OPTIMASS: A Package for the Minimization of Kinematic Mass Functions with Constraints

Reconstructed mass variables, such as $M_2$, $M_{2C}$, $M_T^\star$, and $M_{T2}^W$, play an essential role in searches for new physics at hadron colliders. The calculation of these variables generally involves constrained minimization in a large parameter space, which is numerically challenging. We provide a C++ code, OPTIMASS, which interfaces with the MINUIT library to perform this constrained minimization using the Augmented Lagrangian Method. The code can be applied to arbitrarily general event topologies and thus allows the user to significantly extend the existing set of kinematic variables. We describe this code and its physics motivation, and demonstrate its use in the analysis of the fully leptonic decay of pair-produced top quarks using the $M_2$ variables.Comment: 39 pages, 12 figures, (1) minor revision in section 3, (2) figure added in section 4.3, (3) reference added and (4) matched with published versio

Phase Retrieval via Matrix Completion

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we introduce some theory showing that one can design very simple structured illumination patterns such that three diffracted figures uniquely determine the phase of the object we wish to recover

Dynamical dark energy: Current constraints and forecasts

We consider how well the dark energy equation of state $w$ as a function of red shift $z$ will be measured using current and anticipated experiments. We use a procedure which takes fair account of the uncertainties in the functional dependence of $w$ on $z$, as well as the parameter degeneracies, and avoids the use of strong prior constraints. We apply the procedure to current data from WMAP, SDSS, and the supernova searches, and obtain results that are consistent with other analyses using different combinations of data sets. The effects of systematic experimental errors and variations in the analysis technique are discussed. Next, we use the same procedure to forecast the dark energy constraints achieveable by the end of the decade, assuming 8 years of WMAP data and realistic projections for ground-based measurements of supernovae and weak lensing. We find the $2 \sigma$ constraints on the current value of $w$ to be $\Delta w_0 (2 \sigma) = 0.20$, and on $dw/dz$ (between $z=0$ and $z=1$) to be $\Delta w_1 (2 \sigma)=0.37$. Finally, we compare these limits to other projections in the literature. Most show only a modest improvement; others show a more substantial improvement, but there are serious concerns about systematics. The remaining uncertainty still allows a significant span of competing dark energy models. Most likely, new kinds of measurements, or experiments more sophisticated than those currently planned, are needed to reveal the true nature of dark energy.Comment: 24 pages, 20 figures. Added SN systematic uncertainties, extended discussio

Simplified Algorithm for Dynamic Demand Response in Smart Homes Under Smart Grid Environment

Under Smart Grid environment, the consumers may respond to incentive--based smart energy tariffs for a particular consumption pattern. Demand Response (DR) is a portfolio of signaling schemes from the utility to the consumers for load shifting/shedding with a given deadline. The signaling schemes include Time--of--Use (ToU) pricing, Maximum Demand Limit (MDL) signals etc. This paper proposes a DR algorithm which schedules the operation of home appliances/loads through a minimization problem. The category of loads and their operational timings in a day have been considered as the operational parameters of the system. These operational parameters determine the dynamic priority of a load, which is an intermediate step of this algorithm. The ToU pricing, MDL signals, and the dynamic priority of loads are the constraints in this formulated minimization problem, which yields an optimal schedule of operation for each participating load within the consumer provided duration. The objective is to flatten the daily load curve of a smart home by distributing the operation of its appliances in possible low--price intervals without violating the MDL constraint. This proposed algorithm is simulated in MATLAB environment against various test cases. The obtained results are plotted to depict significant monetary savings and flattened load curves.Comment: This paper was accepted and presented in 2019 IEEE PES GTD Grand International Conference and Exposition Asia (GTD Asia). Furthermore, the conference proceedings has been published in IEEE Xplor

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data