Direct Integration and Non-Perturbative Effects in Matrix Models

We show how direct integration can be used to solve the closed amplitudes of multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, we give explicit expressions for the ring of non-holomorphic modular objects that are needed to express all closed matrix model amplitudes. This allows us to integrate the holomorphic anomaly equation up to holomorphic modular terms that we fix by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg--Witten curve and the ring reduces to the non-holomorphic modular ring of the group $\Gamma(2)$. On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. We use these results to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, we argue that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model.Comment: 51 pages, 8 figure

Probability to produce animal vaccines in insect baculovirus expression system

The insect baculovirus expression system is a valuable tool for the production of vaccine. Many subunit vaccines have been expressed in this system. The first vaccine produced in insect cells for animal use is now in the market. In this study, we reviewed recent progress of animal’s vaccine production for different expression levels and baculovirus genome stability, characteristic features of baculovirus expression vector system (BVES), virus link particles, baculovirus expression in mammalian cell and methodology of produce subunit vaccines. This review showed that BVES is a fantastic tool for vaccine development and it has wonderful feature for future animal vaccine development.Key words: Baculovirus expression system, vaccine, subunit vaccine, DNA vaccine

On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

Spotting Trees with Few Leaves

We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. Second, we show that the iterated random bipartition employed by the algorithm can be improved whenever the host graph admits a vertex coloring with few colors; it can be an ordinary proper vertex coloring, a fractional vertex coloring, or a vector coloring. In effect, we show improved bounds for $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ or with vector chromatic number at most 8

Measuring indirect transmission-reducing effects in tuberculosis vaccine efficacy trials: why and how?

Tuberculosis is the leading bacterial cause of death globally. In 2021, 10·6 million people developed symptomatic tuberculosis and 1·6 million died. Seven promising vaccine candidates that aim to prevent tuberculosis disease in adolescents and adults are currently in late-stage clinical trials. Conventional phase 3 trials provide information on the direct protection conferred against infection or disease in vaccinated individuals, but they tell us little about possible indirect (ie, transmission-reducing) effects that afford protection to unvaccinated individuals. As a result, proposed phase 3 trial designs will not provide key information about the overall effect of introducing a vaccine programme. Information on the potential for indirect effects can be crucial for policy makers deciding whether and how to introduce tuberculosis vaccines into immunisation programmes. We describe the rationale for measuring indirect effects, in addition to direct effects, of tuberculosis vaccine candidates in pivotal trials and lay out several options for incorporating their measurement into phase 3 trial designs

Non-perturbative effects and the refined topological string

The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P1xP1, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.Comment: 38 pages, 5 figure

Spatio-Temporal Characteristics of Global Warming in the Tibetan Plateau during the Last 50 Years Based on a Generalised Temperature Zone - Elevation Model

Temperature is one of the primary factors influencing the climate and ecosystem, and examining its change and fluctuation could elucidate the formation of novel climate patterns and trends. In this study, we constructed a generalised temperature zone elevation model (GTEM) to assess the trends of climate change and temporal-spatial differences in the Tibetan Plateau (TP) using the annual and monthly mean temperatures from 1961-2010 at 144 meteorological stations in and near the TP. The results showed the following: (1) The TP has undergone robust warming over the study period, and the warming rate was 0.318°C/decade. The warming has accelerated during recent decades, especially in the last 20 years, and the warming has been most significant in the winter months, followed by the spring, autumn and summer seasons. (2) Spatially, the zones that became significantly smaller were the temperature zones of -6°C and -4°C, and these have decreased 499.44 and 454.26 thousand sq km from 1961 to 2010 at average rates of 25.1% and 11.7%, respectively, over every 5-year interval. These quickly shrinking zones were located in the northwestern and central TP. (3) The elevation dependency of climate warming existed in the TP during 1961-2010, but this tendency has gradually been weakening due to more rapid warming at lower elevations than in the middle and upper elevations of the TP during 1991-2010. The higher regions and some low altitude valleys of the TP were the most significantly warming regions under the same categorizing criteria. Experimental evidence shows that the GTEM is an effective method to analyse climate changes in high altitude mountainous regions

In vivo imaging and quantitative analysis of leukocyte directional migration and polarization in inflamed tissue

Directional migration of transmigrated leukocytes to the site of injury is a central event in the inflammatory response. Here, we present an in vivo chemotaxis assay enabling the visualization and quantitative analysis of subtype-specific directional motility and polarization of leukocytes in their natural 3D microenvironment. Our technique comprises the combination of i) semi-automated in situ microinjection of chemoattractants or bacteria as local chemotactic stimulus, ii) in vivo near-infrared reflected-light oblique transillumination (RLOT) microscopy for the visualization of leukocyte motility and morphology, and iii) in vivo fluorescence microscopy for the visualization of different leukocyte subpopulations or fluorescence-labeled bacteria. Leukocyte motility parameters are quantified off-line in digitized video sequences using computer-assisted single cell tracking. Here, we show that perivenular microinjection of chemoattractants [macrophage inflammatory protein-1alpha (MIP-1alpha/Ccl3), platelet-activating factor (PAF)] or E. coli into the murine cremaster muscle induces target-oriented intravascular adhesion and transmigration as well as polarization and directional interstitial migration of leukocytes towards the locally administered stimuli. Moreover, we describe a crucial role of Rho kinase for the regulation of directional motility and polarization of transmigrated leukocytes in vivo. Finally, combining in vivo RLOT and fluorescence microscopy in Cx3CR1(gfp/gfp) mice (mice exhibiting green fluorescent protein-labeled monocytes), we are able to demonstrate differences in the migratory behavior of monocytes and neutrophils.Taken together, we propose a novel approach for investigating the mechanisms and spatiotemporal dynamics of subtype-specific motility and polarization of leukocytes during their directional interstitial migration in vivo