Entropic Dynamics of Stocks and European Options

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamics. An important information about the dynamics of a stock's price is scale invariance. By imposing the scale invariant symmetry, we arrive at choosing the logarithm of the stock's price as the proper variable to model. The dynamics of stock log price is derived using two pieces of information, the continuity of motion and the directionality constraint. The resulting model is the same as the Geometric Brownian Motion, GBM, of the stock price which is manifestly scale invariant. Furthermore, we come up with the dynamics of probability density function, which is a Fokker--Planck equation. Next, we extend the model to value the European Options on a stock. Derivative securities ought to be prices such that there is no arbitrage. To ensure the no-arbitrage pricing, we derive the risk-neutral measure by incorporating the risk-neutral information. Consequently, the Black--Scholes model and the Black--Scholes-Merton differential equation are derived

Quantum phases in entropic dynamics

In the Entropic Dynamics framework the dynamics is driven by maximizing entropy subject to appropriate constraints. In this work we bring Entropic Dynamics one step closer to full equivalence with quantum theory by identifying constraints that lead to wave functions that remain single-valued even for multi-valued phases by recognizing the intimate relation between quantum phases, gauge symmetry, and charge quantization.Comment: Presented at MaxEnt 2017, the 37th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 9-14, 2017, Jarinu, Brazil

Understanding the Impact of Cutting in Quantum Circuits Reliability to Transient Faults

Quantum Computing is a highly promising new computation paradigm. Unfortunately, quantum bits (qubits) are extremely fragile and their state can be gradually or suddenly modified by intrinsic noise or external perturbation. In this paper, we target the sensitivity of quantum circuits to radiation-induced transient faults. We consider quantum circuit cuts that split the circuit into smaller independent portions, and understand how faults propagate in each portion. As we show, the cuts have different vulnerabilities, and our methodology successfully identifies the circuit portion that is more likely to contribute to the overall circuit error rate. Our evaluation shows that a circuit cut can have a 4.6x higher probability than the other cuts, when corrupted, to modify the circuit output. Our study, identifying the most critical cuts, moves towards the possibility of implementing a selective hardening for quantum circuits

QuFI: a Quantum Fault Injector to Measure the Reliability of Qubits and Quantum Circuits

Quantum computing is a new technology that is expected to revolutionize the computation paradigm in the next few years. Qubits exploit the quantum physics proprieties to increase the parallelism and speed of computation. Unfortunately, besides being intrinsically noisy, qubits have also been shown to be highly susceptible to external sources of faults, such as ionizing radiation. The latest discoveries highlight a much higher radiation sensitivity of qubits than traditional transistors and identify a much more complex fault model than bit-flip. We propose a framework to identify the quantum circuits sensitivity to radiation-induced faults and the probability for a fault in a qubit to propagate to the output. Based on the latest studies and radiation experiments performed on real quantum machines, we model the transient faults in a qubit as a phase shift with a parametrized magnitude. Additionally, our framework can inject multiple qubit faults, tuning the phase shift magnitude based on the proximity of the qubit to the particle strike location. As we show in the paper, the proposed fault injector is highly flexible, and it can be used on both quantum circuit simulators and real quantum machines. We report the finding of more than 285M injections on the Qiskit simulator and 53K injections on real IBM machines. We consider three quantum algorithms and identify the faults and qubits that are more likely to impact the output. We also consider the fault propagation dependence on the circuit scale, showing that the reliability profile for some quantum algorithms is scale-dependent, with increased impact from radiation-induced faults as we increase the number of qubits. Finally, we also consider multi qubits faults, showing that they are much more critical than single faults. The fault injector and the data presented in this paper are available in a public repository to allow further analysis

Anton's Syndrome and Eugenics

Anton's syndrome is arguably the most striking form of anosognosia. Patients with this syndrome behave as if they can see despite their obvious blindness. Although best known for his description of asomatognosia and visual anosognosia, Gabriel Anton (1858-1933) made other significant contributions to the clinical neurosciences, including pioneering work in neurosurgery, neuropsychology, and child psychiatry. However, it has not been recognized in the English literature that Anton was also a dedicated advocate of eugenics and racial hygiene. This paper provides a case of Anton's syndrome and puts the works of Gabriel Anton into their historic context

Incidence of Chlamydia trachomatis and other potential pathogens in neonatal conjunctivitis.

Abstract Objective: Ocular infection in neonatology is a permanent and important health problem. To improve primary attention, prevention, and control, the study of the potential bacterial etiology of all consecutive cases of conjunctivitis was incorporated as a regular procedure in primary care from July 1995 to December 1998. Materials and Methods: Prof. A. Posadas Hospital (Great Buenos Aires) has an average of 4294 births per year. This report analyzes the results obtained in 332 infants (age range, 0–30 d) with conjunctivitis. Clinical conjunctivitis was diagnosed in inpatients and outpatients by the same specialized staff. Isolation and characterization of bacteria were done by conventional microbiologic methods, including specific search for Neisseria gonorrhoeae and Chlamydia trachomatis . Chlamydia trachomatis was studied by antigen immunodetection and polymerase chain reaction, and genotyped by restriction fragment length polymorphism. Results: Conjunctivitis had an incidence (cases per 1000 live births) of 39.6 in 1995, 25.3 in 1996, 15.4 in 1997, and 15.2 in 1998. Microbial growth was detected in 167 (50.3%) of 332 cases. Ocular C. trachomatis infection was detected in 26 cases (7.83%). Five of seven isolates in tissue cultures belonged to type E and two to type G. Bacteria from respiratory ecology were the main isolates: Haemophilus influenzae (16.9%), Streptococcus pneumoniae (12.3%), and Staphylococcus aureus (8.7%). Haemophilus influenzae isolates were not serotyped and 17.2% of them were β-lactamase producers. In 15 cases both H. influenzae and S. pneumoniae were isolated together. Of S. pneumoniae , 4,9% were oxacillin resistant. Conclusions: There has been a decline in the total number of cases of neonatal conjunctivitis, but the disease is still an important health problem. Chlamydia trachomatis also shows a decreasing profile with an incidence of (cases per 1000 live births) 4.39 in 1995, 1.85 in 1996, 1.01 in 1997, and 0.78 in 1998, and a tendency to show more incidence in spring-summer and significant accumulation of cases in babies between 7 and 9 days of age. Haemophilus influenzae alone (12.3%) or associated with S. pneumoniae (4.5%) appears as a prevalent potential bacterial pathogen. A significant accumulation of H. influenzae and S. pneumoniae cases occurs in winter. In 47.6% of cases, there was no bacterial growth. No significant seasonal differences in percentage of negative cultures or among the three-day age groups were detected. Neisseria gonorrhoeae was not found associated with ophthalmia neonatorum in this series