Financial LPPL Bubbles with Mean-Reverting Noise in the Frequency Domain

The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that daily LPPL returns are typically orders of magnitude smaller than measured price returns, suggesting that noise obscures the underlying LPPL dynamics. However, if noise is mean-reverting, it would quickly cancel out over subsequent measurements. In this paper, we attempt to reject mean-reverting noise from price sequences by exploiting frequency-domain properties of LPPL and of mean reversion. First, we calculate the spectrum of mean-reverting \ou noise and devise estimators for the noise's parameters. Then, we derive the LPPL spectrum by breaking it down into its two main characteristics of power law and of log-periodicity. We compare price spectra with noise spectra during historical bubbles. In general, noise was strong also at low frequencies and, even if LPPL underlied price dynamics, LPPL would be obscured by noise

Scheduling Jobs Before Shut Down

Distributed systems execute background or alternative jobs while waiting for data or requests to arrive from another processor. In those cases, the following shut-down scheduling problem arises: given a set of jobs of known processing time, schedule them on m machines so as to maximize the total weight of jobs completed before an initially unknown deadline. We will present optimally competitive deterministic and randomized algorithms for shut-down scheduling. Our deterministic algorithm is parameterized by the number of machines m. Its competitive ratio increases as the number of machines decreases, but it is optimal for any given choice of m. Such family of deterministic algorithm can be translated into a family of randomized algorithms that use progressively less randomization and that are optimal for the given amount of randomization. Hence, we establish a precise trade-off between amount of randomization and competitive ratios. Distributed systems execute background or alternative jobs while waiting for data or requests to arrive from another processor. In those cases, the following shut-down scheduling problem arises: given a set of jobs of known processing time, schedule them on m machines so as to maximize the total weight of jobs completed before an initially unknown deadline. We will present optimally competitive deterministic and randomized algorithms for shut-down scheduling. Our deterministic algorithm is parameterized by the number of machines m. Its competitive ratio increases as the number of machines decreases, but it is optimal for any given choice of m. Such family of deterministic algorithm can be translated into a family of randomized algorithms that use progressively less randomization and that are optimal for the given amount of randomization. Hence, we establish a precise trade-off between amount of randomization and competitive ratios. (Also cross-referenced as UMIACS-TR-99-72

The Minimum Backlog Problem

We study the minimum backlog problem (MBP). This online problem arises, e.g., in the context of sensor networks. We focus on two main variants of MBP. The discrete MBP is a 2-person game played on a graph $G=(V,E)$. The player is initially located at a vertex of the graph. In each time step, the adversary pours a total of one unit of water into cups that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player's objective is to minimize the backlog, i.e., the maximum amount of water in any cup at any time. The geometric MBP is a continuous-time version of the MBP: the cups are points in the two-dimensional plane, the adversary pours water continuously at a constant rate, and the player moves in the plane with unit speed. Again, the player's objective is to minimize the backlog. We show that the competitive ratio of any algorithm for the MBP has a lower bound of $\Omega(D)$, where $D$ is the diameter of the graph (for the discrete MBP) or the diameter of the point set (for the geometric MBP). Therefore we focus on determining a strategy for the player that guarantees a uniform upper bound on the absolute value of the backlog. For the absolute value of the backlog there is a trivial lower bound of $\Omega(D)$, and the deamortization analysis of Dietz and Sleator gives an upper bound of $O(D\log N)$ for $N$ cups. Our main result is a tight upper bound for the geometric MBP: we show that there is a strategy for the player that guarantees a backlog of $O(D)$, independently of the number of cups.Comment: 1+16 pages, 3 figure

Disease-Modifying Therapies and Coronavirus Disease 2019 Severity in Multiple Sclerosis

