arXiv subjects

Marco Molinaro

Publications and source records attributed to Marco Molinaro.

At least 55 records · Page 3Linked to original sources

arXiv2020

The GAPS Programme at TNG XXVIII -- A pair of hot-Neptunes orbiting the young star TOI-942

Both young stars and multi-planet systems are primary objects that allow us to study, understand and constrain planetary formation and evolution theories. We validate the physical nature of two Neptune-type planets transiting TOI-942 (TYC 5909-319-1), a previously unacknowledged young star (50+30-20 Myr) observed by the TESS space mission in Sector 5. Thanks to a comprehensive stellar characterization, TESS light curve modelling and precise radial-velocity measurements, we validated the planetary nature of the TESS candidate and detect an additional transiting planet in the system on a larger orbit. From photometric and spectroscopic observations we performed an exhaustive stellar characterization and derived the main stellar parameters. TOI-942 is a relatively active K2.5V star (logR'hk = -4.17+-0.01) with rotation period Prot = 3.39+-0.01 days, a projected rotation velocity vsini=13.8+-0.5 km/s and a radius of ~0.9 Rsun. We found that the inner planet, TOI-942b, has an orbital period Pb=4.3263+-0.0011 days, a radius Rb=4.242-0.313+0.376 Rearth and a mass upper limit of 16 Mearth at 1-sigma confidence level. The outer planet, TOI-942c, has an orbital period Pc=10.1605-0.0053+0.0056 days, a radius Rc=4.793-0.351+0.410 Rearth and a mass upper limit of 37 Mearth at 1-sigma confidence level.

astro-ph.EP↗

arXiv2020

Robust Algorithms for Online Convex Problems via Primal-Dual

Primal-dual methods in online optimization give several of the state-of-the art results in both of the most common models: adversarial and stochastic/random order. Here we try to provide a more unified analysis of primal-dual algorithms to better understand the mechanisms behind this important method. With this we are able of recover and extend in one goal several results of the literature. In particular, we obtain robust online algorithm for fairly general online convex problems: we consider the MIXED model where in some of the time steps the data is stochastic and in the others the data is adversarial. Both the quantity and location of the adversarial time steps are unknown to the algorithm. The guarantees of our algorithms interpolate between the (close to) best guarantees for each of the pure models. In particular, the presence of adversarial times does not degrade the guarantee relative to the stochastic part of the instance. Concretely, we first consider Online Convex Programming: at each time a feasible set $V_t$ is revealed, and the algorithm needs to select $v_t \in V_t$ to minimize the total cost $ψ(\sum_t v_t)$, for a convex function $ψ$. Our robust primal-dual algorithm for this problem on the MIXED model recovers and extends, for example, a result of Gupta et al. and recent work on $\ell_p$-norm load balancing by the author. We also consider the problem of Welfare Maximization with Convex Production Costs: at each time a customer presents a value $c_t$ and resource consumption vector $a_t$, and the goal is to fractionally select customers to maximize the profit $\sum_t c_t x_t - ψ(\sum_t a_t x_t)$. Our robust primal-dual algorithm on the MIXED model recovers and extends the result of Azar et al. Given the ubiquity of primal-dual algorithms we hope the ideas presented here will be useful in obtaining other robust algorithm in the MIXED or related models.

cs.DS↗

arXiv2020

Knapsack Secretary with Bursty Adversary

The random-order or secretary model is one of the most popular beyond-worst case model for online algorithms. While it avoids the pessimism of the traditional adversarial model, in practice we cannot expect the input to be presented in perfectly random order. This has motivated research on ``best of both worlds'' (algorithms with good performance on both purely stochastic and purely adversarial inputs), or even better, on inputs that are a mix of both stochastic and adversarial parts. Unfortunately the latter seems much harder to achieve and very few results of this type are known. Towards advancing our understanding of designing such robust algorithms, we propose a random-order model with bursts of adversarial time steps. The assumption of burstiness of unexpected patterns is reasonable in many contexts, since changes (e.g. spike in a demand for a good) are often triggered by a common external event. We then consider the Knapsack Secretary problem in this model: there is a knapsack of size $k$ (e.g., available quantity of a good), and in each of the $n$ time steps an item comes with its value and size in $[0,1]$ and the algorithm needs to make an irrevocable decision whether to accept or reject the item. We design an algorithm that gives an approximation of $1 - \tilde{O}(Γ/k)$ when the adversarial time steps can be covered by $Γ\ge \sqrt{k}$ intervals of size $\tilde{O}(\frac{n}{k})$. In particular, setting $Γ= \sqrt{k}$ gives a $(1 - O(\frac{\ln^2 k}{\sqrt{k}}))$-approximation that is resistant to up to a $\frac{\ln^2 k}{\sqrt{k}}$-fraction of the items being adversarial, which is almost optimal even in the absence of adversarial items. Also, setting $Γ= \tildeΩ(k)$ gives a constant approximation that is resistant to up to a constant fraction of items being adversarial.

