Regular decomposition of large graphs and other structures: scalability and robustness towards missing data

A method for compression of large graphs and matrices to a block structure is further developed. Szemer\'edi's regularity lemma is used as a generic motivation of the significance of stochastic block models. Another ingredient of the method is Rissanen's minimum description length principle (MDL). We continue our previous work on the subject, considering cases of missing data and scaling of algorithms to extremely large size of graphs. In this way it would be possible to find out a large scale structure of a huge graphs of certain type using only a tiny part of graph information and obtaining a compact representation of such graphs useful in computations and visualization.Comment: Accepted for publication in: Fourth International Workshop on High Performance Big Graph Data Management, Analysis, and Mining, December 11, 2017, Bosto U.S.

Large cliques in a power-law random graph

We study the size of the largest clique $\omega(G(n,\alpha))$ in a random graph $G(n,\alpha)$ on $n$ vertices which has power-law degree distribution with exponent $\alpha$. We show that for `flat' degree sequences with $\alpha>2$ whp the largest clique in $G(n,\alpha)$ is of a constant size, while for the heavy tail distribution, when $0<\alpha<2$, $\omega(G(n,\alpha))$ grows as a power of $n$. Moreover, we show that a natural simple algorithm whp finds in $G(n,\alpha)$ a large clique of size $(1+o(1))\omega(G(n,\alpha))$ in polynomial time.Comment: 13 page

On Spatial Point Processes with Uniform Births and Deaths by Random Connection

This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current configuration for some response function $f$. An equivalent view point is that each pair of points of the configuration establishes a random connection at an exponential time determined by $f$, which results in the death of one of the two points. We concentrate on space-motion invariant processes of this type. Under some natural conditions on $f$, we construct the unique time-stationary regime of this class of point processes by a coupling argument. We then use the birth and death structure to establish a hierarchy of balance integral relations between the factorial moment measures. Finally, we show that the time-stationary point process exhibits a certain kind of repulsion between its points that we call $f$-repulsion

Systems weakend by failures

AbstractThe ideas of a dynamic approach to the analysis of multivariate life length distributions, introduced in Arjas (1981a) and Arjas and Norros (1984), are developed further. Basic definitions are given in terms of prediction processes. Properties of martingales jumping downwards at failure times are studied. Finally, the spaecial case of a general multivariate exponential distribution is considered

On the stability of two-chunk file-sharing systems

We consider five different peer-to-peer file sharing systems with two chunks, with the aim of finding chunk selection algorithms that have provably stable performance with any input rate and assuming non-altruistic peers who leave the system immediately after downloading the second chunk. We show that many algorithms that first looked promising lead to unstable or oscillating behavior. However, we end up with a system with desirable properties. Most of our rigorous results concern the corresponding deterministic large system limits, but in two simplest cases we provide proofs for the stochastic systems also.Comment: 19 pages, 7 figure

