Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.Conic Quadratic Program;hidden convexity;implementation error;robust optimization;simultaneous diagonalizability;S-lemma

Hidden Convexity in Partially Separable Optimization

The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.convex relaxation of nonconvex problems;hidden convexity;partially separable functions;robust optimization

New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation

A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schr\"odinger equation with time-dependent potential and to non-linear Schr\"odinger equation will be presented.Comment: 14 page

Influence of Quadrato Motor Training on Salivary proNGF and proBDNF

Previous studies demonstrated exercise-induced modulation of neurotrophins, such as Nerve Growth Factor (NGF) and Brain-Derived Neurotrophic Factor (BDNF). Yet, no study that we are aware of has examined their change as a function of different training paradigms. In addition, the understanding of the possible training-induced relationship between NGF and BDNF change is still lacking. Consequently, in the current study we examined the effect of a Walking Training (WT) and of Quadrato Motor Training (QMT) on NGF and BDNF precursors (proNGF and proBDNF). QMT is a specifically structured sensorimotor training that involves sequences of movements based on verbal commands, that was previously reported to improve spatial cognition, reflectivity, creativity as well as emotion regulation and general self-efficacy. In addition, QMT was reported to induce electrophysiological and morphological changes, suggesting stimulation of neuroplasticity processes. In two previous independent studies we reported QMT-induced changes in the salivary proNGF and proBDNF levels. Our present results demonstrate that following 12 weeks of daily QMT practice, proNGF level increases while proBDNF showed no significant change. More importantly, while no correlation between the two neurotrophins prior to training was detectable, there was a significant correlation between change in proNGF and proBDNF levels. Taken together the current results suggest that the two neurotrophins undergo a complex modulation, likely related to the different pathways by which they are produced and regulated. Since variations of these neurotrophins have been previously linked to depression, stress and anxiety, the current study may have practical implications and aid in understanding the possible physiological mechanisms that mediate improved well-being, and the dynamic change of neurotrophins as a result of training

Can Conformally Coupled Modified Gravity Solve The Hubble Tension?

The discrepancy between early-Universe inferences and direct measurements of the Hubble constant, known as the Hubble tension, recently became a pressing subject in high precision cosmology. As a result, a large variety of theoretical models have been proposed to relieve this tension. In this work we analyze a conformally-coupled modified gravity (CCMG) model of an evolving gravitational constant due to the coupling of a scalar field to the Ricci scalar, which becomes active around matter-radiation equality, as required for solutions to the Hubble tension based on increasing the sound horizon at recombination. The model is theoretically advantageous as it has only one free parameter in addition to the baseline $\Lambda$CDM ones. Inspired by similar recent analyses of so-called early-dark-energy models, we constrain the CCMG model using a combination of early and late-Universe cosmological datasets. In addition to the Planck 2018 cosmic microwave background (CMB) anisotropies and weak lensing measurements, baryon acoustic oscillations and the Supernova H0 for the Equation of State datasets, we also use large-scale structure (LSS) datasets such as the Dark Energy Survey year 1 and the full-shape power spectrum likelihood from the Baryon Oscillation Spectroscopic Survey, including its recent analysis using effective field theory, to check the effect of the CCMG model on the (milder) S8 tension between the CMB and LSS. We find that the CCMG model can slightly relax the Hubble tension, with $H_0 = 69.6 \pm 1.6$ km/s/Mpc at 95% CL, while barely affecting the S8 tension. However, current data does not exhibit strong preference for CCMG over the standard cosmological model. Lastly, we show that the planned CMB-S4 experiment will have the sensitivity required to distinguish between the CCMG model and the more general class of models involving an evolving gravitational constant.Comment: 14 pages, 4 figures, 9 table

Quantum Key Distribution with Classical Bob

Secure key distribution among two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? We present a protocol with this constraint, and prove its robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate users could notice.Comment: 4 and a bit pages, 1 figure, RevTe