On total communication complexity of collapsing protocols for pointer jumping problem

This paper focuses on bounding the total communication complexity of collapsing protocols for multiparty pointer jumping problem ($MPJ_k^n$). Brody and Chakrabati in \cite{bc08} proved that in such setting one of the players must communicate at least $n - 0.5\log{n}$ bits. Liang in \cite{liang} has shown protocol matching this lower bound on maximum complexity. His protocol, however, was behaving worse than the trivial one in terms of total complexity (number of bits sent by all players). He conjectured that achieving total complexity better then the trivial one is impossible. In this paper we prove this conjecture. Namely, we show that for a collapsing protocol for $MPJ_k^n$, the total communication complexity is at least $n-2$ which closes the gap between lower and upper bound for total complexity of $MPJ_k^n$ in collapsing setting

About some limitations in researching the human being. Theological perspective

The concept of a person has gone through several stages of development in the history of thought. In the classical tradition, a person is considered to be a substance. In modernity, John Locke brought forward the notion that social existence and consciousness are the most salient properties of a person, which brought about a possibility of renouncing one’s personhood because of a lack of some perceivable and observable traits. This is why in a Christian anthropology there is such an emphasis on personalism, which from the very beginning of the twentieth century has been opposed to the treatment of people as obscure elements of matter, or elements be manipulated unquestioningly. In this paper we have indicated some elements of anthropology that demonstrate important limitation of any attempt at explaining away the mystery of being a human person.Pojęcie osoby przeszło wiele zmian w historii myśli ludzkiej. W tradycji klasycznej osoba jest uważana za substancję. W oświeceniu John Locke przedstawił pogląd, że egzystencja społeczna i świadomość są najważniejszymi właściwościami osoby, co spowodowało możliwość utracenia godności osobowej z powodu braku pewnych dostrzegalnych i możliwych do zaobserwowania cech. Właśnie dlatego w antropologii chrześcijańskiej kładzie się tak duży nacisk na personalizm, który od samego początku stanowi przeciwwagę wobec traktowania ludzi li tylko jako elementów materii, którymi można dowolnie manipulować. W niniejszym artykule przedstawimy taką charakterystykę antropologii, która ukazuje istotne ograniczenie wszelkich prób wyjaśnienia tajemnicy bycia człowiekiem

INVITED TALKS

On behalf of the Polish scientific community we have the privilege and pleasure to welcome youto Warsaw for the PETRAD2012 Conference. The Conference follows the opening of the Universityof Warsaw Radiopharmaceuticals Production and Research Centre. The main goal of this centreis the production of radioisotopes and radiopharmaceuticals for Positron Emission Tomography(PET) laboratories in Poland as well as research into new, innovative radiopharmaceuticals

Towards an Adequate Anthropology

An adequate anthropology is an anthropology that sees each human being as a person. It reveals fully our complexity and the fascinating dignity of human beings. ‘Adequate anthropology’ is a term proposed by John Paul II and based on three sources: The Bible, theology, and philosophy. Generally speaking, its aim consists in the defense of a large and holistic concept of our existence in opposition to all contemporary reductionistic accounts. Developing an adequate anthropology enables us to discover the very truth about ourselves. While considering the results of scientific research, it never loses sight of revelation. It is through revelation that the Creator of our being gives us the best insights into ourselves. An adequate anthropology begins by reflecting on our existential situation, which is the splintering of God’s image in us, and ends with the incarnate Word as the model of a perfect personhood.Antropologia adekwatna jest antropologią, która postrzega każdą istotę ludzką jako osobę. Ujawnia ona w pełni złożoność i niezwykłą godność człowieka. ‘Antropologia adekwatna’ to wyrażenie zaproponowane przez Jana Pawła II i oparte na trzech źródłach: Biblii, teologii i filozofii. Ogólnie rzecz biorąc, jej celem jest obrona holistycznej koncepcji naszego istnienia w opozycji do wszystkich współczesnych podejść redukcjonistycznych. Rozwijanie antropologii adekwatnej pozwala nam odkryć prawdę o nas samych. Rozważając wyniki badań naukowych, nigdy nie traci z oczu Objawienia. To właśnie poprzez Objawienie Stwórca naszej istoty umożliwia nam najlepszy wgląd w nas samych. Antropologia adekwatna rozpoczyna się od refleksji nad naszą sytuacją egzystencjalną, która jest zniekształceniem Bożego obrazu w nas, a kończy na Wcielonym Słowie, które jest obrazem doskonałego bycia człowiekiem

