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Given a digraph $G$, a lot of attention has been deserved on the maximum number $\phi(G)$ of fixed points in a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ with $G$ as interaction graph. In particular, a central problem in network coding consists in studying the optimality of the classical upper bound $\phi(G)\leq 2^{\tau}$, where $\tau$ is the minimum size of a feedback vertex set of $G$. In this paper, we study the maximum number $\phi_m(G)$ of fixed points in a {\em monotone} Boolean network with interaction graph $G$. We establish new upper and lower bounds on $\phi_m(G)$ that depends on the cycle structure of $G$. In addition to $\tau$, the involved parameters are the maximum number $\nu$ of vertexdisjoint cycles, and the maximum number $\nu^{*}$ of vertexdisjoint cycles verifying some additional technical conditions. We improve the classical upper bound $2^\tau$ by proving that $\phi_m(G)$ is at most the largest sublattice of $\{0,1\}^\tau$ without chain of size $\nu+1$, and with
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VBgroupoids can be thought of as vector bundle objects in the category of Lie groupoids. Just as Lie algebroids are the infinitesimal counterparts of Lie groupoids, VBalgebroids correspond to the infinitesimal version of VBgroupoids. In this work we address the problem of the existence of a VBgroupoid admitting a given VBalgebroid as its infinitesimal data. Our main result is an explicit characterization of the obstructions appearing in this integrability problem as the vanishing of the spherical periods of certain cohomology classes. Along the way, we illustrate our result in concrete examples. Finally, as a corollary, we obtain computable obstructions for a $2$term representation up to homotopy of Lie algebroid to arise as the infinitesimal counterpart of a smooth such representation of a Lie groupoid.
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To any $n$dimensional random vector $X$ we may associate its $L_p$centroid body ${\cal Z}_p(X)$ and the corresponding norm. We formulate a conjecture concerning the bound on the ${\cal Z}_p(X)$norm of $X$ and show that it holds under some additional symmetry assumptions. We also relate our conjecture with estimates of covering numbers and Sudakovtype minorization bounds.
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A twophase HeleShow problem with a timedependent gap describes the evolution of the interface, which separates two fluids sandwiched between two plates. The fluids have different viscosities. In addition to the change in the gap width of the HeleShaw cell, the interface is driven by the presence of some special distributions of sinks and sources located in both the interior and exterior domains. The effect of surface tension is neglected. Using the Schwarz function approach, we give examples of exact solutions when the interface belongs to a certain family of algebraic curves and the curves do not form cusps. The family of curves are defined by the initial shape of the free boundary.
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We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain class of integral operators we provide sufficient conditions for boundedness. In conclusion we apply developed technique to investigate HardySteklov type operators.
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In this paper, the author establishes finitegeneration of the cohomology ring of a classical Lie superalgebra relative to an even subsuperalgebra. A spectral sequence is constructed to provide conditions for when this relative cohomology ring is CohenMacaulay. With finite generation established, support varieties for modules are defined via the relative cohomology, which generalize those of [BKN1]
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The main result of this paper is to generalize from $\Q$ to each of the nine imaginary quadratic fields of class number one a result of Serre and MestreOesterl\'e of 1989, namely that if $E$ is an elliptic curve of prime conductor then either $E$ or a $2$isogenous curve or a $3$isogenous curve has prime discriminant. The proof is conditional in two ways: first that the curves are modular, so are associated to suitable Bianchi newforms; and secondly that a certain levellowering conjecture holds for Bianchi newforms. We also classify all elliptic curves of prime power conductor and nontrivial torsion over each of the nine fields: in the case of $2$torsion we find that such curves either have CM or with a small (finite) number of exceptions arise from a family analogous to the SetzerNeumann family of elliptic curves over $\Q$.
