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The height of a toric variety and that of its hypersurfaces can be expressed in convex-analytic terms as an adelic sum of mixed integrals of their roof functions and duals of their Ronkin functions. Here we extend these results to the $2$-codimensional situation by presenting a limit formula predicting the typical height of the intersection of two hypersurfaces on a toric variety. More precisely, we prove that the height of the intersection cycle of two effective divisors translated by a strict sequence of torsion points converges to an adelic sum of mixed integrals of roof and duals of Ronkin functions. This partially confirms a previous conjecture of the authors about the average height of families of complete intersections in toric varieties., Comment: 46 pages

We study the distribution of the height of the intersection between the projective line defined by the linear polynomial $x_{0}+x_{1}+x_{2}$ and its translate by a torsion point. We show that for a strict sequence of torsion points, the corresponding heights converge to a real number that is a rational multiple of a quotient of special values of the Riemann zeta function. We also determine the range of these heights, characterize the extremal cases, and study their limit for sequences of torsion points that are strict in proper algebraic subgroups. In addition, we interpret our main result from the viewpoint of Arakelov geometry, showing that for a strict sequence of torsion points the limit of the corresponding heights coincides with an Arakelov height of the cycle of the projective plane over the integers defined by the same linear polynomial. This is a particular case of a conjectural asymptotic version of the arithmetic B\'ezout theorem. Using the interplay between arithmetic and convex objects from the Arakelov geometry of toric varieties, we show that this Arakelov height can be expressed as the mean of a piecewise linear function on the amoeba of the projective line, which in turn can be computed as the aforementioned real number., Comment: 47 pages, 6 figures

We present GEO-FPT (Geometric Fitted Perturbation Theory), a new model for the galaxy bispectrum anisotropic signal in redshift space, with functional form rooted in perturbation theory. It also models the dependence of the bispectrum with the geometric properties of the triangles in Fourier space, and has a broader regime of validity than state-of-the-art theoretical models based on perturbation theory. We calibrate the free parameters of this model using high-resolution dark matter simulations and perform stringent tests to show that GEO-FPT describes the galaxy bispectrum accurately up to scales of $k\simeq0.12 h{\rm Mpc}^{-1}$ for different cosmological models, as well as for biased tracers of the dark matter field, considering a survey volume of $100$ (Gpc $h^{-1})^3$. In particular, a joint analysis of the power spectrum and bispectrum anisotropic signals, taking into account their full covariance matrix, reveals that the relevant physical quantities -- the BAO peak position (along and across the line-of-sight), and the growth of structure parameters times the amplitude of dark matter fluctuations, $f\sigma_8$-- are recovered in an unbiased way, with an accuracy better than $0.4\%$ and $2\%$ respectively (which is our $2\sigma$ statistical limit of the systematic error estimate). In addition, the bispectrum signal breaks the $f\sigma_8$ degeneracy without detectable bias: $f$ and $\sigma_8$ are recovered with better than $2.7\%$ and $3.8\%$ accuracy respectively (which is our $2\sigma$ statistical limit of the systematic error estimate). GEO-FPT boosts the applicability of the bispectrum signal of galaxy surveys beyond the current limitation of $k\lesssim 0.08\,h$ Mpc$^{-1}$ % and makes the bispectrum a key statistic to unlock the information content from the mildly non-linear regime in the on-going and forthcoming galaxy redshift surveys., Comment: 37 pages, 14 figures. To be submitted to JCAP, comments welcome

We present the first detection of the integrated trispectrum ($\mathit{i}$-trispectrum) monopole and quadrupoles signal from BOSS CMASS NGC DR12. Extending the FKP estimators formalism to the Fourier transform of the four-point correlation function, we test shot-noise subtraction, Gaussianity of the i-trispectrum data-vector, significance of the detection and similarity between the signal from the data and from the galaxy mock catalogues used to numerically estimate the covariance matrix. Using scales corresponding to modes from minimum $k_\mathrm{min}=0.03\,h/\mathrm{Mpc}$ to maximum $k_\mathrm{min}=0.15\,h/\mathrm{Mpc}$, we find a detection in terms of distance from the null hypothesis of $(10.4,5.2,8.3,1.1,3.1)$ $\sigma$-intervals for the i-trispectrum monopole and quadrupoles respectively. This quantifies the presence of the physical signal of the four-points statistics on BOSS data. For completeness the same analysis is also performed for power spectrum and bispectrum, both monopoles and quadrupoles., Comment: 17 pages plus appendix, 11 figures, matching published version on JCAP

