arXiv subjects

Martin Kolar

Publications and source records attributed to Martin Kolar.

At least 19 recordsLinked to original sources

arXiv2026

The Complete Catalog of Gamma-Ray Transients Observed by GRBAlpha & VZLUSAT-2 CubeSat Missions

We present the largest sample of gamma-ray transients observed by any CubeSat mission so far. Observations were acquired by a 1U CubeSat GRBAlpha, the smallest astrophysical space observatory, and a 3U CubeSat VZLUSAT-2. Both missions were technological pathfinders and carried a novel CsI scintillator-based detector read-out by silicon photomultipliers. They operated on Sun-synchronous low Earth orbits below 550 km for about four years; GRBAlpha between March 2021 and June 2025 while VZLUSAT-2 between January 2022 and November 2025. Despite being technological experiments, they observed over 300 gamma-ray transients including gamma-ray bursts (GRBs), solar flares, soft gamma repeaters and one outburst from an X-ray binary. Among these are the two brightest GRBs ever observed, GRB 221009A and GRB 230307A, without saturation and GRBs at redshifts up to z=4.2. GRBAlpha also contributed to the InterPlanetary Network. Regular monitoring of transients was demonstrated by a detection rate of two transients or one GRB a week and the shortest time between two subsequent detections of only 42 minutes. We show that a constellation of nanosatellites around the Earth would observe at least 60% of Fermi/GBM GRBs with 5$\sigma$ significance and over 90% at 3$\sigma$ level. GRBAlpha and VZLUSAT-2 prove that routine monitoring of the gamma-ray sky can also be done by low-cost and quickly developed nanosatellite missions.

astro-ph.HE↗

arXiv2026

Long-term performance of SiPMs in space environment measured by GRBAlpha, GRBBeta, and VZLUSAT-2 CubeSats

In this work, we report the successful application of silicon photomultipliers (SiPMs) in gamma-ray burst (GRB) detectors used in CubeSats operating in the low Earth orbit (LEO) radiation environment. It is known that SiPMs are susceptible to radiation damage, leading to an increase in the dark count rate. This results in an increase in the low-energy threshold in detectors combining SiPMs and scintillators. Despite this drawback, they became popular in gamma-ray detectors on CubeSats due to their low operating voltage, small size and fast response. Therefore, it is important to characterise their long-term performance in the space environment. Here, we describe the changes in the dark count rate and low-energy threshold of S13360-3050PE multi-pixel photon counters (MPPCs) by Hamamatsu Photonics K.K., using measurements from the GRBAlpha, GRBBeta, and VZLUSAT-2 CubeSats. In the case of GRBAlpha, the measurement of SiPM performance in space lasted over 4 years. GRBAlpha was a 1U CubeSat launched on 2021/03/22 to a 550 km altitude polar orbit carrying a CsI(Tl) scintillator GRB detector employing eight MPPCs and sensitive in the range of ~30-900 keV. GRBAlpha de-orbited on 2025/06/09. VZLUSAT-2 was a 3U CubeSat launched on 2022/01/13 to a 535 km altitude polar orbit and de-orbited on 2025/11/30. GRBBeta was launched on 2024/07/09 to a 580 km altitude, 62{\deg} inclination orbit. Both VZLUSAT-2 and GRBBeta carry detectors similar to the one on GRBAlpha. We have flight-proven the Hamamatsu MPPCs S13360-3050 PE and demonstrated that SiPMs, shielded by 2.5 mm of PbSb alloy, can be used in a LEO environment on a scientific mission lasting beyond 4 years. This shows the potential for SiPMs to be employed in future satellites.