cs.DS↗

arXiv2020

Sparse PSD approximation of the PSD cone

While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD) constraint and only enforce PSD-ness on smaller $k\times k$ principal submatrices --- we call this the sparse SDP relaxation. Surprisingly, it has been observed empirically that in some cases this approach appears to produce bounds that are close to the optimal objective function value of the original SDP. In this paper, we formally attempt to compare the strength of the sparse SDP relaxation vis-à-vis the original SDP from a theoretical perspective. In order to simplify the question, we arrive at a data independent version of it, where we compare the sizes of SDP cone and the $k$-PSD closure, which is the cone of matrices where PSD-ness is enforced on all $k\times k$ principal submatrices. In particular, we investigate the question of how far a matrix of unit Frobenius norm in the $k$-PSD closure can be from the SDP cone. We provide two incomparable upper bounds on this farthest distance as a function of $k$ and $n$. We also provide matching lower bounds, which show that the upper bounds are tight within a constant in different regimes of $k$ and $n$. Other than linear algebra techniques, we extensively use probabilistic methods to arrive at these bounds. One of the lower bounds is obtained by observing a connection between matrices in the $k$-PSD closure and matrices satisfying the restricted isometry property (RIP).

math.OC↗

arXiv2020

Exo-MerCat: a merged exoplanet catalog with Virtual Observatory connection

The heterogeneity of papers dealing with the discovery and characterization of exoplanets makes every attempt to maintain a uniform exoplanet catalog almost impossible. Four sources currently available online (NASA Exoplanet Archive, Exoplanet Orbit Database, Exoplanet Encyclopaedia, and Open Exoplanet Catalogue) are commonly used by the community, but they can hardly be compared, due to discrepancies in notations and selection criteria. Exo-MerCat is a Python code that collects and selects the most precise measurement for all interesting planetary and orbital parameters contained in the four databases, accounting for the presence of multiple aliases for the same target. It can download information about the host star as well by the use of Virtual Observatory ConeSearch connections to the major archives such as SIMBAD and those available in VizieR. A Graphical User Interface is provided to filter data based on the user's constraints and generate automatic plots that are commonly used in the exoplanetary community. With Exo-MerCat, we retrieved a unique catalog that merges information from the four main databases, standardizing the output and handling notation differences issues. Exo-MerCat can correct as many issues that prevent a direct correspondence between multiple items in the four databases as possible, with the available data. The catalog is available as a VO resource for everyone to use and it is periodically updated, according to the update rates of the source catalogs.

astro-ph.EP↗

arXiv2019

Exposing SED Models And Snapshots Via VO Simulation Artefacts

The Virtual Observatory (VO) simulation standards, Simulation Data Model (SimDM) and Simulation Data Access Layer (SimDAL), establish a framework for the discoverability and dissemination of data created in simulation projects. These standards address the complexity of having a standard access and facade for data which is expected to be multifaceted and, of a diverse range. In this paper, we detail the realisation of an application exposing the theoretical products of one such scientific project via the simulation facades proposed by the VO. The scientific project in question, is a study of the evolution of young clusters in dense molecular clumps. The theoretical products arising from this study include a grid of 20 million SED (Spectral Energy Distribution) models for synthetic young clusters and related data products. Details on the implementation of SimDAL components in the application as well as the ways in which the data structures of SimDM are incorporated onto the existing data products are provided.

cs.DL↗

arXiv2019

Integrating the VO Framework in the EOSC

The European Open Science Cloud (EOSC) is in its early stages, but already some aspects of the EOSC vision are starting to become reality, for example the EOSC portal and the development of metadata catalogues. In the astrophysical domain already exists an open approach to science data: the Virtual Observatory view put in place by the International Virtual Observatory Alliance (IVOA) architecture of standards. The ESCAPE (European Science Cluster of Astronomy & Particle physics ESFRI research infrastructures) project has, among its tasks, to demonstrate that the VO architecture can be integrated within the EOSC building one and to provide guidelines to ESFRI partners (European Strategy Forum on Research Infrastructures) in doing this. This contribution reports on the progress of this integration after the first months of work inside ESCAPE.