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In this paper, we study the convergence of Alternating Projection (AP) algorithm for the matrix completion and compressed sensing problems. We also present computational evidence for the excellent performance of the algorithm. Also, in the last section, we prove using algebraicgeometric techniques that, fixing the known positions, if a rank r matrix can be completed in finitely many ways using one given set of known entries, then, for almost all set of known entries, the matrix can be only completed into a rank r matrix in finitely many ways.
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"In Portugal, with no net neutrality, internet providers are starting to split the net into packages," argues a California congressman  retweeting a stunning graphic. An anonymous reader quotes BoingBoing's Cory Doctorow: Since 2006, Net Neutrality activists have been warning that a nonNeutral internet will be an invitation to ISPs to create "plans" where you have to choose which established services you can access, shutting out new entrants to the market and allowing the companies with the deepest pockets to permanently dominate the internet... the Portuguese nonneutral ISP MEO has mistaken a warning for a suggestion, and offers a series of "plans" for its mobile data service where you pay €5 to access a handful of messaging services, €5 more to use social media; and €5 more for videostreaming services. The congressman notes this arrangement offers "a huge advantage for entrenched companies, but it totally ices out startups trying to get in front of people, which
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"San Francisco company Purism announced that they are now offering their Librem laptops with the Intel Management Engine disabled," writes Slashdot reader boudie2. Purism describes Management Engine as "a separate CPU that can run and control a computer even when powered off." HardOCP reports that Management Engine "is widely despised by security professionals and privacy advocates because it relies on signed and secret Intel code, isn't easily alterable, isn't fully documented, and has been found to be vulnerable to exploitation... In short, it's a tiny potentially hackable computer in your computer that you cannot totally control, nor optout of, but it can totally control your system." Purism writes: Disabling the Management Engine is no easy task, and it has taken security researchers years to find a way to properly and verifiably disable it. Purism, because it runs coreboot and maintains its own BIOS firmware update process, has been able to release and ship coreboot that disables
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All diversity sources of a wireless communication channel must be utilized to enable ultrareliable wireless communication links. Hadani et al. propose the two dimensional discrete symplectic Fourier transform (DSFT) as orthogonal precoder for orthogonal frequency division multiplexing (OFDM) in time and frequencyselective channels. In this paper we investigate general orthogonal precoding (OP) and develop a lowcomplexity iterative channel estimation and (near) maximum likelihood detection algorithm using softsymbol feedback. We present a general but compact framework to analyze the performance of OP and its ability to utilize time and frequencydiversity. We are able to proof that all constant modulus sequences, e.g. such as the DSFT or WalshHadamard sequences, lead to the same performance for OP. Our OP receiver is tested by numerical link level simulation for the DSFT, two dimensional discrete prolate spheroidal sequences, and WalshHadamard sequences. We demonstrate that our
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Flexible loads, e.g. thermostatically controlled loads (TCLs), are technically feasible to participate in demand response (DR) programs. On the other hand, there is a number of challenges that need to be resolved before it can be implemented in practice en masse. First, individual TCLs must be aggregated and operated in sync to scale DR benefits. Second, the uncertainty of TCLs needs to be accounted for. Third, exercising the flexibility of TCLs needs to be coordinated with distribution system operations to avoid unnecessary power losses and compliance with power flow and voltage limits. This paper addresses these challenges. We propose a networkconstrained, openloop, stochastic optimal control formulation. The first part of this formulation represents ensembles of collocated TCLs modeled by an aggregated Markov Process (MP), where each MP state is associated with a given power consumption or production level. The second part extends MPs to a multiperiod distribution power flow opti
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The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and entanglement measures can be realized from it. As such, there has been broad interest in generalizing the notion to further understand its most basic properties, one of which is the data processing inequality. The quantum fdivergence of Petz is one generalization of the quantum relative entropy, and it also leads to other relative entropies, such as the PetzRenyi relative entropies. In this paper, I introduce the optimized quantum fdivergence as a related generalization of quantum relative entropy. I prove that it satisfies the data processing inequality, and the method of proof relies upon the operator Jensen inequality, similar to Petz's original approach. Interestingly, the sandwiched Renyi relative entropies are particular examples of the optim
