Phase transition in a log-normal Markov functional model

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase transition at some critical value of the volatility. We investigate the conditions under which this phase transition occurs, and show that it is related to the position of the zeros of an appropriately defined generating function in the complex plane, in analogy with the Lee-Yang theory of the phase transitions in condensed matter physics.Comment: 9 pages, 5 figures. v2: Added asymptotic expressions for the convexity-adjusted Libors in the small and large volatility limits. v3: Added one reference. Final version to appear in Journal of Mathematical Physic

Convertible bond valuation in a jump diffusion setting with stochastic interest rates

This paper proposes an integrated pricing framework for convertible bonds, which comprises firm value evolving as an exponential jump diffusion, correlated stochastic interest rates movements and an efficient numerical pricing scheme. By construction, the proposed stochastic model fits in the framework of affine jump diffusion processes of Duffie et al. [Econometrica, 2000, 68, 1343–1376] with tractable behaviour. We define the firm’s optimal call policy and investigate its impact on the computed convertible bond prices. We illustrate the performance of the numerical scheme and highlight the effects originated by the inclusion of jumps, stochastic interest rates and a non-zero correlation structure between firm value and interest rates

Acute symptomatic status epilepticus: Splitting or lumping? A proposal of classification based on real-world data

This study aimed to group acute symptomatic etiologies of consecutive episodes of status epilepticus (SE) into different subcategories and explore their associations with clinical outcome. Etiologies were first categorized as “acute,” “remote,” “progressive,” “SE in defined electroclinical syndromes,” and “unknown.” Four subcategories of acute etiologies were then defined: (1) withdrawal, low levels, or inappropriate prescription of antiseizure medications, or sleep deprivation in patients with pre-existing epilepsy; (2) acute insults to central nervous system (CNS; “acute-primary CNS”); (3) CNS pathology secondary to metabolic disturbances, systemic infection, or fever (“acute-secondary CNS”); and (4) drug/alcohol intoxication or withdrawal. Poor outcome at discharge, defined as worsening of clinical conditions (modified Rankin Scale [mRS] at discharge higher than mRS at baseline), was reported in 55.6% of cases. The etiological categories of acute-primary CNS (odds ratio [OR] = 3.61, 95% confidence interval [CI] = 2.11–6.18), acute-secondary CNS (OR = 1.80, 95% CI = 1.11–2.91), and progressive SE (OR = 2.65, 95% CI = 1.57–4.47), age (OR = 1.05, 95% CI = 1.04–1.06), nonconvulsive semiology with coma (OR = 3.06, 95% CI = 1.52–6.17), and refractoriness (OR = 4.31, 95% CI = 2.39–7.77) and superrefractoriness to treatment (OR = 8.24, 95% CI = 3.51–19.36) increased the odds of poor outcome. Heterogeneity exists within the spectrum of acute symptomatic causes of SE, and distinct etiological subcategories may inform about the clinical outcome

Quantum projection filter for a highly nonlinear model in cavity QED

Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite-dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case.) One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection on the tangent space with respect to the Fisher metric. Here we apply this approach to the simple but highly nonlinear quantum model of optical phase bistability of a stongly coupled two-level atom in an optical cavity. We observe near-optimal performance of the quantum projection filter, demonstrating the utility of such an approach.Comment: 19 pages, 6 figures. A version with high quality images can be found at http://minty.caltech.edu/papers.ph

Atogepant for the Prevention of Episodic Migraine in Adults: A Systematic Review and Meta-Analysis of Efficacy and Safety