astro-ph.IM↗

arXiv2018

$k$-Servers with a Smile: Online Algorithms via Projections

We consider the $k$-server problem on trees and HSTs. We give an algorithm based on Bregman projections. This algorithm has a competitive ratios that match some of the recent results given by Bubeck et al. (STOC 2018), whose algorithm was based on mirror-descent-based continuous dynamics prescribed via a differential inclusion.

cs.DS↗

arXiv2018

Stochastic $\ell_p$ Load Balancing and Moment Problems via the $L$-Function Method

This paper considers stochastic optimization problems whose objective functions involve powers of random variables. For example, consider the classic Stochastic lp Load Balancing Problem (SLBp): There are $m$ machines and $n$ jobs, and known independent random variables $Y_{ij}$ decribe the load incurred on machine $i$ if we assign job $j$ to it. The goal is to assign each jobs to machines in order to minimize the expected $l_p$-norm of the total load on the machines. While convex relaxations represent one of the most powerful algorithmic tools, in problems such as SLBp the main difficulty is to capture the objective function in a way that only depends on each random variable separately. We show how to capture $p$-power-type objectives in such separable way by using the $L$-function method, introduced by Latała to relate the moment of sums of random variables to the individual marginals. We show how this quickly leads to a constant-factor approximation for very general subset selection problem with $p$-moment objective. Moreover, we give a constant-factor approximation for SLBp, improving on the recent $O(p/\ln p)$-approximation of [Gupta et al., SODA 18]. Here the application of the method is much more involved. In particular, we need to sharply connect the expected $l_p$-norm of a random vector with the $p$-moments of its marginals (machine loads), taking into account simultaneously the different scales of the loads that are incurred by an unknown assignment.

cs.DS↗

arXiv2018

Italian center for Astronomical Archives publishing solution: modular and distributed

The Italian center for Astronomical Archives tries to provide astronomical data resources as interoperable services based on IVOA standards. Its VO expertise and knowledge comes from active participation within IVOA and VO at European and international level, with a double-fold goal: learn from the collaboration and provide inputs to the community. The first solution to build an easy to configure and maintain resource publisher conformant to VO standards proved to be too optimistic. For this reason it has been necessary to re-think the architecture with a modular system built around the messaging concept, where each modular component speaks to the other interested parties through a system of broker-managed queues. The first implemented protocol, the Simple Cone Search, shows the messaging task architecture connecting the parametric HTTP interface to the database backend access module, the logging module, and allows multiple cone search resources to be managed together through a configuration manager module. Even if relatively young, it already proved the flexibility required by the overall system when the database backend changed from MySQL to PostgreSQL+PgSphere. Another implementation test has been made to leverage task distribution over multiple servers to serve simultaneously: FITS cubes direct linking, cubes cutout and cubes positional merging. Currently the implementation of the SIA-2.0 standard protocol is ongoing while for TAP we will be adapting the TAPlib library. Alongside these tools a first administration tool (TASMAN) has been developed to ease the build up and maintenance of TAP_SCHEMA-ta including also ObsCore maintenance capability. Future work will be devoted at widening the range of VO protocols covered by the set of available modules, improve the configuration management and develop specific purpose modules common to all the service components.

astro-ph.IM↗

arXiv2018

Theoretical challenges towards cutting-plane selection

While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to be added to the LP relaxation at a given node of the branch-and-bound tree. In this paper we review the different classes of cutting-planes available, known theoretical results about their relative strength, important issues pertaining to cut selection, and discuss some possible new directions to be pursued in order to accomplish cutting-plane selection in a more principled manner. Finally, we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection.

math.OC↗

arXiv2018

Maximizing Profit with Convex Costs in the Random-order Model

Suppose a set of requests arrives online: each request gives some value $v_i$ if accepted, but requires using some amount of each of $d$ resources. Our cost is a convex function of the vector of total utilization of these $d$ resources. Which requests should be accept to maximize our profit, i.e., the sum of values of the accepted demands, minus the convex cost? We consider this problem in the random-order a.k.a. secretary model, and show an $O(d)$-competitive algorithm for the case where the convex cost function is also supermodular. If the set of accepted demands must also be independent in a given matroid, we give an $O(d^3 α)$-competitive algorithm for the supermodular case, and an improved $O(d^2α)$ if the convex cost function is also separable. Here $α$ is the competitive ratio of the best algorithm for the submodular secretary problem. These extend and improve previous results known for this problem. Our techniques are simple but use powerful ideas from convex duality, which give clean interpretations of existing work, and allow us to give the extensions and improvements.