The different thermo-elastic properties of glass fibers and polymer matrices can generate residual thermal stresses in injection-molded fiber-reinforced plastic (FRP) objects. During cooling from mold to room temperature, these stresses can be relaxed by large deformations resulting from an instability of the unwarped configuration (i.e., buckling). This article investigates the thermal buckling of thin FRP disks via an analytical formulation based on the Foppl-von Karman theory. Expanding on our previous work, cylindrical orthotropy with material parameters varying over the disk thickness is assumed in order to account for thickness dependency of the glass fiber orientation distribution. A disk parameter generalizing the thermal anisotropy ratio for homogeneous orthotropic disks is introduced and its relation with the occurrence and periodicity of buckling is discussed. This is done for a skin-coreskin model, for which the core-to-total thickness ratio is defined. For fiber orientation distributions typical of injection-molded disks, it is found that there exists a value of the thickness ratio for which no buckling occurs. It is also demonstrated that the periodicity of the first buckling mode is described by the generalized thermal anisotropy ratio, thus extending the results obtained for a homogeneous fiber orientation distribution. Improvements in the accuracy of the predictions for experimental data available in the literature when using the skin-core-skin model are shown. Finally, we study the relation between buckling temperature and disk thickness and propose an expression for the dependence of the normalized buckling temperature on the thermal anisotropy ratio. Results of FEM simulations are used to validate the proposed expression, proving its applicability and accuracy., Comment: 34 pages, 3 figures

We perform for the first time a joint analysis of the monopole and quadrupoles for power spectrum, bispectrum and integrated trispectrum (i-trispectrum) from the redshift space matter field in N-body simulations. With a full Markov Chain Monte Carlo exploration of the posterior distribution, we quantify the constraints on cosmological parameters for an object density of $n_\mathrm{p}=5\times10^{-4} (h\,\mathrm{Mpc}^{-1})^{3}$, redshift $z=0.5$, and a covariance corresponding to a survey volume of $V_\mathrm{survey} =25\,(h^{-1}\mathrm{Gpc})^3$, a set up which is representative of forthcoming galaxy redshift surveys. We demonstrate the complementarity of the bispectrum and i-trispectrum in constraining key cosmological parameters. In particular, compared to the state-of-the-art power spectrum (monopole plus quadrupole) and bispectrum (monopole) analyses, we find 1D $68\%$ credible regions smaller by a factor of $(72\%,78\%,72\%,47\%,46\%)$ for the parameters $(f,\sigma_8,f_\mathrm{nl},\alpha_\parallel,\alpha_\perp)$ respectively. This work motivates the additional effort necessary to include the redshift-space anisotropic signal of higher-order statistics in the analysis and interpretation of ongoing and future galaxy surveys., Comment: 42 pages (21 + appendixes and references), 12 figures, 3 tables, matching accepted version after minor revision

Let $X$ be an arithmetic variety over the ring of integers of a number field $K$, with smooth generic fiber $X_K$. We give a formula that relates the dimension of the first Arakelov-Chow vector space of $X$ with the Mordell-Weil rank of the Albanese variety of $X_K$ and the rank of the N\'eron-Severi group of $X_K$. This is a higher dimensional and arithmetic version of the classical Shioda-Tate formula for elliptic surfaces. Such analogy is strengthened by the fact that we show that the numerically trivial arithmetic $\mathbb{R}$-divisors on $X$ are exactly the linear combinations of principal ones. This result is equivalent to the non-degeneracy of the arithmetic intersection pairing in the argument of divisors, partially confirming [GS94, Conjecture 1]., Comment: 18 pages. Minor changes. New Lemma 3.9