Objective: This study was undertaken to assess the impact of immunosuppressive and immunomodulatory therapies on the severity of coronavirus disease 2019 (COVID-19) in people with multiple sclerosis (PwMS). Methods: We retrospectively collected data of PwMS with suspected or confirmed COVID-19. All the patients had complete follow-up to death or recovery. Severe COVID-19 was defined by a 3-level variable: mild disease not requiring hospitalization versus pneumonia or hospitalization versus intensive care unit (ICU) admission or death. We evaluated baseline characteristics and MS therapies associated with severe COVID-19 by multivariate and propensity score (PS)-weighted ordinal logistic models. Sensitivity analyses were run to confirm the results. Results: Of 844 PwMS with suspected (n = 565) or confirmed (n = 279) COVID-19, 13 (1.54%) died; 11 of them were in a progressive MS phase, and 8 were without any therapy. Thirty-eight (4.5%) were admitted to an ICU; 99 (11.7%) had radiologically documented pneumonia; 96 (11.4%) were hospitalized. After adjusting for region, age, sex, progressive MS course, Expanded Disability Status Scale, disease duration, body mass index, comorbidities, and recent methylprednisolone use, therapy with an anti-CD20 agent (ocrelizumab or rituximab) was significantly associated (odds ratio [OR] = 2.37, 95% confidence interval [CI] = 1.18-4.74, p = 0.015) with increased risk of severe COVID-19. Recent use (<1 month) of methylprednisolone was also associated with a worse outcome (OR = 5.24, 95% CI = 2.20-12.53, p = 0.001). Results were confirmed by the PS-weighted analysis and by all the sensitivity analyses. Interpretation: This study showed an acceptable level of safety of therapies with a broad array of mechanisms of action. However, some specific elements of risk emerged. These will need to be considered while the COVID-19 pandemic persists

COVID-19 Severity in Multiple Sclerosis: Putting Data Into Context

Background and objectives: It is unclear how multiple sclerosis (MS) affects the severity of COVID-19. The aim of this study is to compare COVID-19-related outcomes collected in an Italian cohort of patients with MS with the outcomes expected in the age- and sex-matched Italian population. Methods: Hospitalization, intensive care unit (ICU) admission, and death after COVID-19 diagnosis of 1,362 patients with MS were compared with the age- and sex-matched Italian population in a retrospective observational case-cohort study with population-based control. The observed vs the expected events were compared in the whole MS cohort and in different subgroups (higher risk: Expanded Disability Status Scale [EDSS] score > 3 or at least 1 comorbidity, lower risk: EDSS score ≤ 3 and no comorbidities) by the χ2 test, and the risk excess was quantified by risk ratios (RRs). Results: The risk of severe events was about twice the risk in the age- and sex-matched Italian population: RR = 2.12 for hospitalization (p < 0.001), RR = 2.19 for ICU admission (p < 0.001), and RR = 2.43 for death (p < 0.001). The excess of risk was confined to the higher-risk group (n = 553). In lower-risk patients (n = 809), the rate of events was close to that of the Italian age- and sex-matched population (RR = 1.12 for hospitalization, RR = 1.52 for ICU admission, and RR = 1.19 for death). In the lower-risk group, an increased hospitalization risk was detected in patients on anti-CD20 (RR = 3.03, p = 0.005), whereas a decrease was detected in patients on interferon (0 observed vs 4 expected events, p = 0.04). Discussion: Overall, the MS cohort had a risk of severe events that is twice the risk than the age- and sex-matched Italian population. This excess of risk is mainly explained by the EDSS score and comorbidities, whereas a residual increase of hospitalization risk was observed in patients on anti-CD20 therapies and a decrease in people on interferon

DMTs and Covid-19 severity in MS: a pooled analysis from Italy and France

We evaluated the effect of DMTs on Covid-19 severity in patients with MS, with a pooled-analysis of two large cohorts from Italy and France. The association of baseline characteristics and DMTs with Covid-19 severity was assessed by multivariate ordinal-logistic models and pooled by a fixed-effect meta-analysis. 1066 patients with MS from Italy and 721 from France were included. In the multivariate model, anti-CD20 therapies were significantly associated (OR = 2.05, 95%CI = 1.39–3.02, p < 0.001) with Covid-19 severity, whereas interferon indicated a decreased risk (OR = 0.42, 95%CI = 0.18–0.99, p = 0.047). This pooled-analysis confirms an increased risk of severe Covid-19 in patients on anti-CD20 therapies and supports the protective role of interferon

Integrated play-back, sensing, and networked control

Abstract — Sensing, actuation, and decision units can control a remote physical environment and enable physical actions regardless of distance. However, the effectiveness of networked control depends on its ability to tolerate network non-determinism, which in turn can be enhanced by the use of play-back buffers. Although play-back has been intensively studied in multi-media applications, play-back schemes differ significantly in networked control, which is characterized by different performance metrics and a different sequence of communication events. The primary contribution of this paper is an end-to-end algorithm that integrates play-back buffering, sensor sampling, and control. The algorithm is extensively validated on simulations and realtime wide-area emulations. The integrated algorithm canceled the effect of disturbances as much as a proportional controller under ideal network conditions. I