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Most prior works of proactive caching at wireless edge optimize caching policies under the following assumptions: the preference of each user is identical to content popularity, all users request contents with the same active level and at uniformlydistributed locations. In this paper, we investigate what happens without these assumptions. To this end, we establish a framework to optimize caching policy at base stations exploiting user preference, active level, and spatial locality. We obtain optimal caching policy to minimize the weighted sum of the file download time averaged over all file requests and user locations in the network (reflecting network performance) and the maximal weighted download time averaged over possible file requests and locations of each user (reflecting user fairness). To investigate how user preference similarity and active level skewness affect the optimal caching policy, we then provide a method to synthesize user preference for given content popularity and
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It is common knowledge that symmetries arising in integer programs could impair the solution process, in particular when symmetric solutions lead to an excessively large branch and bound (B\&B) search tree. Techniques like isomorphic pruning [11], orbital branching [16] and orbitopal fixing [8] have been shown to be essential to solve very symmetric instances from the literature. This paper focuses on formulations involving a set of 2index variables, also referred to as matrix, such that the corresponding symmetry group is the set of all column permutations. Such formulations arise for example from scheduling problems with a discrete time horizon. Orbitopal fixing as introduced in [8] is restricted to the special case of partitioning (resp. packing) formulations involving a solution matrix with exactly (resp. at most) one 1entry in each row. It relies on the linear description of the partitioning (resp. packing) orbitope [9], i.e., the convex hull of binary matrices with lexicogr
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We consider the problem of reconstructing the dynamic state matrix of transmission power grids from timestamped PMU measurements in the regime of ambient fluctuations. Using a maximum likelihood based approach, we construct a family of convex estimators that adapt to the structure of the problem depending on the available prior information. The proposed method is fully datadriven and does not assume any knowledge of system parameters. It can be implemented in near realtime and requires a small amount of data. Our learning algorithms can be used for model validation and calibration, and can also be applied to related problems of system stability, detection of forced oscillations, generation redispatch, as well as to the estimation of the system state.
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The EinsteinVlasovFokkerPlanck system describes the kinetic diffusion dynamics of selfgravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions and prove the existence of both global solutions and solutions that blowup in finite time depending on the size of certain functions of the initial data. We also derive information on the largetime behavior of global solutions and toward the singularity for solutions which blowup in fine time. Our results entail the existence of a phase of decelerated expansion followed by a phase of accelerated expansion, in accordance with the physical expectations in cosmology.
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We examine the integrability of two models used for the interaction of long and short waves in dispersive media. One is more classical but arguably cannot be derived from the underlying water wave equations, while the other one was recently derived. We use the method of Zakharov and Schulman to attempt to construct conserved quantities for these systems at different orders in the magnitude of the solutions. The coupled KdVNLS model is shown to be nonintegrable, due to the presence of fourthorder resonances. A coupled real KdV  complex KdV system is shown to suffer the same fate, except for three special choices of the coefficients, where higherorder calculations or a different approach are necessary to conclude integrability or the absence thereof.
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Assuming a deep but standard conjecture in the Langlands programme, we prove Fermat's Last Theorem over $\mathbb Q(i)$. Under the same assumption, we also prove that for $p \geq 5$, Fermat's Equation with prime exponent $a^p+b^p+c^p=0$ does not have nontrivial solutions over $\mathbb Q(i), \mathbb Q(\sqrt{2})$ and $\mathbb Q(\sqrt{7})$.
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In this paper we consider stabilizer codes over local Frobenius rings. First, we study the relative minimum distances of a stabilizer code and its reduction onto the residue field. We show that for various scenarios, a free stabilizer code over the ring does not underperform the according stabilizer code over the field. This leads us to conjecture that the same is true for all free stabilizer codes. Secondly, we focus on the isometries of stabilizer codes. We present some preliminary results and introduce some interesting open problems.
