Maximum Entropy Distributions Inferred from Option Portfolios on an Asset

We obtain the maximum entropy distribution for an asset from call and digital option prices. A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimise a formal derivation by Buchen and Kelly. We give a simple and robust algorithm for our method and compare our results to theirs. We present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options. Finally, we apply our approach to options on the S&P 500 index.Comment: 23 pages, 5 figures, to appear in Finance and Stochastic

Maximum Weight Spectrum Codes

In the recent work \cite{shi18}, a combinatorial problem concerning linear codes over a finite field \F_q was introduced. In that work the authors studied the weight set of an $[n,k]_q$ linear code, that is the set of non-zero distinct Hamming weights, showing that its cardinality is upper bounded by $\frac{q^k-1}{q-1}$. They showed that this bound was sharp in the case $q=2$, and in the case $k=2$. They conjectured that the bound is sharp for every prime power $q$ and every positive integer $k$. In this work quickly establish the truth of this conjecture. We provide two proofs, each employing different construction techniques. The first relies on the geometric view of linear codes as systems of projective points. The second approach is purely algebraic. We establish some lower bounds on the length of codes that satisfy the conjecture, and the length of the new codes constructed here are discussed.Comment: 19 page

Quantum Bayesian methods and subsequent measurements

After a derivation of the quantum Bayes theorem, and a discussion of the reconstruction of the unknown state of identical spin systems by repeated measurements, the main part of this paper treats the problem of determining the unknown phase difference of two coherent sources by photon measurements. While the approach of this paper is based on computing correlations of actual measurements (photon detections), it is possible to derive indirectly a probability distribution for the phase difference. In this approach, the quantum phase is not an observable, but a parameter of an unknown quantum state. Photon measurements determine a probability distribution for the phase difference. The approach used in this paper takes into account both photon statistics and the finite efficiency of the detectors.Comment: Expanded and corrected version. 13 pages, 1 figur

Reset and switch protocols at Landauer limit in a graphene buckled ribbon

Heat produced during a reset operation is meant to show a fundamental bound known as Landauer limit, while simple switch operations have an expected minimum amount of produced heat equal to zero. However, in both cases, present-day technology realizations dissipate far beyond these theoretical limits. In this paper we present a study based on molecular dynamics simulations, where reset and switch protocols are applied on a graphene buckled ribbon, employed here as a nano electromechanical switch working at the thermodynamic limit

Microcatheter–Assisted Circumferential Trabeculotomy in Primary Congenital Glaucoma: Long-Term Clinical Outcomes

Purpose: The purpose of this study was to report the long-term efficacy and clinical outcomes of microcatheter-assisted circumferential trabeculotomy (MCT) in children with primary congenital glaucoma (PCG). Methods: This is a single-center retrospective study including consecutive children with PCG who underwent MCT with > two years follow up. The primary outcome was surgical success, defined as intraocular pressure (IOP) ≤ 21 mmHg with (qualified) or without (complete) medications, measured at six months, one year, and then annually. Secondary outcomes were visual acuity (VA), refraction, axial length (AXL), complications, reinterventions, and number of medications. Results: Twelve eyes of ten patients were included. In eight children only one eye was affected. The mean ± standard deviation (SD) age at surgery was 6.3 ± 4.1 months. The mean postoperative follow-up was 66 ± 35 months. The mean IOP was 34.3 ± 9.6 mmHg preoperatively and 14.6 ± 2.3 mmHg postoperatively at the last visit (p < 0.001). Complete success was achieved at all time points in 10 out of 12 eyes, while 2 eyes had a qualified success. At three years of age, the mean VA of the operated eyes was 0.25 ± 0.12 logMAR, the mean spherical equivalent was −0.78 ± 1.43 diopters, and the mean AXL was 23.78 mm. Transient hyphema was the only complication observed. None of the children required additional glaucoma surgery. Conclusions: Circumferential trabeculotomy for PCG effectively lowers the IOP at more than two years after surgery. Following this procedure, the prognosis for the visual function is good, and the refractive error is low. Postoperative complications were not significant

The Immunological Basis of Dry Eye Disease and Current Topical Treatment Options.

Homeostasis of the lacrimal functional unit is needed to ensure a well-regulated ocular immune response comprising innate and adaptive phases. When the ocular immune system is excessively stimulated and/or immunoregulatory mechanisms are disrupted, the balance between innate and adaptive phases is dysregulated and chronic ocular surface inflammation can result, leading to chronic dry eye disease (DED). According to the Tear Film and Ocular Surface Society Dry Eye Workshop II definition, DED is a multifactorial disorder of the ocular surface characterized by impairment and loss of tear homeostasis (hyperosmolarity), ocular discomfort or pain, and neurosensory abnormalities. Dysregulated ocular immune responses result in ocular surface damage, which is a further contributing factor to DED pathology. Several therapeutics are available to break the vicious circle of DED and prevent chronic disease and progression, including immunosuppressive agents (steroids) and immunomodulators (cyclosporine and lifitegrast). Given the chronic inflammatory nature of DED, each of these agents is commonly used in clinical practice. In this study, we review the immunopathology of DED and the molecular and cellular actions of current topical DED therapeutics to inform clinical decision making

A Machine Learning-Based Approach for Audio Signals Classification using Chebychev Moments and Mel-Coefficients

This paper proposes a machine learning-based architecture for audio signals classification based on a joint exploitation of the Chebychev moments and the Mel-Frequency Cepstrum Coefficients. The procedure starts with the computation of the Mel-spectrogram of the recorded audio signals; then, Chebychev moments are obtained projecting the Cadence Frequency Diagram derived from the Mel-spectrogram into the base of Chebychev moments. These moments are then concatenated with the Mel-Frequency Cepstrum Coefficients to form the final feature vector. By doing so, the architecture exploits the peculiarities of the discrete Chebychev moments such as their symmetry characteristics. The effectiveness of the procedure is assessed on two challenging datasets, UrbanSound8K and ESC-50

SiO collimated outflows driven by high-mass YSOs in G24.78+0.08

We imaged the molecular outflows towards the cluster of high-mass young stellar objects G24.78+0.08 at high-angular resolution using SiO emission, which is considered the classical tracer of protostellar jets. We performed SiO observations with the VLA interferometer in the J = 1-0 v=0 transition and with the SMA array in the 5-4 transition. A complementary IRAM 30-m single-dish survey in the (2-1), (3-2), (5-4), and (6-5) SiO lines was also carried out. Two collimated SiO high-velocity outflows driven by the A2 and C millimeter continuum massive cores have been imaged. On the other hand, we detected no SiO outflow driven by the young stellar objects in more evolved evolutionary phases that are associated with ultracompact (B) or hypercompact (A1) HII regions. The LVG analysis reveals high-density gas (10^3-10^4 cm-3), with well constrained SiO column densities (0.5-1 10^15 cm-2). The driving source of the A2 outflow is associated with typical hot core tracers such as methyl formate, vinyl cyanide, cyanoacetilene, and acetone. The driving source of the main SiO outflow in G24 has an estimated luminosity of a few 10^4 Lsun (typical of a late O-type star) and is embedded in the 1.3 mm continuum core A2, which in turn is located at the centre of a hot core that rotates on a plane perpendicular to the outflow main axis. The present SiO images support a scenario similar to the low-mass case for massive star formation, where jets that are clearly traced by SiO emission, create outflows of swept-up ambient gas usually traced by CO.Comment: Astronomy & Astrophysics, in pres