The power spectrum has long been the workhorse summary statistics for large-scale structure cosmological analyses. However, gravitational non-linear evolution moves precious cosmological information from the two-point statistics (such as the power spectrum) to higher-order correlations. Moreover, information about the primordial non-Gaussian signal lies also in higher-order correlations. Without tapping into these, that information remains hidden. While the three-point function (or the bispectrum), even if not extensively, has been studied and applied to data, there has been only limited discussion about the four point/trispectrum. This is because the high-dimensionality of the statistics (in real space a skew-quadrilateral has 6 degrees of freedom), and the high number of skew-quadrilaterals, make the trispectrum numerically and algorithmically very challenging. Here we address this challenge by introducing the i-trispectrum, an integrated trispectrum that only depends on four $k$-modes moduli. We model and measure the matter i-trispectrum from a set of 5000 \textsc{Quijote} N-body simulations both in real and redshift space, finding good agreement between simulations outputs and model up to mildly non-linear scales. Using the power spectrum, bispectrum and i-trispectrum joint data-vector covariance matrix estimated from the simulations, we begin to quantify the added-value provided by the i-trispectrum. In particular, we forecast the i-trispectrum improvements on constraints on the local primordial non-Gaussianity amplitude parameters $f_\mathrm{nl}$ and $g_\mathrm{nl}$. For example, using the full joint data-vector, we forecast $f_\mathrm{nl}$ constraints up to two times ($\sim32\%$) smaller in real (redshift) space than those obtained without i-trispectrum., Comment: accepted: 6th of November 2020, published: 11th of January 2021 , 64 pages (35 pages for the main text), 15 figures

We discuss the impact of a Covid-19--like shock on a simple model economy, described by the previously developed Mark-0 Agent-Based Model. We consider a mixed supply and demand shock, and show that depending on the shock parameters (amplitude and duration), our model economy can display V-shaped, U-shaped or W-shaped recoveries, and even an L-shaped output curve with permanent output loss. This is due to the economy getting trapped in a self-sustained "bad" state. We then discuss two policies that attempt to moderate the impact of the shock: giving easy credit to firms, and the so-called helicopter money, i.e. injecting new money into the households savings. We find that both policies are effective if strong enough. We highlight the potential danger of terminating these policies too early, although inflation is substantially increased by lax access to credit. Finally, we consider the impact of a second lockdown. While we only discuss a limited number of scenarios, our model is flexible and versatile enough to accommodate a wide variety of situations, thus serving as a useful exploratory tool for a qualitative, scenario-based understanding of post-Covid recovery. The corresponding code is available on-line., Comment: 20 Pages. Model description within the main text. Discussion on multiple lockdowns added. See code for paper at https://gitlab.com/sharma.dhruv/markovid

We forecast the benefits induced by adding the bispectrum anisotropic signal to the standard, two- and three-point, clustering statistics analysis. In particular, we forecast cosmological parameter constraints including the bispectrum higher multipoles terms together with the galaxy power spectrum (monopole plus quadrupole) and isotropic bispectrum (monopole) data vectors. To do so, an analytical covariance matrix model is presented. This template is carefully calibrated on well-known terms of a numerical covariance matrix estimated from a set of simulated galaxy catalogues. After testing the calibration using the power spectrum and isotropic bispectrum measurements from the same set of simulations, we extend the covariance modelling to the galaxy bispectrum higher multipoles. Using this covariance matrix we proceed to perform cosmological parameter inference using a suitably generated mock data vector. Including the bispectrum mutipoles up to the hexadecapole, yields 1-D $68\%$ credible regions for the set of parameters $(b_1,b_2,f,\sigma_8,f_\mathrm{NL},\alpha_\perp, \alpha_\parallel)$ tighter by a factor of 30$\%$ on average for $k_\mathrm{max}=0.09\,h$/Mpc, significantly reducing at the same time the degeneracies present in the posterior distribution., Comment: Accepted version for publication in JCAP, 26 pages + Appendix, 15 figures

The essential minimum and equidistribution of small points are two well-established interrelated subjects in arithmetic geometry. However, there is lack of an analogue of essential minimum dealing with higher dimensional subvarieties, and the equidistribution of these is a far less explored topic. In this paper, we introduce a new notion of higher dimensional essential minimum and use it to prove equidistribution of generic and small effective cycles. The latter generalizes the previous higher dimensional equidistribution theorems by considering cycles and by allowing more fexibility on the arithmetic datum., Comment: 37 pages. To appear in Annales de l'Institut Fourier

