Donaldson-Witten theory and indefinite theta functions

We consider partition functions with insertions of surface operators of topologically twisted N=2, SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold has positive scalar curvature, Moore and Witten have shown that the partition function is completely determined by the integral over the Coulomb branch parameter $a$, while more generally the Coulomb branch integral captures the wall-crossing behavior of both Donaldson polynomials and Seiberg-Witten invariants. We show that after addition of a Q-exact surface operator to the Moore-Witten integrand, the integrand can be written as a total derivative to the anti-holomorphic coordinate $\bar a$ using Zwegers' indefinite theta functions. In this way, we reproduce G\"ottsche's expressions for Donaldson invariants of rational surfaces in terms of indefinite theta functions for any choice of metric.Comment: 23 pages + appendices, comments welcome. v2: published versio

Algorithmic trading on Finnish stock market using Deep Reinforcement Learning

The advancement in machine learning due to increased computational capacity and novel algorithms have resulted in copious amount of research done on financial markets where machine learning is harnessed for stock market trading. The promising results of deep learning in many fields have encouraged researchers and practitioners to utilize this novel technique to come up with ground-breaking algorithmic trading strategies that could consistently generate excessive returns. The merits of deep learning are extensive, such as its ability for feature learning, scalability, flexibility, and adaptability, which all are relevant features when considering financial markets. One of the deep learning approaches is deep reinforcement learning, which trains the algorithm by giving feedback for its actions in given environment. The algorithm aims to maximize the feedback it receives, thus convergencing to an optimal trading strategy. This study aims to come up with an algorithmic trading strategy that can consistently outperform benchmark strategies by using Deep Q-Networks, a type of deep reinforcement learning. Additionally, the effect of introducing dynamic stop loss and take profit levels in feedback mechanism is studied. The research is conducted between the beginning of 2022 and the end of 2023 on three individual stocks on Finnish stock market and a broader market index. The information provided for the deep neural network are daily open price, lowest and highest price of the day, closing price, and trading volume of the day. The model performance is evaluated, such as its ability to learn over time, and ultimately the proposed trading strategy is benchmarked against other trading strategies. The model performance analysis suggested that the complexity of stock market leads to large variations in model practicality. Although some improvement was detected where the average reward and Sharpe ratio increased over time, most circumstances indicated high fluctuation and randomness in the model. The proposed trading strategy did outperform benchmark strategies in multiple simulations, but also underperformed considerably in many other scenarios. Therefore, the results show that this strategy can not be used to consistently outperform the benchmark. Furthermore, the use of stop loss and take profit limits to guide the trading algorithm towards optimal trading policy was studied. Contrary to guiding the agent, the trading boundaries further contributed to the complexity of trading environment making the model performance more volatile. This was since crossing stop loss or take profit level triggered relatively large on-off reward which complicated the trading environment to a greater degree. The algorithm was able to generate higher average rewards, but at the cost of stability. Therefore, the application of trading limits into the feedback function did not enhance the performance of the deep q-network strategy.Koneoppimisen kehitys lisääntyneen laskentatehon ja uusien algoritmien ansiosta on johtanut runsaaseen määrään tutkimuksia, joissa koneoppimista hyödynnetään osakemarkkinoiden kaupankäynnissä. Syväoppimisen positiiviset tulokset monilla aloilla ovat rohkaisseet tutkijoita ja ammattilaisia hyödyntämään tätä uutta tekniikkaa kehittääkseen uusia algoritmisia kaupankäyntistrategioita, jotka kykenevät johdonmukaisesti tuottamaan ylituottoa. Syväoppimisen hyödyt ovat laajat, kuten sen kyky ominaisuuksien oppimiseen, skaalautuvuus, joustavuus ja sopeutumiskyky, jotka kaikki ovat olennaisia ominaisuuksia finanssimarkkinoiden kannalta. Yksi syväoppimisen lähestymistavoista on syvävahvistusoppiminen, jossa algoritmia koulutetaan antamalla palautetta sen toiminnasta tietyssä ympäristössä. Algoritmi pyrkii maksimoimaan saamansa palautteen ja siten löytämään optimaalisen kaupankäyntistrategian. Tämä tutkimus pyrkii kehittämään algoritmisen kaupankäyntistrategian, joka voi johdonmukaisesti suoriutua paremmin kuin vertailustrategiat käyttämällä syviä Q-verkkoja, joka on yksi syvävahvistusoppimisen menetelmistä. Lisäksi tutkielmassa tutkitaan dynaamisien stop loss ja take profit -tasojen käytön vaikutusta palautemekanismissa. Tutkimus tehdään vuoden 2022 alusta vuoden 2023 loppuun kolmella yksittäisellä osakkeella Suomen osakemarkkinoilla sekä laajemmalla markkinaindeksillä. Syvälle neuroniverkolle annettu tieto sisältää päivittäisen avauskurssin, päivän alimman ja korkeimman hinnan, päätöskurssin ja päivän kaupankäyntivolyymit. Mallin suorituskykyä arvioidaan, kuten sen kykyä oppia ajan myötä, ja lopulta kehitettyä kaupankäyntistrategiaa vertaillaan muihin kaupankäyntistrategioihin. Mallin suorituskyvyn analysointi osoittaa, että osakemarkkinoiden monimutkaisuus johtaa suuriin vaihteluihin mallin toimivuudessa. Vaikka kehitystä havaittiin, kun keskimääräinen palkkio ja Sharpe-luku kasvoivat ajan myötä, useimmissa tilanteissa mallissa ilmeni kuitenkin suurta vaihtelua ja satunnaisuutta. Kehitetty kaupankäyntistrategia suoriutui paremmin kuin vertailustrategiat useissa eri simuloinneissa, mutta myös alisuoriutui merkittävästi monissa muissa skenaarioissa. Tulokset osoittavat, että tätä strategiaa ei voida käyttää johdonmukaisesti tuottamaan ylituottoja verrattuna vertailustrategioihin. Lisäksi stop loss ja take profit -rajatasojen käyttöä algoritmin tueksi tutkittiin. Päinvastoin kuin että rajatasot olisivat ohjanneet algoritmia, kaupankäyntirajojen käyttö lisäsi kaupankäyntiympäristön monimutkaisuutta, mikä teki mallin suorituskyvystä entistä epävakaampaa. Tämä johtui siitä, että stop loss tai take profit -tason ylittäminen laukaisi suhteellisen suuren kertaluonteisen palkkion, joka monimutkaisti kaupankäyntiympäristöä entisestään. Algoritmi pystyi tuottamaan korkeampia keskimääräisiä palkkioita, mutta tämä heikensi mallin vakautta. Näin ollen kaupankäynnin rajojen soveltaminen palautemekanismiin ei parantanut syvää Q-verkkoa hyödyntävän strategian suorituskyky

