Randomized Solutions to Convex Programs with Multiple Chance Constraints

The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled outcomes of the uncertainty (`scenarios'). A key merit of this approach is that it neither assumes knowledge of the uncertainty set, as it is common in robust optimization, nor of its probability distribution, as it is usually required in stochastic optimization. Moreover, the scenario approach is computationally efficient as its solution is based on a deterministic optimization program that is canonically convex, even when the original chance-constrained problem is not. Recently, researchers have obtained theoretical foundations for the scenario approach, providing a direct link between the number of scenarios and bounds on the constraint violation probability. These bounds are tight in the general case of an uncertain optimization problem with a single chance constraint. However, this paper shows that these bounds can be improved in situations where the constraints have a limited `support rank', a new concept that is introduced for the first time. This property is typically found in a large number of practical applications---most importantly, if the problem originally contains multiple chance constraints (e.g. multi-stage uncertain decision problems), or if a chance constraint belongs to a special class of constraints (e.g. linear or quadratic constraints). In these cases the quality of the scenario solution is improved while the same bound on the constraint violation probability is maintained, and also the computational complexity is reduced.Comment: This manuscript is the preprint of a paper submitted to the SIAM Journal on Optimization and it is subject to SIAM copyright. SIAM maintains the sole rights of distribution or publication of the work in all forms and media. If accepted, the copy of record will be available at http://www.siam.or

Mesoscopic effects in tunneling between parallel quantum wires

We consider a phase-coherent system of two parallel quantum wires that are coupled via a tunneling barrier of finite length. The usual perturbative treatment of tunneling fails in this case, even in the diffusive limit, once the length L of the coupling region exceeds a characteristic length scale L_t set by tunneling. Exact solution of the scattering problem posed by the extended tunneling barrier allows us to compute tunneling conductances as a function of applied voltage and magnetic field. We take into account charging effects in the quantum wires due to applied voltages and find that these are important for 1D-to-1D tunneling transport.Comment: 8 pages, 7 figures, improved Figs., added Refs. and appendix, to appear in Phys. Rev.

Parameter identification problems in the modelling of cell motility

We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree

Coherent quantum transport in narrow constrictions in the presence of a finite-range longitudinally polarized time-dependent field

We have studied the quantum transport in a narrow constriction acted upon by a finite-range longitudinally polarized time-dependent electric field. The electric field induces coherent inelastic scatterings which involve both intra-subband and inter-sideband transitions. Subsequently, the dc conductance G is found to exhibit suppressed features. These features are recognized as the quasi-bound-state (QBS) features which are associated with electrons making transitions to the vicinity of a subband bottom, of which the density of states is singular. Having valley-like instead of dip-like structures, these QBS features are different from the G characteristics for constrictions acted upon by a finite-range time-modulated potential. In addition, the subband bottoms in the time-dependent electric field region are shifted upward by an energy proportional to the square of the electric field and inversely proportional to the square of the frequency. This effective potential barrier is originated from the square of the vector potential and it leads to the interesting field-sensitive QBS features. An experimental set-up is proposed for the observation of these features.Comment: 8 pages, 4 figure

Computationally efficient stochastic MPC: A probabilistic scaling approach

In recent years, the increasing interest in stochastic model predictive control (SMPC) schemes has highlighted the limitation arising from their inherent computational demand, which has restricted their applicability to slow-dynamics and high-performing systems. To reduce the computational burden, in this paper we extend the probabilistic scaling approach to obtain a low-complexity inner approximation of chance-constrained sets. This approach provides probabilistic guarantees at a lower computational cost than other schemes for which the sample complexity depends on the design space dimension. To design candidate simple approximating sets, which approximate the shape of the probabilistic set, we introduce two possibilities: i) fixed-complexity polytopes, and ii) ell_{p-norm based sets. Once the candidate approximating set is obtained, it is scaled around its center so to enforce the expected probabilistic guarantees. The resulting scaled set is then exploited to enforce constraints in the classical SMPC framework. The computational gain obtained with respect to the scenario approach is demonstrated via simulations, where the objective is the control of a fixed-wing UAV performing a crop-monitoring mission over a sloped vineyard

Effects of dietary sources of vegetable fats on performance of dairy ewes and conjugated linoleic acid (CLA) in milk.

