Fourier Analysis-based Iterative Combinatorial Auctions

Recent advances in Fourier analysis have brought new tools to efficiently represent and learn set functions. In this paper, we bring the power of Fourier analysis to the design of combinatorial auctions (CAs). The key idea is to approximate bidders' value functions using Fourier-sparse set functions, which can be computed using a relatively small number of queries. Since this number is still too large for real-world CAs, we propose a new hybrid design: we first use neural networks to learn bidders' values and then apply Fourier analysis to the learned representations. On a technical level, we formulate a Fourier transform-based winner determination problem and derive its mixed integer program formulation. Based on this, we devise an iterative CA that asks Fourier-based queries. We experimentally show that our hybrid ICA achieves higher efficiency than prior auction designs, leads to a fairer distribution of social welfare, and significantly reduces runtime. With this paper, we are the first to leverage Fourier analysis in CA design and lay the foundation for future work in this area

An Optical/NIR Exploration of Forming Cluster Environments at High Redshift with VLT, Keck, and HST

The past decade has been witness to immense progress in the understanding of the early stages of cluster formation both from a theoretical and observational perspective. During this time, samples of forming clusters at higher redshift, termed "protoclusters", once comprised of heterogeneous mix of serendipitous detections or detections arising from dedicated searches around rare galaxy populations, have begun to compete with lower-redshift samples both in terms of numbers and in the homogeneity of the detection methods. Much of this progress has come from optical/near-infrared (NIR) imaging and spectroscopic campaigns designed to target large numbers of typical galaxies to exquisite depth. In this poster talk I will focus on observations from VIMOS on VLT, MOSFIRE/DEIMOS on Keck, and a 50-orbit cycle 29 HST WFC3/G141 grism campaign taken as part of the Charting Cluster Construction with VUDS and ORELSE (C3VO) survey. These observations, combined with novel mapping and search techniques, have uncovered a large number of "protostructures" at 2 < z < 5 that appear to resemble clusters and groups forming in the early universe. I will discuss the development of the methods for finding, confirming, and characterizing proto-clusters and proto-groups in our sample, as well as groups and clusters at intermediate redshifts. Several case studies of spectroscopically-confirmed massive proto-clusters with a diverse set of properties will be presented. I will finally discuss constraints on the relationship between star formation rate, stellar mass, and galaxy density at these redshift

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

Optimizing make-to-stock policies through a robust lot-sizing model

In this paper we consider a practical lot-sizing problem faced by an industrial company. The company plans the production for a set of products following a Make-To-Order policy. When the productive capacity is not fully used, the remaining capacity is devoted to the production of those products whose orders are typically quite below the established minimum production level. For these products the company follows a Make-To-Stock (MTS) policy since part of the production is to fulfill future estimated orders. This yields a particular lot-sizing problem aiming to decide which products should be produced and the corresponding batch sizes. These lot-sizing problems typically face uncertain demands, which we address here through the lens of robust optimization. First we provide a mixed integer formulation assuming the future demands are deterministic and we tighten the model with valid inequalities. Then, in order to account for uncertainty of the demands, we propose a robust approach where demands are assumed to belong to given intervals and the number of deviations to the nominal estimated value is limited. As the number of products can be large and some instances may not be solved to optimality, we propose two heuristics. Computational tests are conducted on a set of instances generated from real data provided by our industrial partner. The heuristics proposed are fast and provide good quality solutions for the tested instances. Moreover, since they are based on the mathematical model and use simple strategies to reduce the instances size, these heuristics could be extended to solve other multi-item lot-sizing problems where demands are uncertain.publishe

Elentári: a massive proto-supercluster at z ∼ 3.3 in the COSMOS field

Motivated by spectroscopic confirmation of three overdense regions in the COSMOS field at z similar to 3.35, we analyse the uniquely deep multiwavelength photometry and extensive spectroscopy available in the field to identify any further related structure. We construct a three-dimensional density map using the Voronoi tesselation Monte Carlo method and find additional regions of significant overdensity. Here, we present and examine a set of six overdense structures at 3.20 &lt; z &lt; 3.45 in the COSMOS field, the most well-characterized of which, PCl J0959 + 0235, has 80 spectroscopically confirmed members and an estimated mass of 1.35 x 10(15) M-circle dot, and is modelled to virialize at z similar to 1.5-2.0. These structures contain 10 overdense peaks with &gt;5 sigma overdensity separated by up to 70 cMpc, suggestive of a proto-supercluster similar to the Hyperion system at z similar to 2.45. Upcoming photometric surveys with JWST such as COSMOS-Web, and further spectroscopic follow-up will enable more extensive analysis of the evolutionary effects that such an environment may have on its component galaxies at these early times

Volitional limbic neuromodulation has a multifaceted clinical benefit in Fibromyalgia patients