INAPPROPRIATE S-ICD PATIENT RECEIVES FALSE POSITIVE SHOCKS

Subcutaneous implantable cardioverter defibrillator (S-ICD) protects the patients at risk for sudden cardiac death while leaving the heart and vasculature untouched. It provides life-saving therapy, but may also deliver inappropriate therapy. Presented case demonstrates a possibility of S-ICD therapy induction due to double-counting. It was original caused by lack of suitable sensing vectors and the solution was possible just particularly. As the inter-individual variability of subcutaneous cardiac signal is considerable, the patient screening should be necessary for identification of such patients, which have an unsuitable subcutaneous sensing signals

THE USE OF PACEMAKER DIAGNOSTICS FOR SUPPORTING THE ANTICOAGULATION TREATMENT MANAGEMENT

In this work, the analysis of data on atrial fibrillation (AF) burden from dual chamber pacemakers is used for supporting the anticoagulation treatment management. The aim is to evaluate the benefit of basic diagnostic functions to support oral anticoagulation therapy in patients with atrial fibrillation. These patients have increased risk of thromboembolism. If patients have an implanted pacemaker, the device’s diagnostic features monitor the frequency and duration of atrial fibrillation episodes. This data can then be used for further decisions. Statistical data processing was performed on a group of 117 patients with an implanted dual chamber pacemaker. From these results, we evaluated the benefits of the algorithms. In the whole group, a trend was observed in increase of the AF burden between the two monitored periods. The increase of AF burden occurred in 17 patients, while the decrease occurred in 6 patients only. Using simple logic functions, the numbers of patients with different binary values of the presence of AF, the presence of oral anticoagulation therapy, the risk CHA2DS2-VASc score and the values of AF burden were determined. Thus, in the whole group of patients, the diagnostic functions of the implanted devices contributed to the change in oral anticoagulation therapy for 24% of patients

Pomiar parametrów elektrycznych i testowanie implantowanych cardio-stymulatorów

The aim of the work was measurement and testing of implantable cardioverter - defibrillator (ICDs) device. There was realised electronic measuring circuit which substitutes human body tissue during the device accuracy testing. This circuit enables to measure defibrillation shock discharge in the whole energy range (0.1- 41J). The presented measuring and testing procedures can easy check-up precision of parameters and functionality of embedded electronic device circuit’s part of the ICDs. Presented suggestion and results of this work can be implemented as verification procedure in various types of ICDs and also pacemakers before their implantation as well.W artykule przedstawiono wpływ indukcji i częstotliwości na straty w żelazie w blachach elektrotechnicznych wykorzystywanych w dławikach pracujących w filtrach wyższych harmonicznych. Podano uogólnioną zależność pozwalającą na obliczenie strat histerezowych i wiroprądowych z uwzględnieniem zastępczej eliptycznej pętli histerezy. Otrzymane wyniki porównano z pomiarami. Wprowadzony do rozważań współczynnik An zależy w praktyce od średniej wartości indukcji występującej w przekroju poprzecznym rdzenia. Uogólniona zależność zawierająca współczynnik An może być stosowana w szerokim zakresie częstotliwości

Operational Valuation for Energy Storage under Multi-stage Price Uncertainties

This paper presents an analytical method for calculating the operational value of an energy storage device under multi-stage price uncertainties. Our solution calculates the storage value function from price distribution functions directly instead of sampling discrete scenarios, offering improved modeling accuracy over tail distribution events such as price spikes and negative prices. The analytical algorithm offers very high computational efficiency in solving multi-stage stochastic programming for energy storage and can easily be implemented within any software and hardware platform, while numerical simulation results show the proposed method is up to 100,000 times faster than a benchmark stochastic-dual dynamic programming solver even in small test cases. Case studies are included to demonstrate the impact of price variability on the valuation results, and a battery charging example using historical prices for New York City

Taming Binarized Neural Networks and Mixed-Integer Programs

There has been a great deal of recent interest in binarized neural networks, especially because of their explainability. At the same time, automatic differentiation algorithms such as backpropagation fail for binarized neural networks, which limits their applicability. By reformulating the problem of training binarized neural networks as a subadditive dual of a mixed-integer program, we show that binarized neural networks admit a tame representation. This, in turn, makes it possible to use the framework of Bolte et al. for implicit differentiation, which offers the possibility for practical implementation of backpropagation in the context of binarized neural networks. This approach could also be used for a broader class of mixed-integer programs, beyond the training of binarized neural networks, as encountered in symbolic approaches to AI and beyond.Comment: 9 pages, 4 figure