Counting approximately-shortest paths in directed acyclic graphs

Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights L_1 and L_2, we show how to approximately count the s-t paths that have length at most L_1 in the first graph and length at most L_2 in the second graph. We believe that our algorithms should find application in counting approximate solutions of related optimization problems, where finding an (optimum) solution can be reduced to the computation of a shortest path in a purpose-built auxiliary graph

Investment under ambiguity with the best and worst in mind

Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity - also called Knightian uncertainty - on investors' decisions. In this paper, we show that a decision maker's attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor's individual ambiguity attitude by applying alpha-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical

Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a $\Pi\Sigma\Pi$ polynomial. We first prove that the first problem is \#P-hard and then devise a $O^*(3^ns(n))$ upper bound for this problem for any polynomial represented by an arithmetic circuit of size $s(n)$. Later, this upper bound is improved to $O^*(2^n)$ for $\Pi\Sigma\Pi$ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for $\Pi\Sigma$ polynomials. On the negative side, we prove that, even for $\Pi\Sigma\Pi$ polynomials with terms of degree $\le 2$, the first problem cannot be approximated at all for any approximation factor $\ge 1$, nor {\em "weakly approximated"} in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time $\lambda$-approximation algorithm for $\Pi\Sigma\Pi$ polynomials with terms of degrees no more a constant $\lambda \ge 2$. On the inapproximability side, we give a $n^{(1-\epsilon)/2}$ lower bound, for any $\epsilon >0,$ on the approximation factor for $\Pi\Sigma\Pi$ polynomials. When terms in these polynomials are constrained to degrees $\le 2$, we prove a $1.0476$ lower bound, assuming $P\not=NP$; and a higher $1.0604$ lower bound, assuming the Unique Games Conjecture

COVID-19 immunity passport to ease travel restrictions?

'Immunity passport' (also called ''immunity certificate'' or ''immunity license'' has been suggested to certify traveler' protection from SARS-CoV-2 infection. Some data have demonstrated development of neutralizing antibodies that may protect against reinfection and reduce disease severity in the short-term, and some tests correlate with virus neutralization. More evidence is needed on serologies for such certification to facilitate travel, to protect travelers and their destination countries.Immunogenetics and cellular immunology of bacterial infectious disease

Probing the stability of superheavy dark matter particles with high-energy neutrinos

Two of the most fundamental properties of the dark matter particle, the mass and the lifetime, are only weakly constrained by the astronomical and cosmological evidence of dark matter. We derive in this paper lower limits on the lifetime of dark matter particles with masses in the range 10 TeV-10^15 TeV from the non-observation of ultrahigh energy neutrinos in the AMANDA, IceCube, Auger and ANITA experiments. For dark matter particles which produce neutrinos in a two body or a three body decay, we find that the dark matter lifetime must be longer than O(10^26-10^28) s for masses between 10 TeV and the Grand Unification scale. Finally, we also calculate, for concrete particle physics scenarios, the limits on the strength of the interactions that induce the dark matter decay.Comment: 17 pages, 6 figures; v2: references added, discussion improved, matches the version published at JCA

DEM simulations of agglomerates impact breakage using Timoshenko beam bond model

Attrition and breakage of agglomerates are prevalent during production and handling processes in many industries. Therefore, it is highly desirable to be able to model and analyse the agglomerate breakage process under various loading conditions. The ensemble strength and breakage patterns of agglomerates are still not well understood despite a significant amount of research being carried out. In this study, three-dimensional discrete element method (DEM) simulation of the impact breakage behaviour of agglomerates were performed using a Timoshenko beam bond model which considers axial, shear, twisting and bending behaviours on the bonds. An advantage of the Timoshenko beam bond model is the pertinent parameters of the bond contact have clear physical meaning and therefore could be determined through corresponding experimental characterisations. The mechanical properties of the bonds in this study were firstly calibrated using experimental measurements. The validation of the Timoshenko beam bond model was then undertaken by direct comparisons between the numerical simulation and experimental results of impact tests. It was shown that the time evolution of the agglomerate breakage process obtained from simulation had good agreement with experimental observations. Numerical results indicate that most of the damage happens at the early stage of the impact and a cone shape fracture zone is formed quickly inside the agglomerate where strong compressive stresses are concentrated. It is found that the exterior of the fracture zone is surrounded by an arch shape tensile stress which dominates the fracture propagation

Arl3 regulates a transport system for farnesylated cargo

Arl3 is a small G-protein that is found exclusively in ciliated organisms. In addition, knocking out of Arl3 results in a plethora of ciliopathies. Arl3 is known to bind the photoreceptor (specialized cilia) specific PDE delta subunit (PDE6D), which in turn bind to prenylated proteins. The significance of this interaction and the function of Arl3 in cilia are poorly understood. Here in this study, by solving the crystal structure of a fully modified prenylated (farnesylated) Rheb in complex with PDE6D and comparing it to a structure of PDE6D in complex with the Arl3 homologue Arl2, we show that Arl3 is an allosteric regulator of PDE6D. Arl3, in a nucleotide dependent manner, releases the farnesylated cargo bound to PDE6D. We explain the molecular mechanism of this release and we further verify the mechanism in vitro and by live cell imaging. Based on this study we hypothesize that Arl3 regulate the targeting of prenylated cargo in and out the cilia

Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

Structure of Fat Jets at the Tevatron and Beyond

Boosted resonances is a highly probable and enthusiastic scenario in any process probing the electroweak scale. Such objects when decaying into jets can easily blend with the cornucopia of jets from hard relative light QCD states. We review jet observables and algorithms that can contribute to the identification of highly boosted heavy jets and the possible searches that can make use of such substructure information. We also review previous studies by CDF on boosted jets and its measurements on specific jet shapes.Comment: invited review for a special "Top and flavour physics in the LHC era" issue of The European Physical Journal C, we invite comments regarding contents of the review; v2 added references and institutional preprint number