Introduction: The inhibition of the calcitonin gene-related peptide (CGRP) pathway has attracted interest in pharmacological research on migraine. Atogepant is a potent, selective, orally available antagonist of the CGRP receptor approved as a preventive treatment of episodic migraine. This systematic review with meta-analysis aims to evaluate the efficacy and safety of atogepant for the prevention of episodic migraine in adult patients. Methods: Randomized, placebo-controlled, single or double-blinded trials were identified through a systematic literature search (December week 4, 2021). Main outcomes included the changes from baseline in monthly migraine days and the incidence of adverse events (AEs) and treatment withdrawal due to AEs. Mean difference (MD) and risk ratio (RR) with 95% confidence intervals (95% CIs) were estimated. Results: Two trials were included, overall enrolling 1550 patients. A total of 408 participants were randomized to placebo, 314 to atogepant 10 mg, 411 to atogepant 30 mg, and 417 to atogepant 60 mg once daily. The mean age of the patients was 41.0 years and 87.7% were women. The reduction in the mean number of migraine days from baseline across the 12-week treatment period was significantly greater among patients treated with atogepant at either the daily dose of 10 mg (MD − 1.16, 95% CI − 1.60 to − 0.73, p < 0.001), 30 mg (MD − 1.15, 95% CI − 1.54 to − 0.76, p < 0.001), or 60 mg (MD − 1.20, 95% CI − 2.18 to − 0.22, p = 0.016) than with placebo. There were no differences in the occurrence of AEs and drug withdrawal due to AEs between atogepant and placebo groups. Constipation was more commonly observed in patients treated with atogepant at 30 mg/day than placebo (RR 5.19, 95% CI 2.00–13.46; p = 0.001). Treatment with atogepant at the daily dose of 60 mg was associated with a higher risk of constipation (RR 4.92, 95% CI 1.89–12.79; p = 0.001) and nausea (RR 2.73, 95% CI 1.47–5.06; p = 0.001) than placebo. Conclusion: Atogepant is an efficacious and overall well-tolerated treatment for the prevention of episodic migraine in adults

Adjunctive Cenobamate for Focal-Onset Seizures in Adults: A Systematic Review and Meta-Analysis

Background: Cenobamate is a novel tetrazole-derived carbamate compound with a dual mechanism of action. This drug can enhance the inactivated state of voltage-gated sodium channels, preferentially inhibiting the persistent component of the sodium channel current, and acts as a positive allosteric modulator of GABAA receptors, binding at a non-benzodiazepine site. Objective: We assessed the efficacy and safety of adjunctive cenobamate for the treatment of focal-onset seizures in adult patients with epilepsy using meta-analytical techniques. Methods: We systematically searched (May, week 4, 2020) MEDLINE (accessed by PubMed), the Cochrane Central Register of Controlled Trials (CENTRAL), and the US National Institutes of Health Clinical Trials Registry (http://www.clinicaltrials.gov). There were no date limitations or language restrictions. Randomized, placebo-controlled, single or double-blinded, add-on trials of cenobamate in adult patients with uncontrolled focal-onset seizures were identified. Main outcomes included the proportion of patients with ≥ 50 and 100% reduction in seizure frequency during the maintenance treatment period compared with baseline and the incidence of treatment withdrawal and adverse events (AEs). Risk ratio (RR) with 95% confidence interval (CI) was estimated for each outcome. Results: Two trials were included, overall enrolling 659 patients (442 for the add-on cenobamate group and 217 for the add-on placebo group). Seizure frequency reduction by at least 50% occurred during the maintenance phase in 50.1% of the patients randomized to cenobamate and 23.5% of the placebo-treated participants (RR 2.18, 95% CI 1.67–2.85; p < 0.001). The pooled estimated RR to achieve seizure freedom for the cenobamate group in comparison with placebo was 3.71 (95% CI 1.93–7.14; p < 0.001). Withdrawal from randomized treatment occurred in 16.7 and 11.1% of participants receiving cenobamate and placebo, respectively (RR 1.34, 95% CI 0.85–2.09; p = 0.205). Treatment was discontinued due to AEs in 12.2 and 4.1% of the patients in the active and control arms (RR 2.27, 95% CI 1.08–4.79; p = 0.031). AEs were reported in 76.9 and 66.8% of the patients during treatment with cenobamate and placebo (RR 1.14, 95% CI 1.02–1.26; p = 0.021). The cenobamate-associated AEs included somnolence, dizziness, fatigue, balance disorder, and diplopia. Conclusions: Adjunctive cenobamate in adult patients with uncontrolled focal-onset seizures is associated with a greater reduction in seizure frequency and a higher rate of AEs than placebo

Efficacy and Safety of Cannabidiol in Epilepsy: A Systematic Review and Meta-Analysis