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We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial differential equations. Here, we focus on parabolic equations which allow for operatortheoretic methods such as the holomorphic functional calculus. Moreover, we investigate stronger conditions than continuity leading to inputtostate stability with respect to Orlicz spaces. This also implies that the notions of inputtostate stability and integralinputtostate stability coincide if additionally the uncontrolled equation is dissipative and the input space is finitedimensional.
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The \emph{distance matrix} of a simple connected graph $G$ is $D(G)=(d_{ij})$, where $d_{ij}$ is the distance between the vertices $i$ and $j$ in $G$. We consider a weighted tree $T$ on $n$ vertices with edge weights are square matrix of same size. The distance $d_{ij}$ between the vertices $i$ and $j$ is the sum of the weight matrices of the edges in the unique path from $i$ to $j$. In this article we establish a characterization for the trees in terms of rank of (matrix) weighted Laplacian matrix associated with it. Then we establish a necessary and sufficient condition for the distance matrix $D$, with matrix weights, to be invertible and the formula for the inverse of $D$, if it exists. Also we study some of the properties of the distance matrices of matrix weighted trees in connection with the Laplacian matrices, ginverses and eigenvalues.
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Dvorak (2013) gave a bound on the minimum size of a distance r dominating set in the terms of the maximum size of a distance 2r independent set and generalized coloring numbers, thus obtaining a constant factor approximation algorithm for the parameters in any class of graphs with bounded expansion. We improve and clarify this dependence using an LPbased argument inspired by the work of Bansal and Umboh (2017).
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We state a simple criterion to prove the infiniteness of the image of ReshetikhinTuraev irreducible representations of the mapping class groups of surfaces. We use it to study some of the ReshetikhinTuraev representations associated to the oneholed torus and derive an alternative proof of a result of Funar.
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We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression operators as a special case. We show the optimality of our reconstruction operator and demonstrate that the usually considered regression operators generally cannot be optimal reconstruction operators. Our estimation theory allows for autocorrelated functional data and considers the practically relevant situation in which each of the $n$ functions is observed at $m$ discretization points. We derive rates of consistency for our nonparametric estimation procedures using a double asymptotic ($n\to\infty, m\to\infty$). For data situations, as in our real data application where $m$ is considerably smaller than $n$, we show that our functional principal components based estimator can provide better rates of convergence than any conventional nonparametric smoo
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We continue our study of a basic but seemingly intractable problem in integer partition theory, namely the conjecture that $p(n)$ is odd exactly $50\%$ of the time. Here, we greatly extend on our previous paper by providing a doublyindexed, infinite framework of conjectural identities modulo 2, and show how to, in principle, prove each such identity. However, our conjecture remains open in full generality. A striking consequence is that, under suitable existence conditions, if any $t$multipartition function is odd with positive density and $t\not \equiv 0$ (mod 3), then $p(n)$ is also odd with positive density. These are all facts that appear virtually impossible to show unconditionally today. Our arguments employ a combination of algebraic and analytic methods, including certain technical tools recently developed by Radu in his study of the parity of the Fourier coefficients of modular forms.
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We show the existence of an inertial manifold (i.e. a globally invariant, exponentially attracting, finitedimensional manifold) for the approximate deconvolution model of the 2D mean Boussinesq equations. This model is obtained by means of the Van Cittern approximate deconvolution operators, which is applied to the 2D filtered Boussinesq equations.
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Hard core bosons in a large class of one or two dimensional flat band systems have an upper critical density, below which the ground states can be described completely. At the critical density, the ground states are Wigner crystals. If one adds a particle to the system at the critical density, the ground state and the low lying multi particle states of the system can be described as a Wigner crystal with an additional pair of particles. The energy band for the pair is separated from the rest of the multiparticle spectrum. The proofs use a Gerschgorin type of argument for block diagonally dominant matrices. In certain onedimensional or treelike structures one can show that the pair is localised. For the onedimensional systems with periodic boundary condition the energy band for the pair is flat.