Two experiments were carried out to study the effects of supplementing the ration of lactating ewes with vegetable fats (sunflower oil, SO or hydrogenated palm oil, HPO; HIDROPALM (R)) on diet digestibility, milk yield and milk composition, and on the concentration of the conjugated linoleic acid (CIA) C18:2 cis-9 trans-11 and C18:1 trans-11 (vaccenic acid, VA) and other main fatty acids in milk fat. Treatments involved a control diet, without added oil, and 2 diets supplemented with either 12 g/kg SO or 12 g/kg HPO on a dry matter (DM) basis. In the first experiment, 6 non-pregnant, non-lactating Lacaune ewes were used following a 3 x 3 replicated Latin Square design. Addition of vegetable fat supplement to the diet increased digestibility of DM, organic matter (OM) and crude protein (CP), but did not affect that of the ether extract (EE), neutral detergent fibre (NDF) or acid detergent fibre (ADF). In the second experiment, 60 Lacaune dairy ewes mid-way through lactation (120 +/- 12 days in milk, 0.98 +/- 0.03 kg/day average milk yield) were divided into three equal-sized groups each of which was assigned to one of the three experimental diets for 4 weeks. Compared with the control treatment, supplementation with H PO increased milk yield and energy-corrected milk. But neither vegetable fat supplement modified percentages of fat and protein in milk. Supplementation with HPO increased C14:1, C16:1 and C16:0 content and reduced C18:0 and C18:1 cis-9 content in milk fat. Supplementation with SO increased the VA content in milk fat by 36% and that of cis-9 trans-11 CLA by 29% in comparison with the control diet. Supplementation with HPO led to milk fat with 15% more cis-9 trans-11 CLA than control milk. In conclusion, adding a moderate dose of HPO or SO to the diets increased CIA concentration in milk fat. Nevertheless, supplementation with SO was more effective than HPO in increasing CLA concentration in milk fat and reducing the atherogenicity index, improving milk quality from the human health standpoint

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

Facile one-spot synthesis of highly branched polycaprolactone

Reported is the first solvent-free (bulk) synthesis of degradable/bioresorbable, highly branched polymers via tin octanoate Sn(Oct2) catalysed controlled ring opening co-polymerisation (ROP) of mono and di-functional lactone monomers that proceed to near quantitative conversion. The successful isolation of solvent soluble, highly branched structures was shown to be dependent on both the concentration of the di-functional monomer and the overall reaction time. Comparison with analogous systems utilising controlled radical polymerisation (CRP) to form the highly/hyper branched polymers suggested significant experimental differences between the two chain growth methods. The maximum proportion of di-functional monomer without gelation ensuing was found to be 0.6 equivalents w.r.t. mono-functional monomer (c.f. 1 with CRP) and the onset of significant levels of branching occurred at approximately 90% conversion (c.f. ~70% with CRP). These differences and significant disparity in reaction times were attributed to (a) the coordination and insertion (C+I) propagation mechanism adopted by the Sn catalyst and (b) the presence of additional trans-esterification reactions at high conversion. Evidence is presented to support the conclusion that there are two mechanisms contributing to the overall branching process in the ROP system at high conversion. First, the C+I mechanism promotes growth of linear polymer until approximately 90% conversion, after which both the C+I and trans-esterification processes contribute to the interchain branching process. The branched nature of the molecular structures was supported by confirmation plots generated from static light scattering. This data demonstrated that the polymers synthesised exhibit varying degrees of branching, consistent with the di-functional monomer (4,4’-bioxepanyl-7,7’-dione - BOD) concentration in the feed. The degree of branching was calculated using 3 different methods and the results were shown to be independent of method. Finally, DSC analysis of the polymers demonstrated correlation between the degree of branching achieved and the observed Tm for the material where increased branching leads to a drop in the recorded Tm

COVID-19: Open-data resources for monitoring, modeling, and forecasting the epidemic

We provide an insight into the open-data resources pertinent to the study of the spread of the Covid-19 pandemic and its control. We identify the variables required to analyze fundamental aspects like seasonal behavior, regional mortality rates, and effectiveness of government measures. Open-data resources, along with data-driven methodologies, provide many opportunities to improve the response of the different administrations to the virus. We describe the present limitations and difficulties encountered in most of the open-data resources. To facilitate the access to the main open-data portals and resources, we identify the most relevant institutions, on a global scale, providing Covid-19 information and/or auxiliary variables (demographics, mobility, etc.). We also describe several open resources to access Covid-19 datasets at a country-wide level (i.e., China, Italy, Spain, France, Germany, US, etc.). To facilitate the rapid response to the study of the seasonal behavior of Covid-19, we enumerate the main open resources in terms of weather and climate variables. We also assess the reusability of some representative open-data sources

Performance and Operation of the CMS Electromagnetic Calorimeter

The operation and general performance of the CMS electromagnetic calorimeter using cosmic-ray muons are described. These muons were recorded after the closure of the CMS detector in late 2008. The calorimeter is made of lead tungstate crystals and the overall status of the 75848 channels corresponding to the barrel and endcap detectors is reported. The stability of crucial operational parameters, such as high voltage, temperature and electronic noise, is summarised and the performance of the light monitoring system is presented