Verouudistusten vaikutukset pk-yritysten voitonjakoon

Opinnäytetyön tarkoituksena oli selvittää vuoden 2014 alussa voimaan tulleen osinko- ja yhtiöverotusuudistuksen vaikutuksia pk-yritysten voitonjakoon. Tutkimuksen avulla pyrittiin selvittämään voitonjaon kannalta oleellisimmat muutokset sekä osoittamaan niiden konkreettiset vaikutukset. Toimeksiantajayrityksen työntekijät voivat hyödyntää tutkimustuloksia jokapäiväisessä työssään neuvoessaan asiakkaitaan. Toimeksiantajana toimi helsinkiläinen tilitoimisto, jossa työskentelee noin kymmenen henkilöä. Heikki Sten on toiminut yrityksen palveluksessa seitsemän vuotta. Toimeksiantajan asiakaskunta koostuu pääasiassa pienistä, listaamattomista pk-yrityksistä minkä vuoksi työ rajattiin koskemaan lähinnä alle 10-hengen pk-yrityksiä. Haastatteluosioissa pyrimme selvittämään kuinka pienyrittäjät itse ovat kokeneet verouudistuksen vaikutukset sekä ovatko he tehneet konkreettisia muutoksia voitonjakoratkaisuihinsa verouudistuksen johdosta. Teoriaosiossa käydään läpi tutkimuksen kannalta olennaista verotusta. Yritysten tuloverojärjestelmä perustuu nettovoiton verottamiseen. Verotus vaikuttaa olennaiselta osin yrityksen voitonjakokelpoisten varojen määrään. Osiossa käydään verouudistus yksityiskohtaisesti läpi. Uudistuksen mukanaan tuomien muutosten tunteminen on välttämätöntä, jotta muutoksia voidaan tulkita. Samalla saadaan selville ne kohdat joihin toimeksiantajayrityksen työntekijöiden on syytä kiinnittää huomiota konsultoidessaan asiakkaitaan voitonjaonoptimoimisessa. Tutkimusaineistoa on kerätty haastattelemalla pienyrittäjiä sekä vertailemalla yritysten tilinpäätöksiä. Myös Heikki Stenin jokapäiväisessä työssään tekemät havainnot ja käytännön kokemus verouudistuksen vaikutuksista kirjanpitäjien arkeen ovat olleet suuressa osassa tutkimusta tehdessä. Tutkimuksen tulokset osoittavat verouudistusten vaikutusten olleen melko vähäiset voitonjakoon. Haastateltavat yrittäjät eivät olleet kokeneet tarpeelliseksi suorittaa erityisiä toimenpiteitä optimoidakseen voitonjakoaan verouudistuksen voimaan tulon myötä. Samaan aikaan kun yritys saa pitää suuremman osan tekemästään voitostaan itsellään, on voitonjakamista ulos yrityksestä kiristetty. Tuloksista on selkeää hyötyä toimeksiantajayrityksen työntekijöille, sillä se onnistuu selkeäsi poimimaan uudistuksesta voitonjaon kannalta olennaisimmat asiat sekä osoittamaan niiden todelliset vaikutukset. Sisäistäessään nämä huomiot, yrityksen kirjanpitäjät ovat valveutuneempia opastamaan asiakkaitansa verouudistuksen jälkimainingeissa.This thesis studies the effects of the 2014 corporate and dividend tax reform and how the reform affected the distribution of profits at small- to medium-sized enterprises (SMEs). The purpose of the study was to identify the most integral changes and to show what the real effects of these changes were. The employees of the client company of this thesis can use the results of the study in their everyday work when they advise their client. The client company of this thesis is an accounting company located in Helsinki. The company has less than 10 employees, and one of the authors, Heikki Sten, has worked for the company for seven years. The client company’s clientele consists of mainly SMEs that have less than ten employees. This is why the study was restricted to companies of a similar size. By interviewing entrepreneurs we wanted to find out how they had felt the effects of the tax reform and if they had had to take any special actions concerning their distribution of profits because of it. In the theoretical section of the thesis report taxation is discussed insofar as it is relevant to this study. The taxation system for corporates is based on a tax on net profits. The prevailing taxation directly affects the amount of distributable wealth that a company has. In this section the tax reform is presented in detail, as knowledge of the essential parts of the reform are necessary in order to fully understand the effects of the reform. At the same time as the essential areas of the reform are discussed, those areas are highlighted that the client company’s employees should particularly take notice of when consulting their clients. The data for this study was collected by interviewing entrepreneurs and by studying various financial statements of SMEs. Also, the findings made by Heikki Sten in his every day work as an accountant and his personal experience of working with SMEs during the tax reform have been essential in collecting data for this study. The results of this study show that the effects the tax reform had on the SME’s distribution of profit have been somewhat minimal. The entrepreneurs that were interviewed did not have to take any special actions in order to be able to distribute their profits in a similar fashion as before. Even though the companies were able to keep more of their profits to themselves the taxation is now harder when distributing the wealth out of the company. This study is of use to the client company as it highlights the essential areas of the tax reform insofar as these concern distribution of profits. It also shows the tangible affects the reform had on the amount of distributable profit for SMEs. When an accountant understands the major points of the tax reform and the effects that they have, he or she is significantly better equipped to answer the needs of their clients