Multiplicative Pacing Equilibria in Auction Markets

Budgets play a significant role in ad markets that implement sequential auctions such as those hosted by internet companies. In “Multiplicative Pacing Equilibria in Auction Markets,” the authors look at pacing in an ad marketplace using the lens of game theory. The goal is understanding how bids must be shaded to maximize advertiser welfare, at equilibrium. Motivated by the real-world auction mechanism, they construct a game where advertisers in the auctions choose a multiplicative factor not larger than 1 to possibly reduce their bids and best respond to the other advertisers. The article studies the theoretical properties of the game such as existence and uniqueness of equilibria, offers an exact algorithm to compute them, connects the game to well-known abstractions such as Fisher markets, and performs a computational study with real-world-inspired instances. The main insights are that the solutions to the studied game can be used to improve the outcomes achieved by a closer-to-reality dynamic pacing algorithm and that buyers do not have an incentive to misreport bids or budgets when there are enough participants in the auction.

Sex-Related Longitudinal Change of Motor, Non-Motor, and Biological Features in Early Parkinson’s Disease

Background: Investigation of sex-related motor and non-motor differences and biological markers in Parkinson’s disease (PD) may improve precision medicine approach. Objective: To examine sex-related longitudinal changes in motor and non-motor features and biologic biomarkers in early PD. Methods: We compared 5-year longitudinal changes in de novo, untreated PD men and women (at baseline N = 423; 65.5%male) of the Parkinson’s Progression Markers Initiative (PPMI), assessing motor and non-motor manifestations of disease; and biologic measures in cerebrospinal fluid (CSF) and dopamine transporter deficit on DaTscanTM uptake. Results: Men experienced greater longitudinal decline in self-reported motor (p < 0.001) and non-motor (p = 0.009) aspects of experiences of daily living, such that men had a yearly increase in MDS-UPDRS part II by a multiplicative factor of 1.27 compared to women at 0.7, while men had a yearly increase in MDS-UPDRS part I by a multiplicative factor of 0.98, compared to women at 0.67. Compared to women, men had more longitudinal progression in clinician-assessed motor features in the ON medication state (p = 0.010) and required higher dopaminergic medication dosages over time (p = 0.014). Time to reach specific disease milestones and longitudinal changes in CSF biomarkers and DaTscanTM uptake were not different by sex. Conclusion: Men showed higher self-assessed motor and non-motor burden of disease, with possible contributions from suboptimal dopaminergic therapeutic response in men. However, motor features of disease evaluated with clinician-based scales in the OFF medication state, as well as biological biomarkers do not show specific sex-related progression patterns.

SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al, CMAME 2016] we are able to show an “almost uniform” error bound (in the sense that the unique term that depends in an unfavourable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result.

The Power of Human–Algorithm Collaboration in Solving Combinatorial Optimization Problems

Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such a problem is maximum clique, which—under standard assumptions in complexity theory—cannot be solved in sub-exponential time or be approximated within the polynomial factor efficiently. However, we show that if a polynomial time algorithm can query informative Gaussian priors from an expert poly(n) times, then a class of combinatorial optimization problems can be solved efficiently up to a multiplicative factor ϵ, where ϵ is arbitrary constant. In this paper, we present proof of our claims and show numerical results to support them. Our methods can cast new light on how to approach optimization problems in domains where even the approximation of the problem is not feasible. Furthermore, the results can help researchers to understand the structures of these problems (or whether these problems have any structure at all!). While the proposed methods can be used to approximate combinatorial problems in NPO, we note that the scope of the problems solvable might well include problems that are provable intractable (problems in EXPTIME).