astro-ph.IM↗

arXiv2026

GRBAlpha, VZLUSAT-2 and GRBBeta -- GRB observations with CubeSats

Results from GRBAlpha, VZLUSAT-2 and GRBBeta CubeSats and their on-board gamma-ray detectors for monitoring transients are summarised in this article. GRBAlpha was a 1U CubeSat launched in March 2021 to a 550 km altitude polar orbit carrying a CsI(Tl) scintillator gamma-ray burst (GRB) detector with a sensitive range of approximately 30-900 keV. It successfully operated for over four years until June 2025 when it de-orbited. VZLUSAT-2 was a 3U CubeSat launched in January 2022 to a 535 km altitude polar orbit and de-orbited in November 2025 after almost four years of smooth operation. It carried on board two GRB detectors very similar to the one used on GRBAlpha. Both missions have detected about 360 gamma-ray transients, including over 170 long and short gamma-ray bursts (GRBs), and including the most intense GRB ever recorded GRB 221009A and the second brightest GRB 230307A. The new family member, GRBBeta 2U CubeSat, integrated at Masaryk University, was launched in July 2024 to a 580 km altitude, 62 degree inclination orbit. It has been detecting GRBs since its launch without any trouble. Gamma-ray detectors on these nanosatellites are based on CsI(Tl) scintillator readout by silicon photomultipliers (SiPMs). These missions also provide a unique opportunity to study the radiation damage of SiPMs in the low Earth orbit environment and monitor the radiation belts. We have demonstrated that CubeSats can be used in missions lasting beyond three years and routinely detect GRBs.

astro-ph.HE↗

arXiv2024

Characterization of more than three years of in-orbit radiation damage of SiPMs on GRBAlpha and VZLUSAT-2 CubeSats

Silicon photomultipliers (SiPMs) are prone to radiation damage which causes an increase of dark count rate. This leads to an increase in low-energy threshold in a gamma-ray detector combining SiPM and a scintillator. Despite this drawback, they are becoming preferred for scintillator-based gamma-ray detectors on CubeSats due to their low operation voltage, small size, linear response to low light intensity and fast response. This increasing popularity of SiPMs among new spaceborne missions makes it important to characterize their long-term performance in the space environment. In this work, we report the change of the dark count rate and low-energy threshold of S13360-3050 PE multi-pixel photon counters (MPPCs) by Hamamatsu, using measurements acquired by the GRBAlpha and VZLUSAT-2 CubeSats at low Earth orbit (LEO) spanning over three years. Such a long measurement of the performance of MPPCs in space has not been published before. GRBAlpha is a 1U CubeSat launched on March 22, 2021, to a 550 km altitude sun-synchronous polar orbit (SSO) carrying on board a gamma-ray detector based on CsI(Tl) scintillator readout by eight MPPCs and regularly detecting gamma-ray transients such as gamma-ray bursts and solar flares in the energy range of ~30-900 keV. VZLUSAT-2 is a 3U CubeSat launched on January 13, 2022 also to a 535 km altitude SSO carrying on board, among other payloads, two gamma-ray detectors similar to the one on GRBAlpha. We have flight-proven the Hamamatsu MPPCs S13360-3050 PE and demonstrated that MPPCs, shielded by 2.5 mm of PbSb alloy, can be used in LEO environment on a scientific mission lasting beyond three years. This manifests the potential of MPPCs being employed in future satellites.

astro-ph.IM↗

arXiv2024

Forecasting Mortality Rates: Unveiling Patterns with a PCA-GEE Approach

Principal Component Analysis (PCA) is a widely used technique in exploratory data analysis, visualization, and data preprocessing, leveraging the concept of variance to identify key dimensions in datasets. In this study, we focus on the first principal component, which represents the direction maximizing the variance of projected data. We extend the application of PCA by treating its first principal component as a covariate and integrating it with Generalized Estimating Equations (GEE) for analyzing age-specific death rates (ASDRs) in longitudinal datasets. GEE models are chosen for their robustness in handling correlated data, particularly suited for situations where traditional models assume independence among observations, which may not hold true in longitudinal data. We propose distinct GEE models tailored for single and multipopulation ASDRs, accommodating various correlation structures such as independence, AR(1), and exchangeable, thus offering a comprehensive evaluation of model efficiency. Our study critically evaluates the strengths and limitations of GEE models in mortality forecasting, providing empirical evidence through detailed model specifications and practical illustrations. We compare the forecast accuracy of our PCA-GEE approach with the Li-Lee and Lee-Carter models, demonstrating its superior predictive performance. Our findings contribute to an enhanced understanding of the nuanced capabilities of GEE models in mortality rate prediction, highlighting the potential of integrating PCA with GEE for improved forecasting accuracy and reliability.