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In this paper we study spaces of holomorphic functions on the Siegel upper halfspace $\mathcal U$ and prove PaleyWiener type theorems for such spaces. The boundary of $\mathcal U$ can be identified with the Heisenberg group $\mathbb H_n$. Using the group Fourier transform on $\mathbb H_n$, OgdenVagi proved a PaleyWiener theorem for the Hardy space $H^2(\mathcal U)$. We consider a scale of Hilbert spaces on $\mathcal U$ that includes the Hardy space, the weighted Bergman spaces, the weighted Dirichlet spaces, and in particular the DruryArveson space, and the Dirichlet space $\mathcal D$. For each of these spaces, we prove a PaleyWiener theorem, some structure theorems, and provide some applications. In particular we prove that the norm of the Dirichlet space modulo constants $\dot{\mathcal D}$ is the unique Hilbert space norm that is invariant under the action of the group of automorphisms of $\mathcal U$.
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Samplingbased kinodynamic planners, such as Rapidlyexploring Random Trees (RRTs), pose two fundamental challenges: computing a reliable (pseudo)metric for the distance between two randomly sampled nodes, and computing a steering input to connect the nodes. The core of these challenges is a Two Point Boundary Value Problem, which is known to be NPhard. Recently, the distance metric has been approximated using supervised learning, reducing computation time drastically. The previous work on such learning RRTs use direct optimal control to generate the data for supervised learning. This paper proposes to use indirect optimal control instead, because it provides two benefits: it reduces the computational effort to generate the data, and it provides a low dimensional parametrization of the action space. The latter allows us to learn both the distance metric and the steering input to connect two nodes. This eliminates the need for a local planner in learning RRTs. Experimental results on
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This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information into the standard recovery procedure by maximizing the correlation between the prior knowledge and the desired signal. We then establish performance guarantees (in terms of the number of measurements) for the proposed method under subGaussian measurements. Specific structured signals including sparse vectors, blocksparse vectors, and lowrank matrices are also analyzed. Furthermore, we present an interesting geometrical interpretation for the proposed procedure. Our results demonstrate that if prior information is good enough, then the proposed approach can (remarkably) outperform the standard recovery procedure. Simulations are provided to verify our results.
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In [AHL] Hardt, Lin and the author proved that the defect set of minimizers of the modified Ericksen energy for nematic liquid crystals consists locally of a finite union of isolated points and H\"older continuous curves with finitely many crossings. In this article, we show that each H\"older continuous curve in the defect set is of finite length. Hence, the defect set is locally rectifiable. For the most part, the proof follows the work of De Lellis, Marchese, Spadaro and Valtorta [DLMSV] on harmonic $\mathcal{Q}$valued maps closely. The blowup analysis in [AHL] allows us to simplify the covering arguments in [DLMSV] and locally estimate the length of line defects in a geometric fashion.
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The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$ does not interpret Robinson's theory $R$. To this end, we borrow tools from model theoryspecifically, we investigate modeltheoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of $\exists\forall$ theories interpretable in existential theories in the process.
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The present analysis deals with the regularity of solutions of bilinear control systems of the type $x'=(A+u(t)B)x$where the state $x$ belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators $A$ and $B$ are skewadjoint and the control $u$ is a real valued function. Such systems arise, for instance, in quantum control with the bilinear Schr\"odinger equation. For the sake of the regularity analysis, we consider a more general framework where $A$ and $B$ are generators of contraction semigroups.Under some hypotheses on the commutator of the operators $A$ and $B$, it is possible to extend the definition of solution for controls in the set of Radon measures to obtain precise a priori energy estimates on the solutions, leading to a natural extension of the celebrated noncontrollability result of Ball, Marsden, and Slemrod in 1982. Complementary material to this analysis can be found in [hal01537743v1]
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We review some recent results on existence and regularity of MongeAmp\`ere exhaustions on the smoothly bounded strongly pseudoconvex domains, which admit at least one such exhaustion of sufficiently high regularity. A main consequence of our results is the fact that the Kobayashi pseudometric k on each of the above domains is actually a smooth Finsler metric. The class of domains to which our result apply is very large. It includes for instance all smoothly bounded strongly pseudoconvex complete circular domains and all their sufficiently small deformations.