We present the GEOMAX algorithm and its Python implementation for a two-step compression of bispectrum measurements. The first step groups bispectra by the geometric properties of their arguments; the second step then maximises the Fisher information with respect to a chosen set of model parameters in each group. The algorithm only requires the derivatives of the data vector with respect to the parameters and a small number of mock data, producing an effective, non-linear compression. By applying GEOMAX to bispectrum monopole measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we reduce the $68\%$ credible intervals for the inferred parameters $\left(b_1,b_2,f,\sigma_8\right)$ by $\left(50.4\%,56.1\%,33.2\%,38.3\%\right)$ with respect to standard MCMC on the full data vector. We run the analysis and comparison between compression methods over one hundred galaxy mocks to test the statistical significance of the improvements. On average GEOMAX performs $\sim15\%$ better than geometrical or maximal linear compression alone and is consistent with being lossless. Given its flexibility, the GEOMAX approach has the potential to optimally exploit three-point statistics of various cosmological probes like weak lensing or line-intensity maps from current and future cosmological data-sets such as DESI, Euclid, PFS and SKA., Comment: 17 pages, 9 figures, accepted version by MNRAS

Cosmological studies of large-scale structure have relied on two-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this cosmic web information by using the minimum spanning tree (MST), for the first time using it to estimate cosmological parameters in simulations. Discrete tracers of dark matter such as galaxies, $N$-body particles or haloes are used as nodes to construct a unique graph, the MST, that traces skeletal structure. We study the dependence of the MST on cosmological parameters using haloes from a suite of COLA simulations with a box size of $250\ h^{-1}{\rm Mpc}$, varying the amplitude of scalar fluctuations $\left(A_{\rm s}\right)$, matter density $\left(\Omega_{\rm m}\right)$, and neutrino mass $\left(\sum m_{\nu}\right)$. The power spectrum $P$ and bispectrum $B$ are measured for wavenumbers between $0.125$ and $0.5$ $h{\rm Mpc}^{-1}$, while a corresponding lower cut of $\sim12.6$ $h^{-1}{\rm Mpc}$ is applied to the MST. The constraints from the individual methods are fairly similar but when combined we see improved $1\sigma$ constraints of $\sim 17\%$ ($\sim 12\%$) on $\Omega_{\rm m}$ and $\sim 12\%$ ($\sim 10\%$) on $A_{\rm s}$ with respect to $P$ ($P+B$) thus showing the MST is providing additional information. The MST can be applied to current and future spectroscopic surveys (BOSS, DESI, Euclid, PSF, WFIRST, and 4MOST) in 3D and photometric surveys (DES and LSST) in tomographic shells to constrain parameters and/or test systematics., Comment: 19 pages, 15 figures (including 2 page appendix with 2 figures), text based edits to match version published in MNRAS

We present a novel method to compress galaxy clustering three-point statistics and apply it to redshift space galaxy bispectrum monopole measurements from BOSS DR12 CMASS data considering a $k$-space range of $0.03-0.12\,h/\mathrm{Mpc}$. The method consists in binning together bispectra evaluated at sets of wave-numbers forming closed triangles with similar geometrical properties: the area, the cosine of the largest angle and the ratio between the cosines of the remaining two angles. This enables us to increase the number of bispectrum measurements for example by a factor of $23$ over the standard binning (from 116 to 2734 triangles used), which is otherwise limited by the number of mock catalogues available to estimate the covariance matrix needed to derive parameter constraints. The $68\%$ credible intervals for the inferred parameters $\left(b_1,b_2,f,\sigma_8\right)$ are thus reduced by $\left(-39\%,-49\%,-29\%,-22\%\right)$, respectively. We find very good agreement with the posteriors recently obtained by alternative maximal compression methods. This new method does not require the a-priori computation of the data-vector covariance matrix and has the potential to be directly applicable to other three-point statistics (e.g. glaxy clustering, weak gravitational lensing, 21 cm emission line) measured from future surveys such as DESI, Euclid, PFS and SKA., Comment: 5 pages, 2 figures, Accepted by MNRAS: Letters