Społeczeństwo wiedzy i demokracja

Knowledge and democracy are commonly viewed the social phenomena and practices which should support each other and should be mutually dependent. However, a knowledge society cannot be fully reconciled with the democratic system as the latter produces ideologies and inspires actions that are mutually contradictory and do not always do a good service to democracy. However, there is nothing peculiar about it since knowledge is based on democratisation, and this is best exemplified in tertiary education. However, one may, and must, eliminate barriers preventing access to knowledge, and this is the purpose that democracy today needs to serve. W potocznym rozumieniu wiedza i demokracja to zjawiska i praktyki społeczne, które powinny się wzajemnie wspierać i warunkować. Społeczeństwa wiedzy nie da się jednak w pełni pogodzić z ustrojem demokratycznym. Wytwarza ono różne ideologie oraz inspiruje działania, które pozostają ze sobą w sprzeczności i nie zawsze dobrze służą demokracji. Nie ma w tym nic osobliwego, bo wiedza opiera się demokratyzacji, co najlepiej widać w szkolnictwie wyższym. Można jednak i trzeba likwidować bariery dostępu do wiedzy - i temu właśnie ma dziś służyć demokracja

Henryk Rzewuski – on the way to Polish national philosophy

The purpose of this article is to present original philosophical concept by Henryk Rzewuski. This nineteenth century Polish thinker was (and still is) extremely controversial person, accused of national “apostasy” for the Tsarist Russia and the spread of beliefs about the irrevocable end of the Polish state. In this text reveals the complexity and ambivalence Rzewuskiego attitude towards the Polish cause. This philosopher believed that indeed the Polish state will not be standing free himself from the Russian political sovereignty. At the same time, however, was an ardent supporter of building the Polish national philosophy, which would illustrate Polishness and develop in the sphere of the ideal and spiritual. Polish history has to be – within its concept – the material from which the philosopher sees that these thoughts and ideas around which crytallized Polish spirit, and that reflect the basic idea of moral. The spirit of the nation and its moral idea meet, according to this philosopher, the functions analogous to that of the soul to the body – is a condition of life and the unity of its geopolitical “body.”The purpose of this article is to present original philosophical concept by Henryk Rzewuski. This nineteenth century Polish thinker was (and still is) extremely controversial person, accused of national “apostasy” for the Tsarist Russia and the spread of beliefs about the irrevocable end of the Polish state. In this text reveals the complexity and ambivalence Rzewuskiego attitude towards the Polish cause. This philosopher believed that indeed the Polish state will not be standing free himself from the Russian political sovereignty. At the same time, however, was an ardent supporter of building the Polish national philosophy, which would illustrate Polishness and develop in the sphere of the ideal and spiritual. Polish history has to be – within its concept – the material from which the philosopher sees that these thoughts and ideas around which crytallized Polish spirit, and that reflect the basic idea of moral. The spirit of the nation and its moral idea meet, according to this philosopher, the functions analogous to that of the soul to the body – is a condition of life and the unity of its geopolitical “body.

Dynamical Isometry is Achieved in Residual Networks in a Universal Way for any Activation Function

We demonstrate that in residual neural networks (ResNets) dynamical isometry is achievable irrespectively of the activation function used. We do that by deriving, with the help of Free Probability and Random Matrix Theories, a universal formula for the spectral density of the input-output Jacobian at initialization, in the large network width and depth limit. The resulting singular value spectrum depends on a single parameter, which we calculate for a variety of popular activation functions, by analyzing the signal propagation in the artificial neural network. We corroborate our results with numerical simulations of both random matrices and ResNets applied to the CIFAR-10 classification problem. Moreover, we study the consequence of this universal behavior for the initial and late phases of the learning processes. We conclude by drawing attention to the simple fact, that initialization acts as a confounding factor between the choice of activation function and the rate of learning. We propose that in ResNets this can be resolved based on our results, by ensuring the same level of dynamical isometry at initialization