stat.AP↗

arXiv2024

Mortality Modelling using Generalized Estimating Equations

This paper presents an application of Generalized Estimating Equations (GEE) for analyzing age-specific death rates (ASDRs), constituting a longitudinal dataset with repeated measurements over time. GEE models, known for their robustness in handling correlated data, offer a reliable solution when individual data records lack independence, thus violating the commonly assumed independence and identically distributed (iid) condition in traditional models. In the context of ASDRs, where correlations emerge among observations within age groups, two distinct GEE models for single and multipopulation ASDRs are introduced, providing robust estimates for regression parameters and their variances. We explore correlation structures, encompassing independence, AR(1), unstructured, and exchangeable structures, offering a comprehensive evaluation of GEE model efficiency in both single and multipopulation ASDRs. We critically examines the strengths and limitations of GEE models, shedding light on their applicability for mortality forecasting. Through detailed model specifications and empirical illustrations, the study contributes to an enhanced understanding of the nuanced capabilities of GEE models in predicting mortality rates.

stat.AP↗

arXiv2023

Forecasting Mortality Rates: A Linear Mixed-Effects Model

A linear mixed-effects (LME) model is proposed for modelling and forecasting single and multi-population age-specific death rates (ASDRs). The innovative approach that we take in this study treats age, the interaction between gender and age, their interactions with predictors, and cohort as fixed effects. Furthermore, we incorporate additional random effects to account for variations in the intercept, predictor coefficients, and cohort effects among different age groups of females and males across various countries. In the single-population case, we will see how the random effects of intercept and slope change over different age groups. We will show that the LME model is identifiable. Using simulating parameter uncertainty in the LME model, we will calculate 95% uncertainty intervals for death rate forecasts. We will use data from the Human Mortality Database (HMD) to illustrate the procedure. We assess the predictive performance of the LME model in comparison to the Lee-Carter (LC) models fitted to individual populations. Additionally, we evaluate the predictive accuracy of the LME model relative to the Li-Lee (LL) model. Our results indicate that the LME model provides a more precise representation of observed mortality rates within the HMD, demonstrates robustness in calibration rate selection, and exhibits superior performance when contrasted with the LC and LL models.

stat.AP↗

arXiv2023

Mortality Forecasting with Generalized Additive Mixed Models

This study introduces a novel generalized additive mixed model (GAMM) for mortality modelling, utilizing the mortality covariate $k_t$ as proposed by Dastranj-Kolar. Our findings indicate that the GAMM effectively addresses this shortcoming. Given that ASDRs constitute longitudinal data, as noted in the LME framework, the GAMM offers a more flexible and suitable approach for both modeling and forecasting mortality rates. Empirical evaluations using data from the Human Mortality Database (HMD) demonstrate the GAMM's strong ability to reproduce observed mortality patterns with high precision. Comparative analyses show that the GAMM consistently outperforms the LL model in both in-sample fit and out-of-sample forecasting across multiple populations. These results highlight the GAMM's potential as a robust and reliable tool for mortality modeling and long-term demographic forecasting.