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The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, overfitting is typically mitigated by adding regularization terms to the objective that penalize hypothesis complexity. In this paper we introduce new regularization techniques using ideas from distributionally robust optimization, and we give new probabilistic interpretations to existing techniques. Specifically, we propose to minimize the worstcase expected loss, where the worst case is taken over the ball of all (continuous or discrete) distributions that have a bounded transportation distance from the (discrete) empirical distribution. By choosing the radius of this ball judiciously, we can guarantee that the worstcase expected loss provides an upper confidence bound on the loss on test data, thus offering new generalization bou
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Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that approximates a population covariance $\Sigma$, and these eigenvectors are often used to extract structural information about the variables (or attributes) of the studied population. Since PCA is based on the eigendecomposition of the proxy covariance $\widehat{\Sigma}$ rather than the groundtruth $\Sigma$, it is important to understand the approximation error in each individual eigenvector as a function of the number of available samples. The recent results of Kolchinskii and Lounici yield such bounds. In the present paper we sharpen these bounds and show that eigenvectors can often be reconstructed to a required accuracy from a sample of strictly smaller size order.
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The primitive equations in a 3D infinite layer domain are considered with linearly glowing initial data in the horizontal direction, which illustrates the global atmospheric rotating or straining flows. On the boundaries, Dirichlet, Neumann or mixed boundary conditions are imposed. The OrnsteinUhlenbeck type operator appears in the linear parts, so the semigroup theory is established by Trotter's arguments due to decomposition of infinitesimal generators. To obtain smoothing properties of the semigroup, derivatives of the associated kernel are calculated. For proving timelocal existence and uniqueness of mild solutions, the adapted FujitaKato scheme is used in certain Sobolev spaces.
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In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations $\sigma$ of symplectic groups $\mathrm{Sp}_{2n}(\mathbb{A})$, which detects the rightmost pole of the $L$function $L(s,\sigma\times\chi)$ for some character $\chi$ of $F^\times\backslash\mathbb{A}^\times$ of order at most $2$, and hence the occurrence of a simple global Arthur parameter $(\chi,b)$ in the global Arthur parameter $\psi$ attached to $\sigma$. We also give a characterisation of first occurrences of theta correspondence by (regularised) period integrals of residues of certain Eisenstein series.
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We survey a host of results from discrete geometry that have bearing on the analysis of geometric models of approval voting. Such models view the political spectrum as a geometric space, with geometric constraints on voter preferences. Results on piercing numbers then have a natural interpretation in voting theory, and we survey their implications for various classes of geometric constraints on voter approval sets.
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In this paper, we propose a lowcomplexity, secrecy capacity achieving polar coding scheme for the cognitive interference channel with confidential messages (CICC) under the strong secrecy criterion. Existing polar coding schemes for interference channels rely on the use of polar codes for the multiple access channel, the code construction problem of which can be complicated. We show that the whole secrecy capacity region of the CICC can be achieved by simple pointtopoint polar codes due to the cognitivity, and our proposed scheme requires the minimum rate of randomness at the encoder.