Pyroelectric current and magnetoelectric coupling measurements on polycrystalline samples of the quadruple perovskite (LaMn$_{3}$)Mn$_{4}$O$_{12}$ give evidence of ferroelectricity driven by the antiferromagnetic ordering of the $B$-site Mn$^{3+}$ ions at $T_{N,B}$=78 K with record values of remnant electric polarization up to $P$=0.56 $\mu$C cm$^{-2}$. X-ray diffraction measurements indicates an anomalous behavior of the monoclinic $\beta$ angle at $T_{N,B}$, which suggests that $P$ lies in the $ac$-plane, where the moments are collinear, so we conclude that exchange striction is the mechanism of spin-driven ferroelectricity. Polarization values $\sim$3 $\mu$C cm$^{-2}$ are expected in single crystals, which would open the avenue towards practical multiferroic applications., Comment: 5 pages, 5 figures

The role of portfolio construction in the implementation of equity market neutral factors is often underestimated. Taking the classical momentum strategy as an example, we show that one can significantly improve the main strategy's features by properly taking care of this key step. More precisely, an optimized portfolio construction algorithm allows one to significantly improve the Sharpe Ratio, reduce sector exposures and volatility fluctuations, and mitigate the strategy's skewness and tail correlation with the market. These results are supported by long-term, world-wide simulations and will be shown to be universal. Our findings are quite general and hold true for a number of other "equity factors". Finally, we discuss the details of a more realistic set-up where we also deal with transaction costs.

We apply two compression methods to the galaxy power spectrum monopole/quadrupole and bispectrum monopole measurements from the BOSS DR12 CMASS sample. Both methods reduce the dimension of the original data-vector to the number of cosmological parameters considered, using the Karhunen-Lo\`eve algorithm with an analytic covariance model. In the first case, we infer the posterior through MCMC sampling from the likelihood of the compressed data-vector (MC-KL). The second, faster option, works by first Gaussianising and then orthogonalising the parameter space before the compression; in this option (G-PCA) we only need to run a low-resolution preliminary MCMC sample for the Gaussianization to compute our posterior. Both compression methods accurately reproduce the posterior distributions obtained by standard MCMC sampling on the CMASS dataset for a $k$-space range of $0.03-0.12\,h/\mathrm{Mpc}$. The compression enables us to increase the number of bispectrum measurements by a factor of $\sim 23$ over the standard binning (from 116 to 2734 triangles used), which is otherwise limited by the number of mock catalogues available. This reduces the $68\%$ credible intervals for the parameters $\left(b_1,b_2,f,\sigma_8\right)$ by $\left(-24.8\%,-52.8\%,-26.4\%,-21\%\right)$, respectively. The best-fit values we obtain are $(b_1=2.31\pm0.17,b_2=0.77\pm0.19,$ $f(z_{\mathrm{CMASS}})=0.67\pm0.06,\sigma_8(z_{\mathrm{CMASS}})=0.51\pm0.03)$. Using these methods for future redshift surveys like DESI, Euclid and PFS will drastically reduce the number of simulations needed to compute accurate covariance matrices and will facilitate tighter constraints on cosmological parameters., Comment: 21 pages, 9 figures, Accepted by MNRAS after addressing the comments by the referee

For a cycle of codimension 1 in a toric variety, its degree with respect to a nef toric divisor can be understood in terms of the mixed volume of the polytopes associated to the divisor and to the cycle. We prove here that an analogous combinatorial formula holds in the arithmetic setting: the global height of a 1-codimensional cycle with respect to a toric divisor equipped with a semipositive toric metric can be expressed in terms of mixed integrals of the $v$-adic roof functions associated to the metric and the Legendre-Fenchel dual of the $v$-adic Ronkin function of the Laurent polynomial of the cycle., Comment: 39 pages. In version 2: Theorem 1.6 rephrased under weaker assumptions, example of binomial hypersurfaces and related results added; other minor changes. Accepted for publication in "Algebra & Number Theory"

