Numerical Analysis of Target Enumeration via Euler Characteristic Integrals: 2 Dimensional Disk Supports

In this paper, we look at the types of errors that are introduced when using the Euler characteristic integral approach to count the number of targets in a discrete sensor field. In contrast to other theoretical analyses, this paper examines discrete sensor fields rather than continuous ones. The probabilities of first and second order errors are worked out combinatorially, and a general formula is found which is discovered to be proportional to much higher order errors. Asymptotic results are also derived. Thus, this work gives us the bias of the Euler characteristic integral as a point estimator for the number of targets in a sensor field, and a general understanding of how the Euler characteristic integral fails, or more often succeeds.Comment: 20 pages, 12 figures, 2 table

Methods of Technical Prognostics Applicable to Embedded Systems

Hlavní cílem dizertace je poskytnutí uceleného pohledu na problematiku technické prognostiky, která nachází uplatnění v tzv. prediktivní údržbě založené na trvalém monitorování zařízení a odhadu úrovně degradace systému či jeho zbývající životnosti a to zejména v oblasti komplexních zařízení a strojů. V současnosti je technická diagnostika poměrně dobře zmapovaná a reálně nasazená na rozdíl od technické prognostiky, která je stále rozvíjejícím se oborem, který ovšem postrádá větší množství reálných aplikaci a navíc ne všechny metody jsou dostatečně přesné a aplikovatelné pro embedded systémy. Dizertační práce přináší přehled základních metod použitelných pro účely predikce zbývající užitné životnosti, jsou zde popsány metriky pomocí, kterých je možné jednotlivé přístupy porovnávat ať už z pohledu přesnosti, ale také i z pohledu výpočetní náročnosti. Jedno z dizertačních jader tvoří doporučení a postup pro výběr vhodné prognostické metody s ohledem na prognostická kritéria. Dalším dizertačním jádrem je představení tzv. částicového filtrovaní (particle filtering) vhodné pro model-based prognostiku s ověřením jejich implementace a porovnáním. Hlavní dizertační jádro reprezentuje případovou studii pro velmi aktuální téma prognostiky Li-Ion baterii s ohledem na trvalé monitorování. Případová studie demonstruje proces prognostiky založené na modelu a srovnává možné přístupy jednak pro odhad doby před vybitím baterie, ale také sleduje možné vlivy na degradaci baterie. Součástí práce je základní ověření modelu Li-Ion baterie a návrh prognostického procesu.The main aim of the thesis is to provide a comprehensive overview of technical prognosis, which is applied in the condition based maintenance, based on continuous device monitoring and remaining useful life estimation, especially in the field of complex equipment and machinery. Nowadays technical prognosis is still evolving discipline with limited number of real applications and is not so well developed as technical diagnostics, which is fairly well mapped and deployed in real systems. Thesis provides an overview of basic methods applicable for prediction of remaining useful life, metrics, which can help to compare the different approaches both in terms of accuracy and in terms of computational/deployment cost. One of the research cores consists of recommendations and guide for selecting the appropriate forecasting method with regard to the prognostic criteria. Second thesis research core provides description and applicability of particle filtering framework suitable for model-based forecasting. Verification of their implementation and comparison is provided. The main research topic of the thesis provides a case study for a very actual Li-Ion battery health monitoring and prognostics with respect to continuous monitoring. The case study demonstrates the prognostic process based on the model and compares the possible approaches for estimating both the runtime and capacity fade. Proposed methodology is verified on real measured data.

Book review: Congo

"Congo." Thomas Turner. Polity. April 2013. --- The Democratic Republic of Congo has become one of the world’s bloodiest hot spots, and despite recent peace agreements and democratic elections, the country is still plagued by army and militia violence. Thomas Turner‘s insightful book discusses how the the deep–rooted causes of conflict have not been adequately addressed, and shows how current attempts to rebuild the shattered state and society of DRC are doomed to fail. Joel Krupa recommends this illuminating and important book for its passionately written chapters and rigorous analysis

The Taste Remembered. On the Extraordinary Testimony of the Women from Terezín

The article presents an attempt to combine food studies (also termed the anthropology of food) with scholarly reflection regarding memory. The analysis focuses on the book entitled In Memory’s Kitchen. A Legacy from the Women of Terezin [ed. Cara de Silva 2006], containing recipes for Jewish dishes written down by women from the Teresienstadt ghetto. But some dozen recipes that have survived do not make it a cookbook, which is essentially meant to be functional. It is more of a remembrance, a testament, and also a source of knowledge of culture at a given point in time. It is also a testimonial document. Recipes collected by de Silva tell much about their authors. They define their roles as wives and mothers. In addition, the Terezin notes point to a culinary heritage, the religious principles of food preparation and the social and economical conditions that shaped the culinary preferences and the diets of women locked in the ghetto. The article demonstrates that the actions of preparing and consuming food are a constantly repeated practice, which is connected in a network of relationships with other practices. This practice it is anchored in the everyday life, embedded in the family’s biography and fused with childhood memories. Food is presented as a sign of identity, the social bond and the community of family and friends, and also as a gift that serves to uphold these ties

Complex oscillations in the delayed Fitzhugh-Nagumo equation

Motivated by the dynamics of neuronal responses, we analyze the dynamics of the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system provides a canonical example of a canard explosion for sufficiently small delays. Beyond this regime, delays significantly enrich the dynamics, leading to mixed-mode oscillations, bursting and chaos. These behaviors emerge from a delay-induced subcritical Bogdanov-Takens instability arising at the fold points of the S-shaped critical manifold. Underlying the transition from canard-induced to delay-induced dynamics is an abrupt switch in the nature of the Hopf bifurcation

On stationarity of Lagrangian observations of passive tracer velocity in a compressible environment

We study the transport of a passive tracer particle in a steady strongly mixing flow with a nonzero mean velocity. We show that there exists a probability measure under which the particle Lagrangian velocity process is stationary. This measure is absolutely continuous with respect to the underlying probability measure for the Eulerian flow.Comment: Published at http://dx.doi.org/10.1214/105051604000000945 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Canard explosion in delayed equations with multiple timescales

We analyze canard explosions in delayed differential equations with a one-dimensional slow manifold. This study is applied to explore the dynamics of the van der Pol slow-fast system with delayed self-coupling. In the absence of delays, this system provides a canonical example of a canard explosion. We show that as the delay is increased a family of `classical' canard explosions ends as a Bogdanov-Takens bifurcation occurs at the folds points of the S-shaped critical manifold.Comment: arXiv admin note: substantial text overlap with arXiv:1404.584