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The investigations on higherorder type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher order logic. However, the epistemological significance of such investigations, and of their often non trivial results, has not received much attention in the contemporary foundational debate. The results recalled in this paper suggest that the question of the circularity of second order logic cannot be reduced to the simple assessment of a vicious circle. Through a comparison between the faulty consistency arguments given by Frege and MartinL\"of, respectively for the logical system of the Grundgesetze (shown inconsistent by Russell's paradox) and for the intuitionistic type theory with a type of all types (shown inconsistent by Girard's paradox), and the normalization argument for second order type theory (or System F), we indicate a bunch of subtle mathem
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Let M be a smooth manifold, and let O(M) be the poset of open subsets of M. Manifold calculus, due to Goodwillie and Weiss, is a calculus of functors suitable for studying contravariant functors (cofunctors) F: O(M)> Top from O(M) to the category of spaces. Weiss showed that polynomial cofunctors of degree <= k are determined by their values on O_k(M), where O_k(M) is the full subposet of O(M) whose objects are open subsets diffeomorphic to the disjoint union of at most k balls. Afterwards Pryor showed that one can replace O_k(M) by more general subposets and still recover the same notion of polynomial cofunctor. In this paper, we generalize these results to cofunctors from O(M) to any simplicial model category C. If conf(k, M) stands for the unordered configuration space of k points in M, we also show that the category of homogeneous cofunctors O(M) > C of degree k is weakly equivalent to the category of linear cofunctors O(conf(k, M)) > C provided that C has a zero
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We show that the eighth power of the Jacobi triple product is a JacobiEisenstein series of weight $4$ and index $4$ and we calculate its Fourier coefficients. As applications we obtain explicit formulas for the eighth powers of thetaconstants of arbitrary order and the Fourier coefficients of the Ramanujan Deltafunction $\Delta(\tau)=\eta^{24}(\tau)$, $\eta^{12}(\tau)$ and $\eta^{8}(\tau)$ in terms of Cohen's numbers $H(3,N)$ and $H(5,N)$. We give new formulas for the number of representations of integers as sums of eight higher figurate numbers. We also calculate the sixteenth and the twentyfourth powers of the Jacobi thetaseries using the basic Jacobi forms.
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In this article we consider combinatorial markets with valuations only for singletons and pairs of buy/sellorders for swapping two items in equal quantity. We provide an algorithm that permits polynomial time marketclearing and pricing. The results are presented in the context of our main application: the futures opening auction problem. Futures contracts are an important tool to mitigate market risk and counterparty credit risk. In futures markets these contracts can be traded with varying expiration dates and underlyings. A common hedging strategy is to roll positions forward into the next expiration date, however this strategy comes with significant operational risk. To address this risk, exchanges started to offer socalled futures contract combinations, which allow the traders for swapping two futures contracts with different expiration dates or for swapping two futures contracts with different underlyings. In theory, the price is in both cases the difference of the two involve
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An anonymous reader quotes a report from Ars Technica: Two House committees announced Tuesday that they would conduct a joint probe into the FBI's handling of the Clinton email investigation. The Clinton investigation concluded with no charges being levied against the former secretary of state who was running for president under the Democratic ticket. House Oversight and Government Reform Committee Chairman Trey Gowdy (RS.C.) and House Judiciary Committee Chairman Bob Goodlatte (RVa.) said in a joint statement that they are unsatisfied with how the probe into Clinton's private email server concluded. Among other things, the chairmen want to know why the bureau publicly said it was investigating Clinton while keeping silent that it was looking into President Donald Trump's campaign associates and their connections to Russia. "Our justice system is represented by a blindfolded woman holding a set of scales. Those scales do not tip to the right or the left; they do not recognize weal