stat.AP↗

arXiv2023

The peak-flux of GRB 221009A measured with GRBAlpha

The brightest gamma-ray burst ever observed, long-duration GRB 221009A, was detected by GRBAlpha nano-satellite without saturation. We present light curves of the prompt emission in 13 energy bands, from 80 keV to 950 keV, and perform a spectral analysis to calculate the peak flux and peak isotropic-equivalent luminosity. Since the satellite's attitude information is not available for the time of this GRB, more than 200 incident directions were probed in order to find the median luminosity and its systematic uncertainty. We found that the peak flux in the $80-800$ keV range (observer frame) was $F_{\rm{ph}}^{\rm{p}}=1300_{-200}^{+1200}$ ph cm$^{-2}$s$^{-1}$ or $F_{\rm{erg}}^{\rm{p}}=5.7_{-0.7}^{+3.7}\times10^{-4}$ erg cm$^{-2}$s$^{-1}$ and the fluence in the same energy range of the first GRB episode lasting 300 s, which was observable by GRBAlpha, was $S=2.2_{-0.3}^{+1.4}\times10^{-2}$ erg cm$^{-2}$ or $S^{\rm{bol}}=4.9_{-0.5}^{+0.8}\times10^{-2}$ erg cm$^{-2}$ for the extrapolated range of $0.9-8,690$ keV. We infer the isotropic-equivalent released energy of the first GRB episode to be $E_{\rm{iso}}^{\rm{bol}}=2.8_{-0.5}^{+0.8}\times10^{54}$ erg in the $1-10,000$ keV band (rest frame at $z=0.15$). The peak isotropic-equivalent luminosity in the $92-920$ keV range (rest frame) was $L_{\rm{iso}}^{\rm{p}}=3.7_{-0.5}^{+2.5}\times10^{52}$ erg s$^{-1}$ and the bolometric peak isotropic-equivalent luminosity was $L_{\rm{iso}}^{\rm{p,bol}}=8.4_{-1.5}^{+2.5}\times10^{52}$ erg s$^{-1}$ (4 s scale) in the $1-10,000$ keV range (rest frame). The peak emitted energy is $E_p^\ast=E_p(1+z)=1120\pm470$ keV. Our measurement of $L_{\rm{iso}}^{\rm{p,bol}}$ is consistent with the Yonetoku relation. It is possible that, due to the spectral evolution of this GRB and orientation of GRBAlpha at the peak time, the true values of peak flux, fluence, $L_{\rm{iso}}$, and $E_{\rm{iso}}$ are even higher. [abridged]

astro-ph.HE↗

arXiv2019

Infinitesimal symmetries of weakly pseudoconvex manifolds

We classify the Lie algebras of infinitesimal CR automorphisms of weakly pseudoconvex hypersurfaces of finite multitype in $\mathbb C^N$. In particular, we prove that such manifolds admit neither nonlinear rigid automorphisms, nor real or nilpotent rotations. As a consequence, this leads to a proof of a sharp 2-jet determination result for local automorphisms. Moreover, for hypersurfaces which are not balanced, CR automorphisms are uniquely determined by their 1-jets. The same classification is derived also for special models, given by sums of squares of polynomials. In particular, in the case of homogeneous polynomials the Lie algebra of infinitesimal CR automorphisms is always three graded. The results provide an important necessary step for solving the local equivalence problem on weakly pseudoconvex manifolds.

math.CV↗

arXiv2019

A complete normal form for everywhere Levi degenerate hypersurfaces in $\mathbb C^{3}$

$2$-nondegenerate real hypersurfaces in complex manifolds play an important role in CR-geometry and the theory of Hermitian Symmetric Domains. In this paper, we construct a complete convergent normal form for everywhere $2$-nondegenerate real-analytic hypersurfaces in complex $3$-space. We do so by developing the homological approach of Chern-Moser in the $2$-nondegenerate setting. This seems to be the first such construction for hypersurfaces of infinite Catlin multitype. Our approach is based on using a rational (nonpolynomial) model for everywhere $2$-nondegenerate hypersurfaces, which is the local realization due to Fels-Kaup of the well known tube over the light cone. As an application, we obtain, in the spirit of Chern-Moser theory, a criterion for the local sphericity (i.e. local equivalence to the model) for a $2$-nondegenerate hypersurface in terms of its normal form. As another application, we obtain an explicit description of the moduli space of everywhere $2$-nondegenerate hypersurfaces.