cs.DS↗

arXiv2018

Lower bounds on the lattice-free rank for packing and covering integer programs

In this paper, we present lower bounds on the rank of the split closure, the multi-branch closure and the lattice-free closure for packing sets as a function of the integrality gap. We also provide a similar lower bound on the split rank of covering polyhedra. These results indicate that whenever the integrality gap is high, these classes of cutting planes must necessarily be applied for many rounds in order to obtain the integer hull.

math.OC↗

arXiv2018

Dicover and access GAPS Time Series: prototyping for interoperability

The GAPS (Global Architecture of Planetary Systems) project is a, mainly Italian, effort for the comprehensive characterization of the architectural properties of planetary systems as a function of the host stars' characteristics by using radial velocities technique. Since the beginning (2012) the project exploited the HARPS-N high resolution optical spectrograph mounted at the 4-m class TNG telescope in La Palma (Canary Islands). More recently, with the upgrade of the TNG near-infrared spectrograph GIANO-B, obtained in the framework of the GIARPS project, it has become possible to perform simultaneous observations with these two instruments, providing thus, at the same time, data both in the optical and in the near-infrared range. The large amount of data obtained in about 5 years of observations provided various scientific outputs, and among them, time series of radial velocity (RV) profiles of the investigated stellar systems. This contribution shows the first steps undertaken to deploy the GAPS Time Series as an interoperable resource within the VO framework designed by the IVOA. This effort has thus a double goal. On one side there's the aim at making the time series data (from RV up to their originating spectra) available to the general astrophysical community in an interoperable way. On the other side, to provide use cases and a prototyping base to the ongoing time domain priority effort at the IVOA level. Time series dataset discovery, depicted through use cases and mapped against the ObsCore model will be shown, highlighting commonalities as well as missing metadata requirements. Future development steps and criticalities, related also to the joint discovery and access of datasets provided by both the spectrographs operated side by side, will be summarized.

astro-ph.IM↗

arXiv2017

Building an interoperable, distributed storage and authorization system

A joint project between the Canadian Astronomy Data Center of the National Research Council Canada, and the italian Istituto Nazionale di Astrofisica-Osservatorio Astronomico di Trieste (INAF-OATs), partially funded by the EGI-Engage H2020 European Project, is devoted to deploy an integrated infrastructure, based on the International Virtual Observatory Alliance (IVOA) standards, to access and exploit astronomical data. Currently CADC-CANFAR provides scientists with an access, storage and computation facility, based on software libraries implementing a set of standards developed by the International Virtual Observatory Alliance (IVOA). The deployment of a twin infrastructure, basically built on the same open source software libraries, has been started at INAF-OATs. This new infrastructure now provides users with an Access Control Service and a Storage Service. The final goal of the ongoing project is to build an integrated infrastructure geographycally distributed providing complete interoperability, both in users access control and data sharing. This paper describes the target infrastructure, the main user requirements covered, the technical choices and the implemented solutions.

astro-ph.IM↗

arXiv2017

Sparse principal component analysis and its $l_1$-relaxation

Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse, that is, we solve PCA with an additional cardinality (l0) constraint. The resulting optimization problem is called the sparse principal component analysis (SPCA). One popular approach to achieve sparsity is to replace the l0 constraint by an l1 constraint. In this paper, we prove that, independent of the data, the optimal objective function value of the problem with l0 constraint is within a constant factor of the the optimal objective function value of the problem with l1 constraint. To the best of our knowledge, this is the first formal relationship established between the l0 and the l1 constraint version of the problem.

math.OC↗

arXiv2017

Minimal cut-generating functions are nearly extreme

We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory-Johnson setting as well as a recent extension by Cornuéjols and Yıldız. We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal function as closely as desired. In other words, the extreme functions are "dense" in the set of continuous (strongly) minimal functions.

math.OC↗

arXiv2017

Characterization of the Split Closure via Geometric Lifting

We analyze split cuts from the perspective of cut generating functions via geometric lifting. We show that $α$-cuts, a natural higher-dimensional generalization of the $k$-cuts of Cornuéjols et al., gives all the split cuts for the mixed-integer corner relaxation. As an immediate consequence we obtain that the $k$-cuts are equivalent to split cuts for the 1-row mixed-integer relaxation. Further, we show that split cuts for finite-dimensional corner relaxations are restrictions of split cuts for the infinite-dimensional relaxation. In a final application of this equivalence, we exhibit a family of pure-integer programs whose split closures have arbitrarily bad integrality gap. This complements the mixed-integer example provided by Basu et al [On the relative strength of split, triangle and quadrilateral cuts, Math. Program. 126(2):281--314, 2011].

math.OC↗