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Janko Roettgers, reporting for Variety: AT&T's DirecTV is getting ready to embrace internetbased content delivery beyond its DirecTV Now service: The company is about to introduce a new TV settop box that's based on Google's Android TV platform and ditches satellite connectivity for overthetop streaming, according to a new FCC filing. The new device, which goes by the model number C71KW400, is being described by these documents as "the new AT&T/DirecTV Wireless 4K OTT Client." A user manual published as part of the filings specifies that the device won't be able to interact with any of DirecTV's existing Genie hardware, and hints at a future hardware product called HS27. Helpfully, the manual also supplies a definition of OTT as "the delivery of video via the internet directly into userconnected devices, allowing access to services anywhere, anytime, on any device." The manual also reveals that the settop will shop with a voice remote with integrated touch pad, and photo
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An anonymous reader quotes a report from New Atlas: The results of two human clinical trials into a stem cell therapy that can reverse symptoms of ageassociated frailty have been published, and the indications are that this landmark treatment is both safe and strikingly effective in tackling key factors in aging. Mesenchymal stem cells (MSCs) are a particular type of adult stem cell generating a great deal of interest in the world of science. This new MSC treatment is targeted at reducing the effects of frailty on senior citizens. This is the first antiaging stem cell treatment directed specifically at the problem of ageassociated frailty to move close to a final FDA approval stage. The treatment derives human mesenchymal stem cells from adult donor bone marrow and in these clinical trials involves a single infusion in patients with an average age of 76. Both Phase 1 and Phase 2 human trials have demonstrated the treatment to have no adverse health effects. Although the two human tr
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NPR reports the death of NASA astronaut Paul Weitz, who spent nearly a month in orbit on the first manned Skylab mission in 1973 and flew a decade later as mission commander on the maiden voyage of the Space Shuttle Challenger. He was 85. From the report: Weitz died in Flagstaff, Ariz., on Monday; he had been diagnosed with myelodysplastic syndrome, a type of blood cancer. Weitz was born in Erie, Pa., and graduated from Penn State. He joined the Navy and became an aviator and test pilot, eventually rising to the rank of captain. He was chosen in NASA's fifth round of astronaut selection in 1966, as the agency was ramping up for the Apollo moon program. On his first space flight, he served as pilot on Skylab2 (SL2), along with Apollo 12 veteran Charles "Pete" Conrad, Jr., and Joseph Kerwin, also a rookie on SL2. The mission to fix Skylab, which had suffered significant damage during the space station's launch, is still considered one of the most difficult and dangerous in the annals
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The FCC on Tuesday voted to eliminate a rule that required broadcast station groups to maintain a physical presence in the community of their primary local coverage area, a move that critics say will help media companies further consolidate their operations and even be a boost to the ambitions of Sinclair Broadcast Group. Variety reports: But FCC Chairman Ajit Pai said the elimination of the rule has been a long time coming and will produce cost savings for stations. He said the "overwhelming majority" of public input favored the elimination of the rule, citing the support for such an action even from National Public Radio. "Continuing to require a main studio would detract from, rather than promote, a broadcaster's ability and incentive to keep people informed and serve the public interest," Pai said. The National Association of Broadcasters supports the rule's elimination, and has argued that it will free up funds for stations to spend on staff and programming. Commissioner Michael O
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The fast iterative soft thresholding algorithm (FISTA) is used to solve convex regularized optimization problems in machine learning. Distributed implementations of the algorithm have become popular since they enable the analysis of large datasets. However, existing formulations of FISTA communicate data at every iteration which reduces its performance on modern distributed architectures. The communication costs of FISTA, including bandwidth and latency costs, is closely tied to the mathematical formulation of the algorithm. This work reformulates FISTA to communicate data at every k iterations and reduce data communication when operating on large data sets. We formulate the algorithm for two different optimization methods on the Lasso problem and show that the latency cost is reduced by a factor of k while bandwidth and floatingpoint operation costs remain the same. The convergence rates and stability properties of the reformulated algorithms are similar to the standard formulations.
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We propose a cheaper version of \textit{a posteriori} error estimator from arXiv:1707.00057 for the linear secondorder wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator preserves all the properties of the previous one (reliability, optimality on smooth solutions and quasiuniform meshes) but no longer requires an extra computation of the Laplacian of the discrete solution on each time step.
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