math.CV↗

arXiv2017

Nonlinear CR automorphisms of Levi degenerate hypersurfaces and a new gap phenomenon

We give a complete classification of polynomial models for smooth real hypersurfaces of finite Catlin multitype in $\mathbb C^3$, which admit nonlinear infinitesimal CR automorphisms. As a consequence, we obtain a sharp 1-jet determination result for any smooth hypersurface with such model. The results also prove a conjecture of the first author about the origin of such nonlinear automorphisms (AIM list of problems, 2010). As another consequence, we describe all possible dimensions of the Lie algebra of infinitesimal CR automorphisms, which leads to a new "secondary" gap phenomenon.

math.CV↗

arXiv2016

Normal forms in Cauchy-Riemann Geometry: a survey

One of effective ways to solve the equivalence problem and describe moduli spaces for real submanifolds in complex space is the normal form approach. In this survey, we outline some normal form constructions in CR-geometry and formulate a number of open problems.

math.CV↗

arXiv2015

Higher order symmetries of real hypersurfaces in $\Bbb C^3.$

We study nonlinear automorphisms of Levi degenerate hypersurfaces of finite multitype. By recent results of Kolar, Meylan and Zaitsev, the Lie algebra of infinitesimal CR automorphisms may contain a graded component consisting of nonlinear vector fields of arbitrarily high degree, which has no analog in the classical Levi nondegenerate case, or in the case of finite type hypersurfaces in $\mathbb C^2$. We analyze this phenomenon for hypersurfaces of finite Catlin multitype in complex dimension three. The results provide a complete classification of such manifolds. As a consequence, we show on which hypersurfaces 2-jets are not sufficient to determine an automorphism. The results also confirm a conjecture about the origin of nonlinear automorphisms of Levi degenerate hypersurfaces, formulated by the first author (AIM 2010).

math.CV↗

arXiv2009

The Catlin multitype and biholomorphic equivalence of models

We consider an alternative approach to a fundamental CR invariant - the Catlin multitype. It is applied to a general smooth hypersurface in $\mathbbC^{n+1}$, not necessarily pseudoconvex. Using this approach, we prove biholomorphic equivalence of models, and give an explicit description of biholomorphisms between different models. A constructive finite algorithm for computing the multitype is described. The results can be viewed a necessary step in understanding local biholomorphic equivalence of Levi degenerate hypersurfaces of finite Catlin multitype.

math.CV↗

arXiv2008

Higher order invariants of Levi degenerate hypersurfaces

The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and analogous results for finite groups. The second part considers hypersurfaces of finite Catlin multitype and the Kohn-Nirenberg phenomenon in higher dimensions. We give a necessary condition for local convexifiability of a class of pseudoconvex hypersurfaces in $\mathbb C^{n+1}$.

math.CV↗

arXiv2007

Local equivalence of symmetric hypersurfaces in $\mathbb C^2$

The Chern-Moser normal form and its analog on finite type hypersurfaces in general do not respect symmetries. Extending the work of N. K. Stanton, we consider the local equivalence problem for symmetric Levi degenerate hypersurfaces of finite type in $\mathbb C^2$. The results give for all such hypersurfaces a complete normalization which respects the symmetries. In particular, they apply to tubes and rigid hypersurfaces, providing an effective classification. The main tool is a complete normal form constructed for a general hypersurface with a tube model. As an application, we describe all biholomorphic maps between tubes, answering a question posed by N. Hanges.

math.CV↗

arXiv2007

The local equivalence problem in CR geometry

This article is dedicated to the centenary of the local CR equivalence problem, formulated by Henri Poincaré in 1907. The first part gives an account of Poincaré's heuristic counting arguments, suggesting existence of infinitely many local CR invariants. Then we sketch the beautiful completion of Poincaré's approach to the problem in the work of Chern and Moser on Levi nondegenerate hypersurfaces. The last part is an overview of recent progress in solving the problem on Levi degenerate manifolds.

math.CV↗