Accounting and analysis of bankruptcies

The textbook introduces the history of the formation of the institute of bankruptcy, conducting reorganization and liquidation procedures in a crisis, diagnosing the financial condition of an enterprise based on situational and coefficient analysis, multiplicative factor models for assessing the threat of bankruptcy, methods for assessing the value of an insolvent enterprise, as well as accounting for operations related to bankruptcy procedures. The possibilities of an integrated approach to the development of a strategy for overcoming the crisis and choosing ways to restructure a bankrupt enterprise are considered. Meets the requirements of the federal state educational standards of higher education of the latest generation. For teachers, postgraduates and students of higher educational organizations, employees of analytical services, anti-crisis managers.

On L(h,k)-labelings of oriented graphs

We compare the behaviour of the $L(h,k)$-number of undirected and oriented graphs in terms of maximum degree, highlighting differences between the two contexts. In particular, we prove that, for every $h$ and $k$, oriented graphs with bounded degree in every block of their underlying graph (for instance, oriented trees and oriented cacti) have bounded $L(h,k)$-number, giving an upper bound on this number which is sharp up to a multiplicative factor $4$.

Neuromodulators enable overlapping synaptic memory regimes and nonlinear transition dynamics in recurrent neural networks

Mood, arousal, and other internal neural states can drastically alter behavior, even in identical external circumstances - the proverbial glass half full or empty. Neuromodulators are critical in controlling these internal neural states, and aberrations in neuromodulatory processes are linked to various neuropsychiatric disorders. To study how neuromodulators influence neural behavior, we modeled neuromodulation as a multiplicative factor acting on synaptic transmission between neurons in a recurrent neural network. We found this simple mechanism could vastly increase the computational capability and flexibility of a neural network by enabling overlapping storage of synaptic memories able to drive diverse, even diametrically opposed, behaviors. We analyzed how local or cell-type specific neuromodulation changes network activity to support such behaviors and reproduced experimental findings of Drosophila starvation behavior. We revealed that circuits have idiosyncratic, non-linear dose-response properties that can be different for chemical versus electrical modulation. Our findings help explain how neuromodulation "unlocks" specific behaviors with important implications for neuropsychiatric therapeutics.

Correction of Tropical Rainfall Measuring Missions Satellite Data of Solar Radiation for the High Andean Areas of Peru

The spatial and temporal quantification of climatic elements is necessary in different regions of the world, as mitigation policies against climate change in recent years the use of renewable energies has been promoted, with solar radiation being an important element, the objective is to correct Tropical Rainfall Measuring Missions (TRMM) satellite data series of solar radiation with respect to the data observed through an automatic meteorological station for a short period at a point located in the southern Peruvian Andes, we proceeded to process the observed data and download satellite information, making use of From a mathematical model, the correction coefficients of the satellite data were determined; The multiplicative factor model better corrects the satellite information, the Pearson correlation improved from R = 0.65 to R = 0.84 for monthly solar radiation, in the series of satellite data corrected for 37 years, a trend was determined -0.0006 Watt/m2/month.

Application of the Oscillation Symmetry to the Electromagnetic Interactions of Some Particles, Nuclei, and Atoms

The oscillation symmetry is first applied to electromagnetic interactions of particles and nuclei. It is shown that the differences between successive masses plotted versus their mean values and the electromagnetic decay widths Γee of 0^−(1^−−) b¯b and c¯c mesons, plotted versus their masses, agree with such symmetry. Then it is shown that the variation of the energy differences between different levels of several nuclei from 8Be to 20Ne, corresponding to given electric or magnetic transitions, display also oscillating behaviours. The electromagnetic widths of the electric and magnetic transitions between excited levels of these nuclei, plotted versus the corresponding differences between energies agree also with this property. The oscillating periods describe also an oscillation, the same for E1, M1, and E2 transitions. It is also the case for the multiplicative factor used β, and for ratios between these parameters. The oscillation symmetry is then applied to atomic energy levels of several neutral atoms from hydrogen to phosphorus. The data exhibit nice oscillations when plotted in the same way as before. The oscillations in various nuclear and atomic periods of different elements (A) exhibit the same shape and can be fitted by the same distribution.