Background: Approximately one-third of patients with epilepsy presents seizures despite adequate treatment. Hence, there is the need to search for new therapeutic options. Cannabidiol (CBD) is a major chemical component of the resin of Cannabis sativa plant, most commonly known as marijuana. The anti-seizure properties of CBD do not relate to the direct action on cannabinoid receptors, but are mediated by a multitude of mechanisms that include the agonist and antagonist effects on ionic channels, neurotransmitter transporters, and multiple 7-transmembrane receptors. In contrast to tetra-hydrocannabinol, CBD lacks psychoactive properties, does not produce euphoric or intrusive side effects, and is largely devoid of abuse liability. Objective: The aim of the study was to estimate the efficacy and safety of CBD as adjunctive treatment in patients with epilepsy using meta-analytical techniques. Methods: Randomized, placebo-controlled, single- or double-blinded add-on trials of oral CBD in patients with uncontrolled epilepsy were identified. Main outcomes included the percentage change and the proportion of patients with ≥ 50% reduction in monthly seizure frequency during the treatment period and the incidence of treatment withdrawal and adverse events (AEs). Results: Four trials involving 550 patients with Lennox–Gastaut syndrome (LGS) and Dravet syndrome (DS) were included. The pooled average difference in change in seizure frequency during the treatment period resulted 19.5 [95% confidence interval (CI) 8.1–31.0; p = 0.001] percentage points between the CBD 10 mg and placebo groups and 19.9 (95% CI 11.8–28.1; p < 0.001) percentage points between the CBD 20 mg and placebo arms, in favor of CBD. The reduction in all-types seizure frequency by at least 50% occurred in 37.2% of the patients in the CBD 20 mg group and 21.2% of the placebo-treated participants [risk ratio (RR) 1.76, 95% CI 1.07–2.88; p = 0.025]. Across the trials, drug withdrawal for any reason occurred in 11.1% and 2.6% of participants receiving CBD and placebo, respectively (RR 3.54, 95% CI 1.55–8.12; p = 0.003) [Chi squared = 2.53, degrees of freedom (df) = 3, p = 0.506; I2 = 0.0%]. The RRs to discontinue treatment were 1.45 (95% CI 0.28–7.41; p = 0.657) and 4.20 (95% CI 1.82–9.68; p = 0.001) for CBD at the doses of 10 and 20 mg/kg/day, respectively, in comparison to placebo. Treatment was discontinued due to AEs in 8.9% and 1.8% of patients in the active and control arms, respectively (RR 5.59, 95% CI 1.87–16.73; p = 0.002). The corresponding RRs for CBD at the doses of 10 and 20 mg/kg/day were 1.66 (95% CI 0.22–12.86; p = 0.626) and 6.89 (95% CI 2.28–20.80; p = 0.001). AEs occurred in 87.9% and 72.2% of patients treated with CBD and placebo (RR 1.22, 95% CI 1.11–1.33; p < 0.001). AEs significantly associated with CBD were somnolence, decreased appetite, diarrhea, and increased serum aminotransferases. Conclusions: Adjunctive CBD in patients with LGS or DS experiencing seizures uncontrolled by concomitant anti-epileptic treatment regimens is associated with a greater reduction in seizure frequency and a higher rate of AEs than placebo

Can a Loan Valuation Adjustment (LVA) Approach Immunize Collateralized Debt from Defaults?

This study focuses on structuring tangible asset backed loans to inhibit their endemic option to default. We adapt the pragmatic approach of a margin loan in the configuring of collateralized debt to yield a quasi‐default‐free facility. We link our practical method to the current Basel III (2017) regulatory framework. Our new concept of the Loan Valuation Adjustment (LVA) and novel method to minimize the LVA converts the risky loan into a quasi risk‐free loan and achieves value maximization for the lending financial institution. As a result, entrepreneurial activities are promoted and economic growth invigorated. Information asymmetry, costly bailouts and resulting financial fragility are reduced while depositors are endowed with a safety net equivalent to deposit insurance but without the associated moral hazard between risk‐averse lenders and borrowers

Central motor and sensory conduction in patients with hepatic myelopathy

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Yield Curve Shapes and the Asymptotic Short Rate Distribution in Affine One-Factor Models

We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be characterized by simple conditions on the present short rate. We give conditions under which the short rate process will converge to a limit distribution and describe the limit distribution in terms of its cumulant generating function. We apply our results to the Vasicek model, the CIR model, a CIR model with added jumps and a model of Ornstein-Uhlenbeck type