Volitional neural modulation using neurofeedback has been indicated as a potential treatment for chronic conditions that involve peripheral and central neural dysregulation. Here we utilized neurofeedback in patients suffering from Fibromyalgia - a chronic pain syndrome that involves sleep disturbance and emotion dysregulation. These ancillary symptoms, which have an amplification effect on pain, are known to be mediated by heightened limbic activity. In order to reliably probe limbic activity in a scalable manner fit for EEG-neurofeedback training, we utilized an Electrical Finger Print (EFP) model of amygdala-BOLD signal (termed Amyg-EFP), that has been successfully validated in our lab in the context of volitional neuromodulation. We anticipated that Amyg-EFP-neurofeedback training aimed at limbic down modulation should improve chronic pain in patients suffering from Fibromyalgia, by balancing disturbed indices for sleep and affect. We further expected that improved clinical status would correspond to successful training as indicated by improved down modulation of the Amygdala-EFP signal. Thirty-Four Fibromyalgia patients (31F; age 35.6 ± 11.82) participated in a randomized placebo-controlled trial with biweekly Amyg-EFP-neurofeedback sessions and placebo of sham neurofeedback (n = 9) for a total duration of five consecutive weeks. Following training, participants in the Real-neurofeedback group were divided into good (n = 13) or poor (n = 12) modulators according to their success in the neurofeedback training. Before and after treatment, self-reports on pain, depression, anxiety, fatigue and sleep quality were obtained, as well as objective sleep Indices. Long-term clinical follow-up was made available, within up to three years of the neurofeedback training completion. REM latency and objective sleep quality index were robustly improved following the treatment course only in the Real-neurofeedback group (both time × group p < 0.05) and to a greater extent among good modulators (both time*sub-group p < 0.05). In contrast, self-report measures did not reveal a treatment-specific response at the end of the treatment. However, the follow-up assessment revealed a delayed improvement in chronic pain and subjective sleep experience, evident only in the Real-neurofeedback group (both time × group p < 0.05). Moderation analysis showed that the enduring clinical effects on pain evident in the follow-up assessment were predicted by the immediate improvements following training in objective sleep and subjective affect measures. Our findings suggest that Amyg-EFP- neurofeedback that specifically targets limbic activity down modulation offers a successful principled approach for volitional EEG based neuromodulation training in Fibromyalgia patients. Importantly, it seems that via its immediate sleep improving effect, the neurofeedback training induced a delayed reduction in the target subjective symptom of chronic pain, far and beyond the immediate placebo effect. This indirect approach to chronic pain management reflects the necessary link between somatic and affective dysregulation that can be successfully targeted using neurofeedback

Crop pests and predators exhibit inconsistent responses to surrounding landscape composition

The idea that noncrop habitat enhances pest control and represents a win–win opportunity to conserve biodiversity and bolster yields has emerged as an agroecological paradigm. However, while noncrop habitat in landscapes surrounding farms sometimes benefits pest predators, natural enemy responses remain heterogeneous across studies and effects on pests are inconclusive. The observed heterogeneity in species responses to noncrop habitat may be biological in origin or could result from variation in how habitat and biocontrol are measured. Here, we use a pest-control database encompassing 132 studies and 6,759 sites worldwide to model natural enemy and pest abundances, predation rates, and crop damage as a function of landscape composition. Our results showed that although landscape composition explained significant variation within studies, pest and enemy abundances, predation rates, crop damage, and yields each exhibited different responses across studies, sometimes increasing and sometimes decreasing in landscapes with more noncrop habitat but overall showing no consistent trend. Thus, models that used landscape-composition variables to predict pest-control dynamics demonstrated little potential to explain variation across studies, though prediction did improve when comparing studies with similar crop and landscape features. Overall, our work shows that surrounding noncrop habitat does not consistently improve pest management, meaning habitat conservation may bolster production in some systems and depress yields in others. Future efforts to develop tools that inform farmers when habitat conservation truly represents a win–win would benefit from increased understanding of how landscape effects are modulated by local farm management and the biology of pests and their enemies

CMB-S4: Forecasting Constraints on Primordial Gravitational Waves

CMB-S4---the next-generation ground-based cosmic microwave background (CMB) experiment---is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semi-analytic projection tool, targeted explicitly towards optimizing constraints on the tensor-to-scalar ratio, $r$, in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2--3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments given a desired scientific goal. To form a closed-loop process, we couple this semi-analytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for $r > 0.003$ at greater than $5\sigma$, or, in the absence of a detection, of reaching an upper limit of $r < 0.001$ at $95\%$ CL.Comment: 24 pages, 8 figures, 9 tables, submitted to ApJ. arXiv admin note: text overlap with arXiv:1907.0447

Planck 2015 results. XVI. Isotropy and statistics of the CMB

We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The “Cold Spot” is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date