Which level of inflation should Central Banks be targeting? We investigate this issue in the context of a simplified Agent Based Model of the economy. Depending on the value of the parameters that describe the behaviour of agents (in particular inflation anticipations), we find a rich variety of behaviour at the macro-level. Without any active monetary policy, our ABM economy can be in a high inflation/high output state, or in a low inflation/low output state. Hyper-inflation, deflation and "business cycles" between coexisting states are also found. We then introduce a Central Bank with a Taylor rule-based inflation target, and study the resulting aggregate variables. Our main result is that too-low inflation targets are in general detrimental to a CB-monitored economy. One symptom is a persistent under-realisation of inflation, perhaps similar to the current macroeconomic situation. Higher inflation targets are found to improve both unemployment and negative interest rate episodes. Our results are compared with the predictions of the standard DSGE model., Comment: 19 pages, 6 figures. The paper is under review for the online journal "Economics". The reviews are public at this link: http://www.economics-ejournal.org/economics/discussionpapers/2017-64 . This version has been modified and improved following the advice of the reviewers and commentators

We explore two methods of compressing the redshift space galaxy power spectrum and bispectrum with respect to a chosen set of cosmological parameters. Both methods involve reducing the dimension of the original data-vector ( e.g. 1000 elements ) to the number of cosmological parameters considered ( e.g. seven ) using the Karhunen-Lo\`eve algorithm. In the first case, we run MCMC sampling on the compressed data-vector in order to recover the one-dimensional (1D) and two-dimensional (2D) posterior distributions. The second option, approximately 2000 times faster, works by orthogonalising the parameter space through diagonalisation of the Fisher information matrix before the compression, obtaining the posterior distributions without the need of MCMC sampling. Using these methods for future spectroscopic redshift surveys like DESI, EUCLID and PFS would drastically reduce the number of simulations needed to compute accurate covariance matrices with minimal loss of constraining power. We consider a redshift bin of a DESI-like experiment. Using the power spectrum combined with the bispectrum as a data-vector, both compression methods on average recover the 68% credible regions to within 0.7% and 2% of those resulting from standard MCMC sampling respectively. These confidence intervals are also smaller than the ones obtained using only the power spectrum by (81%, 80%, 82%) respectively for the bias parameter b_1, the growth rate f and the scalar amplitude parameter A_s., Comment: 27 pages, 8 figures, 1 table, Accepted 2018 January 28. Received 2018 January 25; in original form 2017 September 11. Added clarifications in the text on the bias modelling and compression limits following referee's comments. Removed tetraspectrum term from the pk-bk cross covariance + correction in the appendix

The average portfolio structure of institutional investors is shown to have properties which account for transaction costs in an optimal way. This implies that financial institutions unknowingly display collective rationality, or Wisdom of the Crowd. Individual deviations from the rational benchmark are ample, which illustrates that system-wide rationality does not need nearly rational individuals. Finally we discuss the importance of accounting for constraints when assessing the presence of Wisdom of the Crowd., Comment: 11 pages, 12 figures

Common asset holding by financial institutions, namely portfolio overlap, is nowadays regarded as an important channel for financial contagion with the potential to trigger fire sales and thus severe losses at the systemic level. In this paper we propose a method to assess the statistical significance of the overlap between pairs of heterogeneously diversified portfolios, which then allows us to build a validated network of financial institutions where links indicate potential contagion channels due to realized portfolio overlaps. The method is implemented on a historical database of institutional holdings ranging from 1999 to the end of 2013, but can be in general applied to any bipartite network where the presence of similar sets of neighbors is of interest. We find that the proportion of validated network links (i.e., of statistically significant overlaps) increased steadily before the 2007-2008 global financial crisis and reached a maximum when the crisis occurred. We argue that the nature of this measure implies that systemic risk from fire sales liquidation was maximal at that time. After a sharp drop in 2008, systemic risk resumed its growth in 2009, with a notable acceleration in 2013, reaching levels not seen since 2007. We finally show that market trends tend to be amplified in the portfolios identified by the algorithm, such that it is possible to have an informative signal about financial institutions that are about to suffer (enjoy) the most significant losses (gains).