a matrix defined on the remainder of the graph (excluding the cycle). We also establish a relation between the MD model on the graph and the determinant series, discussed in the first paper, however, considered using simple non-Belief-Propagation choice of the gauge. We conclude with a discussion of possible analytic and algorithmic consequences of these results, as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte

Unusual Loop-Sequence Flexibility of the Proximal RNA Replication Element in EMCV

Picornaviruses contain stable RNA structures at the 5′ and 3′ ends of the RNA genome, OriL and OriR involved in viral RNA replication. The OriL RNA element found at the 5′ end of the enterovirus genome folds into a cloverleaf-like configuration. In vivo SELEX experiments revealed that functioning of the poliovirus cloverleaf depends on a specific structure in this RNA element. Little is known about the OriL of cardioviruses. Here, we investigated structural aspects and requirements of the apical loop of proximal stem-loop SL-A of mengovirus, a strain of EMCV. Using NMR spectroscopy, we showed that the mengovirus SL-A apical loop consists of an octaloop. In vivo SELEX experiments demonstrated that a large number of random sequences are tolerated in the apical octaloop that support virus replication. Mutants in which the SL-A loop size and the length of the upper part of the stem were varied showed that both stem-length and stability of the octaloop are important determinants for viral RNA replication and virus reproduction. Together, these data show that stem-loop A plays an important role in virus replication. The high degree of sequence flexibility and the lack of selective pressure on the octaloop argue against a role in sequence specific RNA-protein or RNA-RNA interactions in which octaloop nucleotides are involved

Robustness and Generalization

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from the complexity or stability arguments, to study generalization of learning algorithms. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property for learning algorithms to work

Sequential cavity method for computing free energy and surface pressure

We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice $\Z^d$. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a suitably modified sublattice of $\Z^d$. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation decay. We illustrate our method for the hard-core and monomer-dimer models, and improve several earlier estimates. For example we show that the exponent of the monomer-dimer coverings of $\Z^3$ belongs to the interval $[0.78595,0.78599]$, improving best previously known estimate of (approximately) $[0.7850,0.7862]$ obtained in \cite{FriedlandPeled},\cite{FriedlandKropLundowMarkstrom}. Moreover, we show that given a target additive error $\epsilon>0$, the computational effort of our method for these two models is $(1/\epsilon)^{O(1)}$ \emph{both} for free energy and surface pressure. In contrast, prior methods, such as transfer matrix method, require $\exp\big((1/\epsilon)^{O(1)}\big)$ computation effort.Comment: 33 pages, 4 figure

A Single Nucleotide in Stem Loop II of 5′-Untranslated Region Contributes to Virulence of Enterovirus 71 in Mice

BACKGROUND: Enterovirus 71 (EV71) has emerged as a neuroinvasive virus responsible for several large outbreaks in the Asia-Pacific region while virulence determinant remains unexplored. PRINCIPAL FINDINGS: In this report, we investigated increased virulence of unadapted EV71 clinical isolate 237 as compared with isolate 4643 in mice. A fragment 12 nucleotides in length in stem loop (SL) II of 237 5'-untranslated region (UTR) visibly reduced survival time and rate in mice was identified by constructing a series of infectious clones harboring chimeric 5'-UTR. In cells transfected with bicistronic plasmids, and replicon RNAs, the 12-nt fragment of isolate 237 enhanced translational activities and accelerated replication of subgenomic EV71. Finally, single nucleotide change from cytosine to uridine at base 158 in this short fragment of 5'-UTR was proven to reduce viral translation and EV71 virulence in mice. Results collectively indicated a pivotal role of novel virulence determinant C158 on virus translation in vitro and EV71 virulence in vivo. CONCLUSIONS: These results presented the first reported virulence determinant in EV71 5'-UTR and first position discovered from unadapted isolates

Packet Forwarding Algorithms in a Line Network

Abstract. We initiate a competitive analysis of packet forwarding poli-cies for maximum and average flow in a line network. We show that the policies Earliest Arrival and Furthest-To-Go are scalable, but not con-stant competitive, for maximum flow. We show that there is no constant competitive algorithm for average flow.

Re-localization of Cellular Protein SRp20 during Poliovirus Infection: Bridging a Viral IRES to the Host Cell Translation Apparatus

Poliovirus IRES-mediated translation requires the functions of certain canonical as well as non-canonical factors for the recruitment of ribosomes to the viral RNA. The interaction of cellular proteins PCBP2 and SRp20 in extracts from poliovirus-infected cells has been previously described, and these two proteins were shown to function synergistically in viral translation. To further define the mechanism of ribosome recruitment for the initiation of poliovirus IRES-dependent translation, we focused on the role of the interaction between cellular proteins PCBP2 and SRp20. Work described here demonstrates that SRp20 dramatically re-localizes from the nucleus to the cytoplasm of poliovirus-infected neuroblastoma cells during the course of infection. Importantly, SRp20 partially co-localizes with PCBP2 in the cytoplasm of infected cells, corroborating our previous in vitro interaction data. In addition, the data presented implicate the presence of these two proteins in viral translation initiation complexes. We show that in extracts from poliovirus-infected cells, SRp20 is associated with PCBP2 bound to poliovirus RNA, indicating that this interaction occurs on the viral RNA. Finally, we generated a mutated version of SRp20 lacking the RNA recognition motif (SRp20ΔRRM) and found that this protein is localized similar to the full length SRp20, and also partially co-localizes with PCBP2 during poliovirus infection. Expression of this mutated version of SRp20 results in a ∼100 fold decrease in virus yield for poliovirus when compared to expression of wild type SRp20, possibly via a dominant negative effect. Taken together, these results are consistent with a model in which SRp20 interacts with PCBP2 bound to the viral RNA, and this interaction functions to recruit ribosomes to the viral RNA in a direct or indirect manner, with the participation of additional protein-protein or protein-RNA interactions